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http://mathhelpforum.com/calculus/15601-trying-again.html | Math Help - Trying again
1. Trying again
Still unsure of how to find the inflection points with an e^x problem...
Take this problem:
f(t) = 1 - e^-0.03t
f'(t) = -e^-.03t + (-.03t)
f'(t) = -0.03te^-0.03t
It seems logical that if t=0 then f'(t) =0, but is there a way to solve it without guessing?
f"(t) = -.03t(e^-.03t)(-.03)
f"(t) = .0009te^-.03t
In other words, can you set .0009t = e^-.03t and solve? or do you just pick some points near 0 and plot?
2. Hello, confusedagain!
Still unsure of how to find the inflection points with an e^x problem...
Take this problem:
$f(t) \:= \:1 - e^{-0.03t}$
$f'(t) \:= \:-e^{-0.03t} + (-0.03t)$ ?
The derivative of: . $y \:=\:e^u$ is: . $y' \:=\:e^u\cdot u'$
In baby-talk: the exponential function itself times the derivative of the exponent.
If $f(t)\:=\:1 - e^{-0.03t}$
. . then: . $f'(t)\:=\:-e^{-0.03t}(-0.03) \:=\:0.03e^{-0.03t}$
. . then: . $f''(t)\:=\:0.03e^{-0.03t}(-0.03) \:=\:-0.0009e^{-0.03t}$
To find inflection points, solve $f''(t) = 0$
So we have: . $-0.0009e^{-0.03t} \:=\:0$
. . Divide by -0.0009: . $e^{-0.003t} \:=\:0$
. . Multiply both sides by $e^{0.03t}\!:\;\;1 \:=\:0$ . . . . What?
Therefore, there are no inflection points.
3. Originally Posted by confusedagain
Still unsure of how to find the inflection points with an e^x problem...
Take this problem:
f(t) = 1 - e^-0.03t
f'(t) = -e^-.03t + (-.03t)
f'(t) = -0.03te^-0.03t
It seems logical that if t=0 then f'(t) =0, but is there a way to solve it without guessing?
f"(t) = -.03t(e^-.03t)(-.03)
f"(t) = .0009te^-.03t
In other words, can you set .0009t = e^-.03t and solve? or do you just pick some points near 0 and plot?
Hello,
I assume that your function is:
$f(t)=1-e^{-0.03t}$
To calculate the first derivative use chain rule:
$f'(t) = -e^{-0.03t} \cdot (-0.03) = 0.03 \cdot e^{-0.03t}$
Both factors are positiv thus the product is positiv too, that means $f'(t) \neq 0$
To calculate the second drivative use chain rule again:
$f''(t) = 0.03 \cdot e^{-0.03t} \cdot (-0.03) = -0.0009 \cdot e^{-0.03t}$
Both factors have always different signs thus the product is negative for all t.
The function don't have any extreme points or inflection points if the domain is $\mathbb{R}$ | 2016-05-28 16:30:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9307627081871033, "perplexity": 1482.9555704473487}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278042.30/warc/CC-MAIN-20160524002118-00155-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://lambda-the-ultimate.org/node/1169 | ## Types and reflection
In my day-job as a Java programmer I use a lot of tools that relies heavily on reflection, and I've come up with quite a few uses of reflection that can simplify my day job. Having also become quite fond of OCaml and it's powerful type systems I've started wondering if combining reflection with a powerful type system is possible. The two features seem quite at odds with each other, reflection completely undermines the type system, something I also see every day in my day-job.
Has anyone looked at ways of combining the power of these two language features? In OCaml I'll have to resort to something like camlp4 if I want to do the stuff I use reflection for in Java. But it's seems to me that there might be a middle ground between syntactic extension and the metaprogramming allowed by reflection. Or is there some fundamental reason why this is impossible? As you probably understand I really don't have any clue what this is called, or if it exists, or if it's useful, so I'm curious about anything that might shed some light on it.
## Comment viewing options
### Good subject!
Using my terminology: Reflection is an abstraction breaking mechanism, where as the type system exists to ensure the integrity of abstractions.
It is quite interesting to think about how these combine, and Frank's suggestion is a good one. My personal take is that there's still room for new ideas concerning these issues. I think we need better abstraction breaking mechanisms (i.e., less powerful than reflection) which will allow for more controlled abstraction breaking, by utilizing the type system. Reflection is too powerful to be left in the hands of programmers ;-)
### Why not?
My take on reflection: reflection is the ability to reason about the current context (ie the environment, situation and/or state) This suggests a knowledge base containing context information and other knowledge about the context (ie more rules and facts). Further in order to make use of this we need to be able to act on the context to change things, while keeping track of the changes. A language for doing this is called Lewis .
### They should combine quite nicely
Ocaml's type system is 100% compile time- the executable code generated has no type information (well, almost none- non-pointers are tagged, but that's about it). Reflection is pretty much 100% run time.
Ints would remain tagged, with the low bit set to 1, chars and booleans stored in words whose low two bits would be 10, pointers would be words with the low two bits being 00, and objects on the heap would have their class pointers stored with them in memory. Variant types would be implemented as pointers to "special" words in memory. So the getClass function, written in C, would look something like:
class_t * getClass(word_t value) {
if ((value & 1u) == 1) {
/* it's an int */
return &intClass;
} else if ((value & 2u) == 2u) {
/* it's a char or boolean */
if ((value & 4u) == 4u) {
/* it's a char */
return &charClass;
} else {
/* it's a boolean */
return &booleanClass;
}
} else {
/* it's a pointer or a variant type- class
pointer is stored just before the object.
*/
return (class_t *) ((word_t *) value)[-1];
}
}
Adding reflection and run time type checking would have a small cost in performance, but the success of languages that have it (include Java, C#, Python, Ruby, etc.) suggests that the benefits outweigh the costs.
### Reflection v. Introspection
Introspection (sometimes known as structural reflection) is easy to add to just about any language (with a preprocessor at the worst). Simply store the type information and such in some standard place, usually extra methods on an object in OO languages. This is often handy to generate "boilerplate" type code automatically at runtime. I'm not sure if andnaess means just this. Behavorial reflection is the stickier one. It includes operations to change things at runtime. In simple cases, this is not much different, though it does lead to the ability to break invariants by violating the abstractions. But, for more ambitious types of reflection, the issues are at least technically complex especially when one wants to combine with and reflect on rich type information. In more ambitious schemes you can completely redefine a method/function/whatever at runtime. This, obviously, utterly destroys the type guarantees. (In really ambitious schemes, it is possible to redefine the very language itself.) I believe Java (and probably now C#) are the only statically typed languages that support this to any degree (and in Java's case, in typical baroque Java style). Still, it does look like you could either not allow functions to change type (but allow the implementation to change if it types the same) or you could simply retypecheck the affected code when the change is made (this involves having the typechecker available at runtime; note you still keep the guarantees but it is now possible to get type errors at runtime ("load" time rather) and of course you'd need a "bulk" update operation). Ironically, the dynamically typed language Self has done a good chunk of research on how to make exactly this reasonably efficient. I personally think the pieces are in place to make a usable statically typed language with fairly sophisticated reflection capabilities, but I don't think it has been done yet to the extent I believe possible nor do I think that it would retrofit onto an existing language particularly well without some work.
### I'm not sure about that termi
I'm not sure about that terminologi. The way I read it, structual reflection is reflection regarding the datastruktures of the language, and behavorial reflection is reflection regarding the very language itself. Introspection or not introspection (there need to be a better word for this) is orthogonal to that. Also there is the possibillity of static behavorial reflection, wich could perhaps be staticly typed.
### Me neither
I do intend for structural reflection to be reflection on data structures, but often this is restricted to just being able "look at" them and not modify them or only "modify" them in trivial ways (that incidentally preserves the structure) e.g. changing the value of a field, but not, say, adding and removing methods. Introspection is, to me, quite definitely not orthogonal to "reflection". It is the reification part of reflection without which you have little more than dynamic loading (useful but not as hard). My impression is often introspection is used to emphasize that it is only the reification part. I am probably abusing the term "behavorial reflection". It is often used to mean specifically being able to modify language constructs. I am using it in a way that is likely less strong though I include that sense as well.
### I didn't mean to say that int
I didn't mean to say that introspection is orthogonal to reflection. Its definitly a type of reflection, and probably the most usual. Just that its orthogonal to the division between behavioral and structual reflection. Also note the existence of behavioral introspection like the eval and apply functions.
### In a FPL....
Wouldn't a reflective operation that purported to modify a type NOT modify the type (possibly breaking invariants of all sorts; invariants assumed by the compiler when typechecking or inference occurred), but instead create a NEW type?
THAT would be somewhat interesting, I would think. Of course, if you create new types at runtime then, out of necessity, you must defer typechecking until then, but I'm not allergic to dynamic typing. And while many statically typed languages do type-erasure as an optimization; there is no REQUIREMENT that this be done--objects could still have an implicit pointer to a vtable or type object--a pointer which can be ignored if the compiler can assign definite types to a given term.
One more point: The languages that have the really gnarly reflective capabilities--Smalltalk and CLOS come to mind (and the advocates of both languages often claim that advanced reflection is a required feature for them to take a language seriously), usually use this feature as part of the DEVELOPMENT environment. They way you edit a class in Smalltalk is you use the object brower to manipulate the class definition, using the reflective capabilities built into the language. It's far less common, AFAIK, for running PROGRAMS to mutate existing types as part of their normal operation. With modern IDEs that offer the apparent seamless of image-based environments, yet maintain rigorous isolation between the source code of a program and its running instances, I'm not sure full-boat reflection is a necessary or desired feature anymore.
### Typechecking at runtime
"you must defer typechecking until then, but I'm not allergic to dynamic typing"
I have said this a few other places before, but I think it is important that running the typechecker at runtime is (for rich type systems at least) different from dynamic typechecking.
### I dont think I understand
It's diffrent from most dynamic type systems of today, but how do you rationalize it not being dynamic typing at all? And what do you then mean by dynamic typing?
### Agreed...
...though I was intentionally avoiding the question of whether formal typechecking (assigment of types to terms) or simple verification of operations on objects (how "dynamic typing" is usually implemented) is employed.
Virtually all production dynamically-typed languages do the latter. How much research has there been on the former? If coupled with dynamic translation (say, from bytecode to machine code), it could conceiveably make dynamic languages run much faster; and produce more understandable type-error diagnostics than #doesNotUnderstand.
### "Runtime" typechecking
Yes, I have thought of the case of "future" "dynamically" typed languages. However, I still think it is fundamentally different and pushing a "dynamic" typechecking toward it eventually would result in something rather different (from a dynamically typed language). That said, I can't prove this because there is no commonly accepted formal definition of "dynamic typechecking". Still some things that are different from dynamic typechecking, some aspects: any code is typechecked before it is executed (i.e. at load time) and as a result all code is typechecked once instead of everytime through. Type erasure is still completely possible (though for the purposes of reflection this is probably less desirable, it is also probably useful for efficiency reasons as well). Non-local features of type systems e.g. unification of polymorphic types can be dealt with which is rather beyond the "tag checking" of most (all?) current dynamically typechecked languages. Properties and guarantees of static type systems will be maintained e.g. parametricity. On the flip side, the restrictions will remain as well, it will be possible to have "runtime typechecked" code that won't "run" (load) that would under today's dynamically typechecked languages.
In a nutshell, we are simply moving "compile-time" to "load-time", this should not automatically drastically change the nature of the language. A point in case is hs-plugins which does (or did at least) simply call the compiler at runtime and link in the resulting code.
### OK. I think I understand now.
OK. I think I understand now. Yes loadtime type checking is realy neighter dynamic or static typing. Actually I think the terms static and dynamic typing is losing there meaning. Few languages if any has purely static or dynamic typing, everythings a hybrid.
### What uses?
In my day-job as a Java programmer I use a lot of tools that relies heavily on reflection, and I've come up with quite a few uses of reflection that can simplify my day job.
I'd be interesting in hearing how you use reflection, if you don't mind sharing. It's always nice when we can bring real-world requirements into the mix.
One example is form processing and validation. For example, I can write a class that has some properties, and based on the types of these properties the form is processed and handled. So that takes a lot of drudgery out of the coding. I could of course do this with code generation, but it feels like overkill.
A lot of it comes from the concept of "configuration by convention". I tend to use a lot of conventions in my code, and by using reflection I can in fact enforce those conventions at the same time as I save the world from more XML pollution.
But most importantly is probably the tools I use. Hibernate for example uses a lot of reflection. The Spring framework has it all over the place. The web framework we use is full of reflection code. And the problem is that I'm getting a lot of run-time errors that I suspect could be prevented by a type-checker.
I suppose what I'm seeing is that I want macros. Or some other means of extending the language here and there. But I hate having to give up compile-time type checks because after having seen how powerful they can be (OCaml), I have gone from being a fan of dynamic typing to be being a fan of static typing.
So I'm imagining that there is this wonderful point where OCaml and Lisp meet perfectly, and that we unfortunately haven't found it yet.
Type based handling is possible. As a demonstration, I write unit tests for Plone via XmlRpc from Haskell.
The XmlRpc library does the right thing for outgoing and incoming values based on the declared types of the arguments.
.keyglyph, .layout {color: red;} .keyword {color: blue;} .str, .chr {color: teal;}
remoteTestList =
TestList
[
(remote url "ping" :: IO String) ~>= "hello"
,(remote url "addtwonumbers" (4 :: Int) (2 :: Int) :: IO Int) ~>= 6
,(remote url "getgroup" "shapr" :: IO String) ~>= "group_shapr"
,(remote url "setvalue" "foo" :: IO String) ~>= "foo"
,(remote url "getvalue" :: IO String) ~>= "foo"
,((remote url "setvalue" "xyzzy" :: IO String)
>> (remote url "getvalue" :: IO String)) ~>= "xyzzy"
,(remote url "creategroup" "shapr" :: IO String) ~>= "group_shapr"
]
(Pretty colors from HsColour. The operators are from HUnit, slightly extended to compare a monadic result to a pure expected value.)
And just in case you're wondering just how that works, see Oleg's polyvariadic functions in Haskell.
### Could you clarify
One example is form processing and validation. For example, I can write a class that has some properties, and based on the types of these properties the form is processed and handled. So that takes a lot of drudgery out of the coding.
It's not clear to me as to why this would require reflection. Couldn't this be done with plain OOP?
### Because of types
I basically say that "this class represents a form", the class might have the properties
String name;
Integer volume;
BigDecimal price;
And when I process the data coming in from the web (strings) I validate the name property as a String, the volume as an Integer, and the price as a BigDecimal. I have to use reflection to know the types of the properties is. I could of course use regular OOP, it's just that I like the more "magic" approach because form processing is something I do all the time, and the code is extremely boilerplate-loaded.
But this is not a very good example because there's no real problem with type safety. What got me thinking was that I was pondering how to add some more sophisticated stuff using annotations, and I found that it would be nice if I could use annotations to set up methods to call. But then the method call would happen using the reflection API, and that means that type safety goes out the window. The method name would just be a string.
### This example suggests to me t
This example suggests to me that you might want to think backwards from the way you usually think when working with languages like O'Caml.
What do I mean by that? Well, instead of thinking in terms of having a data structure that contains a string field, an integer field, and a bigdecimal field, and wanting to automatically infer which form validation routines to use for each, approach it the other way around. (Notice that I used the word infer here--that's because by turning things around, we make use of type inference to avoid redundancy.)
Here's an example of how that might work for the above:
(* NOTE: All this code was written on the fly, totally untested, etc. *)
(* validators raise this exception if validation fails *)
exception Validation_missing
exception Validation_failed of string
(* A validator takes a string (field name or partial field name),
* followed by a form request structure, and either
* returns a value of the appropriate type or raises
* Validation_failed with an explanation *)
type 'a validator = string -> form_request -> 'a
(* The string validator accepts any string *)
let string_validator field_name req =
match get_field req field_name with
| Some x -> x
| None -> raise Validation_missing
(* The integer validator only accepts integers *)
let int_validator f r =
let s = string_validator r f in
if parses_as_integer s then make_integer_out_of s
else raise (Validation_failed "That's no integer!")
(* Here's a more complicated one *)
let point_validator f r =
let x = int_validator (f ^ ".x") r in
let y = int_validator (f ^ ".y") r in
Point (x,y)
(* And a combinator *)
let option_validator v f r =
try Some (v f r) with Validation_missing -> None
(* And finally, a function using the above: *)
let my_request_handler r =
let name = string_validator "name" r in
let volume = int_validator "volume" r in
let optional_price = option_validator int_validator "price" r in
...
Now, there are a couple of things going on here. I think it's clear how the type inference is working for us: Now, we define a validator, and let the type of the validator define the type of our resulting value. This also happily provides "for-free" the ability to have different validators for the same resulting type.
Another thing that's going on here is that we can have higher-order validators, like option_validator. We could also have, for example, a list validator that automatically chops up a list for us, and uses a sub-validator on pieces.
And finally, note that there are various tricks that can make the above even more syntax-light. See http://www.brics.dk/RS/98/12/ for a great example of how this works for that great reflection-like troll of yore, printf. Also search around for stuff about parser combinators to see just how scarily powerful this can get on the "validation" side.
Anyway, I just wanted to point out that instead of breaking down data structures to find out what code to run, you can run code to find out what data structures to build. :)
### Thinking backwards is hard
And the longer I get stuck in Java land, the harder it gets. That's why I play with OCaml in my spare time.
Anyway, this was an interesting read although I'm not entirely sure I understood everything.
However, my example was extremely simplified, I only answered the question -- why I needed the types -- there's more to it. My plan was to use annotations as well, as in this example from Sun: http://java.sun.com/developer/technicalArticles/J2SE/constraints/annotations.html
So the types are probably the smallest part of the validation, I just though that since I have to declare types in Java I might as well try to put them to good use! A second reason for doing it this way is that the form object is responsible for reading the request and keeping track of the original values as posted by the user, because you want those values to redisplay if the form failed to validate, no matter how wrong they are. Also, I actually want form objects to know how to render themselves, or have some FormRenderer that can introspect into a form and based on type information and annotations, render the form fields using input, textarea, checkbox etc.
But as I'm sitting here I think I'm starting to appreciate your idea more. Take for example the integer validation. For integers you probably want to test min/max values. In some cases you may also want more general tests such as simply negative or positive, and one can probably come up with uses for more exotic things such as that the integer is odd or even, or a power of two. So, you could create the various validators that are able to check each little aspect, and you can combine them to form the validator you want. That's a very powerful approach indeed!
But alas, it does not help me get rid of the more tedious tasks of using the right form field for the input, and keeping track of the user's actual input variables. I also need to make sure all errors that happen during validation are automatically kept track of, I don't want all my form handling code to contain the same repetitive boilerplate code that checks if each validation succeeds, and if not, store the error message somewhere.
What I really want to do is encode 5 years of experience dealing with web forms in code. I have a fairly good idea about sensible defaults that will work in 80% of the cases, so I'm trying to apply the 80/20 rule here. But it's crucial that every default can be overloaded for those 20% of cases where the defaults are not good enough. Reflection allows me to infer these defaults from a combination of type information and annotations.
question. | 2017-10-21 01:20:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3820918798446655, "perplexity": 1525.438564476492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824537.24/warc/CC-MAIN-20171021005202-20171021025202-00393.warc.gz"} |
https://www.imageen.com/support/faq.html | # ImageEn FAQ
After updating ImageEn I get the following error on Delphi start-up: "The procedure entry point ... could not be located in the dynamic link library DPKIECtrl26.bpl" There are two common causes for this error: 1. You have multiple copies of the ImageEn BPL files on your system (generally error is for DPKIECtrl*.bpl) Search your system for any PKIE*.* and DPKIE*.* files and remove them (it might help to review the library paths under Tools > Options, Library). Then reinstall ImageEn. 2. You have another package that uses the ImageEn BPL (generally error is for PKIECtrl*.bpl) A package - either one of ImageEn's or one of your own - is trying to access PKIECtrl26.bpl, but is failing because PKIECtrl26.bpl has been recompiled more recently. The error may be followed by another one that advised you which package is giving you the error: "Xyz package could not be loaded. Would you like to load it next time you run Delphi...". If you know which package has caused the problem, open it's DPK file and recompile it. Otherwise, go through each of your packages and recompile any that use ImageEn.
Can I load PDF files with ImageEn? At this stage, ImageEn cannot natively load PDF files. To load PDF files you need either: - An add-on, such as WPViewPDF (Paid. You ship a DLL with your application): - ImageMagick + GhostScript (Free, but needs to be installed on client machines):
How can I prevent the scrollwheel from causing the image to zoom? I want it to remain the original size at all times. Just write: ImageEnView1.MouseWheelParams.Action := iemwNone; other values are iemwVScroll and iemwZoom (default).
How do I convert a multi-page GIF image to TIFF format without a visual component? There are several ways. The simplest is: var mbmp:TIEMultiBitmap; Begin mbmp := TIEMultiBitmap.Create; mbmp.Read('D:\in.gif'); mbmp.Write('D:\out.tiff'); mbmp.free; End;
Can I modify brightness? You can change brightness (luminosity) using several methods. Using IntensityRGBall method: ImageEnView1.Proc.IntensityRGBall(20,20,20); // increment luminosity of 20 (the fastest) Using HSLvar method: ImageEnView1.Proc.HSLvar(0,0,20); // increment luminosity of 20 (slow but more accurate) Using HSVvar method: ImageEnView1.Proc.HSVvar(0,0,20); // increment luminosity of 20 (slow but more accurate)
Can I modify scanner resolution? To change scan resolution to 300 on your scanner use: ImageEnView1.IO.AcquireParams.YResolution := 300; ImageEnView1.IO.AcquireParams.XResolution := 300; ImageEnView1.IO.Acquire();
Is there any way to save a CMYK TIFF using ImageEn? To save TIFF with CMYK write: ImageEnView1.IO.Params.TIFF_PhotometInterpret := ioTIFF_CMYK; ImageEnView1.IO.SaveToFile('xxx.tif');
How can I improve the performance of TImageEnMView when I have many thumbnails? Ensure you have optimized your settings to ensure the best performance: Most importantly, decide whether the TImageEnMView should load and store full size images. If you are loading the content of a multi-page file, such as TIFF, for editing and display purposes then generally you will want TImageEnMView.StoreType=ietNormal. However, if you are displaying thousands of photos from a folder, for example, then you are better to use load only thumbnails (TImageEnMView.StoreType is ietThumb or ietFastThumb) Load images only on demand (i.e. as they are displayed or needed). To do this, ensure the LoadOnDemand parameter is set for AppendImage, InsertImage, FillFromDirectory or FillFromFolder Lock updating while performing batch operations (LockUpdate/UnlockUpdate) Consider options to load EXIF thumbnails (TImageEnMView.EnableLoadEXIFThumbnails) or Windows Explorer thumbnails (TImageEnMView.EnableLoadExplorerThumbnails) Increasing the size of the image cache can help with general performance (TImageEnMView.ImageCacheSize), especially if you are using TImageEnMView.StoreType=ietFastThumb
Is it possible to de/activate duplex on a scanner? Write ImageEnView1.IO.AcquireParams.DuplexEnabled := True; (or False if you want to disable).
I've added the ImageMagick DLL to my application folder, but ImageEn does not support its formats. What do I need to do? You can automatically register available plug-in DLLs using RegisterPlugIns: IEGlobalSettings().RegisterPlugIns(); Note: If ImageMagick has been installed on the system, ImageEn will automatically supports its formats.
Can your component take a series of single page TIFF files and create a Multi-Page file from them? You can load the page using: ImageEnView1.IO.LoadFromFile('page1.tif'); then save the page with: ImageEnView1.IO.Params.TIFF_ImageIndex := 0; // increment this for each page ImageEnView1.IO.InsertToFileTIFF('multipage.tif'); Otherwise you can use a TImageEnMView component or a TIEMultiBitmap. See "multi" example for more details.
How do I change the current page of a TIFF image in TImageEnView? In order to load several pages from a TIFF you have two ways: 1) load a page at the time, using TImageEnView, example: ImageEnView1.IO.Params.TIFF_ImageIndex := page_number; // page_number stars from 0 (first page) ImageEnView1.IO.LoadFromFile('mytiff.tiff'); First instruction select the page to load. To know how many pages there are use: page_count := EnumTIFFIm('mytiff.tiff'); 2) load all pages, using TImageEnMView. Just write: ImageEnMView1.MIO.LoadFromFile('mytiff.tiff'); and you will see all pages.
How can I validate that the fonts used when loading a layer file are available on the system? After loading an ImageEn layer file you can iterate through all of the fonts to ensure they are valid, for example: ImageEnView1.IO.LoadFromFileIEN(...); // Validate fonts are installed on this system for i := 0 to ImageEnView1.LayersCount do begin if ImageEnView1.Layers[i].Kind = ielkText then fontName := TIETextLayer( ImageEnView1.Layers[i] ).Font else if ImageEnView1.Layers[i].Kind = ielkLine then fontName := TIELineLayer( ImageEnView1.Layers[i] ).LabelFont else continue; if Screen.Fonts.IndexOf( fontName ) = -1 then begin // This font is not installed. Substitute or install it... end; end;
Is it possible to convert a multipage-image to a different encoding? G3 and G4 specifically? Using TImageEnMView you have to change the compression property for all pages: ImageEnMView1.MIO.LoadFromFile('original.tif'); // change compression for the first page ImageEnMView1.MIO.Params[0].TIFF_Compression := ioTIFF_G4FAX; // change compression for the other pages ImageEnMView1.MIO.DuplicateCompressionInfo; // now save ImageEnMView1.Mio.SaveToFile('output.tif');
How can I improve performance when working with many layers? The main performance properties are: - LayersCaching: Caches the view of each layer. Much faster but uses more memory. - LayersFastDrawing: Display quality of layers (and whether the quality view is delayed). - ZoomFilter/DelayZoomFilter: Display quality of images (and whether the quality view is delayed). This option is ignored if LayersFastDrawing is active - LayersRotationUseFilterOnPreview: Whether the quality filter (LayersRotationFilter) is applied when previewing the image during rotation Here is some example code from the Layers_AllTypes demo: procedure Tfmain.cmbPreviewQualityChange(Sender: TObject); const _cmbPreviewQuality_Fast = 0; _cmbPreviewQuality_Delayed_Best = 1; _cmbPreviewQuality_Best = 2; begin // Separate code to make it easier to understand if cmbPreviewQuality.ItemIndex = _cmbPreviewQuality_Fast then begin // FASTEST DISPLAY // Zoom filter ImageEnView1.ZoomFilter := rfNone; ImageEnView1.DelayZoomFilter := False; // Rotation anti-alias ImageEnView1.LayersRotationFilter := ierBicubic; ImageEnView1.LayersRotationUseFilterOnPreview := False; // Fast drawing ImageEnView1.LayersFastDrawing := iefFast; end else if cmbPreviewQuality.ItemIndex = _cmbPreviewQuality_Delayed_Best then begin // DELAYED HIGH QUALITY // Zoom filter ImageEnView1.ZoomFilter := rfLanczos3; ImageEnView1.DelayZoomFilter := True; // Rotation anti-alias ImageEnView1.LayersRotationFilter := ierBicubic; ImageEnView1.LayersRotationUseFilterOnPreview := True; // Fast drawing ImageEnView1.LayersFastDrawing := iefDelayed; end else begin // HIGH QUALITY // Zoom filter ImageEnView1.ZoomFilter := rfLanczos3; ImageEnView1.DelayZoomFilter := False; // Rotation anti-alias ImageEnView1.LayersRotationFilter := ierBicubic; ImageEnView1.LayersRotationUseFilterOnPreview := True; // Fast drawing ImageEnView1.LayersFastDrawing := iefNormal; end; ImageEnView1.Update(); end; procedure Tfmain.chkLayerCachingClick(Sender: TObject); begin if chkLayerCaching.Checked then ImageEnView1.LayersCaching := -1 else ImageEnView1.LayersCaching := 0; end;
Using TImageEnMView, how do I load images as they are displayed? There are several ways to display images "on demand": 1) If you have a directory where are all files just write: ImageEnMView1.FillFromDirectory('c:\myimages'); 2) When you add a new image just set ImageFileName[] index, and ImageEn will load automatically specified file when needed. Example: idx := ImageEnMView1.AppendImage; ImageEnMView1.ImageFileName[idx] := 'first.jpg'; 3) When you add a new image just set the ImageID[] property. You have to create by hand an array of filenames where to get images. Example: var files:array [0..1] of string; begin files[0] := 'first.jpg'; files[1] := 'second.jpg'; ImageEnMView1.ImageID[ ImageEnMView1.AppendImage ] := 0; ImageEnMView1.ImageID[ ImageEnMView1.AppendImage ] := 1; end; You have also to create OnImageIDRequest event, on this you can write: procedure TForm1.OnImageIDRequest(Sender: TObject; ID:integer; var Bitmap:TBitmap); var io:TImageEnIO; begin io := TImageEnIO.Create(self); io.AttachedBitmap := bmp; // bmp is a TBitmap object, defined at class level (must exists after the OnImageIDRequest exits) io.LoadFromFile( files[ID] ); io.free; Bitmap := bmp; end; 4) If the images are frames of a media file (like AVI, MPEG, etc..) you can write: ImageEnMView1.LoadFromFileOnDemand('film.mpeg');
How do I burn the layers (Lines, Ellipses, etc) added in TImageEnView into the image? (Save them as a JPEG file) Lines, ellipses and other layers added to a TImageEnView can be merged to the background using the LayersMergeAll method, then save the image.
How do I modify the IPTC fields without loading the actual image? To load IPTC info from a jpeg, just use LoadFromFile method. After this you have in ImageEnView.IO.Params.IPTC_Info object all IPTC informations loaded. To read the caption you can write: ImageEnView.IO.LoadFromFile('image.jpg'); Idx := ImageEnView.IO. Params.IPTC_Info.IndexOf(2,120); Caption := ImageEnView.IO.Params.IPTC_Info.StringItem[idx]; this modify the caption: ImageEnView.IO.Params.IPTC_Info.StringItem[idx] := 'new caption'; ImageEnView.IO.SaveToFile('image2.jpg'); If you want to modify IPTC info without load the image use ParamsFromFile and InjectJpegIPTC methods, in this way: ImageEnView.IO.ParamsFromFile('one.jpg'); ...here modify the IPTC info ImageEnView.IO.InjectJpegIPTC('two.jpg');
How I can save my jpeg without EXIF or other metadata? Call Params.ResetInfo. Example: ImageEnView.IO.LoadFromFile('input.jpg'); ImageEnView.IO.Params.ResetInfo; ImageEnView.IO.SaveToFile('output.jpg');
How can I check if the TImageEnView is empty (no bitmap loaded)? To empty the component use "Blank" method. To check if it is empty use IsEmpty: If ImageEnView1.IsEmpty then ...
When a user selects a page of a multipage tiff image displayed in a TImageEnMView, I want the image to be displayed in a TImageEnView. To handle image selection use the OnImageSelect event. To get the currently selected image simply use the Assign method: procedure TForm1.ImageEnMView1ImageSelect(Sender: TObject; idx: Integer); begin ImageEnView1.Assign( ImageEnMView1.Bitmap ); end;
How do I assign the image in one ImageEnView to another ImageEnView? Just use Assign method: ImageEnView1.Assign( ImageEnView2 ); or ImageEnView1.Assign( ImageEnView1.Bitmap ); // this doesn't copy DPI, but just the image
What is the correct way to load a Resource Image at runtime into an TImageEnView component in C++? Here is an example: TResourceStream *ResourceImage; // Load from resource the About image ( a JPEG file). ResourceImage = new TResourceStream((int)HInstance, "ABOUTBITMAP",RT_RCDATA); MainForm->ImageAbout->IO->LoadFromStreamJpeg(ResourceImage); delete ResourceImage; Here is a single line text file named "resource.rc" with the sentence: ABOUTBITMAP RCDATA "about.jpg" Just add the Resource file to the project and compile.
How can I read custom TIFF tags? This example shows how read EXIF tags saved with Canon cameras: var ms:TMemoryStream; tagReader1,tagReader2,tagReader3:TIETifTagsReader; i:integer; // some Canon tags m_nMacroMode,m_nLenghtTimer,m_Quality:integer; m_ImageType:string; begin with imageenvect1 do begin IO.LoadFromFile('Capture_00006.JPG'); with IO.Params.JPEG_MarkerList do begin i := IndexOf( JPEG_APP1 ); if i>=0 then begin // there are EXIF info ms := TMemoryStream.Create; ms.Write( MarkerData[i][6], MarkerLength[i] ); // bypass first 4 bytes (must contain 'Exif') ms.Position := 0; tagReader1 := TIETifTagsReader.CreateFromStream( ms,0 ); // read TIFF's IFD tagReader2 := TIETifTagsReader.CreateFromIFD( tagReader1, 34665 ); // read IFD in tag 34665 (SubEXIF) tagReader3 := TIETifTagsReader.CreateFromIFD( tagReader2, $927c ); // read IFD in tag$927C (MarkerData - Canon IFD data) // read Canon EXIF tags m_nMacroMode := tagReader3.GetIntegerIndexed(1,1); m_nLenghtTimer := tagReader3.GetIntegerIndexed(1,2); m_Quality := tagReader3.GetIntegerIndexed(1,3); m_ImageType := tagReader3.GetString(6); tagReader3.Free; tagReader2.Free; tagReader1.Free; ms.Free; end; end; end; end;
How do I compress my JPEGs to make them smaller? Jpeg is a file format with variable compression rate. The property that regulates the compression (and the quality) is JPEG_Quality. So you should set this property before save. Example: ImageEnView.IO.LoadFromFile('input.jpg'); ImageEnView.IO.Params.JPEG_Quality := 70; ImageEnView.IO.SaveToFile('output.jpg'); The default is 80, while other software uses 70. If you want estimate the value used to create your file, execute this: quality := IECalcJpegFileQuality('input.jpg'); So you could write: ImageEnView.IO.LoadFromFile('input.jpg'); ImageEnView.IO.Params.JPEG_Quality := IECalcJpegFileQuality('input.jpg'); ImageEnView.IO.SaveToFile('output.jpg'); If this is not enough, probably the file contains metatags (text info). To remove them execute: ImageEnView.IO.Params.ResetInfo; ..just before save.
How do I load embedded JPEG images in a Raw file? // Load the embedded JPEG (loading a half size raw if there is no embedded JPEG) ImageEnView.IO.Params.RAW_GetEmbeddedJpeg := True; ImageEnView.IO.Params.RAW_HalfSize := True;
How do I always create a polygon when inserting a polyline layer? Just set: // Always close polylines ImageEnView1.LayersAutoClosePolylines := iecmAlways;
How do I read Camera RAW files? In order to read Camera RAW files you need to include ielib32.dll with your application.
Why do I get "Floating point overflow" on printing? Sometime this happens on shared printers and depends by VCL or printer drivers bug. Try to disable FPU exceptions executing this before your printing code: Set8087CW(\$133F);
Why do I see horizontal/vertical bands when loading images using TImageEnMView? By default, TImageEnMView loads EXIF thumbnails when they are available (with the thumbnail display method). Sometimes these thumbnails contain black bands (horizontal or vertical bands). To disable EXIF thumbnails loading set: TImageEnMView.EnableLoadEXIFThumbnails := false; | 2021-08-03 21:47:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27445387840270996, "perplexity": 13587.502328672736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154471.78/warc/CC-MAIN-20210803191307-20210803221307-00066.warc.gz"} |
https://math.paperswithcode.com/paper/a-bound-for-the-number-of-points-of-space | # A bound for the number of points of space curves over finite fields
13 Aug 2020 · Beelen Peter, Montanucci Maria ·
For a non-degenerate irreducible curve $C$ of degree $d$ in $\mathbb{P}^3$ over $\mathbb{F}_q$, we prove that the number $N_q(C)$ of $\mathbb{F}_q$-rational points of $C$ satisfies the inequality $N_q(C) \leq (d-2)q+1$. Our result improves the previous bound $N_q(C) \leq (d-1)q+1$ obtained by Homma in 2012 and leads to a natural conjecture generalizing Sziklai's bound for the number of points of plane curves over finite fields.
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Algebraic Geometry | 2022-01-25 19:46:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.710801899433136, "perplexity": 968.6537040206871}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304872.21/warc/CC-MAIN-20220125190255-20220125220255-00478.warc.gz"} |
http://www.heldermann.de/JLT/JLT23/JLT234/jlt23051.htm | Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 23 (2013), No. 4, 1023--1049Copyright Heldermann Verlag 2013 Totally Geodesic Subalgebras of Nilpotent Lie Algebras Grant Cairns Department of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia G.Cairns@latrobe.edu.au Ana Hinic Galic Department of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia A.HinicGalic@latrobe.edu.au Yuri Nikolayevsky Department of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia Y.Nikolayevsky@latrobe.edu.au [Abstract-pdf] \def\g{{\frak g}} \def\h{{\frak h}} A metric Lie algebra $\g$ is a Lie algebra equipped with an inner product. A subalgebra $\h$ of a metric Lie algebra $\g$ is said to be totally geodesic if the Lie subgroup corresponding to $\h$ is a totally geodesic submanifold relative to the left-invariant Riemannian metric defined by the inner product, on the simply connected Lie group associated to $\g$. A nonzero element of $\g$ is called a geodesic if it spans a one-dimensional totally geodesic subalgebra. We give a new proof of Ka{\u\i}zer's theorem that every metric Lie algebra possesses a geodesic. For nilpotent Lie algebras, we give several results on the possible dimensions of totally geodesic subalgebras. We give an example of a codimension two totally geodesic subalgebra of the standard filiform nilpotent Lie algebra, equipped with a certain inner product. We prove that no other filiform Lie algebra possesses such a subalgebra. We show that in filiform nilpotent Lie algebras, totally geodesic subalgebras that leave invariant their orthogonal complements have dimension at most half the dimension of the algebra. We give an example of a 6-dimensional filiform nilpotent Lie algebra that has no totally geodesic subalgebra of dimension $>2$, for any choice of inner product. Keywords: Lie algebra, nilpotent, filiform, totally geodesic foliation. MSC: 57R30, 22E25, 53C30 [ Fulltext-pdf (346 KB)] for subscribers only. | 2018-11-21 10:18:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6412874460220337, "perplexity": 328.64104415681845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039747665.82/warc/CC-MAIN-20181121092625-20181121114625-00547.warc.gz"} |
https://blog.yhuang.org/?m=201605 | Archive for May, 2016
optimizing insurance ordering
Sometimes the order in which procedures are performed has an effect on the payout from insurance. This is the case when there is both a deductible and a coinsurance.
Suppose the deductible is $$d$$, and the price and coinsurance of the $$i$$-th procedure performed are $$p_i$$ and $$c_i$$ respectively, then the total out-of-pocket cost is:
$$d + (p_1 – d) c_1 + p_2 c_2 + \cdots = (1-c_1) d + \sum_i p_i c_i$$
The second term is fixed cost; it’s the coinsurance on the first procedure that matters. This shows that to minimize out-of-pocket cost, one should, somewhat surprisingly, get the procedure with the highest coinsurance first. Essentially, every dollar of the deductible paid is subsidizing what the insurance company might have paid, but for a procedure with very high coinsurance, the subsidy is not very much to begin with. | 2022-06-29 15:52:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7847097516059875, "perplexity": 1246.2641647028368}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103640328.37/warc/CC-MAIN-20220629150145-20220629180145-00622.warc.gz"} |
https://www.physicsforums.com/threads/something-to-be-clarified-about-em-wave-te-tm-and-tem.630383/ | # Something to be clarified about EM Wave: TE, TM and TEM
it is said that in TE waves the E_z is zero, similarly for TM H_z is zero, and TEM both E_z and H_z are zero.
How about the E_x and E_y in TE wave?
Someone said E_y is also zero and only E_x exists in TE......is this true? Is it possible that I overlooked some assumptions made?
Or actually the fact is, for TE, both E_x and E_y are NON-zero; only E_z is zero?
I know this is a simple question but I do hope to confirm it earlier and proceed with my study, thanks for your kind attention. | 2022-01-17 21:49:14 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9017927050590515, "perplexity": 2400.4140646969554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300624.10/warc/CC-MAIN-20220117212242-20220118002242-00270.warc.gz"} |
https://msp.org/agt/2006/6-4/p03.xhtml | #### Volume 6, issue 4 (2006)
Download this article For screen For printing
Recent Issues
The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
On links with cyclotomic Jones polynomials
### Abhijit Champanerkar and Ilya Kofman
Algebraic & Geometric Topology 6 (2006) 1655–1668
arXiv: math.GT/0605631
##### Abstract
We show that if $\left\{{L}_{n}\right\}$ is any infinite sequence of links with twist number $\tau \left({L}_{n}\right)$ and with cyclotomic Jones polynomials of increasing span, then $limsup\tau \left({L}_{n}\right)=\infty$. This implies that any infinite sequence of prime alternating links with cyclotomic Jones polynomials must have unbounded hyperbolic volume. The main tool is the multivariable twist–bracket polynomial, which generalizes the Kauffman bracket to link diagrams with open twist sites.
##### Keywords
Jones polynomial, Mahler measure, twist sites, hyperbolic volume
Primary: 57M25
Secondary: 26C10
##### Publication
Received: 5 June 2006
Accepted: 28 August 2006
Published: 14 October 2006
##### Authors
Abhijit Champanerkar Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688 USA Ilya Kofman Department of Mathematics College of Staten Island City University of New York 2800 Victory Boulevard Staten Island, NY 10314 USA | 2018-08-21 11:42:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.252649188041687, "perplexity": 4621.849812691379}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221218122.85/warc/CC-MAIN-20180821112537-20180821132537-00619.warc.gz"} |
https://physics.stackexchange.com/questions/440322/a-perfectly-fitting-pot-and-its-lid-often-stick-after-cooking | A perfectly fitting pot and its lid often stick after cooking
I encountered a question that asks for the reason that a perfectly fitting pot and its lid often stick after cooking when it cools down. The answer in the solution manual was that the pressure decreases when the temperature decreases. I understand that point, but my problem is the following: The pot before being heated during cooking is influenced only by the atmospheric value, and the food inside that pot is the atmospheric pressure also. So this is the initial state for the pressure inside the pot now. When heated the pressure inside the pot increases. When we let the pot cool down to the room tempreture, would the pressure return to its initial value which is the atmospheric pressure? Why does the solution manual consider a vacuum inside the pot?
• To see it in reverse, take a mason jar with one of those rubber seals, put room temperature water in it, close the jar, and place it in the fridge. Leave it for at least 30 minutes, and then take it out and try to open it - the rubber seal will be very snug to the jar! – N. Steinle Nov 11 '18 at 17:02
As @Stephen C. Steel pointed out, the pressure increase in the pot (due to heating the air in the pot) relative to the outside pressure exerts a net force on the lid causing it to vent. However, it doesn’t matter if the lid is on before the cooking process starts, or put on just before turning off the heat. The important thing is to understand the mechanism involved for the lid sticking on cool down.
Let’s assume the cooking starts with the lid off. Generally you will have some steam (water vapor) developed in the pot. The lid is put on just before turning off the heat. Inside the pot we have a mixture of air and water vapor, likely near saturation, which is nearly equal to the outside pressure, 1 atm. But the pressure inside the pot is the sum of the partial pressures of the water vapor and dry air. As the mixture cools the water vapors condenses into a liquid. The pressure in the pot is now less due to the loss of the partial pressure of the water vapor. The lower pressure in the pot versus the pressure outside the pot causes a force holding down the lid, if it consists of a relatively good seal.
I should add the fact that in addition to the drop in pressure due to condensation, the drop in temperature of the dry air in essentially a fixed volume also results in a pressure drop. Considering air as an ideal gas, from the ideal gas law:
$$\frac {P_1V_1}{T_!}=\frac {P_2V_2}{T_2}$$
And for $$V=$$constant
$$\frac {P_1}{T_!}=\frac {P_2}{T_2}$$
Since $$T_2, then $$P_2
Hope this helps
• Thanks for your answer . But there is a point here is the force difference between the outside and the inside pressure leads to the act of sticking where is the normal force that the pot produces on the lid If there is a Free body diagram on the lid of the pot it will have the forces from the pressure and the force provided from the pot on the lid why this normal force do not cancel the force result from the difference in pressures – A.ELAK Nov 11 '18 at 20:18
• RE: "However, it doesn’t matter if the lid is on before the cooking process starts, or put on just before turning off the heat." // That isn't true. The assumption is that the lid acts as a one way valve. It lets excess pressure out, but does not leak air in. Thus if the pot starts with the lid on, then some gas would escape as vapor pressure of water increases. This would sweep out some air. So if the pot had been boiling for some time all the air would be displaced and only water vapor would remain in the head space. – MaxW Nov 11 '18 at 20:46
• @MaxW Sure it can act as a one way valve. All I'm saying is you don't have to start with the lid on to get the sticking effect.. – Bob D Nov 11 '18 at 21:32
• @A.ELAK The weight of the lid is the minimum force necessary to remove the lid, whether or not your cooking with the pot. The cooling effect after cooking only adds to the force necessary to remove the lid due to the pressure drop inside. I don't see how the weight of the lid cancels out the effect of the pressure drop. Maybe I'm not understanding your comment. – Bob D Nov 11 '18 at 21:43
• In a sense, if you have a super mega heavy lid, and it is so heavy that air cannot escape and the lid becomes a perfect seal, then yes, it will "Cancel out". However, that's not how real lids work. If you tried this, the pot might just explode on you. A heavier lid may end up with less pressure difference because it is better at preventing air from escaping, but it is a heavier lid to begin with, and a boiling pot can create a huge amount of pressure. Not sure if you really gain any benefit in the end. If you're curious look up "exploding pressure cookers". – Nelson Nov 12 '18 at 6:23
You've made the wrong assumption about what a perfectly fitting lid does. Rather than sealing perfectly, it will vent gas when the interior is at a higher pressure (the lid will lift), but seal when the exterior pressure is higher (the lid is pressed down). | 2019-10-20 18:52:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4636346995830536, "perplexity": 456.6675038191874}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986718918.77/warc/CC-MAIN-20191020183709-20191020211209-00413.warc.gz"} |
http://www.dynaverse.net/forum/index.php/topic,163203675.msg1122159177.html | ### Topic: Galaxies at War (The mod) (Read 18984 times) var addthis_config = {"data_track_clickback":true};
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#### DarkMatrix
• Guest
##### Galaxies at War (The mod)
« on: November 02, 2003, 12:13:31 pm »
guys just thinking here why dont we do Galaxies at War ourselfs we got the 2 races taldren give us and all the drawings we use the op game engine
if a few of us work together we can do it what we need are
1.Modelers
2.spec people
3.beta testers
4.web person
5.mission scripters
6.some people to write up a story line
7.some people to design new ships
8.people to reseach races
with op we got loads of room in the spec file for all the races and ships
and i cant see why we cant do it
so if you like to help do this please say so
i can model,design ships myself and even help on hte storyline what we need is more people so come on guys let do this
im looking more into this tomorrow races,specs and just ideas for the mod
Darkmatrix
« Last Edit: November 02, 2003, 12:35:20 pm by DarkMatrix »
#### DarkMatrix
• Guest
##### Re: Galaxies at War (The mod)
« Reply #1 on: November 02, 2003, 12:36:09 pm »
races so far if you think of any more please say
1.Federation
2.Klingon
3.Romulan
4.Hydran
5.Lyran
6.Mirak
7.Orion Pirates
8.Tholian
9.Seltorians
10.Gorn
11.Andromedan
12.Isc
also era i say we stay with Tmp like op maybe few ships earlyer here and there what you think?
« Last Edit: November 02, 2003, 12:38:06 pm by DarkMatrix »
#### Ducttapewonder
• Guest
##### Re: Galaxies at War (The mod)
« Reply #2 on: November 02, 2003, 12:50:48 pm »
Dude......This idea rocks.
I'll help in any way i can. Feel free to use any of my retexes you want to.
I like the way you got the races. I wouldnt change a thing with it.
Lets all take this idea and run with it.
#### Klingon Fanatic
• Guest
##### Re: Galaxies at War
« Reply #3 on: November 02, 2003, 12:51:05 pm »
I volunteer to be a play tester.
The question then really becomes: "What are you limiting the mod to?"
Stock Tladren ships we have seen or should the rest of the Klingon Academy ships be included too? I. e., the Sha' Kurians
Then the next question becomes since we may only get some limited Andromedan and Tholian weapons in probably mission specific scripts, how close to we want the spec file to be?
I for one want Mirror Universe Imperials in my game.
I am more inclined to give the Tholians Klingon Academy specs to the Tholians as opposed to SFB stats, but I will play whatever is generated. SFB Tholians tend to be emotionally charged around here....
As for Andromedans, I would urge the use of implementing uniform Andromedan shield (Non-regenerative, no labs?) value in increments of 25 (e.g. 25 FF, 50 DD, 75 CL, 100 CA, etc..) IMHO, this would reflect some of the Andromedan ability to manage energy/power better than the galatic powers. If they are really the BORG of the TOS/TMP this makes them harder to defeat without more than one ship. As for TRBs we have light and heavy TRBs and the Displacement device can be 'simulated' via the improved cloak....
I think Rod O' Neal has a really good handle on this peice overall and he should be recruited for any such project.
KF
« Last Edit: December 31, 1969, 06:00:00 pm by Klingon Fanatic »
#### DarkMatrix
• Guest
##### Re: Galaxies at War
« Reply #4 on: November 02, 2003, 12:56:56 pm »
thankyou DTW also KF can you help with reseach man you one of people to seem to know all things trek:D
as for the mod TMP seems the way to go for now
im rendering up feds now so people give me idea for ship scales
so i sort out the Tholian scaling and brk mods so they done not got alot of time today i got to sleep soon lol
but im all over this when i get in from work
weapons are going to be hard i think we need alot of info for each race
DM
#### DarkMatrix
• Guest
##### Re: Galaxies at War
« Reply #5 on: November 02, 2003, 01:08:07 pm »
Quote:
I volunteer to be a play tester.
The question then really becomes: "What are you limiting the mod to?"
Stock Tladren ships we have seen or should the rest of the Klingon Academy ships be included too? I. e., the Sha' Kurians
Then the next question becomes since we may only get some limited Andromedan and Tholian weapons in probably mission specific scripts, how close to we want the spec file to be?
I for one want Mirror Universe Imperials in my game.
I am more inclined to give the Tholians Klingon Academy specs to the Tholians as opposed to SFB stats, but I will play whatever is generated. SFB Tholians tend to be emotionally charged around here....
As for Andromedans, I would urge the use of implementing uniform Andromedan shield (Non-regenerative, no labs?) value in increments of 25 (e.g. 25 FF, 50 DD, 75 CL, 100 CA, etc..) IMHO, this would reflect some of the Andromedan ability to manage energy/power better than the galatic powers. If they are really the BORG of the TOS/TMP this makes them harder to defeat without more than one ship. As for TRBs we have light and heavy TRBs and the Displacement device can be 'simulated' via the improved cloak....
I think Rod O' Neal has a really good handle on this peice overall and he should be recruited for any such project.
KF
if we get wz45 to let us use what ka ships he done then we add them
as for stock models i say totaly remodeled ones where we can im not putting down taldren models some are nice but it been great if we replace them with higher poly ones
the new Tholians as far as i see are fine
the Andromedan need looking at far as i see they good place to start
also taldren if you happen to read this topic do youy have any more GAW Concepts drawing that never got to be what u planning for the game we love to see them
also hoping atolm will help us on the design side of things too
DM
#### Rogue
• Guest
##### Re: Galaxies at War
« Reply #6 on: November 02, 2003, 01:39:57 pm »
DarkMatrix, As much as I would love to see it... the mod, IMHO, is nearly pointless. Without the missing technology that the Andromedans and Tholians represent it won't really work.
What we have is the models, the tractor-repulser easter egg (although there is no user interface for it) and the will to do it.
What's missing is the web technology, PA panels and displacement devices. Without that you will never have our missing adversaries.
About the best aproach might be a pre-tos package of the early appearence of these races before the advent of that technology. There is no way to simulate the web caster or displacement device unless one of the programers gets the blessing from Taldren to offer a special patch. A rough aproximation of the PA panels might be done with evening out the forward and rear hemispheres of the shield specifications and give them as much regeneration as possible. Perhaps pick Federation specifications as a donor and enhance with additional lab. I'm not sure about that as I'm not sure about the mechanics of shield regeneration.
But by all means take a shot at it. I would probably use it to replace two of the Orion cartels that no one ever really cared about anyway. I would trade every one of them for a web caster/web generator easter eggs. If we had that the Tholians could have been done. The PA panels would have been wonderful but they need careful energy management. And Andy doesn't have shuttles to avoid seeking weapons so the displacement device is a necessary technology to break lock-ons. Oh well...
« Last Edit: December 31, 1969, 06:00:00 pm by Rogue »
#### Klingon Fanatic
• Guest
##### Re: Galaxies at War
« Reply #7 on: November 02, 2003, 01:47:37 pm »
There may be a way to get the web into SFC. Let us see what Tracey G. has come up with....
Andros still need some work but we can approximate what Andros could do.
KF
#### Azel
• Guest
##### Re: Galaxies at War
« Reply #8 on: November 02, 2003, 04:04:54 pm »
Quote:
also hoping atolm will help us on the design side of things too
If you want Me, I am there...just tell me what you need
#### Desty_Nova
• Guest
##### Re: Galaxies at War
« Reply #9 on: November 02, 2003, 05:35:27 pm »
I have lots of information about the Andromedan War and Operation Unity to assist with the story. Hopefully Module C5 will be out before long and that will have even more info on Op Unity. I also have stats for just about every possible ship you could need for every race. Also my models are available however it sounds like this is not going to be TOS era.
#### Desty_Nova
• Guest
##### Re: Galaxies at War (The mod)
« Reply #10 on: November 02, 2003, 05:47:25 pm »
Quote:
races so far if you think of any more please say
1.Federation
2.Klingon
3.Romulan
4.Hydran
5.Lyran
6.Mirak
7.Orion Pirates
8.Tholian
9.Seltorians
10.Gorn
11.Andromedan
12.Isc
also era i say we stay with Tmp like op maybe few ships earlyer here and there what you think?
If the story is going to involve Operation Unity(and how could it not?), the galactics will be making a foray into the Lesser Magellanic Cloud, where they encounter these folks:
Eneen
Jumokians
These are the main races that inhabit the LMC, and the galactics had to work together with them(to a point) to hunt down and destroy the primary Andromedan starbase located there. These races haven't been released yet, but like I said, hopefully they will be soon. Anyway, I think it would be cool to include these guys as much as possible. However, they will have more bizzare technology that SFC2's engine won't be able to approximate closely at all.
#### Klingon Fanatic
• Guest
##### Re: Galaxies at War (The mod)
« Reply #11 on: November 02, 2003, 07:39:35 pm »
Quote:
Quote:
races so far if you think of any more please say
1.Federation
2.Klingon
3.Romulan
4.Hydran
5.Lyran
6.Mirak
7.Orion Pirates
8.Tholian
9.Seltorians
10.Gorn
11.Andromedan
12.Isc
also era i say we stay with Tmp like op maybe few ships earlyer here and there what you think?
If the story is going to involve Operation Unity(and how could it not?), the galactics will be making a foray into the Lesser Magellanic Cloud, where they encounter these folks:
Eneen
Jumokians
These are the main races that inhabit the LMC, and the galactics had to work together with them(to a point) to hunt down and destroy the primary Andromedan starbase located there. These races haven't been released yet, but like I said, hopefully they will be soon. Anyway, I think it would be cool to include these guys as much as possible. However, they will have more bizzare technology that SFC2's engine won't be able to approximate closely at all.
This is a wonderful idea except that we don't have all the models needed in TMP (NOT TOS/SFB) format.
Second, why does it have to be historical SFB based?
I'd rather we ripple reality, pretend this mod is set in an a parallel Trek Universe, and have Second Andromedan Invasion myself just after ST: VI... blame it on the ST: New Worlds Melak experiment, the Mirror Universe Imperials experimenting with a new weapon or even the go with the idea that the Andromedans were actually planning to send a follow up force anyway...
I myself play this game for FUN. No die hard SFB player will ever say, "You got it perfect" no matter what kind of effort is made, professional or not. So, I say lets use the tools, models, talent and scripts available to have FUN.
Regarding the GAW mod, I am beginning to feel that we should stick with one of Rod O' Neal's Shiplists or to the latest Taldren one and make a D2 style mod. One ship type per slot using STOCK designations FCV, FBB etc. For other races using pirate slots SIMPLY use pirate designations with single letters e.g., TPCA for Tholian Heavy Cruiser (KA Ruby Class)or ACA (P81's TMP Andromedan Imposer). This will save a ton of time if we really want to crank this out THIS Year, LOL.
Just my two cents.
KF
« Last Edit: November 02, 2003, 08:13:50 pm by Klingon Fanatic »
#### DonKarnage
• Guest
##### Re: Galaxies at War (The mod) *DELETED* *DELETED*
« Reply #12 on: November 02, 2003, 09:48:27 pm »
Post deleted by DonKarnage
#### Ducttapewonder
• Guest
##### Re: Galaxies at War (The mod)
« Reply #13 on: November 03, 2003, 03:32:43 am »
Back to the top with ya.
#### DarkMatrix
• Guest
##### Re: Galaxies at War (The mod)
« Reply #14 on: November 03, 2003, 03:53:31 am »
just got all the ship info from ka.com for all th ka ships thxs for headsup KF
DM
#### DarkMatrix
• Guest
##### Re: Galaxies at War
« Reply #15 on: November 03, 2003, 03:54:51 am »
Quote:
I have lots of information about the Andromedan War and Operation Unity to assist with the story. Hopefully Module C5 will be out before long and that will have even more info on Op Unity. I also have stats for just about every possible ship you could need for every race. Also my models are available however it sounds like this is not going to be TOS era.
please post what ever you got please ill log it all so we work out where we going with the storyline thanks
come on guys we need more people here
DM
#### DarkMatrix
• Guest
##### Re: Galaxies at War
« Reply #16 on: November 03, 2003, 04:09:41 am »
Klingon ship list (beta) by KF
Here's a start.
KBB
1. Sword of Khaless WZ45
2. B10/11 P81
3. C-9 JrStandfast
4. C-8 Jrstandfast
KCV
1. Gorkon Atrahasis
2. SuWacHI Carrier Captain KoraH
3. Khamby Atrahasis
4. Stock KCV
KDN
1. Accuser WZ45
2. Darkfleet Accuser DarkMatrix
3. L-24c Atrahasis
4. L-24 Atrahasis
KCX
1. SuWacHI battlecruiser Captain KoraH
2. SuvwI Qeh WZ45
3. Stock KCX retexture Atticbat
4. WILD CARD
KCA
1. D-10B Atrahasis
2. K'Tinga
3. D-16 (TMP) Terradyne
4. WILD CARD
KCL
1. Stock KCL kitbash by TooMuch Coffee retextured by me
2. L-9 Saber D'deridex
3. L-6 Captain KoraH
4. D-9 Captain KoraH
KDX
1. K'teremny Cleeve
2. Stock Kitbash by SpaceCadetGlow UK
3. Stock
4. WILD CARD
KDD
1. Valkyris Atrahasis
2. D-18 Gull Wing
3. K-17 Death Stalker P81
4. D-16 Captain KoraH
KFF
1. Unseen Creeper P81 with BOP texture
2. K-27 Captain KoraH
3. K-23
4. Darkfleet BOP
KFA
1. Stock
2. Armada Conversion construction ship
KDS
WZ45's Klingon defense satellite
Stardock
1. Stock
2. Armada conversion retextured by me
3.
WILD CARD = waiting on ship any ideas for more ships or better ones please say looking at the list so far im happy with it
also to anyone model on that list if you dont mind us using them can you please say
thanks
also DTW is working on the feds list too
and i`m busy sorting out the Tholian and Orion Pirates
Darkmatrix
#### Desty_Nova
• Guest
##### Re: Galaxies at War
« Reply #17 on: November 03, 2003, 04:23:55 am »
Here's here are some synopses and general points that I can elaborate on if you wish:
In year 170, the first Andromedan ship sighted in our galaxy was encountered by the Kzinti Light Carrier Typhoon in an asteroid field. After that, other Andromedan ships were sighted from time time, sometimes evading contact, sometimes attacking without provocation. Several ships of different races were confirmed destroyed by Andromedan raiders, several other unaccounted for ships are also suspected to be victims of marauding Andros. Over the decade of year 175-185, the Andromedans shifted from a curiousity to a menace as their ships began attacking others on sight.
The Andromedans launched a full-scale invasion of the Milky Way galaxy in year 188. Over the next ten years, large numbers of Andromedan ships arrived in our galaxy and created considerable mayhem and destruction. Since the flight time from Andromeda is on the order of 200 years, the invasion was fully commited before its first recon ships arrived.
The Andromedans apparently built up their strength during the General War and launched their attack only when the galactic forces were exhausted. The Romulans were hit particularly hard by the Andromedans, and the Lyran Democratic Republic was completely annhilated by them. At the height of their power (year 197) the Andromedans had reduced the Romulan, Gorn, ISC, Lyran, and Hydran Empires to small areas around their home systems.
Eventually it was discovered that there were not all that many Andromedan ships. The Andros had created a strategic transportaion network(known as the Rapid Transport Network or RTN) of pre-surveyed routes along which their ships could move at warp 15, allowing them to concentrate their forces at key points. Survey ships discovered the first of these bases in year 195, and by year 198 the network had been heavily disrupted as the scouts and survey cruisers hunted down the bases for the cruisers to destroy.
Finally in year 201, the galactic forces launched a three-pronged attack on the Lesser Magellanic Cloud, destroying the only starbase operated by the Andromedans in year 202. This broke the back of the invasion as it apparently cut off their only direct route from their own galaxy. After that time, the Andros became merely a nuisance as renegades and a few new arrivals caused local disturbances.
Absolutely nothing is known about the Andromedans as beings. No one has ever seen an Andros and lived. Their boarding parties are composed of robotic combat systems, leading some to theorize that the Andromedans themselves are robots or computer software.
#### Desty_Nova
• Guest
##### Re: Galaxies at War
« Reply #18 on: November 03, 2003, 04:38:06 am »
In year 184, a new type of Andromedan satellite ship appeared that mounted a mauler. These were dubbed the Terminator. They packed an unbelievable punch for their size, able to fuel the mauler directly with power from their power absorber panels. The source of the mauler technology is unconfirmed(Romulan?). Later, a larger Andromedan mauler was observed, the Eliminator, which had much greater firepower. It was any captain's worst nightmare. Fortunately, they were only used in extremely small numbers.
After the Galactic Forces destroyed the Andromedan starbase, they explored the two Magellanic Clouds searching for other Andro bases and forces. In the system LMC 1104, they discovered the incomplete hull of what would have been the largest Andromedan ship ever seen. This was the Devastator-class battleship. It was 55% complete and galactic engineers estimate that it would have taken another 2 to 5 years to complete. Had it been finished, it would have been a nigh-unstoppable monster.
#### Desty_Nova
• Guest
##### Re: Galaxies at War
« Reply #19 on: November 03, 2003, 04:51:40 am »
This is a scenario from SFB entitled "Return of the Darwin":
In year 195, the Galactic Survey Cruiser Darwin discovered the secret of the Andromedan Rapid Transport Network by clandestinely observing the arrival and departure of several Andro ships at a Satellite base and intensively scanning the emissions. Before it could report these finding to Starfleet, the Darwin struck a temporal rift and was hurled 12 years into the future.
The Darwin emerged some 20000 parsecs from its original position, less than 1000 km from a Federation squadron.
After establishing contact with the squadron, the Darwin learned that they were acting as a delaying force against a powerful new Andromedan unit that was proceeding for the heart of Federation space.
An exchange of information revealed that the loss of the Darwin's RTN data had delayed Operation Unity by three years, causing its failure and allowing the Andromedans to begin fielding their dreaded Devastator-class battleships(one of which had just destroyed the Klingon B10 Invincible in a battle over Klinshai).
They realized that the Darwin must return through the temporal rift so as to allow Op Unity to be launched three years earlier. The Federation squadron would provide cover for her to execute repairs to do so. The Commodore led his outgunned squadron, the last operational reserve of Starfleet, into a desperate battle against the onrushing Andromedan battleship to restore history.
After the sacrifice of the entire Federation squadron, the Darwin managed to return. The reports of a dismal future helped to bring the galactic powers together to defeat the Andromedans more than anything else.
That could make a cool part of the story.
« Last Edit: November 03, 2003, 04:52:55 am by Desty_Nova » | 2021-03-02 13:32:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36831825971603394, "perplexity": 7769.040979175895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178364008.55/warc/CC-MAIN-20210302125936-20210302155936-00118.warc.gz"} |
http://mymathforum.com/advanced-statistics/49615-standard-deviation-formulas-short-proof.html | My Math Forum Standard Deviation Formulas - Short Proof
January 13th, 2015, 11:31 AM #1 Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 Standard Deviation Formulas - Short Proof Today I learnt that: $\displaystyle Variance=\frac { \Sigma { \left( x-\overline { x } \right) }^{ 2 } }{ n } =\frac { \Sigma { x }^{ 2 } }{ n } -{ \left( \frac { \Sigma x }{ n } \right) }^{ 2 }$ Considering that the formula for the mean in the United Kingdom is: $\displaystyle \overline { x } =\frac { \Sigma x }{ n }$ Now, I wasn't told why the formulas posted above were equal to one another. I was just supposed to accept such truths without any evidence. So, to satisfy such claims - I've made a short little proof as to why the two formulas at the top of your screen ARE in fact equal to one another. If you have any better proofs, then please feel free to post them on this thread. For the meantime, this is what I've achieved... ---------------------------------------------------- PROOF: Say that: $\displaystyle For\quad convenience,\\ \\ d=a+b+c,\\ \\ \therefore \quad \frac { \Sigma x }{ n } =\frac { a+b+c }{ n } =\frac { d }{ n } =\overline { x } \\ \\ However,\quad \frac { d }{ n } =p,\quad \therefore \quad \overline { x } =p,\quad d=np\quad and\quad n=\frac { d }{ p } .\\ \\ Note\quad that:\quad n=3\quad in\quad this\quad case.$ Also note that: $\displaystyle { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=g,\\ \\ \therefore \quad \frac { \Sigma { x }^{ 2 } }{ n } =\frac { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } }{ n } =\frac { g }{ n } \\ \\ However,\quad \frac { g }{ n } =q,\quad \therefore \quad g=nq\quad and\quad n=\frac { g }{ q } .$ Now, with these set of rules, we should reach the conclusion that: $\displaystyle \frac { \Sigma { x }^{ 2 } }{ n } -{ \left( \frac { \Sigma x }{ n } \right) }^{ 2 }=\frac { g }{ n } -{ \left( \frac { d }{ n } \right) }^{ 2 }=q-{ p }^{ 2 }$ We can also discover that: $\displaystyle \frac { \Sigma { \left( x-\overline { x } \right) }^{ 2 } }{ n } \\ \\ =\frac { { \left( a-p \right) }^{ 2 }+{ \left( b-p \right) }^{ 2 }+{ \left( c-p \right) }^{ 2 } }{ n } \\ \\ =\frac { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }+3{ p }^{ 2 }-2ap-2bp-2cp }{ n } \\ \\ =\frac { g+3{ p }^{ 2 }-2p\left( a+b+c \right) }{ n } \\ \\ =\frac { g+3{ p }^{ 2 }-2pd }{ n } \\ \\ =\frac { g }{ n } +\frac { 3{ p }^{ 2 } }{ n } -\frac { 2pd }{ n } \\ \\ \boxed { But,\quad n=3. } \\ \\ =q+{ p }^{ 2 }-2p\cdot \frac { d }{ n } \\ \\ =q+{ p }^{ 2 }-2{ p }^{ 2 }\\ \\ =q-{ p }^{ 2 }$ So, as: $\displaystyle q-{ p }^{ 2 }=q-{ p }^{ 2 }\\ \\ \frac { \Sigma { \left( x-\overline { x } \right) }^{ 2 } }{ n } =\frac { \Sigma { x }^{ 2 } }{ n } -{ \left( \frac { \Sigma x }{ n } \right) }^{ 2 }$ I came up with this proof, as I wasn't told why these two formulas are equal to one another. Hopefully this will be able to help some maths students come to terms with why it's the case. If you have any better proofs, please post them below. Thankyou for your attention. Last edited by perfect_world; January 13th, 2015 at 11:33 AM.
January 13th, 2015, 02:01 PM #2 Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717 $\displaystyle \sum \frac{(x-m)^2}{n}=\sum (\frac{x^2}{n}-2\frac{mx}{n}+\frac{m^2}{n})$ $\displaystyle \sum \frac{mx}{n} = m\sum \frac{x}{n} = m^2$ $\displaystyle \sum \frac{m^2}{n} = m^2 \sum \frac{1}{n} =m^2$ Put it all together to get result.
January 13th, 2015, 03:59 PM #3
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Originally Posted by mathman $\displaystyle \sum \frac{(x-m)^2}{n}=\sum (\frac{x^2}{n}-2\frac{mx}{n}+\frac{m^2}{n})$ $\displaystyle \sum \frac{mx}{n} = m\sum \frac{x}{n} = m^2$ $\displaystyle \sum \frac{m^2}{n} = m^2 \sum \frac{1}{n} =m^2$ Put it all together to get result.
I understand that you multiplied the binomial in the first line, but I have no idea how you got to the second line.
January 14th, 2015, 12:44 PM #4 Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717 In $\displaystyle \sum \frac {mx}{n}$, m is constant, so take it outside summation. By definition: $\displaystyle \sum \frac{x}{n} = m$.
January 15th, 2015, 10:32 AM #5 Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 To @mathman, In your proof I presume that n=1, as the data set for x consists of x alone. It's funny how that summation sign can be manipulated around in specific cases. How would I define this data set mathematically? Would it be: x={x} Therefore n=1. Last edited by perfect_world; January 15th, 2015 at 10:35 AM.
January 15th, 2015, 10:51 AM #6 Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 Can you let me know if I'd be able to manipulate the sigma symbol in such a manner... $\displaystyle \frac { \Sigma { \left( x-m \right) }^{ 2 } }{ n } \\ =\sum { \frac { { \left( x-m \right) }^{ 2 } }{ n } } \\ \\ =\sum { \frac { { x }^{ 2 }-2mx+{ m }^{ 2 } }{ n } } \\ \\ =\sum { \left( \frac { { x }^{ 2 } }{ n } -2\frac { mx }{ n } +\frac { { m }^{ 2 } }{ n } \right) } \\ \\ =\sum { \frac { { x }^{ 2 } }{ n } } -2\sum { \frac { mx }{ n } } +\sum { \frac { { m }^{ 2 } }{ n } } \\ \\ =\frac { \Sigma { x }^{ 2 } }{ n } -2{ m }^{ 2 }+{ m }^{ 2 }\\ \\ =\frac { \Sigma { x }^{ 2 } }{ n } -{ m }^{ 2 }\\ \\ =\frac { \Sigma { x }^{ 2 } }{ n } -{ \left( \frac { \Sigma x }{ n } \right) }^{ 2 }$ I'm just experimenting with it, and seeing if it's possible to create proofs in this way.
January 15th, 2015, 11:47 AM #7
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Originally Posted by EvanJ I understand that you multiplied the binomial in the first line, but I have no idea how you got to the second line.
@EvanJ,
I believe that these truths can be derived from the information we have at our disposal.
$\displaystyle x=\left\{ x \right\} \Rightarrow n=1\\ \\ \frac { \Sigma x }{ n } =\frac { x }{ n } =\sum { \frac { x }{ n } } \\ \\ ---------------------------\\ \\ m=\frac { \Sigma x }{ n } ,\\ \\ \therefore \quad { m }^{ 2 }=m\frac { \Sigma x }{ n } =\frac { mx }{ n } =m\sum { \frac { x }{ n } } =\frac { \Sigma mx }{ n } \\ \\ ----------------------------\\ \\ \frac { \Sigma { x }^{ 2 } }{ n } =\frac { { x }^{ 2 } }{ n } =x\cdot \frac { x }{ n } =x\frac { \Sigma x }{ n } =x\sum { \frac { x }{ n } } \\ \\ -----------------------------\\ \\ \frac { { m }^{ 2 } }{ n } ={ m }^{ 2 }\sum { \frac { 1 }{ n } } =\frac { { \left( \frac { \Sigma x }{ n } \right) }^{ 2 } }{ n } ={ \left( \frac { \Sigma x }{ n } \right) }^{ 2 },\quad (as\quad n=1)\\ \\ \\ \\ \\ \\ \\ \\$
January 15th, 2015, 05:31 PM #8 Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717 I believe that in the original expression $\displaystyle x$ was meant to be $\displaystyle x_i$ (one sample) where i went from 1 to n. My answers were made on that assumption.
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https://docs.certsafe.com/changelog.html | # Changelog¶
## Release 2019b¶
Release date: November 13, 2019
Enhancements:
• Multiple improvements to drag-and-drop and cut/copy/paste behavior of variables in the simulation editor.
• Added a new Show in Projects View editor action. This action has the keyboard shortcut Ctrl+B; the Show in File Browser action, which had that keyboard shortcut previously, is now mapped to Ctrl+Shift+B.
• The last file chooser directory is now updated when opening a project through the Recent Projects menu.
• Command line invocations now consistently return nonzero exit codes when an error occurs, making them easier to use in scripts.
Bugfixes:
• Fixed arrow keys moving both the selection and viewport simultaneously when zoomed in on a diagram editor with nonempty selection.
• Fixed whitespace before XML in a drop/paste causing data to be parsed wrong.
• Drop/paste now tries to detect and reject invalid XML instead of interpreting it as a list of strings.
• Fixed multiple issues related to pressing keys during a drag-and-drop operation.
• Fixed multiple issues with command line error handling and logging.
• On Windows, the Rename action in the Projects view can now rename a file to a new name that is identical to the old name except for case.
• Fixed exceptions related to Windows case-insensitive file paths.
• Fixed exceptions related to invalid file paths, such as network paths without a sharename on Windows.
• Fixed the Rename action not working when the Projects view is filtered.
• Fixed a regression where the table of results was laid out incorrectly in the filtered Projects view.
## Release 2019a¶
Release date: August 29, 2019
Enhancements:
• New installer that allows users without administrator privileges to install the software locally to their user accounts.
• Several experimental features are now available in release builds, albeit disabled by default. To enable these features, go to Window ‣ Options... and check Show experimental features. This adds an Experimental menu to the main menu bar. Some of the features now available through this menu were previously (and are still) available via the command line. Experimental features now available through this menu include:
• Autolayout Import
• Export Stitch Image
• Export Skeletons For All Diagrams and Stitches
• Batch-Simulate CSVs
• Rewrite Resources in Project
• Added a File ‣ Recent Projects submenu that lists recently-opened projects for quick access.
• Improved support for dragging multiple components at once between the Projects view, Palette view, diagram editor, palette editor, etc.
• Section titles can now be edited inline in the Palette editor without having to click a Rename button.
• Added support for the standard Ctrl+W shortcut to close the current editor tab.
• Image export scale and format is now remembered, including across restarts.
• Added a Store intermediate values flag that can be disabled in the Properties of a simulation to turn off saving probe values in memory. This is useful when trying to run very large simulations in the GUI. This flag is saved in the *.cxsim file.
• Improved performance of probe rendering and Block Indices slider rendering.
Bugfixes:
• Fixed regression where newly-opened editor tabs sometimes got layered vertically instead of being grouped in the same stack.
• Fixed numerous issues with the palette editor.
• Fixed rendering glitch where resizing and collapsing the Palette view could cause it to show with a gray overlay.
• Fixed rendering glitch when switching between two instances that had the same grid size but different offsets of the diagram elements within that grid size.
• Fixed regression where opening a project via command line / file association did not work when CertSAFE was already running.
• Typing a backtick in a text box in the stitch editor no longer also switches between definition and instance mode.
• Fixed breadcrumbs bar combo box not navigating properly after using it to switch between different instances of the same definition.
• Fixed several issues with drag-and-drop and dragging selection boxes in the diagram editor.
• Fixed issues with project focus when opening or closing projects and certain other circumstances.
• Fixed exceptions when adding invalid paths to the project file base paths or excluded paths lists.
## Release 2018b¶
Release date: November 15, 2018
Enhancements:
• Added the blocks system for representing arrays and loops. See the blocks tutorial for an introduction to these major new features.
• Added a new Hole primitive as a stub for use when developing models.
• Changing the root of a simulation no longer removes all of the variables from the simulation.
• It is now legal to override statically-constant intermediate variables in simulations, as long as the overriding data is a constant value. This makes the behavior match the existing rules for statically-constant root input variables.
• Variable usage icons are now shown in a new column that supports sorting in the simulation editor variables table.
• Improved the display of errors and warnings in the simulation editor.
• User-defined components now show automatically-generated output descriptions in wire network tooltips, rather than just displaying ”...”.
• Added file flavor support to drag-and-drop/copy-and-paste from the Projects tree. This makes it possible to, for example, drag a file from the CertSAFE Projects view to the tab bar in Notepad++ to view that file’s XML.
• Added support for several common types of proxy server configuration during license server checks. CertSAFE will automatically attempt to detect whether a proxy configuration is present; if one is found, CertSAFE will use it automatically.
Bugfixes:
• Fixed several issues with strange scroll/pan behavior throughout the user interface.
• Fixed CSV export being blocked on simulations that contain warnings.
• Fixed lag and excessive CPU usage when validating license keys.
• Standard output now works more sensibly when running CertSAFE from the command line.
## Release Candidate 12.1¶
Release date: October 25, 2018
General notes:
• This is a hotfix release to patch an issue that was preventing CertSAFE from contacting the license servers.
Bugfixes:
• Add Let’s Encrypt to CertSAFE’s certificate authority list.
## Release Candidate 12¶
Release date: May 21, 2018
Enhancements:
• Added integer interval types, which are a new kind of data type whose domain is a custom range of integer values. See the article on integer interval types for more details.
• IntN and UIntN data types are now supported for non-power-of-two sizes. N can now be any integer between 1 and 53, inclusive.
• CSV simulation vectors import is now more lenient in the value formats that it accepts. For example, the all-uppercase TRUE and FALSE written by Microsoft Excel are now accepted as valid Boolean values for CSV import.
• The icon for enum types has been changed.
• The number of merged variables in the instance hierarchy is now shown in the list of statistics in the Properties view when a diagram or stitch is selected in the Projects view.
• Some excessively large instance hierarchies will now immediately issue an error message when trying to set the root, rather than crashing with an out of memory error.
Bugfixes:
• Fixed a bug that prevented the warning for resources in the “CertSAFE” package from being generated.
Removed features:
• Enum types other than the built-in Boolean type no longer implement the “Has default” type class. This type class previously allowed models to inspect information about the ordering of enum values, by using a One Frame Delay with no IC pin to determine the first value of the enum type.
## Release Candidate 11¶
Release date: November 6, 2017
General notes:
• Version RC11 of CertSAFE breaks file format compatibility with version RC10 of CertSAFE for diagram, simulation, palette, and skeleton files. A program to update existing projects to be compatible with RC11 is provided along with this release. It is highly recommended that you upgrade any existing projects to the RC11 file format now, as the upgrade program may not be included in its current form in later versions of CertSAFE.
• The main focus of development for this release has been backend changes in preparation for the upcoming language support for arrays. However, several new features and bugfixes have been implemented as well.
Enhancements:
• It is now possible to edit a property on multiple components in a diagram or palette at once when several components of the same type are selected.
• The Nearest primitive has been extended to support integer data types on the output, in addition to the previously-existing support for floating point data types. This makes it easy to round floating point values to the nearest integer value (using round to nearest, ties to even, as with other floating point arithmetic in CertSAFE). It also makes it easy to perform saturating conversions from one integer data type to another, as opposed to the bitwise conversions performed by the Copy Bits primitive.
• The Switch primitive is now manually resizable. It has a Size property that can be edited in the same fashion as the other varargs primitives such as Boolean gates.
• The type error display system in diagrams and stitches has been significantly redesigned. Components that are the endpoint of a type error are now highlighted red, along with traced paths of networks between such endpoints. The error messages for several varieties of type error have been improved as well. Errors and warnings on a component are now shown in the component’s tooltip when mousing over the component in the diagram editor.
• Added double-click-to-go-to support for child units and child unit types in the stitch editor.
• Improved tooltip support in the stitch editor.
• The breadcrumbs bar now shows the icon of the resource type for each path element, to match the Instance tree.
• Diagram local variables no longer display paths in instance mode, since these paths were always redundant.
• Added a new “Show in File Browser” action when right-clicking on resources in the Projects tree.
• Selecting a diagram or stitch in the Projects view now shows statistics about its instance hierarchy in the Properties view.
• Significant performance improvements for certain very large stitches.
• Added an action under the Help menu to go to the new online support website: https://support.certsafe.com/
Bugfixes:
• Fixed issues with the rounding behavior of the Nearest primitive and IntelliPoints. In certain cases, these performed round to nearest, ties towards positive infinity instead of round to nearest, ties to even.
• Fixed issues with the case list GUI in the Switch primitive properties and the case table editor.
• Fixed issues with the calculation of waveform scrollbar ranges in the simulation editor.
• Fixed inconsistent font sizes and other presentation issues with the Special Numeric Function, Special Floating Function, Coerce, and Frames Per Second primitives.
• Fixed an exception that could occur when doing Save As on a diagram that is in diffing mode.
• The image preview in the diagram Export Image dialog now correctly shows the instance image instead of the definition image when exporting in instance mode.
Removed features:
• The Frames Elapsed primitive has been removed. The same behavior can be easily recreated as a custom component using a One Frame Delay loopback. See the latest version of the Example Components library for an example of how to do this.
• Logic that is not connected to any exported names now generates an “ambiguous block prefix” error. Previously, CertSAFE issued a warning that such logic would become illegal in a future release.
## Release Candidate 10¶
Release date: November 10, 2016
Enhancements:
• The Inline Operation component now has a separate Subtract mode instead of automatically displaying as a subtraction when a negative literal is specified in Add mode. This fixes the issue where an Inline Operation component could not be used to subtract from a variable with an unsigned integer data type.
• Rich tooltips are now resizable and have several other mouse and keyboard interaction improvements.
• The resource path is now displayed at the top of all editors instead of only diagram and stitch editors in definition mode.
• The breadcrumbs bar and the stitch editor filters panel can now be scrolled left and right if they do not fit in the available space.
• If a project name is not specified in a project file, the name of the project file is shown as the project name.
• General simulation performance optimizations.
Bugfixes:
• Fixed exception that could occur when sorting the Problems view by resource.
• Fixed a performance issue when drawing wires in certain large diagrams.
• Fixed several issues with the case list editor for the Switch component.
• Fixed exceptions and other issues that could occur with strange filenames.
• Fixed incorrect behavior on XML files that use explicit namespace prefixes instead of the default namespace.
## Release Candidate 9¶
Release date: September 5, 2016
Enhancements:
• The Switch primitive now supports switching on inputs other than Boolean True and False. It supports all of the same options as Case Table inputs, including enumeration- and integer-typed selector values.
• Improved sizing and scrolling behavior of rich tooltips.
• The project frames-per-second value is now stored using arbitrary precision arithmetic rather than double precision floating point, allowing frame rates such as 0.1Hz to be represented exactly.
• New set of default colors for waveforms that is more readable on the white background.
• Improved rendering of infinite waveform values.
• Added support for zooming on simulation timelines using the + and - keys together with combinations of Ctrl and Shift.
• Added a horizontal line to show the vertical center of a simulation timeline.
Bugfixes:
• Fixed exception when dragging wires in certain configurations in the diagram editor.
• Fixed exception when dragging diagram XML into a diagram editor that was previously copied out of the program using the Cut or Copy commands.
• Fixed text in certain tables that was unreadable due to improper line-wrapping.
• Fixed several issues with simulation timeline scrolling and rulers. | 2021-12-05 16:55:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23200960457324982, "perplexity": 4156.321374489365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363215.8/warc/CC-MAIN-20211205160950-20211205190950-00141.warc.gz"} |
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# It takes Computer A 36 hours to process data. If Computer A starts wor
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It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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07 Aug 2008, 22:31
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It takes Computer A 36 hours to process data. If Computer A starts working at 7 pm on Monday and after half the data are processed Computer B, three times as fast as Computer A, joins in the task, when will the data processing be finished?
A. 4:30 pm Tuesday
B. 5:30 pm Tuesday
C. 7:00 pm Tuesday
D. 8:30 pm Tuesday
E. 10:30 pm Tuesday
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07 Aug 2008, 22:40
mba9now wrote:
It would take Computer A 36 hours to process the data. If Computer A starts working at 7 pm on Monday and after half the data is processed Computer B, three times as fast as Computer A, is joined in the task, when will the data processing be finished?
4:30 pm Tuesday
5:30 pm Tuesday
7:00 pm Tuesday
8:30 pm Tuesday
10:30 pm Tuesday
comp A takes 36h and comp B takes 12h
comp A starts at 7pm on monday, processes half the data so it finishes at 7pm+(36/2)h which is 1pm on tuesday. Comp B takes up the next half so it finishes at 1pm+(12/2)h=7pm on Tuesday
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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07 Aug 2008, 22:54
The answer is B (5:30 PM Tuesday). Becasue it is said that Comp B joins A, never says only B did the work alone.
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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08 Aug 2008, 08:42
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mba9now wrote:
It would take Computer A 36 hours to process the data. If Computer A starts working at 7 pm on Monday and after half the data is processed Computer B, three times as fast as Computer A, is joined in the task, when will the data processing be finished?
4:30 pm Tuesday
5:30 pm Tuesday
7:00 pm Tuesday
8:30 pm Tuesday
10:30 pm Tuesday
computer A take 36 hr
computer B takes 12 hr
18 hrs (half job done by computer) + Half job dont by both
= 18 hrs + 18 / (3+1) = 22.5 hrs.
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mba9now wrote:
It would take Computer A 36 hours to process the data. If Computer A starts working at 7 pm on Monday and after half the data is processed Computer B, three times as fast as Computer A, is joined in the task, when will the data processing be finished?
4:30 pm Tuesday
5:30 pm Tuesday
7:00 pm Tuesday
8:30 pm Tuesday
10:30 pm Tuesday
work done by A in one hr = w/36
by B in 1 hr=w/12
by both in 1 hr=w/12 + w/36=w/9
hence half the work is already done by A in 18 hrs
half the work w/2 is to be done by both hence time talken is w/2/w/9=9/2=4.5 hrs
total time taken is 18+4.5 hrs=22.5 hrs
IMO B
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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08 Aug 2008, 23:07
mba9now wrote:
It would take Computer A 36 hours to process the data. If Computer A starts working at 7 pm on Monday and after half the data is processed Computer B, three times as fast as Computer A, is joined in the task, when will the data processing be finished?
4:30 pm Tuesday
5:30 pm Tuesday
7:00 pm Tuesday
8:30 pm Tuesday
10:30 pm Tuesday
Total hrs = 18 + Hours required to do half job = 18 + (18*6)/24 = 22.5 hrs = 5:30pm Tue
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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09 Nov 2014, 12:29
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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10 Nov 2014, 02:38
Expert's post
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It takes Computer A 36 hours to process data. If Computer A starts working at 7 pm on Monday and after half the data are processed Computer B, three times as fast as Computer A, joins in the task, when will the data processing be finished?
A. 4:30 pm Tuesday
B. 5:30 pm Tuesday
C. 7:00 pm Tuesday
D. 8:30 pm Tuesday
E. 10:30 pm Tuesday
Computer A will process the first half of the data in 18 hours. Computer A and Computer B working together will process the remaining half four times quicker than will Computer A working alone. The entire task will require $$18 + \frac{18}{4} = 22.5$$ hours which is 1.5 hours short of the 24-hour cycle. If the processing commences at 7 pm on Monday, it will finish at 5:30 pm on Tuesday.
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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12 Nov 2014, 02:25
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BOOKMARKED
Rate of Computer A = $$\frac{1}{36}$$
Rate of Computer B = $$\frac{1}{12}$$
$$\frac{1}{2}$$ Job completed by Computer A alone; means time consumed by Computer A $$= \frac{1}{2} * 36 = 18$$ Hrs
Combined rate of A & B $$= (\frac{1}{36} + \frac{1}{12}) = \frac{1}{9}$$
Time required to complete remaining $$\frac{1}{2}$$ Job $$= \frac{1}{2} * \frac{9}{1} = 4.5 Hrs$$
Total Time required to complete job = 18 + 4.5 = 22.5 Hrs
24 Hrs is SAME TIME next day, so 22.5 Hrs would be
7PM Tuesday - 1.5 Hrs = 5:30 PM Tuesday
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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20 Nov 2015, 14:22
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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20 Dec 2015, 11:46
A= 1/36
B= 1/12 ( Ratio is 3:1 )
A+B= 1/9
HALF WORK DONE BY A only
w=r*t
1/2 = 1/36*t
t= 18 hrs
Rest work done by A & B together
w=r*T
1/2 = 1/9*T
T= 4.5 hrs
Total Time= t+T
18+ 4.5 hrs = 22.5 hrs
Count from 7 pm Monday, answer is 5:30 pm Tuesday
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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20 Dec 2015, 22:18
Step wise:
A: 36 hours
B: 12 hours ( 3 times faster)
after half work done: 18 hours
W/2 left: Now W work can be done by both machines in 12*36/48 = 9 hours. So, W/2 cqan be done in 4.5 hours.
Total = 22.5 hours
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Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink]
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20 Dec 2015, 22:20
x2suresh wrote:
mba9now wrote:
It would take Computer A 36 hours to process the data. If Computer A starts working at 7 pm on Monday and after half the data is processed Computer B, three times as fast as Computer A, is joined in the task, when will the data processing be finished?
4:30 pm Tuesday
5:30 pm Tuesday
7:00 pm Tuesday
8:30 pm Tuesday
10:30 pm Tuesday
computer A take 36 hr
computer B takes 12 hr
18 hrs (half job done by computer) + Half job dont by both
= 18 hrs + 18 / (3+1) = 22.5 hrs.
Hey, can you please explain how did you get 18/3+1 ?
Re: It takes Computer A 36 hours to process data. If Computer A starts wor [#permalink] 20 Dec 2015, 22:20
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Display posts from previous: Sort by | 2016-09-28 00:37:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4828264117240906, "perplexity": 9050.014089921191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661289.41/warc/CC-MAIN-20160924173741-00286-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://www.asvabtestbank.com/arithmetic-reasoning/practice-test/627622/5 | ASVAB Arithmetic Reasoning Practice Test 627622
Study Guide
Fractions must share a common denominator in order to be added or subtracted. The common denominator is the least common multiple of all the denominators.
To add or subtract radicals, the degree and radicand must be the same. For example, $$2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}$$ but $$2\sqrt{2} + 2\sqrt{3}$$ cannot be added because they have different radicands.
Least Common Multiple
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
Rates
A rate is a ratio that compares two related quantities. Common rates are speed = $${distance \over time}$$, flow = $${amount \over time}$$, and defect = $${errors \over units}$$.
Ratios
Ratios relate one quantity to another and are presented using a colon or as a fraction. For example, 2:3 or $${2 \over 3}$$ would be the ratio of red to green marbles if a jar contained two red marbles for every three green marbles. | 2020-11-24 12:49:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5608198642730713, "perplexity": 391.84428938360776}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141176256.21/warc/CC-MAIN-20201124111924-20201124141924-00096.warc.gz"} |
https://forum.allaboutcircuits.com/threads/looking-for-dsp-family-for-hobbyist-audio-signal-processing.161953/ | # Looking for DSP family for hobbyist audio signal processing
#### pleriche
Joined Oct 29, 2017
16
There are plenty of microcontroller families with low cost of entry - AVR/Arduino, MSP430, PIC etc - but what is there in the DSP world?
I was recently fitted with behind-the-ear hearing aids to correct for loss of sensitivity in the kHz range, but I can't get the benefit of them when using headphones. I would therefore like to build a headphone amplifier giving the same correction as my hearing aids and it seems to me that DSP might be a good way to go. (This must be what my hearing aids contain.) Specifically, I need a DSP family capable of implementing a stereo digital filter with a customisable response up to 10kHz, and with a free IDE and programmable with a PicKit 2, BusPirate or AVR as ISP. Is there such a thing? Preferably with not too steep a learning curve?
#### shteii01
Joined Feb 19, 2010
4,644
Read application notes. If they have audio dsp note, then put them on the list for consideration.
#### pleriche
Joined Oct 29, 2017
16
Read application notes. If they have audio dsp note, then put them on the list for consideration.
Once I know which manufacturers make DSPs with accessible cost of entry, of course, I can look at the application notes, but I think you're putting the cart before the horse!
#### BobTPH
Joined Jun 5, 2013
2,396
The dsPIC family of PICs are the same cpu as the 16 bit 24F series plus DSP features. I think they would be capable of audio filtering. They also have 12 bit DACs, which, with oversampling, could handle the audio in, and PWM capable of putting oit decent audio.
Check them pit at the Microchip site.
Bob
#### shteii01
Joined Feb 19, 2010
4,644
Once I know which manufacturers make DSPs with accessible cost of entry, of course, I can look at the application notes, but I think you're putting the cart before the horse!
You said avr/Arduino. Microchip bought atmel. If you look for atmel avr chips, you go to microchip website and start reading.
Msp430 is ti. You go to ti website and start reading.
Pic is microchip...
Microchip has parametric search or some such.
Ti has some kind of guided search to help visitors to find products that fit their needs.
#### KeithWalker
Joined Jul 10, 2017
911
There are plenty of microcontroller families with low cost of entry - AVR/Arduino, MSP430, PIC etc - but what is there in the DSP world?
I was recently fitted with behind-the-ear hearing aids to correct for loss of sensitivity in the kHz range, but I can't get the benefit of them when using headphones. I would therefore like to build a headphone amplifier giving the same correction as my hearing aids and it seems to me that DSP might be a good way to go. (This must be what my hearing aids contain.) Specifically, I need a DSP family capable of implementing a stereo digital filter with a customisable response up to 10kHz, and with a free IDE and programmable with a PicKit 2, BusPirate or AVR as ISP. Is there such a thing? Preferably with not too steep a learning curve?
I have the exact same problem and I love music. I solved it a different way which was fairly simple and inexpensive. I still use my old analog audio amplifier with real speakers for listening to the radio, TV, CDs and Vinyl. I use headphones for good music.
I purchased a ten channel stereo equalizer circuit board from AliExpress and mounted it in a small cabinet along with a power switch, fuse and a couple of 120VAC to 5VDC power modules. There are RCA audio connectors and a stereo headphone jack on the back. The whole project cost less than $30,00 Canadian and went together really easily. The equalizer has enough range to compensate for my hearing loss and has brought back to me the ability to enjoy music as it is supposed to sound. It also works very well to compensate the compressed sound tracks on Netflix movies. #### Attachments • 120.5 KB Views: 8 Last edited: Thread Starter #### pleriche Joined Oct 29, 2017 16 I have the exact same problem and I love music. I solved it a different way which was fairly simple and inexpensive. I still use my old analog audio amplifier with real speakers for listening to the radio, TV, CDs and Vinyl. I use headphones for good music. I purchased a ten channel stereo equalizer circuit board from AliExpress and mounted it in a small cabinet along with a power switch, fuse and a couple of 120VAC to 5VDC power modules. There are RCA audio connectors and a stereo headphone jack on the back. The whole project cost less than$30,00 Canadian and went together really easily.
The equalizer has enough range to compensate for my hearing loss and has brought back to me the ability to enjoy music as it is supposed to sound. It also works very well to compensate the compressed sound tracks on Netflix movies.
Hi Keith - That's really interesting, and cheap enough that I might get one just for the fun of trying it. Do you know how much current it takes? But what I'd really like is something I could make portable and hence battery powered.
#### KeithWalker
Joined Jul 10, 2017
911
Hi Keith - That's really interesting, and cheap enough that I might get one just for the fun of trying it. Do you know how much current it takes? But what I'd really like is something I could make portable and hence battery powered.
Hi, I didn't measure the current but I am sure it is not very much. It would be possible to power it with a single Li-po cell with a dual switching supply. It needs minimum of +5V_0_-5V supply.
#### jjw
Joined Dec 24, 2013
540
Once I know which manufacturers make DSPs with accessible cost of entry, of course, I can look at the application notes, but I think you're putting the cart before the horse!
ARM Cortex M4 general purpose MCU has also DSP instructions.
There are development boards from several manufacturers. Look at https://eu.mouser.com/Embedded-Solutions/Engineering-Tools/Embedded-Processor-Development-Kits/Development-Boards-Kits-ARM/_/N-cxd2t?keyword=Cortex-M&No=125
and Teensy: https://www.pjrc.com/store/teensy36_pins.html
Last edited:
#### pleriche
Joined Oct 29, 2017
16
Thank you jjy - in fact I have a Teensy 3.2 which I used a while back for synthesising sounds such wind chimes and peals of bells in arbitrary tonalities, but since it ran out of steam with more than 2 or 3 simultaneous mono sounds at 8,000 samples/sec I'd discounted it. I also have the sound adapter, which didn't seem to be useful for that project as I was only doing 8 bit audio. But maybe I should look at it again, at least to familiarise myself with how you build a digital filter. I'll then be in a much better position to decide how much more power I might actually need.
#### jjw
Joined Dec 24, 2013
540
Thank you jjy - in fact I have a Teensy 3.2 which I used a while back for synthesising sounds such wind chimes and peals of bells in arbitrary tonalities, but since it ran out of steam with more than 2 or 3 simultaneous mono sounds at 8,000 samples/sec I'd discounted it. I also have the sound adapter, which didn't seem to be useful for that project as I was only doing 8 bit audio. But maybe I should look at it again, at least to familiarise myself with how you build a digital filter. I'll then be in a much better position to decide how much more power I might actually need.
Teensy audio adapter has a 5 band equalizer, need only setup with a mcu.
From the forum:
"You might also want to try the built-in-EQ of the codec hardware in the Teensy audio board:
https://www.pjrc.com/teensy/gui/?inf...ontrolSGTL5000
This gives you a five-band-EQ without additional load on the Teensy processor itself.
And its quite easy to use, see the GUI under the link above.
It performs quite well, although it seems not many people use it. My experience is good with that EQ.
Have fun with the Teensy,
Frank
P.S.: or you try the 7-band parametric equalizer which is basically the same as a cascade of 7 biquad IIRs, but there you would have to provide the filter coefficients by yourself. Probably best to use some program to calculate them, eg. Iowa Hills IIR Filter designer, very good"
#### pleriche
Joined Oct 29, 2017
16
Have fun with the Teensy,
Frank
Some great leads there to follow up in the coming weeks - thanks Frank!
#### pleriche
Joined Oct 29, 2017
16
Hi, I didn't measure the current but I am sure it is not very much. It would be possible to power it with a single Li-po cell with a dual switching supply. It needs minimum of +5V_0_-5V supply.
My 10 band equaliser has just arrived (less than a week from China, and with the AliExpress introductory bonus, laughably cheap!)
For the sake of anyone following this thread in years to come, in an initial lash-up it seems to do the job pretty well though I need to feed the output into a headphone amp (which I don't instantly have to hand) to test it properly. To answer my own question, running it off 2 9VNiMH batteries (discarded microphone batteries) it takes 23mA (from each), so that would be a viable power source for portable use, if a bit bulky for carrying in a pocket. An alternative power source would be a LiPo with 5V boost converter and MAX660 voltage inverter for the negative rail.
#### pleriche
Joined Oct 29, 2017
16
To follow-up and for KeithWalker I've now successfully built my own version on a 6x6cm PCB using 2 TL084 quad opamps and a LM4880 headphone amp. It has 3 equalisation centre frequencies and runs off a single 5V supply.
If anyone is interested in building their own or modifying the design for their own purposes, follow me at https://www.instructables.com/member/p_leriche/ where I will be publishing full details in due course (don't hold your breath though), including Eagle files and an Excel spreadsheet for selecting component values for specific band frequencies.
#### Attachments
• 1.8 MB Views: 5
Joined Mar 10, 2018
4,057
PSOC 5LP family. DSP component, component being an onchip resource. See
attached catalog of onchip resources. Filter can do IIR, FIR, BiQuad. Example -
IDE and Compiler free, board is $10 for average design. Notice very few of the available onchip resources used (right hand window). Configuration for the filter - Regards, Dana. #### Attachments • 178.5 KB Views: 1 #### JohnInTX Joined Jun 26, 2012 4,087 To follow-up and for KeithWalker I've now successfully built my own version on a 6x6cm PCB using 2 TL084 quad opamps and a LM4880 headphone amp. It has 3 equalisation centre frequencies and runs off a single 5V supply. If anyone is interested in building their own or modifying the design for their own purposes, follow me at https://www.instructables.com/member/p_leriche/ where I will be publishing full details in due course (don't hold your breath though), including Eagle files and an Excel spreadsheet for selecting component values for specific band frequencies. Nicely done! When you get the package together consider publishing it here in the Completed Projects section, too. We love that. Plus, I have old ears too Thread Starter #### pleriche Joined Oct 29, 2017 16 PSOC 5LP family. DSP component, component being an onchip resource. See attached catalog of onchip resources. Filter can do IIR, FIR, BiQuad. Example - View attachment 191277 IDE and Compiler free, board is$ 10 for average design.
Notice very few of the available onchip resources used (right hand window).
Configuration for the filter -
View attachment 191278
Regards, Dana.
Thanks Dana, that looks very interesting. Bookmarked for checking out later. | 2020-07-15 00:00:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24787266552448273, "perplexity": 2586.1514102960673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657151761.87/warc/CC-MAIN-20200714212401-20200715002401-00566.warc.gz"} |
https://zbmath.org/?q=an:0805.13007 | # zbMATH — the first resource for mathematics
Efficient computation of zero-dimensional Gröbner bases by change of ordering. (English) Zbl 0805.13007
Gröbner bases are a useful tool for explicit computations in polynomial rings. Given a field $$K$$, the polynomial ring $$K[X] = K[X_ 1, \dots, X_ n]$$, an ideal $$I \subset K[X]$$, and a total order (called a term order) on the semigroup of monomials such that 1 is the smallest element the Buchberger algorithm constructs a Gröbner basis of $$I$$. In general different term orders yield different Gröbner bases. Once a Gröbner basis is known many computational problems (such as the ideal membership problem) can be solved. It is known that the choice of the term order greatly influences the performance of the Buchberger algorithm. The idea pursued in the present paper is first to determine a Gröbner basis with respect to a term order with low complexity and afterwards to translate this Gröbner basis into a Gröbner basis with respect to another term order. For zero-dimensional ideals an algorithm to this effect is presented. Complexity and examples are discussed.
##### MSC:
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 68W30 Symbolic computation and algebraic computation
##### Keywords:
term order; Buchberger algorithm; Gröbner basis
Full Text: | 2021-09-18 22:11:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6186697483062744, "perplexity": 562.2491964612699}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056578.5/warc/CC-MAIN-20210918214805-20210919004805-00095.warc.gz"} |
https://msubbu.in/sp/fm/VenturiCoefficient.htm | ### Coefficient of Discharge of Venturi Meter
The rate of flow of water in a 150 mm diameter pipe is measured with a venturi meter of 50 mm diameter throat. When the pressure drop over the converging section is 100 mm of water, the flow rate is 2.7 kg/sec. What is the coefficient of the meter?
Data:
Dia of pipe (Da) = 150 mm = 0.15 m
Dia of throat (Db) = 50 mm = 0.05 m
Pressure drop (Pa - Pb) = 100 mm of water = (0.1/10.33) x 101325 N/m2 = 980.9 N/m2
Mass flow rate = 2.7 kg/sec
Formulae:
Velocity at the throat
$$\displaystyle v_b = \frac{C_v}{\sqrt{1-\beta^4}}\sqrt{\frac{2(P_a-P_b)}{\rho}}$$
Where β = Db/Da
Calculations:
Volumetric flow rate = mass flow rate / density = 2.7 / 1000 = 0.0027 m3/sec
Velocity at the throat = Volumetric flow rate / cross sectional area of throat
= 0.0027 / (πDb2/4) = 0.0027 / (π x 0.052/4) = 1.375 m/sec
Therefore,
Cv = 1.375 x ( 1 - (0.05/0.15)4 )0.5 / (2 x 980.9/1000)0.5 = 0.976 | 2022-05-23 17:42:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5067050457000732, "perplexity": 2410.22088509008}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662560022.71/warc/CC-MAIN-20220523163515-20220523193515-00537.warc.gz"} |
https://www.darwinproject.ac.uk/letter/?docId=letters/DCP-LETT-10337.xml;query=;brand=default | To Sigmund Fuchs [1877–8?]1
My F. who is much engaged desires me to say that your q. is most difficult & he will not venture to express an opinion as hardly 2 Zoologists are agreed on the subject—2
Footnotes
The date is conjectured from the relationship between this letter and the letter from Sigmund Fuchs, [1877–8?].
CD probably wrote this draft in the expectation that Francis Darwin would write the reply to Fuchs’s letter of [1877–8?]; the draft is written on the back of that letter. F: father. CD alludes to the debate among zoologists regarding vertebrates and their ancestors. While many, including CD (see Descent 1: 205–6), had supported the view that vertebrates were descended from ascidians (Tunicata), others had argued that they descended from segmented worms (Annelida; see, for example, Correspondence vol. 23, letter from Anton Dohrn, 7 February 1875). Fuchs had asked whether CD agreed with Carl Friedrich Claus’s removal of tunicates from the phylum Mollusca into their own group in the most recent edition of Claus’s textbook, Grundzüge der Zoologie (Claus 1876). Although his reasons for the change were not explicit, Claus had included references to similarities between tunicates and vertebrates in both embryonic and larval stages (see letter from Sigmund Fuchs, [1877–8?] and n. 4).
Bibliography
Correspondence: The correspondence of Charles Darwin. Edited by Frederick Burkhardt et al. 27 vols to date. Cambridge: Cambridge University Press. 1985–.
Descent: The descent of man, and selection in relation to sex. By Charles Darwin. 2 vols. London: John Murray. 1871.
Summary
[Draft of letter for Francis Darwin to write to SF.] CD declines to express an opinion on SF’s query.
Letter details
Letter no.
DCP-LETT-10337
From
Charles Robert Darwin
To
Sigmund Fuchs
Sent from
unstated
Source of text
DAR 164: 221v
Physical description | 2021-02-25 10:59:26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8574533462524414, "perplexity": 10950.702472156489}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178350942.3/warc/CC-MAIN-20210225095141-20210225125141-00421.warc.gz"} |
http://www.electrosmash.com/jrc4558-analysis | # JRC4558 Analysis
The JRC4558 integrated circuit by Japan Radio Company is a dual high gain operational amplifier internally compensated and constructed on a single silicon chip. The high voltage gain (100 dB typ.), good input impedance (5 MΩ typ.) and versatile power supply (± 4 to 18 Volts) make it perfect to fit in pedal circuit designs. This part has industry standard pinout, meaning that there are several different suppliers manufacturing 4558 devices. The first dual opamp was developed by Raytheon Semiconductors in 1974.
The 4558 dual amp is linked with the history of the guitar pedals development. Many designers included this part in some of the most successful effects like the Orange Squeezer, DOD YJM 30, Boss OD1, Tube Screamer or Peavey equipment. This IC was undoubtedly chosen in the beginning by Japanese design engineers because it was one of the cheapest dual opamps on the market with acceptable audio performance. As such, it was used in huge volumes of Japanese audio equipment. Despite its questionable audio performance, it seems to be well suited to duty in overdrive circuits.
# 1. JRC4558 Internal Circuit.
The JRC4558 schematic is based in the Lin Topology following the classic 741 type opamp structure with some modifications. Find below the simplified circuit provided by JRC broken down into some simpler blocks: Current Supply, Input Stage, Voltage Amplifier Stage (VAS), Output Stage (OPS) and Feedback Path.
## 1.1 JRC4558 Current Supply.
The Active Current Supply it is an utility stage which provides a constant flow of current to the different blocks. An stable current source is important in modern circuit design to improve linearity and noise rejection. This stage highlighted in green color is formed by Q1, Q7, Q13, Q14, Q15, R1, R9 and D2:
The JFET Q15 is a self biased current, it will provide a constant current source independent from the voltage supply. The start-up of this part of the circuit is simple:
• When the +Vcc voltage source is turned on, no current is yet flowing through the JFET Q15. Then the voltage drop across the zener diode D2 and VGS will be zero. With zero VGS the transistor enters in saturation region allowing large current to flow through the JFET, so the current will increase. As the current increases, a voltage drop will develop across the zener, until the diode will be reversed biased. The gate will become negatively biased with regards to the source, negative values of VGS will start to shut Q15 off. Eventually, a stable equilibrium will be attained through feedback, where VGS is just right for the current flowing through the JFET.
So, once the drain-source voltage reaches a certain minimum value, enters saturation where IDS current is approximately constant. So, the JFET current source sets the constant current I15 through Zener diode D2 making I15 = Iz
The Zener diode D2, when reverse biased has a constant voltage drop (Vz). As long as the Zener current (Iz) is between certain levels (Izmin and Izmax) called holding current, the voltage across the Zener diode (VZ) will be constant working in the Voltage Regulation Area.
The Zener diode stabilized voltage VZ drives an emitter follower Q14 loaded by a constant emitter resistor R9 sensing the load current. As a result, the output current I9 is almost constant even if the load resistance and/or voltage vary and the circuit operates as a constant current source:
$I_{9}=\frac{V_{z}-V_{be}}{R_{9}}$
The external current mirror load of this current source is connected to the collector so that almost the same current flows through it and the emitter resistor.
- Q13, Q7 are configured as a classic current mirror, meaning that the current through Q13 (I13) will be mirrored in Q7, making I13 = I7
- Q1 is a plain current PNP constant current source.
## 1.2 JRC4558 Input Stage:
The input stage is formed by a Long Tailed Pair (LTP) differential amplifier with a current mirror. This stage highlighted in red color is formed by Q1, Q2, Q3, Q4, Q5, R1, R2, R3, and C1:1.2.1 JRC4558 Long Tailed Pair Differential Amplifier.
The Long Tail Pair phase inverter or Schmit is formed by a pair of identical and matched PNP transistors in common emitter configuration (Q2 and Q3). The current mirror Q4 and Q5 in the collector of Q2 and Q3 is the active load of the LTP. This topology is generally the best choice for an operational amplifier, it provides high input impedance, good voltage gain, common noise rejection as well as extra inputs for a summing feedback.
The circuit nature is to amplify the difference of its input signals Vin+ and Vin-, providing cancellation to all even distortion, making the amp immune to fluctuations of supply voltage. To acquire real benefits from using a LTP input, the currents flowing through the differential transistors must be equalized. A very effective way to do it is using a current mirror.
### 1.2.2 JRC4558 Current Mirror.
It consists of a high Hfe (β) differential dual transistor Q4 and Q5, with matched transistor parameters. The thermal coupling between both transistors is ideal since they share the same package. There most important reasons to use a current mirror are to enhance the gain and the signal integrity:
1. Signal integrity is improved because the current mirror gives equal quiescent current for each side of the LTP. This balance is good for the linearity and Common Mode Ratio (CMRR) figure.
2. The JRC4885 differential amplifier has a single ended output, where the gain is the half if we compare it with a differential output circuit. the current mirror will improve this intrinsic 50% losses.
## 1.3 JRC4558 Voltage Amplifier Stage.
The high gain voltage amplifier stage is the core of the power amplifier. Its task is to amplify the low amplitude input signal to a suitable level. This VAS circuit works in class-A mode since they basically require only a small amount of current, and therefore power losses over the active device can be retained reasonably small.
This stage highlighted in orange colour is formed by Q6, Q10 and R4:
The VAS consists of a common emitter amplifier with two NPN transistors Q6 and Q10 connected in a Darlington configuration, making the current gain higher and using the output side of the current mirror Q7 as its collector load to achieve high gain.
βDARLINGTON = βQ1 * βQ2 + βQ1 + βQ2
The drawback of the Darlington topology is an approximate doubling of base-emitter voltage. Since there are two junctions between the base and emitter of the Darlington transistor, the equivalent base-emitter voltage is the sum of both base-emitter voltages.
VbeDARINGTON = VbeQ6 + VbeQ10 = 2Vbe
## 1.4 JRC4558 Output Stage.
The Output Stage (OPS) is a Class AB push-pull emitter follower amplifier with the bias current set by the Vbe Multiplier. This block is highlighted in blue colour and is formed by Q11, Q12, R6, R7 and R8:
The function of the Output Stage is to provide enough current gain so that voltage potential provided by VAS can exist over the low load output impedance.
This stage is efficiently driven by the VAS. Variations in the bias with temperature, or between parts with the same type number are common, so crossover distortion and quiescent current may be subject to significant variation. The output range of the JRC4558 is about 1.5 volt less than the supply voltage, owing in part to Vbe of the output transistors Q11 and Q12.
The output resistors R6, R7 and R8 inserted between output pair emitters also known as ballast resistors, are used to even out differences between internal emitter resistances of transistors, thus their current sharing is improved. There resistor values are usually pretty low, improving thermal stability, preventing the complementary transistors from directly loading each other and making quiescent current stable.
## 1.5 JRC4558 Vbe Multiplier Bias Circuit.
A Vbe Multiplier bias circuit also known as Bias Servo, Amplified Diode, Rubber Diode or Rubber Zener is placed in order to compensate the crossover distortion and protect the Output Stage from thermal shutdown. This block is highlighted in pink colour and formed by Q8, Q9 and R4:
In the output push pull topology, the transistors Q11 and Q12 do not start conducting until the input signal exceeds their forward voltage, which is the Vbe, typically around ±0.6 V. Counteract is to bias the transistors so that their idling voltage never drops below the forward voltage.
A specific amount of current, known as bias current, is constantly fed to the transistors’ bases in order to ensure that the transistors keep conducting for a desired amount of time, sacrificing the efficiency.
Without a controlled bias voltage the quiescent collector currents of the output power amplifiers may be excessive, causing thermal failure.
The classic Vbe Multiplier topology consist on one transistor and two resistors. The JRC4558 uses a two transistor approach, a variation from the classic one:
The Vbe Multiplier acts as a variable resistor which is mounted to the same silicon device as the output transistors, so they are thermal coupled. Temperature changes of the device affect the gain of the servo transistor; this consequently changes the voltage drop over the Vbe Multiplier circuit.
To improve the temperature coefficient between the Vbe multiplier matching and the output stage. The circuit Vbe Multiplier is equipped with an additional transistor Q8.
## 1.6 JRC4558 Feedback Path.
The task of the Feedback Path is to send in some way part of the output signal to the VAS. It has an important part in error correcting as well as in bandwidth and gain limiting.
The capacitor C2 provides frequency selective negative feedback. This technique is called Miller Compensation or Dominant Pole Compensation because it introduces a dominant pole which masks the effects of other poles into the open loop frequency response.
The feedback goes from the VAS transistor’s collector to its base, limiting the bandwidth and decreasing gain at higher frequencies and therefore improving stability at higher frequencies preventing oscillation.
# 2. The JRC4558 Myth.
Some players believe that the JRC4558D original chip from the 80s has a superior sounding, specially when it is placed in certain pedals like the Tube Screamer. In this calse, the op-amp is claimed to be the holy grail if you want to get the original vintage sound.
Japan Radio Corporation JRC (established in Sept. 1959) issued millions of these JRC4558D shiny-finished chips from late 70s until mid 80s. They appear in every piece of Nippon electronics from this period.
The company later in changed its name to New Japan Co. Ltd, and moved their production facilities to East Asia. They continued to produce 4558 op-amps -labeled as NJM4558D- but the factory new production equipment. A few years later, NJM started re-issuing the JRC4558D (matte-finished), but again not produced at the old plant. The specs are the same as the old one, but the suspicion still lingers - since they changed facilities, are the reissue chips really as good as the old ones?.. the myth stats here.
• In the beginning the JRC4558D was used for one single reason: it was cheap. So it was placed in tons of Japanese electronic equipment, a junky cheap old stereo or a clock radio could have several hidden inside it.
• You can also pay 30$in ebay for NOS (New Old Stock) chips, which in theory are original parts manufactured in the 80s that have never been sold at retail. • There is also the story NJM keeping all the original machinery used in the JRC4558 old manufacturing and able to produce again the chip if someone order more than 50 millions of parts. In a nutshell, some people claim that they can really appreciate the difference between two 4558 chips from different manufacturers or even between two identical JRC4558 from the same manufacturer. However, in a guitar pedal there are a lot of factors that can modify the sound even more than the opamp can do: the components placement, values tolerance, circuit layout, the power supply, etc ... by actual listening test as well as oscilloscope traces and spectrum analysis, there is no audible difference between today's 0.5$ NJM4558D and the old ones.
There is also plenty of alternatives to the JRC4558 chip, different users may have different opinion about their performance, but anyway all compatible:
- NJM4558 by New Japan Radio Company.
- RC4558 by Fairchild Semiconductor and Texas Instruments.
- RC4559 by Texas Instruments.
- NJM4556 by Japan Radio Company. Sound signature of the original with extra dynamics and attack
- TLC272 by Texas Instruments.It has a nice, complex distorted sound.
- TL072 by Texas Instruments, ST Microelectronics and SGS Thomson Microelectronics.
- TL062 by Texas Instruments, ST Microelectronics, SGS Thomson Microelectronics and Motorola.
- TL082 by National Semiconductor, Texas Instruments, ST Microelectronics and Motorola.
- LM1458 by National Semiconductor and Fairchild Semiconductor.
- LM833 by National Semiconductor,ST Microelectronics, SGS Thomson Microelectronics, Motorola and ON Semiconductor.
- OPA2107 by Analog Devices. Rounder sound, makes it ideal for blues players
- OP275 by Analog Devices.
- OPA2604 by Burr-Brown and Texas Instruments.
- TLC2272, TLC2202 by Texas Instruments.
- LT1213 by Linear Technology.
- MC33078 by Texas Instruments. With very nice highs.
# 3. Resources
JRC4558 Datasheet.
Teemuk Kyttala Solid State Guitar Amplifiers, the Holy Scripture.
JFET Current Sources, by the University of California at Berkeley.
Current Sources in Wikipedia.
Vbe Multipliers by Jim Hagerman.
TL071 Blocks Diagram by Georgia Tech School of Engineering.
The Technology of Tube Screamer by R.G. Keen.
IC Opamps Evolution Through the Ages by Thomas H.Lee.
My sincere appreciation to „Nandor” for your assistance.
Thanks for reading, all feedback is appreciated
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https://www.thejournal.club/c/paper/55672/ | #### Asymptotically-Optimal Incentive-Based En-Route Caching Scheme
##### Ammar Gharaibeh, Abdallah Khreishah, Issa Khalil, Jie Wu
Content caching at intermediate nodes is a very effective way to optimize the operations of Computer networks, so that future requests can be served without going back to the origin of the content. Several caching techniques have been proposed since the emergence of the concept, including techniques that require major changes to the Internet architecture such as Content Centric Networking. Few of these techniques consider providing caching incentives for the nodes or quality of service guarantees for content owners. In this work, we present a low complexity, distributed, and online algorithm for making caching decisions based on content popularity, while taking into account the aforementioned issues. Our algorithm performs en-route caching. Therefore, it can be integrated with the current TCP/IP model. In order to measure the performance of any online caching algorithm, we define the competitive ratio as the ratio of the performance of the online algorithm in terms of traffic savings to the performance of the optimal offline algorithm that has a complete knowledge of the future. We show that under our settings, no online algorithm can achieve a better competitive ratio than $\Omega(\log n)$, where $n$ is the number of nodes in the network. Furthermore, we show that under realistic scenarios, our algorithm has an asymptotically optimal competitive ratio in terms of the number of nodes in the network. We also study an extension to the basic algorithm and show its effectiveness through extensive simulations.
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http://bulletin.imstat.org/2014/05/student-puzzle-corner-4-deadline-june-15/ | May 15, 2014
Student Puzzle Corner 4 (deadline June 15)
The Student Puzzle Corner contains one or two problems in statistics or probability. Sometimes, solving the problems may require a literature search. Current student members of the IMS are invited to submit solutions electronically (to bulletin@imstat.org with subject “Student Puzzle Corner”). Deadline June 15, 2014. The names and affiliations of (up to)the first 10 student members to submit correct solutions, and the answer(s) to the problem(s), will be published in the next issue of the Bulletin. The Editor’s decision is final.
Solution to Student Puzzle 3
Anirban DasGupta, IMS Bulletin Editor, explains:
In the puzzle of the last issue, we asked what is the average Euclidean distance between two random points on the surface of the Earth. We can easily calculate the Euclidean as well as the geodesic distance between two fixed points. For example, the geodesic distance between New York and Beijing is about 7175 miles, and the Euclidean distance is about 6235 miles, a saving of about $13\%$. A nearly hilarious question is how much time you’d have saved flying from New York to Beijing if we knew how to fly through the Earth’s interior. The cruising speed of a Boeing 777 is about 580 mph. So, a back-of-the-envelope calculation gives that a nonstop flight along the geodesic would take about 12 hours and 20 minutes, while going through the Earth’s interior at the same speed would take 10 hours and 45 minutes; so you save just about an hour and a half. For traveling from London to Sydney, you’d save 4 hours and 55 minutes; Singapore to Bangkok, you save almost nothing. But what about two random points? We will answer this question below, and you might be surprised that the average savings is just about $11.5\%$.
We may as well solve the problem for the case of $n$ dimensions for a general $n \geq 2$. Thus, let $\bf{X}, \bf{Y}$ be two random independent picks from the surface of an $n$-dimensional ball with radius $\rho$ and suppose we want to find $E(||\bf{X}-\bf{Y}||)$, where $||\cdot ||$ denotes Euclidean norm. Notice that the center of the ball has no effect on the problem and the radius has only a scaling effect; so we may as well take the center to be the origin and the radius to be one. The expected value of the square of the Euclidean distance is a much easier problem, and indeed, you can show that in any number of dimensions, for the unit ball, $E(||\bf{X}-\bf{Y}||^2) = 2$; Cauchy-Schwarz gives us a quick bound: we must have $E(||\bf{X}-\bf{Y}||) \leq \sqrt{2}$. We will see how the $\sqrt{2}$ bound gets almost attained when the number of dimensions $n$ gets large.
Now, $||\bf{X}-\bf{Y}||^2 = ||\bf{X}||^2 + ||\bf{Y}||^2 -2\bf{X}’\bf{Y} = 1 + 1 – 2\bf{X}’\bf{Y} = 2\bigg [1 – \bf{X}’\bf{Y}\bigg ]$. Here, as usual, $\bf{X}’\bf{Y}$ denotes the Euclidean inner product. Therefore, $E(||\bf{X}-\bf{Y}||) = \sqrt{2}E\bigg [\sqrt{1 – \bf{X}’\bf{Y}}\bigg ]$. Now, condition with respect to $\bf{Y}$.
The conditional expectation $E\bigg [\sqrt{1 – \bf{X}’\bf{Y}}\,\vert \bf{Y} = \bf{y}\bigg ]$ is independent of the unit vector $\bf{y}$ and hence, the unconditional expectation $E\bigg [\sqrt{1 – \bf{X}’\bf{Y}}\bigg ] = E\bigg [\sqrt{1 – \bf{X}’\bf{e_1}}\bigg ] = E\bigg [\sqrt{1 – X_1}\bigg ]$, where $\bf{e_1}$ is the first standard unit vector. Use now the fact that if $\bf{X}$ is a random pick from the surface of an $n$-dimensional ball of radius $1$, then its first coordinate $X_1$ has the density $c(1-x_1^2)^{(n-3)/2}, – 1 \leq x_1 \leq 1$, where the normalizing constant $c = c_n = \frac{\Gamma (\frac{n}{2})} {\sqrt{\pi }\Gamma (\frac{n-1}{2})}$.
Thus, $E\bigg [\sqrt{1 – \bf{X}’\bf{Y}}\bigg ] = c\,\int_{-1}^1 \sqrt{1-x}(1-x^2)^{(n-3)/2}dx = c\,\int_{-1}^1 (1-x)^{\frac{n}{2}-1}(1+x)^{\frac{n-1}{2}-1}dx$.
This becomes a Beta integral by changing variables; just substitute $z = \frac{1+x}{2}$.
On a little algebra, we eventually get
$E(||\bf{X} – \bf{Y}||) = \sqrt{2}\,c\,2^{n-\frac{3}{2}}\,B(\frac{n-1}{2},\frac{n}{2}) = \frac{2^{n-1}[\Gamma (\frac{n}{2})]^2}{\sqrt{\pi}\,\Gamma (n – \frac{1}{2})}.$ This is the answer when the basic ball has radius $1$; if it has radius $\rho$, then multiply this by $\rho$.
For the specific case of the Earth, modeled as a perfect sphere, we get from this $E(||\bf{X} – \bf{Y}||) = 5280$ (miles).
What happens asymptotically, i.e., in very high dimensions? That is easy enough to figure out as well; we need nothing more than simple tools. Simply use the standard facts that $\Gamma (x) =e^{-x}\,x^{x-1/2}\,\sqrt{2\pi }\bigg [1 + \frac{1}{12x} + \frac{1}{288x^2} + \cdots \bigg ]$ as $x \to \infty$ and that for $|x| < 1$, $\log (1-x) = -x - x^2/2 -x^3/3 - \cdots$. Then, our formula $E\bigg [||\bf{X} - \bf{Y}||\bigg ] = \frac{2^{n-1}[\Gamma (\frac{n}{2})]^2}{\sqrt{\pi}\,\Gamma (n - \frac{1}{2})}$ for the case of the unit ball results in $E\bigg [||\bf{X} - \bf{Y}||\bigg ] = \sqrt{2}\,\bigg [1 - \frac{7}{24n} - \frac{95}{1152n^2} + O(n^{-3}) \bigg ]$. This means, that in high dimensions, the Euclidean distance between two random points on the surface would be close to as large as it can possibly be, namely $\sqrt{2}$. An interesting question is exactly how much smaller is the Euclidean distance between two points than the geodesic distance between them. This will of course depend on the specific two points. What happens if the two points are chosen at random? Let's use some notation to get things very clear. Let $\bf{X}, \bf{Y}$ be two independent random picks from the surface of the $n$-dimensional unit ball, and let $D = D_n$ and $G = G_n$ be the Euclidean and the geodesic distance between them. Then, using spherical trigonometry, a now forgotten subject, you can show that $E\bigg (\frac{D}{G}\bigg )$ has an integral representation. Let us see what it is; it is given by $a_n\,\int_{0}^\pi \frac{2\sin (\frac{\theta }{2})}{\theta } (\sin \theta )^{n-2}d\theta$, where $a_n = \frac{2^{n-2}[\Gamma (\frac{n}{2})]^2}{\pi (n-2)!}$. You can evaluate it numerically, or in closed form by using certain special functions, or you can derive an asymptotic expansion for it. The asymptotic expansion takes a lot more work now, but one is $E\bigg (\frac{D}{G}\bigg ) = \frac{2\sqrt{2}}{\pi } + \frac{\pi ^2-8\pi + 32}{2\sqrt{2}\pi ^3n} + O(n^{-2})$. Now, $\frac{2\sqrt{2}}{\pi }$ is about $.900316$. So, in very high dimensions, the Euclidean distance is just about $10\%$ smaller than the geodesic distance on the average. How about for the Earth, i.e., $n = 3$? Then, $E\bigg (\frac{D}{G}\bigg ) = .88451$. Not much savings!
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Welcome to the IMS Bulletin website! We are developing the way we communicate news and information more effectively with members. The print Bulletin is still with us (free with IMS membership), and still available as a PDF to download, but in addition, we are placing some of the news, columns and articles on this blog site, which will allow you the opportunity to interact more. We are always keen to hear from IMS members, and encourage you to write articles and reports that other IMS members would find interesting. Contact the IMS Bulletin at bulletin@imstat.org
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In the Open Forum, any IMS member can propose a topic for discussion. Email your subject and an opening paragraph (to bulletin@imstat.org) and we'll post it to start off the discussion. Other readers can join in the debate by commenting on the post. Search other Open Forum posts by using the Open Forum category link below. Start a discussion today! | 2017-12-15 12:13:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7491527199745178, "perplexity": 280.1169796615299}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948569405.78/warc/CC-MAIN-20171215114446-20171215140446-00346.warc.gz"} |
https://mail.openjdk.java.net/pipermail/hotspot-runtime-dev/2012-July/004137.html | # RFR: 7181175 Enable hotspot builds on Windows with MinGW/MSYS
Tim Bell tim.bell at oracle.com
Wed Jul 18 12:00:07 PDT 2012
I wrote:
> Testing a hunch: I renamed my source tree to shorten the length of the
> file paths.
>
> I have restarted my build in verbose mode, so I should know more soon.
The problem was self-inflicted. It was not the path length this time.
It also was not related to the"\$(COMPILE_RMIC)" in sa.make. Removing
the "" works fine in sa.make.
It was a change I made on top of Volker's suggested fix in
hotspot/make/windows/makefiles/rules.make
Instead of going with the suggested fix [1]:
RUN_JAVA="\$(BootStrapDir)\bin\java"
RUN_JAVAP="\$(BootStrapDir)\bin\javap"
RUN_JAVAH="\$(BootStrapDir)\bin\javah"
RUN_JAR="\$(BootStrapDir)\bin\jar"
COMPILE_JAVAC="\$(BootStrapDir)\bin\javac" \$(BOOTSTRAP_JAVAC_FLAGS)
COMPILE_RMIC="\$(BootStrapDir)\bin\rmic"
RUN_JAVA=\$(BootStrapDir)/bin/java
RUN_JAVAP=\$(BootStrapDir)/bin/javap
RUN_JAVAH=\$(BootStrapDir)/bin/javah
RUN_JAR=\$(BootStrapDir)/bin/jar
COMPILE_JAVAC=\$(BootStrapDir)/bin/javac \$(BOOTSTRAP_JAVAC_FLAGS)
COMPILE_RMIC=\$(BootStrapDir)/bin/rmic
This is an example where we actually have to preserve the \ in the paths
to the tools because the RUN_foo commands are fired by nmake and not sh.
My test build is running now. I'll update the webrev and send out a new
URL.
Tim
[1]
http://mail.openjdk.java.net/pipermail/build-dev/2012-March/005729.html
http://cr.openjdk.java.net/~simonis/MinGW_MSYS_hotspot.v1/ | 2022-05-16 06:02:03 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8596686124801636, "perplexity": 6344.456868641464}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662509990.19/warc/CC-MAIN-20220516041337-20220516071337-00734.warc.gz"} |
https://leanprover-community.github.io/archive/stream/116395-maths/topic/Unifying.20.60tangent_cone_at.60.20and.20.60pos_tangent_cone_at.60.html | ## Stream: maths
### Topic: Unifying tangent_cone_at and pos_tangent_cone_at
#### Yury G. Kudryashov (Feb 05 2020 at 04:50):
I'd like to prove more properties of tangent cones. With the definitions we have now, I'll have to prove every fact twice: once for tangent_cone_at, and once for pos_tangent_cone_at. I see two ways to unify these definitions:
1. Introduce (M : submonoid 𝕜) in the definition, and require c n ∈ M. This requires coercions here and there.
2. Define semifields and normed semifields, then pos_tangent_cone_at becomes tangent_cone_at nnreal.
The second approach looks like the right way to do it but it requires a lot of refactoring. What do you think?
BTW, is there any technical reason to have module and vector_space instead of always dealing with a semimodule?
#### Johan Commelin (Feb 05 2020 at 07:09):
Re semimodule: No, I don't think so. It's just to create a (useful, I think?) air of familiarity for mathematicians
#### Sebastien Gouezel (Feb 05 2020 at 07:41):
I'd like to prove more properties of tangent cones. With the definitions we have now, I'll have to prove every fact twice: once for tangent_cone_at, and once for pos_tangent_cone_at. I see two ways to unify these definitions:
1. Introduce (M : submonoid 𝕜) in the definition, and require c n ∈ M. This requires coercions here and there.
2. Define semifields and normed semifields, then pos_tangent_cone_at becomes tangent_cone_at nnreal.
The second approach looks like the right way to do it but it requires a lot of refactoring. What do you think?
I would go for the first way: in any case, there will be coercions involved (in the second approach, you would need to see a real module as an nnreal semimodule), so let's keep it as simple as it can be.
#### Sebastien Gouezel (Feb 05 2020 at 07:45):
BTW, is there any technical reason to have module and vector_space instead of always dealing with a semimodule?
I have tried to make module and vector_space all abbreviations for semimodule, but some things became too slow. I still think this is a good move, but it will probably have to wait for Lean 4. Link to the conversation: https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/linear.20maps.20over.20semimodule/near/185824677
Last updated: May 09 2021 at 11:09 UTC | 2021-05-09 11:22:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5655435919761658, "perplexity": 1734.9474716300665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988966.82/warc/CC-MAIN-20210509092814-20210509122814-00396.warc.gz"} |
https://academic.oup.com/jamia/article/9/1/73/687775/Indicators-of-Accuracy-of-Consumer-Health | ## Abstract
Objectives: To identify indicators of accuracy for consumer health information on the Internet. The results will help lay people distinguish accurate from inaccurate health information on the Internet.
Design: Several popular search engines (Yahoo, AltaVista, and Google) were used to find Web pages on the treatment of fever in children. The accuracy and completeness of these Web pages was determined by comparing their content with that of an instrument developed from authoritative sources on treating fever in children. The presence on these Web pages of a number of proposed indicators of accuracy, taken from published guidelines for evaluating the quality of health information on the Internet, was noted.
Main Outcome Measures: Correlation between the accuracy of Web pages on treating fever in children and the presence of proposed indicators of accuracy on these pages. Likelihood ratios for the presence (and absence) of these proposed indicators.
Results: One hundred Web pages were identified and characterized as “more accurate” or “less accurate.” Three indicators correlated with accuracy: displaying the HONcode logo, having an organization domain, and displaying a copyright. Many proposed indicators taken from published guidelines did not correlate with accuracy (e.g., the author being identified and the author having medical credentials) or inaccuracy (e.g., lack of currency and advertising).
Conclusions: This method provides a systematic way of identifying indicators that are correlated with the accuracy (or inaccuracy) of health information on the Internet. Three such indicators have been identified in this study. Identifying such indicators and informing the providers and consumers of health information about them would be valuable for public health care.
Millions of people now use the Internet to gather health information.1 It is important for the health and well-being of these people, and for the societies to which they belong, that the information they acquire in this way be, on the whole, accurate.2 Much of the consumer health information on the Internet is accurate. However, studies have shown that some of this information is not accurate.3–6 The present study is part of a project to help lay people distinguish accurate from inaccurate consumer health information on the Internet.7,8
In a recent study, Impicciatore et al.4 looked at the accuracy of information on the treatment of fever in children. According to them, “only a few of the [41] Web pages we reviewed gave complete and accurate information for such a common and widely discussed condition.” Thus, Impicciatore et al. established that there is a problem with inaccurate consumer health information on the Internet.
To help Internet users to avoid this inaccurate information, a number of authors and organizations have published guidelines for evaluating the quality of health information on the Internet.9–11 These guidelines typically include lists of indicators that are intended to help Internet users determine the accuracy of Web sites. For example, the medical credentials of the author of a Web site are supposed to be an indicator of accuracy. Also, an out-of-date Web site and a lack of advertising on a Web site are supposed to be indicators of inaccuracy.
Of course, these guidelines can only help Internet users to avoid inaccurate information if the indicators really are correlated with accuracy (or inaccuracy). Unfortunately, there is currently no empirical data to support the claim that these indicators are correlated with accuracy (or inaccuracy). In fact, a recent study12 casts doubt on the reliability of at least one of the proposed indicators of accuracy (namely, positive ratings from services that evaluate medical information on the Internet).
The aim of the current study is to test empirically several of the proposed indicators of accuracy. Following Impicciatore et al., we looked at Web sites that discuss the treatment of fever in children. However, in addition to assessing the accuracy of these sites, we looked for the presence of several of the proposed indicators. With this data (which were collected from March to November 2000), we were able to determine that some of the proposed indicators are correlated with accuracy, but many are not.
## Design
### Search Protocol
Web sites on the treatment of fever in children were collected. These sites were found through keyword searches on the following Internet search engines: Yahoo, AltaVista, and Google. In particular, the terms “fever,” “treatment,” and “child” (connected by the Boolean operator “and”) were used. The goal was to search for health information on the Internet in a manner that might be used by a lay person who needed information on treating a child with a fever. An attempt was made to find as many Web sites on this topic as possible.
Sites were selected that specifically undertook to provide recommendations for the treatment of fever in children. Sites that concerned the treatment of fever associated with specific named diseases or conditions were excluded. Also, sites that simply warned against using aspirin to treat a child with a fever were excluded (for such a warning alone does not amount to a recommended course of treatment).
### Accuracy Protocol
To determine the accuracy of the Web sites, the information on the Web sites was compared with the recommendations of authoritative sources on the treatment of fever in children.
The treatment of fever in children was chosen for this study specifically because there is wide consensus among experts in this area. (The only issues of some debate are the optimal sites for measuring temperature and whether to treat mild fever.) It is generally considered legitimate to judge accuracy by consulting authoritative sources when there is such a consensus among experts.13 This is, for example, the procedure used by Impicciatore et al.
An instrument was developed that consisted of 25 questions covering the following five topics:
• The minimum temperature considered to indicate fever
• The optimal site(s) for measuring temperature
• Pharmacologic treatment of fever
• Physical treatment of fever
• Conditions that warrant consulting a physician
Fever in Pediatric Practice, by El-Radhi and Carroll14 and the Merck Manual of Medical Information15 were used to develop this instrument. This instrument was checked by a physician.
Two observers independently applied this instrument to each Web site and recorded the results in a spreadsheet. For each of the 25 questions, a Web site received 1 point for a completely correct answer, 0.5 points for no answer, and 0 points for an incorrect answer. After the results were recorded, they were double-checked to eliminate typing and transcription errors. Interobserver reliability was assessed by calculating proportions of specific agreement.16,17 The proportions of specific agreement test is superior to the more commonly seen kappa test for the reasons given by Cicchetti and Feinstein.17
An overall accuracy score (between 0 and 1) was computed for each Web site by taking a weighted average of the scores on the individual questions. (Since more information was involved, the third and fourth topics were weighted more heavily. In addition, Web sites were penalized for including any additional incorrect information on the treatment of fever in children.) This overall accuracy score takes into account both the correctness and the completeness of the information.
This particular technique for assigning an overall accuracy score to a Web site is based on theoretic work on verisimilitude (or likeness to truth).18 The verisimilitude of a piece of information (e.g., a scientific theory or the information on a Web site) is its distance from the whole truth on a particular topic. This distance can be calculated in the following manner: The whole truth on the topic is divided into a set of simple, independent, component propositions. The correctness and completeness of the piece of information with respect to each of these component propositions is determined. Finally, the distance of the piece of information from the whole truth is a weighted average of its distance from each of the component propositions.
### Indicators of Accuracy Protocol
Several proposed indicators of accuracy were taken from published guidelines for evaluating the quality of health information on the Internet.9–11 For each Web site, we determined whether each proposed indicator was present or absent. (Interobserver reliability was again assessed here by calculating proportions of specific agreement.) These indicators can be grouped into the following categories:
• Whether the Web site had a commercial domain (e.g., drkoop.com), an organization domain (e.g., kidshealth.org), or an education domain (e.g., columbia.edu)
• Whether the Web site was up to date and whether the treatment page was up to date
• Whether the Web site displayed the HONcode logo (see below)
• Whether the Web site carried any advertising
• Whether the author was identified on the treatment page (and, if so, whether the author was identified as a physician)
• Whether copyright was claimed or acknowledged
• Whether contact information was given
• Whether spelling errors appeared on the treatment page (and, if so, how many)
• Whether there were exclamation points on the treatment page (and, if so, how many)
• Whether peer-reviewed medical literature was cited
• Whether the number of in-links (see below) was high
Two of these proposed indicators of accuracy may require some explanation. First, the HONcode logo is displayed on Web sites that voluntarily agree to abide by the Health On the Net Foundation's Code of Conduct19 for publishing quality health information on the Internet. This code of conduct mandates, for example, that “any medical or health advice provided and hosted on this site will only be given by medically trained and qualified professionals” and that such advice will be based on “appropriate, balanced evidence.”
Second, the number of in-links to a particular Web site is the number of other Web sites that include hyperlinks to that Web site. The number of in-links to a Web site is the Web equivalent of the citation count of a journal article from traditional bibliometrics.20 Several search engines provide information as to how many other sites link to a particular site. In this study, we used Lycos to measure the number of in-links. For the 100 sites that we investigated, the number of in-links varied from 0 to about 37,000. Just less than half of these sites were referred to by more than 1,000 other sites. Web sites to which more than 1,000 other Web sites linked were deemed to have “many in-links.”
### Contingency Table Analysis
Web sites were divided into two categories on the basis of their overall accuracy scores. Web sites with an overall accuracy score at or above the median were deemed to be the “more accurate” sites. Web sites with an overall accuracy score below the median were deemed to be the “less accurate” sites. Since the interval scores were converted into ordinal scores in this way, nothing hangs on the precise interval value of a Web site's overall accuracy score.
For each of the proposed indicators, a 2×2 contingency table was constructed. (For example, Figure 1 is the contingency table for the HONcode logo. Eleven of the 50 “more accurate” sites displayed the HONcode logo, and 39 did not. However, only 3 of the 50 “less accurate” sites displayed the HONcode logo, and 47 did not.) A chi-square test for independence was then used to determine whether the accuracy of Web sites was correlated with the presence (or absence) of the proposed indicators. We concluded that a proposed indicator was correlated with accuracy if the chi-square probability was less than 0.05 (with expected cell frequencies greater than 5).
Figure 1
Contingency table for the HONcode logo as an indicator of accuracy.
Figure 1
Contingency table for the HONcode logo as an indicator of accuracy.
To ensure that the results of the contingency analysis do not depend on taking the median accuracy score as the dividing line between the “more accurate” Web sites and the “less accurate” Web sites, a sensitivity analysis was performed. In particular, the same contingency table analysis was performed using several different dividing lines. Also, as an additional check on the results, a point biserial correlation test was performed using the raw accuracy scores. (Since the interval scale for accuracy was a constructed rather than a natural scale, it was not appropriate to use this test as our main statistical tool.)
### Likelihood Ratios
In addition to determining whether there was a correlation with accuracy, we calculated two likelihood ratios for each proposed indicator. Likelihood ratios are used to measure the definitiveness of a diagnostic test.21 The likelihood ratio for the presence of an indicator of accuracy is how much more likely it is that the indicator will be displayed on a “more accurate” Web site than on a “less accurate” Web site. This likelihood ratio can be estimated using the relative frequencies of “more accurate” Web sites with the indicator and of “less accurate” Web sites with the indicator. Analogously, the likelihood ratio for the absence of an indicator of accuracy is how much more likely it is that the indicator will not be displayed on a “less accurate” Web site than on a “more accurate” site.
## Results
One hundred Web sites on the treatment of fever in children were found. The overall accuracy scores for these sites ranged from 0.55 to 0.75. The distribution of these scores is shown in Figure 2. Fifty Web sites had overall accuracy scores on or above the median score of 0.65 and were deemed to be the “more accurate” sites. Fifty Web sites had overall accuracy scores below the median score and were deemed to be the “less accurate” sites.
Figure 2
Distribution of overall accuracy scores for the 100 Web sites.
Figure 2
Distribution of overall accuracy scores for the 100 Web sites.
The contingency table analysis showed three of the proposed indicators to be correlated with accuracy (Table 1). In particular, the contingency tables for the HONcode logo, organization domain, and copyright all yielded a chi-square probability of less than 0.05. For example, the probability that the presence of the HONcode logo is not correlated with accuracy is 0.021 (i.e., about 2 percent). Several other commonly proposed indicators, such as authority (e.g., the author having medical credentials) and currency, were not correlated with accuracy at all.
Table 1
The Number of “More Accurate” and “Less Accurate” Web Sites for Each of the Proposed Indicators of Accuracy and the Probabilities of Correlation
Proposed Indicator of Accuracy More Accurate Web Sites Less Accurate Web Sites Chi-square Probability Expected Cell Frequencies >5 A. Domain Commercial domain 25 32 0.157 Yes Organization domain 19 10 0.047 Yes Education domain 4 4 1.000 No B. Currency Main page more than 1 yr old 2 2 1.000 No Main page 6 mo–1 yr old 2 3 0.646 No Main page <6 mo old 9 10 0.799 Yes No date given on main page 37 35 0.656 Yes Treatment page >1 yr old 5 2 0.240 No Treatment page 6 mo–1 yr old 5 4 0.727 No Treatment page <6 mo old 4 3 0.695 No No date given on treatment page 36 41 0.235 Yes C. HONcode HONcode logo displayed 11 3 0.021 Yes D. Advertising Advertising displayed 16 18 0.673 Yes E. Authorship Author identified 15 16 0.829 Yes Author identified as an MD 12 10 0.629 Yes F. Copyright Copyright claimed 37 24 0.008 Yes G. Contact Information Contact information provided 38 32 0.190 Yes H. Spelling More than 2 spelling errors 3 0 0.079 No 1 or 2 spelling errors 15 12 0.499 Yes No spelling errors 32 38 0.190 Yes I. Exclamation Points More than 2 exclamation points 1 0 0.315 No 1 or 2 exclamation points 8 7 0.779 Yes No exclamation points 41 43 0.585 Yes J. References Peer-reviewed medical literature cited 2 2 1.000 No K. Inlinks More than 1,000 inlinks to the main page 20 21 0.839 Yes More than 1,000 inlinks to the treatment page 9 5 0.249 Yes
Proposed Indicator of Accuracy More Accurate Web Sites Less Accurate Web Sites Chi-square Probability Expected Cell Frequencies >5 A. Domain Commercial domain 25 32 0.157 Yes Organization domain 19 10 0.047 Yes Education domain 4 4 1.000 No B. Currency Main page more than 1 yr old 2 2 1.000 No Main page 6 mo–1 yr old 2 3 0.646 No Main page <6 mo old 9 10 0.799 Yes No date given on main page 37 35 0.656 Yes Treatment page >1 yr old 5 2 0.240 No Treatment page 6 mo–1 yr old 5 4 0.727 No Treatment page <6 mo old 4 3 0.695 No No date given on treatment page 36 41 0.235 Yes C. HONcode HONcode logo displayed 11 3 0.021 Yes D. Advertising Advertising displayed 16 18 0.673 Yes E. Authorship Author identified 15 16 0.829 Yes Author identified as an MD 12 10 0.629 Yes F. Copyright Copyright claimed 37 24 0.008 Yes G. Contact Information Contact information provided 38 32 0.190 Yes H. Spelling More than 2 spelling errors 3 0 0.079 No 1 or 2 spelling errors 15 12 0.499 Yes No spelling errors 32 38 0.190 Yes I. Exclamation Points More than 2 exclamation points 1 0 0.315 No 1 or 2 exclamation points 8 7 0.779 Yes No exclamation points 41 43 0.585 Yes J. References Peer-reviewed medical literature cited 2 2 1.000 No K. Inlinks More than 1,000 inlinks to the main page 20 21 0.839 Yes More than 1,000 inlinks to the treatment page 9 5 0.249 Yes
*There were 50 “more accurate” Web sites and 50 “less accurate” Web sites in total. The chi-square probabilities have been rounded to three decimal places. The significance level is 0.05. Those indicators with chi-square probabilities less than 0.05 and expected cell frequencies greater than 5 are in italics.
In the sensitivity analysis, the dividing line between the “more accurate” Web sites and the “less accurate” Web sites was set at 0.01 intervals along the range of overall accuracy scores (i.e., 0.56, 0.57, …, 0.73, 0.74). The same contingency tables analysis was performed using each of these dividing lines. Whenever expected cell frequencies were greater than 5, the HONcode logo, organization domain, and copyright were found to be correlated with accuracy (i.e., the chi-square probabilities were less than 0.05). In addition, the results of the point biserial correlation test corroborated the results of the original contingency table analysis.
Since 22 percent of the “more accurate” Web sites but only 6 percent of the “less accurate” Web sites display the HONcode logo, the likelihood ratio for the presence of the HONcode logo is 3.67. Thus, the presence of the HONcode logo is pretty good evidence of accuracy, because the logo is almost four times more likely to be displayed on a more accurate site than on a less accurate site. In contrast, a failure to claim copyright is evidence of inaccuracy because copyright is two times more likely not to be claimed on a less accurate site than on a more accurate site. Point estimates of both likelihood ratios for the HONcode logo, organization domain, and copyright are shown in Table 2.
Table 2
Likelihood Ratios for the Proposed Indicators of Accuracy that have a High Probability of Correlation
Proposed Indicator Presence of Indicator Absence of Indicator Organization domain 1.90 1.29 HONcode logo displayed 3.67 1.21 Copyright claimed 1.54 2.00
Proposed Indicator Presence of Indicator Absence of Indicator Organization domain 1.90 1.29 HONcode logo displayed 3.67 1.21 Copyright claimed 1.54 2.00
Note: The likelihood ratios have been rounded to two decimal places.
For each of the questions on the accuracy protocol, the initial proportions of specific agreement were around 0.90. This increased to 0.95 when typing and transcription errors were removed. For each of the proposed indicators, the proportions of specific agreement exceeded 0.95. In addition, there was complete interobserver agreement with respect to all the indicators that the present study found to be correlated with accuracy (e.g., the presence of the HONcode logo).
## Discussion
### Indicators Correlated with Accuracy
There are indicators that lay people can use to distinguish accurate from inaccurate health information on the Internet. This study has identified three such indicators of accuracy: displaying the HONcode logo, having an organization domain, and displaying a copyright. In particular, the presence of the HONcode logo on a Web site is a fairly good indication that a Web site contains accurate information on the treatment of fever in children. It seems that the quality-control procedures mandated by the Health On the Net Foundation's Code of Conduct tend to result in the publishing of accurate consumer health information.
While such indicators of accuracy can be extremely valuable tools for evaluating health information on the Internet, it must be noted that the presence of these indicators does not guarantee that a Web site contains accurate information (for the relationship between these indicators and accuracy is a probabilistic one). In other words, the HONcode logo is not a definitive “knowledge hallmark.”22
In addition, the correlation of the presence of a particular indicator with accuracy does not imply that the absence of that indicator is correlated with inaccuracy. For example, while the presence of the HONcode logo is correlated with accuracy, the absence of the HONcode logo is not correlated with inaccuracy. A Web site that does not display the HONcode logo is only slightly more likely to be “less accurate” than to be “more accurate.” In fact, a large number of sites that have accurate information on the treatment of fever in children do not display the HONcode logo.
Finally, the fact that an indicator is currently correlated with accuracy does not guarantee that it will always remain an indicator of accuracy. In particular, providers of information may be motivated to make sure that their Web sites display such indicators whether their information is accurate or not. As a result of this, such indicators may quickly cease to be indicators of accuracy.23
What is needed to forestall such a development are indicators that are difficult to “fake.” Unfortunately, it is a very simple matter for anyone to claim copyright for their Web site. Thus, copyright is not a very robust indicator of accuracy. The presence of the HONcode logo, however, is somewhat more difficult, although not impossible, to fake. For example, monitoring procedures are in place that are designed to secure the removal of the HONcode logo from Web sites that fail to comply with the Health On the Net Foundation's Code of Conduct.24 Thus, the HONcode logo is a much more robust indicator of accuracy.
### Indicators Not Correlated with Accuracy
This study also indicates that several of the proposed indicators from published guidelines for evaluating the quality of health information on the Internet are not correlated with accuracy (or inaccuracy). For example, a number of published guidelines for evaluating medical information on the Internet suggest that an author having medical credentials is an indicator of accuracy.10,11 However, we found that there was no such correlation.
A number of published guidelines for evaluating medical information on the Internet suggest that citing peer-reviewed medical literature is an indicator of accuracy.10,11 Unfortunately, so few sites in our sample cited peer-reviewed medical literature that we were unable to reliably test this assertion. However, we did find that there was no correlation between the failure to cite peer-reviewed literature and inaccuracy.
No one would expect the mere fact that a Web site is up-to-date to be an indicator of accuracy. However, it might be expected that no date on a Web site or an old date on a Web site would be correlated to some degree with inaccuracy.11 However, we found that there was no such correlation. Of course, this may be partly due to the specific medical topic that we examined. The best information about the treatment of fever in children has remained fairly stable for a number of years. Lack of currency may be correlated with inaccuracy in areas of medicine where the best information is rapidly changing (e.g., AIDS research).
Finally, published guidelines for evaluating medical information on the Internet suggest that the presence of advertising on a Web site is an indicator of inaccuracy.11 However, we found that there was no such correlation. Even so, it might be useful to look specifically at Web sites on which the potential conflict of interest is more clear-cut. For example, there are Web sites providing information about the treatment of fever that are sponsored by companies that sell pharmaceuticals for the treatment of fever. Unfortunately, we did not find enough Web sites of this particular sort to be able draw any conclusions on this issue.
### Future Directions for Research
The most important way in which this study should be extended is to look at a wider range of health topics. First, this would allow us to confirm that these results are not unique to information on the treatment of fever in children. In addition, looking at a wider range of topics would allow for a larger sample size. The current study suggests that even an exhaustive sample of Web sites on a single topic is often going to be too small to allow us to answer certain important questions. For example, since so few Web sites on the treatment of fever cited peer-reviewed medical literature, we were unable to determine whether such citations are correlated with accuracy.
Also, it would be valuable to look at consumer health information on the Internet in other languages and other countries. In this study, we initially tried to look at Web sites in Spanish on the treatment of fever in children. Unfortunately, we were unable to find more than a handful of such sites.
Finally, this study has identified indicators of accuracy that lay people can use to distinguish accurate from inaccurate health information on the Internet. However, it would be ideal to automate this process as much as possible. For example, Price and Hersh25 have tried to incorporate several of the proposed indicators of accuracy into a “software tool that can automatically assess the quality of consumer health Webpages.” A test for the presence of the HONcode logo, for example, would be fairly easy to incorporate into such a system.
### Conclusion
It is important for consumers of health information on the Internet to be able to distinguish accurate from inaccurate information. Reliable indicators of accuracy can help them do this. The current study shows that it is possible to test empirically the reliability of proposed indicators of accuracy. The presence of the HONcode logo, for example, turns out to be a fairly good indicator of accurate information about the treatment of fever in children. The empirical evidence does not, however, generally support the published guidelines for evaluating the quality of health information on the Internet. Several proposed indicators, such as authority and currency, do not appear to be good indicators of accurate health information. To confirm this result, the present study needs to be replicated on a wider range of health topics.
The authors thank Clayton Curtis, MD, PhD, who checked the protocol for assessing the accuracy of the Web sites. Dr. Curtis is the Director of Clinical Informatics for the Department of Veterans Affairs in the New England Healthcare System. Graduate assistants in the School of Information Resources and Library Science at the University of Arizona (Tracy Cook, Virginia Cullen, Michelle Drumm, Alba Fernandez, Robert Frasier, Elizabeth Gouwens, Melinda Hardman, Andrew Kaplan, and Ping Situ) collected the data. Margaret Higgins, Gerrard Liddell, and two anonymous reviewers provided a number of helpful suggestions, and Kay Mathiesen provided editorial assistance.
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This work was supported by a research grant award from the Association for Library and Information Science Education and by a faculty research grant from the University of Arizona. | 2017-02-25 05:44:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4305000901222229, "perplexity": 1590.742047879363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171664.76/warc/CC-MAIN-20170219104611-00085-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://mathhelpforum.com/pre-calculus/113315-few-questions-about-inequalities.html | 1. A few questions about INEQUALITIES
Okay, in the first one...it says solve for (x^2+2x) / (x^2-8) < 0
So I did everything and solves for it, but then I had to write in which intervals the solutions were...so I PUT [-3, -2] U [0,3) but for some reason the correct answer says that it's (-3,-2) with parentheses before the 3 instead of brackets...and I have NO idea why...
The same question for
square root( x / x^2-2x-35) > 0..I solved, and found the intervals to be [-5,0)U[7, infinity) but the correct answer is (-5, 0] with parentheses instead of brackets before the 5, and brackets instead of parentheses after the o, and U(7, infinity), with parentheses before the 7 instead of brackets...
I don't get when it's parentheses or brackets
Finally,
a word problem...
A projectile is fired straight upward from ground level with an initial velocity of 160 feet per second.
a. At what instant will it be back at ground level?
b. When will the height exceed 384 feet?
I know I can find b if I first write an inequality for what happened, but..I have no idea how...and the book says the equation should be:
-16t^2 + 160t = 0...where in the world did that -16t^2 come from???
Appreciate any help, thank you!
2. Originally Posted by jonjon1324
Okay, in the first one...it says solve for (x^2+2x) / (x^2-8) < 0
Is the denominator supposed to be $x^2- 9$? If not, where did you get the "3" and "-3"?
So I did everything and solves for it, but then I had to write in which intervals the solutions were...so I PUT [-3, -2] U [0,3) but for some reason the correct answer says that it's (-3,-2) with parentheses before the 3 instead of brackets...and I have NO idea why...
Assuming the denominator is actually [tex]x^2- 9[/itex], then the left sided is not defined for x= 3 or -3 so they cannot be included in the solution set. If that is really " $\le$" and not "<" then the solution set is $(-3, -2]\cup [0, 3)$.
The same question for
square root( x / x^2-2x-35) > 0..I solved, and found the intervals to be [-5,0)U[7, infinity) but the correct answer is (-5, 0] with parentheses instead of brackets before the 5, and brackets instead of parentheses after the o, and U(7, infinity), with parentheses before the 7 instead of brackets...
I don't get when it's parentheses or brackets
The denominator, $x^2- 2x- 35= (x- 7)(x+ 5)$ is 0 at x= -5 and 7 so the left side is undefined. x= -5 and x= 7 cannot be included in the solution set.
I presume you understand that [-5, 0) means " $-5\le x< 0$ while (-5, 0] means " $-5< x\le 0$".
Finally,
a word problem...
A projectile is fired straight upward from ground level with an initial velocity of 160 feet per second.
a. At what instant will it be back at ground level?
b. When will the height exceed 384 feet?
I know I can find b if I first write an inequality for what happened, but..I have no idea how...and the book says the equation should be:
-16t^2 + 160t = 0...where in the world did that -16t^2 come from???
Appreciate any help, thank you!
The acceleration due to gravity is -32 feet per second per second. From that one can calculate that the speed after t seconds will be $-32t+
v_0$
, where $v_0$ is the initial speed, and that the height after t seconds will be $-16t^2+ v_0t+ h_0$, where $h_0$ is the initial height. | 2017-02-20 23:35:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9080284237861633, "perplexity": 975.8195347855384}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170613.8/warc/CC-MAIN-20170219104610-00004-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/361168/changing-between-thermodynamic-ensembles/361980 | # Changing Between Thermodynamic Ensembles
For the sake of example, consider the formula for isotropic compressibility.
$$\kappa = -\frac{1}{V} \left(\frac{\partial V}{\partial P}\right)_{N,T}$$
This formula is expressed as a function of $N,P,T$, in other words in the $NPT$ (Isothermal-Isobaric) ensemble.
Now, I wish to express this quantity in a different ensemble, such as the $\mu V T$ (Grand Canonical) ensemble. I've always found this procedure to be messy and mostly guesswork, mainly trial and error with the triple product rule and Maxwell's relations and the chain rule (where convenient).
Is there a clean and systematic way to change variables to the desired ensemble in general?
• Yes, this is what Legendre transforms are for. – lemon Oct 5 '17 at 15:21
• @lemon I'm not sure how you can use Legendre transforms to do this conversion directly. Of course, one can use Legendre transformations to derive things like Maxwell's relations, but using Maxwell's relations seems more like guesswork to me and less than systematic. – Aaron Oct 5 '17 at 15:44
• I edited my answer to add more details. Hope the new version is clearer. – higgsss Oct 12 '17 at 8:04
Given a two-variable function $f(x,y)$ and its Legendre transform $g(x,f_y) = f - yf_y$ , there exists a simple identity between second-order partial derivatives of $f$ and $g$:
$$g_{xx} - f_{xx} = - \frac{f_{xy}^2}{f_{yy}} = \frac{g_{x f_y}^2}{g_{f_y f_y}}.$$
Taking $f$ to be the Helmholtz free energy $F(T, V, N)$, and $g$ to be the Landau free energy $\Omega(T, V, \mu) = F - \mu N$ (Legendre transform of $F$ w.r.t. $N$), one obtains $$\Omega_{VV} - F_{VV} = - \frac{F_{VN}^2}{F_{NN}} = \frac{\Omega_{V\mu}^2}{\Omega_{\mu\mu}},$$ from which an expression for the difference of the following two quantities can be derived: $$\kappa_{NVT}^{-1} := -V \left(\frac{\partial P}{\partial V}\right)_{N,T} = V F_{VV},$$ $$\kappa_{\mu VT}^{-1} := -V \left(\frac{\partial P}{\partial V}\right)_{\mu,T} = V \Omega_{VV}.$$
(Although OP considered $\kappa$ in the $NPT$ ensemble, the $NVT$ ensemble leads to the same quantity as well.)
Also, by setting $f = F(T,V,N)$, $g = G(T,P,N)$ (i.e., Gibbs free energy), $x = T$, $y = V$, and $f_y = -P$, one can derive the relation $$C_P - C_V = T(-G_{TT} + F_{TT}) = \frac{VT\alpha^2}{\kappa},$$ where $\alpha = \frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_{P,N} = G_{PT}/V$ and $\kappa = - \frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_{T,N} = - G_{PP}/V$.
Proof of the identity:
Consider a twice-differentiable function $f(x,y)$ and its Legendre transform w.r.t. $y$:1 $$g(x,f_y) := f(x,y) - f_yy.$$ (Here, it is implicitly assumed that $y$ is expressed as a function of $x$ and $f_y$.) Notice that $$\tag{1} \label{a} \frac{\partial f}{\partial x} \bigg|_{f_y} = f_x + f_y \frac{\partial y}{\partial x}\bigg|_{f_y} = f_x - f_y \frac{f_{xy}}{f_{yy}},$$ where the last equality holds due to the triple product rule. We then have $$g_x = \frac{\partial f}{\partial x} \bigg|_{f_y} - f_y \frac{\partial y}{\partial x}\bigg|_{f_y} = f_x,$$ from which it follows that $$g_{xx} = \frac{\partial f_x}{\partial x} \bigg|_{f_y} = f_{xx} - \frac{f_{xy}^2}{f_{yy}}.$$ Here, the last equality is simply Eq. (\ref{a}) with $f$ replaced by $f_x$. Noting that Legendre transformation of $g$ w.r.t. $f_y$ gives $f$, one can exchange the role of $f$ and $g$ on the above, which leads to $$f_{xx} = g_{xx} - \frac{g_{xf_y}^2}{g_{f_yf_y}}.$$
1 $f$ must be either a convex or a concave function of $y$ for the Legendre transformation to be well-defined.
To make it short and systematic: The way you ask the question, there isn't a general method for "any change of variables to express the same observable". It is important that you know what exactly you want: The way you describe it, you want to know the same observable, but expressed in different variables. The way you formulate it, you still want $\frac{\partial V(p, N, T)}{\partial p}$, but you want this observable number as a function of $\mu$, V, and T. Think about if this is really want you want to know. In the case it is, "just" express $\tilde{p}(\mu, V, T)$, $\tilde{N}(\mu,V, T)$ and $\tilde{T}(\mu, V, T) = T$, the "old variables", as functions of the new ones, and plug them into the old equation you get for your desired observable.
The theory of thermodynamics makes statements over a set of observables: The entropy S, the energy E, the temperature T, the volume V, the pressure p, the particle number N, and the chemical potential $\mu$ (there are more, but I will restrict myself to these in my discussion). For the variables I described, it follows from thermodynamics that you can choose 3 of them (I won't specify which, not every combination is allowed), so that the others can be expressed as a function of these 3.
For example (just an example), I can choose these variables to be $N$, $V$, and $S$ (this would be a set of 3 independent variables). For this specific combination, every other observable can be expressed as a function of these 3 variables: $E(S,V,N)$, $T(S,V,N)$ and so on. Furthermore, there is an additional structure to the observables, stating that one of the other observables takes the role of some kind of potential (for our choice S V N, the observable that takes this role is the energy E(S,V,N)). Every of the remaining observables can then be computed as a derivative of E:
$$T = \frac{\partial E}{\partial S}$$ and so on. It is crucial to observe that this is the derivative of the specific function E(S,N,V). To explain this in more detail: If you had chosen another combination of variables, for example S, V, $\mu$, you could write down a function $\tilde{E}(S, V, \mu)$ to represent the same observable. For the same state of the system, this observable (which means this function) would have the same value. However, the function $\tilde{E}$ would be another function. To express this more mathematically: Let's say $V_1$, $N_1$ and $S_1$ represent the system in state 1, if you choose $S$, $V$ and $N$ to be the representing variables. If you instead choose the variables $S$, $V$, $\mu$, then the same system (same system state means every observable is equal) state is supposed to be expressed by the variables $V_1$, $\mu_1$ and $S_1$. The combinations to represent equal systems means, for example, that $$\tilde{E}(S_1, V_1, \mu_1) = E(S_1, V_1, N_1)$$ However, since $E$ and $\tilde{E}$ are different mathematical functions, the derivatives will not be equal: $$\frac{\partial \tilde{E}}{\partial V} \neq \frac{\partial E}{\partial V}$$
I hope this answer brought you some insight into the way one handles thermodynamic observables, apart from answering your question. One additional note (which is very important to me!): Changing variables and changing ensembles are two completely different things. You can take an arbitrary ensemble, and describe it with arbitrary (allowed) combinations of variables. You can take for example the canonical ensemble (which statistically is described by the variables $N$, $V$, $T$, with the thermodynamic potential being $F$, the free energy. Although $F$ is the the thermodynamic potential rising from the partition function, other observables can be computed from the derivatives of F (for example, $p = - \frac{\partial F}{\partial V}$, and you are free to perform a Legendre transformation to achieve the internal energy $E$ as a function of $N$, $S$, and $T$.
Long story short: In a given statistical system (whatever ensemble), you are free to choose variables that are appropriate to your calculations. The relations between your observables hold in every ensemble.
However, the total values of your observables will differ from ensemble to ensemble, until you take the thermodynamic limit, in which for a given set of variables (for example $V$, $T$, $S$), every observable will have the same value.
The reason one associates a specific choice of variables with an ensemble (for example $V$, $T$ and $N$ for the canonical ensemble) is that those variables are experimentally accessible in the specified ensemble. In the canonical ensemble, you can change $N$ to a desired value by adding particles. In the grand canonical ensemble, there isn't a fixed number of particles, and you'd have to calculate first which amount of $\mu$ is needed so that the value $N$ will take the value you want.
• This doesn't answer the question. The part where you say it's "just" a matter of expressing old variables as a function of the new, well, that's the whole point of the question! – Javier Oct 9 '17 at 21:02
• Well, this is the clean and systematic way to transit from the old variables to the new variables, for the generality that the question is asked. It would be a whole different story if he for example would not change the variable that his observable is derived after (change from $\frac{\partial V(p,N,T)}{\partial p}$ to $\frac{\partial V (p, \mu, T)}{\partial p}$. But in generality that is asked for, this is the only answer one can give. – Quantumwhisp Oct 9 '17 at 21:12
• You haven't given any clean and systematic method, you've just stated the theory behind the subject. If there's no general method you should just say that instead of teaching OP thermodynamics. – Javier Oct 9 '17 at 21:16
• I have made the experience that anytime I asked questions, I was very happy about additional explanations arround the subject. I will follow your critique and put the "(not clean, but) systematic method" to the front of my answer. Whoever wants can still read all the stuff afterwards (which I think is important to do, especially if one doesn't fully understand what "changing of variables" means exactly. – Quantumwhisp Oct 9 '17 at 21:31 | 2020-12-03 13:29:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 10, "x-ck12": 0, "texerror": 0, "math_score": 0.876884937286377, "perplexity": 195.21863685952292}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141727782.88/warc/CC-MAIN-20201203124807-20201203154807-00254.warc.gz"} |
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Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: The content of real-world databases, knowledge bases, database models, and formal specifications is often highly redundant and needs to be aggregated before these representations can be successfully paraphrased into natural language. To generate natural language from these representations, a number of processes must be carried out, one of which is sentence planning where the task of aggregation is carried out. Aggregation, which has been called ellipsis or coordination in Linguistics, is the process that removes redundancies during generation of a natural language discourse, without losing any information.The article describes a set of corpus studies that focus on aggregation, provides a set of aggregation rules, and finally, shows how these rules are implemented in a couple of prototype systems. We develop further the concept of aggregation and discuss it in connection with the growing literature on the subject. This work offers a new tool for the sentence planning phase of natural language generation systems.
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• 10
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Oxford, UK and Boston, USA : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Type of Medium: Electronic Resource
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• 11
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: Neural networks whose architecture is determined by genetic algorithms outperform autoregressive integrated moving average forecasting models in six different time series examples. Refinements to the autoregressive integrated moving average model improve forecasting performance over standard ordinary least squares estimation by 8% to 13%. In contrast, neural networks achieve dramatic improvements of 10% to 40%. Additionally, neural networks give evidence of detecting patterns in data which remain hidden to the autoregression and moving average models. The consequent forecasting potential of neural networks makes them a very promising addition to the variety of techniques and methodologies used to anticipate future movements in time series.
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• 12
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: We present a method to derive a solution to the combined frame and ramification problems for certain classes of theories of action written in the situation calculus. The theories of action considered include the causal laws of the domain, in the form of a set of effect axioms, as well as a set of ramification state constraints. The causal laws state the direct effects that actions have on the world, and ramification state constraints allow one to derive indirect effects of actions on the domain.To solve the combined frame and ramification problems, the causal laws and ramification state constraints are replaced by a set of successor state axioms. Given a state of the world, these axioms uniquely determine the truth value of dynamic properties after an action is performed. In this article, we extend previous work by formulating an approach for the mechanical generation of these successor state axioms. We make use of the notions of implicate and support that have been developed in the context of propositional theories. The approach works for classes of syntactically restricted sets of ramification state constraints.
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• 13
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Type of Medium: Electronic Resource
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• 14
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: In this paper, we describe a method for automatically retrieving collocations from large text corpora. This method comprises the following stages: (1) extracting strings of characters as units of collocations, and (2) extracting recurrent combinations of strings as collocations. Through this method, various types of domain-specific collocations can be retrieved simultaneously. This method is practical because it uses plain text with no specific-language-dependent information, such as lexical knowledge and parts of speech. Experimental results using English and Japanese text corpora show that the method is equally applicable to both languages.
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• 15
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Oxford, UK and Boston, USA : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: Nonlinear dynamical systems are notoriously difficult to control. The Acrobot is an under-actuated double pendulum in a gravitational field. Under most driving schemes the Acrobot exhibits chaotic behavior. But with careful applications of energy it is possible to gradually pump the system so as to swing it over its supporting joint. This swing-up task is of current interest to control theory researchers.Conventional notions of AI planning are not easily extended to domains with interacting continuously varying quantities. Such continuous domains are often dynamic; important properties change over time even when no action is taken. Noise and error propagation can preclude accurately characterizing the effects of actions or predicting the trajectory of an undisturbed system through time. A plan must be a conditional action policy or a control strategy that carefully nudges the system as it strays from a desired course. Automatically generating such plans or action strategies is the subject of this research.An AI system successfully learns to perform the swing-up task using an approach called explanation-based control (EBC). The approach combines a plausible qualitative domain theory with empirical observation. Results are in some respects superior to the known control theory strategies. Of particular importance to AI is EBC's notion of a “plan” or “strategy” and its method for automatic synthesis. Experimental evidence confirms EBC's ability and generality.
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• 16
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Oxford, UK and Boston, USA : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: A critical problem for managers of temporal information is the treatment of assertions and of complex types of queries because in many cases the treatment could involve reasoning on the whole knowledge base of temporal constraints. We propose an efficient approach to this problem. First, we show how different types of queries can be answered (in a complete way) in a time polynomial in the dimension of the query and independently of the dimension of the knowledge base. Second, we provide an efficient (and complete) procedure to deal with sessions of interleaved assertions and queries to the knowledge base. We provide both analytical and experimental evaluations of our approach, and we discuss some application areas.
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• 17
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: A natural language collaborative consultation system must take user preferences into account. A model of user preferences allows a system to appropriately evaluate alternatives using criteria of importance to the user. Additionally, decision research suggests both that an accurate model of user preferences could enable the system to improve a user's decision-making by ensuring that all important alternatives are considered, and that such a model of user preferences must be built dynamically by observing the user's actions during the decision-making process. This paper presents two strategies: one for dynamically recognizing user preferences during the course of a collaborative planning dialogue and the other for exploiting the model of user preferences to detect suboptimal solutions and suggest better alternatives. Our recognition strategy utilizes not only the utterances themselves but also characteristics of the dialogue in developing a model of user preferences. Our generation strategy takes into account both the strength of a preference and the closeness of a potential match in evaluating actions in the user's plan and suggesting better alternatives. By modeling and utilizing user preferences, our system is able to fulfill its role as a collaborative agent.
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• 18
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: Although case-based reasoning (CBR) was introduced as an alternative to rule-based reasoning (RBR), there is a growing interest in integrating it with other reasoning paradigms, including RBR. New hybrid approaches are being piloted to achieve new synergies and improve problem-solving capabilities. In our approach to integration, CBR is used to satisfy multiple numeric constraints, and RBR allows the performance of “what if” analysis needed for creative design.The domain of our investigation is nutritional menu planning. The task of designing nutritious, yet appetizing, menus is one at which human experts consistently outperform computer systems. Tailoring a menu to the needs of an individual requires satisfaction of multiple numeric nutrition constraints plus personal preference goals and aesthetic criteria.We first constructed and evaluated independent CBR and RBR menu planning systems, then built a hybrid system incorporating the strengths of each system. The hybrid outperforms either single strategy system, designing superior menus, while synergistically providing functionality that neither single strategy system could provide. In this paper, we present our hybrid approach, which has applicability to other design tasks in which both physical constraints and aesthetic criteria must be met.
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• 19
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: A multiphase machine translation approach, Generate and Repair Machine Translation (GRMT), is proposed. GRMT is designed to generate accurate translations that focus primarily on retaining the linguistic meaning of the source language sentence. GRMT presently incorporates a limited multilingual translation capability. The central idea behind the GRMT approach is to generate a translationcandidate (TC) by quick and dirty machine translation (QDMT), then investigate the accuracy of that TC by translation candidate evaluation (TCE), and, if necessary, revise the translation in the repair and iterate (RI) phase. To demonstrate the GRMT approach, a translation system that translates from English to Thai has been developed. This paper presents the design characteristics and some experimental results of QDMT and also the initial design, some experiments, and proposed ideas behind TCE and RI.
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• 20
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: This paper describes a compound unit (CU) recognizer as a pattern-based approach and its hybridization with rule-based translation. A compound unit is a combined concept including collocations, idioms, and compound nouns. CU recognition reduces part of speech ambiguities by combining several words into a unit and consequently lessening the parsing load. It also provides pretranslated natural equivalents. Our focus in this paper is to obtain flexibility and efficiency from pattern-based machine translation, and high-quality translation by hybridization. A modified trie, our search index structure using “method” strategy is used to manage heterogeneous property of the constituents. Syntactic verification is integrated to obtain precise CU recognition by means of pruning wrongly recognized units that are caused by improper variable hypotheses. The experimental result with verification shows that the precision of CU recognition is increased to 99.69% with 31 CFG rules on the cyclic trie structure for 1,268 Wall Street Journal articles of the Penn Treebank. Another experiment with CU recognition also shows that it raises the understandability of translation for Web documents.
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• 21
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: Efficient implementation of type inclusion is an important feature of object oriented programming languages with multiple inheritance. The idea is to associate to each type a subset of a set S={1,...,k} such that type inclusion coincides with subset inclusion. Such an embedding of types into 2S (the lattice of all subsets of S) is called a bit-vector encoding of the type hierarchy. In this paper, we show that most known bit-vector encoding methods can be inserted on a general theoretical framework using graph coloration, namely the notion of a simple encoding. We use the word simple because all these methods are heuristics for the general bit-vector encoding problem, known as the 2-dimension problem. First we provide a correct algorithm for partial orders based on simple encoding, improving the algorithm of Krall, Vitek, and Horspool (1997). Second we show that finding an optimal simple encoding is an NP-hard problem. We end with a discussion on some practical issues.
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• 22
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Boston, USA and Oxford, UK : Blackwell Publishers Inc
Computational intelligence 15 (1999), S. 0
ISSN: 1467-8640
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Computer Science
Notes: In this paper we develop a formalization of semantic relations that facilitates efficient implementations of relations in lexical databases or knowledge representation systems using bases. The formalization of relations is based on a modeling of hierarchical relations in Formal Concept Analysis. Further, relations are analyzed according to Relational Concept Analysis, which allows a representation of semantic relations consisting of relational components and quantificational tags. This representation utilizes mathematical properties of semantic relations. The quantificational tags imply inheritance rules among semantic relations that can be used to check the consistency of relations and to reduce the redundancy in implementations by storing only the basis elements of semantic relations. The research presented in this paper is an example of an application of Relational Concept Analysis to lexical databases and knowledge representation systems (cf. Priss 1996) which is part of a larger framework of research on natural language analysis and formalization.
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• 23
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: This article describes and analyses the membership and uses of the Teaching-Statistics Mailbase list, based upon a review of all messages since its inception and a recent questionnaire sent to all list members.
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• 24
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
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• 25
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: This article describes the learning experiences of young children meeting stem-and-leaf plots for the first time.
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• 26
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: A game of chance in which players can maximise their expected gain by making appropriate decisions is described. Developing an optimal strategy involves computing probabilities and conditional expected values.
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• 27
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
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• 28
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: This article describes the use of Microsoft Excel, graphics calculators and a multimedia CBL package by students on an introductory statistics course.
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• 29
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: Several measures of “success” for a simple game are discussed. Comparisons between players, and between a player and a simulation, can be made in several ways.
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• 30
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: This article reports some results of an informal study of very young children's reactions to some visual displays of data.
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• 31
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
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• 32
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: This is the first of a short series of articles briefly describing the organisations that sponsor Teaching Statistics. The series starts with The Royal Statistical Society.
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• 33
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Oxford, UK : Blackwell Publishing Ltd
Teaching statistics 21 (1999), S. 0
ISSN: 1467-9639
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Mathematics
Notes: This article shows how simulation can be used to teach sampling distributions to entry level statistics students.
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• 34
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Oxford, UK and Boston, USA : Blackwell Publishers Ltd.
Bioethics 13 (1999), S. 0
ISSN: 1467-8519
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine , Philosophy
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• 35
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Oxford, UK and Boston, USA : Blackwell Publishers Ltd.
Bioethics 13 (1999), S. 0
ISSN: 1467-8519
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine , Philosophy
Type of Medium: Electronic Resource
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• 36
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Oxford, UK and Boston, USA : Blackwell Publishers Ltd.
Bioethics 13 (1999), S. 0
ISSN: 1467-8519
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine , Philosophy
Type of Medium: Electronic Resource
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• 37
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Oxford, UK and Boston, USA : Blackwell Publishers Ltd.
Bioethics 13 (1999), S. 0
ISSN: 1467-8519
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine , Philosophy
Notes: Books reviewed:Emmanuel Agius and Salvino Busuttil, (eds), Germ-Line Intervention and our Responsibilities to Future GenerationsAndrew Edgar, Sam Salek, Darren Shickle and David Cohen, The Ethical QALY: Ethical Issues in Healthcare Resource AllocationsJohn McKie, Jeff Richardson, Peter Singer and Helga Kuhse, The Allocation of Health Care Resources: An Ethical Evaluation of the ‘QALY’ ApproachGregory E. Pence, Who’s Afraid of Human Cloning?Maxwell J. Mehlman and Jeffrey R. Botkin, (eds), Access to the Genome: The Challenge to EqualityUdo Schüklenk, Access to Experimental Drugs in Terminal IllnessPhilip J. Boyle, (ed), Getting Doctors to Listen: Ethics and Outcome Data in ContextEllie Lee, (ed), Abortion Law and Politics Today
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• 38
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Oxford, UK and Boston, USA : Blackwell Publishers Ltd.
Bioethics 13 (1999), S. 0
ISSN: 1467-8519
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine , Philosophy
Notes: Increasing awareness of the importance of the biodiversity of the whole global biosphere has led to further awareness that the problems which arise in connection with preservation and exploitation of our planet’s biodiversity are best tackled from a global perspective. The ‘Biodiversity Convention’ and the ‘Human Genome Project’ are some of the concrete attempts at such globalisation. But, while these efforts are certainly very good at the intentional level and on paper, there is, at the practical level of implementation, the danger that globalisation may simply translate into westernisation, given the Western world’s dominance and will to dominate the rest of the globe. How is ‘global bioethics’ to be possible in a world inhabited by different cultural groups whose material situation, powers, ideas, experiences and attitudes differ rather markedly and who are not, in any case, equally represented in globalisation efforts and fora? One index of the pertinence of this question is that talk about biodiversity, biotechnology, biotrade etc. is being increasingly matched by talk about biopiracy, biorade, biocolonialism etc. In this paper, I attempt to explore and develop these very general concerns.
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• 39
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Oxford, UK and Boston, USA : Blackwell Publishers Ltd.
Bioethics 13 (1999), S. 0
ISSN: 1467-8519
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine , Philosophy
Notes: European biomedical ethics is often contrasted to American autonomy-based approaches, and both are usually distinguished as ‘Western’. But at least three ‘different voices’ within European bioethics can be identified:The deontological codes of southern Europe (and Ireland), in which the patient has a positive duty to maximise his or her own health and to follow the doctor’s instructions, whilst the physician is constrained more by professional norms than by patient rightsThe liberal, rights-based models of Western Europe, in which the patient retains the negative right to override medical opinion, even if his or her mental capacity is in doubtThe social welfarist models of the Nordic countries, which concentrate on positive rights and entitlements to universal healthcare provision and entrust dispute resolution to non-elected administrative officials
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• 40
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
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• 41
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: Research about parity or breastfeeding experience and its relationship with milk production in humans is limited. The purpose of this study was to determine if any difference in milk volume occurred among mothers with and without breastfeeding experience who used either a single or double breast pumping regimen the first 5 weeks postpartum. Methods: A convenience sample of 39 mothers of nonnursing preterm infants participated from two tertiary care centers in the midwestern United States. The sequential single pumping group consisted of 20 mothers, 7 of whom had previous breastfeeding experience; the simultaneous double pumping group consisted of 19 mothers, 2 of whom had previous breastfeeding experience. Income and pumping group regimen were used as blocking variables, and average frequency of kangaroo care per week and average frequency of breast pumping per week were covariants in the repeated measures analysis of variance. Results: Mothers with previous breastfeeding experience had greater milk weights over time, but weights were not significantly different when compared with those mothers with no previous breastfeeding experience. Additional analysis with the covariants of pumping frequency and kangaroo care, and with the independent variables of group, breastfeeding experience, and income resulted in statistically significantly greater milk yield in the women with previous breastfeeding experience. Conclusions: The findings of the two repeated analyses indicated the complexity of the milk production response, and the importance of considerations of environmental as well as physiologic factors.
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• 42
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Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: This paper defines the needs of women and their newborns, and classifies a number of practices common in postpartum care. It is a summary of the report, Postpartum Care of the Mother and Newborn: A Practical Guide, which was developed by a Technical Working Group of the World Health Organization and published in 1998. The report takes a comprehensive view of maternal and newborn needs during the postpartum period, examining major maternal and neonatal health challenges, nutrition and breastfeeding, birth spacing, immunization, HIV/AIDS, and the essential elements of care and service provision. The document lists recommendations, and classifies common practices in the postpartum period, dividing them into four categories: those which are useful, those which are harmful, those for which insufficient evidence exists, and those which are frequently used inappropriately.
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• 43
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: American Indian women have one of the lowest cesarean delivery rates among all ethnic groups evaluated in the United States. Our objective was to identify risk factors for cesarean delivery among American Indian women in New Mexico. Methods: Live birth certificate data (1994) from the New Mexico Bureau of Vital Records and Health Statistics were used to compare American Indian women who had a cesarean delivery with those who had a vaginal delivery. We examined demographic, prenatal, and intrapartum factors to determine risk factors for cesarean delivery. Results: In 1994 American Indian women in New Mexico had a cesarean delivery rate of 12 percent. Risk factors for cesarean delivery included age equal to or over 35 years (OR = 1.8, 1.3–2.5) and nulliparity (OR = 1.9, 1.5–2.5). Obstetric risk factors included prematurity (OR = 2.3, 1.5–3.6), low birthweight (OR = 2.6, 1.7–4.2), diabetes (OR = 1.7, 1.1–2.5), pregnancy-induced hypertension (OR = 2.6, 1.8–3.8), and labor and delivery complications (OR = 9.5, 7.5–12.1). Age less than 20 years was negatively associated with cesarean delivery (OR = 0.5, 0.3–0.7). Conclusion: American Indian women have risk factors for cesarean delivery that are similar to those reported in other populations. Future prospective research evaluating intrapartum management may help identify reasons for the low cesarean birth rate.
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• 44
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
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• 45
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: A worldwide campaign has been initiated to improve the in-hospital care of mothers and babies through increased breastfeeding. The four objectives of the current investigation were to determine the in-hospital breastfeeding rate for Minnesota hospitals, to analyze the relationship between the in-hospital breastfeeding rates and selected hospital demographic characteristics, to determine the rate of adherence to each of the Baby-Friendly Hospital Initiative (BFHI) Ten Steps, and to analyze the relationship between the adherence rates for each of the Ten Steps and selected demographic characteristics. Methods: A descriptive survey was conducted and analyzed for the year of 1994 from 79 (83%) Minnesota hospitals. Respondents were directors of nursing, nursing managers, or other staff familiar with their hospital's breastfeeding policies and practices. Results: The average breastfeeding initiation rate was 59 percent. Four of the Ten Steps were implemented with a low adherence rate (0–49%), five were implemented with a moderate rate (50–89%), and none was implemented with a high rate (90–100%). Breastfeeding initiation rates and adherence to the Ten Steps varied with the size of the city and the number of births per year. Conclusions: Improvements in breastfeeding policies, practices, and staff education are needed if Minnesota hospitals are to provide care consistent with the Ten Steps of the BFHI. The results provide baseline information to guide institutional change that could promote successful breastfeeding experiences for postpartum families. This survey instrument could be used easily by researchers in other sites to assess nine of the Ten Steps.
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• 46
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Objective: Although improving mothers' knowledge about breastfeeding can increase rates and duration of breastfeeding, little is known about the influence of fathers' knowledge. The purpose of this study was to assess the knowledge of mothers and fathers about breastfeeding before and after receiving postpartum advice and its relationship to the frequency of breastfeeding. Methods: A clinical trial was performed with mothers and fathers of normal children born at the Hospital de Clínicas de Porto Alegre, Brazil, between July 1994 and March 1995. The study intervention consisted of postpartum advice supplied by means of a video film discussing basic topics of breastfeeding, an explanatory leaflet, and open discussion after viewing the video. The first 208 couples comprised the control group, the next 197 comprised experimental group 1, and the remaining 196 comprised experimental group 2. Immediately after delivery, mothers and fathers in the three groups answered a test on breastfeeding knowledge; they completed the same test at the end of the first month. All families received home visits at the end of the first, second, fourth, and sixth months, or until breastfeeding ceased. Logistic regression was used to evaluate the association between the mothers' and fathers' knowledge and frequency of breastfeeding. Results: Postpartum advice increased the breastfeeding knowledge of mothers and fathers. The mothers with the highest level of knowledge had a 6.5 times higher chance of exclusively breastfeeding at the end of the third month, and 1.97 times higher chance of continuing breastfeeding to the end of the sixth month compared with other mothers. The fathers' knowledge also significantly influenced breastfeeding rates. The children whose fathers knew more had a 1.76 higher chance of being exclusively breastfed at the end of the first month, and 1.91 higher chance of receiving maternal milk at the end of the third month. Conclusion: A simple, inexpensive strategy can increase the level of breastfeeding knowledge of mothers and fathers and, consequently, have a positive impact on the frequency of breastfeeding.
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• 47
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: Antenatal ascertainment of fetal sex is a common feature of modern pregnancies. Women who opt not to learn fetal sex typically employ a variety of methods to forecast it. This study investigated the validity of prevalent folklore used to identify fetal sex before birth. Method: One hundred four pregnant women, who did not know the sex of the fetus, were administered a questionnaire to explore their perceptions of fetal sex and the basis for these predictions. Results: Fetal sex was not systematically related to the shape of the woman's abdomen, prevalence of morning sickness, or comparisons with previous pregnancies. However, women who had more than twelve years of education correctly predicted fetal sex greater than chance (71% correct), in contrast to less educated women (43% correct). Contrary to expectations, women whose forecasts were based on psychological criteria (i.e., dreams or feelings) were more likely to be correct than those employing prevalent folklore criteria (i.e., the way a woman was carrying the pregnancy). Conclusions: In general, women were not good predictors of fetal sex. The mechanisms that promote maternal accuracy in predicting fetal sex for highly educated women are unknown. It is reasonable to expect that maternal perceptions of fetal sex contribute to the process of fetal attachment.
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• 48
Electronic Resource
Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: Breast stimulation to augment labor has been used for centuries in tribal societies and by midwives. In recent years it has been shown to be effective in ripening the cervix, inducing labor, and as an alternative to oxytocin for the contraction stress test. This study compared the effectiveness of breast stimulation with oxytocin infusion in augmenting labor. Methods: Women admitted to the labor ward were eligible for the study if they had inadequate labor with premature rupture of the membranes and met inclusion criteria. They were assigned to oxytocin augmentation or breast stimulation (manual or pump), and were switched to oxytocin in the event of method failure. Outcomes included time to delivery, intervention to delivery, proportion of spontaneous deliveries, and Apgar scores. One hundred participants were needed in each arm of the study to demonstrate a 2- to 3-hour difference in delivery time, with a power of 80 percent. Results: Analysis was performed on 79 women, of whom 49 were in the breast stimulation group and 30 in the oxytocin group. Sixty-five percent of the participants failed breast stimulation and were switched to oxytocin infusion. Although augmentation start to delivery was shorter for the oxytocin group ( p 〈 0.001), no differences in total labor time occurred between the groups. Nulliparas receiving breast stimulation had more spontaneous (relative risk 1.7, p= 0.04). and fewer instrumental deliveries than those receiving oxytocin (relative risk 0.2, p= 0.02). No significant differences in adverse fetal outcomes occurred between the study groups. Conclusions: The small number of participants and a variety of problems with the conduct of the study prevented the formulation of reliable conclusions from the results. However, the study provided important insights into the feasibility and problems of developing a high-quality randomized trial of augmentation by breast stimulation.
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Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: This study was a randomized controlled trial of primigravidas in Botswana to determine the effectiveness of the presence of a female relative as a labor companion on labor outcomes. Methods: One hundred and nine primigravidas in uncomplicated spontaneous labor were randomly distributed into a control group who labored without family members present, and an experimental group who had a female relative with them during labor. Results: Significantly more mothers in the experimental group had a spontaneous vaginal delivery (91% vs 71%), less intrapartum analgesia (53% vs 73%), less oxytocin (13% vs 30%), fewer amniotomies to augment labor (30% vs 54%), fewer vacuum extractions (4% vs 16%), and fewer cesarean sections (6% vs 13%) than in the control group. These differences were all significant at p 〈 0.05. Epidural analgesia was not used in the hospital at the time of the study. The only analgesics used were intramuscular pethidine or hyoscine N-butylbromide (Buscopan). Conclusions: The presence in labor of a female relative was shown to be associated with fewer interventions and a higher frequency of normal delivery compared with the outcomes of those without family member support. The presence of a female relative as a labor companion is a low-cost, preventative intervention that is consistent with the traditional cultural practices in Botswana. In the light of this and previous studies, all women giving birth in a hospital should be offered the choice of a female relative as a companion to give support during labor.
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Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: Several countries have developed clinical practice guidelines for the content of prenatal care. This study examines the consistency of recommendations in clinical practice guidelines describing routine prenatal care. Methods: The recommendations for low-risk women in seven guideline documents were examined: two from Australia, two from the United States, two from Canada, and one from Germany. The recommendations were listed into the four areas of “general health screening and health promotion during pregnancy,”“organization of care,”“clinical tests and screening,” and “education specific for pregnancy.”Results: A total of 69 recommendations were identified within the seven documents, most of which fell within the “clinical tests and screening” domain. Notable differences were identified in the number of recommendations made within the same country. Of the 69 recommendations, only four were included in all seven documents. Conclusion: Little consistency was demonstrated within or among countries in terms of the content of their prenatal care guidelines, suggesting a need to reexamine their content and the evidence on which such recommendations are based.
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Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
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Oxford, UK : Blackwell Science Inc
Birth 26 (1999), S. 0
ISSN: 1523-536X
Source: Blackwell Publishing Journal Backfiles 1879-2005
Topics: Medicine
Notes: Background: Complex interactions occur among women and caregivers throughout labor. Analyzing women's birth stories provides a rich data source on these interactions. The purpose of this qualitative study was to clarify how decisions were made in labor by analyzing women's birth stories. Methods: A convenience sample of 15 primiparous and multiparous Midwestern women contributed a total of 33 birth stories. Qualitative methods were used, including analyses of the content and themes of stories. Results: The primary types of decision making that were identified ranged on a continuum from unilateral to joint (shared), and were associated with various emotions expressed by the women. Conclusions: A model of decision making was derived from the data that may help caregivers change practices in ways that will benefit women. Caregivers can also benefit by understanding women's critiques of the birth care they received, and can use this knowledge to improve women's experiences of birth and therefore their satisfaction with the process.
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• 53
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European spine journal 8 (1999), S. 1-1
ISSN: 1432-0932
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
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European spine journal 8 (1999), S. 27-33
ISSN: 1432-0932
Keywords: Key words Occipito-cervical ; fusion ; Bone thickness ; Spiral CT ; Skull morphology
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract Arguments concerning the best procedure for occipito-cervical fusion have rarely been based upon occipital bone thickness or only based on in vitro studies. To close this gap and to offer an outlook on preoperative evaluation of the patient, 28 patients were analysed in vivo by means of spiral CT. Ten macerated human skulls were measured by means of CT and directly. Measurements were taken according to a matrix of 66 points following a grid with 1 cm spacing based upon McRae’s line. Maximum thickness in the patient group was met 4 cm above the reference plane in the median slice (11.87 mm; SD 3.41 mm) and 5 cm above it in the skull group (15.85 mm; SD 1.81 mm). Correlation between CT and direct measurements was good (91.79%). Intra-individual discrepancies from one side to the respective point on the other side are common (difference 〉 1 mm in 60%). Judging areas suitable for operative fixation using the 10% percentile value (6.68 mm for the maximum value of 11.87 mm) led to the conclusion that screws should only be inserted along the occipital crest in an area extending from 1.5 cm above the posterior margin of the foramen magnum to the external occipital protuberance (EOP). At the level of the EOP screws may also be inserted up to 1 cm lateral of the midline. A reduction of screw length to 7 mm (9 mm for the EOP) is proposed. Preoperative evaluation of the patient should be carried out by spiral CT with 1 mm slicing and sagittal reconstructions.
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European spine journal 8 (1999), S. 40-45
ISSN: 1432-0932
Keywords: Key words Leg length inequality ; Orthopaedics ; Posture ; Scoliosis
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract A small leg length inequality, either true or functional, can be implicated in the pathogenesis of numerous spinal disorders. The correction of a leg length inequality with the goal of treating a spinal pathology is often achieved with the use of a shoe lift. Little research has focused on the impact of this correction on the three-dimensional (3D) postural organisation. The goal of this study is to quantify in control subjects the 3D postural changes to the pelvis, trunk, scapular belt and head, induced by a shoe lift. The postural geometry of 20 female subjects (x – = 22, σ = 1.2) was evaluated using a motion analysis system for three randomised conditions: control, and right and left shoe lift. Acute postural adaptations were noted for all subjects, principally manifested through the tilt of the pelvis, asymmetric version of the left and right iliac bones, and a lateral shift of the pelvis and scapular belt. The difference in the version of the right and left iliac bones was positively associated with the pelvic tilt. Postural adaptations were noted to vary between subjects for rotation and postero-anterior shift of the pelvis and scapular belt. No notable differences between conditions were noted in the estimation of kyphosis and lordosis. The observed systematic and variable postural adaptations noted in the presence of a shoe lift reflects the unique constraints of the musculoskeletal system. This suggests that the global impact of a shoe lift on a patient’s posture should also be considered during treatment. This study provides a basis for comparison of future research involving pathological populations.
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European spine journal 8 (1999), S. 485-490
ISSN: 1432-0932
Keywords: Key words Thoracolumbar burst fractures ; Recombinant human bone morphogenetic protein-7 ; Transpedicular transplantation ; Clinical results ; Bone graft ; substitute
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract The study presented here is a pilot study in five patients with unstable thoracolumbar spine fractures treated with transpedicular OP-1 transplantation, short segment instrumentation and posterolateral fusion. Recombinant bone morphogenetic protein-7 in combination with a collagen carrier, also referred to as OP-1, has demonstrated ability to induce healing in long-bone segmental defects in dogs, rabbits and monkeys and to induce successful posterolateral spinal fusion in dogs without need for autogenous bone graft. Furthermore OP-1 has been demonstrated to be effective as a bone graft substitute when performing the PLIF maneuver in a sheep model. Five patients with single-level unstable burst fracture and no neurological impairment were treated with intracorporal OP-1 transplantation, posterior fixation (USS) and posterolateral fusion. One patient with osteomalacia and an L2 burst fracture had an additional intracorporal transplantation performed proximal to the instrumented segment, i.e. OP-1 into T 12 and autogenous bone into T 11. Follow-up time was 12–18 months. On serial radiographs, Cobb and kyphotic angles, as well as anterior, middle and posterior column heights, were measured. Serial CT scans were performed to determine the bone mineral density at fracture level. In one case, radiographic and CT evaluation after 3 and 6 months showed severe resorption at the site of transplantation, but after 12 months, new bone had started to fill in at the area of resorption. In all cases there was loss of correction with regard to anterior and middle column height and sagittal balance at the latest follow-up. These preliminary results regarding OP-1 as a bone graft substitute and stimulator of new bone formation have been disappointing, as the OP-1 device in this study was not capable of inducing an early sufficient structural bone support. There are indications to suggest that OP-1 application to a fracture site in humans might result in detrimental enhanced bone resorption as a primary event.
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European spine journal 8 (1999), S. 495-500
ISSN: 1432-0932
Keywords: Key words Burst fractures ; Outcome ; Short segment fixation ; Fusion
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract There continues to be controversy surrounding the management of thoracolumbar burst fractures. Numerous methods of fixation have been described for this injury, but to our knowledge, spinal fusion has always been part of the stabilising procedure, whether this involves an anterior or a posterior approach. Apart from an earlier publication from this centre, there have been no reports on the use of internal fixation without fusion for this type of fracture. The aim of the study was to determine the outcome of patients with thoracolumbar burst fractures who were treated with short segment pedicle screw fixation without fusion. This is a retrospective review of 28 consecutive patients who had short segment pedicle screw fixation of thoracolumbar burst fractures without fusion performed between 1990 and 1993. All patients underwent a clinical and radiological assessment by an independent observer. Outcome was measured using the Low Back Outcome Score. The minimum follow-up period was 2 years (mean 3.1 years). Fifty percent of patients achieved an excellent result with the Low Back Outcome Score, while 12% were assessed as good, 20% fair and 16% obtained a poor result. The only significant factor affecting outcome was the influence of a compensation claim (P 〈 0.05). The implant failure rate (14% of patients) and the clinical outcome was similar to that from series where fusion had been performed in addition to pedicle screw fixation. The results of this study support the view that posterolateral bone grafting is not necessary when managing patients with thoracolumbar burst fractures by short segment pedicle screw fixation.
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European spine journal 8 (1999), S. 501-504
ISSN: 1432-0932
Keywords: Key words Thoracic vertebrae ; Fractures ; Paraplegia ; Aortic ; rupture ; Intraoperative ; complications
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract Numerous vertebral fracture patterns have been reported in the literature. We present the case of a patient who sustained severe trauma to the back that resulted in a very unusual and not previously reported rotational injury consisting in complete 180° rotation of the T6 vertebral body along a vertical axis, with only limited anteroposterior and lateral displacement. An unsuspected aortic tear resulted in severe evolution with fatal outcome following surgical attempt. The aetiology of such displacement is unknown. The possibility of late vascular complications should be kept in mind while treating thoracic spine fractures with rotational displacement.
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European spine journal 8 (1999), S. 505-509
ISSN: 1432-0932
Keywords: Key words Cervical osteotomy ; Ankylosing spondylitis ; Internal fixation
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract Ankylosing spondylitis can produce severe fixed flexion deformity in the cervical spine. This deformity may be so disabling that it interferes with forward vision, chewing, swallowing and skin care under the chin. The only treatment available is an extension osteotomy of the cervical spine. Existing techniques of cervical osteotomy may be associated with risk of neurological injury. We describe a variation on an existing technique, which provides a controlled method of reduction at the osteotomy site, eliminating sagittal translation. The method employs a modular posterior cervical system consisting of lateral mass and thoracic pedicle screws linked to titanium rods. Our technique substitutes the titanium rod with a temporary malleable rod on one side, allowing controlled reduction of the osteotomy as this rod bends and slides through the thoracic clamps. Once reduction is complete definitive contoured rods are inserted to maintain the correction while fusion takes place. This method appears less hazardous by eliminating sagittal translation, and may reduce the risk of neurological injury during surgery. It achieves rigid internal fixation, obviating the need for a halo vest in the postoperative period.
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European spine journal 8 (1999), S. 323-328
ISSN: 1432-0932
Keywords: Key words Lumbar spinal stenosis ; ligamentum flavum ; histology ; Lumbar spinal stenosis ; ligamentum flavum ; calcification ; Lumbar spinal stenosis ; ligamentum flavum ; elastic fibres
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract The degree of calcification as well as the structural changes of the elastic fibres in the ligamentum flavum in patients with degenerative lumbar spinal stenosis were evaluated and the results were compared to those of patients without spinal stenosis. In 21 patients (13 male, 8 female) with lumbar spinal stenosis the ligamentum flavum was removed, histologically processed and stained. The calcification, the elastic/collagenous fibre ratio as well as the configuration of the fibres were evaluated with an image analyzing computer. As a control group, 20 ligaments of 10 human corpses were processed in the same way. The results were statistically analysed using the Mann-Whitney-Wilcoxon test (α = 0.05) and the t-test (α = 0.05). Nearly all the ligaments of patients with lumbar spinal stenosis were calcified (average 0.17%, maximum 3.8%) and showed relevant fibrosis with decreased elastic/collagenous fibre ratio. There was a significant correlation between age and histological changes (P 〈 0.05). In the control group we only found minimal calcification in 3 of 20 segments (average 0.015%). No relevant fibrosis was found and the configuration of elastic fibres showed no pathologic changes. The results of this study illustrate the important role of histological changes of the ligamentum flavum for the aetiology of lumbar spinal stenosis.
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European spine journal 8 (1999), S. 337-337
ISSN: 1432-0932
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
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European spine journal 8 (1999), S. 329-331
ISSN: 1432-0932
Keywords: Key words Congenital scoliosis ; Cor pulmonale ; Halofemoral ; traction ; Sliding rods
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract In severe congenital scoliosis, traction (whether with a halo or instrumental) is known to expose patients to neurologic complications. However, patients with restrictive lung disease may benefit from halo traction during the course of the surgical treatment. The goal of treatment of such deformities is, therefore, twofold: improvement of the respiratory function and avoidance of any neurologic complications. We report our technique to treat a 17-year-old girl with a multi-operated congenital scoliosis of 145 ° and cor pulmonale. Pre-operative halo gravity traction improved her vital capacity from 560 cc to 700 cc, but led to mild neurologic symptoms (clonus in the legs). To avoid further neurologic compromise, her first surgery consisted of posterior osteotomies and the implantation of two sliding rods connected to loose dominoes without any attempt at correction. Correction was then achieved over a 3-week period with a halofemoral traction. This allowed the two rods to slide while the neurologic status of the patient was monitored. Her definitive surgery consisted of locking the dominoes and the application of a contralateral rod. Satisfactory outcome was achieved for both correction of the deformity (without neurologic sequels) and improvement of her pulmonary function (1200 cc at 2 years). This technique using sliding rods in combination with halofemoral traction can be useful in high-risk, very severe congenital scoliosis.
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European spine journal 8 (1999), S. 354-359
ISSN: 1432-0932
Keywords: Key words Internal spinal fixator ; Load measurement ; Body position ; Telemetry ; Spine
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract Telemeterized internal spinal fixation devices were implanted in ten patients. The loads acting on the fixators were compared for different body positions, including standing, sitting, and lying in a supine, prone, and lateral position. Implant loads differed considerably from patient to patient depending, for example, on the indication for surgery and the surgical procedure. They were altered by anterior interbody fusion. Mostly, only small differences in implant loads were found for the various lying positions. Flexion bending moments were significantly higher in upright than in lying body positions. Loads on the fixators were not higher for sitting than for standing. Patients who have undergone mono- or bisegmental spine stabilization should therefore be allowed to sit as soon as they can leave the bed.
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European spine journal 8 (1999), S. 360-365
ISSN: 1432-0932
Keywords: Key words Cervical spine ; Odontoid ; Fracture ; Treatment ; Patient’s age
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract Odontoid fractures are frequent in patients over 70 years of age, and in patients over 80 years of age they form the majority of spinal fractures. In a retrospective analysis of 23 geriatric (〉 70 years) patients with a fracture of the odontoid, we compared some of the clinical features to a contemporary series of patients younger than 70 years of age. Whereas in the younger patients high-energy trauma accounted for the majority of the fractures, low-energy falls were the underlying cause in 90% of the odontoid fractures in the elderly. In contrast to the younger age group, in elderly patients predominantly type II fractures (95%) were identified. Anterior and posterior displacement were recorded with equal frequency on the first postinjury radiograph in the younger age group, whereas in geriatric patients displacement was mainly posterior. The number of associated injuries was significantly higher in younger patients. There was no difference in the occurrence of neurological deficits (13%) between the two age groups, and neurological compromise was mainly related to posterior dislocation of the odontoid in both groups. The overall complication rate was significantly higher in elderly patients (52.2% vs 32.7%), with an associated in-hospital mortality of 34.8%. Loss of reduction and non-union after non-operative treatment, a complicated postoperative course and complications due to associated injuries accounted primarily for this high complication rate. Elderly patients with a fracture of the odontoid are a high-risk group with a high morbidity and mortality rate. An aggressive diagnostic approach to detect unstable fractures and application of a halo device or early primary internal stabilisation of these fractures is recommended.
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European spine journal 8 (1999), S. 371-381
ISSN: 1432-0932
Keywords: Key words Atlanto-axial ; instability ; Transoral approach ; Decompression ; Rheumatoid ; arthritis ; C1/C2 fusion
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract Thirty-six consecutive patients with cervical spine instability due to rheumatoid arthritis (RA) were treated surgically according to a stage-related therapeutic concept. The aim of this study was to investigate the clinical results of these procedures. The initial change in RA of the cervical spine is atlanto-axial instability (AAI) due to incompetence of the cranio-cervical junction ligaments, followed by development of a peridontoid mass of granulation tissue. This results in inflammatory involvement of, and excessive dynamic forces on, the lateral masses of C1 and C2, leading to irreducible atlanto-axial kyphosis (AAK). Finally, cranial settling (CS) accompanied by subaxial subluxation (SAS) occurs. According to these three separate pathological and radiological lesions, the patients were divided into three therapeutic groups. Group I comprised 14 patients with isolated anterior AAI, who were treated by posterior wire fusion. Group II comprised 15 patients with irreducible AAK, who were treated by transoral odontoid resection. The fixation was done using anterior plating according to Harms in combination with posterior wire fusion according to Brooks. Group III comprised seven patients with CS and additional SAS, who were treated with occipito-cervical fusion. Pre- and postoperatively, evaluation was performed using the parameters pain (visual analog scale), range of motion (ROM), subjective improvement and Health Assessment Questionnaire (HAQ). The neurologic deficit was defined according to the classification proposed by Ranawat. Radiographs including lateral flexion and extension views, and MRI scans were obtained. The average clinical and radiographic follow-up of all patients was 50.7 ± 19.3 months (range 21–96 months). No perioperative fatality occurred. Postoperative pain was significantly relieved in all groups (P 〈 0.001). In group II a slight improvement in the HAQ was obtained. In groups I and II the ROM of all patients increased significantly (average gain of motion in group I: 11.3°± 7.8° for rotation; 7.8°± 5.6° for bending; average gain of motion in group II: 21.5°± 14.0° for rotation; 17.2°± 5.5° for bending), while it decreased significantly in group III (10.7°± 18.1° for rotation; 6.7°± 18.5° for bending). Preoperatively 27 patients had a manifest neurologic deficit. At follow-up four patients remained unchanged, all others improved by at least one Ranawat class. All patients, except one, showed solid bony fusion. According to the significantly improved postoperative subjective self-assessment and the clinical and radiological parameters, transoral plate fixation combined with posterior wire fixation after transoral odontoid resection represents an effective reliable and safe procedure for the treatment of irreducible AAK in rheumatoid arthritis.
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European spine journal 8 (1999), S. 396-401
ISSN: 1432-0932
Keywords: Key words MRI ; Disc ; degeneration ; Facet joint ; Osteoarthritis ; Lumbar spine
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract The role of MRI in assessing facet joint osteoarthritis is unclear. By developing a grading system for severity of facet joint osteoarthritis on MRI, the relationship between disc degeneration and facet joint osteoarthritis was determined. The accuracy of MRI in assessing facet joint osteoarthritis against CT was 94%. Under 40 years of age, the degree of disc degeneration varied among individuals. Over the age of 60, most of the discs were markedly degenerated. Under 40 years of age osteoarthritic changes in facet joints were minimal. Over the age of 60, variable degrees of facet joint osteoarthritis were observed but some facets did not show osteoarthritis. No facet joint osteoarthritis was found in the absence of disc degeneration and most facet joint osteoarthritis appeared at the intervertebral levels with advanced disc degeneration. Disc degeneration is more closely associated with aging than with facet joint osteoarthritis. The present study supports the hypothesis that “disc degeneration precedes facet joint osteoarthritis”, and also supports the concept that it may take 20 or more years to develop facet joint osteoarthritis following the onset of disc degeneration.
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European spine journal 8 (1999), S. 402-405
ISSN: 1432-0932
Keywords: Key words Scoliosis ; Brace ; treatment ; Self-image
Source: Springer Online Journal Archives 1860-2000
Topics: Medicine
Notes: Abstract To evaluate the effect of brace treatment on self-image in patients with adolescent idiopathic scoliosis, 54 consecutive patients admitted for brace treatment were interviewed before bracing. A prevalidated questionnaire including the following five aspects of self-image was used: (1) body-image, (2) self-perception of skills and talents, (3) emotional well-being, (4) relations with family, and (5) relations with others. As a control group, the answers of 3465 normal school children were used. Forty-six patients participated in a follow-up interview 1.7 (range 0.8–3.0) years later. In addition, during the first interview, the scoliosis patients answered selected questions about their social circumstances and attitudes towards their forthcoming brace treatment. Grossly, the patient group lived in stable family conditions with a high percentage (40%) of fathers and/or mothers with an academic education or with a high employee status. The patients’ relations with families were generally good. Nearly all believed that the brace would affect their posture, but only a few thought that wearing the brace would influence their growth. Two-thirds believed that it would be difficult to wear the brace, and often reflected on the use of it. There were no statistically significant differences between the scoliosis patients and the age-matched controls at the pre-bracing nor at the follow-up interviews. Neither were there any statistically significant differences between the answers of the scoliosis patients in the pre-bracing and follow-up interviews. This was valid for the total score as well as for each subscale item score. It is concluded that wearing the brace does not affect the self-image of adolescents with idiopathic scoliosis negatively.
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Constructive approximation 15 (1999), S. 109-134
ISSN: 1432-0940
Keywords: Key words. Numerical conformal mapping, Quadrilaterals, Conformal modules, Domain decomposition. AMS Classification. 30C30, 65E05, 30E10, 30C35.
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Abstract. We consider the conformal mapping of strip-like'' domains and derive a number of asymptotic results for computing the conformal modules of an associated class of quadrilaterals. These results are then used for the following two purposes: (a) to estimate the error of certain engineering formulas for measuring resistance values of integrated circuit networks; and (b) to compute the modules of complicated quadrilaterals of the type that occur frequently in engineering applications.
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Constructive approximation 15 (1999), S. 135-151
ISSN: 1432-0940
Keywords: Key words. Orthogonal matrix polynomials, Matrix moment problem. AMS Classification. 42C05, 44A60.
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Abstract. We describe the image through the Stieltjes transform of the set of solutions V of a matrix moment problem. We extend Riesz's theorem to the matrix setting, proving that those matrices of measures of V for which the matrix polynomials are dense in the corresponding ${\cal L}$ 2 space are precisely those whose Stieltjes transform is an extremal point (in the sense of convexity) of the image set.
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ISSN: 1432-0959
Source: Springer Online Journal Archives 1860-2000
Topics: Physics
Notes: In the Navier-Stokes equations the removal of the turbulent fluctuating velocities with a frequency above a certain fixed threshold, employed in the Large Eddy Simulation (LES), causes the appearance of a turbulent stress tensor that requires a number of closure assumptions. In this paper insufficiencies are demonstrated for those closure models which are based on a scalar eddy viscosity coefficient. A new model, based on a tensorial eddy viscosity, is therefore proposed; it employs the Germano identity [1] and allows dynamical evaluation of the single required input coefficient. The tensorial expression for the eddy viscosity is deduced by removing the widely used scalar assumption of the high-frequency viscous dissipation and replacing it by its tensorial counterpart arising in the balance of the Reynolds stress tensor. The numerical simulations performed for a lid driven cavity flow show that the proposed model allows to overcome the drawbacks encountered by the scalar eddy viscosity models.
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ISSN: 1432-0959
Source: Springer Online Journal Archives 1860-2000
Topics: Physics
Notes: Ice shelves consist of two layers, an upper layer of meteoric ice nourished by the flow from the connected inland ice and precipitation, and a lower layer of marine ice that is built by the melting and freezing processes at the ice-ocean interface and the accretion of frazil ice from the underlying ocean. The governing thermomechanical equations in the two layers are formulated as are the boundary and transition conditions that apply at the free surface, the material interface between the meteoric and the marine ice and the ice-ocean interface. The equations comprise in the bulk mass balances for the ice and the salt water (in marine ice), momentum balance and energy balance equations, and at the boundaries kinematic equations as well as jump conditions of mass, momentum and energy. The side boundary conditions involve a prescription of the mass flow along the grounding line from the inland ice and a kinematic law describing the mass loss by calving along the floating ice-shelf front. An appropriate scaling, in which the shallowness of the ice shelves is used, gives rise to the development of a perturbation scheme for the solution of the three-dimensional equations. Its lowest-order approximation – the shallow-shelf approximation (SSA) – shows the ice flow to be predominantly horizontal with a velocity field independent of depth, but strongly depth-dependent temperature and stress distributions. This zeroth order shallow-shelf approximation excludes the treatment of ice rumples, ice rises and the vicinity of the grounding line, but higher-order equations may to within second-order accuracy in the perturbation parameter accommodate for these more complicated effects. The scaling introduced finally leads to a vertical integrated system of non-linear partial integro-differential equations describing the ice flow and evolution equation for temperature and the free surfaces.
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ISSN: 1432-0959
Source: Springer Online Journal Archives 1860-2000
Topics: Physics
Notes: Relativistic Extended Thermodynamics is a very important scientific achievement of the last decades, and has inspired many subsequent authors to apply its methodology to lots of other possible applications. In short it furnishes field equations which are “closed” by imposing the relativity principle and the entropy principle up to second order, with respect to equilibrium; the linear closure is explicitly reported. Here these principles are imposed up to fourth order; the second order closure is explicitly reported, while the subsequent ones are reported as implicit functions. It is also proved that no internal inconsistencies are generated by the theory. In fact, in the process of computations many complicated conditi | 2020-07-06 11:18:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35827183723449707, "perplexity": 7494.209208688383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655880616.1/warc/CC-MAIN-20200706104839-20200706134839-00017.warc.gz"} |
https://brilliant.org/problems/solvers-of-this-must-be-the-king/ | # Solvers of this must be the King!
Geometry Level 3
Let ABC be a triangle with AB = 26, AC = 28, BC = 30. Let X, Y , Z be the midpoints of arcs BC, CA, AB (not containing the opposite vertices) respectively on the circumcircle of ABC. Let P be the midpoint of arc BC containing point A. Suppose lines BP and XZ meet at M , while lines CP and XY meet at N. Find the square of the distance from X to MN.
×
Problem Loading...
Note Loading...
Set Loading... | 2017-01-19 11:04:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9088889360427856, "perplexity": 1007.3260293608071}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280587.1/warc/CC-MAIN-20170116095120-00451-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://yuvalfilmus.cs.technion.ac.il/publications/papers/?id=858 | # PublicationsPapers
## Asymptotic redundancy and prolixity
Yuval Dagan, Yuval Filmus and Shay Moran
Manuscript
Given a distribution $\mu$ and a set of queries $Q$ (for example, all comparison queries), the cost of $Q$ on $\mu$ is the average depth of a decision tree that locates an item in the support of $\mu$ using only queries from $Q$.
The cost of any set of queries on $\mu$ is always at least the entropy $H(\mu)$, and the redundancy of $Q$ is the maximal gap between the cost of $Q$ on a distribution and its entropy.
The prolixity of a set of queries is defined in the same way, with the entropy replaced by the cost of the optimal unrestricted decision tree.
The redundancy and prolixity of a set of queries is often achieved on degenerate distributions which have very low entropy, and this suggests studying their asymptotic variants, in which we consider distributions whose min-entropy tends to infinity.
Gallager showed that the asymptotic redundancy of unrestricted decision trees is 0.086.
We obtain bounds, and in some case determine, the non-asymptotic and asymptotic redundancy and prolixity of several sets of queries, including comparison queries, comparison and equality queries, and interval queries.
The results in this paper are extracted from the full version of our STOC paper. | 2021-09-19 14:12:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.797447681427002, "perplexity": 619.7876388514968}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056890.28/warc/CC-MAIN-20210919125659-20210919155659-00305.warc.gz"} |
https://www.unige.ch/gap/quantum/publications:bib:zambrini_cruzeiro2019a | # Bell Inequalities with One Bit of Communication
Authors: Emmanuel Zambrini Cruzeiro, Nicolas Gisin Entropy 21, 1-12 (2019) http://dx.doi.org/10.3390/e21020171 We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved the scenario where Alice and Bob choose between three inputs, finding a total of 668 inequivalent facet inequalities (with respect to relabelings of inputs and outputs). We also show that some of these inequalities are constructed from facet inequalities found in scenarios without communication, that is, the well-known Bell inequalities. zambrini_cruzeiro2019a.pdf
# BibTeX Source
@Article{e21020171,
AUTHOR = {Zambrini Cruzeiro, Emmanuel and Gisin, Nicolas},
TITLE = {Bell Inequalities with One Bit of Communication},
JOURNAL = {Entropy},
VOLUME = {21},
YEAR = {2019},
NUMBER = {2},
pages = {1-12},
ARTICLE-NUMBER = {171},
URL = {http://www.mdpi.com/1099-4300/21/2/171},
ISSN = {1099-4300},
ABSTRACT = {We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved the scenario where Alice and Bob choose between three inputs, finding a total of 668 inequivalent facet inequalities (with respect to relabelings of inputs and outputs). We also show that some of these inequalities are constructed from facet inequalities found in scenarios without communication, that is, the well-known Bell inequalities.},
DOI = {10.3390/e21020171}
} | 2019-05-20 17:14:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8237136006355286, "perplexity": 1307.242657771514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256082.54/warc/CC-MAIN-20190520162024-20190520184024-00135.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-sum-of-the-series-n-2-from-n-0-to-n-4 | # How do you find the sum of the series n^2 from n=0 to n=4?
Nov 22, 2016
${\sum}_{n = 0}^{4} {n}^{2} = 30$
#### Explanation:
We need the standard formula ${\sum}_{r = 1}^{n} {r}^{2} = \frac{1}{6} n \left(n + 1\right) \left(2 n + 1\right)$
$\therefore {\sum}_{n = 0}^{4} {n}^{2} = \frac{1}{6} \left(4\right) \left(4 + 1\right) \left(8 + 1\right)$
$\therefore {\sum}_{n = 0}^{4} {n}^{2} = \frac{1}{6} \left(4\right) \left(5\right) \left(9\right)$
$\therefore {\sum}_{n = 0}^{4} {n}^{2} = 30$
Alternatively, as there are only a few terms we could just write them out and compute the sum;
${\sum}_{n = 0}^{4} {n}^{2} = {0}^{2} + {1}^{2} + {2}^{2} + {3}^{2} + {4}^{2}$
$\therefore {\sum}_{n = 0}^{4} {n}^{2} = 1 + 4 + 9 + 16$
$\therefore {\sum}_{n = 0}^{4} {n}^{2} = 30$, as before | 2019-07-21 06:50:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9613580703735352, "perplexity": 624.7400480214957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526931.25/warc/CC-MAIN-20190721061720-20190721083720-00546.warc.gz"} |
https://www.jkcs.or.kr/journal/view.php?number=4458 | J. Korean Ceram. Soc. > Volume 34(2); 1997 > Article
Journal of the Korean Ceramic Society 1997;34(2): 115.
에멀젼 건조법에 의한 Bi-2223 초전도 분말과 테이프 제조 장중철, 이응상, 이희균1, 홍계원1 한양대학교 무기재료공학과1한국 원자력 연구소 초전도 연구실 The Preparation of Bi-2223 Superconducting Powder and Tape by Emulsion Drying Method ABSTRACT The powder preparation by using emulsion drying method, one of the chemical powder fabrication methods has the advantages; easy to control the chemical stoichiometry and to fabricate homogeneously fine particles. In the present study, the initial morphology and size distribution of the powder fabricated by using emulsion dry-ing method were controlled and were improved the homogeneity. By carefully controlling the mixing ratio of oil phase and aqueous solution and surfactant of preventing emulsion separation, the Bi(Pb)-Sr-Ca-Cu-O su-perconducting powders were prepared. The properties of the superconducting powder fabricated by this method and the microstructures and superconducting properties of the pelletized samples were investigated. The microstructures and electric properties of the tapes prepared by oxide powder-in-tube method were in-vestigated. The fabricated powder was spherical with less than 1$mu$m but most of them was agglomerated with 2~5$mu$m in size. The critical temperature of the pelletized sample annealed at 84$0^{circ}C$ for 72 hours in oxygen par-tial pressure of 1/13atm in Ar atmosphere was 108K. And the critical current of the first and second annealed tapes in air prepared by oxide powder-in-tube process were 0.4A and 1.5A, respectively. Key words: Emulsion drying method, Bi(Pb)-Sr-Ca-Cu-O superconducting powder, Critical temperature, Critical current
TOOLS | 2021-05-13 07:09:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.609257698059082, "perplexity": 14195.882484494674}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991537.32/warc/CC-MAIN-20210513045934-20210513075934-00178.warc.gz"} |
http://www.bccvietnam.com/819tzad/71d4db-filter-in-electronics | ## filter in electronics
What Is A Filter. MTK Electronics, Inc. is a leading designer and virtually integrated manufacturer of custom magnetics, EMI/RFI filters used in the military and commercial applications. On the other hand in a capacitor filter, it is varying inversely with the load resistance. The figure below shows the circuit diagram of a LC filter. High Pass Filter- Explained. The filters in this illustration are all fifth-order low-pass filters. {\displaystyle \ s} s The power supply block diagram clearly explains that a filter circuit is needed after the rectifier circuit. The number of elements determines the order of the filter. Any given filter transfer function may be implemented in any electronic filter topology. Let us try to construct a few filters, using these two components. For distributed-element types, see, A low-pass electronic filter realised by an, The American Radio Relay League, Inc.: "The ARRL Handbook, 1968" page 50, CS1 maint: multiple names: authors list (, Filter (signal processing) § Technologies, Learn how and when to remove this template message, National Semiconductor AN-779 (TI SNOA224a), Fundamentals of Electrical Engineering and Electronics, Some Interesting Filter Design Configurations & Transformations, https://en.wikipedia.org/w/index.php?title=Electronic_filter&oldid=973665021, Articles lacking in-text citations from March 2013, Srpskohrvatski / ÑÑпÑкоÑ
ÑваÑÑки, Creative Commons Attribution-ShareAlike License, This page was last edited on 18 August 2020, at 14:25. {\displaystyle s} To separate and to combine several telephone conversations onto a single channel can be done using analog filters. Thus we, get the desired pure dc output at the load. The simplest passive filters, RC and RL filters, include only one reactive element, except hybrid LC filter which is characterized by inductance and capacitance integrated in one element.[1]. A filter is an AC circuit that separates some frequencies from others within mixed-frequency signals. As a capacitor allows ac through it and blocks dc, a filter called Shunt Capacitor Filter can be constructed using a capacitor, connected in shunt, as shown in the following figure. : The transfer function of all linear time-invariant filters, when constructed of lumped components (as opposed to distributed components such as transmission lines), will be the ratio of two polynomials in A filter circuit can be constructed using both inductor and capacitor in order to obtain a better output where the efficiencies of both inductor and capacitor can be used. The remaining dc components present in the signal are collected at the output. s Active filters are implemented using a combination of passive and active (amplifying) components, and require an outside power source. These inductive or capacitive pieces of metal are called stubs. However, their upper frequency limit is limited by the bandwidth of the amplifiers. Although not widely used today as a result of the fact that their response is inferior to other forms of filter, they do have the advantage that the design equations can be particularly easy to calculate, and this means that they can be used by many who do not have filter design experience. Multipole LC filters provide greater control of response form, bandwidth and transition bands. Filters of some sort are essential to the operation of most electronic circuits. That means that it can be inserted in a transmission line, resulting in the high frequencies being passed and low frequencies being reflected. A wide variety of uses of filters in electronics options are available to you, such as material. The outputs of all these rectifier circuits contains some ripple factor. Filters using passive filter and active filter technology can be further classified by the particular electronic filter topology used to implement them. Alibaba.com offers 3,301 uses of filters in electronics products. The figure below shows a circuit for $\pi$ filter (Pi-filter). The following figure shows the functionality of a filter circuit. Together with improved filters by Otto Zobel and others, these filters are known as image parameter filters. Now, from that signal, few more ac components if any present are grounded so that we get a pure dc output. Electronic filters can be: low-pass filter… is constant over a frequency range from zero to cut off frequency, . Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. Passive implementations of linear filters are based on combinations of resistors (R), inductors (L) and capacitors (C). , i.e. If such a pulsating d.c. is applied in an electronics circuit, it will produce a hum. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. Unlike the image method, there is no need for impedance matching networks at the terminations as the effects of the terminating resistors are included in the analysis from the start.[4]. The above filter types discussed are constructed using an inductor or a capacitor. s The output of this filter is a better one than the previous ones. In electronics there is a wide range of frequencies to deal with. The filters we have discussed in our previous articles are also efficient in removing AC ripples from the output voltage of rectifier, but Pi filter is more efficient in removing ripples as it consists of one more capacitor at the input side. RF filters are used to remove or accept signals that fall in certain areas of the radio spectrum. You need to filter them to get the specific frequency that you want. These components can be in discrete packages or part of an integrated circuit. Frequency response of hi-pass filter. In other words, high-frequency signals go through much easier and low-frequency signals have a much harder getting through, which is why it's a high pass filter. If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to high-frequency signals than low-frequency signals and therefore is a high-pass filter. That is, using components and interconnections that, in analysis, can be considered to exist at a single point. Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. Analog filter is typically used in electronics and is considered as a basic building block of signal processing. Filters are used in many areas of electronics. And there’s more. The particular implementation â analog or digital, passive or active â makes no difference; their output would be the same. Resistors on their own have no frequency-selective properties, but are added to inductors and capacitors to determine the time-constants of the circuit, and therefore the frequencies to which it responds. The transfer function A major step forward was taken by Wilhelm Cauer who founded the field of network synthesis around the time of World War II. and then passes no signal above that frequency is called an ideal low-pass filter. X A Bode plot is a graph plotting waveform amplitude or phase on one axis and frequency on the other. In this circuit, we have a capacitor in parallel, then an inductor in series, followed by another capacitor in parallel. What Is A Filter Circuit A rectifier is actually required to produce pure d.c. supply for using at various places in the electronics circuits. Electronic filters are electrical circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both. {\displaystyle X(s)} An L filter consists of two reactive elements, one in series and one in parallel. A filter in which the signal passes through an inductor, or in which a capacitor provides a path to ground, presents less attenuation to low-frequency signals than high-frequency signals and is therefore a low-pass filter. See the article on linear filters for details on their design and analysis. The rectified output when passed through this filter, the ac components present in the signal are grounded through the capacitor which allows ac components. . The high-pass T filter in the illustration, has a very low impedance at high frequencies, and a very high impedance at low frequencies. Capacitor C2 − Now the signal is further smoothened using this capacitor so that it allows any ac component present in the signal, which the inductor has failed to block. The constant k filters were the first filters that could approach an ideal filter for of response. Here, two capacitors and one inductor are connected in the form of Ï shaped network. They can be: The most common types of electronic filters are linear filters, regardless of other aspects of their design. s Operational amplifiers are frequently used in active filter designs. This is another type of filter circuit which is very commonly used. {\displaystyle \ s} This kind of analysis is usually only carried out for simple filters of 1st or 2nd order. A high pass filter is a filter which passes high-frequency signals and blocks, or impedes, low-frequency signals. 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https://brainduniya.com/thermometry/ | # Thermometer
## What is a Thermometer?
A thermometer is defined as a device which is used to measure the temperature of a body. Temperature is basically a measure of the amount of kinetic energy of the particles possessed by the body or system.
The process of measurement of temperature of anything is called Thermometry. Nowadays, there are many different types of thermometers are used in thermometry.
Following are of most important –
1. Glass tube thermometer.
2. Thermistor.
3. Thermocouple.
5. Pyrometer etc.
### Thermometry
The branch of physics which deals with the measurement of temperature is called thermometry.
• Temperature is a measure of amount of kinetic energy possessed by a body.
• Thermometry is the process of measuring of this energy by using thermometers.
### Thermometric Property
The property of a material which has linear relation with rise of temperature is called thermometric property. A thermometer uses the thermometric property of a material to measure temperature.
Example –
1. Due to thermal expansion height of a mercury column in a glass tube changes linearly with rise in temperature. This property is used in the working principle of a glass tube mercury thermometer.
2. By Charle’s law, the pressure of a gas changes linearly with rise in temperature at constant volume. This property is used in the working principle of a Constant volume gas thermometers.
3. By Boyle’s law, the volume of a gas changes linearly with rise in temperature at constant pressure. This property is used in the working principle of Constant pressure gas thermometers.
4. By Ohm’s law, the electrical resistance of a metal wire changes linearly with rise in temperature. This property is used in the working principle of Platinum resistance thermometers.
5. By Seebeck effect, e.m.f produced in a thermocouple is proportional to the temperature difference of junctions. This property is used in the working principle of thermoelectric thermometer uses
## Thermometer Scale
A thermometer scale is consists of a graduated temperature scale between two fixed points. To construct a temperature scale, following fixed points are chosen –
1. Lower fixed point – It is the temperature at which pure ice melts at standard pressure.
2. Upper fixed point – It is the temperature at which pure water boils at standard pressure.
Range between these two fixed temperatures is called fundamental interval. Fundamental interval is sub divided into equal divisions.
Different types of commonly used thermometer scales are tabulated below –
Thermometer scale Lower fixed point Upper fixed point Range CELSIUS SCALE 0 \degree C 100 \degree C 100 divisions. FAHRENHEIT SCALE 32 \degree F 212 \degree F 180 divisions. REAUMER SCALE 0 \degree R 80 \degree R 80 divisions. KELVIN SCALE 273 \degree K 373 \degree C 100 divisions.
### Conversion of Thermometer Scales
A relation between different thermometer scales has derived for used in conversion of the temperature from one scale to another scale.
• This relation is based on the principle of thermal expansion of substance.
• Thermal expansion between upper and lower fixed points is common for all the scales of measurement.
Let, ( T_C, \ T_F, \ T_R, \ T_K ) are the temperatures of a body measured in Celsius, Fahrenheit, Reaumer and Kelvin scales respectively.
Then, \left ( \frac {\text {Temperature of body - Lower fixed point}}{\text {Range}} \right ) will be common for all scales.
Therefore, \left ( \frac { T_C - 0 }{ 100 } \right ) = \left ( \frac { T_F - 32 }{ 180 } \right ) = \left ( \frac { T_R - 0 }{ 80 } \right ) = \left ( \frac { T_K - 273 }{ 100 } \right )
## Absolute Scale of Thermometer
According to Charle’s law, if ( V_{t} ) and ( V_{0} ) are the volumes at ( t \degree C ) and ( 0 \degree C ) respectively of a given mass of a gas at constant pressure ( P ) , then –
V_t = V_0 \left ( 1 + \frac { t }{ 273 } \right )
Therefore, volume of gas below ( 0 \degree C ) will be less than ( V_0 ) .
Thus, volume of gas at ( - t \degree C ) will be –
V_{-t} = V_0 \left ( 1 - \frac { t }{ 273 } \right )
Therefore, a decrease in temperature results in decrease in volume of the gas. This has been shown by plotting the volume of a given mass of gas against temperature at constant pressure as shown in figure.
• The graph is a straight line.
• If we extrapolate the straight line it meets the temperature axis at ( - 273 \degree C ) , where volume of gas becomes zero.
Hence, a gas occupies zero volume at ( - 273 \degree C ) .
Therefore, a temperature of less than ( - 273 \degree C ) is not possible to achieve, because the volume of gas will become negative which is not feasible.
• Hence, the possible lowest temperature of ( - 273 \degree C ) at which a gas have zero volume and zero pressure and entire molecular motion of gas stops, is called the absolute zero temperature.
• Kelvin suggested a new scale of temperature starting with ( - 273 \degree C ) as its lower fixed point. This scale of temperature is known as Kelvin scale or absolute scale of temperature.
In this scale ice point or triple point of water is assigned a value of ( 273 \degree K ) .
Therefore, \quad T (K) = ( t \degree C + 273 )
## Types of Thermometer
Thermometers are classified according to the thermometric material used in it. Thermometers are of following types –
### 1.Liquid Thermometer
• Thermometric property – Linear expansion of liquid column with rise in temperature.
• Governing thermometric relation
T = \left [ \left ( \frac { l_t - l_0 }{ l_{100} - l_0 } \right ) \times 100 \degree C \right ]
Where, ( l ) is the length of liquid column.
Examples
1. Mercury thermometer.
2. Alcohol thermometer.
### 2.Gas Thermometer
• Thermometric property – Linear change in pressure of gases with rise in temperature at constant volume.
• Governing thermometric relation
T = \left [ \left ( \frac { P_t - P_0 }{ P_{100} - P_0 } \right ) \times 100 \degree C \right ]
Where, ( P ) is the pressure of gas at constant volume.
Examples
1. Helium gas thermometer.
2. Nitrogen gas thermometer.
1. These thermometers are more sensitive than liquid thermometers because gas expansion is large with small change in temperature.
2. These are most accurate and used to calibrate other thermometers.
3. These thermometers can be used for a wide range of measurement such as ( -270 \degree C ) using helium gas and up to ( 1600 \degree C ) using nitrogen gas.
### 3.Resistance Thermometer
• Thermometric property – Linear variations of electrical resistance or resistivity of conductors with rise in temperature.
• Governing thermometric relation
T = \left [ \left ( \frac { R_t - R_0 }{ R_{100} - R_0 } \right ) \times 100 \degree C \right ]
Where, ( R ) is the electrical resistance of a conductor.
Examples
1. Platinum resistance thermometer.
2. Germanium resistance thermometer.
It works on the principle of wheat stone bridge.
### 4.Thermocouple Thermometer
T = \left [ \left ( \frac { ξ_t - ξ_0 }{ ξ_{100} - ξ_0 } \right ) \times 100 \degree C \right ]
Where, ( ξ ) is the induced e.m.f due to thermo-electric effect.
Examples
1. Chromel – Alumel thermometer.
2. Iron – Constantan thermometer.
Normal range of thermo-electric thermometer is ( - 200 \degree C ) \ to \ ( 1600 \degree C ) . In industrial applications these are used as probes and thermo-sensors.
### 5.Optical Pyrometers
These are non contact type radiation thermometers. These are used to measure very high temperature.
• Thermometric property – Variations of radiation energy with change in temperature.
• Governing thermometric relation –
\lambda_{m} T = b ( A constant).
This constant is called Wien’s constant.
Where, ( \lambda_{m} ) is the wavelength of radiation of source.
Pyrometers are of two types – | 2023-01-30 04:52:07 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9610349535942078, "perplexity": 1624.0771001975966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499801.40/warc/CC-MAIN-20230130034805-20230130064805-00081.warc.gz"} |
https://proofwiki.org/wiki/Finite_Complement_Space_is_Irreducible | # Finite Complement Space is Irreducible
## Theorem
Let $T = \struct {S, \tau}$ be a finite complement topology on an infinite set $S$.
Then $T$ is irreducible.
## Proof
Let $U_1, U_2 \in \tau$ be non-empty open sets of $T$.
By definition, $S$ is infinite.
By definition, $\relcomp S {U_1}$ and $\relcomp S {U_2}$ are finite.
From Complement of Finite Subset of Infinite Set is Infinite, it follows that $U_1$ and $U_2$ are both infinite.
$U_1 \cap U_2\ne \O$
That is, $U_1$ and $U_2$ intersect each other.
As $U_1$ and $U_2$ are arbitrary, the result follows by definition of irreducible space.
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https://www.greencarcongress.com/2016/09/20160927-eea.html | EEA: large-scale roll-out of EVs will help EU shift to green transport, but may challenge power grid
27 September 2016
A large scale roll-out of electric cars on European roads would result in significantly lower greenhouse gas emissions and lower levels of certain air pollutants, according to a new European Environment Agency (EEA) assessment. However, widespread use of such vehicles would pose challenges for Europe’s power grid in meeting increased electricity demand.
The EEA briefing Electric vehicles and the energy sector — impacts on Europe’s future emissions looks at the impact of different scenarios that take into account the increased use of electric cars and their effect on the European Union’s (EU) energy system, and on emissions of greenhouse gases and selected air pollutants.
Electric vehicles powered by renewable energy sources can play a bridging role in the EU’s plans to move towards a greener, more sustainable transport system, and in meeting its goal to reduce greenhouse gas emissions by 80‒95 % by 2050. However, larger numbers of electric vehicles will not be enough for the shift to a low-carbon economy.
—Hans Bruyninckx, EEA Executive Director
The report explores several scenarios, including one model in which electric cars have an 80% share of the EU’s total car fleet in 2050. Additional electricity generation will be required in the EU to meet the higher energy demand. The need for extra power will be higher if other sectors like industry or households do not follow through on planned energy efficiency improvements. The use of renewable energy in 2050 will also have an effect on the level of emissions from the power-generating sector.
Overall, the resulting CO2 emission reductions in the road transport sector would outweigh the higher emissions caused by the continued use of fossil fuels in the power-generating sector. In the EU, a net reduction of 255 million tonnes of CO2 could be delivered in 2050. This amount is equivalent to around 10% of the total emissions estimated for that year.
However, in countries with a high share of fossil power plants, environmental benefits would be lower. This would also lower the benefits of using electric vehicles in these countries.
An 80% share of electric vehicles would also significantly reduce overall emissions of certain air pollutants such as nitrogen oxides (NOx) and particulate matter (PM). For other pollutants such as sulphur dioxide (SO2), emissions could increase due to the continued use of coal in the electricity generation sector.
Assuming an 80% share of EVs in 2050. Source: EEA. Click to enlarge.
A larger number of electric cars on the road may pose future challenges for Europe’s power production capacities and put stress on existing power grids. Under the 80% scenario, the share of Europe’s total electricity consumption from electric vehicles would increase from around 0.03% in 2014, to 9.5% by 2050.
A more extensive infrastructure providing more public charging points would be key as well as increased power capacity able to handle a larger European car fleet. The assessment stresses that closer coordination between the road transport and energy sectors on policy making and investments will be crucial.
The EEA complemented the release of the report with the publication of a new EEA guide on electric vehicles in Europe, which provides a non-technical summary of the latest information on electric cars in Europe, including those with hybrid technologies.
The guide specifically focuses on the electric passenger cars currently on the market, and describes how they work and the challenges and incentives in place they face in achieving their broader use. Sales and use of electric vehicles are increasing, but they currently only make up 1.2% of total passenger car sales in the EU. Current estimates also show that electric cars only account for 0.15% of Europe’s total car fleet.
A lot of it will come down to having cars with large enough batteries to give flexibility in charging times.
Thus, if you have to charge every night, you have to do it there and then; but if you only have to charge every second night, you could schedule it when it is windiest, or sunniest.
When you think about solar, you have to install loads of charge points at people's places of work so they can charge during the day.
Europe is already awash with renewables, especially Germany, and this would be one way of soaking it up.
If there isn't enough energy, you would have to use hybrids or PHEVs.
I think the challenges for every region will be different but where I live I expect the market will adjust quite easily. We have lots of sun. We have many work place parking spots with plug-ins for block heaters; we have a need for heat in winter which can be integrated into CHP's in many locations. And if all that fails we can always build an NPP.
My biggest concern is that the cost of electricity is cheap relative gasoline and when EV's become affordable there will be a major increase in travel.
I think that a Heat Pump(s) (Ground Source Geothermal as opposed to Air Source exchange) in combination with CHP is the optimal for residential/commercial space heating. Natural Gas is cheap in most NA suburban/urban areas, so it is slow to develop. There is a lot of wasted potential here. Perhaps CHP should be mandated wherever NG/Propane space heating is applied.
We are located in the rural foot hills of the metro DC area. I built the house we are in 25 years ago, and the WaterFurnace Geothermal has worked great all this time. I wish we had cheap NG here as well. I would like to add CHP if we had an Economical source of NG/Propane. The Grid electrical costs are relatively low here.
The report explored several scenarios and only one, a model in which electric cars have an 80% share of the EU’s total car fleet in 2050, is giving them cause to worry. Please remember that in this scenario the EU goes from having 0.15% of Europe’s total car fleet being EVs now to 80% in just 34 years.
A9.5% increase in electricity consumption, by going from ICEV to EVs (at 80%)in 34 years, is nothing to worry about.
Better use of e-energy could easily liberate 9.5% for EVs. Secondly, EV owners could charge at night when plenty of unused electricity is available or install their own solar panels to recharge the EV's battery or offset the extra load.
EPRI in the U.S. says we have enough night time power capacity for one million cars.
The main obstacle to realising transition from fossil fuels is reluctance on the part of politicians to give clear notice to miners and grid operators that renewable will be supported and that the change will happen at an accelerating rate.
Battery technology and proven vehicles models are improving at astonishing rate,although there is a lot of inertia from old technology owners still to overcome.
The capacity for renewable power generation is also capable of meeting any target, unfortunately the bastions of some grid operators and miners would rather sit on their thumbs or employ political lobbyists to run scare campaigns.
If we could see the needed increase in transfer of investment from fossil fuel extraction, then the increase in CO2 emissions can be turned.
Thus, if you have to charge every night, you have to do it there and then; but if you only have to charge every second night, you could schedule it when it is windiest, or sunniest.
The sky can be cloudy and the winds calm for days and weeks. The idea of EVs as the white knight riding to the rescue of flaky, unreliable ruinable generators is attractive, but wrong. It won't work because it can't work, and it leads to fossl-fuel lock in: just what the oil and gas industry are pushing for.
Europe is already awash with renewables, especially Germany, and this would be one way of soaking it up.
IIRC, I calculated last year that Germany's existing PV would require on the order of 1 Chevy Volt per capita to absorb its sunny-day surpluses. It must be quite a bit more now.
in this scenario the EU goes from having 0.15% of Europe’s total car fleet being EVs now to 80% in just 34 years.
Note that the active LDV fleet will turn over at least 3x in 34 years.
A large and growing EV fleet plus a carbon tax will feed a rapid growth of nuclear power, where politics allows. The load-levelling effect of overnight charging, plus the price-floor on backup power created by a carbon tax, reverses the economic war of "renewables" on nuclear. Making "renewables" forego subsidies and mandates and accept tax-backed wholesale prices will make them temporarily attractive, but that attraction will disappear when they are all selling into a saturated wholesale market whenever they are generating. Generators who are able to build e.g. Cal Abel's salt-storage LMFBR plant will just buy up zero-price electricity, dump it to heaters in their salt tanks, and sell the energy back to the grid when the surplus is gone and it's worth something again. The wind and PV farms will either shrink so that such surpluses don't occur any more, or just fold.
@EP,
I am under no illusions that you can build a wind+solar+battery grid, you will always need a dispatchable source, such as gas to balance the load when, as you point out, the wind doesn't blow and the sun doesn't shine.
And that dispatchable source could be as large as the whole grid because both can happen at the same time.
The problem of a solar+wind+gas grid will be overabundance, and for this, we can use the EVs to soak up some of the excess.
Obviously, you could just build a nuclear+gas grid as the French have done, but this is not politically acceptable or affordable in most of "the west". Which is a huge shame as we could solve the CO2 problem at a stroke with nukes. (The national carbon suicides of Germany and Japan really annoy me - keep the old Nukes going as long as possible, IMO).
The problem of a solar+wind+gas grid will be overabundance
No, it will be feast-or-famine. Even if capacity can be way overbuilt for the average, events like the BPA multi-week wind droughts will produce famine conditions as well.
for this, we can use the EVs to soak up some of the excess.
Only by sacrificing their primary purpose, which is mobility. The watchword for EVs today is "range anxiety", caused by batteries which are too small (or charging opportunities too infrequent) to handle the contingencies of life. If EVs are going to soak up excesses, they have to have a lot of un-charged and available battery capacity. If you reduce the effective range of EVs in order to have that "sponge" available, you slash the utility of the vehicles and bring range anxiety right back.
Germany is pushing H2 as the storage element, allowing months rather than hours of capacity. The problem with H2 is that the round-trip losses are massive, and the net cost so high that no article on the matter dares to deal with it head-on. It is ALL a scam.
The ideal clean e-energy source is more a matter of cost than technology used.
Recent NPPs cost over $0.22/kWh and near future units will probably cost up to$0.30/kWh and takes up to 12 years to build.
Clean Solar or Wind (with storage) cost $0.05/kWh +$0.10/kWh for a total of $0.15/kWh and less than 2 years to build. The choice is 100% in favour of Solar+Wind and Germany? Info: The current retailed price for electricity in France is between$0.16/kWh to $0.19/kWh (USD) depending on max load purchased (3 KW to 36 KW). The current retailed price for homes in Ontario-Canada is$0.13/kWh (CAN) plus sale taxes.
The current average retailed price for homes anywhere in Quebec-Canada is $0.065/kWh (CAN) plus sale taxes. Basically, electricity cost 3X and/or 2X more for nuclear energy in France and Ontario than for clean Hydro-Wind in Quebec. That says it all? NPPs are more costly to build and operate. The current retailed price for electricity in France is between$0.16/kWh to $0.19/kWh (USD) depending on max load purchased (3 KW to 36 KW). The current average retailed price for homes anywhere in Quebec-Canada is$0.065/kWh (CAN) plus sale taxes.
Which is not comparable in the least. In France, "there are several taxes that are applied to electricity consumption (see below), and when put together, they represent about 31% of the cost of electricity for residential customers". In short, the French taxes alone are almost as much as the HQ base rate. The German "renewable" surcharge alone is MORE than the HQ base rate, at €0.06354/kWh (USD 0.0714/kWh)*.
electricity cost 3X and/or 2X more for nuclear energy in France and Ontario than for clean Hydro-Wind in Quebec.
So tell us, Harvey... how are you going to give Quebec's low population density and large amount of rainfall and relief to France, so the French can live up to your expectations for them?
That says it all? NPPs are more costly to build and operate.
And they're both cheaper and much cleaner than the "Green" solutions of Denmark and Germany; the German rate is about €0.287/kWh (USD 0.323/kWh).
HQ should have refurbished Gentilly in the anticipation of carbon taxes and cross-border sales opportunities, but ideology triumphed over economics and the environment both.
The current retailed price for electricity in France is between $0.16/kWh to$0.19/kWh (USD) depending on max load purchased (3 KW to 36 KW).
The current average retailed price for homes anywhere in Quebec-Canada is $0.065/kWh (CAN) plus sale taxes. Which is not comparable in the least. In France, "there are several taxes that are applied to electricity consumption (see below), and when put together, they represent about 31% of the cost of electricity for residential customers" [1]. In short, the French taxes alone are almost as much as the HQ base rate. The German "renewable" surcharge alone is MORE than the HQ base rate, at €0.06354/kWh (USD 0.0714/kWh) [2]. electricity cost 3X and/or 2X more for nuclear energy in France and Ontario than for clean Hydro-Wind in Quebec. So tell us, Harvey... how are you going to give Quebec's low population density and large amount of rainfall and relief to France, so the French can live up to your expectations for them? That says it all? NPPs are more costly to build and operate. And they're both cheaper and much cleaner than the "Green" solutions of Denmark and Germany; the German rate is about €0.287/kWh (USD 0.323/kWh). HQ should have refurbished Gentilly in the anticipation of carbon taxes and cross-border sales opportunities, but ideology triumphed over economics and the environment both. Links in next comment, because they send it to moderation. [1] http://en.selectra.info/energy-france/guides/electricity-cost#structure-electricity-bill-France [2] https://www.cleanenergywire.org/factsheets/what-german-households-pay-power I compared cost of electricity for homes in Nuclear France and Nuclear Ontario with/versus Quebec single rate Hydro/Wind electricity. Even at those low cross network single rates, HQ's profits are close to 30%. QC government gets close to 15% dividends to pay for schools and hospitals and to reduce deficits. Granted that sale taxes are as bit higher (instead of Dividends) in France but are a slight bit lower in Ontario. France could go more Wind/Solar + storage (@ about$0.15/kWh) without raising retail prices much. Solar could be installed in many places including roofs etc. H2 could be an excellent storage medium.
PHEVs with Long Electric Range (PHEVLERs) and battery electric vehicles (BEVs) do not have to challenge the electric power grid. Over the coming years we can generate enough additional electricity to power both transportation and domestic needs by gradually adding 6 to 8 Kw of solar or wind electric generators for each PHEVLER or BEV sold.
In addition, economical low power EV charging stations should be installed at all the places where EVs are parked for long periods of time (e.g. homes and workplaces). This will allow intelligent nighttime charging when other electric demands are low, and/or daytime charging when electricity from solar PV and wind is plentiful. In the long run, the management of energy by the electric power companies will be needed to manage and coordinate between the renewably generated electricity sources, the batteries for electricity storage and the bidirectional chargers in BEVs and PHEVLERs.
See: "PHEVLERs are the Zero CO2 Clean Green Machines of the Future"
http://www.greencarcongress.com/2016/04/20160422-phevler.html
Dr. Frank, I don't know what your personal experience is with PHEVs, but I've been driving one for 3.5 years now and you don't need the long-range feature to slash fuel demand by 2/3. I used to drive a turbodiesel sedan averaging about 38 MPG, but my Fusion Energi's lifetime average is 129.7 MPG as of tonight, more than 3x as much.
Your prescription of solar or wind generators is, however, somewhere between misguided and flat wrong. The thing which most affects my fuel-replacement isn't wattage of generation, but availability of supply. The car takes a rated maximum of 240 VAC 16 A*, so anything more than what its charger can take is wasted. Periods of dark and calm would throw it back on liquid fuel.
If we expect to replace petroleum and charge our vehicles during off-peak hours, we have to have absolutely reliable power available to do it. Wind and solar fail utterly at this; doing it carbon-free requires hydro or nuclear.
* I'd love to see if it could handle rectified pulsating DC from 208 VAC 3φ, which would have a lower peak voltage but considerably higher RMS voltage and could sustain closer to 4.4 kW of power at the same current. A lot of the chargers I use are fed from 208 VAC 3φ and the car's peak charging power on them is about 3.3 kW.
EGOsphere knows more than Dr. Frank...no way.
The comments to this entry are closed. | 2023-01-30 21:14:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33207640051841736, "perplexity": 2763.5695271045092}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499829.29/warc/CC-MAIN-20230130201044-20230130231044-00542.warc.gz"} |
https://forum.bebac.at/forum_entry.php?id=18787&order=time | ## 100% raw data presentation in BA report [Bioanalytics]
Hi John,
» Does anyone know what items are required to be presented in the "100% Raw data" tables in a BA report (For FDA)? Is there such a list of required items?
FDA – no idea.
In the EU inspectors love to see the time of analysis of each sample (in order to check whether the batch was interrupted and/or the validated bench-top/autosampler stability exhausted). Hence, a table with these columns:
sample № – timestamp – subject id – sample № / period (or: scheduled time) – period – concentration
If’ve seen ones where the dilution factor or alternatively a lower sample volume (if validated) is given in an additional column. Never saw retention times in any table. 20% of chromatograms are mandatory over here and nowadays most CROs provide 100% anyway. If an assessor is interested in the RTs (s)he can look it up there.
» […] I have came across reports from several labs and they don't have the same # of items presented in this "100% raw data" table. Of course the crucial ones are presented, but some such as dilution factor, analysis date, IS and analyte retention times are absent from the tables generated by some labs.
OK, that’s a different story. Never seen a single table including everything (would be confusing – at least for me). Generally different ones:
• Results of unknows (as above)
• Calibrators
• QC samples
• Repeats
• ISR
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Ing. Helmut Schütz | 2022-05-26 17:13:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22514677047729492, "perplexity": 7519.445671839128}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662619221.81/warc/CC-MAIN-20220526162749-20220526192749-00482.warc.gz"} |
https://brilliant.org/problems/can-you-solve-this-8/ | # Can you solve this?
Algebra Level 1
If the value of
$2^{1998} - 2^{1997} - 2^{1996} + 2^{1995} = k \cdot 2^{1995}$
What is the value of $$k?$$
× | 2017-07-27 14:53:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5294711589813232, "perplexity": 5329.0897622430775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549428300.23/warc/CC-MAIN-20170727142514-20170727162514-00532.warc.gz"} |
https://stats.stackexchange.com/questions/314500/variance-comparison-between-ols-and-wls | # variance comparison between OLS and WLS
Suppose $Y \sim N(X\beta, \Sigma)$. Ordinary LS $\hat{\beta_{OLS}} = (X'X)^{-1}X'y$ and weighted LS $\hat{\beta_{WLS} }= (X'WX)^{-1}X'Wy$, where $W = \Sigma^{-1}$. It is well known that $Var(\hat{\beta_{OLS}}) \ge Var(\hat{\beta_{WLS}})$. This implies for the predicted value $Var(X\hat{\beta_{OLS}}) \ge Var(X\hat{\beta_{WLS}})$. Can we conclude that for the residual $Var(Y-X\hat{\beta_{OLS}}) \le Var(Y-X\hat{\beta_{WLS}})$ ?
I think this does not hold since the variance decomposition does not hold for the OLS under $Y \sim N(X\beta, \Sigma)$. Does anybody have any thought on this ? | 2019-05-23 23:16:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9807172417640686, "perplexity": 178.97155592943986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257432.60/warc/CC-MAIN-20190523224154-20190524010154-00022.warc.gz"} |
https://jcsentertains.com/6b2an/velocity-before-impact-formula-9ffb0a | We have step-by-step solutions for … They are four initial velocity formulas: (1) If time, acceleration and final velocity are provided, the initial velocity is articulated as. Velocity = (Xf ‰ÛÒ Xi) / t. Velocity = d / t (where d= displacement and t = change in time) Velocity, being a vector quantity, has both magnitude and direction. As an object falls from rest, its gravitational potential energy is converted to kinetic energy. These applications will - due to browser restrictions - send data between your browser and our server. The SI unit for flow rate is m 3 /s, but a number of other units for Q are in common use. Due to geometry, L 1 is perpendicular to the line passing through the center of … In the horizontal direction, the object travels at a constant speed v 0 during the flight. Anonymous. During an impact, the energy of a moving object is converted into work, and force plays an important role. The misconception is that speed and velocity are the same things but in reality, it is just the opposite. For a given initial velocity of an object, you can multiply the acceleration due to a force by the time the force is applied and add it to the initial velocity to get the final velocity. In this example, we will use the time of 8 seconds. Fmax = 1/2 (2000 kg) (16.7 m/s)2 / (0.5 m), Note that the gravitation force (weight) acting on the car is only. The energy of the falling body when it hits the ground can be calculated using (4) as. The Velocity of the Ball just before it hits the ground: The horizontal velocity V x=20 m/s is always the in this problem. Note! For example, you may be in a car or on a walk when you suddenly accelerate in a particular direction. It is the velocity at which the motion starts. The impact creates a force 28 times gravity!! The coefficient of restitution is a parameter of a ball/surface, and reflects the fraction of velocity just after the bounce divided by the velocity just before. The line L 1 is drawn at a tangent to both balls at the point of contact. The F term is force, the m is mass, the v means velocity (think speed with direction) and the t is time. Since you know velocity, mass, and kinetic energy, can you predict the force of impact. So taking V o = 0 you get T = sqrt(2d/g) and V=sqrt(2dg). A. Please read AddThis Privacy for more information. what is the formula for the speed of a falling object? A force acting upon an object for some duration of time results in an impulse. Homework Statement A person jumps from the roof of a house 3.4 meters high. = J, which is of course equal to its initial potential energy. Initial Velocity is the velocity at time interval t = 0 and it is represented by u. The initial velocity of the ball is 15.0 m/s horizontally. What is the average force exerted on the 0.057-kg tennis ball by Venus Williams’ racquet, assuming that the ball’s speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)? You do this by calculating the kinetic energy of the asteroid just before it strikes the earth. 2). Initial Velocity Formula. Thus, the impact velocity is simply composed of the initial x velocity, v_x and the final y velocity, v_y. For example, the solution for the impact velocity of a falling object is much easier by energy methods. The conservation of the total momentum before and after the collision is expressed by: + = +. Impact forces acts on falling objects hitting ground, crashing cars and similar The dynamic kinetic energy of a moving object, like a falling ball or a driving car, can be expressed as E = 1/2 m v2 (1) After two seconds, you're falling 19.6 m/s, and so on. Source(s): https://shorte.im/a9coJ. The relative velocity has the same magnitude, but opposite sign, before and after the collision. Velocity as a term has, however, become so widely used in the Agile community that it makes no sense for me to refer to it as Speed. For this example we use an impact distance of 3/4 inch (0.0625 ft) to calculate the impact force: In metric units - person with weight 90 kg, falling distance 1.2 m and impact distance 2 cm: Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse! If the mass is m = kg, then the kinetic energy just before impact is equal to K.E. Its initial speed is 10 m/s. The impact force can be calculated as, Favg = (2000 kg) (9.81 m/s2) (14.2 m) / (0.5 m). If the ball has a mass 5 Kg and moving with the velocity of 12 m/s collides with a stationary ball of mass 7 kg and comes to rest. The table below outlines how the impact level of a risk is determined in the ERM risk assessment process. AddThis use cookies for handling links to social media. In this case mass of liquid striking the plate per second = ρa (V – v) Relative velocity normal to the plate before impact = (V – v) sin θ. sqrt(v_x^2 + v_y^2) = magnitude = V (speed) angle = atan(v_y/v_x) Now, a … Impulses cause objects to change their momentum. Cookies are only used in the browser to improve user experience. To create an equation for the force of any impact, you can set the equations for energy and work equal to each other and solve for force. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 meters. You can target the Engineering ToolBox by using AdWords Managed Placements. If the collision was elastic, e = 1. Velocity is constant so that final velocity is same as initial velocity. The elastic collision formula is applied to calculate the mass or velocity of the elastic bodies. The coefficient of restitution between the ball and club is 0.79. Also, assume it is free falling (no air resistance) and the average time it takes to hit the ground it 1.16 seconds. The dynamic energy in a falling object at the impact moment when it hits the ground can be calculated as, Fweight = force due to gravity - or weight (N, lbf), ag = acceleration of gravity (9.81 m/s2, 32.17405 ft/s2), If the dynamic energy from the fall is converted to impact work - equation 2 and 4 can be combined to, The deformation slow-down distance can be expressed as, The same car as above falls from height 14.2 m and crashes on the crumple zone with the front down on a massive concrete tarmac. Roughly 90% of shock absorber applications can be modelled if the following 4 factors are known: 1. The coefficient of restitution (COR), also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide.It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision. 2. https://goo.gl/JQ8NysCalculus Impact Velocity. The average velocity formula describes the relationship between the length of your route and the time it takes to travel. The front impacts 0.5 m (slow down distance) as above. Trying to figure out if a character who fell off a 600' cliff would have a second round so they could try and use the Fly power before hitting the bottom. Ifafter head on impact the velocity of ba B is observed to be 3 m/s to the right, the coefficient of restitution is 0.4kg 0.6 kg B. Instantaneous velocity, as the name itself suggests, is the velocity of a moving object, at a particular instant of time. After one second, you're falling 9.8 m/s. Everybody knows about velocity but there is a misconception about it. Note that the National Highway Traffic Safety Administration (NHTSA) states that "the maximum chest acceleration shall not exceed 60 times gravity for time periods longer than 3 milliseconds". The force calculator can be used to solve for mass, velocity, impact force and time contact during impact. In this case, just like displacement and velocity, acceleration, a, is a vector. I need the formulas for: speed at impact… Dorthey. The quantity impulse is calculated by multiplying force and time. Calculate the final free fall speed (just before hitting the ground) with the formula v = v₀ + gt = 0 + 9.80665 * 8 = 78.45 m/s. Mass to slow down m (kg) 2. These same two concepts could be depicted by a table illustrating how the x- and y-component of the velocity vary with time. A person sitting inside the car with seat belts on will de-accelerate with a force 28 times gravity. The sign changes because A and B are approaching each other before the collision but moving apart after the collision. If the mass is m = kg, then the kinetic energy just before impact is equal to K.E. In an elastic collision, both momentum and kinetic energy are conserved. I'm pretty sure you would get about 15 m/s. v = distance / time = 500m / … Likewise, the conservation of the total kinetic energy is expressed by: + = +. The initial velocity can be broken down using an equation relating the sine and cosine: 1 = cos 2 θ + sin 2 θ. For example, if you drive a car for a distance of 70 miles in one hour, your average velocity equals 70 mph. Note! If an object is dropped from height h = m, then the velocity just before impact is v = m/s. A body is projected upward at an angle of 30 o with the horizontal from a building 5 meter high. Only emails and answers are saved in our archive. To compute the velocity after impact, u, we use the formula: u = root 2gh. h. where: v f is the velocity at impact of a free fall ; h is the height of the free fall; g is the acceleration due to gravity; This equation, Free Fall (Velocity at Impact), references 1 page Show. A perfectly inelastic collision has a coefficient of … The magnitude of our total velocity is going to be equal to square root-- this is just straight from the Pythagorean theorem-- of 5.21 squared plus 29.03 squared. Newton's laws are used for the solution of many standard problems, but often there are methods using energy which are more straightforward. Simplify the experimental ratio of kinetic energy before collision to the kinetic energy after collision, 1/2*mv^2/1/2(m+M)u^2 to a theoretical ratio involving only the masses by using equation 1 (found below). If the mass of his torso (excluding legs) is 41 kg. When a crumple zone deforms in a car crash the average impact force is designed to be as constant as possible. If the collision was perfectly inelastic, e = 0. If you are at the surface of the earth the acceleration is g = 32.2 feet/sec 2 or 9.8 meter/sec 2.Integrating the acceleration once gives V = V o + g T where V o is the initial velocity, presumably zero, and T is the time of fall. Well you need one more fact, the acceleration. Acceleration of gravity is 10 m/s Shocks per hour C (hr) W 1 Kinetic enerngy (Nm) W 2 Propelling energy (Nm) W 3 Total energy per cycle … Please Subscribe here, thank you!!! The velocity formula is a simple one and we can best explain it with a simple example. After 5.00 s, what is the magnitude of the velocity of the ball? A person with weight (gravitational force) of 200 lbs (lbf) falls from a 4 feet high table. Decide whether the object has an initial velocity. The impact on a human body can be difficult to determine since it depends on how the body hits the ground - which part of the body, the angle of the body and/or if hands are used to protect the body and so on. The velocity that is given has both x and y components, because it is in a direction 60.0° up from the horizontal (x) direction. Projectile motion equations. Choose how long the object is falling. The simplest approach is to assume that that everyone on a team can do everything. One or more holidays with greater than normal impact occur during the period; The Simplest Approach. The funny triangle actually means "change in". Impact Force Free online impact force calculator with which you can calculate the impact force on impact of a moving body given its mass, velocity at impact, and time contact during impact. The impact force can be calculated as. - The deformation slow-down distance is very important and the key to limit the forces acting on passengers in a car crash. For the zero launch angle, there is no vertical component in the initial velocity. Finding velocity before impact Thread starter seanbugler; Start date Sep 15, 2009; Sep 15, 2009 #1 seanbugler. - a car crash in 90 km/h (25 m/s) compares to a fall from 32 m!! Escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero. You measure that the bullet has a mass of 50 grams, that the wooden block has a mass of 10.0 kilograms, and that upon impact, the block rises 50.0 centimeters into the air. This is equal to the impact energy. where V is the volume and t is the elapsed time. But the question doesn’t say you know the object mass or how high it was freed. We don't save this data. Then use the velocity formula to find the velocity Hence, the formula for velocity can be expressed as: Velocity = (Final position ‰ÛÒ Initial position) / Change in time . P = (Mass striking the plate per second) x (Change in velocity normal to the plate) P = M (V sin θ – 0) = ρaV.V sin θ ∴ P = ρaV 2 sin θ Newton . Thank you! impact velocity (v) 4.188294 {m/s} impacting object mass (mᵢ) 2 {kg} gravitational acceleration (g) 9.80663139027614 {m/s²} beam mass (m/L) 2.551972 {kg/m} THS 42.4x2.6 made from steel: beam depth (d) 0.0424 {m} outside diameter of THS 26.9x4: beam length (L) 1 {m} Young's modulus of beam (E) 207000000000 {N/m²} Young's modulus for steel: second beam moment … I'm pretty sure you would get about 15 m/s. From there, calculating the force of an impact is relatively easy. Impact lasts for 0.00043 s. The launch angle of the ball after impact is 13.1°. Textbook solution for Physics: Principles with Applications 6th Edition Douglas C. Giancoli Chapter 7 Problem 76GP. The front of the car impacts 0.5 m (the deformation distance). Impact Force from Falling Object Even though the application of conservation of energy to a falling object allows us to predict its impact velocity and kinetic energy, we cannot predict its impact force without knowing how far it travels after impact. Relative velocity normal to the plate after impact = 0 In the previous section, we have introduced the basic velocity equation, but as you … Assume that you’ve just managed to hit a groundball in a softball […] The duration of the flight before the object hits the ground is given as T = \sqrt {\frac {2H} {g}}. And finally, the impulse an object experiences is equal to the momentum change that results from it. What we have in the above formula and what we will actually be measuring is a Scalar – the speed of the team. When calculating the velocity of the object, follow these steps: First, change the minutes into seconds: 60 x 3 minutes = 180 seconds. Calculate the final free fall speed (just before hitting the ground) with the formula v = … The front of the car impacts 0.5 m (the deformation distance). Determining how fast something will be traveling upon impact when it is released from a given height. In an impact where the object is not deformed - the work made by the impact force slowing down the moving object equals to the work done by a spring force - and can be expressed as, Fmax = maximum force at the end of the deformation (N, lbf), In a car crash the dynamic energy is converted to work and equation 1 and 2 can be combined to, The average impact force can be calculated as, Favg = 1/2 m v2 / s (3b), The deformation slow-down distance can be calculated as. Using physics, you can calculate what happens when you swerve. Consider particles 1 and 2 with masses m 1, m 2, and velocities u 1, u 2 before collision, v 1, v 2 after collision. Answer: The velocity of the ball after 5.00 s has two components. Just prior to impact with a golf ball (0.042 kg), a clubhead (0.195 kg) is travelling with a velocity of 33.7 m/s horizontally towards the target and a vertical velocity of 0 m/s. or V = = v_x i + v_y j. During impact the ball behaves as a linear spring with a … For example, the final velocity (v f) formula that uses initial velocity (v i), acceleration (a) and time (t) is: v_f = v_i + aΔt. 4 0. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. The average velocity formula and velocity units. Some of our calculators and applications let you save application data to your local computer. = J, which is of course equal to its initial potential energy. Determining how fast something will be traveling upon impact when it is released from a given height. Velocity component normal to the plate before impact = V sin θ. Velocity component normal to the plate after impact = 0. It is the speed needed to “break free” from a gravitational field without further propulsion. Let the angle between the jet and the plate be θ. Let the velocity of the jet and the vane be V and v in the same direction. Calculate the velocity of the ball of mass 7 Kg ball after the collision. The difference between initial and final velocity in equations for conservation of momentum or equations of motion tell you the velocity of an object before and after something happens. For example, the heart of a resting adult pumps blood at a rate of 5.00 liters per minute (L/min). 1). Consider particles 1 and 2 with masses m 1, m 2, and velocities u 1, u 2 before collision, v 1, v 2 after collision. Projectile Motion Formulas Questions: 1) A child kicks a soccer ball off of the top of a hill. If you want to promote your products or services in the Engineering ToolBox - please use Google Adwords. Final velocity before the object hits the ground. For instance, you have an object that travels at 500 meters in three minutes. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected. If an object of mass m= The duration of the flight before the object hits the ground is given as T = \sqrt{\frac{2H}{g}}. Click hereto get an answer to your question ️ The velocities of two steel balls before impact are shown. How to solve: A rubber ball with a mass of 0.3 kg is dropped onto a steel plate. Impact velocity v D (m/s) 3. You can easily estimate the impact energy of an asteroid. Model/formula for bouncing ball. ∴ Force exerted by the jet normal to the plate . Uff, that was a lot of calculations! Calculate final velocity before the object hits the ground! Plugging in those values gives you your result: The initial velocity is This is probably not true but it can be a starting point in deciding how to adjust velocity. Solved Examples. Average velocity cannot tell you how the velocity of an object changed at particular instants of time. Example 1. Propelling force F (N) 4. The calculator uses the standard formula from Newtonian physics to figure out how long before the falling object goes splat: The force of gravity, g = 9.8 m/s 2 Gravity accelerates you at 9.8 meters per second per second. Note that the gravitation force (weight) acting on the car is … This is probably not true but it can be a starting point in deciding how to adjust velocity. If an object is dropped from height h = m, then the velocity just before impact is v = m/s. The important concept depicted in the above vector diagram is that the horizontal velocity remains constant during the course of the trajectory and the vertical velocity changes by 9.8 m/s every second. Comment/Request Worked great, and was quick to use while we took out 5 minute break. Likewise, the conservation of the total kinetic energy is expressed by: Integrating once more gives d = V o T + gT 2 /2. Textbook solution for Physics: Principles with Applications 6th Edition Douglas C. Giancoli Chapter 7 Problem 76GP. The coefficient of restitution (COR), also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide.It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision. The application of the conservation of energy principle provides a powerful tool for problem solving. One or more holidays with greater than normal impact occur during the period; The Simplest Approach. Then use the velocity formula to find the velocity. All the answers go to math and gravity acceleration or energy. Besides, most of the people consider them the same and use them interchangeably. Write the formula for computing the uncertainty in u. 6 years ago. en: impact force energy work acceleration, es: fuerza de impacto aceleración trabajo de energÃa, de: Schlagkraft Energiearbeit Beschleunigung. thus . The vertical velocity starts out at zero V y @0D=0 but increases to V y @tD which is calculated using V y @tD2=V y @0D2+2 g Y =2 g Y . A car with a mass of 2000 kg drives with speed 60 km/h (16.7 m/s) before it crashes into a massive concrete wall. If you did a video analysis of the falling piano, you could get the velocity right before it hits. % of shock absorber velocity before impact formula can be as constant as possible often there methods! Now i assume you are asking about the impact energy of the total momentum before and the. Team can do everything ( the deformation distance ) as which is of course equal to the be. 2M/S Projectile Motion Formulas Questions: 1 torso decelerates over an approximate distance of 70 in. You can easily estimate the impact creates a force 28 times gravity ( same parameters above... The kinetic energy of a moving object, at a rate of 5.00 liters per minute ( L/min.. An important role some of our calculators and Applications let you save data! Not true but it can be a starting point in deciding how to the., impact force energy work acceleration, es: fuerza de impacto aceleración de... ’ s being pulled on by gravity write the formula for the zero launch angle there! Integrating once more gives d = V o = 0 you get t sqrt. Collision was perfectly velocity before impact formula or V = < v_x, v_y point deciding... L/Min ): impact force is designed to be as constant as.... At 500 meters in three minutes km/h ( 25 m/s ) 2 / ( 0.5 m ( the distance., 2009 ; Sep 15, 2009 ; Sep 15, 2009 # 1 seanbugler a and B approaching! For … the velocity after impact, and kinetic energy all this information could someone please how... 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Formulas for: speed at impact, the formula V = < v_x, v_y > = v_x +... In Physics involve calculating an initial and final velocity velocity before impact formula same as velocity! In our archive f max velocity before impact formula 1/2 ( 2000 kg ) 2 V m/s. Of course equal to its initial potential energy visitor statistics force exerted by the and! And examples of calculation shock absorber Applications can be modelled if the mass is =... Years, 9... this means that the impact time will be 64 gravity. Lbs ( lbf ) falls from a building 5 meter high collision formula is applied calculate... 0 and it is the elapsed time constant speed V 0 during the period ; the simplest is. Basic information for Engineering and Design of Technical Applications and t is the velocity of the conservation energy! Are only used in the same thing as before, what is the velocity the... Fall just before impact Thread starter seanbugler ; Start date Sep 15, 2009 1... - a car or on a team can do everything also a useful approach the! The time it takes to travel is no vertical component in the initial velocity. Physics: Principles with Applications 6th Edition Douglas C. Giancoli Chapter 7 problem.! Will talk about the impact time the magnitude ( speed ) and V=sqrt ( 2dg ) his so., most of the falling body when it hits the surface to improve user experience near the earth object or. Values and do exactly the same things but in reality, it just. S has two components 4 m/s 2m/s Projectile Motion Formulas Questions: 1 is formula. Application of the car impacts 0.5 m ( the deformation slow-down distance is very important and the time of seconds. From rest, its gravitational potential energy approach is to assume that that on! A tool permits the calculation of the ball after 5.00 s, what do. Are the same things but in reality, it is the velocity formula is a simple.! ( gravitational force ) of 200 lbs ( lbf ) falls from a given height Basic information Engineering... Si unit for flow rate is m 3 /s, but opposite sign before... Lasts for 0.00043 s. the launch angle of the car impacts 0.5 m ) = 558 kN ( ).: impact force is designed to be perfectly inelastic collision has a coefficient of,. Your route and the plate it takes to travel the ball and is..., we use the velocity velocity before impact formula ) falls from a gravitational field without further propulsion with 90 km/h 25. There is no vertical component in the initial velocity formula is applied to calculate mass...
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https://quantumcomputing.stackexchange.com/questions/1958/are-true-projective-measurements-possible-experimentally?noredirect=1 | # Are true Projective Measurements possible experimentally?
I have heard various talks at my institution from experimentalists (who all happened to be working on superconducting qubits) that the textbook idea of true "Projective" measurement is not what happens in real-life experiments. Each time I asked them to elaborate, and they say that "weak" measurements are what happen in reality.
I assume that by "projective" measurements they mean a measurement on a quantum state like the following:
$$P\vert\psi\rangle=P(a\vert\uparrow\rangle+ b\vert\downarrow\rangle)=\vert\uparrow\rangle \,\mathrm{or}\, \vert\downarrow\rangle$$
In other words, a measurement which fully collapses the qubit.
However, if I take the experimentalist's statement that real measurements are more like strong "weak"-measurements, then I run into Busch's theorem, which says roughly that you only get as much information as how strongly you measure. In other words, I can't get around not doing a full projective measurement, I need to do so to get the state information
So, I have two main questions:
1. Why is it thought that projective measurements cannot be performed experimentally? What happens instead?
2. What is the appropriate framework to think about experimental measurement in quantum computing systems that is actually realistic? Both a qualitative and quantitative picture would be appreciated.
• To clarify the scope of the question: you're using superconducting qubits just to give some background, but your question is general, right? (As opposed to the more particular question 'Are true projective measurements possible experimentally using superconducting qubits?'). Apr 30 '18 at 5:18
• Good point, yes I referred to superconducting qubits but I am interested in the general question. Although, I've only heard this point of view from those who study superconducting qubits, but that may be my limited experience. Apr 30 '18 at 5:50
Let's step back from QC for a moment and think about a textbook example: the projector onto position, $|x\rangle$. This projective measurement is obviously unphysical, as the eigenstates of $|x\rangle$ are themselves unphysical due to the uncertainty principle. The real measurement of position, then, is one with some uncertainty. One can treat this either as a weak measurement of position, or as a projective measurement onto a non-orthonormal basis (a strong POVM), where the various basis elements have some support on multiple values of $x$: say pixels on a detector.
Going back into QC, most systems' measurements are pretty close to projective, or are 'strong' measurements at the least. In some systems, like ion traps, the readout can be thought of as a series of weak measurements that collectively form a strong one. A photon counter, on the other hand, is very close to a projective measurement with some odd projectors due to finite efficiency--no click corresponds to a projector onto $|0\rangle + (1-e)^n|n\rangle$, for instance.
On the other hand, that projector doesn't leave behind the state listed above, because the apparatus also absorbs the photon.
To sum up, thinking of things as POVMs (Positive operator-valued measures) is probably the most-right intuition, where you can think of the outcomes of the POVM mostly as non-orthonormal projectors. Non-projective POVMs also exist, but are less common in practice in systems I've thought about.
• Thanks for the answer! I do have some concerns though. While the eigenstate of the position operator is unphysical for very fundamental reasons (special relativity, QFT etc.), the states of the harmonic oscillator are not unphysical. So I don't totally follow the logic here. Is it accurate to say that measurements in current implementations have too large uncertainties to be seen as projective? Apr 30 '18 at 17:05
• Also, could you go into a bit more detail about POVMs and how that formalism works? That's a concept I'm not familiar with. Thanks again! Apr 30 '18 at 17:07
• Yes--and measurements of harmonic-oscillator-like things tend to be more like textbook projective measurements than measurements of continuous variables. Photon number, for instance, is a harmonic oscillator almost precisely, and you can think of a perfect number-counting detector as pretty close to a projective measurement. Similarly, measuring the state of an electron's energy level, if done strongly, is very close to a projective measurement. It does take time to get signal, and so can be done 'weakly' as well, though not particularly usefully. Apr 30 '18 at 17:12
• POVMs are to density matrices as projective measurements are to kets, roughly speaking. As long as 1. All input states output some measurement outcome and 2. some probability conservation requirements hold, it turns out that you don't need orthogonal projectors to make your measurement work. The simplest example is a 4-outcome qubit measurement: we choose randomly between measuring {$|0\rangle,|1\rangle$} and {$\0±1\rangle$}, and then measure in one of those bases. This whole operation can be treated as either a conditional gate and a projective meassurement, or as a 4-outcome POVM. Apr 30 '18 at 17:17
• @D.H.Smith I'm a bit late to the party: But I'm not sure that I agree with This projective measurement is obviously unphysical, as the eigenstates of |x⟩ are themselves unphysical due to the uncertainty principle. Any pair of incompatible observables will have a related uncertainty relation. Will they therefore all be 'unphysical'? What do you mean by this? Jun 12 '18 at 9:12
An assumption in general measurements: The measuring device itself has no degrees of freedom and it does not couple with the qudit in any form of interaction, which is not true.
1) A projective measurement is ideal and non-realistic because it is always assumed that there is no extension of this Projector to a bigger Hilbert space or more degrees of freedom than the Qudit degrees of freedom. But actually what happens experimentally is the fact that, to measure on a qubit we always have to assign a classical operation called a "Pointer" that is a link between your classical outcome by the measurement and the quantum measurement. By doing this the system is always exposed to a non-unitary and open environment where the measurement becomes non-deal and the information is leaked in outer degrees of freedom when the system coupled with the measuring device. This in principle itself is a nature's inherent property that forbids an ideal Quantum Measurement.
2) To go about this, as you pointed out, the true realistic method is a weak measurement method. To minimize the coupling with the environement and be close to a true quantum measurment.
However, there are certain cases which are special, certain states called "Pointer states" allow true ideal measurement w.r.t particular Measurement operators (Because they retain their quantum properties like Coherence, entanglement, etc) in the smaller Hilbert space and do not couple with higher degrees of freedom of the measuring device. | 2021-10-17 03:49:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7128690481185913, "perplexity": 579.4087066602701}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585120.89/warc/CC-MAIN-20211017021554-20211017051554-00465.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/mcrf.2011.1.353 | # American Institute of Mathematical Sciences
September 2011, 1(3): 353-389. doi: 10.3934/mcrf.2011.1.353
## Global stabilization of a coupled system of two generalized Korteweg-de Vries type equations posed on a finite domain
1 Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box 68530, CEP 21941-909, Rio de Janeiro, RJ, Brazil, Brazil 2 Institut Élie Cartan, UMR 7502 UHP/CNRS/INRIA, B.P. 239, F-54506 Vandoeuvre-lès-Nancy Cedex
Received November 2010 Revised April 2011 Published September 2011
The purpose of this work is to study the internal stabilization of a coupled system of two generalized Korteweg-de Vries equations under the effect of a localized damping term. The exponential stability, as well as, the global existence of weak solutions are investigated when the exponent in the nonlinear term ranges over the interval $[1, 4)$. To obtain the decay we use multiplier techniques combined with compactness arguments and reduce the problem to prove a unique continuation property for weak solutions. Here, the unique continuation is obtained via the usual Carleman estimate.
Citation: Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Global stabilization of a coupled system of two generalized Korteweg-de Vries type equations posed on a finite domain. Mathematical Control & Related Fields, 2011, 1 (3) : 353-389. doi: 10.3934/mcrf.2011.1.353
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[1] Eduardo Cerpa, Emmanuelle Crépeau. Rapid exponential stabilization for a linear Korteweg-de Vries equation. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 655-668. doi: 10.3934/dcdsb.2009.11.655 [2] Eduardo Cerpa. Control of a Korteweg-de Vries equation: A tutorial. Mathematical Control & Related Fields, 2014, 4 (1) : 45-99. doi: 10.3934/mcrf.2014.4.45 [3] M. Agrotis, S. Lafortune, P.G. Kevrekidis. On a discrete version of the Korteweg-De Vries equation. Conference Publications, 2005, 2005 (Special) : 22-29. doi: 10.3934/proc.2005.2005.22 [4] Guolian Wang, Boling Guo. Stochastic Korteweg-de Vries equation driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5255-5272. doi: 10.3934/dcds.2015.35.5255 [5] Muhammad Usman, Bing-Yu Zhang. Forced oscillations of the Korteweg-de Vries equation on a bounded domain and their stability. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1509-1523. doi: 10.3934/dcds.2010.26.1509 [6] Pierre Garnier. Damping to prevent the blow-up of the korteweg-de vries equation. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1455-1470. doi: 10.3934/cpaa.2017069 [7] Ludovick Gagnon. Qualitative description of the particle trajectories for the N-solitons solution of the Korteweg-de Vries equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1489-1507. doi: 10.3934/dcds.2017061 [8] Arnaud Debussche, Jacques Printems. Convergence of a semi-discrete scheme for the stochastic Korteweg-de Vries equation. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 761-781. doi: 10.3934/dcdsb.2006.6.761 [9] Qifan Li. Local well-posedness for the periodic Korteweg-de Vries equation in analytic Gevrey classes. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1097-1109. doi: 10.3934/cpaa.2012.11.1097 [10] Anne de Bouard, Eric Gautier. Exit problems related to the persistence of solitons for the Korteweg-de Vries equation with small noise. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 857-871. doi: 10.3934/dcds.2010.26.857 [11] Shou-Fu Tian. Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval. Communications on Pure & Applied Analysis, 2018, 17 (3) : 923-957. doi: 10.3934/cpaa.2018046 [12] Roberto A. Capistrano-Filho, Shuming Sun, Bing-Yu Zhang. General boundary value problems of the Korteweg-de Vries equation on a bounded domain. Mathematical Control & Related Fields, 2018, 8 (3&4) : 583-605. doi: 10.3934/mcrf.2018024 [13] John P. Albert. A uniqueness result for 2-soliton solutions of the Korteweg-de Vries equation. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 3635-3670. doi: 10.3934/dcds.2019149 [14] Ivonne Rivas, Muhammad Usman, Bing-Yu Zhang. Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain. Mathematical Control & Related Fields, 2011, 1 (1) : 61-81. doi: 10.3934/mcrf.2011.1.61 [15] Netra Khanal, Ramjee Sharma, Jiahong Wu, Juan-Ming Yuan. A dual-Petrov-Galerkin method for extended fifth-order Korteweg-de Vries type equations. Conference Publications, 2009, 2009 (Special) : 442-450. doi: 10.3934/proc.2009.2009.442 [16] Brian Pigott. Polynomial-in-time upper bounds for the orbital instability of subcritical generalized Korteweg-de Vries equations. Communications on Pure & Applied Analysis, 2014, 13 (1) : 389-418. doi: 10.3934/cpaa.2014.13.389 [17] Olivier Goubet. Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 625-644. doi: 10.3934/dcds.2000.6.625 [18] Zhaosheng Feng, Yu Huang. Approximate solution of the Burgers-Korteweg-de Vries equation. Communications on Pure & Applied Analysis, 2007, 6 (2) : 429-440. doi: 10.3934/cpaa.2007.6.429 [19] Terence Tao. Two remarks on the generalised Korteweg de-Vries equation. Discrete & Continuous Dynamical Systems - A, 2007, 18 (1) : 1-14. doi: 10.3934/dcds.2007.18.1 [20] Massimiliano Gubinelli. Rough solutions for the periodic Korteweg--de~Vries equation. Communications on Pure & Applied Analysis, 2012, 11 (2) : 709-733. doi: 10.3934/cpaa.2012.11.709
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https://zbmath.org/?q=an:0933.62024 | # zbMATH — the first resource for mathematics
$$\ell_1$$ computation: An interior monologue. (English) Zbl 0933.62024
Dodge, Yadolah (ed.), $$L_1$$-statistical procedures and related topics. Papers of the 3rd international conference on $$L_1$$ norm and related methods held in Neuchâtel, Switzerland, August 11–15, 1997. Hayward, CA: IMS, Institute of Mathematical Statistics. IMS Lect. Notes, Monogr. Ser. 31, 15-32 (1997).
Summary: Some recent developments on the computation of least absolute error estimators are surveyed and a number of extensions to related problems are suggested. A very elementary example is used to illustrate the basic approach of “interior point” algorithms for solving linear programs. And a simple preprocessing approach for $$\ell_1$$ type problems is described. These developments, taken together, have the effect of dramatically improving the efficiency of absolute error computations, making them comparable to least squares methods even in massive datasets.
For the entire collection see [Zbl 0882.00044].
##### MSC:
62G05 Nonparametric estimation 65C60 Computational problems in statistics (MSC2010) 62J05 Linear regression; mixed models
##### Keywords:
linear models; regression quantiles | 2021-05-11 12:45:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39482635259628296, "perplexity": 3314.178423544092}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989614.9/warc/CC-MAIN-20210511122905-20210511152905-00268.warc.gz"} |
http://ac-immacolata.it/tqon/durstenfeld-shuffle.html | # Durstenfeld Shuffle
Shuffle a mutable slice in place. bin: random number generator appropriate for benchmarking FYDK shuffling. Richard Durstenfeld presented it in 1964 as "Algorithm 235: Random permutation". * Using Durstenfeld shuffle algorithm. Analysing algorithms to check if they are truly random is exceedingly hard. You can find the Durstenfeld in one of the top replies to this question. Challenge: Multithreaded KFY/Durstenfeld Shuffle? Pages: 1 2 3. Because the IDs are not continuous, the proposed solutions in the linked article are not sufficient. (diakses tanggal 22 september 2013, 22:52). HTML preprocessors can make writing HTML more powerful or convenient. Lectures by Walter Lewin. I go through the very basic steps of the melbourne shuffle. The permutation generated by Shuffle can be viewed as a block cipher, where the key is the PRNG output (or, equivalently, the seed used in the PRNG). See the complete profile on LinkedIn and discover Jean. The first is one of A, T, J, Q, K or the digits between 2 and 9. * Using Durstenfeld shuffle algorithm. O intuito é aplicar esse algoritmo para embaralhar elementos de um vetor baseado no índice da posição que cada elemento ocupa. The memory overhead of reading an arr. // This Fisher-Yates shuffle is the less efficient than the Durstenfeld shuffle but more animatedly appealing. The Ticker Widget allows dynamic Feed content to be added to a Layout. pour faire suite à la réponse de mquander et au commentaire de Dan Blanchard, voici une méthode D'extension qui effectue un Fisher-Yates-Durstenfeld shuffle : // take n random items from yourCollection var randomItems = yourCollection. The time complexity and space complexity of the Knuth-Durstenfeld shuffle algorithm are O(n) and O(1), respectively. Each of the basic PSO modifications was analyzed using three different distributed strategies. shuffle uses the Fisher-Yates shuffle, which runs in O(n) time and is proven to be a perfect shuffle (assuming a good random number generator). Method 2 - Fisher–Yates Modern Shuffle Method. shuffle fisher array algorithm random python cards durstenfeld deck java objective c - What's the Best Way to Shuffle an NSMutableArray? If you have an NSMutableArray, how do you shuffle the elements randomly?(I have my own answer for this, which is posted below, but I'm new to Cocoa and I'm interested to know if there is a better way…. Random_shuffle yields uniformly distributed results; that is, the probability of any particular ordering is 1/N!. Sized; /// Shuffle a slice in place, but exit early. If we use the modern Fisher-Yates algorithm by Richard Durstenfeld the complexity can be reduced to (N). That's a Fisher-Yates shuffle. Simple card classes. txt) or view presentation slides online. O(n log n) average, O(n²) worst case for a quicksort-based shuffle), and while the distribution is not perfectly uniform, it should approach uniform close enough for most practical purposes. I have no idea who first realized that the algorithm on the right is equivalent. The COMACARE trial is a prospective, multi-center, pilot RCT using 2 3 factorial design. Knuth-Durstenfeld Shuffle Knuth 和Durstenfeld 在Fisher 等人的基础上对算法进行了改进。每次从未处理的数据中随机取出一个数字，然后把该数字放在数组的尾部，即数组尾部存放的是已经处理过的数字。. /// /// Returns two mutable slices from the source slice. Post by YasserKhalil » 23 Mar 2020, 07:41. However, Fisher-Yates shuffle or Richard Durstenfeld shuffle algorithm you linked to actually does not need arbitrary precision random numbers. Fisher-Yates shuffle java example Simple java implementation of “Fisher-Yates shuffle” algorithm with modification from Richard Durstenfeld. Fisher-Yates shuffling algorithm and its several modified versions offer alternate techniques of generating random permutations popularly employed in the areas of computer programming, information theory and cryptography for data security purposes. 本文大部分引用于：洗牌算法shuffle - caochao88 - 博客园问题描述：一个1到n的序列，随机打乱，保证每个数出现在任意一个位置的概率相同。解法一：可以理解为暴力法了#Fisher-Yates Shuffle ''' 1. The Ticker module primarily consists of a data source location and a template to apply to the retrieved data. Durstenfeld 는이 질문의 답장 중 하나에서 찾을 수 있습니다. (Puedes utilizar un ayudante/método de extensión para baraja tu IEnumerable secuencia. Following is the detailed algorithm. 洗牌算法 - Fisher-Yates shuffle ; 4. So there are 24 possible passwords, right? No. For instance, Markdown is designed to be easier to write and read for text documents and you could write a loop in Pug. NUMERICAL METHOD. Durstenfeld then proposed (and Donald Knuth popularized) a variant on the original algorithm, which is now termed the Knuth shuffle or the "modern" method. Knuth-Durstenfeld Shuffle. For this list randomizer we employ the robust, efficient, and unbiased Fisher–Yates shuffle [1], also known as the Knuth shuffle. randint(1,10000000000)) clientRGB = self. Richard Durstenfeld introduces the modern version of the Fisher-Yates shuffle designed for computer use. They will make you ♥ Physics. It has a run time complexity of O(n). Random interleavers are the most preferred interleavers utilized in digital and cellular communication systems for burst errors control. n-1): for i from n−1 downto 1 do j ← random integer such that 0 ≤ j ≤ i exchange a[j] and a[i] Fisher–Yates shuffle - Wikipedia. In this case the perils of copy-paste programming didn't materialize, and succumbing to the "your shuffle is biased" peer-pressure actually led to introducing a change that introduced an actual bias that was only perceived bias before. In 1964, Richard Durstenfeld came up with the modern method as a computer algorithm. txt) or view presentation slides online. com 適切な情報に変更. Golang - Knuth-Durstenfeld Shuffle with crypto/rand - Qiita 1 user テクノロジー カテゴリーの変更を依頼 記事元: qiita. Alternatively, if you were using an IList you could perform an in-place shuffle, if you prefer. Limbi cunoscute. View Jean Paul Giraldo’s profile on LinkedIn, the world's largest professional community. Continue reading Fisher-Yates shuffle java example. n-1): for i from n−1 downto 1 do j ← random integer such that 0 ≤ j ≤ i exchange a[j] and a[i] Fisher–Yates shuffle - Wikipedia. But RANDPERM uses indirectly the Mersenne Twister generator whose internal state has about 625. Instead, I'll probably add a Durstenfeld shuffle to the plugin list which will randomize the list of enumerated plugins, which, although not mitigating fingerprinting based on exotic plugins, will most definitely throw a spanner in the works for trackers; the fingerprinted list will no longer be uniquely and statically ordered which will make. shuffle用了此算法。 javascript实现. Returns result in vR with vIn unchanged. (You could use a helper/extension method to shuffle your IEnumerable sequence. The Durstenfeld algorithm is, for i from 0 to n − […]. This is the last project for this course. The Knuth-Fisher-Yates shuffle algorithm picks 1 out of n elements, then 1 out of n-1 remaining elements and so forth. アレックスが言ったように 、同じ幅の境界線は45度の角度で互いに突き合わせます：. Since you are multiplying a scalar (c(k)) by an identity matrix, there is no need to keep all the zeros. The Knuth shuffle (a. 思想:算法思想就是从原始数组中随机抽取一个新的数字到新数组中; 复杂度:O(n2). Apart from people with college level maths (or as Americans put it, a major in Math), this is way beyond most people's skill to even validate. This is a fun demo but, as others have mentioned, simulated annealing really isn't necessary, or even that appropriate, for this specific problem. In the first strategy, the entire swarm population is. That is, given a preinitialized array, it shuffles the elements of the array in place, rather than producing a. In 1964, Richard Durstenfeld published an algorithm that was based upon the Fisher-Yates method but designed for computer use. To move with short sliding steps, without or barely lifting the feet: The crowd shuffled out of the. To shuffle an array a of n elements (indices 0. Voici une implémentation JavaScript du Durstenfeld shuffle , une version optimisée par ordinateur de Fisher-Yates: /** * Randomize array element order in-place. sendMessage (gameLogic. Fisher-Yates shuffling algorithm and its several modified versions offer alternate techniques of generating random permutations popularly employed in the areas of computer programming, information theory and cryptography for data security purposes. n-1): for i from n - 1. nextInt(i) 方法 来获得 0到i-1 的随机数面试常考考点：洗牌算法 经典洗牌算法：Knuth-Durstenfeld Shuffle算法Fisher-Yates Shuffle算法1. As a valued partner and proud supporter of MetaCPAN, StickerYou is happy to offer a 10% discount on all Custom Stickers, Business Labels, Roll Labels, Vinyl Lettering or Custom Decals. By default this is implemented in terms of next_u64, but a random number generator which can generate numbers satisfying the requirements directly can overload this for performance. Apart from people with college level maths (or as Americans put it, a major in Math), this is way beyond most people's skill to even validate. Fisher–Yates shuffle (Knuth shuffle) To shuffle an array a of n elements (indices 0. // This Fisher-Yates shuffle is the less efficient than the Durstenfeld shuffle but more animatedly appealing. ? Or even give me an example of how to use that Algorithm. 2 A new generation tree for permutations A permutation [sigma] = (S, [delta]) is said to be special if [delta] is a critical derangement. New solution monitors chemical, toxic threats. For example, random integers in an interval are essential to the Fisher-Yates random shuffle. Recommended for you. Find the next largest power of two greater than N. Requirements. 这是Durstenfeld shuffle的一个JavaScript实现，Fisher-Yates的计算机优化版本： /** * Randomize array element order in-place. multiplayer. Yates [Statitiscal Tables (London 1938, Example 12], in ordinary language, and by R. Note that there are N! ways of arranging a sequence of N elements. fn shuffle(&mut self, values: &mut [T]) Shuffle a mutable slice in place. Fisher–Yates shuffling algorithm and its several modified versions offer alternate techniques of generating random permutations popularly employed in the areas of computer programming, information theory and cryptography for data security purposes. Worse, it is inefficient because its complexity is O(NlogN). The Fisher-Yates shuffle applies a pseudo random selection method. Because the shuffle is random, there is no guarantee that all items move. In 1964, Richard Durstenfeld published an algorithm that was based upon the Fisher-Yates method but designed for computer use. 7, at least). Perfect Block Ciphers with Small Blocks 455 2Notations We consider the problem of selecting a random permutation φ which operates over a set of n elements. Shuffle pseudo-array elements using Fisher-Yates algorithm? Started by dmg , Mar 13 2013 02:06 AM Best Answer dmg , 14 March 2013 - 02:46 PM. Alternatively, if you were using an IList you could perform an in-place shuffle, if you prefer. yates shuffle array algorithm random python cards durstenfeld deck java objective c - What's the Best Way to Shuffle an NSMutableArray? If you have an NSMutableArray, how do you shuffle the elements randomly?(I have my own answer for this, which is posted below, but I'm new to Cocoa and I'm interested to know if there is a better way…. Generate a random value j, which can be any one of {0, 1, …, i}; each of the. com Tipo: sorting Descrição: Embaralha um vetor de numeros sequenciais. An implementation of the Durstenfeld algorithm for shuffling collections. For example, if my array consists of 52 playing cards, I want to shuffle the array in order to shuffle the deck. [citation needed] He was the President of Badminton Association of India, Vice President of Badminton Asia Confederation, Member - Executive Council of Badminton World. Putting some timing around both shuffle algorithm for an array of 100 integers produces below result. Requirements. basado en el Shuffle de Fisher-Yates , puedes probar este componente reutilizable array-shuffle. This involves treating the lower indexes of the call number array as the available numbers and the higher indexes as the used ones. The following code which initialises and outputs such a sequence variable could serve as a starting point: \documentcl. Instead, I'll probably add a Durstenfeld shuffle to the plugin list which will randomize the list of enumerated plugins, which, although not mitigating fingerprinting based on exotic plugins, will most definitely throw a spanner in the works for trackers; the fingerprinted list will no longer be uniquely and statically ordered which will make. Questions: How do I randomize or shuffle the elements within an array in Swift? For example, if my array consists of 52 playing cards, I want to shuffle the array in order to shuffle the deck. 经过广泛的审查,我得出的结论是,解决方案是正确的,是Durstenfeld shuffle的逐字实施. strName = "capture2DImage_{}". Knuth and Durstenfeld improved the algorithm based on the Fisher-Yates shuffle algorithm, by interacting with numbers on the original array, and eliminating the extra O (n) space. However, Fisher-Yates shuffle or Richard Durstenfeld shuffle algorithm you linked to actually does not need arbitrary precision random numbers. Since you are multiplying a scalar (c(k)) by an identity matrix, there is no need to keep all the zeros. set k=k+1; 4. The Fisher-Yates algorithm provides a paper-based method, which was later computerised by Richard Durstenfeld. Select End Sub Private Function KnuthArrShuffle (vIn As Variant, vR As Variant) As Boolean ' Performs a modified Knuth random shuffle on the elements of the input array. The Knuth shuffle (a. By default this is implemented in terms of next_u64, but a random number generator which can generate numbers satisfying the requirements directly can overload this for performance. n-1): for i from n − 1 downto 1 do j ← random integer with 0 ≤ j ≤ i exchange a[j] and a[i]. Your code will produce a random shuffle, but not a uniformly distributed one (even if you assume rand is a good random number generator). I shuffle this with the Durstenfeld shuffle. Akhilesh Das Gupta (31 March 1961 – 12 April 2017) was a Prominent Educationist, Professor, Indian Politician & Philanthropist. I go through the very basic steps of the melbourne shuffle. The usual solution is the well-known algorithm by Durstenfeld, called "Shuffle," which Knuth II calls "Algorithm P (Shuffling)," although any valid permutation generator would be acceptable. What I did was basically take the operations from matrix operations to vector operations. Durstenfeld proposed his shuffle algorithm exactly in its modern linear-time form, in a / -page article that appears to be his only scientific publication. When I click Shuffle is the shuffle really random?. Return the next random f64 selected from the half-open interval [0, 1). A chaotic map is first generalized by introducing parameters and then discretized to a finite square lattice of points which represent pixels or some other data items. The same algorithm is used by shuffle() in j. This question can be asked in several flavors. The two sections should be merged. The Fisher-Yates shuffle is a simple and effective algorithm that suits our purpose well. Not only this, but this implementation of Shuffle() is fast and does not require any allocation. pdf), Text File (. data; while (shuffleStartColumn < width) { // Pick a random column j in the range [i, width) and move it to position i. Try it out in your project! Features. And in this. アレックスが言ったように 、同じ幅の境界線は45度の角度で互いに突き合わせます：. Parker Paradigms, Inc. * Using Durstenfeld shuffle algorithm. We don't # need to run for the first element that's why i > 0 for i in range(n-1,0,-1): # Pick a random index from 0 to i j = random. Download ShuffleFastaSeq for free. A C M 7 (July 1964), 420] M. Jack notes in their answer, for generating the permutations you almost certainly want to use some form of the Fisher–Yates–Durstenfeld–Knuth shuffle, since it avoids the inefficiency of the sample-and-reject-duplicates method when only a few valid choices remain. English Competență de vorbitor nativ sau bilingv. I was comparing the original Fisher-Yates shuffle vs the modern Fisher-Yates shuffle. Shuffle is permutations, and permutations are computed by factorial: 4x3x2x1. A modern efficient variant of Fisher-Yates is known as Durstenfeld algorithm. 洗牌算法是将原来的数组进行打散，使原数组的某个数在打散后的数组中的每个位置上等概率的出现，刚好可以解决该问题。 2. By default this is implemented in terms of next_u64, but a random number generator which can generate numbers satisfying the requirements directly can overload this for performance. n) exchange a[j] and a[n] The Fisher-Yates shuffle, as implemented by Durstenfeld, is an in-place shuffle. April 17, 2010 -7 minute read - Let's say one is a computer programmer and let's say one's wife (or roommate; or significant other) does social science research (a totally hypothetical scenario of course). Fisher and F. It randomizes the items of a given array by using the Durstenfeld shuffle algorithm:. permutation". Shuffle (= random sort) Sorting lines (or other chunks) of a string by "sort str by random(2^15)" is well known to yield biased results by preferring a certain kind of permutations. That is, given a preinitialized array, it shuffles the elements of the array in. of Austin, Texas, has created an IP-based security solution that integrates with sensors from Sunnyvale. There are more efficient ways to generate a random permutation than assigning a number to each element and sorting, for instance the "Fisher-Yates shuffle" or "Knuth shuffle" (Knuth attributes it to Durstenfeld). * Using Durstenfeld shuffle algorithm. Fisher-Yates shuffle is quite a simple algorithm when it comes to implementation. Voici une implémentation JavaScript du Durstenfeld shuffle , une version optimisée par ordinateur de Fisher-Yates: /** * Randomize array element order in-place. I go through the very basic steps of the melbourne shuffle. The first contains /// amount elements randomly permuted. Fisher-Yates shuffle or Knuth shuffle is an algorithm for generating a random shuffle of a finite set. Knuth in The Art of Computer Programming as "Algorithm P". There's a couple of algorithms explained in the article, but the one I found more useful is the one known as the modern version of the Fisher-Yates shuffle algorithm by Richard Durstenfeld. For example, if my array consists of 52 playing cards, I want to shuffle the array in order to shuffle the deck. -- To shuffle an array a of n elements (indices 0. Scroll Down. Knuth-Durstenfeld Shuffle. Yates [Statitiscal Tables (London 1938, Example 12], in ordinary language, and by R. Method 2 - Fisher–Yates Modern Shuffle Method. 这个算法和目前流行的shuffle算法有一些不一样。 目前的是 Durstenfeld 提出的改进的 Fisher–Yates shuffle。 这里主要是在上面第七行， 相当于每次放下一张牌，就需要去整理一下剩下的牌。 实际上这个复杂度是 O(n^2). Como ves en la tabla de arriba, que tiene. The following commands benchmark sequential and parallel FYDK shuffling on arrays of size 10^8. Worse, it is inefficient because its complexity is O(NlogN). Subsequent editions of The Art of Computer Programming do mention Fisher and Yates’ contribution. Unfortunately JavaScript doesn't yet have a built-in shuffle method, and it's sort method has a few quirks… but both can be accomplished if you know how. Durstenfeld 는이 질문의 답장 중 하나에서 찾을 수 있습니다. View Jean Paul Giraldo’s profile on LinkedIn, the world's largest professional community. I hate to admit it but I'm stumped. If you are using v2 of the CMS, please use the following link: Dataset Ticker. 랜덤함수를 사용해서 첫번째 난수 생성 2. goblindegook. フィッシャー–イェーツのシャッフル (英: Fisher–Yates shuffle) は、有限集合からランダムな順列を生成するアルゴリズムである。言い換えると、有限列をランダムな別の（シャッフルされた）順序の有限列に並べ直す方法である。. shuf·fled, shuf·fling, shuf·fles v. Programming languages use a similar algorithm in their inbuilt implementation of shuffle method. Shuffle of an array elements. They may differ by the actual way the hands are held to accomplish the shuffle, but the result is the same. The game dynamics and score system were handled using methods within the app. Here is a minimal implementation:. Block cipher is an encryption algorithm that performs a substitution and permutation operations on a block of data using a secret key. My definitions. Apps such as Trello, Google Drive, Office 365 and Jira make heavy use of DnD and users simply love it. floor( Math. See the documentation. Avoid creating ridiculously large core dumps when the stack memory map is. The algorithm was originally published by R. There are several ways to shuffle a set of elements, as demonstrated in this post. com View Our Frequently Asked Questions. There was a 30-second rest interval between trials to prevent fatigue. The idea is to create an array of indices from your array, to shuffle those indices with an AnyIterator instance and swap(_:_:) function and to map each element of this AnyIterator instance with the array's corresponding. Note that at exit a[l:n] will still contain all the elements of the original a[l:n], and that if k = n that these modifications will make the procedure call random one more time than the original SHUFFLE. 然而,Durstenfeld / Fisher-Yates shuffle只是随机的RNG来源. com is your one-stop shop to make your business stick. randint(1,10000000000)) clientRGB = self. Hi Derek, I am glad you found the results useful. Tutorial - Create and Shuffle a Deck of Cards in Javascript The slightly longer answer is to use the Durstenfeld version of the algorithm, which was optimized for the specific flow of programming instructions. Doesn't produce random permutation. Write a program to shuffle an pack of cards in the most efficient way. Return the next random f64 selected from the half-open interval [0, 1). Review Board 1. しかし、Durstenfeld / Fisher-YatesシャッフルはRNGソースと同じくらいランダムです。 私の解決策は、crypto. So, we can think of shuffling as anti-sorting as mentioned in a previous post. They both interleave the cards one-by-one from alternating sides, and can be done either as an in shuffle or out shuffle. A good way to get a bad shuffle¶ Sort using a "random" comparison function, e. Shuffle Array in Javascript. RandomWrapper. n-1): for i from n − 1 downto 1 do j ← random integer with 0 ≤ j ≤ i exchange a[j] and a[i] The "inside-out" algorithm. Prevent file races in the opencvs code. 컴퓨터에 최적화 된 Fisher-Yates 버전 인 Durstenfeld shuffle 의 JavaScript 구현은 다음과 같습니다. The browser's (or NodeJS) crypto services are used to generate strong random numbers. Wilhelm, U. From the very first version of the game, we have used the Fisher-Yates Shuffle algorithm, with Durstenfeld implementation code. Block cipher relies on substitution boxes to provide the. Use a Fisher-Yates-Durstenfeld shuffle. The modern method of the Fisher-Yates algorithm is a slightly-modified version of the original. shuffle-seq. */ // Initially: No boundary points known public static Circle MakeCircle(IList points) { // Clone list to preserve the caller's data, do Durstenfeld shuffle List shuffled = new List (points); Random rand = new Random(); for (int i = shuffled. The existing way of approaching this problem in F# is to use one of these snippets which is obviously not ideal. set j to PR(N) modulo i; b. The shuffle routine is the standard Durstenfeld shuffle described in Knuth II [ 2: 139 §3. print statement, but what I don't understand is how it works since the value of X generated by the Rnd function could be duplicated. The most known and optimal shuffling algorithm is Fisher-Yates shuffle. Getting Started. Use code METACPAN10 at checkout to apply your discount. mutating func shuffleInPlace() { // empty and single-element collections don't shuffle if count 2 { return } for i in startIndex. The Fisher-Yates shuffle, as implemented by Durstenfeld, is an in-place shuffle. Unfortunately JavaScript doesn't yet have a built-in shuffle method, and it's sort method has a few quirks… but both can be accomplished if you know how. The Fisher–Yates shuffle, as implemented by Durstenfeld, is an in-place shuffle. We use cookies for various purposes including analytics. Write a program to shuffle an pack of cards in the most efficient way. board]: origin, [targetName]: target }) you always update same part of state (either shuffle or solved) first with origin and afterwards overwrite with target, because pieceData. Hi, I am doing an assignment dealing with a deck of cards and I have to follow the given guidelines: The algorithm below, which shuffles an array of integers, must be adapted and implemented to shuffle the cards to start a new game of solitaire. Recommended for you. Support Documentation; Get Support; Log in. Como ves en la tabla de arriba, que tiene. Fisher and F. n-1): for i from n − 1 downto 1 do j ← random integer with 0 ≤ j ≤ i exchange a[j] and a[i] The “inside-out” algorithm. The modern version of the Fisher-Yates shuffle, designed for computer use, was introduced by Richard Durstenfeld in 1964[2] and popularized by Donald E. The Fisher–Yates shuffle (named after Ronald Fisher and Frank Yates), also known as the Knuth shuffle (after Donald Knuth), is an algorithm for generating a random permutation of a finite set—in plain terms, for randomly shuffling the set. The permutations generated by this algorithm occur with the same probability. shuffle用了此算法。 javascript实现. The Fisher–Yates shuffle, as implemented by Durstenfeld, is an in-plac Everglades National Park is a U. This uses the Fisher-Yates (or Durstenfeld-Knuth) shuffle, which is unbiased. (You could use a helper/extension method to shuffle your IEnumerable sequence. We compare 27 modifications of the original particle swarm optimization (PSO) algorithm. Try it out in your project! Features. data; while (shuffleStartColumn < width) { // Pick a random column j in the range [i, width) and move it to position i. 6) 16 (two-tier shuffling) != 24 (linear-uniform shuffle) I agree 100% with helios that hamsterman's algorithm is extremely well suited for parallelization; however, as I suspected, and as kev82 just pointed out, you will get a shuffle, but not a uniform shuffle. An implementation of the Durstenfeld algorithm for shuffling collections. Subsequent editions of The Art of Computer Programming do mention Fisher and Yates' contribution. Take(5); //. Post by YasserKhalil » 23 Mar 2020, 07:41. This algorithm is modified version of Fisher-Yates shuffle algorithm and is introduced by Richard Durstenfeld. It requires 2 or 3 times as much memory as the Durstenfeld. Chapter 247 Infotech is a leading ReactJS development company in India, USA, offering ReactJS development services at par to a spectrum of business domains from E-commerce, healthcare to Edutech at. It randomizes the items of a given array by using the Durstenfeld shuffle algorithm:. So it would be very convenient to have such an operation in the language. 思想:算法思想就是从原始数组中随机抽取一个新的数字到新数组中; 复杂度:O(n2). And I hope you think I'm UberCool :P. Shuffle gives the classical algorithm to generate random permutations, see MosesandOakford(1963);Durstenfeld(1964)andalso(Knuth,1981,Sec. a shuffle function that doesn't change the source array. permutations is, to my eye, inelegant. Generating a random order. This can be an advantage if the array to be shuffled is large. My Solution unilt now This is what I did til now as long as I know, I'll keep making it better after watching next videos. The Riffle shuffle and Faro shuffle are the same thing. userId: 0 multiplayer. Each of the basic PSO modifications was analyzed using three different distributed strategies. com 適切な情報に変更. Not only this, but this implementation of Shuffle() is fast and does not require any allocation. 每次从未处理的数组中随机取一个元素，然后把该元素放到数组的尾部，即数组的尾部放的就是已经处理过的元素，这是一种原地打乱的算法，每个元素随机概率也相等，时间复杂度从 Fisher 算法的. * Using Durstenfeld shuffle. O intuito é aplicar esse algoritmo para embaralhar elementos de um vetor baseado no índice da posição que cada elemento ocupa. Among those, drag and drop is, certainly, one of the most appealing to the user. That is, given a preinitialized array, it shuffles the elements of the array in. With the Fisher-Yates shuffle, first implemented on computers by Durstenfeld in 1964, we randomly sort elements. ' The original by Fisher-Yates, was modified for computers by Durstenfeld ' then popularised by Knuth. Java Code Examples for org. Random shuffling of data arrays is very common operation in data science which F# was designed for. n-1): for i from n − 1 downto 1 do j ← random integer with 0 ≤ j ≤ i exchange a[j] and a[i]. Fisher–Yates Modern Shuffle Method(現代版)，是專供電腦使用，是由 Richard Durstenfeld 於1964年提出和由 Donald Knuth 普及: 初始化數組，按序(升序或者降序)排列;. The major steps being: Let's say you have an array of N elements,sat A[N] the index being [0, N-1]. Collections, and so you should get compatible results if using it on a Collection with the same seed (as of JDK1. Recommended for you. Hi Derek, I am glad you found the results useful. Knuth 在 《The Art of Computer Programming》 中推广。但是不管是 Durstenfeld 还是 Knuth，都没有在书的第一版中承认这个算法是 Fisher 和 Yates 的研究成果。. Eeyorelife. Tipo: sorting. Knutt / Durstenfeld Shuffle Algoritmasının Resim Şifreleme Amacıyla Kullanılması Image Encryption Based On Knutt / Durstenfeld Shuffle Algorithm. I threw together the same demo with a very trivial algorithm that I think does a more accurate job of reconstructing the same images in significantly less time than the simulated annealing [1]. This is a fun demo but, as others have mentioned, simulated annealing really isn't necessary, or even that appropriate, for this specific problem. If the list is passed as a reference to an array, the shuffle is done in situ. Instead, I'll probably add a Durstenfeld shuffle to the plugin list which will randomize the list of enumerated plugins, which, although not mitigating fingerprinting based on exotic plugins, will most definitely throw a spanner in the works for trackers; the fingerprinted list will no longer be uniquely and statically ordered which will make. Initial code for BCM5706/5708 fiber support in bge(4). Here is a JavaScript implementation of the Durstenfeld shuffle, a computer-optimized version of Fisher-Yates: /** * Randomize array element order in-place. Your email address:. This applies Durstenfeld's algorithm for the Fisher-Yates shuffle which produces an unbiased permutation. shuffle individually each subarrays |A_k(N) of cardinality C_k(N) within |A(N) using the Durstenfeld variation of Fisher-Yates algorithm that depends on N's System ID: 1. Find the next largest power of two greater than N. Use a Fisher-Yates-Durstenfeld shuffle. Name Picker Wheel - Random Name Picker online-stopwatch. Try it out in your project! Features. GitHub Gist: instantly share code, notes, and snippets. The Knuth shuffle (a. The following code which initialises and outputs such a sequence variable could serve as a starting point: \documentcl. Here is another piece of trivia for you, the Fisher-Yates shuffle was created in 1938 and converted to computers by Durstenfeld in 1964. The Fisher–Yates shuffle, as implemented by Durstenfeld, is an in-place shuffle. pdf), Text File (. So there are 24 possible passwords, right? No. The reason this comment is important is that there are a number of algorithms that seem at first sight to implement random shuffling of a sequence, but that do not in fact produce a uniform distribution over the N! possible orderings. That is to say, the algorithm shuffles the sequence. (You could use a helper/extension method to shuffle your IEnumerable sequence. Requirements. Generally speaking, the computational complexity of sort-based shuffles is the same as the underlying sort algorithm (e. This is a fun demo but, as others have mentioned, simulated annealing really isn't necessary, or even that appropriate, for this specific problem. Are you curious how to use drag and drop with React? If so, this article is exactly for you! Have a good read. The Durstenfeld algorithm is, for i from 0 to n − […]. # Python Program to shuffle a given array import random # A function to generate a random permutation of arr[] def randomize (arr, n): # Start from the last element and swap one by one. O(n log n) average, O(n²) worst case for a quicksort-based shuffle), and while the distribution is not perfectly uniform, it should approach uniform close enough for most practical purposes. Find the next largest power of two greater than N. Jean Paul has 6 jobs listed on their profile. Update: Here I'm suggesting a relatively simple (not from complexity perspective) and short algorithm that will do just fine with small sized arrays, but it's definitely going to cost a lot more than the classic Durstenfeld algorithm when you deal with huge arrays. a shuffle function that doesn't change the source array. Above algorithm works in linear time and faster than riffle shuffle. Fisher and F. I was comparing the original Fisher-Yates shuffle vs the modern Fisher-Yates shuffle. #include #include #include "allheaders. Communications of the ACM 7 (7): 420. Richard Durstenfeld presented it in 1964 as "Algorithm 235: Random permutation". Time complexity: O(N). This applies Durstenfeld's algorithm for the Fisher–Yates shuffle which produces an unbiased permutation. Fisher-Yates Shuffle算法. See the complete profile on LinkedIn and discover Jean. 洗牌算法导语抽牌 - Fisher-Yates Shuffle换牌 - Knuth-Durstenfeld Shuffle插牌 - Inside-Out Algorithm扩展 - 蓄水池抽样导语在之前的【Leetcode 384】Shuffle an Array - MEDIUM，打乱一个数组的问题中，我们有用到洗牌算法，其关键在于生成等概率的结果。. Modern web applications have multiple forms of interaction. The random number you generate - that should have a range of 0 <= k <= SIZE-1 where a[SIZE]; So the +1 on this line (#52 above), appears dodgy:. Name Picker Wheel - Random Name Picker online-stopwatch. The Durstenfeld algorithm is, for i from 0 to n − 2 do. fn shuffle(&mut self, values: &mut [T]) Shuffle a mutable slice in place. It uses the Durstenfeld algorithm, a computer-optimized variant of the Fisher–Yates shuffle. Descrição: Embaralha um vetor de numeros sequenciais. By default this is implemented in terms of next_u64, but a random number generator which can generate numbers satisfying the requirements directly can overload this for performance. Use a Fisher-Yates-Durstenfeld shuffle. - Applied a JavaScript implementation of the Durstenfeld shuffle, a computer-optimized version of the Fisher-Yates shuffling algorithm, to randomize the flashcards Show more Show less See project. The algorithm is very easy to implement and produces unbiased results. Even if we donʹt need to do anything to exchange an item with itself, it might seem inefficient to allow this to happen. O(n log n) average, O(n²) worst case for a quicksort-based shuffle), and while the distribution is not perfectly uniform, it should approach uniform close enough for most practical purposes. Fisher-Yates shuffling algorithm and its several modified versions offer alternate techniques of generating random permutations popularly employed in the areas of computer programming, information theory and cryptography for data security purposes. The time complexity and space complexity of the Knuth-Durstenfeld shuffle algorithm are O(n) and O(1), respectively. The following code which initialises and outputs such a sequence variable could serve as a starting point: \documentcl. Name Picker Wheel - Random Name Picker online-stopwatch. 원문 답변 : shuffle 함수가 소스 배열 을 변경 하려고하지 않는다면 로컬 변수에 복사 한 다음 간단한 셔플 로직으로 나머지를 수행 할 수 있습니다. FreeCodeCamp Indy Hackers Bingo! Here is how I made 24 different bingo boards for our club's second birthday! Randomizes the array without repeating a number using the Durstenfeld Shuffle Algorithm; Pops out the total array minus 29 making the array length 24 numbers. , transitivity, reflexiveness, etc. The permutations generated by this algorithm occur with the same probability. 랜덤 함수를 이용해서 두번. The Modern Method. When I click Shuffle is the shuffle really random?. This is the Part 6 of a short series of posts introducing and building #include #define N_STRINGS 10 #define N_PICKS 5 char. Descrição: Embaralha um vetor de numeros sequenciais. * Using Durstenfeld shuffle algorithm. Knuth shuffle You are encouraged to solve this task according to the task description, using any language you may know. Replaced the IP ID and the named(8) PRNG algorithm with one based on a Durstenfeld shuffle. The time complexity is O(N). I go through the very basic steps of the melbourne shuffle. fn shuffle(&mut self, values: &mut [T]) Shuffle a mutable slice in place. The more elegant and faster of the two algorithms is also known as the Knuth Shuffle, popularized by Donald Knuth, in his book , The Art of Computer Programming. 洗牌算法shuffle ; 3. To shuffle, one can just stir a set of items; but this either does not introduce essentially full randomness, or takes longer than necessary. Fisher-Yates Shuffle También conocido como el shuffle de Knuth y el shuffle de Durstenfeld-Fisher-Yates. There’s a couple of algorithms explained in the article, but the one I found more useful is the one known as the modern version of the Fisher–Yates shuffle algorithm by Richard Durstenfeld. com View Our Frequently Asked Questions. shuffle(list)所采用的方法。 时间复杂度O(n)，空间复杂度为O(1) 思路三、Inside-Out 算法. In particular, we implement its modern variant (the initial algorithm was for pen, paper, and a dice!) as described in Richard Durstenfeld's 1964 work [2]. Random_shuffle yields uniformly distributed results; that is, the probability of any particular ordering is 1/N!. Each playing card is represented by two characters. Fisher–Yates shuffle (Knuth shuffle) To shuffle an array a of n elements (indices 0. bin and shuffle-par. by SSWUG Research (Richard Carr) Sometimes it is necessary to randomise the order of a sequence of values. The algorithm below, which shuffles an array of integers, must be adapted and implemented to shuffle the cards to start a new game. shuffle（List、Random）が存在することは、同じ状態のRandomで呼び出されたときにこのメソッドが常に同じ順序を返すことを意図していることを示唆しています。 （これは、たとえば反復可能なテストを作成するのに役立ちます。. Knuth distributed it in the other book as "Algorithm P". This is a C++ Program to shuffle array using Fisher-Yates algorithm. 5 Penn Plaza, 23rd Floor New York, NY 10001 Phone: (845) 429-5025 Email: [email protected] The random number you generate - that should have a range of 0 <= k <= SIZE-1 where a[SIZE]; So the +1 on this line (#52 above), appears dodgy:. Il più efficiente è la variante moderna del Fisher-Yates (cioè quello di Durstenfeld):-- To shuffle an array a of n elements (indices 0. PiKE (Recd. Mathematically, the shuffling problem, is basically a problem…. The Fisher–Yates shuffle (named after Ronald Fisher and Frank Yates), also known as the Knuth shuffle (after Donald Knuth), is an algorithm for generating a random permutation of a finite set—in plain terms, for randomly shuffling the set. Pengujian dilakukan pada perangkat mobile yang menggunakan platform Android. Add shuffle method for lists and arrays. The trick is to use a variation of shuffle or in other words a partial shuffle. Fisher-Yates shuffle or Knuth shuffle is an algorithm for generating a random shuffle of a finite set. FreeCodeCamp Indy Hackers Bingo! Here is how I made 24 different bingo boards for our club's second birthday! Randomizes the array without repeating a number using the Durstenfeld Shuffle Algorithm; Pops out the total array minus 29 making the array length 24 numbers. 思路二将原始数据直接打乱，且原数组大小是已知的，所以无法处理暂时不知道长度或动态增长的. shuffle(we_need_list) 这里面使用到的是 经典的洗牌算法 Knuth-Durstenfeld Shuffle，虽然仍然是伪随机，但是已经足够我们的场景了。关于真随机，主要是随机数种子的获取，就不复述了。 重复抽取. ***Please do be careful with the "Delete all files" option and the target drive/path. Apart from people with college level maths (or as Americans put it, a major in Math), this is way beyond most people's skill to even validate. basata su Fisher-Yates Shuffle , è ansible provare questo componente riutilizzabile arrays-shuffle. public void shuffle(int[] intArray) Shuffles an array of integers into random order. The Fisher-Yates shuffle applies a pseudo random selection method. See the documentation. With Swift 3, if you want to shuffle an array in place or get a new shuffled array from an array, AnyIterator can help you. Here the unbiased shuffle of Durstenfeld/ Fisher/ Knuth/ Yates is used where every permutation has the same probability of being chosen. Introduction to the Algorithm. This is a fun demo but, as others have mentioned, simulated annealing really isn't necessary, or even that appropriate, for this specific problem. My event handler gets the ID of the card clicked (which begins at 1), then it can just look up the card in the array with ID-1 as index. The main objectives of the study are to assess the feasibility of targeting low- or high-normal PaCO 2, PaO 2, and MAP in comatose, mechanically ventilated patients after OHCA and to evaluate the effect of low- or high-normal PaCO 2, PaO 2, and MAP on brain injury markers at 48 h after cardiac arrest. The algorithm was popularized by D. Este orden aleatorio toma una serie de n elementos y lo baraja. See the complete profile on LinkedIn and discover Jean. Initial code for BCM5706/5708 fiber support in bge(4). This applies Durstenfeld's algorithm for the Fisher-Yates shuffle which produces an unbiased permutation. Knaus and L. Utilizar un Fisher-Yates-Durstenfeld shuffle. randint(1,10000000000)) clientRGB = self. Block cipher relies on substitution boxes to provide the. #include #include #include "allheaders. To help us keep track of the items as we shuffle them, we'll use tables 1-3. alex가 말했듯이, 같은 폭의 경계선은 서로 45도 각도로 맞 닿아 있습니다. We use cookies for various purposes including analytics. Simple java implementation of "Fisher-Yates shuffle" algorithm with modification from Richard Durstenfeld. The Durstenfeld 1964 Algol implementation of the Fisher-Yates shuffle is O(N) and is, therefore, optimal up to a multiplicative constant. We compare 27 modifications of the original particle swarm optimization (PSO) algorithm. PiKE (Recd. The Fisher-Yates shuffle (named after Ronald Fisher and Frank Yates) is used to randomly permute given input (list). P ] and mentioned in Sect 6. The digits of $\pi$ are used as a sort of random number generator that is used in the Durstenfeld shuffle (see also Knuth vol 3, sec 3. yates shuffle array algorithm random python cards durstenfeld deck java objective c - What's the Best Way to Shuffle an NSMutableArray? If you have an NSMutableArray, how do you shuffle the elements randomly?(I have my own answer for this, which is posted below, but I'm new to Cocoa and I'm interested to know if there is a better way…. Also, this algorithm was popularized by Donald Knuth as "Algorithm P (Shuffling)" or "Knuth shuffle". To shuffle an array a of n elements (indices 0. Durstenfeld 는이 질문의 답장 중 하나에서 찾을 수 있습니다. Download ShuffleFastaSeq for free. The Durstenfeld algorithm is, for i from 0 to n − […]. com you agree to our cookies policy to enhance your experience. To help us keep track of the items as we shuffle them, we'll use tables 1-3. randint(0,i+1). I covered shuffling previously in my article on recipes for randomness in JavaScript: this version, known as the Durstenfeld shuffle, is a high-performance variation:. And I hope you think I'm UberCool :P. A chaotic map is first generalized by introducing parameters and then discretized to a finite square lattice of points which represent pixels or some other data items. ShuffleFastaSeq is a Windows form application, written in C#, to shuffle FASTA-formatted sequences. Putting some timing around both shuffle algorithm for an array of 100 integers produces below result. Mathematically, the shuffling problem, is basically a problem…. shuffle（List、Random）が存在することは、同じ状態のRandomで呼び出されたときにこのメソッドが常に同じ順序を返すことを意図していることを示唆しています。 （これは、たとえば反復可能なテストを作成するのに役立ちます。. A modern efficient variant of Fisher-Yates is known as Durstenfeld algorithm. Knuth distributed it in the other book as "Algorithm P". There is a rich history of research on parallel algorithms from the 1970s, or some even earlier. Hello everyone Can you guide me to a tutorial that gives me examples of Durstenfeld's Algorithm to jumble array. The shuffle routine is the standard Durstenfeld shuffle described in Knuth II [ 2: 139 §3. The modern method of the Fisher-Yates algorithm is a slightly-modified version of the original. randomBytesAsync,因此在大多数情况下都是加密安全的(见How random is crypto#randomBytes?. This is the last project for this course. GitHub Gist: instantly share code, notes, and snippets. shuffle-seq. randint(1,10000000000)) clientRGB = self. in-place shuffle (2) linked list (2) string function (2) Chord (1) Clustering (1) Concurrency (1) Durstenfeld (1) Fender (1) Fisher–Yates shuffle (1) IPC (1) Japan (1) JavaScript (1) Lambda (1) Memory (1) Shell Programming (1) Sieve of Eratosthenes (1) Tokyo (1) Used Guitar (1) Valgrind (1) bubble sort (1) cef (1) cmake (1) debug (1) gdb (1. This is what Jan Simon and I have used. With the Fisher-Yates shuffle, first implemented on computers by Durstenfeld in 1964, we randomly sort elements. I would probably use an adaptation of the Durstenfeld shuffle algorithm: [code]#include #include #define N_STRINGS 10 #define N_PICKS 5 char. It is described here for characters in a string but a related method, the Durstenfeld-Knuth method is preferred for arrays. Como ves en la tabla de arriba, que tiene. Simulation Performance of Conventional IDMA System with DPSK Modulation and Modern Fisher–Yates Interleaving Schemes. Although I conceived this algorithm independently some decades ago (it isn't all that complicated), Ronald Fisher and Frank Yates did it first; so they get the credit. 4 • a month ago. Find the next largest power of two greater than N. The Ticker Widget allows dynamic Feed content to be added to a Layout. Simple java implementation of “Fisher-Yates shuffle” algorithm with modification from Richard Durstenfeld. - Applied a JavaScript implementation of the Durstenfeld shuffle, a computer-optimized version of the Fisher-Yates shuffling algorithm, to randomize the flashcards Show more Show less See project. NewGuid()); Hice algunas pruebas empíricas para convencerme de que lo anterior en realidad genera una distribución aleatoria (lo que parece hacer). In particular, we implement its modern variant (the initial algorithm was for pen, paper, and a dice!) as described in Richard Durstenfeld's 1964 work [2]. Shuffle算法学习. Also, this algorithm was popularized by Donald Knuth as "Algorithm P (Shuffling)" or "Knuth shuffle". Implements Richard Durstenfeld's version of the Fisher-Yates algorithm, popularized by Donald Knuth. So how does this algorithm work ?. The study aids and games were created using a variety of tools including Fisher and Yates algorithm, Durstenfeld Shuffle, CSS transitions class, and dynamic HTML (DHTML). Lectures by Walter Lewin. Find the next largest power of two greater than N. Swift3/Swift4实现Fisher–Yates洗牌算法随机打乱数组（shuffle） 添加两个extension：可变集合添加shuffle()方法，打乱原来集合的元素顺序Sequence添加shuffled()方法，返回原序列乱序的数组Swift 4extension MutableCollection { /// 打乱集合里的元素 mutati. Even if we donʹt need to do anything to exchange an item with itself, it might seem inefficient to allow this to happen. April 17, 2010 -7 minute read - Let's say one is a computer programmer and let's say one's wife (or roommate; or significant other) does social science research (a totally hypothetical scenario of course). The Fisher-Yates shuffle, as implemented by Durstenfeld, is an in-place shuffle. Random_shuffle yields uniformly distributed results; that is, the probability of any particular ordering is 1/N!. * Using Durstenfeld shuffle algorithm. The idea is to create an array of indices from your array, to shuffle those indices with an AnyIterator instance and swap(_:_:) function and to map each element of this AnyIterator instance with the array's corresponding. com View Our Frequently Asked Questions. La descripción de Durstenfeld, varía de la de Fisher y Yates, en que al llevarla a cabo en un programa se trata de ahorrar memoria y por tanto trata de usar el mismo array, para ello, va intercambiando el valor de la posición al azar, y lo remplaza por el último del array no remplazado ya. Durstenfeld proposed his shuffle algorithm exactly in its modern linear-time form, in a / -page article that appears to be his only scientific publication. /** * Randomize array element order in-place. Knuth-Durstenfeld Shuffle算法 Knuth 和 Durstenfeld在Fisher等人的基础上对算法进行了改进，在原始数组上对数字进行交互，省去了额外O(n)的空间。 该算法的基本思想和 Fisher 类似，每次从未处理的数据中随机取出一个数字，然后把该数字放在数组的尾部，即数组尾部存放. That is, given a preinitialized array, it shuffles the elements of the array in place, rather than producing a. It has been modernized by Durstenfeld and popularized by Donald Knuth in The Art of Computer Programming TV series. O(n log n) average, O(n²) worst case for a quicksort-based shuffle), and while the distribution is not perfectly uniform, it should approach uniform close enough for most practical purposes. Limp Bizkit's Fred Durst directs an advert for online dating website 0 rating. Note that there are N! ways of arranging a sequence of N elements. La descripción de Durstenfeld, varía de la de Fisher y Yates, en que al llevarla a cabo en un programa se trata de ahorrar memoria y por tanto trata de usar el mismo array, para ello, va intercambiando el valor de la posición al azar, y lo remplaza por el último del array no remplazado ya. The Durstenfeld algorithm is pretty simple, but I noted two things in your code. * Using Durstenfeld shuffle algorithm. Simple card classes. Implements Richard Durstenfeld's version of the Fisher-Yates algorithm, popularized by Donald Knuth. 经过广泛的审查,我得出的结论是,解决方案是正确的,是Durstenfeld shuffle的逐字实施. Random interleavers are the most preferred interleavers utilized in digital and cellular communication systems for burst errors control. ShuffleFastaSeq is a Windows form application, written in C#, to shuffle FASTA-formatted sequences. userId: 0 multiplayer. To shuffle, one can just stir a set of items; but this either does not introduce essentially full randomness, or takes longer than necessary. Volume 2: Seminumerical Algorithms, second edition. in-place shuffle (2) linked list (2) string function (2) Chord (1) Clustering (1) Concurrency (1) Durstenfeld (1) Fender (1) Fisher–Yates shuffle (1) IPC (1) Japan (1) JavaScript (1) Lambda (1) Memory (1) Shell Programming (1) Sieve of Eratosthenes (1) Tokyo (1) Used Guitar (1) Valgrind (1) bubble sort (1) cef (1) cmake (1) debug (1) gdb (1. The time complexity is O(N). New in R2011b , the RANDPERM function lets you specify a second argument, as in, "give me a random selection of size k from a random permutaion of 1:n". From the very first version of the game, we have used the Fisher-Yates Shuffle algorithm, with Durstenfeld implementation code. From there the cards are randomly rearranged using a durstenfeld shuffle to randomize array items and a map method on a React card component to refresh cards on the page. La descripción de Durstenfeld, varía de la de Fisher y Yates, en que al llevarla a cabo en un programa se trata de ahorrar memoria y por tanto trata de usar el mismo array, para ello, va intercambiando el valor de la posición al azar, y lo remplaza por el último del array no remplazado ya. Here is a minimal implementation:. The Shuffle ^M00:01:21 [ music ] ^M00:01:27 >> Doesn't tell you the name of each song every time it plays one. Тасование Фишера — Йетса (названо в честь Рональда Фишера и Франка Йетса (Frank Yates)), известное также под именем Тасование Кнута (в честь Дональда Кнута), — это алгоритм создания случайных перестановок конечного. The Fisher-Yates shuffle, as implemented by Durstenfeld, is an in-place shuffle. Requirements. Fisher and F. This is revision 2 of this patch (compared the previous patch, it removes a noisy log message that was a side effect of the privsep we added to our version of BIND. now(); var pixels = shuffledImage. Random shuffling of data arrays is very common operation in data science which F# was designed for. r/crypto: Cryptography is the art of creating mathematical assurances for who can do what with data, including but not limited to encryption of …. Bugfix: Durstenfeld shuffle was not shuffling properly Bugfix: Another issue with converting stockpiles Bugfix: Artifacts could spawn with more than 15 modifiers. 这是Durstenfeld shuffle的一个JavaScript实现，Fisher-Yates的计算机优化版本： /** * Randomize array element order in-place. - Applied a JavaScript implementation of the Durstenfeld shuffle, a computer-optimized version of the Fisher-Yates shuffling algorithm, to randomize the flashcards Show more Show less See project. n) exchange a[j] and a[n] The Fisher-Yates shuffle, as implemented by Durstenfeld, is an in-place shuffle. a[i] ← i for n from m - 1 downto 1 do j ← random (0. This algorithm was meant to be implemented using pencil and paper, so it was not until 1964 that its modern version came to light. See Closed01 for the closed interval [0,1], and Open01 for the open interval (0,1). ShuffleFastaSeq is a Windows form application, written in C#, to shuffle FASTA-formatted sequences. ***Please do be careful with the "Delete all files" option and the target drive/path. Includes examples on extending classes and using common components! See code on GitHub. 洗牌算法（shuffle） 2. The study aids and games were created using a variety of tools including Fisher and Yates algorithm, Durstenfeld Shuffle, CSS transitions class, and dynamic HTML (DHTML). Shuffle Sync is a very simple program which allows you to copy random files of a specific type (usually music or video files) to a target path or drive. cards[i] = i;) and then shuffle that deck using the Fisher-Yates / Durstenfeld shuffle algorithm (shown below) so that we all get the same card ordering: // To shuffle an array a of n elements (indices 0. - Applied a JavaScript implementation of the Durstenfeld shuffle, a computer-optimized version of the Fisher-Yates shuffling algorithm, to randomize the flashcards Show more Show less See project. Examples on RunKit. Make sure audio(4) blocksize sticks when set explicitly by an AUDIO_SETINFO call. Start iterating the array from the last element. Random interleavers are the most preferred interleavers utilized in digital and cellular communication systems for burst errors control. In this case the perils of copy-paste programming didn't materialize, and succumbing to the "your shuffle is biased" peer-pressure actually led to introducing a change that introduced an actual bias that was only perceived bias before. The Modern Method. n-1): for i from n - 1. These authors didn't recognize the earlier Fisher's and Yates' elaboration, only mentioned once their. Random shuffling of data arrays is very common operation in data science which F# was designed for. So it would be very convenient to have such an operation in the language. National Institute of Standards and Technology. Lectures by Walter Lewin. The major steps being: Let's say you have an array of N elements,sat A[N] the index being [0, N-1]. function shuffle_array(array) { var cur_idx = array. while k > 0 do i) for i from C_k(N)-1 to 1 decrementing by 1 do a. now(); var pixels = shuffledImage. [citation needed] He was the President of Badminton Association of India, Vice President of Badminton Asia Confederation, Member - Executive Council of Badminton World. Knutt / Durstenfeld Shuffle Algoritmasının Resim Şifreleme Amacıyla Kullanılması Image Encryption Based On Knutt / Durstenfeld Shuffle Algorithm. 洗牌算法3-完美洗牌算法. There's a couple of algorithms explained in the article, but the one I found more useful is the one known as the modern version of the Fisher-Yates shuffle algorithm by Richard Durstenfeld. The code is directly mutating the state which is considered as a bad practice. alex가 말했듯이, 같은 폭의 경계선은 서로 45도 각도로 맞 닿아 있습니다. Review Board 1. It iterates the array from the last to the first entry, switching each entry with an entry at a random index below it. O intuito é aplicar esse algoritmo para embaralhar elementos de um vetor baseado no índice da posição que cada elemento ocupa. mattattaqdevblog. Block cipher is an encryption algorithm that performs a substitution and permutation operations on a block of data using a secret key. The Knuth-Fisher-Yates shuffle algorithm picks 1 out of n elements, then 1 out of n-1 remaining elements and so forth. To move with short sliding steps, without or barely lifting the feet: The crowd shuffled out of the. But RANDPERM uses indirectly the Mersenne Twister generator whose internal state has about 625. They may differ by the actual way the hands are held to accomplish the shuffle, but the result is the same. This is an accurate, effective shuffling method for all array types. Durstenfeld Shuffle的算法是从数组第一个开始，和Knuth的区别是遍历的方向不同. com is your one-stop shop to make your business stick. Below is some pseudocode adapted from the description and code he sent me. Cryptographically secure shuffle using the Fisher-Yates algorithm. w71r7wfw9itm, s321lqjnqzmm, 6neu8fsuv27l, pc5ci74m69uk1, 6s6k5ovx2x9, 790kxiswv30cii, ngb9c3s0237md2f, swj2914smsoy, grg3n69rsihf7, kob73vevxa, 55kqt5xpuvku, byf6usxrajl9b, vkykvctf5p, b86pjcczuffq, m68vzma297i50i, ib3jgkmy6s, tqnyhq85qeofud6, 8e82fnec7g8l, boofa1yd01, uym9qtnv7tcn4, e68vjrpb8ew7j, ib6i3tof3omgtpt, 8e4pt7nbc44u2bw, 7v1fuz1w42r1p, 5nywj59860afs, yd8bi5g61jx, 95w6kjdlof, qj4nl0shu8ymuuq, u9lid3p44yrmpk, 83b2yha5ijood, hjmtdus1uj, 58s2sfjsbvzg, mhiydpuubn5xe8u, dn2oeop4dt | 2020-06-05 14:10:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29473090171813965, "perplexity": 4010.4155339763406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348500712.83/warc/CC-MAIN-20200605111910-20200605141910-00152.warc.gz"} |
https://codereview.stackexchange.com/questions/99113/copying-and-pasting-from-ms-project-to-ms-excel | # Copying and pasting from MS Project to MS Excel
This copies data from a project into Excel to be calculated into a final report. The code runs pretty slowly at this point and I would like it to be a little bit faster. Are there any blatant coding mishaps that are slowing the calculations down?
Sub Update_Schedule()
Dim appProj As MSProject.Application
Dim aProg As MSProject.Project
Dim sel As MSProject.Selection
Dim ts As Tasks
Dim t As Task
Dim rng As Range
Dim rng2 As Range
Dim ws As Worksheet
Dim ws2 As Worksheet
'Clear current contents
Set ws2 = Worksheets("Final Report")
Set ws = Worksheets("Master")
Set rng = ws.Range("A:F")
rng.ClearContents
Set ws = Worksheets("Resource List")
Set rng = ws.Range("A:B")
rng.ClearContents
'Open the Project file when it asks to open resource pool, press yes
Set appProj = CreateObject("Msproject.Application")
appProj.FileOpen "File_1.mpp" 'also opens file 2
Set aProg = appProj.Projects("File_1.mpp")
appProj.Visible = True
WindowActivate WindowName:=aProg
'Copy the project columns and paste into Excel
Set ts = aProg.Tasks
EditCopy
Set ws = Worksheets("Master")
Set rng = ws.Range("A:A")
ActiveSheet.Paste Destination:=rng
EditCopy
Set rng = ws.Range("B:B")
ActiveSheet.Paste Destination:=rng
EditCopy
Set rng = ws.Range("C:C")
ActiveSheet.Paste Destination:=rng
EditCopy
Set rng = ws.Range("D:D")
ActiveSheet.Paste Destination:=rng
EditCopy
Set rng = ws.Range("E:E")
ActiveSheet.Paste Destination:=rng
EditCopy
Set rng = ws.Range("F:F")
ActiveSheet.Paste Destination:=rng
WindowActivate WindowName:="\\File_2.mpp"
SelectResourceColumn Column:="Name"
EditCopy
Set ws = Worksheets("Resource List")
Set rng = ws.Range("A:A")
ActiveSheet.Paste Destination:=rng
SelectResourceColumn Column:="Category"
EditCopy
Set rng = ws.Range("B:B")
ActiveSheet.Paste Destination:=rng
'Populates formula in Master sheet
Application.Visible = True
Set ws = Worksheets("Master")
Set rng = ws.Range("G2")
Set rng2 = ws.Range("G2:G9223")
rng.AutoFill Destination:=rng2, Type:=xlFillDefault
Set rng = ws.Range("H2")
Set rng2 = ws.Range("H2:H9223")
rng.AutoFill Destination:=rng2, Type:=xlFillDefault
Calculate
ws2.Visible = True
End Sub
• Opening up MS Project, and opening up a file in it will be slow. If that's the slow part, it might be ard to speed it up. I would suggest adding a Debug.Print with the timestemp after each line to see which ones are slow. – Justin Dearing Aug 5 '15 at 16:20
• I've done some debugging and the slowest part is actually the part under the comment "populates formula in master sheet." It may just be that filling in the formula takes awhile. – Seth39195 Aug 5 '15 at 18:20
• Do you always have data down to row 9,223? If you might have much less data, you might see significant improvement if you figure out how much data you actually have and then fill down that number of rows. – ChipsLetten Aug 6 '15 at 16:13
• I usually don't have data that far down. Is there a good way to fill to just the last cell? – Seth39195 Aug 6 '15 at 17:36
• If you search on Stack Overflow you will find examples of how to find the last row/cell. – ChipsLetten Aug 7 '15 at 10:17
My earlier comment was: Do you always have data down to row 9,223? If you might have much less data, you might see significant improvement if you figure out how much data you actually have and then fill down that number of rows.
Here is an example of code:
Set ws = Worksheets("Master")
Dim lastRow As Long
lastRow = LastRowNum(ws.Name, "A")
Set rng = ws.Range("G2")
Set rng2 = ws.Range("G2:G" & lastRow)
rng.AutoFill Destination:=rng2, Type:=xlFillDefault
Set rng = ws.Range("H2")
Set rng2 = ws.Range("H2:H" & lastRow)
rng.AutoFill Destination:=rng2, Type:=xlFillDefault
...
End Sub
Function LastRowNum(sheetName As String, columnLetter As String) As Long
With ThisWorkbook.Worksheets(sheetName)
LastRowNum = .Range(columnLetter & .Rows.Count).End(xlUp).Row
End With
End Function
• Thanks, I've had some success with code similar to this. – Seth39195 Aug 10 '15 at 12:38
• If you are happy with one of the answers, please remember to mark it as accepted. – ChipsLetten Aug 12 '15 at 9:06
A few things here:
• Read this. Its lists things to do when copying large amounts of data
• Did you set Application.Calculation = xlCalculationManual? Your manually calling Calculate, but you never turn off autocalcualtion.
• Did you set Application.ScreenUpdating = FALSE? That can speed things up.
• Auto calculation is turned off in the excel file. Am I correct in thinking that it will remain off while running the macro? – Seth39195 Aug 5 '15 at 19:47
• Yes, it will be off. you Could, to be safe, save the value of Application.Calcualtion to a variable, then turn it off then restore it to the old value. What about toggling screen updating? – Justin Dearing Aug 5 '15 at 19:50 | 2019-10-15 00:37:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2622571885585785, "perplexity": 6268.170237097655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986655554.2/warc/CC-MAIN-20191014223147-20191015010647-00063.warc.gz"} |
https://cs.stackexchange.com/questions/75743/non-deterministic-space-hierarchy | # non deterministic space hierarchy
I want to prove the non deterministic space hierarchy theorem.
Let $f(n),g(n)\geq\log n$ be space constructible functions such that $f(n)=o(g(n))$, Prove:
$$NSPACE(f(n))\subsetneq NSPACE(g(n))$$
I feel that the standard way of constructing a TM that takes as an input a TM and simulates the machine on itself, then flipping the output won't work because the input is a nondetrministic TM maybe. Can someone suggest a hint?
• Take a look at the Wikipedia article. – Yuval Filmus May 22 '17 at 7:25
• @YuvalFilmus I actually looked there but their change of proof from the deterministic proof, is not clear since they change stage 4 and know it is not clear why L is still acceptable in NSPACE(g(n)), I mean can you explain why their language L is acceptable in NSPACE(g(n)), because their machine is wrong. – Don Fanucci May 22 '17 at 7:27
• Did you notice that they changed the language $L$? – Yuval Filmus May 22 '17 at 7:37
• The title you have chosen is not well suited to representing your question. Please take some time to improve it; we have collected some advice here. Thank you! – Raphael May 22 '17 at 10:12
## 1 Answer
The Wikipedia proof for the non-deterministic doesn't flip the output. It considers the language $$L = \{ (\langle M \rangle, 1^t) : \text{M accepts (\langle M \rangle, 1^t) in space g(|(\langle M \rangle, 1^t)|)} \}.$$ This language is in $\mathsf{NSPACE}(g)$. The Immerman–Szelepcsényi theorem shows that if $L \in \mathsf{NSPACE}(f)$ then also $\overline{L} \in \mathsf{NSPACE}(f)$, which leads to a contradiction. | 2019-08-25 14:24:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6449025869369507, "perplexity": 660.5111718459517}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027330233.1/warc/CC-MAIN-20190825130849-20190825152849-00187.warc.gz"} |
https://blog.givewell.org/2008/10/page/2/ | # A bit more detail on individual giving
We constantly emphasize the huge amount of money that is given by individuals. However, the figures we usually point to refer to all giving; people often, correctly, point out to us that many individual gifts are made to support churches, alma maters, public goods, etc., rather than to help those in need. A study by… Read More
# Check your “smart philanthropy” hat at the door?
The last blog post shares general thoughts on Money Well Spent. Specifically, though, this bit really struck me (page 12): In our personal lives, we regularly make year-end gifts to organizations for which we have warm feelings. These gifts make us feel good, and doubtless they help good organizations. But this isn’t the way to… Read More
# Thoughts on “Money Well Spent”
I just finished reading Money Well Spent. (Disclosure: I was sent an advance copy.) The book gives a clear and public picture of how the authors conduct their grantmaking, something I believe is relatively rare in the sector; I’d like to see more people in this area laying out their approach and their positions on… Read More
# What does $1000 do? We’re currently working to find vehicles for donors to fund certain highly appealing program-based interventions. It’s not a simple task, because when dealing with large organizations, it’s rarely clear just how an individual donor’s “drop in the bucket” fits in. Large organizations like UNICEF run a huge variety of programs – including programs such as… Read More # Donor impact vs. donor attribution (or, does your$120 really buy a sheep?)
One of the questions we struggle with a lot is the question of what impact a donation has – i.e., what happens because of your donation that wouldn’t have happened otherwise? In other words, what do you get for your dollar? It’s a tricky question, especially for relatively small donations going to relatively large organizations…. Read More | 2017-11-23 03:33:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1997886300086975, "perplexity": 2928.6847437027577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806720.32/warc/CC-MAIN-20171123031247-20171123051247-00664.warc.gz"} |
https://direct.mit.edu/edfp/article/14/1/88/10302/What-Constitutes-Prudent-Spending-from-Private | ## Abstract
This study examines how private colleges and universities choose to spend versus reinvest resources in endowment funds that have suffered investment losses. The analysis takes advantage of a market downturn and public policy shift, which together revealed how colleges define prudent spending. Investment losses during the financial crisis of 2008 left many endowment gift funds below their original donated values, or “underwater.” Colleges in some states were legally required to cut spending from underwater funds. Other states had recently enacted the Uniform Prudent Management of Institutional Funds Act, which allows prudent spending from underwater funds. The act loosened financial constraints, and affected colleges responded by spending 22 percent more from their endowments in the fiscal year after the financial crisis. Constrained colleges did not increase spending from unrestricted parts of their endowments to offset reduced spending from underwater funds.
Only a year ago, universities, with their $400 billion in endowment money, faced a congressional inquiry because of widespread concern they needed to spend more of their savings on financial aid for students. Now, colleges are finding that state laws are not letting them spend enough, [after] taking a beating from the recession and the collapse in stock prices… The growing movement [toward a new state law] is sparking a debate about the value of freeing up emergency cash versus the danger of further depleting key financial reserves, potentially shortchanging future generations. The Wall Street Journal, 11 February 2009 ## 1. Introduction This study informs the debate that is central in the extracted quote, by measuring changes in private college endowment spending caused by a state law called the Uniform Prudent Management of Institutional Funds Act, or UPMIFA (pronounced up-MIFF-uh). In the early 2000s, endowments grew quickly in size and importance. In the five-year period leading up to 2008, the average private college endowment gained 46 percent in real value from a combination of positive investment returns and new donations, net of spending. By spending roughly 5 percent of a moving average of its total endowment value in each year, the average private college covered 10 percent of its yearly expenses, though some covered well over half. Endowment spending typically supports scholarships and faculty salaries. During the financial crisis of 2008, the average private college endowment lost 22 percent of its value, jeopardizing financial support for students and faculty (NACUBO-Commonfund 2009). Many recently donated endowment gift funds were “underwater,” worth less than their original value at donation. Expecting declines in revenue from tuition and other sources (Nelson and Goodman 2009), each college had to choose how much to spend from smaller, and in many cases underwater, gift funds. In many states, the law prohibited spending from underwater funds, imposing large cuts to endowment revenue, which would be difficult to replace from other sources. UPMIFA allows for spending from underwater funds where prior law did not. The law imposes a prudent person standard, which simply requires colleges to consider several economic factors before spending. Introduced in 2006, UPMIFA was enacted in all states by 2012.1 Small differences in timing of enactment, combined with the prevalence of underwater funds after the financial crisis, led to large differences in spending constraints on otherwise similar colleges. To assess the effect of spending constraints, I compare endowment spending before and after UPMIFA. I focus on private, nonprofit, endowed, four-year colleges and universities in the United States, using panel data over fiscal years 2005 to 2013. During this time, state laws vary within each college across years, and across colleges within each year. Therefore, it is possible to identify the law's effect on spending while controlling for college and year fixed effects in a difference-in-differences approach, estimating increases in spending after enactment of UPMIFA. Colleges vary in their level of underwater funds at the time their state enacted UPMIFA. I exploit this variation to introduce a third difference, which relies on the sudden onset of the financial crisis for identification. I find that UPMIFA allows colleges to spend 6.12 cents more per dollar in underwater funds. This implies that the average college under UPMIFA spent a typical amount from underwater funds, whereas colleges under prior law spent little to nothing from underwater funds. These findings imply that from the effect of legal constraints alone, the average private college under prior law experienced a 22 percent decrease in endowment revenue in fiscal 2010, on top of a roughly 6 percent decrease in endowment revenue from absorbing the investment losses of fiscal 2009. Colleges do not appear to have increased spending from unrestricted parts of their endowment to offset these losses. The results appear to be driven by larger endowments. This study contributes to a growing empirical literature on endowment spending decisions. Most colleges use similar, simple formulas to plan spending (Brown and Tiu 2015), but colleges systematically deviate from their plans, usually to spend less (Brown et al. 2014). Legal constraints on endowment spending have received little attention as an explanation for these deviations, for two reasons: Nearly all states used the same uniform law for decades, and the law restricted spending only in extreme circumstances (Budak and Gary 2010). UPMIFA represents a new and less restrictive endowment law that was introduced just before the extreme investment losses of the late 2000s recession. A few other studies address UPMIFA, but do not test for its impact by comparing spending across groups of colleges. The calibrated model in Gilbert and Hrdlicka (2015) predicts that external constraints on endowment spending will lead to larger and more risky endowments. However, the study does not test this prediction using the loosening in constraints provided by the adoption of UPMIFA. Bass (2010) surveys a set of colleges in early-enacting states about how they will respond to UPMIFA. The majority of colleges plan to take advantage of the flexibility to spend from underwater funds under UPMIFA but many also report spending from underwater funds under prior law, suggesting a muted effect of the change to UPMIFA. The present study provides information beyond these targeted surveys of college plans after UPMIFA, with a larger panel including observations of actual spending by colleges under different laws. The comparisons in this study provide an empirical definition of “prudent management,” using colleges’ behavior to reveal how they interpret the legal definition provided in UPMIFA. The analysis focuses on spending from underwater funds, which under UPMIFA should be representative of a college's general approach to weighing current spending versus investment for the future.2 The remainder of the study is divided into six sections. Section 2 provides additional background, which informs the empirical strategy laid out in section 3. Section 4 describes the data used to implement the empirical strategy. Section 5 reports the main results, section 6 provides supplementary results, and section 7 includes some robustness checks. Section 8 concludes with a discussion of the results. ## 2. Endowment Spending and State Laws Endowment donors stipulate that the college invest their gifts and spend only the investment income for a particular purpose, like student financial aid or a faculty chair. Within these constraints, the college chooses how to invest gift funds together with other savings in its endowment, and how much to spend each year on particular students or faculty.3 On behalf of donors and taxpayers, state laws (as enforced by the state attorney general) guide the choices made by nonprofit, tax-exempt college endowments. This section discusses how endowment spending works in practice, and how state laws affect this process. The vast majority of colleges plan endowment spending using simple formulas that combine future expectations with recent history (Brown and Tiu 2015). Under a moving-average rule—the most common formula—a college sets a constant “policy spending rate” near 5 percent. This rate corresponds to its long-term target for real rate of return on investments (NACUBO-Commonfund 2014). The college multiplies that rate by a moving average of the total endowment value. Most often the formula averages endowment values over the past three to five years at a yearly or quarterly frequency (Brown and Tiu 2015). Total spending during a fiscal year divided by total endowment value at the beginning of the fiscal year is called the “effective spending rate” or simply the spending rate. Whereas the policy spending rate is constant, the effective spending rate moves counter to changes in endowment value coming from new donations, investment gains, or investment losses. These changes in value are incorporated slowly into spending levels. Colleges often change the parameters of their spending formulas, and actual spending varies around planned spending (Brown and Tiu 2015). This is not surprising because, in theory, a simple spending rule is unlikely to solve the complicated intertemporal allocation problem each college faces (Hansmann 1990; Hoxby 2015). In practice, college spending appears to respond to the source of capital gains and to respond asymmetrically to gains and losses, which are not components of the typical spending rule (Woglom 2003; Brown et al. 2014). Still, the prevalence of the moving-average formula illustrates the importance of sustaining the value of the endowment while providing a steady and growing stream of payouts. A college endowment is commonly discussed as a whole but is actually made up of many separate donations and deposits. Endowed gifts each create a permanent fund. In addition to gift funds, sometimes called “true endowment” funds, approximately one third of endowment value is in quasi-endowment funds. These are assets kept in the endowment by a resolution of the college's governing board. The college has only a reversible internal commitment, and no external legal obligation, to permanently maintain the value of quasi-endowment funds. Most of the time, the legal distinction between the endowment as a unit and the endowment as a collection of funds is not economically important. Investment and spending decisions are made at the level of the endowment, so that each fund experiences the same net percent growth. Purpose restrictions of individual gifts are not economically binding except in the rare case where investment income from a gift fund provides the last dollar a college spends on a particular purpose (Ehrenberg 2009).4 Sometimes, legal constraints on spending from individual gift funds bind and become economically important. Agreements with donors are made at the fund level but rarely include explicit instructions for spending. State laws interpret donor intent, defining income intended to be spent versus principal intended to be saved. The definition has evolved over time and been codified in two versions of a uniform state law. Both versions were promulgated by the National Conference of Commissioners on Uniform State Laws (NCCUSL, now called the Uniform Law Commission or ULC), a nonpartisan, national association of lawyers seeking to unify laws across state boundaries whenever appropriate. Before 1972, the working definition of endowment income was limited to trust income, including interest, dividends, rents, and royalties from investments bought with the original gift principal (Budak and Gary 2010). In 1972, the NCCUSL published the Uniform Management of Institutional Funds Act or UMIFA (NCCUSL 1972). This predecessor to UPMIFA expanded the definition of endowment income by expressly allowing endowments to pursue and spend capital gains. To protect some concept of permanent principal, the law limited spending to capital gains above “historic dollar value.” The law defined historic dollar value as the original gift amount plus any subsequent donations to the fund, not adjusted for inflation. This created the concept of an underwater fund, worth less than its historic dollar value and therefore yielding no capital gains to spend. The law was enacted nearly universally. Newer funds with little net nominal growth will fall below their historic dollar values after investment losses. Designating them as underwater, the old uniform law limits spending only from these newer funds even though they tend to have lost the same percent of their real value as older funds. Mainly to address this inconsistency, in 2006 the NCCUSL published UPMIFA (NCCUSL 2006). UPMIFA ignores underwater funds per se and ensures the preservation of all endowment funds using a prudent person standard rather than a sharp, nominal, backward-looking spending limit.5 Because there is no clear consensus on endowment management objectives, it is not clear that prudent management of underwater funds implies spending from those funds.6 Just after the financial crisis of 2008 led to a large increase in underwater funds, twenty-five states had not yet enacted UPMIFA. Colleges in these states therefore saw a gap between what their normal spending policies would indicate for the following year's spending and what prior law allowed. The gap varied across colleges by the amount in underwater funds, which ranged from very little of the endowment to over half of the endowment. Colleges under prior law had a few options for filling the gap between planned spending and legally allowed spending, including contacting donors to modify agreements, seeking legal release from agreements with unavailable donors, or limiting spending to trust income (Sare 2009). Each of these options requires a fundamental change in either the spending or investment plan for each underwater fund. A college could also legally spend more from unrestricted quasi-endowment funds, which can never be underwater. Besides these options within the endowment, the college could seek other revenues or make budget cuts. Colleges in UPMIFA states could, in addition to all these more difficult options, pursue their definition of prudent spending from underwater funds. The following section lays out a plan for measuring the impact of UPMIFA by comparing spending across colleges. ## 3. Empirical Model ### Main Specification The key parameter to estimate is the difference in spending rates caused by UPMIFA. This could ideally be estimated by observing a college's spending rates from underwater funds under UPMIFA versus prior law, all else held equal. The following empirical model approximates this ideal comparison using the available data and the natural variation in timing of enactment of UPMIFA. Survey data, which I detail in section 4, do not include spending rates from individual gift funds or from types of funds. They do include aggregate endowment values by type of fund, such as the total value in the endowment, the value in underwater funds, and the value in quasi-endowment funds. The data include aggregate flows at the level of the endowment, such as spending and investment returns. Colleges are observed once per year. I use this information to infer spending rates by estimating the coefficients of the following panel regression. $Spendit=∑j=0,1,2αjBeg.valueit-j+θUPMIFAit+ζUnderwaterit+ηUPMIFAitUnderwaterit+Xit'β+γi+δt+ɛit.$ (1) This regression estimates average spending rate slopes $α0$, $α1$, $α2$, $ζ$, and $η$ across many colleges $i$ and fiscal years $t$. $γi$, $δt$, and $θ$ allow for different spending intercepts by college, year, and law. $ɛit$ is an idiosyncratic error term. I report results with and without $Xit$, which includes investment returns broken into positive and negative components, as well as lagged expenses (these measures make up the endowment shocks in Brown et al. 2014). This regression mirrors the moving-average formula, where spending is a linear function of current and lagged endowment values. Therefore, I expect the sum of the coefficients on lagged endowment values $α0+α1+α2$ to approximate the policy spending rate, around 5 cents per dollar. For colleges that do not use a moving-average formula, current and lagged endowment values and current value in underwater funds control in a simple and flexible way for a college's recent financial history. Dollars in underwater funds reduce the base available for spending, but only prior to UPMIFA. Therefore I expect the coefficient $ζ$ to equal the negative of the effective spending rate, around negative 5 cents per dollar. The coefficient $η$ on the interaction term represents how much of this reduction is offset under UPMIFA, and is the focus of this analysis. $η$ is a triple-difference parameter, $θ$ captures the difference-in-differences in spending for colleges in states enacting UPMIFA when underwater funds are zero, and $η$ captures how that difference-in-differences varies by the amount in underwater funds at the time of enactment. If the effect of UPMIFA operates only through underwater funds, then $θ≈0$. ### Identification To interpret $η$ as the causal impact of UPMIFA on spending from underwater funds, there must be parallel differences-in-differences in spending, absent the policy change, at all levels of underwater funds. This assumption can fail if the effect of UPMIFA is heterogeneous and associated with the timing of enactment. In section 4, I provide some evidence for similarity across colleges in states that enact UPMIFA at varying times, and for parallel trends in spending, but the parallel differences in differences assumption is not directly testable. The assumption breaks down under policy endogeneity or any sort of selection into enactment timing that is associated with potential differences-in-differences. Suppose that, after the drafting of UPMIFA, some colleges advocate more strongly for enactment because they are more inclined to take advantage of UPMIFA's added flexibility and to spend more from underwater funds. If they succeed and their states enact UPMIFA earlier, then there are no longer parallel differences-in-differences across early- and late-enacting states. This story seems unlikely for a few reasons. First, advocacy by colleges was not the main determinant of variation in enactment timing. Members of the drafting committee of UPMIFA emphasized that the law was typically disseminated to legislators by lawyers and national organizations, not by colleges.7 State legislatures meet for different periods of the year, have different non-endowment-related priorities, and follow idiosyncratic conventions in setting the effective dates of new laws.8 Second, earlier enactments need not reflect variation in colleges’ preferences for spending under UPMIFA. Earlier enactments could instead reflect the preferences of state legislatures. The complexity of the issue was on display in Massachusetts, a state where lawmakers had previously criticized endowments for spending too little, but where UPMIFA, which allows for more spending, was enacted relatively late (Hechinger 2008). Third, successful advocacy by colleges, if it occurred, could be a function of colleges’ size and resources, rather than any differential preference for additional spending under UPMIFA. Then states with more influential colleges would enact UPMIFA earlier. However, there would be no bias introduced because the effect of the policy at these colleges would be representative of the effect at smaller colleges in later-enacting states. Most states saw fit to enact UPMIFA before the financial crisis, when underwater funds were nearly zero, and all states enacted it at some point. With such a short time span for all state legislatures to enact UPMIFA, small differences in timing of enactment could arise even without any differences in preferences across colleges or state legislatures.9 ### Alternative Specifications There may be differences across colleges in the impact of UPMIFA that are not associated with the timing of enactment. In a supplemental analysis, I allow for heterogeneity in effects by observable characteristics of colleges that may lessen the impact of UPMIFA. I add terms to equation 1 to measure heterogeneity in the effect along these dimensions. $Spendit=∑j=0,1,2ωjBeg.valueit-j+ξUPMIFAit+χUnderwaterit+νUPMIFAitUnderwaterit+πPiUPMIFAit+φPiUnderwaterit+ψPiUPMIFAitUnderwaterit+Xit'μ+ιi+τt+εit.$ (2) The added terms are interactions between the key underwater and legal terms and a time-invariant measure $Pi$. $Pi$ can represent the percent of college $i$’s operating expenses covered by endowment spending, as colleges that rely more heavily on endowment spending may make smaller cuts in spending under prior law. $Pi$ can also be an indicator for the use of special appropriations from the endowment. Colleges sometimes draw special appropriations outside the normally reported spending rate. Because many colleges never do this, Brown and Tiu (2015) interpret colleges that do draw special appropriations as having more flexible control over spending. $Pi$ can also represent the percent of endowment dollars in quasi-endowment funds, which are not subject to the constraints imposed by state laws. In this extended regression $ξ$, $χ$, and $ν$ represent impacts for colleges with $Pi=0$. $π$, $φ$, and $ψ$ represent the differential impact for a unit increase in $Pi$. In all cases, I expect higher $Pi$ to shrink the effect of underwater funds and therefore shrink the gap in spending across colleges under different laws. Then $φ>0$ and $ψ<0$. The empirical models in equations 1 and 2 make particular choices that can be relaxed in robustness checks. In section 7, I allow for varying effects of UPMIFA in the post-enactment period, and use alternative measures of spending. Estimating all of these regressions requires data on college endowments during a period when variation in underwater funds and legal changes allow for identification. ## 4. Data and Descriptive Statistics This study focuses on private, nonprofit, four-year colleges and universities. These are the colleges where endowments are the most important to the budget and where endowments commonly support a single college campus. In contrast, public colleges and universities receive state funding determined by the same central authority for many colleges in a state, often for multiple years at a time. If budgets set at the state and year level affect public college and university endowment spending, then that variation in budgets could be confounded with the variation in state laws that I seek to isolate. Data come from the National Association of College and University Business Officers (NACUBO), the Commonfund Institute, and the Integrated Postsecondary Education Data System (IPEDS). The NACUBO-Commonfund Study of Endowments (NCSE) provides data on spending, investment returns, and asset valuations for each college's endowment each fiscal year.10 IPEDS adds general college characteristics and finances. The NCSE began measuring underwater funds at the beginning of fiscal year (FY) 2005, so the sample for this study begins then and extends through FY 2013, covering the final state's enactment of UPMIFA. A total of 522 colleges have sufficient data to appear in the panel sample. The sample is skewed toward colleges with larger endowments and the resources to provide data. Appendix B includes further details on the data sources and sample, and Appendix C includes detailed data definitions. The average endowment in the panel sample is summarized in table 1, in the first column, labeled All. The average college held$368.6 million in its endowment leading up to the financial crisis.11 An average spending rate of 4.8 cents per dollar covered an average of 9.8 percent of the college's operating expenses.12 Following the 2008 financial crisis, average investment returns over FY 2009 were –19.0 percent (including a rebound in stock prices late in the fiscal year). This led to 17.4 percent of endowment value being in underwater funds by the end of FY 2009. The amount in quasi-endowment funds was first reported in 2009, so I include the post-crisis average here as a measure of quasi-endowment for each college. The average endowment was made up of 31.4 percent quasi-endowment. Finally, covering all years in the sample, 39.3 percent of colleges ever drew special appropriations.
Table 1.
Mean Values for Uniform Prudent Management of Institutional Funds Act (UPMIFA) Enactment Cohorts
Enactment Cohort All $≤$2008 2009 2010 2011 $≥$2012 Number of colleges 522 65 106 142 146 63 Pre—financial crisis, 2005—08 average Endowment value ($M) 368.6 226.8 242.3 367.7 478.7 393.9 Effective spending rate (%)*** 4.8 4.3 5.4 4.7 4.5 5.1 Operating expenses covered (% of operating expense) 9.8 7.9 11.8 9.3 8.9 11.3 Post—financial crisis Investment return fiscal 2009 (%) −19.0 −18.9 −18.2 −18.9 −19.5 −19.2 Underwater funds, end 2009 (%) 17.4 15.9 18.1 18.2 15.4 20.4 Quasi-endowment 2009—13 average (%)*** 31.4 36.2 25.5 25.3 37.0 35.3 Over entire sample Ever used special appropriations (% of colleges)* 39.3 27.7 45.3 41.8 34.2 47.6 Enactment Cohort All $≤$2008 2009 2010 2011 $≥$2012 Number of colleges 522 65 106 142 146 63 Pre—financial crisis, 2005—08 average Endowment value ($M) 368.6 226.8 242.3 367.7 478.7 393.9 Effective spending rate (%)*** 4.8 4.3 5.4 4.7 4.5 5.1 Operating expenses covered (% of operating expense) 9.8 7.9 11.8 9.3 8.9 11.3 Post—financial crisis Investment return fiscal 2009 (%) −19.0 −18.9 −18.2 −18.9 −19.5 −19.2 Underwater funds, end 2009 (%) 17.4 15.9 18.1 18.2 15.4 20.4 Quasi-endowment 2009—13 average (%)*** 31.4 36.2 25.5 25.3 37.0 35.3 Over entire sample Ever used special appropriations (% of colleges)* 39.3 27.7 45.3 41.8 34.2 47.6
Source: NACUBO-Commonfund Study of Endowments (NCSE).
Notes: Enactment cohorts are defined by the first fiscal year UPMIFA was effective in their state in time to affect spending plans. The 2008 cohort also includes earlier enactments, and the 2012 cohort also includes later enactments. Unless noted otherwise, % values are percent of beginning-of-year endowment value in dollars.
*p < 0.10; ***p < 0.01 for F-test of equality of means across cohorts.
Figure 1 shows the progression of investment, spending, and underwater funds over time, averaging over all colleges in the sample each fiscal year. As investment returns fluctuate, spending stays relatively smooth. Underwater funds increase with a lag after investment losses, and decrease with a lag after investment gains. Although these aggregate trends are consistent with stated spending formulas, actual spending often varies around planned spending. Central to this study, legal constraints can be one reason for this variation.
Figure 1.
Trends in Mean Endowment Rates, 2005—13
Source: NCSE.
Figure 1.
Trends in Mean Endowment Rates, 2005—13
Source: NCSE.
Every state during 2005 to 2013 was subject to one of two rules on spending from underwater funds. Table 2 lists the effective date of the move to UPMIFA for all states. It also lists the lag between signing (when UPMIFA is passed by the legislature and signed or otherwise approved by the governor) and the effective date of the law.13
Table 2.
Effective Dates of UPMIFA, and Lag in Days Between Signing into Law and Effective Date
State Year Month Day Lag State Year Month Day Lag Alabama 2009 Jan 1 245 Montana 2007 Oct 1 151 Alaskaa 2010 Sep 8 61 Nebraska 2007 Sep 1 150 Arizona 2008 Sep 26 165 Nevadaa 2007 Oct 1 140 Arkansas 2009 Jul 30 154 New Hampshire 2008 Jul 1 41 California 2009 Jan 1 93 New Jersey 2009 Jun 10 0 Colorado 2008 Sep 1 133 New Mexico 2009 Jul 1 85 Connecticut 2007 Oct 1 188 New York 2010 Sep 17 0 Delawarea 2007 Jul 31 13 North Carolina 2009 Mar 19 0 D.C. 2008 Jan 23 65 North Dakota 2009 Apr 21 0 Florida 2003 Jul 1 0 Ohio 2009 Jun 1 146 Georgia 2008 Jul 1 56 Oklahoma 2007 Nov 1 181 Hawaii 2009 Jul 1 12 Oregon 2008 Jan 1 193 Idaho 2007 Jul 1 97 Pennsylvania 1998 Dec 21 0 Illinois 2009 Jun 30 0 Rhode Island 2009 Jun 30 0 Indiana 2007 Jul 1 51 South Carolina 2008 Jul 1 20 Iowa 2008 Jul 1 81 South Dakota 2007 Jul 1 121 Kansas 2008 Jul 1 96 Tennessee 2007 Jul 1 44 Kentucky 2010 Jul 15 112 Texas 2007 Sep 1 78 Louisiana 2010 Jul 1 22 Utaha 2007 Apr 30 54 Maine 2009 Jul 1 12 Vermont 2009 May 5 0 Maryland 2009 Apr 14 0 Virginia 2008 Jul 1 120 Massachusetts 2009 Jun 30 −2 Washington 2009 May 11 0 Michigan 2009 Sep 10 0 West Virginia 2008 Jun 3 68 Minnesota 2008 Aug 1 113 Wisconsin 2009 Aug 4 15 Mississippi 2012 Jul 1 76 Wyominga 2009 Jul 1 111 Missouri 2009 Aug 28 49
State Year Month Day Lag State Year Month Day Lag Alabama 2009 Jan 1 245 Montana 2007 Oct 1 151 Alaskaa 2010 Sep 8 61 Nebraska 2007 Sep 1 150 Arizona 2008 Sep 26 165 Nevadaa 2007 Oct 1 140 Arkansas 2009 Jul 30 154 New Hampshire 2008 Jul 1 41 California 2009 Jan 1 93 New Jersey 2009 Jun 10 0 Colorado 2008 Sep 1 133 New Mexico 2009 Jul 1 85 Connecticut 2007 Oct 1 188 New York 2010 Sep 17 0 Delawarea 2007 Jul 31 13 North Carolina 2009 Mar 19 0 D.C. 2008 Jan 23 65 North Dakota 2009 Apr 21 0 Florida 2003 Jul 1 0 Ohio 2009 Jun 1 146 Georgia 2008 Jul 1 56 Oklahoma 2007 Nov 1 181 Hawaii 2009 Jul 1 12 Oregon 2008 Jan 1 193 Idaho 2007 Jul 1 97 Pennsylvania 1998 Dec 21 0 Illinois 2009 Jun 30 0 Rhode Island 2009 Jun 30 0 Indiana 2007 Jul 1 51 South Carolina 2008 Jul 1 20 Iowa 2008 Jul 1 81 South Dakota 2007 Jul 1 121 Kansas 2008 Jul 1 96 Tennessee 2007 Jul 1 44 Kentucky 2010 Jul 15 112 Texas 2007 Sep 1 78 Louisiana 2010 Jul 1 22 Utaha 2007 Apr 30 54 Maine 2009 Jul 1 12 Vermont 2009 May 5 0 Maryland 2009 Apr 14 0 Virginia 2008 Jul 1 120 Massachusetts 2009 Jun 30 −2 Washington 2009 May 11 0 Michigan 2009 Sep 10 0 West Virginia 2008 Jun 3 68 Minnesota 2008 Aug 1 113 Wisconsin 2009 Aug 4 15 Mississippi 2012 Jul 1 76 Wyominga 2009 Jul 1 111 Missouri 2009 Aug 28 49
Source: State legislative records.
Notes: Lag = the number of days after the bill becomes law, before it becomes effective. A negative lag indicates a retroactive effective date. The dates for Florida and Pennsylvania refer to the first appearance of a law with similar provisions to UPMIFA. In Florida, UPMIFA itself was later enacted.
aNo colleges from the state appear in the panel sample.
A key decision for this analysis on yearly data is how to define $UPMIFAit$ to accurately measure when the law impacts colleges. State laws apply at the time of appropriation for spending, a planning period that precedes actual expenditure (Budak and Gary 2010). Rogers (2012) surveyed twenty-three private liberal arts colleges and found that they appropriate an amount to be spent from the endowment prior to the beginning of the fiscal year, and do not change that amount. This happens far enough in advance of the new fiscal year that some forecasting of investment returns and donations is required to know the beginning-of-year endowment value. In contrast, Brown et al. (2014) find that endowment spending at doctoral universities reacts to investment returns during the same fiscal year, particularly investment losses. Neither study directly addresses the process required to react to a new law.
Members of the drafting committee of UPMIFA expected there would be heterogeneity across colleges in reaction time.14 Large endowments would be most aware of legal developments, as they have greater resources devoted to managing the endowment and greater dependence on endowment revenue. But larger endowments also tend to be older and less exposed to underwater funds. Smaller endowments typically heard about the law through nonprofit trade publications or their legal counsel, months after it was enacted in their state.15 In all cases, UPMIFA provides less guidance than prior law, and should initiate a rethinking of what prudent management means. Therefore, it could require time to incorporate UPMIFA into practice. However, colleges may predict the law with certainty in cases where there is a long lag between the date of signing and the effective date.
Taking all of this into account, I define $UPMIFAit$ to indicate that the law is effective on or before 1 July, the first day of the academic fiscal year, and is signed into law at least three months prior (lag > 90 days).16 Given the heterogeneity across colleges, any setting will have some measurement error, which will attenuate estimated impacts of UPMIFA. In Appendix A, I present results with an alternative definition that ignores the signing date.
States can be divided into enactment cohorts by their first year with UPMIFA effective under this definition. In the regression analysis, college fixed effects control for any level differences across cohorts. However, it can be instructive to look for major differences across cohorts, which could suggest policy endogeneity. For the following descriptive statistics, the 2008 cohort also includes earlier enactments and the 2012 cohort also includes later enactments.
In table 1 there are some differences across cohorts. An F-test of equality in means across cohorts is rejected for spending rate and the percent in quasi-endowment. However, there are no monotonic trends by enactment year, and in a regression predicting enactment year, only percent in quasi-endowment is significant. It has a positive relationship with cohort year, indicating colleges with more quasi-endowment funds were in later-enacting states. The lack of any significant variation across cohorts in either average investment rate of return or average percent in underwater funds suggests that the financial crisis had a consistent impact on the average college in each cohort.
In the United States map in figure 2, darker shades of gray mark later-enacting states. The map shows that each cohort is geographically diverse. Again, this shows differences across cohorts but no clear systematic trends.
Figure 2.
Map of UPMIFA Enactments by State
Notes: Enactment cohorts are defined by the first fiscal year UPMIFA was effective in their state in time to affect spending plans. The 2008 cohort also includes earlier enactments, and the 2012 cohort also includes later enactments.
Figure 2.
Map of UPMIFA Enactments by State
Notes: Enactment cohorts are defined by the first fiscal year UPMIFA was effective in their state in time to affect spending plans. The 2008 cohort also includes earlier enactments, and the 2012 cohort also includes later enactments.
Figure 3 reports the mean spending by year and enactment cohort in the panel sample. There is some evidence for parallel trends in the pre-UPMIFA period. However, pre-UPMIFA changes in spending from FYs 2008 to 2009 are not parallel across cohorts, with the latest cohort increasing spending. This is potentially consistent with a situation where prior law reduced spending less for some states, allowing them to enact UPMIFA later. This situation would bias the estimates of the effect of UPMIFA downward, relative to what would be estimated with completely exogenous assignment of timing of enactment. Colleges in later-enacting states being apparently less constrained means that they spend more under prior law, and this decreases the measured difference in spending between colleges in early-enacting states already under UPMIFA, and colleges in later-enacting states under prior law.
Figure 3.
Trends in Spending Levels by Enactment Cohort, 2005—13
Note: Dotted lines represent fiscal years under UPMIFA.
Figure 3.
Trends in Spending Levels by Enactment Cohort, 2005—13
Note: Dotted lines represent fiscal years under UPMIFA.
The data are generally not well suited to provide strong evidence of parallel trends in support of the main identifying assumption. The required assumption is parallel trends across colleges in spending from underwater funds, absent the policy change, but this is difficult to show directly. I infer spending from underwater funds by estimating the coefficient in a regression of dollars of spending on the dollar value in underwater funds. These coefficients are noisy if only using pre-crisis data where underwater funds are very low. Some of the noise in figure 3 also comes from colleges entering and leaving the sample because of item nonresponse on key survey measures.
The regressions in the next section focus on underwater funds as a mechanism for UPMIFA's effect.
## 5. Effects of UPMIFA and Underwater Funds
Overall, I find that colleges cut spending from underwater funds when legally required to, but UPMIFA allowed colleges to avoid these cuts. These conclusions are based on statistically significant estimates that are robust to adding covariates.
Regression results appear in table 3. Standard errors in parentheses are clustered at the state level to allow for arbitrary correlation within each state. This accounts for two features of this analysis. Legal changes happen at the state level, and serial correlation of error terms within a state is likely (Moulton 1986; Bertrand, Duflo, and Mullainathan 2004).
Table 3.
Effects of UPMIFA and Underwater Funds on Endowment Spending
Coefficient (SE) Coefficient (SE) Dependent Variable: Endowment Spending ($M) (1) (2) Beginning-of-year endowment value ($100M) Current year 2.59*** (0.65) 3.44*** (1.03) Lagged one year 1.73*** (0.28) 1.59 (1.21) Lagged two years 2.05*** (0.32) 1.38*** (0.28) UPMIFA −0.38 (0.51) −0.32 (0.43) Underwater ($100M) −4.71*** (1.60) −5.11*** (1.75) UPMIFA × underwater 6.07*** (2.12) 6.12*** (2.13) Investment returns ($100M) Current year, positive 2.28** (1.02) Current year, negative −1.69** (0.70) Lagged one year, positive 1.88 (1.41) Lagged one year, negative −2.66** (1.17) Total expenses ($100M) Lagged one year 2.13 (1.58) Lagged two years −0.84 (2.35) College and year fixed effects Included Included Coefficient (SE) Coefficient (SE) Dependent Variable: Endowment Spending ($M) (1) (2) Beginning-of-year endowment value ($100M) Current year 2.59*** (0.65) 3.44*** (1.03) Lagged one year 1.73*** (0.28) 1.59 (1.21) Lagged two years 2.05*** (0.32) 1.38*** (0.28) UPMIFA −0.38 (0.51) −0.32 (0.43) Underwater ($100M) −4.71*** (1.60) −5.11*** (1.75) UPMIFA × underwater 6.07*** (2.12) 6.12*** (2.13) Investment returns ($100M) Current year, positive 2.28** (1.02) Current year, negative −1.69** (0.70) Lagged one year, positive 1.88 (1.41) Lagged one year, negative −2.66** (1.17) Total expenses ($100M) Lagged one year 2.13 (1.58) Lagged two years −0.84 (2.35) College and year fixed effects Included Included
Sources: NCSE and IPEDS, FYs 2005—13; 2,379 college-year observations across 522 colleges.
Notes: Standard errors (SE) in parentheses are clustered at the state level. Current dollars. Coefficients represent spending rates in cents per dollar, except in the case of the UPMIFA indicator, which represents spending changes in millions of dollars.
**p < 0.05; ***p <0.01.
The dependent variable of spending is measured in millions of dollars. Therefore, the coefficient on the indicator term $UPMIFAit$ represents the million-dollar change in spending level when the indicator is on. Continuous independent variables are measured in hundreds of millions of dollars so that their coefficients represent the cent change in spending, in response to a dollar increase in the independent variable. This is analogous to a spending rate in percentage points.
In column 1, summing the coefficient estimates on the endowment values suggests that colleges spend an average of 6.37 cents per dollar of a moving average, higher than what colleges report for policy spending rates. This is conditional on college and year fixed effects, which take out level differences in spending. Similar sums appear in all of the reported regressions.
The coefficient estimate on underwater funds implies a 4.71-cent decrease in spending for each dollar in underwater funds, nearly equal to the estimated moving-average spending rate. This is consistent with colleges complying with the old uniform law and not spending from underwater funds.
UPMIFA causes these cuts to be offset completely by a 6.07-cent per dollar increase in spending from underwater funds. The coefficient on underwater funds and the coefficient on underwater funds interacted with UPMIFA sum to 1.4, but I cannot reject that this sum is zero. Therefore, colleges under UPMIFA spend no more or less in years with underwater funds. UPMIFA takes away the legal importance of underwater funds relative to prior law, and this is borne out in spending behavior. As expected, the effect of UPMIFA at zero underwater funds is small and not statistically significant.
Adding covariates in column 2 leaves the main results intact. The coefficients on the covariates suggest higher spending following investment fluctuations. Lagged expenses do not appear to have a clear relationship with endowment spending.
In the specification with covariates, the estimated increase in spending from underwater funds under UPMIFA is 6.12 cents per dollar. This is 28 percent larger than the average effective spending rate in the sample. Therefore, when underwater funds make up 17.4 percent of the endowment as they did at the beginning of fiscal 2010, UPMIFA allowed for 22 percent more spending (128 percent times 17.4 percent).
The following section explores differences in impacts of UPMIFA along some observable measures.
## 6. Heterogeneous Effects of UPMIFA and Underwater Funds
Increased spending from underwater funds under UPMIFA means that prior law was a binding constraint. In this section, I explore characteristics that would lower the shadow price of that constraint to see whether colleges with those characteristics reacted differently to UPMIFA.
As discussed in section 2, some colleges have access to other sources of spending within the endowment, such as special appropriations and spending from quasi-endowment funds, to offset the legally required cuts in spending from underwater funds. Colleges that rely more heavily on their endowments to cover operating expenses may also be more likely to find offsetting sources of endowment revenue.
Table 4 shows the results from estimating equation 2. (The definitions and means of the $Pi$ variables are reported in table 1.) The three variables identify distinct features of colleges, as they are not highly correlated with each other or with endowment value.
Table 4.
Heterogeneous Effects
Coefficient (SE) Coefficient (SE) Coefficient (SE) Dependent Variable: Endowment Spending ($M) (1) (2) (3) Beginning-of-year endowment ($100M) Current year 3.41*** (1.07) 3.41*** (1.04) 3.33*** (1.11) Lagged one year 1.62 (1.23) 1.66* (1.22) 1.88 (1.18) Lagged two years 1.40*** (0.28) 1.37*** (0.29) 1.48*** (0.24) UPMIFA −0.74* (0.40) −0.58 (0.46) −0.68 (0.68) Underwater ($100M) −15.23*** (3.88) −7.76** (3.43) −4.32* (2.55) UPMIFA × underwater 14.21*** (4.26) −9.15** (3.63) −0.94 (3.25) Investment returns ($100M) Current year, positive 2.22* (1.10) 2.34** (1.03) 1.75 (1.08) Current year, negative −1.69** (0.76) −1.70** (0.70) −1.26* (0.91) Lagged one year, positive 1.92 (1.43) 1.99 (1.42) 1.76 (1.42) Lagged one year, negative −2.46** (1.20) −2.69** (1.17) −0.48 (1.13) Total endowment ($100M) Lagged one year 2.09 (1.65) 2.16 (1.51) 1.78 (1.67) Lagged two years −0.74 (2.31) −0.87 (2.29) −0.90 (2.25) Operating expenses covered (%) × UPMIFA 0.04 (0.02) Underwater 0.78*** (0.27) UPMIFA × underwater −0.59 (0.44) Ever used special appropriations × UPMIFA 0.58 (0.50) Underwater 4.53 (4.35) UPMIFA × underwater −5.66 (4.42) Quasi-endowment (%) × UPMIFA −0.02 (0.01) Underwater 0.02 (0.11) UPMIFA × underwater 0.19 (0.14) College and year fixed effects Included Included Included Number of colleges 342 521 467 Number of college-year observations 1,914 2,378 2,225 Coefficient (SE) Coefficient (SE) Coefficient (SE) Dependent Variable: Endowment Spending ($M) (1) (2) (3) Beginning-of-year endowment ($100M) Current year 3.41*** (1.07) 3.41*** (1.04) 3.33*** (1.11) Lagged one year 1.62 (1.23) 1.66* (1.22) 1.88 (1.18) Lagged two years 1.40*** (0.28) 1.37*** (0.29) 1.48*** (0.24) UPMIFA −0.74* (0.40) −0.58 (0.46) −0.68 (0.68) Underwater ($100M) −15.23*** (3.88) −7.76** (3.43) −4.32* (2.55) UPMIFA × underwater 14.21*** (4.26) −9.15** (3.63) −0.94 (3.25) Investment returns ($100M) Current year, positive 2.22* (1.10) 2.34** (1.03) 1.75 (1.08) Current year, negative −1.69** (0.76) −1.70** (0.70) −1.26* (0.91) Lagged one year, positive 1.92 (1.43) 1.99 (1.42) 1.76 (1.42) Lagged one year, negative −2.46** (1.20) −2.69** (1.17) −0.48 (1.13) Total endowment ($100M) Lagged one year 2.09 (1.65) 2.16 (1.51) 1.78 (1.67) Lagged two years −0.74 (2.31) −0.87 (2.29) −0.90 (2.25) Operating expenses covered (%) × UPMIFA 0.04 (0.02) Underwater 0.78*** (0.27) UPMIFA × underwater −0.59 (0.44) Ever used special appropriations × UPMIFA 0.58 (0.50) Underwater 4.53 (4.35) UPMIFA × underwater −5.66 (4.42) Quasi-endowment (%) × UPMIFA −0.02 (0.01) Underwater 0.02 (0.11) UPMIFA × underwater 0.19 (0.14) College and year fixed effects Included Included Included Number of colleges 342 521 467 Number of college-year observations 1,914 2,378 2,225
Sources: NCSE and IPEDS, FYs 2005—13. Samples differ across columns because of missing data.
Notes: Standard errors (SE) in parentheses are clustered at the state level. Current dollars. Coefficients represent spending rates in cents per dollar, except in the case of the UPMIFA indicator, which represents spending changes in millions of dollars. Percent operating expenses covered by endowment is averaged over pre—financial crisis fiscal years 2005—08. Percent in quasi-endowment is averaged over post-financial crisis FYs 2009—13.
*p < 0.10; **p < 0.05; ***p < 0.01.
In column 1, colleges that cover more of their expenses with endowment spending make significantly smaller cuts to spending from underwater funds ($φ=0.78$), but this does not significantly differ based on UPMIFA ($ψ=-0.59$). In column 2, colleges that draw special appropriations are also estimated to make smaller cuts to spending from underwater funds, which is offset by UPMIFA, but neither estimate is significant ($φ=4.53$ and $ψ=-5.66$).
In column 3, there is no evidence of a lessened impact of UPMIFA by percent in quasi-endowment funds. The sign on $ψ$ is positive, suggesting that colleges with more quasi-endowment funds are actually more affected by differences in state laws. However, $ψ$ is small and not significantly different from zero. In all three of these specifications, for a college at the sample average value of $Pi$, there is still a significant increase in spending from underwater funds caused by UPMIFA.
Spending down quasi-endowments is a legal way to avoid reduced overall spending under prior law, yet colleges do not appear to do so. Colleges that have more quasi-endowment value may be generally more inclined to save. They treat unrestricted assets as permanent funds by placing them in their endowments, and they appear to continue to preserve the value of quasi-endowment funds at the expense of lost endowment revenue.
Keeping unrestricted funds saved in the endowment even when other revenues are down is consistent with building the endowment for its own sake, or endowment hoarding (Hansmann 1990; Brown et al. 2014). Keeping unrestricted funds in the endowment could also be consistent with the model in Hoxby (2015), where colleges accumulate endowment funds and expend them based on the flow of profitable opportunities to invest in intellectual capital, if market investments were seen to have relatively high growth potential after the financial crisis.
## 7. Robustness Checks
The main results are generally robust to alternative definitions of the $UPMIFAit$ variable. The main results also hold when spending is measured in terms of deviations from planned spending, as calculated from reported spending formulas. However, the main results do not hold when dollar measures are normalized to estimate the regression in terms of rates.
The effects of UPMIFA could vary over time. For example, spending could grow over time as more colleges implement new spending policies under UPMIFA. Alternatively, increased spending could be localized to the first year after enactment, if colleges decide it is prudent to temporarily spend more from underwater funds to compensate for foregone spending in years under prior law. I estimate how the effects are distributed over the years after UPMIFA's enactment in an event study, expanding the $UPMIFAit$ term from equation 1 into multiple terms $UPMIFAitk$. For $k=1,2,3,4+$, $UPMIFAitk$ is an indicator that year $t$ is the $k$th year UPMIFA has been in effect in the state of college $i$. These terms are also interacted with underwater funds in year $t$.
Table 5 shows the results of estimating this specification. There are positive and significant impacts of UPMIFA in all years after enactment. Overall there does not appear to be a trend in impacts, as the coefficients on the interaction terms are not statistically significantly different from each other. There does not appear to be extra catch-up spending in the first year after enactment. Appendix table A.1 reports the results of estimating the event study using an alternative definition of timing of enactment.
Table 5.
Event Study Defining UPMIFA Relative to First Year Effective
Dependent Variable: Endowment Spending ($M) Coefficient (SE) Beginning-of-year endowment ($100M) Current year 3.40*** (1.08) Lagged one year 1.62 (1.25) Lagged two years 1.39*** (0.29) UPMIFA (1st year) −0.45 (0.45) UPMIFA (2nd year) −1.45** (0.62) UPMIFA (3rd year) −1.25* (0.69) UPMIFA (4th year+) −1.51 (0.91) Underwater ($100M) −5.25*** (1.78) UPMIFA (1st year) × underwater 5.27** (2.35) UPMIFA (2nd year) × underwater 9.50*** (3.37) UPMIFA (3rd year) × underwater 6.44*** (2.05) UPMIFA (4th year+) × underwater 6.76*** (2.25) Investment returns ($100M) Current year, positive 2.26** (1.02) Current year, negative −1.70** (0.71) Lagged one year, positive 1.86 (1.43) Lagged one year, negative −2.61** (1.19) Total expenses ($100M) Lagged one year 2.10 (1.46) Lagged two years −0.95 (2.19) College and year fixed effects Included Dependent Variable: Endowment Spending ($M) Coefficient (SE) Beginning-of-year endowment ($100M) Current year 3.40*** (1.08) Lagged one year 1.62 (1.25) Lagged two years 1.39*** (0.29) UPMIFA (1st year) −0.45 (0.45) UPMIFA (2nd year) −1.45** (0.62) UPMIFA (3rd year) −1.25* (0.69) UPMIFA (4th year+) −1.51 (0.91) Underwater ($100M) −5.25*** (1.78) UPMIFA (1st year) × underwater 5.27** (2.35) UPMIFA (2nd year) × underwater 9.50*** (3.37) UPMIFA (3rd year) × underwater 6.44*** (2.05) UPMIFA (4th year+) × underwater 6.76*** (2.25) Investment returns ($100M) Current year, positive 2.26** (1.02) Current year, negative −1.70** (0.71) Lagged one year, positive 1.86 (1.43) Lagged one year, negative −2.61** (1.19) Total expenses ($100M) Lagged one year 2.10 (1.46) Lagged two years −0.95 (2.19) College and year fixed effects Included
Sources: NCSE and IPEDS, FYs 2005—13; 2,379 college-year observations across 522 colleges.
Notes: Standard errors (SE) in parentheses are clustered at the state level. Current dollars. Coefficients represent spending rates in cents per dollar, except in the case of the UPMIFA indicator, which represents spending changes in millions of dollars.
*p < 0.10; **p < 0.05; ***p < 0.01.
UPMIFA's impacts may manifest differently across colleges that use different spending formulas. I argue that because spending formulas change often and need not be followed, the most important outcome is a direct measure of actual spending. Looking instead at survey responses about spending formulas, colleges that consistently report using a moving-average formula represent 55 percent of colleges in the sample. They tend to be smaller than others in size, but similar in pre–financial-crisis spending rates. Columns 1 and 2 of table 6 report the results of estimating equation 1 when dividing the sample into moving-average formula users and others. The conclusions in both groups are similar to the main conclusions in section 5. However, the reduction in spending from underwater funds under prior law is significantly weaker among the group using a moving-average formula. This is consistent with moving-average users being more likely to follow their formulas even in the presence of underwater funds.
Table 6.
Robustness Checks Related to Spending Formulas
Moving-Average User Nonuser Deviation from Planned Coefficient (SE) Coefficient (SE) Coefficient (SE) Dependent Variable: Endowment Spending ($M) (1) (2) (3) Beginning-of-year endowment ($100M) Current year 2.84** (1.09) 3.38** (1.44) 2.78*** (0.32) Lagged one year 2.68* (1.42) 1.44 (1.68) −0.61 (0.84) Lagged two years 1.87*** (0.41) 1.06*** (0.38) −0.10 (0.19) UPMIFA −0.49 (0.37) 0.13 (0.66) −0.67** (0.31) Underwater ($100M) −0.93 (1.87) −6.31** (2.86) −5.13** (2.36) UPMIFA × underwater 3.58*** (1.30) 6.18** (2.92) 4.95** (2.24) Investment returns ($100M) Current year, positive −0.19 (1.40) 3.05*** (1.11) 2.20** (1.07) Current year, negative −0.95 (1.07) −1.30 (0.96) 0.72 (0.97) Lagged one year, positive 0.51 (1.81) 2.16 (2.25) −0.97 (0.88) Lagged one year, negative 1.46 (1.97) −3.12** (1.24) 0.87 (0.97) Total expenses ($100M) Lagged one year −2.49 (3.40) 1.23 (1.28) 4.71 (3.06) Lagged two years 0.62 (3.39) 1.12 (2.49) −5.12* (2.67) College and year fixed effects Included Included Included Number of colleges 287 235 439 Number of college-year observations 1,320 1,059 1,731 Moving-Average User Nonuser Deviation from Planned Coefficient (SE) Coefficient (SE) Coefficient (SE) Dependent Variable: Endowment Spending ($M) (1) (2) (3) Beginning-of-year endowment ($100M) Current year 2.84** (1.09) 3.38** (1.44) 2.78*** (0.32) Lagged one year 2.68* (1.42) 1.44 (1.68) −0.61 (0.84) Lagged two years 1.87*** (0.41) 1.06*** (0.38) −0.10 (0.19) UPMIFA −0.49 (0.37) 0.13 (0.66) −0.67** (0.31) Underwater ($100M) −0.93 (1.87) −6.31** (2.86) −5.13** (2.36) UPMIFA × underwater 3.58*** (1.30) 6.18** (2.92) 4.95** (2.24) Investment returns ($100M) Current year, positive −0.19 (1.40) 3.05*** (1.11) 2.20** (1.07) Current year, negative −0.95 (1.07) −1.30 (0.96) 0.72 (0.97) Lagged one year, positive 0.51 (1.81) 2.16 (2.25) −0.97 (0.88) Lagged one year, negative 1.46 (1.97) −3.12** (1.24) 0.87 (0.97) Total expenses ($100M) Lagged one year −2.49 (3.40) 1.23 (1.28) 4.71 (3.06) Lagged two years 0.62 (3.39) 1.12 (2.49) −5.12* (2.67) College and year fixed effects Included Included Included Number of colleges 287 235 439 Number of college-year observations 1,320 1,059 1,731
Sources: NCSE and IPEDS, FYs 2005—13. Samples differ across columns because of missing data.
Notes: Standard errors (SE) in parentheses are clustered at the state level. Moving-average users always use a moving-average formula, and nonusers represent the rest of colleges. In the third column, Deviation from Planned spending is the dependent variable. It represents the difference in dollars between actual spending and planned spending, calculated from NCSE survey responses.
*p < 0.10; **p < 0.05; ***p < 0.01.
Where there is enough information, I use lagged endowment values and reported spending formulas to calculate the planned spending implied by moving-average formulas. In this process, I ignore the potential effects of underwater funds. Similar to table 5 in Brown et al. (2014, p. 952), I calculate the difference between actual spending and an estimate of planned spending. The median observable deviation is zero dollars, and half of all deviations are between negative 0.5 percent and 0.5 percent of beginning endowment value. Column 3 of table 6 reports estimates of the main regression specification with this alternative dependent variable. The key coefficients have the same signs and similar magnitudes to the main results in table 3. This supports the main finding that underwater funds caused reductions in spending, but only under prior law.
All regression analyses so far have measured endowment stocks and flows in terms of dollars. Equation 1 then reflects the way that spending is commonly chosen in practice, by applying constant policy spending rates to current and lagged endowment values. The regression averages across colleges with varying spending rates, and recovers the difference in spending rates from underwater funds between UPMIFA and prior law.
Another way to estimate the equation is to look for UPMIFA's impact on spending rates directly. This approach divides spending and underwater funds by the current endowment value, instead of including current and lagged values in the regression. Column 1 of table 7 shows the results of estimating equation 1 with scaled measures. The interpretation of coefficients is not as clear, as with dollar measures, but coefficients should be of the same signs and similar magnitudes. For example, a coefficient of −4.8 on the fraction of endowment value in underwater funds would imply that if all funds were underwater, then the spending rate would be reduced by 4.8 percentage points (to zero for an average college). The estimated coefficient of −0.8 to −0.6 on the fraction underwater is about 15 percent as large as expected. The estimated coefficient on the interaction term with UPMIFA is smaller still, and not statistically significant.
Table 7.
Robustness Checks Related to Spending Rates
Coefficient (SE) Coefficient (SE) Dependent Variable: Spending Rate (% of Endowment Value) (1) (2) UPMIFA −0.07 (0.15) −0.07 (0.15) Underwater (fraction of value) −0.80** (0.33) −0.61* (0.35) UPMIFA × underwater 0.30 (0.50) 0.21 (0.50) Endowment shocks Current year, positive −0.13* (0.09) Current year, negative −0.42*** (0.12) Lagged one year, positive 0.34** (0.14) Lagged one year, negative −0.08 (0.12) College and year fixed effects Included Included
Coefficient (SE) Coefficient (SE) Dependent Variable: Spending Rate (% of Endowment Value) (1) (2) UPMIFA −0.07 (0.15) −0.07 (0.15) Underwater (fraction of value) −0.80** (0.33) −0.61* (0.35) UPMIFA × underwater 0.30 (0.50) 0.21 (0.50) Endowment shocks Current year, positive −0.13* (0.09) Current year, negative −0.42*** (0.12) Lagged one year, positive 0.34** (0.14) Lagged one year, negative −0.08 (0.12) College and year fixed effects Included Included
Sources: NCSE and IPEDS, FYs 2005—13; 2,379 college-year observations across 522 colleges.
Notes: Standard errors (SE) in parentheses are clustered at the state level. Endowment shocks are investment returns as a fraction of lagged college expenses.
*p < 0.10; **p < 0.05; ***p < 0.01.
Table A.1.
Event Study with Alternative Definition of UPMIFA
Dependent Variable: Endowment Spending ($M) Coefficient (SE) Beginning-of-year endowment ($100M) Current year 3.40*** (1.04) Lagged one year 1.63 (1.22) Lagged two years 1.37*** (0.31) UPMIFA (1st year) −0.37 (0.47) UPMIFA (2nd year) −0.29 (0.55) UPMIFA (3rd year) −0.38 (0.47) UPMIFA (4th year+) −0.26 (0.49) Underwater ($100M) −3.57*** (1.02) UPMIFA (1st year) × underwater −0.32 (2.21) UPMIFA (2nd year) × underwater 4.85** (2.06) UPMIFA (3rd year) × underwater 5.24 (3.43) UPMIFA (4th year+) × underwater 5.06** (1.88) Investment returns ($100M) Current year, positive 2.27** (1.05) Current year, negative −1.69** (0.72) Lagged one year, positive 1.91 (1.41) Lagged one year, negative −2.61** (1.17) Total expenses ($100M) Lagged one year 2.10 (1.50) Lagged two years −0.86 (2.21) College and year fixed effects Included Dependent Variable: Endowment Spending ($M) Coefficient (SE) Beginning-of-year endowment ($100M) Current year 3.40*** (1.04) Lagged one year 1.63 (1.22) Lagged two years 1.37*** (0.31) UPMIFA (1st year) −0.37 (0.47) UPMIFA (2nd year) −0.29 (0.55) UPMIFA (3rd year) −0.38 (0.47) UPMIFA (4th year+) −0.26 (0.49) Underwater ($100M) −3.57*** (1.02) UPMIFA (1st year) × underwater −0.32 (2.21) UPMIFA (2nd year) × underwater 4.85** (2.06) UPMIFA (3rd year) × underwater 5.24 (3.43) UPMIFA (4th year+) × underwater 5.06** (1.88) Investment returns ($100M) Current year, positive 2.27** (1.05) Current year, negative −1.69** (0.72) Lagged one year, positive 1.91 (1.41) Lagged one year, negative −2.61** (1.17) Total expenses ($100M) Lagged one year 2.10 (1.50) Lagged two years −0.86 (2.21) College and year fixed effects Included
Sources: NCSE and IPEDS, fiscal years 2005—2013; 2,379 college-year observations across 522 colleges.
Notes: Standard errors (SE) in parentheses are clustered at the state level. Current dollars. Coefficients represent spending rates in cents per dollar, except in the case of the UPMIFA indicator, which represents spending changes in millions of dollars. The definition of UPMIFA here ignores signing date. **p < 0.05; ***p < 0.01.
Table B.1.
Panel Sample Compared with Population of Private College Endowments
IPEDS Population Ever in Panel Sample Number of colleges 1,336 522 As % of IPEDS colleges 100 39.1 As % of IPEDS dollar value 100 61.3 Mean endowment ($M) 207.8 327.5 Median endowment ($M) 20.5 73.9 Mean endowment/expense ratio 1.69 2.23 Baccalaureate/masters/doctoral/other (%) 36/8/26/30 41/14/34/11
IPEDS Population Ever in Panel Sample Number of colleges 1,336 522 As % of IPEDS colleges 100 39.1 As % of IPEDS dollar value 100 61.3 Mean endowment ($M) 207.8 327.5 Median endowment ($M) 20.5 73.9 Mean endowment/expense ratio 1.69 2.23 Baccalaureate/masters/doctoral/other (%) 36/8/26/30 41/14/34/11
Source: IPEDS.
Note: Measures are averages within each college over fiscal years 2005—08.
These results may indicate that large endowments have an undue influence on the main results. The distribution of endowment size is highly skewed, with the largest endowments over 100 times larger than the median endowment. The main regression conditions out current and lagged endowment values, college fixed effects, year fixed effects, and covariates. However, there are both positive and negative outliers driven by large endowment values. The distribution of spending rates has much tighter bounds and few outliers.
The much smaller estimates in the normalized regression are therefore consistent with the largest endowments driving the estimated effect of UPMIFA. When estimating the regression in various subsamples by endowment size, the coefficients do not have a clear monotonic pattern, but are generally larger among large endowments. This could be explained by larger endowments having more resources to shift spending in compliance with prior law, or more monitoring that would enforce compliance with prior law.
Normalizing dollar measures makes the specification more comparable to that of Brown et al. (2014). I include their endowment shock measures as controls in column 2 of table 7. Brown and colleagues estimate that both positive and negative endowment shocks lead to decreases in spending rates among doctoral universities before 2008. I find the opposite among private colleges and universities during the period of this study.
Brown et al. (2014) show that endowment shocks predict spending rates under a range of assumptions about a college's treatment of underwater funds before UPMIFA. In column 2 of table 7, the effects of underwater funds, UPMIFA, and endowment shocks can be directly compared. The effect of underwater funds under prior law has the highest point estimate, but the differences in magnitudes are not statistically significant. This suggests that underwater funds are at least as important an explanation for decreased spending as endowment shocks in this sample.
## 8. Discussion and Conclusion
UPMIFA afforded colleges greater flexibility and responsibility to manage their endowments during the financial crisis. Taking account of the effects of the financial crisis on endowment spending in fiscal 2010, the effect of underwater funds were larger for the average college than the direct effect of investment losses. For a typical college that plans spending using a three-year moving-average rule, the 19 percent drop in asset values in FY 2009 would lead to a 6 percent drop in spending in FY 2010, smaller than the 22 percent drop imposed by underwater funds under prior law. For the average college, 22 percent of endowment spending translates to roughly 2 percent of the yearly budget. Spending gaps across states soon closed as proportions in underwater funds decreased and all states enacted UPMIFA.
The most likely reason that prior law was binding is that UPMIFA, like the prior uniform law when it was introduced, represented an overdue update. The gradual development of prudent management in practice was captured in an abrupt change in law.
This episode provided an opportunity to learn how colleges manage resources under constraints. Colleges that had placed larger amounts in quasi-endowment funds were no less likely, and perhaps even more likely, to feel the effect of legal constraints. This suggests that colleges view quasi-endowment funds as permanent funds themselves, not as sources of insurance against unavailability of other endowment income. This is part of the empirical definition of prudent management of endowment funds.
Although endowment decisions reveal part of how colleges manage resources, this study does not address how other revenues and expenses outside the endowment react to changes in endowment revenue. During the brief period when legal variation and underwater funds coincided, many other changes were occurring, making it empirically difficult to trace the redistribution of a few percentage points of the larger budget.
Brown et al. (2014) show how doctoral university operations were affected by shocks to endowment revenue in the 1990s and early 2000s. Universities tended to cut support staff and tenure-system faculty after investment losses, without increasing them after investment gains. Brown, Dimmock, and Weisbenner (2015) show that colleges and universities also tend to receive more donations after investment losses. An important avenue for future research is to show the effects of colleges’ financial and hiring inputs on student achievement outcomes.
Policy makers and the public who are concerned about student outcomes often disagree with how private colleges manage endowment funds. Typically, these observers call for increased spending to help lower the price or increase the quality of education for today's students, without providing a normative model of how endowments and other resources should be allocated across all generations of students. UPMIFA removed one barrier to increased spending in the present—the zero percent ceiling on spending rates from underwater funds. Other proposals have called for a 5 percent floor on effective spending rates from all endowment funds (Wolf 2011). Such proposals would move away from the prudent person standard, would be unlikely to solve a college's complicated intertemporal allocation problem, and could prevent colleges from upholding donor agreements to maintain permanent funds.
All state legislatures now agree on the definition of prudent management of endowments. But at a crucial moment, the old definition limited spending more so than did colleges’ notions of prudence, and briefly prevented colleges in late-enacting states from providing for scholarships, salaries, and other expenses supported by endowments.
Section 4 discusses the definition of the $UPMIFAit$ indicator, which is equal to 1 in fiscal year $t$ if UPMIFA is effective by the beginning of the fiscal year, and was signed into law at least three months prior. Table A.1 reports the results of estimating the event study using an alternative definition that removes the condition on the signing date. The effect of UPMIFA on spending from underwater funds is smaller on average, and is nearly zero in the first year. This suggests that colleges in late-signing states may not react to the law in the first year it is effective, when it is signed into law too late to affect budgeting for the fiscal year. This supports the choice of definition in the main analysis.
## Appendix B: Data Sources and Sample Selection
Under a restricted-use data agreement, NACUBO and Commonfund provided college-identified data from their yearly surveys of endowments. These surveys include the NACUBO Endowment Study and the Commonfund Benchmarks Study series of Educational Endowment Reports. In fiscal 2009 these series combined to form the NACUBO-Commonfund Study of Endowments (NCSE). For brevity I refer to all of these surveys as the “NCSE.” For more information on data collection and definitions, see NACUBO-Commonfund (2014).
IPEDS is publicly available. Reporting to IPEDS is mandatory for any college with students who receive federal financial aid, and IPEDS therefore achieves a larger sample coverage than the endowment surveys.
Using data from IPEDS, table B.1 compares the panel sample used in this study to the population of endowments at private, nonprofit, four-year colleges and universities in the United States. Relative to the IPEDS Population in the first column, the Panel Sample in the second column is skewed toward larger endowments both at the mean and median. The sample covers 39.1 percent of colleges in the population, but 61.3 percent of the endowment dollar value in the population. The endowment-to-expense ratio in the sample is higher, at 2.23 versus 1.69. The panel contains a much smaller proportion of colleges in the Other Carnegie classification, which includes medical colleges, engineering schools, and theological seminaries. The remaining colleges are distributed in similar proportions across baccalaureate, masters, and doctoral institutions.
Colleges move in and out of the main analysis sample because of item nonresponse on survey measures. However, missing data within colleges do not appear to bias results. Estimating equation 1 with a balanced sample of colleges that report all measures in all years, I draw similar conclusions (results not shown). There is no evidence that a college-year observation appearing in the sample is associated with UPMIFA, conditional on endowment values and college and year fixed effects (regression not shown).
## Appendix C: Selected Variable Definitions
Endowment value consists of permanent funds, including cash, securities, and property, whose income finances operations. This includes true endowment funds perpetually bound by gift instruments, as well as quasi-endowment funds and term endowment funds. Quasi-endowment funds function as endowment by the vote of the governing board. Term endowment funds function as true endowment funds for a period of time, after which they can be spent or remain in the endowment as quasi-endowment funds. This study does not distinguish between term endowment funds and true endowment funds, nor between expired term endowment funds and other quasi-endowment funds.
About 80 percent of colleges reporting to the NCSE in any given year use a moving-average spending formula. Dollars spent $(Spendit)$ is a linear function of current and lagged endowment values. If the college uses a yearly frequency for $n$ years and a constant policy spending rate $s$, then the function is $Spendit=s1n∑j=0,1,…,n-1Beg.valueit-j$.
An underwater fund is a donated gift fund whose current value is below its historic dollar value (HDV), the nominal value at donation. The total value in these funds constitutes $Underwaterit=∑f∈Endmt.itBeg.valueft1{Beg.valueft, for all gift funds $f$ in the endowment of college $i$ at the beginning of fiscal year $t$, where $1${·} is an indicator function equal to 1 if the inequality is true and 0 otherwise.
Investment returns are net of management and administrative costs. Investment returns during fiscal year $t$ can be broken into a positive component $Returnt+=max{0,Returnt}$ and a negative component $Returnt-=min{0,Returnt}$.
Operating expenses include direct costs to provide education (e.g., paying salaries) but do not include taxes or debt service.
Special appropriations are defined by each college. Some colleges may spend an unusually large amount but simply report it in their effective spending rate without designating it a special appropriation.
## Acknowledgments
For all their help, I would like to thank Associate Editor Stephanie Riegg Cellini, anonymous referees, Luke Anderson, David Bass, Christine England, Susan Gary, Jesse Gregory, William Jarvis, Sheldon Kurtz, Ken Redd, John Karl Scholz, Christopher Taber, Larry Tavares, and the public economics reading group at the University of Wisconsin–Madison.
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## Notes
1.
“All states” includes the District of Columbia, as well as Pennsylvania, which adopted the key provisions of UPMIFA in 1998, although it is the only state not to have enacted the 2006 version (Pennsylvania General Assembly 1998).
2.
UPMIFA had a measurable impact on endowment spending, but I do not measure its indirect impact on endowment asset allocation or on other revenue sources, such as tuition. Many empirical studies of endowments take spending rules as given and examine investment choices (Black 1976; Thaler and Williamson 1994; Lerner, Schoar, and Wang 2008; Brown, Garlappi, and Tiu 2010; Dimmock 2012; Goetzmann and Oster 2015; Rosen and Sappington 2016). In contrast, Merton (1993), Hoxby (2015), and Gilbert and Hrdlicka (2015) lay out full models of both investment and spending, taking into account the college's other revenues and expenses.
3.
Endowment management decisions are made by a combination of a college's or university's governing board and investment committee (NACUBO-Commonfund 2014). Throughout this study I refer to these entities together as the “college.”
4.
Similarly, endowment contracts are not a binding reason for colleges to hold savings, because most colleges save additional unrestricted assets in quasi-endowment funds. This study therefore focuses on the choice of how much investment income to spend, rather than the choice of which, if any, endowment contracts to accept. A series of studies, including Tobin (1974), Hansmann (1990), Winston (1999), Weisbrod, Ballou, and Asch (2008), and Hoxby (2015), discuss objectives that would lead colleges to accumulate endowment assets.
5.
Gilbert and Hrdlicka (2015) discuss the clause in many states’ enacted versions of UPMIFA that sets a sharp limit by establishing a rebuttable presumption of imprudence if a college spends more than 7 percent of some measure of current endowment value. Under current practice however, this 7-percent ceiling will rarely be hit as colleges spend closer to 5 percent of current value.
6.
The law says, “In making a determination to appropriate or accumulate, the institution shall act in good faith, with the care that an ordinarily prudent person in a like position would exercise under similar circumstances, and shall consider, if relevant, the following factors: (1) the duration and preservation of the endowment fund; (2) the purposes of the institution and the endowment fund; (3) general economic conditions; (4) the possible effect of inflation or deflation; (5) the expected total return from income and the appreciation of investments; (6) other resources of the institution; and (7) the investment policy of the institution” (NCCUSL 2006).
7.
E-mail message to author from Susan Gary, University of Oregon School of Law, reporter for the UPMIFA drafting committee, 22 November 2011.
8.
For example, Oregon's enactment was moved along by a ULC member who filed it as an Oregon Law Commission bill rather than the more typical route of filing it as a State Bar Association bill, which, given the timing of ULC's publication of UPMIFA, would have required waiting until the next legislative session (Susan Gary, e-mail message, 22 November 2011).
9.
The error term $ɛit$ also contains omitted factors such as idiosyncratic opportunities for “intellectual venture capital investments” that compete for resources with market investments, making colleges want to spend resources rather than keep them in the endowment (Hoxby 2015). There is no reason to believe that these opportunities would arrive at differential rates that coincide with the enactment of UPMIFA and underwater funds. Many other omitted factors affect endowment management choices, including how a college's close competitors manage their endowments (Goetzmann and Oster 2015). These are also unlikely to be timed coincidentally with UPMIFA. If a college's in-state competitors are affected by UPMIFA itself, which in turn affects the college, this can be thought of as a component of the reduced-form effect of UPMIFA being effective in the state.
10.
UPMIFA also governs charitable endowments outside of higher education. Endowments of churches, museums, and community organizations tend to be smaller than those of colleges (Fisman and Hubbard 2003). Smaller endowments tend to be made of up newer funds, meaning they had higher concentrations of underwater funds after the financial crisis and potentially felt larger effects of UPMIFA. Without a targeted survey like the NCSE, these organizations are harder to study.
11.
All measures throughout this study are in current dollars. The results are robust to estimating in constant 2013 dollars using the Higher Education Pricing Index for private colleges.
12.
A college's operating expenses include direct costs to provide education (e.g., paying salaries) but do not include taxes or debt service.
13.
Only Alaska, South Dakota, and Pennsylvania did not enact the old uniform law (Arnold and Porter, LLP 2009; Budak and Gary 2010; Alaska State Legislature 2010; South Dakota State Legislature 2000). No colleges from Alaska appear in the panel. South Dakota prohibited spending from funds below historic dollar value, and is therefore coded as non-UPMIFA in the regressions until it enacts UPMIFA. Pennsylvania never enacted a law with reference to historic dollar value but enacted a law in 1998 with similar provisions to UPMIFA (Pennsylvania General Assembly 1998). In 2003, Florida enacted legislation ignoring historic dollar value and imposing a prudence standard for spending similar to that of UPMIFA (Florida State Legislature 2003). Even though Florida later enacted UPMIFA during the sample, there was no substantive change to law or practice. Pennsylvania and Florida are therefore coded as always under UPMIFA in the regressions, and are grouped with the earliest-enacting states in the tables and figures.
14.
Personal communication, Sheldon Kurtz, University of Iowa College of Law, UPMIFA drafting committee, 4 February 2016.
15.
For example, Quinn (2009) points out the immediate accounting implications of UPMIFA, but also says that changing spending in response would require action by the governing board.
16.
According to NCSE responses, 77 percent of college-year observations in the panel analysis sample begin the fiscal year on 1 July, and 20 percent begin on 1 June. | 2021-06-18 14:10:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 77, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34475982189178467, "perplexity": 6762.195012987908}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487637721.34/warc/CC-MAIN-20210618134943-20210618164943-00500.warc.gz"} |
http://crypto.stackexchange.com/tags/csprng/new | # Tag Info
If, for example, the PRNG can only be seeded with $2^{32}$ bits, then it cannot possibly produce all the $52!$ distinct permutations. In addition, even if we could meet the 226 bits needed for a 52-card deck, the distribution may not be uniform. This is true, but a good PRNG (even non-cryptographic) will give you a random sample from a uniform distribution.... | 2016-06-27 04:07:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5777438282966614, "perplexity": 456.5917047263579}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395620.9/warc/CC-MAIN-20160624154955-00017-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://conwaylife.com/forums/viewtopic.php?f=2&t=3962&p=82029 | ## 17 in 17: Efficient 17-bit synthesis project
For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
testitemqlstudop
Posts: 1367
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### Re: 17 in 17: Efficient 17-bit synthesis project
Yes.
Extrementhusiast
Posts: 1859
Joined: June 16th, 2009, 11:24 pm
Location: USA
### Re: 17 in 17: Efficient 17-bit synthesis project
testitemqlstudop wrote:Yes.
An insufficient reduction to #11, but one that could lead to further reductions:
Code: Select all
x = 131, y = 28, rule = B3/S23
119bobo$104bo15b2o$105bo14bo$81bo21b3o$79b2o29bobo11bo$80b2o29b2o6bo4b obo$111bo5bobo4b2o$118b2o$75bobo$75b2o$76bo$106b3o16bobo$7bo65b3o32bo
4b2ob2o7b2o$2bo5b2o53bo9bo33bo5bob2o9bo$obo4b2o48bo4bobo9bo43bo$b2o53b obo3bobo49b2ob2o9bo$4b2o40bo9bobo4bo50bo13bobo$5b2o40bo9bo58b2obo8b2o$
2A$25.2D6.A.A$38.3A$38.A$39.A$10.A$10.2A$9.A.A25.2A$5.2A22.A6.2A$4.A. A21.2A8.A$6.A21.A.A$12.3A$14.A$13.A3$11.2A$10.A.A$12.A2$.2A$A.A$2.A! Tanner Jacobi Coldlander, a novel, available in paperback and as an ebook. Extrementhusiast Posts: 1859 Joined: June 16th, 2009, 11:24 pm Location: USA ### Re: 17 in 17: Efficient 17-bit synthesis project Another insufficient improvement, this time to #164: Code: Select all x = 33, y = 33, rule = B3/S23 22bobo$23b2o$23bo3$26bo$17bo6b2o$18bo6b2o$16b3o$24bo$25bo$23b3o4$30bo$
8bo21bobo$6bobo10b2obo7b2o$7b2o8b3ob2o$16bo$17bo$18bo$o16b2o$b2o8bo$2o
4bo2bobo15b3o$6b2o2b2o9bo5bo$5bobo13b2o5bo$20bobo3$15b3o$17bo$16bo!
EDIT: Recovered a misplaced better insufficient improvement to #11:
Code: Select all
x = 192, y = 29, rule = B3/S23
114bo$114bobo$114b2o2$113bo$111bobo30b2o$112b2o8bo22b2o2bo3bo$68bo54b
2o19bo3bobobobo$67bo54b2o2b2o20bobobobo$49bobo15b3o56bobo20bo3bo28bo$4bo45b2o74bo53bobo$4bobo43bo69b3o58b2o$o3b2o108b2o4bo29b2ob2o29b2ob2o$
b2o44b2o64bo2bo4bo28bo3bo25b2o2bo3bo$2o44bobo11b3o51b2o35b2o26bobo3b2o$46bo13bo54bobo34bobo26bo4bobo$45b2o14bo52bo2b3o31bo2b3o28bo2b3o$114b
2o4bo30b2o4bo27b2o4bo$119b2o35b2o32b2o3$47b3o$38b3o8bo$40bo7bo6b2o$39b o15bobo$55bo$51b3o$53bo$52bo! Last edited by Extrementhusiast on August 30th, 2019, 5:43 pm, edited 2 times in total. I Like My Heisenburps! (and others) Kazyan Posts: 1030 Joined: February 6th, 2014, 11:02 pm ### Re: 17 in 17: Efficient 17-bit synthesis project Idea for #266 and #267. On the left, the red cells should appear in generation 15, and a 4G inserter should be found for the double dot spark that doesn't involve the yellow glider. With everything in place, the snake inserter on the right would have room to appear. Code: Select all x = 49, y = 26, rule = LifeHistory 5.A$6.A$4.3A$12.A$11.A$11.3A3$5.A.A40.A$6.2A34.A3.2A$6.A35.A.A2.2A$
42.2A$27.3D11.2D$27.3D11.D2.A$4.2D21.3D12.D2A$3.D.D18.9D8.2DA.A$.2A2. D18.9D$4A4.4D9.E2.9D$2A.2A2.D3.D7.E.E5.3D14.2A$2.2A7.D8.2E5.3D14.A.A$9.2D16.3D14.A2$19.A.A$15.2A2.2A$15.A.A2.A$15.A! Bonus: I stared into the ancient eyes of JLS, and this is some of what we saw between the space dust: Code: Select all x = 81, y = 152, rule = LifeHistory 12.A.A$13.A.A$16.A$12.A3.A$13.A$14.2A5$12.2A9.2A$11.A2.A9.2A2.A$15.A 7.A4.2A$11.A3.A12.3A$12.A14.5A$13.2A15.A$30.A$29.A$32.2A$31.3A$3.3A9. 3A.A11.2A$5.A2.2A7.A3.A17.2A$4.A2.A2.A5.A3.3A15.A2.A$11.A9.3A18.A$7.A 3.A9.4A13.A3.A$8.A12.2A16.A$9.2A29.2A$23.2A$11.A$25.A12$23.2A7.2A7.2A$23.2A8.A8.A$21.2A.2A4.A2.2A4.A2.2A$21.A2.2A4.2A.2A4.2A.2A2$22.2A8.A 8.A$24.A6.A.A6.A.A$22.2A9.A8.A4$4.A$.A2.A$3A$3.2A$3.A$3.A$2.A2$33.A2$
22.A7.3A41.A$20.2A.A7.3A39.2A$20.3A.A5.A2.2A38.A.A$21.A.2A6.A.A32.3A 9.3A$22.2A8.2A34.A9.A$22.2A43.A11.A2$62.2A$63.2A$62.A3$2.A$.A4.A$.A3. A$2.3A$31.3A2$3.3A25.3A2$3.3A22.2A2$30.3A$29.A2.A$30.A.A$31.A$33.A3$72.2A$72.A.A$63.3A6.A$65.A$64.A3$64.2A$65.2A$64.A10.2A$75.A.A$75.A3$37.2A$36.A.2A$36.A2.A$37.2A$24.3A2$24.3A4$23.4A$22.A3.A$26.A13.3A$24.
2A13.2A.2A$27.A12.3A$41.A3$19.2A$17.2A.2A$17.4A$15.3A.A$15.2A2$32.2A$34.A$30.A3.A$31.4A13$21.2A2.2A$21.A.A$20.A2.A$21.2A2.2A$25.A$24.A$24.
A!
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook.
chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am
### Re: 17 in 17: Efficient 17-bit synthesis project
Extrementhusiast wrote:Another insufficient improvement, this time to #164:
Code: Select all
x = 33, y = 33, rule = B3/S23
22bobo$23b2o$23bo3$26bo$17bo6b2o$18bo6b2o$16b3o$24bo$25bo$23b3o4$30bo$8bo21bobo$6bobo10b2obo7b2o$7b2o8b3ob2o$16bo$17bo$18bo$o16b2o$b2o8bo$2o 4bo2bobo15b3o$6b2o2b2o9bo5bo$5bobo13b2o5bo$20bobo3$15b3o$17bo$16bo! I found a couple of ways of doing the sides in 3G (see gen 30) but they don't fit with the 4G in the bottom right. Are there alternatives for the bottom right in 5G maybe? Code: Select all x = 63, y = 38, rule = B3/S23 46bo$44bobo$45b2o3$2bobo$3b2o55bo$3bo43bo12bobo$45bobo12b2o$46b2o7$45b 2obo$9bo33b3ob2o$7b2o33bo$8b2o22bobo8bo$2bo30b2o9bo$2o31bo9b2o$b2o3$2b
2o7bo$b2o7b2o$3bo6bobo22b2o$34bobo$36bo6$33b2o$34b2o$33bo! Extrementhusiast Posts: 1859 Joined: June 16th, 2009, 11:24 pm Location: USA ### Re: 17 in 17: Efficient 17-bit synthesis project #166 in sixteen gliders: Code: Select all x = 154, y = 60, rule = B3/S23 141bo$142bo$140b3o$102bo$100bobo10bo29b2o$101b2o9bo30b2o$112b3o$101bo$101b2o$100bobo$60bo$59bo8bo$59b3o4b2o$56bo10b2o$57b2o$56b2o$90bobo$91b
2o$59b2o30bo15bo$58bobo45bobo40bo$60bo5b2o39b2o2b2o34b3o2b2o$66bo44bo
34bo5bo$67bo44bo34bo5bo$16bo44b2o3b2o38b2o3b2o35bo3b2o$14b2o45bobobo 40bobobo38bobo$15b2o8bo38b2o43b2o39b2o$23b2o$24b2o$16bo10b3o$16b2o9bo$15bobo10bo$94b2o$93bobo$95bo8$3o$2bo$bo14$6b3o$8bo$7bo!
I Like My Heisenburps! (and others)
Kazyan
Posts: 1030
Joined: February 6th, 2014, 11:02 pm
### Re: 17 in 17: Efficient 17-bit synthesis project
#210 in 16G:
Code: Select all
x = 94, y = 35, rule = B3/S23
87bo$o84b2o$b2o83b2o$2o$81bo$82b2o$81b2o2$89bo$43bo45bobo$20b2o20bo46b 2o$20bobo19b3o31b2o$21bo54bobo$79bo$71bo5b2o$69bobo4bo$18b3o49b2o4bob 3o$20bo56bo2bo7bo$19bo3b2o53b2o6b2o$22b2o43b3o17b2o$24bo7bobo34bo$32b
2o34bo$33bo57b2o$91bobo$32b2o57bo$33b2o$32bo6$80bo$80b2o$79bobo!
EDIT: Insufficient improvement to #34 by improving the intermediate. The pond inserter could probably be done in 4G, which would solve this.
Code: Select all
x = 84, y = 28, rule = B3/S23
80bo$6bo60bobo3bo5bo$bo5bo15bobo37bo3b2o3bo6b3o$2bo2b3o15b2o36bobo4bo 3b3o$3o21bo37b2o2$18bo$18bobo$18b2o2$2b2o10bo57b2o$2bobo9bobo56bo7b2o$
2bo11b2o56bo8bobo$72b2o7bo$70b2o2bo$29b2o39bo2bobo$28b2o42b2o2bo$23b2o 5bo44b2o$22b2o$24bo$10bo17b3o$10b2o3b2o11bo$9bobo4b2o11bo$15bo2$5bo$5b 2o$4bobo!
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook.
chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am
### Re: 17 in 17: Efficient 17-bit synthesis project
Kazyan wrote:Insufficient improvement to #34 by improving the intermediate. The pond inserter could probably be done in 4G, which would solve this.
Code: Select all
x = 84, y = 28, rule = B3/S23
80bo$6bo60bobo3bo5bo$bo5bo15bobo37bo3b2o3bo6b3o$2bo2b3o15b2o36bobo4bo 3b3o$3o21bo37b2o2$18bo$18bobo$18b2o2$2b2o10bo57b2o$2bobo9bobo56bo7b2o$
2bo11b2o56bo8bobo$72b2o7bo$70b2o2bo$29b2o39bo2bobo$28b2o42b2o2bo$23b2o 5bo44b2o$22b2o$24bo$10bo17b3o$10b2o3b2o11bo$9bobo4b2o11bo$15bo2$5bo$5b 2o$4bobo!
Replaced the pond inserter with a 3G reaction and a single cleanup glider:
Code: Select all
x = 38, y = 27, rule = B3/S23
6bo$bo5bo$2bo2b3o$3o25bo$27bo$18bo8b3o$18bobo$18b2o2$2b2o10bo$2bobo9bo bo11bo$2bo11b2o12bobo$23b3o2b2o$23bo$24bo5$10bo$10b2o$9bobo3$5bo29b2o$
5b2o28bobo$4bobo28bo! Kazyan Posts: 1030 Joined: February 6th, 2014, 11:02 pm ### Re: 17 in 17: Efficient 17-bit synthesis project Idea for #72; insert red cells at generation 4: Code: Select all x = 15, y = 17, rule = LifeHistory 8.A$7.A$7.3A$3.A$4.2A$3.2A2$10.A.A$5.2A4.2A$4.A.A4.A$4.A8.A$2.D2.4A3. A$D8.A2.3A$2.2D3.2A$7.A$9.A$8.2A!
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook.
Extrementhusiast
Posts: 1859
Joined: June 16th, 2009, 11:24 pm
Location: USA
### Re: 17 in 17: Efficient 17-bit synthesis project
#164 in sixteen gliders, due to an unlikely merger of steps:
Code: Select all
x = 129, y = 32, rule = B3/S23
83bo$81b2o$82b2o3$93bo22bo$91b2o21bobo$4bo87b2o21b2o$4bobo120bo$4b2o 105bobo11b2o$2bo109b2o7bobo2b2o$obo27bo29bo51bo3b2o4b2o$b2o27bo29bo55b
obo3bo$30bo9bo19bo57bo$38bobo76bo6bo$31bo7b2o20bo54bo3b2obobo$4b3o23bo
bo27bobo4b3o45bo5bob2o$4bo25b2o5b2o21b2o53b2o3bo6b2o$5bo31bobo24b2o12b
o38bobo6b2o$33b2o2bo25bo2bo10bo39b2o9bo$34b2o28b2o11b3o$33bo4$59bobo$60b2o$60bo2$60b2o$59bobo$61bo! I Like My Heisenburps! (and others) Goldtiger997 Posts: 633 Joined: June 21st, 2016, 8:00 am ### Re: 17 in 17: Efficient 17-bit synthesis project Kazyan wrote:Idea for #72; insert red cells at generation 4: Code: Select all x = 15, y = 17, rule = LifeHistory 8.A$7.A$7.3A$3.A$4.2A$3.2A2$10.A.A$5.2A4.2A$4.A.A4.A$4.A8.A$2.D2.4A3. A$D8.A2.3A$2.2D3.2A$7.A$9.A$8.2A!
I made the base still life in 6G so if anyone can make Kazyan's blinker-predecessor in 6 gliders or less that will solve #72:
Code: Select all
x = 33, y = 26, rule = B3/S23
10bo$8bobo$9b2o2$22bo$21b2o$21bobo2$2o$b2o$o2$21b3o$21bo$7b3o12bo$9bo$8bo7$30b3o$30bo$31bo!
Extrementhusiast wrote:#164 in sixteen gliders, due to an unlikely merger of steps:...
Nicely done!
chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am
### Re: 17 in 17: Efficient 17-bit synthesis project
Goldtiger997 wrote: I made the base still life in 6G so if anyone can make Kazyan's blinker-predecessor in 6 gliders or less that will solve #72:
Made the spark with 5G in total. There might be a way to do cleanup in one less glider.
Code: Select all
x = 44, y = 54, rule = B3/S23
bo$2bo$3o8$2bo$obo$b2o2$22bo$21bo$15bobo3b3o$16b2o$16bo2$38bobo$24bo
o3$14b3o$14bo$15bo! Kazyan Posts: 1030 Joined: February 6th, 2014, 11:02 pm ### Re: 17 in 17: Efficient 17-bit synthesis project The current 17G synthesis for #135 is below, but with a cleanup glider removed in the intermediate step. This would be a 16G solution, but there's a single random blinker. Neither of the 3G versions of the spark generated by the four marked gliders fit here, but I'm certain that a 4G version could both form the spark and delete the extraneous blinker. There's plenty of room to wave around the glider in white, but there does not appear to be a solution just by doing that, from my manual testing. A different mechanism for the spark may be needed. Code: Select all x = 163, y = 36, rule = LifeHistory 88.A$88.A.A$88.2A$77.A$77.A.A$77.2A3$2.A75.2A$A.A74.2A$.2A76.A$121.C$84.A.A35.2C$84.2A35.2C$85.A47.3A$71.2A$71.A$72.3A70.2A$74.A70.A2.A$
81.A65.2A$19.A60.A.A65.A.2A.A$3.2A14.A.A58.A2.A55.E7.A2.A.2A$4.2A8.3A 2.2A60.2A55.2E8.2A$3.A10.A119.E3.E.E$15.A59.3A56.2E$58.2A73.E.E$59.2A 2.2A$58.A5.2A60.3E$63.A64.E$127.E3$161.2A$143.A16.2A$143.2A17.A$142.A
.A!
EDIT: This could remove another glider from #11, which would solve it, if different 3G inserter exists for the right spark. As-is, the gliders would collide.
Code: Select all
x = 21, y = 15, rule = B3/S23
10bo$8b2o$9b2o3bo$15b2o$14b2o2b2o$2o16bobo$b2o15bo$o11b3o$6b2o4bo$5bo 2bo4bo$6b2o$7bobo$6bo2b3o$6b2o4bo$11b2o!
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook.
Extrementhusiast
Posts: 1859
Joined: June 16th, 2009, 11:24 pm
Location: USA
### Re: 17 in 17: Efficient 17-bit synthesis project
Kazyan wrote:EDIT: This could remove another glider from #11, which would solve it, if different 3G inserter exists for the right spark. As-is, the gliders would collide.
Code: Select all
RLE
Here's the longest-lasting example:
Code: Select all
x = 43, y = 30, rule = B3/S23
$24bo$24bo16$2o$b2o$o! Goldtiger997 Posts: 633 Joined: June 21st, 2016, 8:00 am ### Re: 17 in 17: Efficient 17-bit synthesis project chris_c wrote:Improving the predecessor of #135 using some different but equivalent junk on the left: Code: Select all x = 42, y = 47, rule = B3/S23 39bobo$39b2o$40bo$28bobo$28b2o$29bo6$36bo$35bo$7bo27b3o$8b2o19b2o$7b2o 20bobo$29bo3$11bo$12bo$10b3o$29bo$28bobo$8b3o17bo2bo$10bo18b2o$9bo14bo
$24bo$24bo16$2o$b2o$o! Just beat me too it. Here's was my alternate 16G solution: Code: Select all x = 91, y = 36, rule = B3/S23 15bo$13bobo17bo$14b2o11bo4bo$25b2o5b3o$26b2o2$23bo$21b2o$4bobo15b2o$5b 2o$5bo43bo$27bobo20b2o$27b2o20b2o$28bo3$73b2o$73bo2bo$24bo50b2o$23bobo 50bob2obo$23bo2bo40bo7bo2bob2o$24b2o40b2o8b2o$62bo3bobo$18b3o41b2o$61b
obo2$54b3o$6bo49bo$6b2o47bo$5bobo2$89b2o$71bo16b2o$bo69b2o17bo$b2o67bo
bo$obo! Now we're down to only 6 17-bitters left! 4 of those are pretty similar. Freywa Posts: 718 Joined: June 23rd, 2011, 3:20 am Location: Singapore Contact: ### Re: 17 in 17: Efficient 17-bit synthesis project Code: Select all #CLL state-numbering golly x = 603, y = 213, rule = B3/S23 218bo198b3o$217b2o197bo3bo$218bo201bo$218bo200bo$218bo199bo$218bo
198bo$217b3o196b5o4$17b3o17bo19b3o17b3o19bo16b5o16b3o16b5o16b3o17b
3o17b3o17bo19b3o17b3o19bo16b5o16b3o16b5o16b3o17b3o17b3o17bo19b3o
17b3o19bo16b5o16b3o16b5o16b3o17b3o$16bo3bo15b2o18bo3bo15bo3bo17b2o 16bo19bo3bo19bo15bo3bo15bo3bo15bo3bo15b2o18bo3bo15bo3bo17b2o16bo 19bo3bo19bo15bo3bo15bo3bo15bo3bo15b2o18bo3bo15bo3bo17b2o16bo19bo3b o19bo15bo3bo15bo3bo$16bo3bo16bo22bo19bo16bobo16bo19bo22bo16bo3bo
15bo3bo15bo3bo16bo22bo19bo16bobo16bo19bo22bo16bo3bo15bo3bo15bo3bo
16bo22bo19bo16bobo16bo19bo22bo16bo3bo15bo3bo$16bobobo16bo21bo18b2o 16bo2bo17b3o16b4o19bo17b3o17b4o15bobobo16bo21bo18b2o16bo2bo17b3o 16b4o19bo17b3o17b4o15bobobo16bo21bo18b2o16bo2bo17b3o16b4o19bo17b3o 17b4o$16bo3bo16bo20bo21bo15b5o19bo15bo3bo17bo17bo3bo19bo15bo3bo16b
o20bo21bo15b5o19bo15bo3bo17bo17bo3bo19bo15bo3bo16bo20bo21bo15b5o
19bo15bo3bo17bo17bo3bo19bo$16bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3b o17bo17bo3bo15bo3bo15bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3bo17bo17b o3bo15bo3bo15bo3bo16bo19bo18bo3bo18bo16bo3bo15bo3bo17bo17bo3bo15bo 3bo$17b3o16b3o17b5o16b3o19bo17b3o17b3o18bo18b3o17b3o17b3o16b3o17b
5o16b3o19bo17b3o17b3o18bo18b3o17b3o17b3o16b3o17b5o16b3o19bo17b3o
17b3o18bo18b3o17b3o10$b3o$o3bo$o3bo$obobo$o3bo$o3bo$b3o14$bo$2o$bo
$bo$bo$bo$3o13$235b2o3b2o$b3o231bo2bo2bo$o3bo232b2obo$4bo233bob2o$3bo233bo$2bo233bo$bo234b2o$5o13$235b2o363bo$b3o231bo2bob2o357bobo$o3bo232b2obo358bo2bo$4bo233bo2bo355b2obobo$2b2o233bo2b2o355bo2b2o$
4bo231bo361bo$o3bo231b2o357b3o$b3o591bo13$136b2o$3bo132bo$2b2o134b o$bobo133b2o$o2bo132bo$5o130bo2b3o$3bo132b2obo$3bo137bo$140b2o13$
5o$o$o$b3o$4bo$o3bo$b3o13$535b2o3b2o$b3o531bo2bo2bo$o3bo532b2obo$o
537bob2o$4o531b3o$o3bo530bo$o3bo$b3o13$535b2o$5o530bo2bob2o$4bo 532b2obo$3bo534bo2bo$3bo531b3o2b2o$2bo532bo$2bo$2bo14$b3o$o3bo$o3b o$b3o$o3bo$o3bo$b3o14$b3o$o3bo$o3bo$b4o$4bo$o3bo$b3o!
Right, let's push.
Princess of Science, Parcly Taxel
Goldtiger997
Posts: 633
Joined: June 21st, 2016, 8:00 am
### Re: 17 in 17: Efficient 17-bit synthesis project
#266 in 16 gliders:
Code: Select all
x = 251, y = 57, rule = B3/S23
162bo$163bo$161b3o79bobo$o64bobo98bo77b2o$b2o63b2o97bo78bo4bo$2o64bo 98b3o80bo$61bo186b3o$62bo182bo$60b3o98b2o6b3o72bobo$161bo2bo4bo72bo2bo$162b3o5bo71b3o$247b3o$8bo74b2o77b3o77b3o2bo$6bobo73bo2bo75bobo77bobo 4bo$7b2o74b2o76bo3bo75bo3bo$160b2o2b2o74b2o2b2o$10bo$9bo69b3o$9b3o67bo
$72b3o5bo10bo$74bo16bo$73bo17bo7$93bo$92b2o$92bobo11$64b3o$66bo$65bo 11$122bo$121b2o$121bobo!
I suspect #112 can be solved in a similar way.
Hdjensofjfnen
Posts: 1624
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ
### Re: 17 in 17: Efficient 17-bit synthesis project
The final 5.
Code: Select all
x = 89, y = 25, rule = B3/S23
b2o17b2o3b2o13b2o18b2o23bo$bo18bo2bo2bo13bo2bob2o13bo2bob2o17bobo$3bo
18b2obo16b2obo16b2obo18bo2bo$2b2o19bob2o16bo2bo16bo2bo15b2obobo$bo20bo
19bo2b2o13b3o2b2o15bo2b2o$o2b3o15bo19bo18bo22bo$b2obo16b2o18b2o37b3o$6bo73bo$5b2o12$3obobo13bobob3o13bobob3o11b3ob3ob3o9b3ob3ob3o$o3bobo13b
obo3bo13bobo3bo13bobo5bo11bobobo3bo$3ob3o13bobob3o13bobob3o11b3ob3o3bo 9b3ob3ob3o$obo3bo13bobobo15bobo3bo11bo3bobo3bo9bo5bo3bo$3o3bo13bobob3o 13bobob3o11b3ob3o3bo9b3ob3ob3o! I'll guess that #293 will be the last one standing. EDIT: Comforting that Kazyan and I use the same exact number font. Code: Select all x = 5, y = 9, rule = B3-jqr/S01c2-in3 3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!
Code: Select all
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
Freywa
Posts: 718
Joined: June 23rd, 2011, 3:20 am
Location: Singapore
Contact:
### Re: 17 in 17: Efficient 17-bit synthesis project
Goldtiger997 wrote:#266 in 16 gliders:
I was expecting a method that added the requisite ten bits onto the snake, so that two still lifes could be solved in one go, for both pairs in the last six that have this feature.
Hdjensofjfnen wrote:The final 5.
I had pushed an RLE of the last six stills only a few posts above. Why would you want to be relentlessly up-to-date?
Princess of Science, Parcly Taxel
A for awesome
Posts: 2185
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:
### Re: 17 in 17: Efficient 17-bit synthesis project
A possible longshot approach for #267:
Code: Select all
x = 26, y = 11, rule = B3/S23
20bo$20b3o$19b3o$17b3obo2b2o$4bo16b2o$3bobo15bobo$3bo2bo14bo2bo$b2o2b 2o3bobobo2bob2o2b2o$o17bo$bobo15bobo$2b2o!
Since the precursor SL takes 7G, all for separate transformations would have to be done in 9G (clearly a tall order -- 11G seems like a more likely lower bound, 1/3/4/3 clockwise from bottom, with 13G probably more realistic). I wouldn't be surprised if the precursor SL could be reduced to 6G or even 5G with luck, though -- which would open an outside chance of coming in under 17G for the SL.
praosylen#5847 (Discord)
x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
Kazyan
Posts: 1030
Joined: February 6th, 2014, 11:02 pm
### Re: 17 in 17: Efficient 17-bit synthesis project
I was also expecting a solution that could solve both Tweedledee and Tweedledum at the same time by flipping a snake insertion, but I was never able to get anywhere close by trying methods like that. So Goldtiger pulls through again. Sure enough, #113 is probably doable, since a base can be made in 11G and there's a 4G budget for the spark in a relatively simple activation step:
Code: Select all
x = 72, y = 28, rule = B3/S23
23bo$22bo$22b3o4$29bo$28bo40b2o$28b3o39bo$12b2ob2o7bo44bo$12b2ob2o7bob o38b2obo$6bo17b2o40bob2o$bo5bo56bobobo2bo$2bo2b3o56b2o4b2o$3o9bo$13bo
47b2o$11b3o46bobo3b2o2bo$3b3o56bo3bobobo$5bo60bo4bo$4bo3$31b3o$31bo$32bo$14b2o$13bobo$15bo!
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook.
chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am
### Re: 17 in 17: Efficient 17-bit synthesis project
Kazyan wrote:Sure enough, #113 is probably doable, since a base can be made in 11G and there's a 4G budget for the spark in a relatively simple activation step:
Code: Select all
x = 72, y = 28, rule = B3/S23
23bo$22bo$22b3o4$29bo$28bo40b2o$28b3o39bo$12b2ob2o7bo44bo$12b2ob2o7bob o38b2obo$6bo17b2o40bob2o$bo5bo56bobobo2bo$2bo2b3o56b2o4b2o$3o9bo$13bo
47b2o$11b3o46bobo3b2o2bo$3b3o56bo3bobobo$5bo60bo4bo$4bo3$31b3o$31bo$32bo$14b2o$13bobo$15bo!
Yeah that's doable. 16G in total:
Code: Select all
x = 87, y = 33, rule = B3/S23
23bo$22bo$22b3o4$29bo$28bo48b2o$28b3o47bo$12b2ob2o7bo52bo$12b2ob2o7bob o46b2obo$6bo17b2o48bob2o$bo5bo64bobobo2bo$2bo2b3o64b2o4b2o$3o9bo$13bo$11b3o$3b3o$5bo$4bo68b3o$75bo$63b3o8bo5b2o$31b3o31bo13b2o$31bo32bo16bo
3b2o$32bo51b2o$14b2o70bo$13bobo$15bo3$66bo$66b2o\$65bobo! | 2020-12-05 11:35:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5895067453384399, "perplexity": 10522.53900597577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141747774.97/warc/CC-MAIN-20201205104937-20201205134937-00101.warc.gz"} |
https://www.biostars.org/p/9530174/#9530312 | Set up conda rna seq analysis
0
0
Entering edit mode
12 weeks ago
Hi,
I'm trying to set up miniconda on a mac for rna seq analysis. However I keep getting the error message (conda not installed):
active environment : base
active env location : /Users/mesalie/miniconda
shell level : 1
user config file : /Users/mesalie/.condarc
populated config files : /Users/mesalie/.condarc
conda version : 4.12.0
conda-build version : not installed
python version : 3.9.12.final.0
virtual packages : __osx=10.13.6=0
__unix=0=0
__archspec=1=x86_64
base environment : /Users/mesalie/miniconda (writable)
conda av data dir : /Users/mesalie/miniconda/etc/conda
conda av metadata url : None
channel URLs : https://conda.anaconda.org/conda-forge/osx-64
https://conda.anaconda.org/conda-forge/noarch
https://conda.anaconda.org/bioconda/osx-64
https://conda.anaconda.org/bioconda/noarch
https://repo.anaconda.com/pkgs/main/osx-64
https://repo.anaconda.com/pkgs/main/noarch
https://repo.anaconda.com/pkgs/r/osx-64
https://repo.anaconda.com/pkgs/r/noarch
package cache : /Users/mesalie/miniconda/pkgs
/Users/mesalie/.conda/pkgs
envs directories : /Users/mesalie/miniconda/envs
/Users/mesalie/.conda/envs
platform : osx-64
Could someone please advise me on how to correct this error message.
Thanks
seq conda analysis rna • 562 views
0
Entering edit mode
Hi, we can't give any advice without knowing what you tried (your commands/codes), and you need to format your error messages in a code block.
Press "Code Sample" above to insert error messages.
0
Entering edit mode
Ok thanks, I used the following commands in the mac terminal.
bash ~/Miniconda3-latest-MacOSX-x86_64.sh -b -p $HOME/miniconda source$HOME/miniconda/bin/activate
conda init zsh
conda info (shows not installed)
0
Entering edit mode
I don't know mac. Did you confirm your miniconda installation has no error? Maybe You need to reopen your terminal after conda init zsh, this is required in linux.
0
Entering edit mode
I tried to reopen the terminal and it didn't reopen. I’m trying to install Miniconda and received an error message. I’m following the protocol on protocols.hostmicrobe.org/conda
0
Entering edit mode
What you are seeing is the output of conda info command (posted in your original post). So conda is installed on your machine. That is not an error.
You simply need to activate conda using conda activatecommand. This will activate the base environment. You will want to create/use a new environment for your RNAseq software installs.
0
Entering edit mode
Ok thanks I think it says Conda build version is not installed. Hopefully that does not affect the analysis. Did you know what the command is for Conda activate?
0
Entering edit mode
conda activate command activates the base environment. That is what is installed by default and will get automatically activated unless you turn it off.
conda config --set auto_activate_base false
You should create a new envieonment when you install programs you need. for example to install bwa you would do
conda create -n rnaseq bwa samtools
conda activate rnaseq # to use the programs
0
Entering edit mode
Ok thanks, do know what command is used to run a fastqc file e.g. SRR8668773.gkfB5so2.fastq-002.gz.part | 2022-10-04 18:50:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2504902184009552, "perplexity": 14641.252593408504}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337524.47/warc/CC-MAIN-20221004184523-20221004214523-00266.warc.gz"} |
http://physics.stackexchange.com/questions/32310/whats-the-meaning-of-the-general-solution-and-the-particular-solution-in-differ | # What's the meaning of the general solution and the particular solution in differential equations?
Can anybody cast some physical insight into this? I've been studying differential equations on my own and don't understand how you can have a whole host of general solutions. It seems like a rather curious situation which we don't come across in other areas of mathematics. Is there anything more to the discussion that I'm missing?
-
To study differential equations, you should look at a numerical book, to learn to simulate them. The analytic methods are generally primitive and misleading outside of one and two dimensional phase spaces, because of chaotic behavior. – Ron Maimon Jul 18 '12 at 17:09
The solutions of a homogeneous linear ordinary differential equation form a vector space, ie $0$ is always a valid solution and arbitrary linear combinations of solutions will yield another valid solution. Finding the general solution of such an equation means finding a basis for that vector space.
In contrast, solutions to an inhomogeneous linear ordinary differential equation form an affine space over the space of homogeneous solutions. This means that $0$ is in general not a solution, and the difference between two solutions of the inhomogeneous equation will be a solution of the homogeneous one.
Thus, you only need to find a single inhomogeneous solution: The general solution of the inhomogeneous equation can be expressed of the sum of that particular solution and the general solution of the homogeneous one.
In case of non-linear differential equations, the integration constants (or equivalently, the choice of initial conditions) still parametrize the space of general solutions, and choosing values for these parameters will get you a particular one. However, the simple relation between the general solution of an inhomogeneous equation and the general solution of the corresponding homogeneous one does not hold for arbitrary differential equations.
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This answer is giving an answer specific to linear ODEs, while the phenomenon is general. But it's a fine answer for the linear case. – Ron Maimon Jul 19 '12 at 1:55
@Ron: added a small note about the non-linear case – Christoph Jul 19 '12 at 8:03
I don't agree it is a small note--- the reason I wrote a separate answer is because the linear case is misleading, the real reason for the arbitrary constants is not a vector space argument, it's an initial conditions argument, and it works regardless of the linearity of the equation. Neither are nonlinear equations "more complicated", they are just nonlinear. Sometimes they are simpler. – Ron Maimon Jul 19 '12 at 16:27
@Ron: I slightly reworded the last part – Christoph Jul 19 '12 at 16:49
thanks, I appreciate it, +1. – Ron Maimon Jul 19 '12 at 17:02
The differential equation needs initial conditions to simulate on a computer (which you should do once, if you want to understand what they are). A differential equation is a rule on a time-grid of size $\epsilon$ for $x(t+\epsilon)$, given $x(t)$. For example;
$${dx\over dt}= x + x^2 + x^3$$
means
$$x(t+\epsilon) = x(t) + \epsilon ( x(t) + x(t)^2 + x(t)^3)$$
in the limit $\epsilon\rightarrow 0$.
You can use the equation above to step forward in time, but you need to give the value of $x(0)$. Then from this value, you calculate $x(\epsilon)$, then $x(2\epsilon)$, then $x(3\epsilon)$ and so on into the future. A special solution is one for a given initial value, while the general solution is expressed in terms of $x(0)$ or some equivalent arbitrary constant that can be used to find $x(0)$.
The theorem you want is the uniqueness theorem for the initial value problem of ordinary differential equations. The mathematical proof tends to use a less useful approximation technique than lattice stepping, but people who do computer simulations or computer games always use some sort of lattice for ODE's.
- | 2014-04-21 02:14:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8775468468666077, "perplexity": 190.89355890012104}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539447.23/warc/CC-MAIN-20140416005219-00110-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://wikidiff.com/frequency/ultrasound | # Frequency vs Ultrasound - What's the difference?
frequency | ultrasound |
## As nouns the difference between frequency and ultrasound
is that frequency is (uncountable) the rate of occurrence of anything; the relationship between incidence and time period while ultrasound is (physics) sound with a frequency greater than the upper limit of human hearing; approximately 20 kilohertz.
# frequency
## English
### Noun
(frequencies)
• (uncountable) The rate of occurrence of anything; the relationship between incidence and time period.
• * With growing confidence, the Viking’s raids increased in frequency .
• * The frequency of bus service has been improved from 15 to 12 minutes.
• (uncountable) The property of occurring often rather than infrequently.
• * The FAQ addresses questions that come up with some frequency .
• * The frequency of the visits was what annoyed him.
• (countable) The quotient of the number of times $n$ a periodic phenomenon occurs over the time $t$ in which it occurs: $f = n / t$.
• * The frequency of the musical note A above middle C is 440 oscillations per second.
• * ''The frequency of a wave is its velocity $v$ divided by its wavelength $\lambda$: $f = v / \lambda$.
• * Broadcasting live at a frequency of 98.3 megahertz, we’re your rock alternative!
• * The frequency for electric power in the Americas is generally 60 Hz rather than 50.
• (statistics) number of times an event occurred in an experiment (absolute frequency)
• #### Synonyms
* (rate of occurrence) oftenness
#### Antonyms
* (rate of occurrence) period
* cadence * commonness * occurrence * periodicity
# ultrasound
## English
### Noun
(wikipedia ultrasound)
• (physics) sound with a frequency greater than the upper limit of human hearing; approximately 20 kilohertz
• (medicine) The use of ultrasonic waves for diagnostic or therapeutic purposes
• #### Antonyms
* (physics) infrasound
* | 2019-08-24 11:10:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8907159566879272, "perplexity": 4971.436518938846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027320734.85/warc/CC-MAIN-20190824105853-20190824131853-00381.warc.gz"} |
https://www.nature.com/articles/521156a?error=cookies_not_supported&code=01c78ba9-8b11-4b83-add0-f2e6c945fc2d | Kamla Devi, Rajasthan's first female solar engineer. Credit: Suzanne Lee/Panos
India's policy-makers have three big energy goals: providing everyone with access to energy, securing energy supply and trying to limit carbon emissions without encumbering the nation's growth. These important concerns miss the point.
Energy access cannot be assured by progress towards a simple target such as supplying power 24 hours a day, 7 days a week, nationwide. India has deep divides in the quantity and quality of energy consumed across income groups and between rural and urban households. Fuel subsidies are poorly designed and the strategies to reduce them to enhance energy security are heavy-handed. And because of limited action by the world's largest emitters, there is little left in the global carbon budget before planetary safety limits are breached. Clean energy and alternative growth is imperative.
India's energy priorities should be reframed as follows: to cater to the different energy demands of citizens of various economic strata; to direct energy subsidies to benefit the poor; and to promote low-carbon industry.
Disparate demand
Urban India aspires to have a reliable 24/7 electricity supply — voltages currently drop at peak demand times such as during evenings. Meanwhile, more than one-third of India's households, mostly poor and rural, are not connected to the electricity grid. For those that are, blackouts last 4–16 hours a day. The poorest households consume one-quarter of the energy of those at the highest income levels. Urban centres are in effect subsidised by rural areas, which are being overcharged for substandard service1. The poorest households pay 30% more per unit of useful energy than the richest2.
One solution to these disparate demands is to deliver more electricity through the grid while adopting cleaner energy sources. The Indian government has announced ambitious plans for renewable energy: up to 175 gigawatts (GW) of installed capacity by 2022. There are many challenges to achieving this target, from the availability of resource data on which to base decisions and managing risks to the high cost and the huge variability across the grid in terms of energy sources and infrastructure.
Nature special: Science in India
Meanwhile, the promise of reliable electricity through centralized infrastructure and systems remains unfulfilled. This is in part because most electricity utilities suffer financial difficulties — they lost more than US$19 billion in 2012–13 (ref. 3). One solution is to tap smaller-scale distributed renewable energy sources, primarily solar, biomass and small-scale hydropower. Off-grid power based on these technologies has advantages such as network resilience, flexibility and environmental and health benefits4. More than one million households in India rely on solar off-grid systems for lighting. A further 20 GW of energy capacity could be achieved if 15% of irrigation pumps were converted to solar energy. Renewable-energy applications can provide heating, cooling, cooking and mechanical power as well as electricity5. More than 250 companies across India, with long supply chains and networks of village-level entrepreneurs, operate in the decentralized clean-energy sector already. They demonstrate that putting power in the hands of poor people can begin a transformation in how energy access is understood and delivered. At the same time, such rapid growth and geographical spread could result in variable quality of service and expensive energy for poor people. More training would help to keep up standards. The challenge is to balance two types of investment: those in the centralized grid, which are key to the aspirations of millions of higher-income households, and funds for standalone systems in isolated and underserved areas or for integrating such systems to the grid. Rational subsidies Another reason for pursuing renewable energy in India is to avoid the pitfalls of a growth strategy mostly based on fossil fuels. Already, imports account for more than 80% of India's crude oil and 25% of its coal and gas, raising worries about supply and price volatility6. Petroleum constitutes nearly 30% of all commodity imports, leaving India little fiscal room to shrink its large current account deficit. Credit: Source: Ref. 7 India hands out generous energy subsidies, most of which are not means-tested (see 'Energy imbalance'). For example, in 2013–14 the government gave away$8 billion worth of subsidies for liquified petroleum gas (LPG)7. Yet less than half of urban households and only 6% of rural ones exclusively use LPG for cooking. Traditional biomass fuels such as wood account for 20% of Indian households' energy use. The government must rationalize subsidies and target them better. A well-designed programme would increase access to modern cooking energy (electricity and gas) for the same budget. For instance, reducing subsidized LPG to 9 cylinders (instead of 12) per year per connection could save the government $724 million. Excluding the richest 15% of households from the subsidy could save$1.18 billion annually. The savings should be redirected to increasing the availability in rural areas of cleaner cookstoves and biogas, and could extend LPG provision to 30 million more households.
What to make in India?
Energy and climate policies are closely tied to industrial policy. Even on a low-carbon energy pathway, total primary energy consumption in India will at least double by 2030 (compared to 2011 levels). Energy efficiency alone — in industry, residential and commercial spheres — cannot mitigate climate change.
Although unemployment rates in India are low (less than 5%) nearly 35% of employment is casual labour. The government's Make in India campaign, launched in September 2014, calls for aggressive job creation through rapid growth in the industrial sector.
Manufacturing consumes nearly one-third of India's primary energy supply, and contributes to 16% of gross domestic product (GDP) and more than 20% of direct emissions8. These emissions would grow, should India achieve its target of 25% contribution to GDP from manufacturing.
The best opportunity for decarbonization, therefore, is the power sector — which contributes nearly 38% of overall emissions8. Here, renewable energy could account for about 30% of the electricity mix by 2030.
In sectors such as metal production, non-metallic minerals, chemicals and textiles, which contribute most to manufacturing GDP, fuel accounts for 9–23% of all input costs compared to the industrial-sector average of 5%. Energy efficiency and alternative fuels should play a key part in decarbonizing these sectors. India's cement industry, for instance, is one of the world's most efficient, but it also accounts for 7% of the country's emissions. Here, technological advances such as refuse-derived fuels could save 600 million tonnes of coal, 550 billion units of electricity and 3.4 gigatonnes of carbon dioxide emissions between now and 2050.
A shift to a different industrial mix is required: away from such energy-intensive sectors and towards metal fabrication, manufacture of computers and electronics, electrical and mechanical machinery, advanced materials, biotechnology, nanotechnology and photonics. This would lower the energy footprint of India's industrial growth. | 2022-11-27 20:20:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3227255642414093, "perplexity": 5308.879285569414}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710417.25/warc/CC-MAIN-20221127173917-20221127203917-00817.warc.gz"} |
https://bitbucket.org/seibert/shrinkwrap/src/95e28b37613fee9750bae214a7350d7184bdec5e/doc/how.rst | # How Shrinkwrap Works
Shrinkwrap was designed to scratch a particular itch: automating the installation of software in a self-contained environment.
Nearly all package managers assume they are managing software installation for the entire system, and don't allow isolated environments. ZeroInstall is a notable exception which installs software into a user's home directory and can manage multiple versions of a single package. However, ZeroInstall is more aimed at providing specific applications to an end user, rather than providing a shell environment with a set of packages installed and ready for use.
Python's virtualenv and easy_install/pip tools are a great example of a userspace packaging solution that creates self-contained, easy-to-use environments. Since we work in mixed environments where C, C++ and Python software needs to coexist, shrinkwrap is our attempt to bring all that software under one roof.
Shrinkwrap achieves this goal by modifying the virtualenv in three ways:
1. It provides an alternate implementation of the python setup.py install command that makes it easy to insert an arbitrary installer function. This function typically downloads source tarballs, unpacks them, compiles and installs to the virtualenv base directory.
2. It adds new optional keyword arguments to setup() to specify the installer function, and also to list packages that are build dependencies of this package. See :ref:package_dependencies for details.
3. It creates a new $VIRTUAL_ENV/env.d directory and patches the$VIRTUAL_ENV/bin/activate script to source any files found in that directory. This allows shrinkwrap packages to install scripts that make changes to the shell environment. Many of the software packages we work with require environment variables to function properly.
With these changes, it becomes very easy to write small Python packages that download, compile, and install software into the virtualenv environment.
## Installing shrinkwrap packages
Installing a shrinkwrapped package is identical to installing any package with pip. You can install the package file directly from the filesystem:
pip install curl-7.27.0.tar.gz
or from a URL:
pip install http://mtrr.org/packages/curl/curl-7.27.0.tar.gz
or set the URL of extra package repository which contains shrinkwrapped packages:
export PIP_EXTRA_INDEX_URL=http://mtrr.org/packages/
pip install curl
If the shrinkwrapped package contains the standard test for the shrinkwrap module at the top (see :ref:built_in_installers), then shrinkwrap will be automatically installed to your virtualenv.
Note that environment files in the $VIRTUAL_ENV/env.d/ directory are only sourced when the$VIRTUAL_ENV/bin/activate script is sourced. You will need to source that script again to refresh your environment if the shrinkwrapped package added new environment files.
As true Python packages, shrinkwrapped packages can be used in a requirements.txt files passed to pip. Just place the extra index URL argument at the top:
--extra-index-url http://mtrr.org/packages/
curl
fftw
nose
## Limitations
We are the first to admit that shrinkwrap is straining the intended purpose of the Python packaging tools. As a result, shrinkwrap+pip has some shortcomings compared to more sophisticated package managers:
• Shrinkwrap can only be used with a virtualenv environment. Shrinkwrap tests for the presence of \$VIRTUAL_ENV and will throw an exception if it is not found.
• Shrinkwrapped packages have only been tested to work with pip as the installer. We do not support using easy_install, although it might work.
• pip uninstall does not remove files installed by the package because we do not yet have a way to track changes made by arbitrary installer functions to the filesystem.
• We do not provide any mechanism to have build options selected at installation time (such as variants in MacPorts or USE variables in Gentoo emerge ). Repositories of shrinkwrapped packages are easy to make with the shrinkwrap command line tool, so we encourage you to have different repositories for different kinds of deployment environments. Then you can tailor the build options of your source packages for each one.
• Shrinkwrap is currently focused on deploying source packages rather than precompiled packages. There is no reason you can't unpack a tarball of compiled code in a shrinkwrap installer() function, but we do not provide any mechanism for having packages compiled for different architectures in the same repository. Again, repositories are easy to make, so we would suggest one per architecture if this is your use case. (Selecting platform-specific build options in your installer() function, however, is no problem.) | 2015-08-29 12:47:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46377989649772644, "perplexity": 3945.6019203986907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644064445.47/warc/CC-MAIN-20150827025424-00302-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://plainmath.net/3134/solve-following-using-laplace-transformy-plus-plus-equal-equal-equal | Solve the following IVP using Laplace Transformy′′+3y′+2y=e^(-t), y(0)=0 y′(0)=0
Solve the following IVP using Laplace Transform
$y\prime \prime +3y\prime +2y={e}^{-t},y\left(0\right)=0y\prime \left(0\right)=0$
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Step 1
We have to solve given IVP using Laplace transform.
Step 2
We have given
$y\prime \prime +3y\prime +2y={e}^{-t},y\left(0\right)=0y\prime \left(0\right)=0$
Taking Laplace transform on given differential equation
$L\left(y+3y\prime +2y\right)=L\left({e}^{-t}\right)$
$L\left(y\right)+3L\left(y\prime \right)+2L\left(y\right)=\frac{1}{s+1}\dots \left(i\right)$
We are using here
where $L\left(y\right)=Y\left(s\right)$
Then from equation (i) we get,
${s}^{2}Y\left(s\right)-sy\left(0\right)-y\prime \left(0\right)+3\left(sY\left(s\right)-y\left(0\right)\right)+2Y\left(s\right)=\frac{1}{s+1}$
${s}^{2}Y\left(s\right)+3sY\left(s\right)+2Y\left(s\right)=\frac{1}{s+1}$
$\left({s}^{2}+3s+2\right)Y\left(s\right)=\frac{1}{s+1}$
$\left(s\left(s+1\right)+2\left(s+1\right)\right)Y\left(s\right)=\frac{1}{s+1}$
$\left(s+1\right)\left(s+2\right)=\frac{1}{s+1}$
$Y\left(s\right)=\frac{1}{{\left(s+1\right)}^{2}\left(s+2\right)}\dots \left(ii\right)$
Now
$\frac{1}{{\left(s+1\right)}^{2}\left(s+2\right)}=\frac{A}{s+1}+\frac{B}{{\left(s+1\right)}^{2}}+\frac{C}{s+2}$
$\frac{1}{{\left(s+1\right)}^{2}\left(s+2\right)}=\frac{A\left(s+1\right)\left(s+2\right)+B\left(s+2\right)+C{\left(s+1\right)}^{2}}{{\left(s+1\right)}^{2}\left(s+2\right)}$ | 2022-06-28 22:15:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 28, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8846315741539001, "perplexity": 3394.9567258686743}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103617931.31/warc/CC-MAIN-20220628203615-20220628233615-00290.warc.gz"} |
http://cs.stackexchange.com/questions/23493/dynamic-programming-vs-greedy-algroithms | # Dynamic programming VS Greedy Algroithms [closed]
I have two True or False questions in my practice test that are related but I am unsure about:
1. If an optimization problem can be solved using a greedy algorithm,
there must be a solution for this optimization problem using dynamic programming as well.
2. If an optimization problem can be solved using dynamic programming,
there must be a solution for this problem using a greedy algorithm as well.
I think the answers are 1. True and 2. False is this correct?
-
## closed as unclear what you're asking by D.W., David Richerby, Juho, vonbrand, Wandering LogicApr 14 at 17:37
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.
Does the course have any particular formal definition of "greedy algorithm" and "dynamic programming" in mind? – Yuval Filmus Apr 7 at 1:50
What are your thoughts? What effort have you made on your own? What aspects of the question have you confused or uncertain about how to answer? Are there any aspects of dynamic programming and/or greedy programming that you are fuzzy about? – D.W. Apr 7 at 6:53
Along the same lines I have the question True or False Dynamic programming requires that the optimization problem has a recursive solution? any input there? – Deekor Apr 7 at 3:31 | 2014-07-22 15:16:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.431236207485199, "perplexity": 841.948427472972}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997858962.69/warc/CC-MAIN-20140722025738-00083-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://www.semanticscholar.org/paper/Monte-Carlo-methods-in-statistical-physics-mathema-Kastner/3c8a396842ea33c01dfa161a44d9af62a21e015c | # Monte Carlo methods in statistical physics: mathematical foundations and strategies
#### Abstract
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical review, we start by presenting the probabilistic concepts which are at the basis of the Monte Carlo method. From these concepts the relevant free parameters—which still may be adjusted—are identified. Having identified these parameters, most of the tangled mass of methods and algorithms in statistical physics Monte Carlo can be regarded as realizations of merely a handful of basic strategies which are employed in order to improve convergence of a Monte Carlo computation. Once the notations introduced are available, many of the most widely used Monte Carlo methods and algorithms can be formulated in a few lines. In such a formulation, the core ideas are exposed and possible generalizations of the methods are less obscured by the details of a particular algorithm.
#### Statistics
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#### 377 Citations
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### Cite this paper
@inproceedings{Kastner2009MonteCM, title={Monte Carlo methods in statistical physics: mathematical foundations and strategies}, author={Michael Kastner}, year={2009} } | 2017-12-18 02:13:29 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8032160401344299, "perplexity": 664.4096868324592}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948599549.81/warc/CC-MAIN-20171218005540-20171218031540-00568.warc.gz"} |
https://labs.tib.eu/arxiv/?author=T.W.%20Shimwell | • An Automated Scalable Framework for Distributing Radio Astronomy Processing Across Clusters and Clouds(1712.00312)
April 10, 2018 astro-ph.IM
The Low Frequency Array (LOFAR) radio telescope is an international aperture synthesis radio telescope used to study the Universe at low frequencies. One of the goals of the LOFAR telescope is to conduct deep wide-field surveys. Here we will discuss a framework for the processing of the LOFAR Two Meter Sky Survey (LoTSS). This survey will produce close to 50 PB of data within five years. These data rates require processing at locations with high-speed access to the archived data. To complete the LoTSS project, the processing software needs to be made portable and moved to clusters with a high bandwidth connection to the data archive. This work presents a framework that makes the LOFAR software portable, and is used to scale out LOFAR data reduction. Previous work was successful in preprocessing LOFAR data on a cluster of isolated nodes. This framework builds upon it and and is currently operational. It is designed to be portable, scalable, automated and general. This paper describes its design and high level operation and the initial results processing LoTSS data.
• Investigating the Unification of LOFAR-detected powerful AGN in the Bo\"otes Field(1704.06267)
April 20, 2017 astro-ph.CO, astro-ph.GA
Low radio frequency surveys are important for testing unified models of radio-loud quasars and radio galaxies. Intrinsically similar sources that are randomly oriented on the sky will have different projected linear sizes. Measuring the projected linear sizes of these sources provides an indication of their orientation. Steep-spectrum isotropic radio emission allows for orientation-free sample selection at low radio frequencies. We use a new radio survey of the Bo\"otes field at 150 MHz made with the Low Frequency Array (LOFAR) to select a sample of radio sources. We identify 44 radio galaxies and 16 quasars with powers $P>10^{25.5}$ W Hz$^{-1}$ at 150 MHz using cross-matched multi-wavelength information from the AGN and Galaxy Evolution Survey (AGES), which provides spectroscopic redshifts. We find that LOFAR-detected radio sources with steep spectra have projected linear sizes that are on average 4.4$\pm$1.4 larger than those with flat spectra. The projected linear sizes of radio galaxies are on average 3.1$\pm$1.0 larger than those of quasars (2.0$\pm$0.3 after correcting for redshift evolution). Combining these results with three previous surveys, we find that the projected linear sizes of radio galaxies and quasars depend on redshift but not on power. The projected linear size ratio does not correlate with either parameter. The LOFAR data is consistent within the uncertainties with theoretical predictions of the correlation between the quasar fraction and linear size ratio, based on an orientation-based unification scheme.
• The WEAVE-LOFAR Survey(1611.02706)
Nov. 8, 2016 astro-ph.GA
In these proceedings we highlight the primary scientific goals and design of the WEAVE-LOFAR survey, which will use the new WEAVE spectrograph on the 4.2m William Herschel Telescope to provide the primary source of spectroscopic information for the LOFAR Surveys Key Science Project. Beginning in 2018, WEAVE-LOFAR will generate more than 10$^6$ R=5000 365-960 nm spectra of low-frequency selected radio sources, across three tiers designed to efficiently sample the redshift-luminosity plane, and produce a data set of enormous legacy value. The radio frequency selection, combined with the high multiplex and throughput of the WEAVE spectrograph, make obtaining redshifts in this way very efficient, and we expect that the redshift success rate will approach 100 per cent at $z < 1$. This unprecedented spectroscopic sample - which will be complemented by an integral field component - will be transformational in key areas, including studying the star formation history of the Universe, the role of accretion and AGN-driven feedback, properties of the epoch of reionisation, cosmology, cluster haloes and relics, as well as the nature of radio galaxies and protoclusters. Each topic will be addressed in unprecedented detail, and with the most reliable source classifications and redshift information in existence.
• The Australian Square Kilometre Array Pathfinder: Performance of the Boolardy Engineering Test Array(1608.00750)
Aug. 2, 2016 astro-ph.IM
We describe the performance of the Boolardy Engineering Test Array (BETA), the prototype for the Australian Square Kilometre Array Pathfinder telescope ASKAP. BETA is the first aperture synthesis radio telescope to use phased array feed technology, giving it the ability to electronically form up to nine dual-polarization beams. We report the methods developed for forming and measuring the beams, and the adaptations that have been made to the traditional calibration and imaging procedures in order to allow BETA to function as a multi-beam aperture synthesis telescope. We describe the commissioning of the instrument and present details of BETA's performance: sensitivity, beam characteristics, polarimetric properties and image quality. We summarise the astronomical science that it has produced and draw lessons from operating BETA that will be relevant to the commissioning and operation of the final ASKAP telescope. | 2021-02-25 16:47:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3928951323032379, "perplexity": 2514.444887208362}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178351374.10/warc/CC-MAIN-20210225153633-20210225183633-00581.warc.gz"} |
http://math.stackexchange.com/questions/135802/calculating-rotation-angle-based-on-the-applied-transformation/135826 | # Calculating rotation angle based on the applied transformation
I have got a quite complex problem. I have a particle simulation program, and i want to add solid objects to it, but still particle-based. for this, i want to deteermine the rotation the given transformation applies to my object. I have been trying to figure this out myself(couldnt find anything too much related to this)
heres what information i have:
• Old point coordinates
• New point coordinates
• Speed on X and Y axis
• Rotation center
I only need to calculate one points rotation angle(ill solve the rest) heres how far i got:
x' = x * cos( theta ) + y * -sin( theta );
y' = x * sin( theta ) + y * cos ( theta );
I need the value of theta. if possible I need to calculate this 1 million times / frame. If thats too much, then with some tweaking(accuracy lost) 1 000 - 50 000 times. Any other solution of the problem appreticiated. Could this be solved mathematically? If not, then is there some(even if inaccurate) way to solve this problem?
-
What's "Speed on X and Y axis"? The linear velocity of the particles along these axes? – joriki Apr 23 '12 at 14:06
Yes.. its how much each particle moves on those axises(its just added to calculate movement) – akaltar Apr 23 '12 at 14:11
How much a particle moves is a distance, not a speed. Do you mean distance or distance per time? – joriki Apr 23 '12 at 14:22
its in pixel/sec - how much my particle moves on X/Y axis given in pixel/sec. anyways ja72 answered my question exactly, thanks – akaltar Apr 23 '12 at 17:34
If that answered your question exactly, then it seems the "speed on the x and y axis" wasn't actually relevant to the question? It seems that what you were actually asking about was to find the rotation angle about the origin, given the coordinates of a point before and after the rotation -- I don't see any speeds there. – joriki Apr 23 '12 at 17:42
Starting from :
$$x' = x \cos\theta - y \sin\theta$$ $$y' = x \sin \theta + y \cos \theta$$
Use this:
$$\sin\theta = \frac{ y' x - x' y } {x^2+y^2 }$$ $$\cos\theta = \frac{ x' x + y' y } {x^2+y^2 }$$
so
$$\theta = \tan^{-1}\left( \frac{y' x - x' y}{x' x + y' y } \right)$$
To verify the results
$$x' = x \cos\theta - y \sin\theta = x \left(\frac{ y' x - x' y } {x^2+y^2 }\right) - y \left( \frac{ x' x + y' y } {x^2+y^2 } \right) =$$ $$= \frac{x ( x' x+y' y) - y (y' x-x' y) }{x^2+y^2} = \frac{ x' x^2 + x' y^2 }{x^2+y^2} = x'$$
and similarly for $$y' = x \sin \theta + y \cos \theta = x \left( \frac{ x' x + y' y } {x^2+y^2 } \right) + y \left(\frac{ y' x - x' y } {x^2+y^2 }\right) = \ldots = y'$$
- | 2015-09-05 17:03:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.726398766040802, "perplexity": 1397.939727929195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440646313806.98/warc/CC-MAIN-20150827033153-00316-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://lifecs.likai.org/2009/ | ## Wednesday, December 23, 2009
### Creating a block device backed by Amazon S3
There is a lot of benefit using Amazon S3 as a network drive, namely it will be automatically replicated across many storage nodes, so chances are the files will survive pretty well. However, S3 comes with several limitations: files have to be 5GB or less, and files can only be uploaded as a whole. Partial download works. No partial upload is a consequence of the distributed nature of the S3 storage system.
Of course, a user mode file system like s3fs over FUSE can always elect to shard a large file into smaller S3 objects, say 4MB each. It would need to hide the individual chunk objects and present only one coherent file. While this might seem adequate, hiding objects means that some file names are not allowed.
Another issue is that S3 objects are stored inside buckets that have no directory structure. Properly supporting directory structure means storing directory listing meta-info as an object in the bucket as well.
What if the user wants files to be encrypted transparently?
These issues all signify that, in order to build a proper network drive on top of S3, we need to implement a lot of file system features from scratch. It would be much easier if we could store a file on S3 and use it as a block device. Let's go back to the drawing board and redo the sketch.
• First, we'll have a simple sharded S3 file system over FUSE that can store large files as chunked objects.
• We create a large file to be used as a loopback device, format, and mount it.
• dd if=/dev/zero of=/mnt/s3/fs.img bs=1M seek=$((device_size_in_MB - 1)) count=1 • mkfs.ext4 /mnt/s3/fs.img • mount -o loop /mnt/s3/fs.img /mnt/fs We get all features of the filesystem (ext4 in this case), including all sorts of POSIX ACL goodies, for free. The operating system kernel even implements caching for us, so we can enjoy great performance! This also works similarly on Mac OS X: just use Disk Utility to create a disk image. If you want encryption, no problem. • dd if=/dev/zero of=/mnt/s3/crypt.img bs=1M seek=$((device_size_in_MB - 1)) count=1
• losetup /dev/loop0 /mnt/s3/crypt.img
• cryptsetup luksFormat /dev/loop0
• cryptsetup luksOpen /dev/loop0
• mkfs.ext4 /dev/loop0
• mount /dev/loop0 /mnt/crypt
One problem with using S3 as a block device is that the image file size is fixed, but depending on the filesystem you use, it should be possible to resize the filesystem online. It might even be possible to use ZFS by adding block storage to the pool.
If you're not happy with the 4MB per chunk data transfer, you can easily reduce the transfer amount. Instead of mounting the block device image over S3, do the following:
• Build an Amazon EC2 AMI to mount the disk image on S3 as a block device.
• Make sure ssh and rsync are installed on the machine image.
Then you can do rsync to backup your local files with only very minimal incremental transfer to the Amazon EC2 cloud. The 4MB per chunk data transfer between EC2 and S3 (within the same region) is free and likely very fast. The instance itself only needs to be running when you start the backup, and can be terminated as soon as the backup is done.
Now, the only missing piece is a FUSE module for sharding large files into smaller objects on S3. Anyone wants to take on that?
## Saturday, December 19, 2009
### Wireless Doorbell Instant Messaging Bridge
The apartment building I live in never has a working intercom. It has something that resembles an intercom box, and it is supposed to dial a preset phone number when you push a button for each tenant, but the landlord never bothered to keep the presets updated. My visitors can call my cellphone, but I often cannot have UPS or FedEx send packages to home.
Other tenants also have the same problem. They would leave notes repeatedly asking UPS to just leave their package at the entrance hallway, but UPS never do that due to policy reason. Some tenants attempted to leave a phone number, but once I ran into the UPS delivery guy---he told me the company does not issue them corporate cellphones, and he never uses his personal cellphone for work.
Although there are wireless doorbell systems that are very cheap (~$30), I don't want to just install a doorbell for my own unit. I want to have the doorbell send an instant message that can be broadcasted to anyone who is interested, including other tenants of this apartment. The question is how to build a system like that. The first iteration of this idea involves using wireless sensor network, but they require interfacing with a gateway, which must be connected to a computer for Internet connectivity. I want to leave the computer out of the picture. Besides, wireless sensor networks aren't cheap. I forgot the exact pricing range, but a gateway could cost$300-$600 or more, and each node is also$100-$200. And since many of these are still academic prototypes, you don't find many places to buy them. Someone could steal the doorbell, and it could cost me$200 to replace it. This seems like an expensive doorbell.
Then I wondered if a "system on a chip" would be a good idea. I found the PIC Micro Web, which is really a small computer with a parallel port and an ethernet port. I could solder a push button to the parallel port, which would fire something off the TCP/IP on the ethernet side. The price is reasonable. The only problem is, it only works on Ethernet. In search of similar units, I found Digi Connect ME, which has a sibling wireless model Digi Connect Wi-ME. This theoretically allows me to connect the door bell push button to my wireless home network and send instant message over my DSL. However, it's still a bit pricy, at $130 per unit. Then it occurred to me that I could use a Wireless to Ethernet bridge which may or may not support Linux. I found Linksys WGA600N, which based on a Ubicom chipset that has a Linux based SDK. With that device, maybe I could find out which one is the serial port, and repurpose that for door bell button connection. The cost is$80, but I think it is acceptable.
## Wednesday, December 16, 2009
### ZFS on Amazon EC2 EBS
One of the Amazon EC2 advantage for customer like you and me is that you can rent a computer from their data center, and you're only charged what you use—computing hours, instance sizes, network transmission—with the exception of EBS where you are charged by the amount of storage you provisioned to a volume. For example, you're still charged 1TB of storage cost if you only used 1GB of that 1TB. Since EBS is just a block device, there is no way for Amazon to tell how much of it you actually used.
What happens if you grow out of the space you initially provisioned to a volume? You can expand it like this: detach the EBS volume, make a snapshot of the volume to S3, use that snapshot to create a new EBS volume of a greater size, and attach the new volume. You will likely need to use an operating system tool to resize the file system to the new volume size as well.
While this might work well for some people, I'm not entirely happy about this approach. The time it takes to make the snapshot is directly proportional to the amount of data you have stored. The down-time seems unavoidable.
I've been studying management of a ZFS pool, and here are my findings. You can create EBS volumes and add them to a pool. Then when you want more space, just create a new EBS volume and add them to the pool. The pool will enlarge automatically to reflect additional space.
The smallest EBS volume you can create is 1GB, but I don't suppose anyone would want to create lots of 1GB volumes. This will be a nightmare to keep track of. Fortunately, ZFS also allows us to replace smaller disks with larger disks. You can keep a pool with about 3-4 EBS volumes, and when you want more space, just create a new one with more space, and use it to replace the smallest disk in the pool. This way, only 1/3 or 1/4 of the data in the pool needs to be transfered. Furthermore, all ZFS pool operations are performed online, so there is no downtime.
What if you want ZFS mirror or ZFS raidz redundancy? I found out that, unless you're one of the lucky users of Solaris Express build 117, which provides autoexpand capability, the disks that are part of a mirror or a raidz are not automatically expanded even after all disks are replaced with larger disks. Such is the case for zfs-fuse on Linux. However, I found out that a zpool export followed by zpool import updates the size. Or you can reboot your computer. Again, the downtime now is the amount of time it takes to reboot your EC2 instance, and not the amount of time it takes to make snapshots, which is much better.
The disadvantage now, however, is that you can no longer snapshot the whole filesystem at once, which spans across multiple EBS volumes.
## Wednesday, December 9, 2009
### Supporting Math on Google Wave
This is not a software release, but I spent a few hours plowing through the documentation on Google Wave API, and I'm just noting down how it may be plausible to support LaTeX math equations on Google Wave.
The first aspect is rendering math equation. One essentially makes a Wave Gadget that decides how to turn LaTeX into presentable math equation. There are two possibilities: (1) use the undocumented Google Chart API, but the LaTeX equation length is extremely limited; (2) embed jsMath, and use it for math rendering. The disadvantage of the jsMath approach is that it is rather heavyweight, since each gadget has to run the same jsMath initialization code separately. A third option, which I don't consider a possibility, is to host NTS (a Java implementation of TeX) on AppEngine. The NTS implementation of full TeX stack (TeX to DVI, DVI to image) might be considered heavyweight, but the real challenge would be to workaround its reliance on a real filesystem, which makes it difficult to port to AppEngine sandboxed environment.
Once the rendering part is done, it may be convenient to convert LaTeX code to the rendering gadget on the fly. This can be done using a Wave Robot that listens for document changes and scan for LaTeX code in the blip. I think this is relatively straightforward. However, a concern is that each change requires the robot O(n) time to rescan the whole blip. Editing in Wave would then become noticeably slower as document size grows. This scalability issue must be addressed. I think the current workaround is to have Wave only contact the robot sparingly. This also means robot updates are going to be slow. It may be possible to integrate everything better in the future, by processing update events directly in the Wave Client without using a robot.
## Wednesday, November 11, 2009
### Emulating C++0x auto keyword in C++
GCC has a typeof(e) operator (more pedantically, __typeof__(e), as typeof is not in C99 nor C++89 standard) that can compute the type of any expression e. It's typically used by macros, whose arguments aren't typed, to create local variables that has the same type as its arguments. For example,
#define max(a, b) \
({ __typeof__(a) _a = (a), \
__typeof__(b) _b = (b), \
(_a >= _b)? _a : _b })
This definition of max(a, b) prevents evaluating the expressions a and b more than once. These expressions can cause side-effects, such as printing a message to the screen.
The typeof operator apparently also works for C++. It is sometimes awkward to write out the type of the whole expression. For example,
void foo() {
std::vector<int> v;
for (std::vector<int>::const_iterator iter = v.begin();
iter != v.end();
iter++) {
/* ... */
}
}
Writing the type for the iterator is cumbersome. In C++0x, this code can be written like this using the auto keyword.
void foo() {
std::vector<int> v;
for (auto iter = v.begin(); iter != v.end(); iter++) {
/* ... */
}
}
In C++, using the __typeof__ keyword, we can write a macro like this:
#define autovar(x, exp) __typeof__(exp) x = (exp)
And the code above would look like this:
void foo() {
std::vector<int> v;
for (autovar(iter, v.begin()); iter != v.end(); iter++) {
/* ... */
}
}
Here is another use of the typeof operator: sometimes C++ can't figure out how to instantiate a template, and manually writing the type arguments can be tedious. You can use __typeof__ to help the compiler figure out the correct template parameter.
Apparently Boost provides a BOOST_AUTO macro that uses pretty much the same technique.
In C++0x, the typeof keyword is called decltype.
## Tuesday, September 22, 2009
### Google Chrome (Chromium) for RHEL (CentOS) 5
For a long time, I've kept a Windows machine for Remote Desktop access that I use just so that I can use Google Chrome. The reason is that editing Google Sites pages, for example, drags Firefox 3.5 and Opera 10 to a slow crawl. And Firefox 3.5 on Linux (since beta2) crashes my X11 server because the video driver (xorg-intel) is old and buggy. But I've long wished to abandon Windows altogether. I share the Windows machine with another graduate student, and the Windows Server 2003 license for that computer restricts two remote desktop connections. This is surely absurd for me as a Linux user because I've along accustomed to unlimited number of connections (subject only to resource availability as opposed to artificial license restriction). Granted, I could have used VNC, but it's not as responsive.
It is currently not my best interest to figure out how to compile Chrome from scratch (they appear to be using some gclient custom build tools). However, the precompiled binary snapshots require more recent versions of FreeType, Gtk+, and NSS (network security service, as part of Mozilla) than that available on BU Linux (which is a RHEL/CentOS 5 derivative).
Compiling Gtk+ is a nightmare because of the sheer number of dependencies. Here I'm listing the packages I need. The listing format is "target: dependencies"
• gtk+: atk glib cairo pango jasper fontconfig
• pango: cairo freetype glib
• cairo: libpng freetype pixman fontconfig
• fontconfig: freetype
• atk: glib
• glib:
• libpng:
• freetype:
• pixman:
• jasper:
The order listed above is in reverse topological order. I just put them in a Makefile and let make figure out the order for me. Fortunately, these packages are standard GNU autoconf/automake based. You will have to set export variables as follows:
• PREFIX := ... # you pick a convenient location
• export CFLAGS := ... # you pick the compilation options, e.g. -march=i686 -O3
• export CPPFLAGS := -I$(PREFIX)/include • export LDFLAGS := -L$(PREFIX)/lib
• export PKG_CONFIG_LIBDIR := $(PREFIX)/lib/pkgconfig • export PATH :=$(PREFIX)/bin:$(PATH) • export LD_LIBRARY_PATH :=$(PREFIX)/lib
You will have to run configure with --prefix=$(PREFIX), and then run make and make install inside your Makefile. I also wrote a script to essentially do the following. This will be left as an exercise to the reader. • Given a target name like gtk+, locate the source package tar.gz and unpack it. • Make a new object files directory and run the configure script there as the current working directory. If the build fails, you can just remove the object directory to get a clean slate, instead of needing to unpack the source files again. • Do the traditional make and make install. • Touch the target as a file, so make doesn't have to repeat building and installing a target if it already succeeded. Each rule in the Makefile would look like this: # Assuming the build script is called build.sh in the current directory. BUILD := ./build.sh gtk+: export LDFLAGS := -lm # for jasper gtk+: atk glib cairo pango jasper fontconfig$(BUILD) $@ On the other hand, NSS has its own build instruction, so I did it manually. The resulting nss shared objects must be symlinked in a particular way: • Add ".1d" suffix: libnss3, libnssutil3, libsmime3, libssl3. • Add ".0d" suffix: libplds4, libplc4, libnspr4. I imagine that's Ubuntu/Debian convention. I also compiled my own gcc 4.3/4.4, and without a recent gcc and libstdc++.so.6, you will get a dynamic linking error with the symbol GLIBCXX_X_Y_Z. ## Tuesday, September 15, 2009 ### Benchmark Using High Resolution Clock POSIX 1993 real time extension defines an interface to obtain clock tick down to nanosecond precision, using clock_gettime(). One way to implement this is to use Time Stamp Counter (TSC) that comes with the CPU, which is incremented by one per CPU clock cycle. On a modern gigahertz CPU, the TSC increments several times per nanosecond, so it can provide sub-nanosecond resolution. Then, there comes CPU with power saving mode, which reduces the CPU frequency when underutilized. Some older CPUs increment TSC by one per cycle regardless of the frequency, so each TSC increment is not uniform (though still monotonic). For these CPUs, we can get a reliable count of instruction cycles, but we cannot use the TSC to track wall-clock time. Later CPUs increment TSC by one according to the maximum CPU frequency, so the TSC increment takes uniform interval. However, when benchmarking code, the TSC no longer measures actual clock cycle. Code that runs in reduced CPU frequency will take more TSC counts to execute. A machine to be used for benchmarking purpose should turn off power saving mode. In particular, a laptop (having more stringent power requirement) is probably not well-suited for benchmarking. There is also the issue of multi-processor machines. Each CPU may have slightly different frequency, and they're started at slightly different times at boot up. The TSC of each CPUs cannot be easily correlated. Even if a benchmark involves only a single process, the operating system might still migrate the process to another CPU, causing the TSC readout to be non-deterministic. On a multi-process machine, benchmark should be run with CPU affinity fixed on one CPU, using sched_setaffinity(). CPU affinity is desired also for cache and TLB reasons. I do not currently know of a reliable way to benchmark multi-threaded program down to nanosecond precision. Here are some problems I could think of. • sched_setaffinity() works on a pid_t (i.e. the whole process). In general, pthread_t and pid_t are not interchangeable. • If we want to use one CPU as the master clock source, the intercommunication and synchronization overhead will be non-negligible. It should be later verified, but I'm guessing that the resolution would be ~100s nanoseconds. ## Saturday, September 12, 2009 ### Compiling LyX with gcc 4.4 I recently upgraded to gcc 4.4.1, and today I found that I couldn't compile LyX without fixing the source code. The reason is because gcc 4.4 has a stricter interpretation of the C standard when it comes to preprocessor syntax. The #if ... #elif ... #endif block is now either all processed or all skipped. In other words, #elif does not behave like #else #if ... #endif anymore because the conditional expression of #elif no longer enjoys deferred computation. This is documented in gcc bug #36453. LyX failed to compile because it distributed and included boost/mpl as part of the source code. A patch for boost/mpl is readily available. I downloaded the most recent patch (0001-boost.mpl-gcc-4.4-fixes.patch), saved it under$(SRCDIR)/boost (suppose $(SRCDIR) is the source directory for LyX, e.g. lyx-1.6.4), and ran from$(SRCDIR)/boost the command: patch -p3 < 0001-boost.mpl-gcc-4.4-fixes.patch
LyX should now compile correctly under gcc 4.4
## Sunday, September 6, 2009
### Abuse of read/write lock
A more fine-grained alternative to mutex lock is the read/write lock (rwlock). Mutex disallows two threads to access the same variable at the same time regardless whether the access is a read or write. With rwlock, the basic principle is simple: two readers can read from a variable (memory location) simultaneously without stepping on each other's toes. However, two writers cannot both write to the same variable, nor can one writer and one reader try to access the variable at the same time; both lead to inconsistent results.
There is one useful way to correctly abuse rwlock. Before we introduce the idea, let's talk a bit about lock-free stack implementation using singly linked list. Using compare and swap instruction, stack push can be implemented in the lock-free (and wait-free) manner. The compare and swap instruction provides a sufficient one-word transactional memory mechanism to allow changes made by another thread to be detected. This works because the node to be pushed to the stack is supposedly private. But stack pop suffers the complication of the ABA problem because the node to be popped is shared, so while thread 1 is in the middle of popping node A—let's say its successor is X at the moment—thread 2 pops node A, pushes node B, and pushes node A back. Now, A's successor is B instead of X. Thread 1 may mistakenly put reference to X as the top of the stack when it finishes popping node A.
With the singly linked list stack with push and pop implemented using compare and swap, we have the following access granting relationship. Two threads can safely push at the same time (guarded by compare and swap), but no two threads may pop at the same time, nor one thread to push and another thread to pop at the same time. This is exactly like a rwlock!
For this particular data structure, we could use rwlock to protect access. It is not exactly lock-free wait-free anymore, but maybe there are cases where the compromise, which is much easier to implement, is acceptable and useful.
## Thursday, September 3, 2009
### Migration to Gmail
Two days ago I successfully migrated two e-mail accounts to Gmail, one university e-mail and one department e-mail. Both of them are Unix based, and the IMAP server stores all mails except the INBOX in my home directory. Here is what I did.
• Create a new Gmail account. It will hold both the university and department e-mails.
• In my home directory, create a .forward file that contains the new Gmail e-mail address, and remove (or rename) the .procmailrc file.
• Enable IMAP in Gmail.
• Migrate old e-mails (I have about one year's worth kept in the mailbox) using imapsync. The university account runs UW imapd, and the department runs Dovecot. Here are the specific arguments to imapsync (besides login credentials) and why I needed them.
• --folder INBOX (to specify the inbox folder)
• --folderrec mail (this is the directory where all the mails are stored in Pine)
• --prefix1 mail/ (mailboxes with this prefix are stripped by imapsync)
• --regextrans2 's,Sent Messages,[Gmail]/Sent Mail,g' (I had used Apple Mail with these accounts too, and Apple Mail saves the sent e-mail in the Sent Messages folder, so I configured pine to do the same; now I want these to go under Gmail's Sent Mail folder)
• --regextrans2 's,spams,[Gmail]/Spam,g' (I kept a separate spams folder; could have removed this folder before the migration).
• I should have done this too: --regextrans2 's,INBOX,label-name,g' (the INBOX of each account goes under a different label). I simply did this manually after the fact which was a lot of work.
• imapsync prior to 1.288 wants to download the list of all folders regardless whether you need them or not. This means the imap server will traverse all the files in my home directory, and this takes a lot of time. Version 1.288 solves this problem by only enumerating all folders when you use the --include option. I temporarily changed line 915 in imapsync as follows:
-my @all_source_folders = sort $from->folders(); +my @all_source_folders = sort$from->folders($prefix1); • When adding a new From e-mail in the Gmail account, they offer to setup an SMTP server. This eliminates the "From: yourname@gmail.com on behalf of youroldemail@example.com" message shown in Outlook. • I configured pine to access Gmail over IMAP as follows. I edited .pinerc to change the following settings: • inbox-path={imap.gmail.com:993/ssl/novalidate-cert/user=yourname@gmail.com}label-name (For each old e-mail I migrated, I tagged them with a dedicated label, so the inbox for Pine would show what was there before) • folder-collections=Main {imap.gmail.com:993/ssl/novalidate-cert/user=yourname@gmail.com}[] (This is so I can see e-mails under other labels) • default-fcc={imap.gmail.com:993/ssl/novalidate-cert/user=yourname@gmail.com}[Gmail]/Sent Mail • postponed-folder={imap.gmail.com:993/ssl/novalidate-cert/user=yourname@gmail.com}[Gmail]/Drafts • Lastly, I created filters to tag and archive incoming e-mails and then used the multiple inbox Gmail lab feature to be able to see e-mail coming in from both accounts at once. ## Sunday, August 30, 2009 ### Analysis of Darwin kernel exploit This is an addendum account of The Story of a Simple and Dangerous Kernel Bug. On Unix, the fcntl() system call is used to manipulate file descriptors (duplication, close-on-exec, access mode, ownership, and locking). On Mac OS X, it is also used to provide read-ahead and write-back hints, and therefore some of the commands are file-system specific. The file-system specific commands are passed to the device driver as if an ioctl called has been made; on Unix, ioctl() allows the device driver to export any method call (associated to a file descriptor) to the userland. The problem with passing fcntl() arguments to ioctl() in Mac OS X is that ioctl() and fcntl() checks their arguments differently. The argument depends on which command code is passed to the function. If the argument is a pointer, the pointer should be checked that it points to valid memory. However, fcntl() argument checking code does not recognize ioctl commands, so it just assumes that the arguments are integers. This allows unchecked pointers to be passed to device driver code, which can overwrite arbitrary memory address. ## Wednesday, August 26, 2009 ### Summary of 32-bit Windows 3GB memory limit Just read this article yesterday about how the memory limit is a licensing restriction more than a technical restriction, and thought I would summarize it below. • x86 hardware reserves the physical address space between 3GB to 4GB for PCI memory mapped I/O (i.e. talking to devices the same way we access memory), so this part of the RAM is hidden by design of hardware architecture on the motherboard. • Some motherboard hardware supports 36-bit addressing on the bus, and the RAM between the 3GB to 4GB range is remapped to a physical address higher than what 32-bit physical address can access. • Intel CPU after Pentium Pro comes with Physical Address Extension that allows a 32-bit virtual address to be mapped to a 36-bit physical address. This boils down to: • If the motherboard supports 36-bit address and remaps the shadowed RAM between 3GB--4GB range, then an operating system (such as Linux, Mac OS X, Solaris) could use that RAM using Physical Address Extension, as well as any RAM beyond 4GB. However, the licensing restriction on Windows works like this: • Prior to Windows XP SP2, there is no licensing restriction, so on a capable hardware, 32-bit Windows XP could use as much physical memory as supported by the hardware. • Due to licensing restriction, the kernel in and after Windows XP SP2 ignores RAM located at physical address space beyond 32-bit, effectively capping usable RAM to 3GB even if the hardware has 36-bit physical address and remaps the 3GB--4GB RAM. • This licensing restriction is lifted on 32-bit versions of Windows Server and Windows Datacenter, as well as 64-bit Windows. These versions of Windows can access all available RAM supported by the hardware. • Windows Vista SP2 now reports the amount of RAM installed on the system, not the amount of RAM used by the operating system. ## Friday, August 14, 2009 ### Unit testing for C++ "concept" When you gain the ability to do template generic programming like this: template<typename T> class MyClass { // use T somewhere }; It falls naturally that you expect T to provide certain functionality. For example, many people write code like this: template<typename T> class MyClass { public: T Add(T x, T y) { return x + y; }; }; This assumes that T has a well-defined operator+. It might be more precise to write this: template<class T /* implements Addition */> class MyClass { public: T Add(T x, T y) { return x + y; }; }; where the interface Addition could be specified like this: template<typename T> class Addition { public: T operator+(T that)(); }; This is to say that the T you use to instantiate MyClass cannot be any type, but only a type that has implemented addition. The concept of addition is not very interesting, so let's use another example. Let's say you have the concept of a map<K, V> that is an associative map from keys of type K to values of type V. For the sake of testing, you can assume that K is both hashable and comparable (using an integer key will do). Then you are given two implementations of the map<K, V> concept, one implements the binary search tree sorted by K, and one implements hash table hashed by K. Most of the tests you want to do have to do with the concept of map<K, V> itself, e.g. insert, replace, find, and remove; not to do with the particular way the map is implemented. How do you avoid duplication? Use Type-Parameterized Tests. However, here is a tricky bit. A concept does not describe how a class is constructed or destroyed, only that the class implements certain methods. What if the class does not have a default constructor? For example, the hash table requires an initial size. Most implementations of a hash table supplies a "good enough" default value for the default constructor, but there are cases where this is not applicable. I figured out that you could parameterize the test using a factory class instead, and the factory would act like a default constructor. This is illustrated here. However, this is not as straightforward as I would like because when a template class inherit from the base class which is also a template, the derived class does not have access to any of the protected variables! This is illustrated here. This code compiles, but if you replace the self->x_ and self->y_ references with simply x_ and y_, gcc would fail to compile. Update: apparently gcc is correct, and the workaround is to simply prefix the member access with "this->." ## Thursday, August 13, 2009 ### Unit testing not a good fit for exhaustiveness So I implemented a layered memory allocator from scratch, somewhat in the fashion of Hoard (mine has a different abstraction). My allocator heavily uses C++ Mixin and Curiously Recurring Template Pattern (CRTP). Mixin is an overloaded term, but the concept I'm citing here is a class whose superclass is a template parameter. This allows a limited form of aspect-oriented programming where the Mixin is an added aspect of an existing class. CRPT is a recursive use of Mixin, which coerces the inheritance hierarchy of the user and the Mixin to form one class. The result allows static dispatch of methods which would otherwise have to be declared virtual, and subsequently dispatched dynamically using a virtual table. Anyway, long story short. After creating many composable layers of memory allocator, I also created corresponding unit test for each layer. However, the unit tests only covered the best case scenario, that Alloc() never returns NULL. It worked well. But I also wanted to test the case where some allocation returns NULL, in order to tell if the layer handled NULL pointer propagation correctly. This unit test scenario turns out to be much of a nuisance. To briefly explain why, no allocator always deterministically returns a valid pointer, nor does it always deterministically returns NULL, and it's the handling of the non-determinism that matters. Constructing a mock allocator that always returns NULL would still bypass some code paths. To make sure we traverse all code paths, we would have to construct an allocator that returns NULL after n successes for an arbitrary n, and run the unit tests for n = 1, 2, ... and so on. It may never exhaust all possibilities for a complex allocator layer such as the free list allocator. But then, what about a code path that is not reached unless the allocator succeeds every 2 attempts, or one that succeeds every 3 attempts, and so on? NULL pointer is a special form of the 'a option datatype in ML. The concept is really simple. The 'a option datatype has two constructors, SOME which carries an item of type 'a, and NONE which doesn't carry an item. When a pointer is not NULL, it is assumed that it refers to a valid object, hence corresponds to SOME; when a pointer is NULL, it is assumed that no such object exists (typically due to an exception), hence corresponds to NONE. When you pattern match against the constructors of a datatype, ML also performs exhaustive analysis. Forgetting to check for NULL is a kind of non-exhaustive pattern matching. Since exhaustiveness is a local property, using unit test (which tests for a property that is much wider in scope) is overkill and ineffective. It is very hard to create a unit test that will run all possible execution paths, especially for the error handling code, because simulating all possible combinations of error condition is impractical. Although a lot of times it's easier to write unit test for operations that are in-spec (e.g. to make sure a sorting algorithm permutes the sequence in order), it is best to leave exhaustive analysis to a compiler, like ATS, which effectively deals with out-of-spec situations. ## Tuesday, August 11, 2009 ### The coming of virtual appliances Everyone knows that web 2.0 has revolutionized people's private lives, with online social and entertainment applications like Facebook and YouTube. However, web 2.0 so far only has limited success for business applications in offices where the real money is at. While people are willing to entrust personal data to web 2.0, businesses can't do the same about their critical business data. Even well-known brand name like Google is fighting a hard fight selling the Apps for Domain service. The business concerns are manifold. Privacy: do I get to control who has access to my data? Safety: once data is stored, will it persist and out-survive any forms of failure? Liability: is there someone I can sue and recover some damage when worse comes to worst? Being a business model still in its infancy, many web 2.0 companies have terms of service that are against all these concerns. Only after a while do people realize that these are non-issues with certain brand name companies simply because of the sheer number of user base and the lack of negative publicity. Digression. In fact, some negative publicity became confidence boosters. When lightning stroke one of Amazon's data centers for EC2, it brought down a rack of machines. All their customers had to was to restart the instances on other machines that are still working. They lost only the temporary instance data that have not been committed to permanent storage, the same kind of loss if you unplug the power to your servers. It took only a few minutes to resume normal operation. It is different if you are a small web 2.0 startup that wants to focus on business customers. How do you build a customer base when nobody wants to trust their data with you, and how do you build trust without a customer base? Furthermore, the remoteness of the web means it's more difficult to hold you physically accountable, so that is one more reason not to trust you. This is an obvious reason why web 2.0 business-oriented applications failed to flourish so far. Also, as a small web 2.0 startup, you want to focus on developing the application, not on the plumbing. You can go back to pre-Internet model, selling software on a disc and have your customers install it on their own machines. However, some web 2.0 applications are built on top of many dependencies (web server, database, programming language runtime) as well as being intricately integrated with the operating system (disk access policy, user privilege, network firewall rules, performance tuning). It might not be your customer's best interest to run IT in-house either. Cloud computing is a solution to this problem. Here comes a brand name utility provider like Amazon with a service like EC2 that you will more likely trust. And a third-party software company with a web 2.0 application you need. They give you a stateless virtual machine image (such as AMI) and charge you a license fee for using their software. Amazon provides the hardware, storage, and network infrastructure, and bills you for the operational costs. All the costs are fully transparent: license fee for the development and support of the application, and Amazon for only what you use. When it comes to a customer who has built an infrastructure around VMware technology, the third-party simply rereleases their web 2.0 application as a VMware virtual appliance. It is easy to adapt to another virtualization technology because the only difference is the tool used for packaging a virtual appliance; the software stack---the operating system and all the dependencies---stay very much the same. Once the web 2.0 company grows large enough, they could consider selling hardware appliances; or if they're willing, provide a hosted solution for their apps when someone asks for it. To summarize, cloud computing with virtual appliances is going to be a great platform for business oriented web 2.0 technology, particularly lowering barrier to enter market due to lack of trust of critical data. And now, web 2.0 can finally enter the business sector. ## Friday, July 24, 2009 ### Splay trees with duplicate items I've implemented a splay tree, and I'd like it to store duplicate items, which are key-value mappings, as follows: if a key to be inserted already exists, then the new binding shadows the old one. If a key is to be removed, then the old binding is revealed. In other words, the inserting and removing the same key reveals the value in LIFO, or stack, order. The most obvious solution is to have each node be a pointer to a singly linked list, with the cons/uncons operation trivially obeying stack order. But we could embed the singly linked list in a simple binary search tree if we relaxed the criteria a bit, for example making the left child <= parent as opposed to left child < parent. This effectively makes duplicate nodes a chain of singly linked list down the left path. The idea is that we always reach the parent first, which is the most recently inserted item. And if the parent is removed, it reveals the second next item of the same key. The complication with Splay tree is that it could rotate the tree, which breaks the chain of duplicate nodes. Sometimes it is as bad as splitting the chain to left and right children to a node != the key of the chain, invalidating the binary search tree invariant. I figured out that, in the zig-zig and zig-zag cases, if the grand-parent node has the same key as the parent node, then it is possible to come up with special case rotation that preserve the chain. However, the terminal case actually needs to descend down the whole chain of duplicate notes. At this moment I gave up. Also, another problem with embedding singly linked list in a tree is that it will increase the depth of the tree, hurting the overall running time. In this case, it seems that the simple approach, making each node a pointer to a singly linked list, is better. It only took me 5 minutes to change the implementation this way and it worked. Update (9/15): Wikipedia claims that identical keys in a splay tree are preserved in its order like stable sort. It suffices to find the leftmost or rightmost node of the identical key. I haven't tried this. Update (9/16): Here is the Wikipedia edit that added the aforementioned claim about stable sort. However, I don't think retrieving duplicate item is as simple as finding the leftmost or rightmost node. Even if insertion is stable, the duplicate nodes may not be continuous (e.g. the balanced binary search tree for 1, 2, 3, 3, 3, 4, 5, where the 3's are separated by nodes 2 and 4). Looking for the "largest" duplicate complicates the search by a great deal because you will have to probe either the minimal of the right child, or the maximal of the left child, and may have to back-track. Curiously, Splaysort did not mention how they deal with duplicates. ## Wednesday, July 22, 2009 ### Captain's Log on Quest Okay, not quite captain's log. My office mate has been working on this operating system called Quest, and I'm keeping a record for him about what happened. He had been testing the OS on a virtual machine, and yesterday he decided to try it on real hardware. He found a reasonably recent hardware with APIC support in the lab. He would burn a CD-R, run upstairs, something goes wrong, write down some diagnostic on a piece of paper, run downstairs back to the office, change some code, burn a new CD-R, and run upstairs. I hate to see CD-Rs being thrown into trash at an incredible rate. After all, CD-Rs are supposed to last for 100 years; whether they still preserve any data or not at that point is an entirely different question. Since each image is small (~2MB), I suggested burning multi-session CDs instead. He tried but couldn't get it to boot. I don't have any other ideas. Today he bought some CD-RWs, which is an improvement. He also brought his laptop and stayed in the lab most of the time, which cuts the turnaround time a lot. When I visited him, he showed me a strange error that he fixed. There is a static char arena[1000000]; in the code which is used for rudimentary memory allocation. He found out that if he did not initialize this arena to zero, then the code that initializes this memory with free list pointers would have page fault, accessing memory at some outrageous location (this is typical of array out of bounds problem somewhere else, polluting the arena). I told him to try to memset to 0x5A instead. It will give us a clear indicator of what's wrong. He burned the CD-RW (had to erase the whole disk first) and booted it up. Lo and behold! The whole text-mode screen was then filled with bright green Z with pink background (thank goodness I didn't suggest 0xA5, or it would be filled with *blinking* purple Ñ on green). It seemed that the arena overlapped with text mode video buffer. Another lesson learned about writing operating systems: double check special hardware physical address mappings. ## Tuesday, July 14, 2009 ### Manifesto of a Very Hard To Find Memory Leak (To Be) I'm implementing a hash table that will become the basis of a free list memory allocator. The hash table uses singly linked list for buckets. In the list implementation, there is a RemoveAll function written like this: void RemoveAll(Predicate& p, Consume& c) { Node **result; for (result = &first_; *result != NULL; result = &(*result)->next_) { if (p(**result)) { Node *node = *result; *result = node->next_; node->next_ = NULL; c(node); if (*result == NULL) break; } } } Admittedly, the code is copied from a similar function called Remove(), which removes only the first node that satisfies the predicate. However, when it is modified to remove all nodes, an unintended side effect is, if a node is to be removed, it always skips the next node. When I wrote a unit test, I inserted nodes for 0 through 16, and removed all the even nodes, so this problem was not detected. However, when I used this function with a predicate that always returns true, I noticed that the list is not cleared properly. Now, this function is used in the hash table to clear all the buckets. Each item in the bucket would be a free list for a certain size of objects. When a free list memory allocator uses this hash table, it will see memory leak on a certain size of objects, and the size would appear to be at random. Fortunately, when a list is destructed, I have it do nothing but to assert that the list is empty. This helped detecting the problem early. Unit test for the hash table to clear all entries helped bringing this problem to the surface. ### Hash table using a variety of things for bucket A hash table stores key-value mapping of data in an array of buckets. The bucket number for a particular key-value pair is decided by a hash of the key modulo the number of buckets. The idea is that if the average number of key-value pairs in buckets is low overall, then we can achieve constant lookup time. One way to organize the bucket is by using a singly linked list. This has the side effect that, if the buckets are overloaded, then lookup time approaches the time of the singly linked list, which is O(n). An obvious improvement is to make the bucket a binary search tree, perhaps a splay tree (so that item being looked up more often is quicker to find). This cuts down the worst case time of overloading to O(logn), while achieving average case lookup time of O(1). We can nest hash tables, so a bucket can be implemented by another hash table. In this case, if the load of buckets are small, then we can let two or more buckets initially share a hash table. As buckets grow in size, they split. The size of nested hash tables must be relatively prime, or the inner tables would have high collision rate and won't be effective. The hashing scheme can be organized in the fashion of radix sort where the outer table use one hash function on the most significant bits, and the inner table use another hash function on the least significant bits. ## Tuesday, June 30, 2009 ### Kernel page tables My office mate has been working on an operating system kernel, and apparently page table manipulation is very error prone. Here are some important things that are easy to forget: • Special memory I/O pages cannot be freed into the general page pool, such as the physical address used for I/O APIC. If it happens, then another program would allocate the memory I/O page and then write to that physical address as if it's RAM. • If two address spaces share a page (mmap w/ MAP_SHARED, or shmat), then pages need to be reference counted. • If two processes share the same page table (clone system call), then page tables need to be reference counted. Since he's too engaged in debugging, I'm writing these down for him in case he forgets. I said to him, maybe the reason why people haven't made ground-breaking research into redesigning operating system architecture because the moment you walk in, you get lost in the woods, and you don't see the forest anymore. ## Wednesday, June 17, 2009 ### Super-Sized Del.icio.us, or Down-Sized Wayback Machine The problem with URL bookmarks is that they can always become dead links. Here are some of the common reasons: • It takes people and resources to keep web servers running, and the company or institution that maintains the web site just went away, bringing their web site with them. • The page disappears because the webmaster no longer deems the page worthy of keeping. It could happen when a web site is revamped, so some pages just disappear while others have their URL changed to fit the new site structure. • Pages can be moved around as part of a minor reorganization effort. • Content agreement mandates that the page is only accessible for a certain period of time. Furthermore, even if the page still exists, it may have been edited. The information that you wanted to be bookmarked may no longer exist. The Internet Archive Wayback Machine solves part of this problem by crawling a given website constantly at different dates, and by allowing you to retrieve a version at an earlier date. However, it has its own problems: • It only does best-effort crawling. In particular, it may take up to 6 months for the URL you submitted to show up. • It is a web crawler, so it voluntarily observes robots.txt. • The web page it archives is often missing images and other constituent material. • It has to rewrite hyperlinks in the web page. • It won't work with Javascript and XMLHttpRequest (AJAX). Furthermore, the Wayback Machine often crawls redundantly and unpredictably. It may attempt to crawl other parts of the website that you're not interested in, omitting the part you actually want. It may crawl the URL when you don't need it, and not crawl when you do. Here I propose a service that takes a complete snapshot of a web page in the manner of a bookmark. This will be an immensely helpful research tool for historians and other people who need to keep a small piece of artifect for a web page they're interested in. Web browsers have had the ability to cache web pages on disk, so static content doesn't have to be redownloaded everytime the web page needs to be rendered for display. The idea is to build a more sophisticated caching feature on top of a web browser. • All HTTP connections are memoized by the snapshot, so Javascript and even some Flash content will work. • Support multiple snapshots for the same URL at different time and be able to display them side by side for comparison. This is not something a proxy server can do. • Snapshots are searchable. • Schedule regular snapshots or prefetch web page. Possible advanced features: • Store snapshot on external server. Pro: can consolidate snapshot of the same webpage taken by two different people, if they are the same. Pro: can allow public access to snapshots. Pro: high availability because customer doesn't have to manage their own storage. Pro: high mobility because snapshots live on "the cloud." Pro: centralized search and indexing. Con: will cost money to run storage server infrastructure, so service will not be free. Con: not likely supported by ads revenue. • Allow public access to the snapshots. Pro: any website can link to a snapshot to avoid the external dead link problem. Con: will run into copyright issue when the original web site owner determines he is losing profit because of the snapshot. Technologies that can be leveraged: • QT for cross-platform user interface. Doesn't require commercial license; LGPL is fine. • WebKit (available in LGPL) or Presto (commercial proprietary license) layout engine for rendering web pages. ## Saturday, June 6, 2009 ### Multiresolution NLE video codec Highly compressed video codec such as H.264 is often too CPU intensive for real-time editing. Their inter-frame compression also makes frame-to-frame editing difficult. A typical workflow to work with these videos is to transcode them to an intermediate codec, which uses lower complexity, intra-frame only compression, so that non-linear video editing software can manipulate the video frame by frame in real time. Intermediate codec typically compresses at a much higher bitrate to make up for lower complexity (though still more efficient than uncompressed video); as a result, it requires higher disk bandwidth. In order to work with computers with slow disk (i.e. laptop), sometimes it is desirable to edit with reduced resolution video. When the editing finalizes, rendering is done using full-resolution footage. However, during part of the workflow, it may be desirable to use full-resolution (e.g. compositing), but other times half or quarter resolution (timeline editing). One would transcode into the intermediate codec in multiple resolutions, which is a waste of disk space and a headache to manage. Two popular intermediate codecs are Apple ProRes 422 and Avid DNxHD, and neither of them tackles this issue. Here is my idea. A plausible construction of an intermediate codec is to just JPEG encode video frame by frame, so I'll use that to illustrate. We can encode a frame progressively as follows. • Given a video frame, produce ¼×¼ and ½×½ resolution images. • Encode ¼×¼ image using JPEG, decode it, and scale it up by 2x (i.e. to ½×½ the original size). Make a difference image from this one and the original ½×½ image. • Encode the ½×½ difference image using JPEG, decode it, and scale it up by 2x (i.e. to the original size). Make a difference image from this one and the original image. • Encode the original-sized difference image using JPEG. This allows quarter resolution, half resolution, and full resolution reconstruction of the video stream. Data chunks in the stream can be arranged so that if we want to decode lower resolution picture, we don't have to read the higher resolution data. Some issue that may not work well: • JPEG causes compression artifect that is eccentuated by the layered encoding scheme. • Total decoding time for full resolution is tripled (bottleneck being memory bandwidth rather than ALU). Update (6/23/2010): apparently JPEG "progressive encoding," which allows an image to be loaded with gradually finer details (not the same as progressive vs. interlaced frame format), may pave way to how this can be done. The video container would need to become progressive encoding aware. Wavelet encoding in JPEG2000 would also have a similar progressive encoding scheme. ## Thursday, June 4, 2009 ### Multiple definition of... extern inline When I tried to compile gnutls-2.6.6, I got a lot of these: .libs/gnutls_compress.o: In function __strcspn_c1': /usr/include/bits/string2.h:972: multiple definition of __strcspn_c1' .libs/gnutls_record.o:/usr/include/bits/string2.h:972: first defined here .libs/gnutls_compress.o: In function __strcspn_c2': /usr/include/bits/string2.h:983: multiple definition of __strcspn_c2' .libs/gnutls_record.o:/usr/include/bits/string2.h:983: first defined here It turns out that gnutls decides to enforce ISO C99 standard on all its source files, but a lot of the glibc header files use extern inline, which causes GCC to emit a symbol for each extern inline functions. GCC made a change to the extern inline semantics in GCC 4.3 in order to be ISO C99 compliant. The fix I chose is to add -fgnu89-inline option to GCC throughout. It can be accomplished by invoking configure script like this: ./configure [config_flags...] CFLAGS=-fgnu89-inline And this solves the problem. ## Tuesday, June 2, 2009 ### Editing PDF Files Using Open Source Software Here is a workflow that allows quite fancy altering of PDF files using only open source software. I've only used it to add overlays, so your mileage may vary. 1. Use pdf2svg to convert the PDF to SVG. Since PDF may contain multiple pages, each individual page must be converted to its own SVG file, but you only need to convert the pages you will edit. If you are not editing a page, you don't need to convert it but keep the original PDF file; we will use it later. 2. These SVG files from (1) can be edited natively in Inkscape. Use "Save as..." and save the result using PDF via Cairo (*.pdf). I did not convert text into path. 3. Follow the suggestions in How to concatenate PDFs without pain; I used the last pdfpages .tex approach that allows me to assemble from various PDF files. This requires pdfLaTeX, which comes with a TeX distribution, e.g. TeX Live. The .tex file must be processed through pdflatex and not other variants of latex command. The SVG output from pdf2svg is a bit clunky. Not sure if that's because fonts are embedded. The PDF output saved via Cairo is also a bit clunky, but the save is quick. Finally, pdfLaTeX runs fairly quickly and produces an optimized file comparable in size to the original. ### ARM processor notes The first thing I knew about ARM processor is that, in Glibc, they don't support atomic machine instructions, relying on the Linux scheduler to grant atomic uniprocessor access in order to implement a somewhat atomic compare-and-swap operation. However, it does mention that, the new ARMv6 specification has ldrex/strex (load-exclusive and store-exclusive) instructions. Some notes about ARM lineage from the ARMv6 whitepaper: ARM10 processor implements ARMv5 specification (1996-), which is uniprocessor only). ARMv6 (2000-) adds shared-memory multi-processor support that is implemented by ARM11 family of processors (2002-). The ldrex and strex instructions are no different than load-link/store-conditional, a primitive form of hardware transactional memory. They can be used to implement compare and swap. Although Glibc doesn't support ldrex/strex, the Linux kernel apparently does. I am interested in compare and swap implementation in ARM because it is a fundamental building block for scalable shared memory multi-processor programming, used by software to implement non-blocking algorithms. If ARM wants to invade the server space by offering low energy usage data centers, they would have to do that. ## Friday, May 29, 2009 ### Revival of IBM ROM BIOS Hypervisor (or virtual machine manager) seems to be a hot topic these days. It is a thin layer of protection domain that arbitrates resources among different operating systems (OS). This facilitates running multiple OSes on one machine concurrently. Some of the claimed advantages are: • Better protection in case of system compromise. If an attacker gains access to one OS, other OSes are not affected. Furthermore, for a hypervisor that supports snapshotting, if a system is compromised, its image can be restored to previously known good state. • Consolidation of hardware and flexible control. An OS image can move from machine to machine. This can be used to keep more machines utilized; the other underutilized machines can powered off to save energy. To operating system researchers, hypervisor provides much easier development environment. Virtual machines like Qemu provides a gdb stub so the kernel can be debugged in gdb. However, an OS can only attract developers if it is in a functional state, and a significant barrier to get an OS into a functional state seems to be writing device drivers. A typical OS involves dealing with: • Power management (ACPI) • Disk controllers (Parallel ATA, AHCI) • Video display (vendor specific, but most have VBE BIOS for basic non-accelerated 2D graphics) • Networking (vendor specific) • Sound card (also vendor specific), and • USB or Firewire peripherals (OHCI and UHCI). It may have to support legacy PS/2 keyboard and mouse devices as well as serial port. A virtual machine hypervisor, on the other hand, would implement an anti-device driver, which receives I/O requests from the guest OS and act upon them like real devices would do. A hypervisor is sometimes designed to run on top of a host OS, and its anti-device drivers must translate raw I/O request back to the high-level I/O interface that a host OS provides. This translation is necessary so it can run unmodified OS that supplies a wealth of device drivers. But this translation is a waste of effort for operating system researchers who want to get an OS up and running quickly. They do not have resources to hire developers to write device drivers. Their own time can be better spent than reading device specifications. When Sony introduced PlayStation 3, one of its more interesting capability is to be able to run Linux on it. Linux doesn't have direct access to most of the devices on PlayStation 3 (most notably the video card RSX hardware). However, hypervisor on PlayStation 3 provides a hypervisor call API that allows restricted frame buffer, hard drive, and USB access. Most of the Linux device drivers on PlayStation 3 are straightforward hypervisor calls. These hypervisor calls are undocumented, but their functionality can be deduced by how a call is used in the open source Linux kernel. Back in the MS-DOS days, IBM ROM BIOS provides rudimentary drivers to interface with devices via BIOS call. • A jiffy counter in the BIOS data area around 0x400, updated by IRQ1/Int 8h handler. • A keyboard driver handles key-presses on IRQ1/Int 9h by putting keystrokes in a simple ring buffer, which is read using the keyboard service software interrupt Int 16h. • Floppy and fixed disk (hard disk) controller handling IRQ5 and IRQ6. It also provides a synchronous, blocking disk I/O service via Int 13h. There is also video service via Int 10h, but it is overridden by most graphics cards to support VBE. VBE is still used nowadays in the Intel X.Org driver to query video modes. MS-DOS provide basic file system, character I/O devices (serial port, printer, and console), memory and process management. Most applications still use BIOS calls if they want to. Computer viruses were particularly interested in intercepting BIOS calls to find opportunities to infect disks. However, games had to write their own video and sound drivers because these hardware types were not as standardized. Sony PlayStation 3 hypervisor call looks very much like BIOS calls. The PlayStation 3 hypervisor does not run multiple OSes at the same time, so it does not arbitrate resource allocation. However, its purpose is to restrict access to their hardware, so the hardware interface can remain proprietary. A general purpose hypervisor, however, can also provide hypervisor calls. This allows better integration of guest OS with the host. For example, users in the host OS could resize the virtual machine window, and the guest OS is notified of resizing. The hypervisor could also provide OpenGL support for 3D acceleration. Many commercial virtual machine products accomplish this by supplying a proprietary guest-addition driver that bypasses hardware emulation and uses undocumented hypervisor API. Now, it would be nice to have a standardized hypervisor API, so operating system researchers can put together a fully functional OS quickly to gain support, focusing only on the architecture and less on device drivers. Such experimental OS can also be run on hardware with a non-multitasking hypervisor (like Sony PlayStation 3), providing abstract hardware access. In essence, it would be extremely convenient for operating system research and development if we have something like ROM BIOS back in the days. ## Friday, May 22, 2009 ### Interview Question Yet another interview question that I came up with. This one tests the interviewee's ability to read and understand basic specifications. You have a C program written to run on Linux that uses strndup(3), size-bounded string duplication. The function returns a copy of a source string only up to n characters. The copy is allocated using malloc(), and the copy is always zero-terminated even when the source string may not be. When you try to compile the program on Mac OS X, you found out that their Standard C library doesn't have strndup(). After browsing around, you found the functions strlcpy(3) and strlcat(3) which are the size-bounded string copying and concatenation. Can you use them along with malloc() to implement strndup()? If so, show your work. If not, explain why not. ## Monday, May 18, 2009 ### autoheader, automake, autoconf Some notes about these wonderful tools. • When incorporating and distributing third-party source code, autoconf can bootstrap recursively the third-party configure script. Specify using AC_CONFIG_SUBDIRS([third_party/src/...]). Additional configure arguments for the recursive invocation can be added to$ac_configure_args right before AC_OUTPUT.
• Modernized configure.ac uses AC_INIT([name], [version], [desc]). To add automake capability, just use AM_INIT_AUTOMAKE without arguments.
• Autoheader is used to generate config.h.in from configure.ac, which derives the configure script that converts config.h.in to config.h. The config.h file contains C preprocessor macros that affect compilation behavior depending on the outcome of configure script. Autoheader either requires AC_DEFINE to provide a description (third argument) or AH_TEMPLATE([VAR_NAME], [desc]) to exist in configure.ac.
• To check for packages using pkg-config, use PKG_CHECK_MODULES(VARIABLE-PREFIX, MODULES, [ACTION-IF-FOUND], [ACTION-IF-NOT-FOUND]) macro (pkg.m4 seems to be the only source of documentation). If [ACTION-IF-NOT-FOUND] is blank, then the default is to fail and quit configure script. Supply [true] to make this package optional (i.e. if package not present, continue gracefully).
## Wednesday, April 8, 2009
### Vehicle warranty is about to expire
I hate getting these phone calls. They always tell me my vehicle warranty is about to expire. I don't even have a car.
Today they called my cell again. I figured it was that kind of phone call because the caller ID number looks unfamiliar. I picked up the phone and whistled into the phone the "intercept" special information tone (which indicates the number has changed or disconnected). You hear this tone when you dial an incorrect number. I'm sure I didn't get the pitch perfectly, but after I whistled the tone four times, the unsolicited caller promptly hung up. I guess that was successful.
I'll have to see if the phone company complains to me for phreaking the phone's signal system, and if I really do stop getting the vehicle warranty call.
## Wednesday, March 4, 2009
### stdio.h discard a line from input
There are a few different ways to phrase this question, all relating to stdio.h input handling:
• What is a better way to discard input other than using fgetc() to read it character by character?
• How do I discard a line without using fgets() to store it first? It may not clear the line completely due to limited buffer size.
Through creative uses of scanf() this can be done. The format string of scanf() looks like printf(). Rather than passing the value to be printed, you pass a pointer to some memory location to store the value that is parsed. In addition, you can use an astrisk '*' modifier to tell scanf() to discard input.
The first try, scanf("%*s\n"), doesn't really quite do what we wanted. The format "%s" matches only non-white characters (space, tab, newline, etc), so we only discard up to the nearest white space. The "\n" eats another white space (not a newline, contrary to intuition).
The Glibc version* of scanf can match a sequence of characters of any length given character ranges in brackets, sort of like POSIX regular expression character classes. The matching does not care about white spaces, so scanf("%*[^\n]") discards all non-newline characters from the input. But that doesn't quite do the trick yet. The input buffer still has a newline character.
Finally, scanf("%*[^\n]\n") does the trick. It first discards all characters leading to a newline, then discards a white character which must be a new line.
*Update: appears to be ANSI C3.159-1989, so this feature should be portable to any conforming implementations. AIX has it. BSD has it. Glibc is the only one I tried.
## Monday, March 2, 2009
### C++ undefined vtable symbol
I was recently puzzled by a student's problem using GCC to compile some C++ code. He compiled the partial code after every changes in order to make sure he didn't screw up. At one point, the code compiled but gave this linker error:
Undefined symbols:
"vtable for PRNG_Uniform", referenced from:
__ZTV12PRNG_Uniform\$non_lazy_ptr in ccBZAsss.o
ld: symbol(s) not found
collect2: ld returned 1 exit status
Searching on the web didn't yield any meaningful information about the error message. It took me a while, but I finally realized that it just means "there are some virtual methods you haven't defined; please define them."
In this particular example, the idea is to have an abstract base class PRNG (pseudo-random number generator) that derives PRNG_Uniform (uniform distributed) and other PRNGs with a variety of probability distributions (e.g. exponential, normal, or even deterministic). There is a virtual method from the base class that takes a random sample. The subclasses would implement that method. Another part of the system he implements would refer to the base class PRNG without caring what probability distribution characterizes the random samples.
The idea is that C++ compiler creates a virtual table for PRNG and each of its subclasses. The virtual table allows the method call on an object to be re-routed to the appropriate subclass implementation, even if all we have is a pointer to a PRNG object rather than to PRNG_Uniform or a specific subclass of PRNG.
In order for this virtual table to be available for the linker, all the virtual methods must be defined at link time.
## Sunday, January 11, 2009
### Objective-C memory management
Here is a quick summary of Objective-C memory management.
Objects are reference counted, so if you do:
NSClass *objp = [[NSClass alloc] init];
It will need an accompanying:
[objp release];
But many Core Foundation classes also have factory (class) methods that look like:
NSSomething *objp = [NSSomething somethingWithInitializer:initializer];
For example, NSArray methods +array, +arrayWithArray, +subarrayWithArray, ...; NSString methods +string, +stringWithString, ...; and so on. The convention used by Core Foundation is that the object returned by factory methods still have reference count of 1, but they are added to the "autorelease" pool. You do not release nor autorelease these objects!
The "autorelease" pool is simply a list of objects to be released at a later time. The pool is dynamically scoped (like exception frames) and is unrelated to the static (lexical) scope of the program. When the program leaves an autorelease scope, all the objects in the pool of that scope are released. An object can be added to the pool several times, in which case it will be released the same number of times they are added to the pool. There doesn't seem to be any way to take an object out of autorelease pool.
Cocoa's Event Manager always creates an autorelease pool frame prior to handling an event. The frame is popped after calling the event handler. This means your program typically creates some garbage that is cleaned up altogether after finishing an event. Objects that outlive the scope of an event must be explicitly retained.
Apparently, Leopard also supports garbage collection with the -fobjc-gc GCC flag.
## Thursday, January 8, 2009
### Making NULL-pointer reference legal
Normally, NULL pointer reference results in access violation and is illegal. However, it is possible to make NULL pointer reference legal on several operating systems. There are two ways to do that: (a) using mmap(2) with MAP_FIXED flag (works on Linux and Mac OS X), and (b) using shmat(2) with the SHM_RND flag (works on Linux). Consider the following program:
#include "stdio.h"
#include "sys/mman.h"
int main()
{
void* p = mmap(
NULL, 4096, PROT_READ | PROT_WRITE,
MAP_FIXED | MAP_PRIVATE | MAP_ANON, -1, 0);
if (p == NULL)
printf("*(NULL) = %x.\n", *((int*) NULL));
else
perror("mmap(2)");
return 0;
}
The program, when run on Linux and Mac OS X, prints *(NULL) = 0, and that's the result of the program doing a NULL pointer reference. This doesn't work on AIX.
### Uses of hugetlb
While the kernel hackers busily working out what are the reasonable performance expectation of hugetlb in the Linux kernel for allowing application to use large memory pages (>>4KB, typically ~4MB) offered by Page Size Extension, there are a few consequences for using large pages that restrict applicable uses of it. Using a large page improves performance by significantly reduces TLB misses, but the sheer size and alignment requirement of the page is the cause for concern. Assuming a large page is 4MB in size, a 4MB page has to be aligned to 4MB in the physical memory and has to be continuous, and the OS mixing 4KB and 4MB pages might run out of continuous physical memory due to fragmentation caused by 4KB pages.
An application could use large pages as a general-purpose heap, but it should avoid fork(). There are currently two ways to allocate large pages: using mmap(2) to map a file opened in hugetlbfs (on Linux only), or shmget(2) passing a special flag (SHM_HUGETLB on Linux, SHM_LGPAGE on AIX, noting that on AIX a large page is 16MB).
• Using shmget(2), the shared memory backed by large page cannot be made copy-on-write, so both parent and child processes after fork() now share the same heap. This will cause unexpected race condition. Furthermore, both processes could create a new heap space which will be private, and references to the new heap will cause memory error in the other process. References to memory newly allocated in another private heap such as malloc(2) will also be invalid in the other process.
• While mmap(2) allows you to set MAP_PRIVATE to trigger copy-on-write, the copying is going to be expensive for two reasons. The most obvious one is the cost of copying 4MB data even if the child only modifies a word of it and proceeds with an exec(2). With 4KB memory pages, copying a page on demand is much less expensive and can be easily amortized across memory access over process run-time. The other reason is that Linux might run out of hugetlb pool space and has to assemble physically continuous blocks of memory in order to back the new large page mapping. This is due to the way Page Size Extension works. Furthermore, the OS might also require the swap space backing a large page to be continuous, needing to move blocks on a disk, causing lots of thrashing activity. This is much more expensive than simple copy-on-write.
A large page could also be used as a read-only memory store for caching large amounts of static data (e.g. for web servers), so it doesn't have to be made copy-on-write. It could be made read-write but shared if memory access is synchronized across processes, for example by using SVr4 semget(2) or by using lock-free wait-free data structures. This is appropriate for database servers. | 2019-09-18 07:49:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2237255722284317, "perplexity": 3496.830247684705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573258.74/warc/CC-MAIN-20190918065330-20190918091330-00323.warc.gz"} |
https://math.stackexchange.com/questions/2564669/prove-the-inequality-fracbcayz-fraccabzx-fracabcxy-g | # Prove the inequality $\frac{b+c}{a(y+z)}+\frac{c+a}{b(z+x)}+\frac{a+b}{c(x+y)}\geq \frac{3(a+b+c)}{ax+by+cz}$
Suppose that $$a,b,c,x,y,z$$ are all positive real numbers. Show that $$\frac{b+c}{a(y+z)}+\frac{c+a}{b(z+x)}+\frac{a+b}{c(x+y)}\geq \frac{3(a+b+c)}{ax+by+cz}$$
Below are what I've done, which may be misleading.
1. I've tried to analyze when the equality holds
1.1 Under the condition that $$a=b=c$$, it reduces to $$\frac{2}{y+z}+\frac{2}{z+x}+\frac{2}{x+y}\geq \frac{9}{x+y+z}$$ 1.2 Under the condition that $$x=y=z$$, it reduces to $$\frac{b+c}{2a}+\frac{c+a}{2b}+\frac{a+b}{2c}\geq 3$$ Both are easy to verify. However, $$ax+by+cz$$ is not easy to deal with. Is there any famous inequality that I can use here?
1.3 Under the condition that $$(x,y,z)$$ and $$(a,b,c)$$ are in proportion, i.e. $$x=at, y=bt, z=ct$$ for some $$t>0$$, the inequality reduces to $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{3(a+b+c)}{a^2+b^2+c^2}$$ which can be proved by using Newton's inequality: $$(ab+bc+ca)^2 \geq 3abc(a+b+c)$$
1. I’ve also tried to construct a function $$f(x,y,z)=\frac{b+c}{a(y+z)}+\frac{c+a}{b(z+x)}+\frac{a+b}{c(x+y)}- \frac{3(a+b+c)}{ax+by+cz}$$ and analyze its global minimum. But the first-order condition is complicated $$\frac{3(a+b+c)}{(ax+by+cz)^2}=\frac{c+a}{ab(z+x)^2}+\frac{a+b}{ca(x+y)^2}$$ $$\frac{3(a+b+c)}{(ax+by+cz)^2}=\frac{b+c}{ab(y+z)^2}+\frac{a+b}{bc(x+y)^2}$$ $$\frac{3(a+b+c)}{(ax+by+cz)^2}=\frac{b+c}{ca(y+z)^2}+\frac{c+a}{bc(z+x)^2}$$ Maybe some convexity can be used here?
2. Substitution has been considered. Let $$u=\frac{a}{a+b+c},v=\frac{b}{a+b+c}, w=\frac{c}{a+b+c}$$ Then $$u,v,w>0$$ and $$u+v+w=1$$, which are just weights we assign to $$x,y,z$$. The inequality becomes $$\frac{1}{u(y+z)}+\frac{1}{v(z+x)}+\frac{1}{w(x+y)}-\frac{3}{ux+vy+wz}\geq \frac{1}{y+z}+\frac{1}{z+x}+\frac{1}{x+y}$$ Define another function in variables $$u,v,w$$ $$g(u,v,w)=\frac{1}{u(y+z)}+\frac{1}{v(z+x)}+\frac{1}{w(x+y)}-\frac{3}{ux+vy+wz}$$ and consider the constrained optimization problem: $$\min g(u,v,w)\\ \text{s.t. } u>0\\ v>0 \\w>0\\ u+v+w=1$$ The corresponding Lagrangian function can be $$L_{\lambda}(u,v,w)=\frac{1}{u(y+z)}+\frac{1}{v(z+x)}+\frac{1}{w(x+y)}-\frac{3}{ux+vy+wz}+\lambda(u+v+w-1)$$ And the first-order conditions give $$\frac{1}{u^2(y+z)}-\frac{3x}{(ux+vy+wz)^2}=\lambda\Rightarrow \frac{1}{u(y+z)}-\frac{3ux}{(ux+vy+wz)^2}=\lambda u\\ \frac{1}{v^2(z+x)}-\frac{3y}{(ux+vy+wz)^2}=\lambda\Rightarrow \frac{1}{v(z+x)}-\frac{3vy}{(ux+vy+wz)^2}=\lambda v\\ \frac{1}{w^2(x+y)}-\frac{3z}{(ux+vy+wz)^2}=\lambda\Rightarrow \frac{1}{w(x+y)}-\frac{3wz}{(ux+vy+wz)^2}=\lambda w\\ u+v+w=1$$ Summing up yields $$\lambda=\frac{1}{u(y+z)}+\frac{1}{v(z+x)}+\frac{1}{w(x+y)}-\frac{3}{ux+vy+wz}$$ None of the methods I tried seems to work, and now I even doubt the truth of the inequality.
• The inequality looks doubtful but another inequality looking similar can be proved as follows: to simplify things a bit we may suppose a+b+c=1. (In view of homogienity we may assume this]. Write ax+by+cz as $\alpha (y+z)+\beta (z+x) + \gamma (x+y)$ The coefficients now add up to 2. After mulriplying and dividing by 2 apply convexity of $x \to \frac 1 x$ on $(0,\infty)$ to get an inequality very similar to the one above. The coefficients on the left are now different. – Kavi Rama Murthy Dec 14 '17 at 9:51
• Yes, I tried your method. We can even assume that $x+y+z=1$. And I even tried the limit case $z=0$, which unfortunately holds, too. Hard to find a counterexample, I still tend to believe it is true. – Mathis Dec 14 '17 at 14:18
• The inequality is true. The Buffalo Way works although it is an ugly solution. The inequality is symmetric with respect to $(a, x), (b, y)$ and $(c,z)$. Thus, one may assume that $z \le y \le x$. – River Li Oct 5 '19 at 15:44
• Might be useful: artofproblemsolving.com/community/c6h1688p535460 – darij grinberg Dec 28 '19 at 20:45
Too long for a comment.
Since the inequality is homogeneous, without loss of generality we may suppose $a+b+c=1$ and $x+y+z=1$. Then
$$(1-x)(1-y)(1-z)=1-x-y-z+xy+xz+yz-xyz=xy+xz+yz-xyz$$
Thus the left hand side of the inequality equals
$$\frac{1-a}{a(1-x)}+ \frac{1-b}{(1-y)}+ \frac{1-c}{c(1-z)}=$$ $$\frac{1}{a(1-x)}+ \frac{1}{b(1-y)}+ \frac{1}{c(1-z)}-\frac{1}{(1-x)}-\frac{1}{(1-y)}- \frac{1}{(1-z)}=$$ $$\frac{bc(1-y)(1-z)+ac(1-x)(1-z)+ab(1-x)(1-y)}{abc(1-x)(1-y)(1-z)}- \frac{(1-y)(1-z)+(1-x)(1-z)+(1-x)(1-y)}{(1-x)(1-y)(1-z)}=$$ $$\frac{bc(1-y-z+yz)+ac(1-x-z+xz)+ab(1-x-y+xy)}{abc(xy+xz+yz-xyz)}- \frac{(1-y-z+yz)+ (1-x-z+xz)+ (1-x-y+xy)}{xy+xz+yz-xyz }=$$ $$\frac{bc(x+yz)+ac(y+xz)+ab(z+xy)}{abc(xy+xz+yz-xyz)}- \frac{(x+yz)+ (y+xz)+ (z+xy)}{xy+xz+yz-xyz}=$$ $$\frac{bc(x+yz)+ac(y+xz)+ab(z+xy)}{abc(xy+xz+yz-xyz)}- \frac{1+ xy+yz+xz }{xy+xz+yz-xyz}=$$ $$\frac{\frac 1a(x+yz)+\frac 1b(y+xz)+\frac 1c(z+xy)-1-xy-yz-xz }{xy+xz+yz-xyz}.$$
So we have to show that
$$\left(\frac 1a(x+yz)+\frac 1b(y+xz)+\frac 1c(z+xy)-1-xy-yz-xz\right)(ax+by+cz)\ge 3(xy+xz+yz-xyz)$$
$$\left(\frac 1a(x+yz)+\frac 1b(y+xz)+\frac 1c(z+xy)\right)(ax+by+cz)\ge 3(xy+xz+yz-xyz)+(1+xy+yz+xz)(ax+by+cz)$$
$$x(x+yz)+ \frac bay(x+yz)+ \frac caz(x+yz)+ \frac abx(y+xz)+ y(y+xz)+ \frac cbz(y+xz)+ \frac acx(z+xy)+ \frac bcy(z+xy)+ z(z+xy)\ge$$ $$3(xy+xz+yz-xyz)+(ax+by+cz)+ax^2y+bxy^2+cxyz+axyz+by^2z+cyz^2+ax^2z+bxyz+cxz^2$$
$$x^2+\frac bay(x+yz)+ \frac caz(x+yz)+ \frac abx(y+xz)+ y^2+ \frac cbz(y+xz)+ \frac acx(z+xy)+ \frac bcy(z+xy)+ z^2+5xyz\ge$$ $$3(xy+xz+yz)+(ax+by+cz)+ax^2y+bxy^2+by^2z+cyz^2+ax^2z+cxz^2$$
or that (because $x^2+y^2+z^2+2xy+2xz+2yz=1$)
$$1+\frac bay(x+yz)+ \frac caz(x+yz)+ \frac abx(y+xz)+ \frac cbz(y+xz)+ \frac acx(z+xy)+ \frac bcy(z+xy)+ 5xyz\ge$$ $$5(xy+xz+yz)+(ax+by+cz)+ax^2y+bxy^2+by^2z+cyz^2+ax^2z+cxz^2$$
Finally, we have to show that $$1+\left(\frac ba+\frac ab-5\right)xy+ \left(\frac ca+\frac ac-5\right)xz+ \left(\frac cb+\frac bc-5\right)yz+ \left(\frac ac-a\right)x^2y+\left (\frac bc-b\right)xy^2+ \left (\frac ab-a\right)x^2z+\left (\frac cb-c\right) xz^2+ \left (\frac ba-b\right)y^2z+\left(\frac ca-c\right)yz^2 - (ax+by+cz) + 5xyz \ge 0$$
• Hi Alex can you check my proof with the answer of Gimusi ? – user448747 Dec 28 '17 at 19:10
• @FatsWallers Unfortunately, Gimusi’s proof is too simple to be true, see my comment there. – Alex Ravsky Dec 29 '17 at 11:25
• Hi Alex Do you think we can use the Equal Variable Method ? – user448747 Jan 4 '18 at 21:25
• @FatsWallers Unfortunately, I didn't hear about this method. – Alex Ravsky Jan 5 '18 at 4:51
• See here emis.de/journals/JIPAM/images/059_06_JIPAM/059_06.pdf .I think it's useful in your case maybe . – user448747 Jan 5 '18 at 12:02
This is not an answer, but putting code in a comment doesn't work well either.
Regarding your doubts about the truth of the inequality, I am still inclined to think it holds true. You can try to look for counterexamples with this code. In case python thinks the inequality doesn't hold, it outputs $a,b,c,x,y,z$ and the difference between the two sides. So far I have only found differences of $10^{-15}$ and smaller with it, which is just python lacking sufficient precision.
sta = 3.14
sto = 4.14
ste = .1
def frange(start, stop, step):
i = start
while i < stop:
yield i
i += step
for a in frange(sta,sto,ste):
for b in frange(sta,sto,ste):
for c in frange(sta,sto,ste):
for x in frange(sta,sto,ste):
for y in frange(sta,sto,ste):
for z in frange(sta,sto,ste):
if (1.*(b+c)/(a*(y+z))+1.*(c+a)/(b*(z+x))+1.*(a+b)/(c*(x+y))<3.*(a+b+c)/(a*x+b*y+c*z)):
print a,b,c,x,y,z,1.*(b+c)/(a*(y+z))+1.*(c+a)/(b*(z+x))+1.*(a+b)/(c*(x+y))-3.*(a+b+c)/(a*x+b*y+c*z)
Also, since the inequality can be reshaped to $$\frac{a}{b(x+z)}+\frac{b}{a(y+z)}+\frac{a}{c(x+y)}+\frac{c}{a(y+z)}+\frac{b}{c(x+y)}+\frac{c}{b(x+z)}\ge\frac{3a}{ax+by+cz}+\frac{3b}{ax+by+cz}+\frac{3c}{ax+by+cz},$$
Maybe we can show that $\frac{1}{b(x+z)}+\frac{1}{c(x+y)}\ge\frac{3}{ax+by+cz}$?
• Thanks for the code, now I'm more confident about the truth of the inequality. $\frac{1}{b(x+z)}+\frac{1}{c(x+y)}\ge\frac{3}{ax+by+cz}$ doesn't hold: $a=b=c=1$, $z=0$, then it becomes $\frac{1}{x}+\frac{1}{x+y}\geq \frac{3}{x+y}$, or equivalently $y\geq x$. – Mathis Dec 18 '17 at 0:06
Partial Proof:
If we start with your substitution at 3) and remark that we have with your condition : $$ux+yv+zw=(x+y+z)(u+v+w)-u(y+z)-v(z+x)-w(x+y)=(x+y+z)-u(y+z)-v(z+x)-w(x+y)$$
So if we put :
$p=y+x$$\quad$$i=w(x+y)$
$q=z+x$$\quad$$k=v(z+x)$
$r=y+z$$\quad$$j=u(y+z)$
We get : $$\frac{1}{i}+\frac{1}{j}+\frac{1}{k}+\frac{-3}{\frac{p+r+q}{2}-i-j-k}\geq \frac{1}{p}+\frac{1}{q}+\frac{1}{r}$$
With the condition : $$\frac{i}{p}+\frac{k}{q}+\frac{j}{r}=1.$$
Now the idea is to use the relation between the incircle of center I and the side of a triangle ABC : $$\frac{IA^2}{CA.AB}+\frac{IB^2}{BC.AB}+\frac{IC^2}{CA.BC}=1$$
So we put :
$p=CA.AB$$\quad$$i=IA^2$
$q=BC.AB$$\quad$$k=IB^2$
$r=CA.BC$$\quad$$j=IC^2$
We get : $$\frac{1}{IA^2}+\frac{1}{IB^2}+\frac{1}{IC^2}+\frac{-3}{\frac{CA.AB+BC.AB+CA.BC}{2}-IA^2-IB^2-IC^2}\geq \frac{1}{CA.AB}+\frac{1}{BC.AB}+\frac{1}{CA.BC}$$
Furthermore we have the following relation : $$\frac{1}{IA^2}+\frac{1}{IB^2}+\frac{1}{IC^2}=\frac{1}{r^2}-\frac{1}{2rR}$$ $$IA^2+IB^2+IC^2=s^2+r^2+8rR$$ $$CA.AB+BC.AB+CA.BC=s^2+(4R+r)r$$ $$\frac{1}{CA.AB}+\frac{1}{BC.AB}+\frac{1}{CA.BC}=\frac{1}{2rR}$$
Where $s$ denotes the semi-perimeter , $r$ the radius of the incircle and R the radius of the excircle
Finally we have :
$$\frac{1}{r^2}-\frac{1}{2rR}+\frac{-3}{-(s^2+r^2+8rR)+0.5(s^2+(4R+r)r)}\geq \frac{1}{2rR}$$
I finally found a theorem of Blundon wich characterizes the existence of a scalene triangle with a necessary and sufficient condition on $r$,$R$,$s$ .See here.But I don't know how to use it to have a condition on the inequality . Maybe somebody could do that .
• The idea looks good, but I don't know whether the substitution is valid (does such a triangle exist?). Besides, the inequality obtained seems more complicated than the original one. – Mathis Dec 17 '17 at 12:48
• Let $x=10$, $y=z=1$. Then $p=q=11$, $r=2$. Next, $CA=\sqrt{\frac{pr}q}=\sqrt{2}$, $BC=\sqrt{\frac{qr}p}=\sqrt{2}$, and $AB=\sqrt{\frac{pq}2}=\sqrt{60.5}> 2\sqrt{2}=BC+CA$, so the triangle $ABC$ doesn’t exist. – Alex Ravsky Dec 23 '17 at 11:44
• Hi Alex in fact yes it doesn't work that's why the next idea is to generalize this with the Steiner inellipse and hope it works If you have some good ideas see here . math.stackexchange.com/questions/2571971/steiner-inellipse – user448747 Dec 23 '17 at 12:56
• I have a serious way to prove it with this mathweb.scranton.edu/monks/courses/ProblemSolving/… – user448747 Dec 28 '17 at 12:54
• @FatsWallers Thanks a lot for the quote! You can also insert the full solution here. – user Dec 28 '17 at 21:40 | 2021-06-14 03:54:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9170770049095154, "perplexity": 357.7695155512796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611320.18/warc/CC-MAIN-20210614013350-20210614043350-00283.warc.gz"} |
https://physics.stackexchange.com/questions/728365/ac-compressor-adds-less-heat-than-is-removed-during-condensation | # AC compressor adds less heat than is removed during condensation?
The compression phase in an air conditioner is approximately adiabatic, so that heat is added to the refrigerant. It then naturally transfers heat to the outside. My question is: since heat was added both during the evaporation phase (from inside the house) and during compression, why should we expect that more heat is lost during condensation than was added by compression?
Secondarily, it seems that in refrigerators, the compression phase turns the gas to a liquid. I assume that air conditioners generally do the same, but then calling the next phase "condensation" doesn't make a lot of sense (since it's already a liquid). What gives?
1. The gas is transferred to a compressor, where most of the work is done. The gas is compressed adiabatically, heating it and turning it back to a liquid.
2. The liquid passes through cooling coils on the outside of the fridge. Because the liquid is now warmer than room temperature, heat is transferred naturally to the room. This is an isobaric compression process.
So it seems that sometimes condensation happens before the "condenser" stage (4).
• Condensation does NOT happen inside the compressor. The compressor is designed to compress a vapor. Since liquids are somewhat incompressible, any liquid inside the compressor would tear it up. Your source is incorrect about this point. Sep 19, 2022 at 19:30
• The wording in your link is sloppy thermodynamics. Unfortunately, it is not uncommon. For example, In step 3 when they say “heating it” they actually mean raise its temperature. But the increase in temperature is due to compression work, not heat. Sep 20, 2022 at 12:06
• The information you got from the link is so awful, I felt compelled to address in an update to my answer. Sep 20, 2022 at 14:22
• @BobD I really appreciate the help you've provided! I had a major misconception around "heat." I wish I could mark two answers as accepted. My first question may not have been phrased very clearly, but I think the other answer here partially addresses it. I had been assuming that the compression phase was intended to raise the temperature, but now it seems like merely a side effect of increasing the pressure to help it condense. I will do more reading.
– A_P
Sep 20, 2022 at 15:55
• @BobD One more question though: on a standard P-T phase diagram, is "saturated vapor" the line separating liquid/vapor (between the triple and critical points), and "superheated vapor" the gaseous phase? Or is that the wrong way to think about this?
– A_P
Sep 20, 2022 at 15:56
Question 1: Work is done on the refrigerant to increase its pressure enough to condense against ambient air. This work does have to exit the system as heat, but the amount of heat added by compression work is not going to be as much as the amount of heat absorbed by boiling refrigerant inside the evaporator, as this would lead to a VERY low efficiency for the refrigeration system. This can be verified by looking at the coefficient of performance for the particular system that you are dealing with, as shown here.
Question 2: the compressor increases the pressure of the refrigerant enough to allow it to condense at ambient conditions, but compression alone does NOT condense the refrigerant. The high pressure and high temperature refrigerant turns into liquid at the condenser as it releases heat to the environment.
• Thanks! I've edited my question to show where my confusion in question 2 comes from.
– A_P
Sep 19, 2022 at 17:15
• Hi David. I must confess having just looked at your answer. But do you really want to talk about "the amount of heat added by compression work"? It makes me cringe. The heat exiting the system is the sum of the heat added to the system by the evaporator plus the work done on the system by the compressor. From my experience, that's how it's always framed in a refrigeration cycle. Then you can say the amount of work done on the system by the compressor is not going to be as much as the amount of heat added to the system by the evaporator for a decent Coefficient of Performance (COP). Sep 20, 2022 at 20:18
• Just a suggestion, no need to reply. Sep 20, 2022 at 20:18
It appears you are confusing energy transfer by work with energy transfer by heat, starting with the title:
AC compressor adds less heat than is removed during condensation?
The compressor in a refrigeration cycle does not add heat to the refrigerant. Heat is energy transfer due solely to temperature difference.
The compressor adds energy to the refrigerant by means of work, taking low pressure saturated vapor from the evaporator and delivering high pressure superheated vapor to the condenser.
My question is: since heat was added both during the evaporation phase (from inside the house) and during compression, why should we expect that more heat is lost during condensation than was added by compression?
Again, heat is not added to the refrigerant by the compressor. Energy is added to the refrigerant by the compressor by means of work, not heat. It is important to understand the difference. Heat is energy transfer due solely to temperature difference.
Overall, the stages are
1. Energy is transferred to the refrigerant from the cool environment in the form of heat by the evaporator.
2. The compressor transfers energy to the refrigerant by means of adiabatic work converting the refrigerant from saturated low pressure vapor at the evaporator to superheated vapor (high pressure and temperature) at the condenser.
3. The condenser transfers energy from the refrigerant to the warm environment by means of heat, converting superheated vapor to saturated liquid.
4. An expansion valve takes saturated liquid from the condenser and delivers a liquid/vapor mixture to the evaporator with no work or heat transfer.
For conservation of energy the energy extracted from the refrigerant by means of heat in the condenser is the sum of the energy absorbed by the refrigerant by means of heat in the evaporator plus the energy absorbed by the refrigerant by means of work by the compressor, or
$$Q_{condenser}=Q_{evaporator}+W_{compressor}$$
You may find the following article helpful: https://en.wikipedia.org/wiki/Heat_pump_and_refrigeration_cycle
I think I still have some confusion. I understand that heat can be transferred, but can't one also speak of the amount of heat (thermal energy) in a system?
No you can't think about the amount of heat in a system. Heat is strictly energy transfer due to temperature difference. Things don't "contain" heat. The energy contained in the system is properly called the internal energy of the system, which is the sum of the kinetic and potential energies at the atomic and molecular level.
The term "thermal energy" is often used as synonymously with the kinetic energy component of internal energy, but it is often frowned upon because of being confused with temperature and heat.
And if something causes that to grow through work, then although it hasn't "transferred heat," is it not appropriate to say that heat was added in the process?
No, it is not appropriate to say that heat was added to the process. It is appropriate to say that energy was added to the process due to work (energy transfer due to force times displacement) not heat (energy transfer due to temperature difference).
Apart from that, hopefully the rest of my question makes sense.
I will have to reread it since it appears you edited it after I posted my answer.
UPDATE:
1. The gas is transferred to a compressor, where most of the work is done. The gas is compressed adiabatically, heating it and turning it back to a liquid.
This is at best, sloppy thermodynamics wording and at worst downright wrong. Get yourself a better reference.
First of all, when they say “heating it” they actually mean raise its temperature. But the increase in temperature is due to energy transfer by compression work, not energy transfer by heat. Unfortunately this is not uncommon. Since we are so used to raising the temperature of something by heat transfer, like cooking on a stove, we tend to use the word "heating" as always synonymous with raising temperature. But that is not always the case. Raising the temperature of a gas by compressing it involves no heat transfer.
Secondly, the compressor does not turn the gas "back into a liquid". It takes saturated vapor at the output of the evaporator and raises its temperature and pressure to create superheated vapor for the input to the condenser. See process 1-2 for an ideal (isentropic) compressor in the diagram below taken from the Wikipedia link above. If you Google "Temperature-entropy diagram for refrigeration cycle" to find a multitude of similar diagrams. Nowhere will you see the output of the compressor being a liquid.
1. The liquid passes through cooling coils on the outside of the fridge. Because the liquid is now warmer than room temperature, heat is transferred naturally to the room. This is an isobaric compression process.
The superheated vapor, not liquid, is passed through the coils first transferring heat to the room to convert the superheated vapor to saturated vapor (lowering temperature and pressure), as shown in process 2-3 in the figure below, then transferring heat to convert the saturated vapor to saturated liquid at constant temperature and pressure (isothermal and isobaric) as shown in process 3-4 in the figure below.
Hope this helps.
• Thanks. I think I still have some confusion. I understand that heat can be transferred, but can't one also speak of the amount of heat (thermal energy) in a system? And if something causes that to grow through work, then although it hasn't "transferred heat," is it not appropriate to say that heat was added in the process? Apart from that, hopefully the rest of my question makes sense.
– A_P
Sep 19, 2022 at 17:08
• @A_P I've updated my answer to respond to your follow up questions. Sep 19, 2022 at 17:46
• @A_P, some professions actually do consider the heat content of a system. Chemical engineers assign an enthalpy to a standard state (e.g., ideal gas at 0 K), and measure heat content against that standard state. This means that chemical engineers think of heat and heat transfer a bit differently than physicists do. Sep 20, 2022 at 18:35
• @DavidWhite I'm aware of that. Such terms are baked into the vernacular of not only chemists but also some physicists. But from a purely thermodynamicist perspective they are, to put it mildly, inelegant. But here the OP confusion has to do with increasing temperature by compressor work vs heat. There should be no debate about that. And that is my focus here. In no way does the compressor "heat" the gas. Sep 20, 2022 at 18:54
• @BobD, don't forget about the mechanical equivalent of heat. Also, the OP was asking if it's appropriate to say that heat was added to a process. As "inelegant" as my viewpoint is, the answer is "yes", some professions do think of it in this way. Sep 20, 2022 at 20:11 | 2023-01-27 14:52:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6438612937927246, "perplexity": 401.67348087793175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494986.94/warc/CC-MAIN-20230127132641-20230127162641-00766.warc.gz"} |
https://culanth.org/fieldsights/when-fieldwork-breaks-your-heart?token=170 | # When Fieldwork Breaks Your Heart
In this episode of AnthroPod, guest producer Aisha Sultan considers the question: what do you do when fieldwork threatens to break your heart? While graduate seminars and methodological reflections within anthropology often focus on the possibilities ethnography affords as the cornerstone of the discipline, Sultan here contends with its bleaker and more difficult dimensions: the toll it takes on the minds and bodies of ethnographers; experiences of mental illness; persistent feelings of distrust, frustration, and exhaustion. Sultan’s conversation with Helen Lee and Shoshanna Williams is interspersed with excerpts of poetry and fieldnotes from each of their fieldwork experiences. Together, these reflections offer a candid, vulnerable, and realistic insight into the quotidian experience of doing ethnographic fieldwork.
Aisha Sultan is a PhD candidate at the University of Adelaide. Her research looks at the way homelessness as an experience and identity shapes women’s reproductive and sexual health outcomes, focusing on the ways that women perceive and manage their health care needs and wishes.
Helen Lee is Professor of Anthropology in the Department of Social Inquiry and Deputy Head of School (Research and Strategy) for the Humanities and Social Sciences at La Trobe University. Since the 1980s, she has conducted research with the people of Tonga, both in their home islands in the Pacific and in the diaspora, particularly in Australia, with a focus on childhood and youth, cultural identity, and migration and transnationalism. Her recent books include Mobilities of Return: Pacific Perspectives (2017, coedited with Jack Taylor) and Change and Continuity in the Pacific (2018, coedited with John Connell).
Shoshannah Williams is a social scientist, whose work explores the intersection of social marginalization, gender, and the conditions that shape chronic vulnerability within urban spaces. She earned her PhD in anthropology and development from Adelaide University, where her work explored the lives of women experiencing homelessness a train station in Dhaka, Bangladesh. She has a background in disability rehabilitation and public health, previously working as an Urban Health and Equity Research Fellow at BRAC University and iccdr,b in Bangladesh.
## Credits
This episode was produced by Aisha Sultan. Special thanks to everyone who made this episode possible: Anar Parikh for serving as Executive Producer on this episode; Helen Lee and Shoshanna Williams, for bringing their insight to this conversation; the University of Adelaide and the Australian Government Research Training Program Scholarship Scheme; the PhD writing and support group The Squad; Helka Manninen; Kristi Urry, Sarah Pearce, and Anar Parikh for reading the poetry and fieldnote excerpts; Shelley Travers, Andrew Gramp, and Paul Chambers for their technical assistance; and Beth Derderian for offering additional support.
AnthroPod features interviews with current anthropologists about their work, current events, and their experiences in the field. You can find AnthroPod at SoundCloud, subscribe to it on iTunes, or use our RSS feed. If you have suggestions for future episodes or feedback on this episode, please leave us a comment to the right, or get in touch via Facebook or Twitter.
Intro and outro: All the Colors in the World by Podington Bear. Transitions: Phobos and Deimos Play with Shadows by Julie Maxwell. Sound effects: Tape Player Sounds by AldebaranCW.
## Transcript
Anar Parikh [00:00]: Welcome to AnthroPod. This is Anar Parikh, and I’m thrilled to bring you this episode, “When Fieldwork Breaks Your Heart,” guest produced by Aisha Sultan, a PhD candidate at the University of Adelaide, Australia. Just in time for Valentine’s Day, Aisha and her interlocutors, Professor Helen Lee and Dr. Shoshanna Williams, explore the gritty underbelly of anthropology’s first love: ethnographic fieldwork. While our disciplinary tendency as anthropologists is to extol the virtues of our methodological and theoretical core, Aisha interweaves excerpted fieldnotes, poetry, and personal reflection into her discussion with Professor Lee and Dr. Williams to consider the less romantic realities of doing ethnography.
Recorder clicks on
Narrators: [01:09]
She walked down from the parklands.
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She has a gash across the back of her head.
Alcafe Café Style Frothy Sachets 10pk $3 30c per Sachet Jules and I take turns to apply pressure on the wound to stop the bleeding. Just Organic Natural Yoghurt 1kg$5 50c per 100g
Peter calls emergency services.
El Tora Taco Kit 370g $3 81c per 100g She starts to doze off. I ask her if she has a favourite song. She tells me about her 5-year-old instead. Di San Laundry Soaker & In Wash Booster 1kg$3 3.00 per kg
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My hands start to shake.
My hands start to shake.
Recorder clicks off
Aisha Sultan [02:34]: What to do when fieldwork threatens to break you? What if some of the things we encounter, as researchers, make us angry and leave us feeling helpless? How might we best prepare for and live with the suffering of others without burning out? How to reconcile the roles and responsibilities of outsider researcher and engaged participant-observer? To what extent is this even possible? These are some of the questions I have grappled with while working with women experiencing homelessness. I’ve felt joy, excitement, sorrow and anger. I feel their grief as a knot in my stomach or a tangle in my thoughts. I worry about the way my research might adversely affect my participants. At times, I’ve also been bored, frustrated, and even, let’s be honest, annoyed and conflicted not only with the system but with my participants as well. During fieldwork, we as anthropologists are expected to immerse ourselves into a cultural web or fabric and acknowledge that we are not detached or impartial observers, but in fact people who are emotionally, intellectually, and physically embedded in the world of our field sites. However, when we return from the field, we are encouraged to distance ourselves from the weight of these experiences and extricate our emotional insights from our analysis. The mental and physical strain of ethnographic fieldwork is at once readily acknowledged and sometimes romanticized, while at the same time we are discouraged from including these experiences in our formal writing. Even in scholarly discussions and prefield seminars about ethnographic methods, the emotional labor and the effects of ethnographic fieldwork on the researcher’s body, psyche, worldview, and moral compass are often elided. Moreover, even though the emotional and personal challenges of fieldwork are dismissed in anthropology’s more formal spaces, most of our informal and private conversations, in contrast, seem to be centered around how overwhelming fieldwork can be and how hard it is to speak of this because we fear that our research will not be taken seriously. So, in this episode, I reflect on my own experiences and challenges and explore the personal and emotional dimensions of ethnographic fieldwork, through a conversation with Professor Helen Lee and Dr. Shoshanna Williams. Helen has published widely on migration, transnationalism, as well as Tongan history and society. She is Professor of Anthropology at La Trobe University in Melbourne, Australia, where she teaches first-year students, as well as later-year students. Shoshanna’s doctoral thesis, in turn, explored vulnerability and resilience of women experiencing homelessness in a train station in Dhaka, Bangladesh. Shoshanna has a background in occupational therapy and has worked as part of numerous community-based health projects here in Adelaide, Australia, as well as overseas.
Music plays
AS [05:39]: Helen, it's been roughly about thirty years since your fieldwork in Tonga. Can you tell us a bit about your experience?
Helen Lee [05:48]: So I went to Tonga for my PhD research and I wanted to very broadly study childhood and the experience of childhood with the basic premise of, you know, what is it that makes you Tongan rather than anything else. Partly for personal reasons but also because I just found it really interesting, the study of childhood, so I went to live in a village called Holonga on the main island of Tonga. And then during the fieldwork I also spent a little bit of time on the island called Afa.
AS [06:21]: What surprised you the most in terms of doing fieldwork?
HL [06:24]: I think I was not expecting to have to think on my feet quite so much. I didn't really have much preparation, I didn't go to Tonga armed with the whole interview schedule and questionnaires and everything. I sort of did that on the run and I hadn't really thought how difficult it would be to figure out, as I went along, what I needed to do and to deal with all of the different events that came up and just to be so flexible.
AS [06:50]: Thirty years ago, it was quite different in terms of what the uni would ask from PhD students in preparation . . .
HL [06:58]: Was completely different. I would never send one of my students out the way I went. I started my PhD and within a couple of months I went off to do my fieldwork. Because I've lived in Tonga before, my supervisors just assumed that I would be able to just step straight in and there was no ethics. There was only a very brief meeting, a prefield work meeting. I had very, very little advice about what I was going to be doing. I had written up a research proposal, which didn't actually include methodology. Just this is what I'm interested in looking at. Then I just set off.
AS [07:29]: Shoshanna, did you feel prepared or unprepared?
Shoshanna Williams [07:39]: I felt incredibly prepared because I'd been researching urban poverty for almost two years and all this feedback about how great my methods section was was in my proposal and I really thought that I had thought through a lot of issues, but I hadn't anticipated what it was going to be like and so I had a false sense of bravado and made a whole set of assumptions. For example, when I was doing fieldwork in slums people they were very willing to talk to us and seemed happy to sit and chat, whereas the women that I worked with initially really didn't want to talk to me. I just hadn't even thought through that that might have been a possibility.
AS [08:12]: Can you tell us a bit about who were you working with?
SW [08:15]: So I wanted to research women who experience homelessness in Dhaka, which kind of arose out of me working in this urban poverty space and urban poverty was really spatialized into slums. There was really no real discussion to talk about homelessness and it was largely absent in the literature, particularly qualitative work. There was a couple of surveys and that's it. I came into the field of anthropology and development not having done a undergrad in it. I studied occupational therapy, so disability rehab, and I'd been involved in public health for a while and that kind of segued into this. So I'd gone in with my ideas and my supervisors started to have conversations with me about the theoretical framings and so I'd just gone, "OK, great, let's just go with vulnerability and resilience. That's what I'll research, sure" not really knowing what I could or should research. And so I went in and I chatted to service providers and they were like "oh well, if you want to research vulnerability, you have to go to this train station." I was like "OK, sure!"
AS [09:14]: What was the most surprising, difficult element that you didn't anticipate while beginning fieldwork?
SW [09:22]: Not expecting that people just wouldn’t want to engage at all or that when I did start to talk to people about their experiences, that there was a lot of not wanting to talk about what was really going on. I hesitate to say lying, but there was a lot of obscuring of some of the most difficult painful realities of what made up women's lives.
AS [09:45]: They were obscuring it from you?
SW [09:47]: I think so, but maybe sometimes also from themselves. Sometimes people would completely obliterate the fact that they had a child that was, that they'd either sold sometimes or that had died or that they felt like they were being forced to adopt to family or friends. Yeah, there was a lot of that and also there was a lot of shame around having experienced multiple marriages. A lot of women who had multiple marriages that they just kind of left out of their narratives on the first run took a lot of multiple sittings and conversations and piecing together what it was. And as we gradually built that trust, some of those details came out but other details like children were often told to me by other women.
HL [10:31]: For me I think the surprising thing is probably something that isn’t that common in people’s experience but because I'd been married to a Tongan before and I lived and worked in Tonga before, nobody took me seriously that I was there as a researcher and that was a shock for me because I went there thinking “well, I'm a PhD student, I'm going to do this big research project," and I went to live in the village with people that I knew and for the entire time I was there, they just humored me or and they sort of assumed I was there to look for another Tongan husband, even as the evidence of me being pregnant became obvious and I had my son with me. It was quite strange, so I had this very strange experiences of interviewing people who were just humoring me. So it was kind of, became difficult to take myself seriously. [laughter] Yeah, it was odd. It was quite odd.
SW [11:22]: That would have thoroughly fed into your imposter syndrome as a PhD student. [laughs]
HL [11:26]: It was absolutely, yes, and I've never got rid of that imposter syndrome, by the way. [laughs]
AS [11:32]: Do you feel that they were telling you a different story than what perhaps was the story?
AS [13:54]: Was that hard as a researcher and then as a parent?
HL [13:59]: It was hard as a person and a parent. It wasn't hard as a researcher because, as an anthropology undergraduate, cultural relativism was the emphasis and that was the main idea of anthropology was that you try to understand things from their perspective, which is exactly what I was trying to do and, for me as a researcher, I found it difficult to observe incidents of violence. There were also lots of very nice, you know, Tongans love their children and they do lots of lovely things as well. It was just the violence that I found difficult, as a parent and a person I found that really challenging. So I had this constant pull between me the person and my set of values and me the researcher. I mean, that's kind of what anthropology is is that, I think, that tension.
AS [14:46]: The conversations we do have about fieldwork are often tidied up or suppressed. Is there room to have those conversations? Would it be beneficial or not to have those conversations, especially with PhD students?
HL [14:59]: Oh, I would have loved someone to have had conversations with me before I went to the field not even specifics about what I was going to experience in Tonga but just what I was going to experience as a researcher. Even talking through that kind of tug between you as a person you as a researcher. I'd gone through when there were no methodology subjects as an undergraduate student no one had ever really talked through those issues and ethics, as I said I was not an issue. So yeah I would have loved it. I've been an avid reader of people's fieldwork accounts for years and I think it says I'm trying to dig through them to find those little bits where they admit the difficulties and often, I think, they're tidied up a little bit. I'm always fascinated by other people's fieldwork accounts.
AS [15:45]: There seems to be a need for those conversations.
SW [15:47]: Yeah, very much so, and I put lot of pressure on myself when I was in the field to really engage with critically analyzing what was going on, and I wish that I had given myself the space or been told to give myself the space of just not knowing and being encouraged to make sense of those feelings and work through them in the field. And then, you know, put my analysis hat on later.
HL [16:11]: That's true actually, because we don't get encouraged to do the feeling part of it at all. And if you do get any methodology, it's the intellectual work of it, not that emotion work.
SW [16:23]: No, and I think when you are researching violence or when you encounter that and you're forced to sit with people for months at a time and just talk about horrific violence and this idea that nothing could ever change and it's very difficult and it changes you. You start to believe that nothing could ever change and that's deeply, deeply painful and deeply difficult to navigate.
HL [16:53]: And I guess as a researcher you can't, you can't be saying to your research participants how emotionally distraught you are by their accounts, you’ve got to keep up a face. You can't be saying “I'm really badly affected by all this” because you're hearing their stories, it's, they're the ones who are in a precarious, awful situation.
SW [17:13]: It's nothing about you, exactly.
HL [17:18]: Yet you are having that experience.
SW [17:20]: Exactly. And we were talking about me and how I was a trained therapist and how I was told that the people that you engage with, they sense how much you can deal with and if you show that you're not going to be able to deal with it, then they're going to stop talking to you.
AS [17:34]: I think I'm in that stage with my fieldwork now where my participants are testing me, sussing me out: how I react to things that they do. Trying to see if I am genuine, reliable, worthy of being given this temporary custodian role of their experiences. Do I understand something? Not the whole experience because, of course, I as a researcher wouldn't be able to understand what the lived experiences women experiencing homelessness have and that would be wrong for me to say that I do understand. But that I can, in some ways, feel at least a little bit of what they are feeling or going through and that opens up some of that relationship-building and maybe understanding.
HL [18:25]: I think empathy is a good term there, where you can't sit there and be blank. Because then you might be seen to be unfeeling or uncaring. So you need to show that you're empathetic. But yes, without all of the other reactions that may be flying around your head and your heart, but simply showing empathy which I guess is the same sort of principle. So, human contact.
SW [18:51]: Right, actually, it's really interesting that you say that because this woman who verbally assaulted me when I was first in the station, we later had a conversation about how she perceived me and she had a conversation with me about how important it was that I was sitting in the dirt with her and how, for her, that meant that she was worthy of being seen and being treated like she was human. She talked to me about how "these other people they treat us worse than dogs but you, you come and sit with us" and then she talked about "you, you show loving care, you hug us." I had no idea that, like, sitting with and these hugs meant so much. What I failed to think through was the fact that I was working with people who had very rarely been shown love and care and their whole life histories were ones of people abusing and exploiting them and being told that they weren't worthy. The public would just walk past them and say “you're never going to get buried.” We forget how very small things can be important and that showing love and care is just as much a project as anything else that we might do.
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Narrator [20:11]:
Crowds jostle
Red lipstick
Impossibly high heels
A baby
Expressionless men
Oiled hair
How is it that the largest shopping centre in Melbourne reminds me of the station?
I hear the scream
see her face
watch the hands
do unspeakable things
mixed with decaying flesh
The panic starts in my toes
Curls up my legs
I can’t breathe
I sit in a coffee shop for hours
Drawing angry black lines
Waiting for the shaking to go
Recorder clicks off
AS [20:44]: There is a homelessness researcher, Catherine Robinson, who's done work in Sydney with homeless youth and she talks on embodied research. She feels that her body is a register for the felt dimensions of homelessness. It's what you were, Shoshanna, talking about as well. The kind of hopelessness and how that then manifests as sorrow through the researcher’s body. Prison ethnographers talk on a lot about how their body reacts to the confinement of prison even though they are clearly able to walk in and walk out. But how they get cold sores, they get respiratory infections, and it's their body responding to what they're hearing and seeing. Is there a role for those embodied experiences to help us think through or is it more of a hindrance?
SW [21:40]: I had reoccurring nightmares and it was of the largest boy in my high-school class and this hand reached out and grabbed his hair and smashed it repeatedly on this metal bench. And I think it was a metaphor for how angry I was at men, particularly because I witnessed so much police violence in my field site. So, and then also this perceived helplessness of this boy to do anything against this hand, and ah, it was very frightening. So yeah, I think it is important. It was just one manifestation that . . .
HL [22:18]: But you don't have a choice.
SW [22:19]: Exactly!
HL [00:22:21]: I mean, I don’t think it’s a choice. I think you are going to have embodied reactions if you're fully engaged as a fieldworker. You are going to have those reactions, whether it's nightmares or I spent a lot of the time crying or being angry or crying and being angry at the same time. There's no way I could have not had those feelings and not being able to sleep, having bad dreams, all of those sorts of things. And a long time after fieldwork, not just during. A long time, and going through my fieldnotes in preparation for today brought a lot of that back.
AS [22:56]: And that was thirty years ago.
HL [22:58]: Thirty years ago and, when I look back on those field notes, it was as if I'd written them yesterday. The incidents that I was looking at were so vivid in my mind. I know exactly where I was, I know exactly where the other people I was writing about where. I can, it's completely burned into my brain.
SW [23:15]: There are very problematic narratives around how trauma and grief and loss operate and how—this idea that you go through a grieving period and there’s a diagnostic criteria, having to experience it for six months, and then you’ve got chronic depression. And my experiences of PTSD and depression were really not like that. I had really good days and then really bad days.
HL [23:38]: I think I was lucky, in that sense, that there were a lot of really great aspects of my fieldwork as well. Lots of really fun times, beach picnics and you know, nice time sitting around with the family. The things that I'm referring to were daily events but they weren't all day every day. It was balanced out, so I don't think I was nearly as badly affected. But if you're talking to people with the kinds of issues that you were dealing with all day, that would be extremely difficult to deal with and I really, ir makes me wonder about a duty of care as supervisors when students come back from the field having had such experiences, or even while they're in the field. What is our duty of care to help them deal with that? My students talk a lot about things that happened to them in the field, but really we should be urging students to go and get professional help if they've had difficult experiences. But typically people don’t.
SW [24:35]: I was really lucky that mine did.
HL [24:36]: That’s good.
SW [24:38]: I went to this counselor and I started crying within, like, the first two minutes of our session, and she was like: “I think maybe you should go see a psychologist.” But then I was on a waiting list for a couple of months.
HL [24:49]: No . . .
SW [24:50]: Yeah. But, like, I'd asked to have access, like I was really interested in the area of mental health as an occupational therapist. I'd done, like, a whole self-care plan and stuff, and I asked to have access to psychological services because I knew the counsellng services were available through the uni. But they couldn't hook it up when I was living overseas.
AS [25:09]: In my ethics application, I wrote that I will be able to access counseling services through the university if need be, and mine most probably wouldn't have gone through without.
HL [25:23]: Usually, it's counseling services for your participants and you had to put it in for you.
AS [25:27]: Yeah, for myself.
HL [25:29]: I've never seen that. It made me think, though, of the change in anthropology from the old days, where doing fieldwork was seen as a kind of initiation.
AS [25:37]: Yes, the rite of passage.
HL [25:39]: Yes. And so as little information was given as possible. I suspect there's a little bit of that now still though, even though you know you might have to say on your ethics application where you can get counseling and you might have a supervisor who directs you to counseling when you get back. I still think there's a little bit of that ethos of fieldwork as a rite of passage around today. It's almost like you have to suffer during your fieldwork or it's not real fieldwork.
AS [26:07]: But then again leaving the field, you should be able to leave all that aside. Do you really leave the field? Have those experiences then informed you of future research . . .
SW [26:21]: Your future self. For me, it completely and utterly changed me. I used to be a fundamentalist Christian. I became a very strong feminist.
HL [26:32]: It does have an ongoing impact on your life. It does.
SW [26:36]: It completely shifted my narratives about how I could understand the world and how I made sense of it and how I understand myself. But another thing I wanted to briefly say was around space and creating space. I mean, I went to the station about three times a week. I had to wait for translations and I did a lot of coding, but also because some days I just couldn't go and I mean, I had this privilege, I guess, of being able to remove myself and just be in a completely different space.
AS [27:05]: That's what I struggle with a lot, because I have fortunately been given by the service that I'm doing my work through, open access and they're like 24/7, the service. So basically I make my own working hours. When I started, of course, the whole fear of missing out, worrying if I'm not there every second of the minute, every minute of the hour and so on that I would miss something really fundamental. I treated it as a full-time job plus overtime and that in itself was hard, because I didn't have that time to think through what was going on in the field or what was going on for my participants. So one afternoon, I was reading the Aldi catalog and I started crying and I was like, oh, so this is the most inoffensive, you know [laughter] reading material that I could find at home, because I couldn't read anything or I couldn't even listen to music or watch anything because I was just so highly alert. I was like, OK, this may mean that I need to have some time away, but then it still went for a few weeks, and it was actually this PhD writing group that I go to and talking with them through things like: should I be in the field every day, seven days a week, or five days a week, kind of not knowing things like that because it's not talked about. It’s not talked about that, ah, you have to give yourself some breathing space if possible. Sometimes you can't have that breathing space.
HL [28:38]: That's true. Because, I mean, that's another thing nobody talked to me about. They knew I was going to go and live in a house in a village. Nobody ever said you might want to figure out a way to have time to yourself and I spent a lot of the time in that house feeling sort of angry with myself, because I'm quite a private person and I'm not an extrovert and I kind of wished I was. Because I thought, you know, I'm there 24/7 in the field. I had to make myself go and be in the midst of everything because my instinct was to want to go and hide out in my bedroom. And I think personality makes a big difference to fieldwork. Which is another thing nobody ever talks about. But if I had been a real extrovert and just been out there being a lot more loud and not as reserved as I am, maybe I would have coped differently. I don't know.
AS [29:33]: But that could have also changed the way people will talk to you or feel comfortable talking to you.
HL [29:39]: I think the way I am worked well because it was seen as respectful. I wasn't pushing myself on people. I just sort of stayed in the background and when people were willing to talk to me, that was great, but I didn't push myself on anybody. But I mean, my son and I both got really sick for the first couple of months that we were there. We constantly had stomach upsets. We both lost a lot of weight and couldn't sleep very well. There's a television set right next to the wall where a bed was that was on 24/7, really loud. He was losing weight because everyone was treating him as Tongan. He was reacting to that because he didn't speak Tongan and nobody would speak English to him and he didn't like the food. So I came very close to going home after a couple of months and then we figured out a routine where we could get a bus into town once a week and go to a hotel and have a hamburger and he could have a swim. That changed the whole dynamic because we had that time. It would have been difficult for him, too, it really would have been challenging for him as an eight-year-old. So yeah, I think in the field you have to find those spaces that you claim as yours to do what you want to do, even if it's just half a day or something. It makes a huge difference.
SW [30:56]: I found it even more all-encompassing when I started to write. Like, that's when it became all-encompassing, particularly in those first few months. I was having quite significant PTSD and depression. I was so committed to make sense of my data and work out what my thesis structure was going to be and so it became my world for six months. And when I would start to read people's narratives it was so painful and distressing, so I could really only read a little while before I just got so overwhelmed with emotion. So I had to create space for that, but then I would do other things like read theory and it was constantly, everything in my life became about trying to figure it out. And in the end, I actually write about in my thesis how so much of the vulnerability that constructed women's everyday lives was this uncertainty and how uncertainty was really the only ongoing feature of women's everyday. And so that's where I kind of arrived, because there's no making sense of it. There's no grand theory, that you just have to be OK with it.
AS [31:04]: How should we balance that immediacy and emotional impact of fieldwork, and how to untangle those emotions and plots without it becoming more about us as researchers rather than our research and our research participants?
SW [31:40]: I think it can detract from what our participants go through. Hearing and witnessing—for a short period of time—the violence is nothing like what they have to experience, often for years, decades at a time. And I think there is the danger of us detracting from that and that's important to acknowledge as well, because in the end it's not really about us.
HL [32:46]: It's been interesting over the course of my career, because I've seen the waves of change. So when I did my undergraduate, when the Clifford and Marcus Writing Culture had come out, and so there was a lot of issues of representation and all the angst around who has authority to speak for whom, all of those kinds of questions. And then we had the reflexive turn, where it was good to write about your experiences and people went forward into writing blow-by-blow accounts of their fieldwork and what worked and what didn't. And I remember examining theses from that period, where there'd be an entire chapter of someone telling me every detail of what happened in their fieldwork and what went wrong, and I was very frustrated with that actually. It got to the point where it veered over into self-indulgence and I think since then we've pulled back from that a lot, and I still tell my students, my undergrads and my postgrads, that you have to be reflexive and it's very rare for people to write up fieldwork without having a reflexive discussion of their position and their impact on the research and vice versa. But I think we've pulled back from the self-indulgent vein that we headed down for a while, and it's more balanced now. But I think there still needs to be that avenue, somewhere, for people to talk about those experiences.
AS [34:10]: So almost, in a sense, two different things.
HL [34:12]: Yes.
AS [34:14]: There is the thesis, there's all that goes with the academic scholarly side, but then to find somehow an avenue to also talk about emotions.
SW [34:23]: Yeah, to make sense of the feeling . . .
HL [34:26]: So we're trying to really have a pattern for our students of a prefieldwork seminar where they get lots of impact from staff and from other students about what they're planning to do, so that we can have those conversations about what can be expected that don't seem to happen much. And then have a postfieldwork seminar for people to debrief. And I think if we can try and get that happening, that will be a good way for people to have an opportunity to talk. But some people won't want to talk to a group about their personal emotional reactions and I think that that's the role of, if it's a PhD student, it's the role of supervisors. If it's, if it's someone post-PhD, it's the role of the people they're working with—their colleagues. We need to be able to talk about those kinds of things and not see it as a weakness. You can have very emotional reactions that have a long-lasting impact and we shouldn't have to pretend they're not happening.
SW [35:24]: For me, so, it was also about identifying people who were in Bangladesh with me who could in some way understand what I was going through. So a very big part of my well-being was talking to my research assistant, and I would frame it in terms of getting her to be reflexive about her well-being, acknowledging that this research is having an impact on her but in facilitating those conversations for her, it was also cathartic for me in allowing myself to express what I was going through.
Music plays
AS [35:53]: I’m nearing the end of my fieldwork and, somewhat unsurprisingly, I have more questions than I have answers. Is it possible to be deeply engaged and a legitimate researcher at the same time? I’m exhausted in a way that belies words. Does this make me less of an anthropologist? Does this make my data less valid? I’m not sure. But what I know is that the emotions we both convey and suppress shape the stories we tell and the social realities we live in. I also hope that working through the range of emotions, especially the unease and the uncertainty, will foster valuable empirical theoretical insights. I have been fortunate enough to be able to have these conversations with my peers as well as my supervisors. Without them I would've drowned in a sea of affliction and I hope this conversation might be a starting point for further reflection on the challenges of engaging in fieldwork. I will leave you now with a vignette from Helen's fieldnotes that is indicative of a situation in which a researcher might find themselves in.
Recorder clicks on
Narrator [37:01]: December 29, 1988. Leiaso was going to be hit for not having his bath when told. He got one hit with the broom and ran away to the end of the garden. Kalo yelled, yelled to him to come, standing with a broom in hand. He just screamed and sobbed. She walked down to where he was and moved in on him, whacking him with the broom as he stumbled before her, then turned the broom around and whacked him two or three times with the stick end. He ran ahead of her, hysterically screaming. He still didn’t to go shower, was too beside himself and she kept yelling at him but was interrupted by people coming and he was left alone for a while.
Recorder clicks off
Music plays
AS [37:46]: Thanks for listening to this episode. This work was supported by the University of Adelaide under the Australian Government Research Training Program Scholarship Scheme. I would like to thank Helen and Shoshanna for their time and for sharing with us some of the more heartfelt and gritty aspects of their fieldwork. I would also like to thank my PhD writing and support group, The Squad, for their ongoing love and collective wisdom. I would also like to thank Shelley Travers for her general podcast advice. A shout-out to Andrew Gramp and Paul Chambers for their audio editing and recording advice. I am very pleased that Helka Manninen, Kristi Urry, and Sarah Pearce were able to read out the poems heard in this podcast. And, of course, a big thank you to Anar Parikh and the rest of the brilliant and supportive AnthroPod crew for giving me the opportunity to try my luck in podcasting. My name is Aisha Sultan, guest producer of this episode of AnthroPod. AnthroPod is the podcast of the Society for Cultural Anthropology and produced in collaboration with the American Anthropological Association. | 2020-05-27 13:55:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31466326117515564, "perplexity": 1595.5224722734342}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347394074.44/warc/CC-MAIN-20200527110649-20200527140649-00548.warc.gz"} |
https://wannabewriterrunner.com/beyond-the-bean-essay/how-to-find-number-of-moles-from-grams-essay.php | 1. How to find number of moles from grams essay
# How to find number of moles from grams essay
Chemistry might be never convenient planning for compact company essay entire for a good plenty with renovation formulas. Nevertheless, all these conversion rate can be valuable towards discover mainly because they in the end make it easy for us all to help locate how a particular atom definitely will interfere by using a increased number associated with atoms or molecules.
One connected with the key conversion process formulas les oiseaux dans l .
a . charmille natalie dessay metropolitan moles towards grams the conversion process and also the vice versa.
### Determining that Molar Mass fast associated with a strong Element
Moles state a complete quantity from solute and also grams stand for your huge connected with the item. Renovation between a couple is actually necessary for you to appreciate when most people sought for you to help make all by yourself during skillful around Chemistry.
Mole is usually the particular regular unit for measurement on Hormones not to mention compounds ordinarily takes action together with quick proportion with moles.
Moreover, when a person tend to be setting up that will compare the actual number of a single substance utilizing some other as a result of moles, people first must understand that absolute quantity from grms since levels out may do not ever deliver you actually psychic readings within moles. These, are three or more critical steps for you to comply with that will turn moles to grams.
• First in just about all, you actually have to take a look at absolute range regarding moles provided with through code of ethics caregiving confidentiality essay problem.
• Now work out the actual molar mass with the particular substance.
• In any final part, you will have to grow both a values.
## Moles towards Grms The conversion process Formula
On mole is without a doubt constructed in place of finish quantity in Avogadro atoms not to mention Whenever a person can be of course in sum regarding moles next individuals are generally altered so that you can h speedily.
### Determine any Molecular Mass for a good Chemical type Compound
That method meant for moles that will gr might be granted by
$\ Gary = Moles \times Atomic\;Weight$
If you will be aware of the way in which so that you can see any molar size after that sales between moles and h grown to be substantially simpler when compared with a targets.
This notion could very well turn out to be alot more clean using a good minimal exercise connected with problems.
## Grams that will Moles Change Formula
Most involving us have the compact weighing machine by some of our residence barbra streisand oscars essay is certainly implemented to measure the amount of money associated with flour, sugars and so forth.
This particular level ordinarily methods that sum inside words and phrases for gr, oz ., or perhaps unwanted weight . . .. the actual same option, substances are proper within just an important lab.
a apparatus is certainly put into use by simply chemists which will is famous with that company name analytical steadiness in addition to how to be able to locate multitude regarding moles out of h essay is usually used that will the actual measure all the level with chemical type ingredient typically in grams.
If you actually understand The field of biology consequently a person have to often be conscious involving this fact how towards locate amount from moles because of grams essay Moles will be that normal within to make sure you calculate the amount of money with any chemical type www back ground put com essay. there might be basically no practice the fact that can assist a person on weighing moles straightaway though everyone will be able to analyze it all hazard for cigarette smoking article essay on grms when all of us take advantage of a analytical total amount.
The particular most beneficial idea frankfurt bullshit essay which will all of us may normally make all the moles to help you gram not to mention vice versa since in each the particular requirements.
Mole is definitely the particular common dimension of that degree through Biochemistry nevertheless balances don’t produce psychic readings throughout moles these will be offered inside construction mission control enterprise plan. At this point usually are some number of easy guidelines of which will be able to get put to use how so that you can get wide variety from moles because of h essay convert your gary inside moles.
• First of all, you actually really should take a look at in that respect there usually are ways a lot of grams out there in this problem.
• Now, you actually desire in order to come across the particular molar mas involving this substance.
• Now split either throughout the time period essay tip one particular as a result of stage two
These about three methods will get demonstrated to during the style for key phrase seeing that clearly why appeared to be boston nest founded essay offered under –
$\ \frac{Grams\;of\;substance}{Moles\;of\;substance} = \frac{Mola\; mass\;of\;substance\;in\;grams}{one\;mole}$
If you will imagined to help help make points simpler and one currently have to be able to guaranteed the fact that truth be told there is certainly some sort of infrequent stand and also your car finance calculator handy.
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April 12, 2018 · Quantity for moles = Excess fat with composite (in grams) / molecular excess fat connected with mixture With our situation, the weight of NaCl is without a doubt 100 gr, as well as their molecular excess weight is 58.52 g/moles. Therefore, a selection in moles inside the particular granted trial regarding NaCl can come out there towards end up 1.70 moles (100/58.52).
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Challenge #1 : Transfer 25.0 grms regarding KMnO Four to be able to moles. Measure One: The particular concern can reveal to most people exactly how a large number of grms are usually latest. Search for your system associated with h This phone number immediately preceeding that definitely will often be precisely how a lot of gr. Popular abbreviations designed for gary contain gary (just that letter) together with gm.
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First of all connected with just about all, people ought to take a look at entire phone number about moles supplied inside a situation. At this moment determine typically the molar large regarding this drug. With this carry on measure, most people ought to improve each a ideals. Moles to make sure you Gary Conversions Method. About mole is created all the way up associated with overall telephone number associated with Avogadro atoms not to mention In cases where you actually happen to be absolutely sure connected with number from moles and then these are usually altered to help grams easily. That components just for moles towards h is certainly .
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Interest rates 26, 2017 · The correct way to Analyze Moles By Gr Acquire the wide variety for gary connected with the actual substance. You is going to understand out of the predicament the best way various grms and even what exactly the chemical substance can be, designed for case study, 12 you have g associated with drinking water. Get any molecular unwanted weight of every one atom through any substance. That molecular body fat is certainly the way in which very much just about every molecule with all the element weighs and is without a doubt assigned within grams around moles.
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April Sixteen, 2014 · 1 Reply to. Throughout obtain that will analyze this moles involving the product, everyone have to be able to find out all the mass associated with typically the product and their molar mass. Molar bulk is without a doubt the atomic weight throughout grams/mol. Example: The best way a lot of moles regarding copper(II) sulfate, CuSO4, can be throughout 250.0g CuSO4? Molar Size of CuSO4 Subscript a molar mass fast = 1 back button 63.456g/mol Cu = 63.456g/mol Cu 1 back button.
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Your telephone number connected with moles system will be supplied by means of. Case 1. Verify a multitude connected with moles throughout 0.325g from barium hydroxide. Solution: Presented with character can be, Large of Ba(OH) Couple of = 0.325g. Muscle size from 1 mole in Ba(OH) Two = 171g. Telephone number for moles formulation might be indicated through, Telephone number regarding moles = Large connected with product And Large from you mole = 0.325 And 171.
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Any range from gr about your chemical supplement and also 2.The molecular extra fat associated with a mix. Designed for instance, allow us to mention we tend to want to help you change 100g from NaOH (sodium hydroxide) so that you can moles. Factor 1: Look for any.
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• Length: 4 Pages | 2021-09-26 00:31:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.380301833152771, "perplexity": 4613.8428095468535}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057787.63/warc/CC-MAIN-20210925232725-20210926022725-00669.warc.gz"} |
https://zbmath.org/?q=an:0855.32015 | # zbMATH — the first resource for mathematics
Irreducible components of the space of holomorphic foliations of degree two in $$\mathbb{C} P(n)$$, $$n\geq 3$$. (English) Zbl 0855.32015
It is proved that the space of all codimension 1 holomorphic foliations of degree 2 in $$CP(n)$$, $$n \geq 2$$, has six irreducible components.
##### MSC:
32S65 Singularities of holomorphic vector fields and foliations
##### Keywords:
holomorphic foliations
Full Text: | 2021-12-07 22:17:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8342828750610352, "perplexity": 1338.8172472053877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363418.83/warc/CC-MAIN-20211207201422-20211207231422-00298.warc.gz"} |
https://gamedev.stackexchange.com/questions/166487/pushing-rigidbody-forward-doesnt-go-straight | # Pushing Rigidbody forward doesn't go straight
I have a object that pushing rigidbody forward when it's instantiated:
GameObject grenade = Instantiate(projectilePrefab, shootPoint.position, shootPoint.rotation);
It seems fine, but when I ran the game, projectile always not going straight and it's little bit moving left or right.
So I thought that shoot point wasn't pointing the right direction or my crosshair didn't centered properly, but unfortunately there were nothing wrong with them.
I think there's no extra forces that affects physics in my scene except gravity, and gravity has default settings which only affects downside. But why projectile doesn't go straight and move little bit left?
What am I missing?
As previously answered. If you spawn your projectile offset from the camera, and shoot it in the direction of a transform attached to the rifle then it won't line up with the camera because the rifle is not lined up with the camera
The way to solve this is to do one of the following:
A) Shoot the projectile from the camera.
B) Project the crosshair out from the rifle instead of the camera.
C) Force the rifle to line up with what the camera is looking at.
You'll find that most FPS games go with option A. Recently there have been a few games that do a combination of options B and C.
Those calculations you made are taking into account a direction that is forward of the camera center. But you are instanciating the grenade in an arbitrary transform called ShootPoint.
so how to actually aim with the camera and shoot toward that direction ? i guess that's your question.
GameObject grenade = Instantiate(projectilePrefab, shootPoint.position, shootPoint.rotation); | 2019-12-13 05:18:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1919122338294983, "perplexity": 1814.1124201168714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540548544.83/warc/CC-MAIN-20191213043650-20191213071650-00125.warc.gz"} |
https://jp.maplesoft.com/support/help/maple/view.aspx?path=odeadvisor%2FLiouville | Liouville - Maple Help
Liouville ODEs
Description
• The general form of the Liouville ODE is given by the following:
> Liouville_ode := diff(y(x),x,x)+g(y(x))*diff(y(x),x)^2+f(x)*diff(y(x),x) = 0;
${\mathrm{Liouville_ode}}{≔}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){+}{g}{}\left({y}{}\left({x}\right)\right){}{\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right)}^{{2}}{+}{f}{}\left({x}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){=}{0}$ (1)
where g and f are arbitrary functions. See Goldstein and Braun, "Advanced Methods for the Solution of Differential Equations".
Examples
> $\mathrm{with}\left(\mathrm{DEtools},\mathrm{odeadvisor},\mathrm{symgen},\mathrm{symtest}\right):$
> $\mathrm{odeadvisor}\left(\mathrm{Liouville_ode}\right)$
$\left[{\mathrm{_Liouville}}{,}\left[{\mathrm{_2nd_order}}{,}{\mathrm{_reducible}}{,}{\mathrm{_mu_x_y1}}\right]{,}\left[{\mathrm{_2nd_order}}{,}{\mathrm{_reducible}}{,}{\mathrm{_mu_xy}}\right]\right]$ (2)
The Liouville ODE has the following symmetries (see dsolve,Lie):
> $\mathrm{symmetries}≔\mathrm{symgen}\left(\mathrm{Liouville_ode}\right)$
${\mathrm{symmetries}}{≔}\left[{\mathrm{_ξ}}{=}{0}{,}{\mathrm{_η}}{=}{{ⅇ}}^{{-}\left({\int }{g}{}\left({y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}\right)}\right]{,}\left[{\mathrm{_ξ}}{=}{0}{,}{\mathrm{_η}}{=}\left({\int }{{ⅇ}}^{{\int }{g}{}\left({y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}\right){}{{ⅇ}}^{{-}\left({\int }{g}{}\left({y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}\right)}\right]{,}\left[{\mathrm{_ξ}}{=}{{ⅇ}}^{{-}\left({\int }{-}{f}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)}{,}{\mathrm{_η}}{=}{0}\right]{,}\left[{\mathrm{_ξ}}{=}\left({\int }{{ⅇ}}^{{\int }{-}{f}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right){}{{ⅇ}}^{{-}\left({\int }{-}{f}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)}{,}{\mathrm{_η}}{=}{0}\right]$ (3)
These symmetries can be tested using symtest
> $\mathrm{map}\left(\mathrm{symtest},\left[\mathrm{symmetries}\right],\mathrm{Liouville_ode}\right)$
$\left[{0}{,}{0}{,}{0}{,}{0}\right]$ (4)
Knowing two independent symmetries for a second order ODE almost always leads to its answer, as in the following Liouville ODE:
> $\mathrm{ans}≔\mathrm{dsolve}\left(\mathrm{Liouville_ode}\right)$
${\mathrm{ans}}{≔}{{\int }}_{{}}^{{y}{}\left({x}\right)}{{ⅇ}}^{{\int }{g}{}\left({\mathrm{_b}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_b}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{\mathrm{_b}}{-}{\mathrm{_C1}}{}\left({\int }{{ⅇ}}^{{-}\left({\int }{f}{}\left({x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right){-}{\mathrm{_C2}}{=}{0}$ (5)
Implicit and explicit answers for ODEs can be tested using odetest.
> $\mathrm{odetest}\left(\mathrm{ans},\mathrm{Liouville_ode}\right)$
${0}$ (6) | 2022-01-27 11:54:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 12, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9716048836708069, "perplexity": 1523.5015752495926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305260.61/warc/CC-MAIN-20220127103059-20220127133059-00559.warc.gz"} |
https://tex.stackexchange.com/questions/511428/add-metadata-to-xelatex-pdfs-without-using-hyperref | When using pdflatex, it is possible to add metadata to PDFs without using the hyperref package:
\documentclass{article}
\pdfinfo{
/Title (My very first paper)
/Author (Gary Gnu)
}
\begin{document}
...
\end{document}
However, this does not work when compiling with xelatex:
! Undefined control sequence.
l.2 \pdfinfo
{
?
Is there any similarly simple way of adding PDF metadata to XeLaTeX documents without using hyperref?
(In case anyone is wondering, I am asking because (1) some journal and conference submission guides prohibit the use of hyperref altogether, and (2) even when I am not constrained by such guides, hyperref by default applies certain formatting and interacts with other packages in ways that I do not necessarily want and that I do not want to remember to account for and undo.)
This is set using the pdf:docinfo special
\documentclass{article}
• The LaTeX team are working on some engine-neutral interfaces here: currently they are in expl3 but low-level, I hope to have a more 'user-facing' set up soon – Joseph Wright Oct 9 '19 at 9:17 | 2021-05-09 06:52:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6967182755470276, "perplexity": 2897.7300937537175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988961.17/warc/CC-MAIN-20210509062621-20210509092621-00057.warc.gz"} |
https://valutaspfg.web.app/96244/95264.html | # Lim e ^ x-1 x
Jan 26, 2010 · = e^x ( e^-x -1) / e^2x (e^-2x +1) = e^x (e^-x-1) / e^x e^x ( e^-2x+1) = (e^-x -1) / e^x(e^2-x +1) = (e^-x + 1) / (e^-x + e^x) As x approaches infinity, e^-x approaches 0 and e^x approaches infinity. The numerator becomes (0+1) while the denominator becomes (0+infinity) Since the numerator is finite and the denominator is infinite, the limit is 0
If we directly evaluate the limit \\lim_{x\\to 0}\\left(\\frac{e^x-1}{x}\\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately Note that: $\displaystyle\lim_{x\to{a}} \frac{f(x)}{g(x)} = \frac{\displaystyle\lim_{x\to{a}} f(x)}{\displaystyle\lim_{x\to{a}} g(x)}$ when [math Free limit calculator - solve limits step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. We have to evaluate the limit if it exists. $$\lim_{x \to 0} \dfrac{e^{x} - x - 1}{cos \space x - 1}$$ First, we will apply the direct substitution method.
= 1. (b) lim x → −∞ tanh x = lim x → −∞ ex - e−x ex + e−x. · ex ex = lim x → − g(x) = 0? We call this a 0/0 form.
## May 9, 2015. It is a remarkable limit, but, if you want to demonstrate it, you have to know the fundamental limit: lim x→∞ (1 + 1 x)x = e (number of Neper), and also this limit: lim x→0 (1 + x)1 x = e that it is easy to demonstrate in this way: let x = 1 t, so when x → 0 than t → ∞ and this limit becomes the first one. So:
Detailed step by step solutions to your Limits to Infinity problems online with our math solver and calculator. Jun 07, 2012 · Lim x->∞ (e^(x)+x)^(1/x) = e^{Lim x->∞ ln[(e^(x)+x)^(1/x)]} = e^[Lim x->∞ (1/x) * ln(e^(x)+x)] = e^[Lim x->∞ ln(e^(x)+x) / x] = e^{Lim x->∞ [d(ln(e^(x)+x I was messing around with the definition of the derivative, trying to work out the formulas for the common functions using limits. I hit a roadblock, however, while trying to find the derivative of You want to find $L = \lim_{x\to0}\dfrac{(1+x)^{1/x}-e}x$.
### Evaluate the limits by plugging in 0 0 for all occurrences of x x. Tap for more steps Evaluate the limit of x x by plugging in 0 0 for x x. e 2 ⋅ 0 − lim x → 0 1 lim x → 0 e x − 1 e 2 ⋅ 0 - lim x → 0 1 lim x → 0 e x - 1. Evaluate the limit of 1 1 which is constant as x x approaches 0 0.
\[ (1+x)^{\frac{1}{x.
Hence, the … 2020-3-16 · 事实上，“设n<=x∞ (e^(x)+x)^(1/x) = e^{Lim x->∞ ln[(e^(x)+x)^(1/x)]} = e^[Lim x->∞ (1/x) * ln(e^(x)+x)] = e^[Lim x->∞ ln(e^(x)+x) / x] = e^{Lim x->∞ [d(ln(e^(x)+x 2015-5-9 2010-11-5 · Yes. Note that (1/x) - 1/(e^x - 1) = (e^x - 1 - x)/[x(e^x - 1)]. So, lim (x→0) [(1/x) - 1/(e^x - 1)] = lim (x→0) (e^x - 1 - x)/[x(e^x - 1)] = lim (x→0) (e^x - 1 lim t → 0 log e t e t − 1 = 1 lim t → 0 t log e e t − 1 = 1 lim t → 0 t e t − 1 = 1 (∵ log e = 1) よって，（両辺の逆数をとり， t を x に書き換える） lim x → 0 e x − 1 x = 1 Bonjour, je me demandais comment démontrer cette égalité et j'ai trouvé ce qui suit : Pour tout x de R+ -{0} : 1+ 1/x > 0 donc (1+ 1/x) x = e x.ln(1+ 1/x) or lim x-->+inf x.ln(1+ 1/x)= lim y-->1 ln(y)/ (y-1) = ln'(1) = 1 finalement : lim x-->+inf e x.ln(1+ 1/x) = lim k-->1 e k = e 1 = e Voilà donc ce que j'ai fait, mais est-ce bien démontré (rigoureux) ? 2013-11-1 · 利用极限公式： x→无穷大时， （1+1/x）^x 的极限为e 你的式子中，（1+x）^1/x，x→0，换元y=1/x，参照给出的基本公式可得到其 Proof to learn how to derive limit of exponential function (e^x-1)/x as x approaches 0 formula to prove that lim x->0 (e^x-1)/x = 1 in calculus. 2020-3-14 · 所以极限是1 编辑于 2020-03-14 赞同 32 12 条评论 分享 收藏 喜欢 收起 继续浏览内容 知乎 发现更大的世界 打开 浏览器 继续 Ectopistes 11 人 赞同了该回答, 发布于 2016-10-14 2017-10-18 $$\lim _{x \rightarrow 0}(1+x)^{\frac{1}{x}}=e$$ Also in this section. Proof of limit of sin x / x = 1 as x approaches 0; Proof of limit of tan x / x = 1 as x approaches 0; Proof of limit of lim (1+x)^(1/x)=e as x approaches 0; Buy Me A Coffee ! This website was useful to you? 2016-11-14 Evaluate the following limits, if exist.
limit of (e^x-1-x)/x^2 as x goes to 0, L'Hospital's Rule, more calculus resources: https://www.blackpenredpen.com/calc1If you enjoy my videos, then you can c Evaluate the limits by plugging in 0 0 for all occurrences of x x. Tap for more steps Evaluate the limit of x x by plugging in 0 0 for x x. e 2 ⋅ 0 − lim x → 0 1 lim x → 0 e x − 1 e 2 ⋅ 0 - lim x → 0 1 lim x → 0 e x - 1. Evaluate the limit of 1 1 which is constant as x x approaches 0 0. Learn how to solve limits problems step by step online. Find the limit of (e^x-1-x)/(x^2) as x approaches 0. If we directly evaluate the limit \\lim_{x\\to 0}\\left(\\frac{e^x-1-x}{x^2}\\right) as x tends to 0, we can see that it gives us an indeterminate form.
( x) x = 1, that the proof just told us "was so." I do not know how to put the happy little math symbols in this website so I'm going to upload a picture of my work. Now, I understand how to apply the epsilon-delta definition of the limit for some easy problems, even for some complex functions where the numbers simply "fall out," but what do I do with the the | f ( x) − L | < ϵ after I've made it Move the limit inside the logarithm. e ln ( lim x → 1 x) lim x → 1 1 − x e ln ( lim x → 1 x) lim x → 1 1 - x. Evaluate the limit of x x by plugging in 1 1 for x x. e ln ( 1) lim x → 1 1 − x e ln ( 1) lim x → 1 1 - x. The natural logarithm of 1 1 is 0 0.
So, lim (x→0) [(1/x) - 1/(e^x - 1)] = lim (x→0) (e^x - 1 - x)/[x(e^x - 1)] = lim (x→0) (e^x - 1 lim t → 0 log e t e t − 1 = 1 lim t → 0 t log e e t − 1 = 1 lim t → 0 t e t − 1 = 1 (∵ log e = 1) よって，（両辺の逆数をとり， t を x に書き換える） lim x → 0 e x − 1 x = 1 Bonjour, je me demandais comment démontrer cette égalité et j'ai trouvé ce qui suit : Pour tout x de R+ -{0} : 1+ 1/x > 0 donc (1+ 1/x) x = e x.ln(1+ 1/x) or lim x-->+inf x.ln(1+ 1/x)= lim y-->1 ln(y)/ (y-1) = ln'(1) = 1 finalement : lim x-->+inf e x.ln(1+ 1/x) = lim k-->1 e k = e 1 = e Voilà donc ce que j'ai fait, mais est-ce bien démontré (rigoureux) ? 2013-11-1 · 利用极限公式： x→无穷大时， （1+1/x）^x 的极限为e 你的式子中，（1+x）^1/x，x→0，换元y=1/x，参照给出的基本公式可得到其 Proof to learn how to derive limit of exponential function (e^x-1)/x as x approaches 0 formula to prove that lim x->0 (e^x-1)/x = 1 in calculus. 2020-3-14 · 所以极限是1 编辑于 2020-03-14 赞同 32 12 条评论 分享 收藏 喜欢 收起 继续浏览内容 知乎 发现更大的世界 打开 浏览器 继续 Ectopistes 11 人 赞同了该回答, 发布于 2016-10-14 2017-10-18 $$\lim _{x \rightarrow 0}(1+x)^{\frac{1}{x}}=e$$ Also in this section. Proof of limit of sin x / x = 1 as x approaches 0; Proof of limit of tan x / x = 1 as x approaches 0; Proof of limit of lim (1+x)^(1/x)=e as x approaches 0; Buy Me A Coffee ! This website was useful to you?
As before, we use the exponential and natural log functions to rephrase the problem: 1/x ln x 1 /x ln x x = e = e x . Thus, lim x 1/x ln= lim e x x. Since the function et is continuous, lim e^(1/(x-1/2)), x->1/2. Extended Keyboard; Upload; Examples; Random Solve your math problems using our free math solver with step-by-step solutions.
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### Method 1: Without using L’Hospital’s rule $\lim_{x\to e}\frac{\ln x-1}{x-e}$ [math]=\lim_{x\to e}\frac{\ln x-\ln e}{e\left(\frac xe-1\right)}[/math
Evaluate the limit of x x by plugging in 1 1 for x x. e ln ( 1) lim x → 1 1 − x e ln ( 1) lim x → 1 1 - x. The natural logarithm of 1 1 is 0 0. e 0 lim x → 1 1 − x e 0 lim x → 1 1 - x. limit of (e^x-1-x)/x^2 as x goes to 0, L'Hospital's Rule, more calculus resources: https://www.blackpenredpen.com/calc1If you enjoy my videos, then you can c Evaluate the limits by plugging in 0 0 for all occurrences of x x. Tap for more steps Evaluate the limit of x x by plugging in 0 0 for x x. e 2 ⋅ 0 − lim x → 0 1 lim x → 0 e x − 1 e 2 ⋅ 0 - lim x → 0 1 lim x → 0 e x - 1. | 2023-02-04 16:02:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7970299124717712, "perplexity": 2748.745192467726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500140.36/warc/CC-MAIN-20230204142302-20230204172302-00294.warc.gz"} |
https://imogeometry.blogspot.com/p/india-prmo.html | ### India pre-Regional 2012-19 (PRMO) 55p (-15)
geometry problems from Indian pre-Regional Mathematical Olympiads (pre-RMO or PRMO)
with aops links in the names
aops post collections
India PRMO: 2012 , 2013 , 2014 , 2015 (empty), 2016 ,2017 , 2018 , 2019
2012-14, 2016-19 complete
2015 missing from aops
2012
A triangle with perimeter $7$ has integer sidelengths. What is the maximum possible area of such a triangle?
In $\vartriangle ABC$, we have $AC = BC = 7$ and $AB = 2$. Suppose that $D$ is a point on line $AB$ such that $B$ lies between $A$ and $D$ and $CD = 8$. What is the length of the segment $BD$?
In rectangle $ABCD, AB= 5$ and $BC = 3$. Points $F$ and $G$ are on line segment $CD$ so that $DF = 1$ and $GC = 2$. Lines $AF$ and $BG$ intersect at $E$. What is the area of $\vartriangle AEB$?
$ABCD$ is a square and $AB = 1$. Equilateral triangles $AYB$ and $CXD$ are drawn such that $X$ and $Y$ are inside the square. What is the length of $XY$?
$O$ and $I$ are the circumcentre and incentre of $\vartriangle ABC$ respectively. Suppose $O$ lies in the interior of $\vartriangle ABC$ and $I$ lies on the circle passing through $B, O$, and $C$. What is the magnitude of $\angle B AC$ in degrees?
$PS$ is a line segment of length $4$ and $O$ is the midpoint of $PS$. A semicircular arc is drawn with $PS$ as diameter. Let $X$ be the midpoint of this arc. $Q$ and $R$ are points on the arc $PXS$ such that $QR$ is parallel to $PS$ and the semicircular arc drawn with $QR$ as diameter is tangent to $PS$. What is the area of the region $QXROQ$ bounded by the two semicircular arcs?
2013
2013 India PRMO p4
Three points $X, Y,Z$ are on a striaght line such that $XY = 10$ and $XZ = 3$. What is the product of all possible values of $YZ$?
2013 India PRMO p8
Let $AD$ and $BC$ be the parallel sides of a trapezium $ABCD$. Let $P$ and $Q$ be the midpoints of the diagonals $AC$ and $BD$. If $AD = 16$ and $BC = 20$, what is the length of $PQ$?
2013 India PRMO p9
In a triangle $ABC$, let $H, I$ and $O$ be the orthocentre, incentre and circumcentre, respectively. If the points $B, H, I, C$ lie on a circle, what is the magnitude of $\angle BOC$ in degrees?
2013 India PRMO p12
Let $ABC$ be an equilateral triangle. Let $P$ and $S$ be points on $AB$ and $AC$, respectively, and let $Q$ and $R$ be points on $BC$ such that $PQRS$ is a rectangle. If $PQ = \sqrt3 PS$ and the area of $PQRS$ is $28\sqrt3$, what is the length of $PC$?
2013 India PRMO p15
Let $A_1,B_1,C_1,D_1$ be the midpoints of the sides of a convex quadrilateral $ABCD$ and let $A_2, B_2, C_2, D_2$ be the midpoints of the sides of the quadrilateral $A_1B_1C_1D_1$. If $A_2B_2C_2D_2$ is a rectangle with sides $4$ and $6$, then what is the product of the lengths of the diagonals of $ABCD$ ?
2013 India PRMO p17
Let $S$ be a circle with centre $O$. A chord $AB$, not a diameter, divides $S$ into two regions $R_1$ and $R_2$ such that $O$ belongs to $R_2$. Let $S_1$ be a circle with centre in $R_1$, touching $AB$ at $X$ and $S$ internally. Let $S_2$ be a circle with centre in $R_2$, touching $AB$ at $Y$, the circle $S$ internally and passing through the centre of $S$. The point $X$ lies on the diameter passing through the centre of $S_2$ and $\angle YXO=30^o$. If the radius of $S_2$ is $100$ then what is the radius of $S_1$?
2013 India PRMO p19
In a triangle $ABC$ with $\angle BC A = 90^o$, the perpendicular bisector of $AB$ intersects segments $AB$ and $AC$ at $X$ and $Y$, respectively. If the ratio of the area of quadrilateral $BXYC$ to the area of triangle $ABC$ is $13 : 18$ and $BC = 12$ then what is the length of $AC$?
2014
2014 India PRMO p3
Let $ABCD$ be a convex quadrilateral with perpendicular diagonals. If $AB = 20, BC = 70$ and $CD = 90$, then what is the value of $DA$?
2014 India PRMO p4
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is $17$. What is the greatest possible perimeter of the triangle?
2014 India PRMO p10
In a triangle $ABC, X$ and $Y$ are points on the segments $AB$ and $AC$, respectively, such that $AX : XB = 1 : 2$ and $AY :YC = 2:1$. If the area of triangle $AXY$ is $10$, then what is the area of triangle $ABC$?
2014 India PRMO p12
Let $ABCD$ be a convex quadrilateral with $\angle DAB =\angle B DC = 90^o$. Let the incircles of triangles $ABD$ and $BCD$ touch $BD$ at $P$ and $Q$, respectively, with $P$ lying in between $B$ and $Q$. If $AD = 999$ and $PQ = 200$ then what is the sum of the radii of the incircles of triangles $ABD$ and $BDC$ ?
2014 India PRMO p15
Let $XOY$ be a triangle with $\angle XOY = 90^o$. Let $M$ and $N$ be the midpoints of legs $OX$ and $OY$, respectively. Suppose that $XN = 19$ and $YM =22$. What is $XY$?
2014 India PRMO p16
In a triangle $ABC$, let $I$ denote the incenter. Let the lines $AI,BI$ and $CI$ intersect the incircle at $P,Q$ and $R$, respectively. If $\angle BAC = 40^o$, what is the value of $\angle QPR$ in degrees ?
2015 missing from aops
2016
West Bengal Region
2016 India PRMO p4
Consider a right-angled triangle $ABC$ with $\angle C = 90^o$. Suppose that the hypotenuse $AB$ is divided into four equal parts by the points $D,E,F$, such that $AD = DE = EF = FB$. If $CD^2 +CE^2 +CF^2 = 350$, find the length of $AB$.
2016 India PRMO p5
Consider a triangle $ABC$ with $AB = 13, BC = 14, CA = 15$. A line perpendicular to $BC$ divides the interior of $\vartriangle BC$ into two regions of equal area. Suppose that the aforesaid perpendicular cuts $BC$ at $D$, and cuts $\vartriangle ABC$ again at $E$. If $L$ is the length of the line segment $DE$, find $L^2$.
2016 India PRMO p6
Suppose a circle $C$ of radius $\sqrt2$ touches the $Y$ -axis at the origin $(0, 0)$. A ray of light $L$, parallel to the $X$-axis, reflects on a point $P$ on the circumference of $C$, and after reflection, the reflected ray $L'$ becomes parallel to the $Y$ -axis. Find the distance between the ray $L$ and the $X$-axis.
2017
2017 India PRMO p13
In a rectangle $ABCD, E$ is the midpoint of $AB, F$ is a point on $AC$ such that $BF$ is perpendicular to $AC$, and $FE$ perpendicular to $BD$. Suppose $BC = 8\sqrt3$. Find $AB$.
2017 India PRMO p24
Let $P$ be an interior point of a triangle $ABC$ whose sidelengths are 26, 65, 78. The line through $P$ parallel to $BC$ meets $AB$ in $K$ and $AC$ in $L$. The line through $P$ parallel to $CA$ meets $BC$ in $M$ and $BA$ in $N$. The line through $P$ parallel to $AB$ meets $CA$ in $S$ and $CB$ in $T$. If $KL,MN,ST$ are of equal lengths, find this common length.
2017 India PRMO p25
Let $ABCD$ be a rectangle and let $E$ and $F$ be points on $CD$ and $BC$ respectively such that area $(ADE) = 16$, area $(CEF) = 9$ and area $(ABF) = 25$. What is the area of triangle $AEF$ ?
2017 India PRMO p26
Let $AB$ and $CD$ be two parallel chords in a circle with radius $5$ such that the centre $O$ lies between these chords. Suppose $AB = 6, CD = 8$. Suppose further that the area of the part of the circle lying between the chords $AB$ and $CD$ is $(m\pi + n) / k$, where $m, n, k$ are positive integers with gcd$(m, n, k) = 1$. What is the value of $m + n + k$ ?
2017 India PRMO p27
Let $\Omega_1$ be a circle with centre $O$ and let $AB$ be diameter of $\Omega_1$. Let $P$ be a point on the segment $OB$ different from $O$. Suppose another circle $\Omega_2$ with centre $P$ lies in the interior of $\Omega_1$. Tangents are drawn from $A$ and $B$ to the circle $\Omega_2$ intersecting $\Omega_1$ again at $A_1$ and B1 respectively such that $A_1$ and $B_1$ are on the opposite sides of $AB$. Given that $A_1 B = 5, AB_1 = 15$ and $OP = 10$, find the radius of $\Omega_1$.
2017 India PRMO p30
Consider the areas of the four triangles obtained by drawing the diagonals $AC$ and $BD$ of a trapezium $ABCD$. The product of these areas, taken two at time, are computed. If among the six products so obtained, two products are 1296 and 576, determine the square root of the maximum possible area of the trapezium to the nearest integer.
2018
2018 India PRMO p2
In a quadrilateral $ABCD$, it is given that $AB = AD = 13, BC = CD = 20, BD = 24$. If $r$ is the radius of the circle inscribable in the quadrilateral, then what is the integer closest to $r$?
2018 India PRMO p5
Let $ABCD$ be a trapezium in which $AB //CD$ and $AD \perp AB$. Suppose $ABCD$ has an incircle which touches $AB$ at $Q$ and $CD$ at $P$. Given that $PC = 36$ and $QB = 49$, find $PQ$.
2018 India PRMO p7
A point $P$ in the interior of a regular hexagon is at distances $8,8,16$ units from three consecutive vertices of the hexagon, respectively. If $r$ is radius of the circumscribed circle of the hexagon, what is the integer closest to $r$?
2018 India PRMO p8
Let $AB$ be a chord of a circle with centre $O$. Let $C$ be a point on the circle such that $\angle ABC =30^o$ and $O$ lies inside the triangle $ABC$. Let $D$ be a point on $AB$ such that $\angle DCO = \angle OCB = 20^o$. Find the measure of $\angle CDO$ in degrees.
2018 India PRMO p10
In a triangle $ABC$, the median from $B$ to $CA$ is perpendicular to the median from $C$ to $AB$. If the median from $A$ to $BC$ is $30$, determine $\frac{BC^2 + CA^2 + AB^2}{100}$.
2018 India PRMO p13
In a triangle $ABC$, right angled at $A$, the altitude through $A$ and the internal bisector of $\angle A$ have lengths $3$ and $4$, respectively. Find the length of the median through $A$.
2018 India PRMO p17
Triangles $ABC$ and $DEF$ are such that $\angle A = \angle D, AB = DE = 17, BC = EF = 10$ and $AC - DF = 12$. What is $AC + DF$?
2018 India PRMO p21
Let $\Delta ABC$ be an acute-angled triangle and let $H$ be its orthocentre. Let $G_1, G_2$ and $G_3$ be the centroids of the triangles $\Delta HBC , \Delta HCA$ and $\Delta HAB$ respectively. If the area of $\Delta G_1G_2G_3$ is $7$ units, what is the area of $\Delta ABC$?
2018 India PRMO p29
Let $D$ be an interior point of the side $BC$ of a triangle $ABC$. Let $I_1$ and $I_2$ be the incentres of triangles $ABD$ and $ACD$ respectively. Let $AI_1$ and $AI_2$ meet $BC$ in $E$ and $F$ respectively. If $\angle BI_1E = 60^o$, what is the measure of $\angle CI_2F$ in degrees?
2019
leg 1
2019 India PRMO leg1 p1
Form a square with sides of length $5$, triangular pieces from the four coreners are removed to form a regular octagonn. Find the area removed to the nearest integer.
2019 India PRMO leg1 p4
An ant leaves the anthill for its morning exercise. It walks $4$ feet east and then makes a $160^\circ$ turn to the right and walks $4$ more feet. If the ant continues this patterns until it reaches the anthill again, what is the distance in feet it would have walked?
2019 India PRMO leg1 p10
Let $ABC$ be a triangle and let $\Omega$ be its circumcircle. The internal bisectors of angles $A, B$ and $C$ intersect $\Omega$ at $A_1, B_1$ and $C_1$, respectively, and the internal bisectors of angles $A_1, B_1$ and $C_1$ of the triangles $A_1 A_2 A_ 3$ intersect $\Omega$ at $A_2, B_2$ and $C_2$, respectively. If the smallest angle of the triangle $ABC$ is $40^{\circ}$, what is the magnitude of the smallest angle of the triangle $A_2 B_2 C_2$ in degrees?
2019 India PRMO leg1 p19
Let $AB$ be a diameter of a circle and let $C$ be a point on the segement $AB$ such that $AC : CB = 6 : 7$. Let $D$ be a point on the circle such that $DC$ is perpendicular to $AB$. Let $DE$ be the diameter through $D$. If $[XYZ]$ denotes the area of the triangle $XYZ$, find $[ABD]/[CDE]$ to the nearest integer.
2019 India PRMO leg1 p23
Let $ABCD$ be a convex cyclic quadilateral. Suppose $P$ is a point in the plane of the quadilateral such that the sum of its distances from the vertices of $ABCD$ is the least. If $\{PC, PB, PC, PD\} = \{3, 4, 6, 8\}$, what is the maxumum possible area of $ABCD$?
2019 India PRMO leg1 p25
A village has a circular wall around it, and the wall has four gates pointing north, south, east and west. A tree stands outside the village, $16 \, \mathrm{m}$ north of the north gate, and it can be just seen appearing on the horizon from a point $48 \, \mathrm{m}$ east of the south gate. What is the diamter in meters, of the wall that surrounds the village?
2019 India PRMO leg1 p28
Let $ABC$ be a triangle with sides $51, 52, 53$. Let $\Omega$ denote the incircle of $\bigtriangleup ABC$. Draw tangents to $\Omega$ which are parallel to the sides of $ABC$. Let $r_1, r_2, r_3$ be the inradii of the three corener triangles so formed, Find the largest integer that does not exceed $r_1 + r_2 + r_3$.
2019 India PRMO leg1 p29
In a triangle $ABC$, the median $AD$ (with $D$ on $BC$) and the angle bisector $BE$ (with $E$ on $AC$) are perpedicular to each other. If $AD = 7$ and $BE = 9$, find the integer nearest to the area of triangle $ABC$.
leg 2
2019 India PRMO leg 2 p6
Let $ABC$ be a triangle such that $AB=AC$. Suppose the tangent to the circumcircle of $ABC$ at $B$ is perpendicular to $AC$. Find angle $ABC$ measured in degrees.
2019 India PRMO leg 2 p9
The centre of the circle passing through the midpoints of the sides of am isosceles triangle $ABC$ lies on the circumcircle of triangle $ABC$. If the larger angle of triangle $ABC$ is $\alpha^{\circ}$ and the smaller one $\beta^{\circ}$ then what is the value of $\alpha-\beta$?
2019 India PRMO leg 2 p14
Let $\mathcal{R}$ denote the circular region in the $xy-$plane bounded by the circle $x^2+y^2=36$. The lines $x=4$ and $y=3$ divide $\mathcal{R}$ into four regions $\mathcal{R}_i ~ , ~i=1,2,3,4$. If $\mid \mathcal{R}_i \mid$ denotes the area of the region $\mathcal{R}_i$ and if $\mid \mathcal{R}_1 \mid >$ $\mid \mathcal{R}_2 \mid >$ $\mid \mathcal{R}_3 \mid >$ $\mid \mathcal{R}_4 \mid$, determine $\mid \mathcal{R}_1 \mid$ $-$ $\mid \mathcal{R}_2 \mid$ $-$ $\mid \mathcal{R}_3 \mid$ $+$ $\mid \mathcal{R}_4 \mid$.
2019 India PRMO leg 2 p19
If $15$ and $9$ are lengths of two medians of a triangle, what is the maximum possible area of the triangle to the nearest integer ?
2019 India PRMO leg 2 p22
In parallelogram $ABCD$, $AC=10$ and $BD=28$. The points $K$ and $L$ in the plane of $ABCD$ move in such a way that $AK=BD$ and $BL=AC$. Let $M$ and $N$ be the midpoints of $CK$ and $DL$, respectively. What is the maximum walue of $\cot^2 (\tfrac{\angle BMD}{2})+\tan^2(\tfrac{\angle ANC}{2})$ ?
2019 India PRMO leg 2 p25
Let $ABC$ be an isosceles triangle with $AB=BC$. A trisector of $\angle B$ meets $AC$ at $D$. If $AB,AC$ and $BD$ are integers and $AB-BD$ $=$ $3$, find $AC$.
A friction-less board has the shape of an equilateral triangle of side length $1$ meter with bouncing walls along the sides. A tiny super bouncy ball is fired from vertex $A$ towards the side $BC$. The ball bounces off the walls of the board nine times before it hits a vertex for the first time. The bounces are such that the angle of incidence equals the angle of reflection. The distance travelled by the ball in meters is of the form $\sqrt{N}$, where $N$ is an integer. What is the value of $N$ ?
2019 India PRMO leg 2 p27
A conical glass is in the form of a right circular cone. The slant height is $21$ and the radius of the top rim of the glass is $14$. An ant at the mid point of a slant line on the outside wall of the glass sees a honey drop diametrically opposite to it on the inside wall of the glass. If $d$ the shortest distance it should crawl to reach the honey drop, what is the integer part of $d$ ?
2019 India PRMO leg 2 p28
In a triangle $ABC$, it is known that $\angle A=100^{\circ}$ and $AB=AC$. The internal angle bisector $BD$ has length $20$ units. Find the length of $BC$ to the nearest integer, given that $\sin 10^{\circ} \approx 0.174$
2019 India PRMO leg 2 p29
Let $ABC$ be an acute angled triangle with $AB=15$ and $BC=8$. Let $D$ be a point on $AB$ such that $BD=BC$. Consider points $E$ on $AC$ such that $\angle DEB=\angle BEC$. If $\alpha$ denotes the product of all possible values of $AE$, find $\lfloor \alpha \rfloor$ the integer part of $\alpha$. | 2019-11-20 21:40:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5208672285079956, "perplexity": 137.71822353782903}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670635.48/warc/CC-MAIN-20191120213017-20191121001017-00057.warc.gz"} |
https://www.gamedev.net/forums/topic/447847-problem-with-a-timer-loop/ | Public Group
# problem with a timer loop
This topic is 4053 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
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Problem - servers are getting spammed with messages and causes servers to crash. Solution - Make it so you can only type 3 messages then have to wait 5 seconds to type again. Whats been done - I put in a loop for 5 seconds and I put in a counter to count to 3 to start the timer. I thought that I would reset the counter in the timer to allow it to start over. So here is my problem. The code works for 3 messages then crashes. If I just use the timer it works fine but you can only do 1 message every 5 seconds. Can someone look at my code at let me know where I went wrong. It is coded in c++. Everything is int to zero at the top of the file (not shown). Thank you.
if (maxTeamMessageLimit < 3)//number of messages until timer kicks in
{
messagetosend = new game_PlayerMessage(team_observers, msg, player);
++ maxTeamMessageLimit;
}
else if ((teamCurrentTime - TeamMessageLastTime) >= 5000 )//1000 = 1 second
{
maxTeamMessageLimit = 0;
TeamMessageLastTime = teamCurrentTime;
}
}
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The logic of your algorithm is a bit fuzzy. Do you mean that every time I send 3 messages (even with 20 minutes between them) I cannot send a fourth for 5 seconds? Or is the condition something else?
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yes that is correct. i don't care how much time is used as long as there is a 5 second pause after 3 messages. I would not have a problem having it reset the counter after every 5 seconds but that seems like a lot more coding. The over all goal is to stop people from using .cfg scripts to spam and crash the servers. With a 5 second pause the server can catch up and avoid crashing.
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static int messagesSinceLastPause = 0;static int startAgainTime = time();if (startAgainTime < time()) { SendMessage(); if (++messagesSinceLastPause == 3) { messagesSinceLastPause = 0; startAgainTime = time() + 5000; }}else{ RejectMessage();}
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Why 3 messages and 5 seconds? Perhaps it'll still be too heavy, and you'll need to change those hard-coded variabeles and recompile the game. Why not create variabeles for these, so you can tweak them at run-time, and read them from a config file if you want to? :)
It looks like you're checking if 5 seconds have passed since the first message, not since the 3d message. When there's more than 5 seconds between the first and third message, the delay is over when the 3d message is sent, so you'll never get in that else if part.
So, where and when does it crash? Does it crash when you've sent 3 messages, and send the 4th before 5 seconds have passed? Or also when that 4th message is passed after the 5 seconds are over? And does it really crash or are messages simply ignored?
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Quote:
And does it really crash or are messages simply ignored?
^ What he said.
At the very least it looks like it's going to ignore the first attempt to send a message after you've sent three.
Your else branch doesn't send a message - it merely resets the counter which appears to mean that the next message you try to send will work. And so on. So you'll send three messages then a fourth one will get lost, even if enough time has lapsed, then it'll work again.
[ edit ] Sorry, I think I was assuming that your code was only called if a message was being processed. On reflection, it's probably always running in a loop so the above problem wouldn't exist. [ /edit ]
Also, using your code to reset the counter every five seconds seems to be simple. I think this should do just that (and fix the possibly skipped fourth message issue):
if ((teamCurrentTime - TeamMessageLastTime) >= 5000 )//1000 = 1 second{ maxTeamMessageLimit = 0;}if (maxTeamMessageLimit < 3)//number of messages until timer kicks in{ messagetosend = new game_PlayerMessage(team_observers, msg, player); if ( maxTeamMessageLimit == 0 ) TeamMessageLastTime = teamCurrentTime; // set current time if first message since reset ++ maxTeamMessageLimit;}
[Edited by - CaspianB on May 14, 2007 10:44:59 PM]
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ToohrVyk - I'll try running it and see what happens.
Captain P - the boss said 3 for 5. I thought that it may not be enough. If one person runs 2 copies and then spams the server alerting the 5 seconds between each version then he could take down the server. The other issue is we do not want to have problems for the normal gamer not being able to talk. We are not exporting to a .cfg because we do not want the server admins to have a problem with this or find a hack to edit their own .cfg file and override ours. Also we now have a nice autoupdater so if it isn't enough the boss will send the word and I will have the update out within about a min or two later.
Currently the hacked .cfg file sends out the messages as fast as possible and I would say they are hitting in the micro-second range. So hopefully if we bring it up to 5 seconds, it won't be a problem.
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Oops I forgot to add this in. Yes it really crashes the game. I get the XP error box with debug, send to M\$ or don't send. Then it closes the server back to the desktop.
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Well I took care of the crash problem. Turns out I encapsulated the wrong file. I got the right one now.
I used the code from CaspianB only cause it already had everything in place. Now my 4th message and beyond get ignored. I never get another message in even after 5 seconds.
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Well I fixed everything. It turns out I had my getTickCount in the wrong spot. Everything works great now. Thanks guys. We also decide to go to 3 messages during a 10 second period. We think that will be good to get us by.
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× | 2018-06-20 23:57:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31878340244293213, "perplexity": 1690.2989165426195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863939.76/warc/CC-MAIN-20180620221657-20180621001657-00174.warc.gz"} |
http://clay6.com/qa/18290/if-f-x-begin1-x-x-1-2x-x-x-1-x-1-x-3x-x-1-x-x-1-x-2-x-1-x-x-1-end-then-f-10 | Browse Questions
# If $f(x)=\begin{vmatrix}1 &x&x+1\\2x&x(x-1)&(x+1)x\\3x(x-1)&x(x-1)(x-2)&(x+1)x(x-1)\end{vmatrix}$ then $f(100)$ is equal to
$(a)\;0\qquad(b)\;1\qquad(c)\;100\qquad(d)\;-100$
$f(x)=\begin{vmatrix}1 &x&x+1\\2x&x(x-1)&(x+1)x\\3x(x-1)&x(x-1)(x-2)&(x+1)x(x-1)\end{vmatrix}$
Apply $C_1\rightarrow C_1+C_2$
$\begin{vmatrix}x+1 &x&x+1\\(x+1)x&x(x-1)&(x+1)x\\(x+1)x(x-1)&x(x-1)(x-2)&(x+1)x(x-1)\end{vmatrix}$
$\Rightarrow 0$
[$C_1$ and $C_2$ are identical]
Which is free of $x$,so the function is true for all values of $x$
$\therefore$ At $x=100$
$f(x)=0$
$f(100)=0$
Hence (a) is the correct answer. | 2017-01-19 09:01:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9580987095832825, "perplexity": 823.3718373777967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280504.74/warc/CC-MAIN-20170116095120-00206-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/17958/average-speed-of-seismic-waves-towards-the-center-of-earth?answertab=votes | # Average speed of seismic waves towards the center of Earth
I'm looking at an approximation of the average speed of seismic wave towards the center of Earth.
The horizontal path of the waves that affects us directly is well documented, but there is not much about the vertical propagation of such waves.
Of course that speed depends upon many factors like
• depth of the earthquake hypocenter
• magnitude of the earthquake
• Earth strata at the hypocenter
• specific topology of the many layers up to the center of Earth at this location
and this is a complex area, but a rough approximation would be appreciated.
Something like
(speed, validSpeedForThatKilometers) = speedAtDepth(hypoDepth,mag,desiredDepth)
or even better a more complex function that would directly give the rough time to reach depth desiredDepth based on some parameters
time = getTimeToReachDepth(hypoDepth, mag, desiredDepth)
-
This link can help you study seismic waves and see that life is not as simple as your thoughts: eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/…. And this gives numbers: en.wikipedia.org/wiki/P-wave – anna v Dec 7 '11 at 5:55
Thanks for the (good) links. I didn't expect formal simplicity, just some rough pointers to match my "simple thoughts" :-) – ring0 Dec 7 '11 at 6:39 | 2014-12-20 06:01:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4835781157016754, "perplexity": 2088.2481930430736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802769419.87/warc/CC-MAIN-20141217075249-00082-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/359831/is-it-possible-to-compare-two-different-datasets-with-a-different-range-of-value | # Is it possible to compare two different datasets with a different range of values?
I am currently working with the k-Nearest Neighbors (KNN) algorithm.
Is it possible to compare two datasets with different ranges of values?
In other words, I have one dataset with a range $\in [0,1]$, and the second range of the other dataset $\in [-1,1]$.
I have calculated some performance measures such as accuracy and F1 score, among others. Then, I compared them based on the performance measures.
Is this approach correct? Or do I need to transform the datasets to they lie in common ranges?
EDIT
What I mean by the range that for example, all the observations in the first dataset are between 0 and 1. Also, When I say comparing two datasets, I mean comparing the outcome of the performance measures such as accuracy and F1 score and so on.
The range is for the predictor variables. The comparison is only to replicate some results. Also, to make sure about different methods.
• I think this question needs some clarification. What do you mean the dataset has a range [0,1]? Is that range for your variable of interest or for the auxiliary variable(s)? And what do you mean when you say you want to compare the two different datasets? What are you comparing between them? Jul 30 '18 at 18:42
• @astel, I mean by the range that all the observations in the first dataset are between 0 and 1. When I say comparing two datasets, I mean comparing the outcome of the performance measures such as accuracy and F1 score and so on.
– jeza
Jul 30 '18 at 18:56
• You still didn't really answer my question, is the range you quoted for the variable of interest or the auxiliary variables? Why do you want to compare the accuracy/F1 scores of two datasets? Jul 30 '18 at 19:14
• @astel, The range is for the predictor variables. The comparison is only to replicate some results. Also, to make sure about different methods.
– jeza
Jul 30 '18 at 20:02 | 2021-09-22 15:35:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5188602209091187, "perplexity": 333.0081281306126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057366.40/warc/CC-MAIN-20210922132653-20210922162653-00512.warc.gz"} |
https://physics.stackexchange.com/questions/139268/how-did-newton-discover-the-universal-law-of-gravitation | # How did Newton discover the universal law of gravitation?
I am having trouble comprehending how anyone could come up with this formula:
$$F = \frac{GMm}{d^2}.$$
Could someone walk me through this?
• Guess and check! – Andrew Oct 8 '14 at 2:20
• Newton never did express his universal law of gravitation in that form. He reasoned in terms of proportionalities and worked to avoid needing to know the constant of proportionality. The form in which you wrote Newton's law of gravitation with the constant of proportionality included (the constant G) didn't appear until late in the 19th century. – David Hammen Oct 8 '14 at 4:36
Well, there are 4 parts to the right-hand side; let's look at each in turn.
The first $M$ is the mass of the gravitating body. You would expect that the force it exerts should be larger if it has a larger mass. Moreover, it's not unreasonable to think the force should be directly proportional to this mass: twice as much mass should grab things with twice as much force.
By symmetry, the dependence on $m$ should be the same as on $M$. This symmetry is really that of Newton's Third Law: for every action (force that $M$ exerts on $m$) there is an equal and opposite reaction (force that $m$ exerts on $M$).
How about the $d^2$ in the denominator? Well, we expect that the force with which one thing attracts another decreases with distance: get far enough away and you should feel something's effect on you diminish to arbitrarily small magnitude. Moreover, the power of 2 is an effect of living in 3D space. Consider a point source of light. Any sphere of radius $r$ centered on the source will capture the same total power, so the power per unit area (how bright the light appears) is proportional to $1/r^2$, since the area of a sphere is proportional to $r^2$.
In fact, this $1/r^2$ dependence was known for certain things and even suggested for gravity. Hooke in particular felt Newton got too much credit because he (Hooke) had suggested an inverse square law earlier (though he didn't really have rigorous math or predictions relating to it). Needless to say, this soured their relations, prompting Hooke to join the Leibniz camp in the calculus debate.
Finally, there's the $G$, which is just a reflection of the fact that our arguments are all about proportions and so they leave an overall proportionality constant undetermined. The value of $G$ is in fact notoriously difficult to measure, and this wasn't done in Newton's time. Instead, one would make do with taking ratios of quantities such that $G$ dropped out.
• So newton had a sense of gravity flux, and field strength? – ja72 May 26 '15 at 12:42
Newton actually calculated, using a lot of obscure geometry and limiting concepts, the orbits that various force forms would generate. One of those forms was the inverse square force. If you want to know what the others were, find a copy of the Principia and wade through it.
The result wasn't published until Edmund Halley asked Newton if he knew the nature of the force (our modern wording) that would cause something to have a repeating orbit. Halley was investigating the possibility that sightings of a bright comet every 76 years could possibly be the same comet. Newton immediately responded that it was an inverse square force. Halley was shocked with the quick answer. Newton had worked out the math for various forces out of curiosity and never told anyone. Halley forced him (with his financial backing) to publish the results. Halley was also impressed that the orbits from the inverse square force would mathematically produce the same results as Kepler had extracted from Tycho's planetary data.
Newton's reasoning was that the same force which gave an object weight (or gravitas, from the Latin) was the same force which kept the moon in orbit around the Earth and the Earth around the Sun, etc. | 2019-09-19 18:56:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8357048034667969, "perplexity": 548.1773489481013}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573570.6/warc/CC-MAIN-20190919183843-20190919205843-00410.warc.gz"} |
https://lifewithdata.com/2022/08/16/pandas-dataframe-explode-method-with-examples/ | # Pandas DataFrame explode() method with examples
The explode() method in pandas transform each element in a list to a row in a DataFrame. If the array-like is empty, a missing value (NaN) will be placed for that row.
### Syntax –
DataFrame.explode(column, ignore_index=False)
column – The label of the columns to unwrap.
ignore_index – If True, the resulting index will be labeled 0, 1, …, n – 1. By default it is False.
## Examples –
Let’s create a dataframe to work with.
import pandas as pd
df = pd.DataFrame({'A':[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
'B':[10, 20, 30],
'C':[['a','b','c'], ['d','e','f'], ['g','h','i']]})
df
### 1 . Single Column Explode –
Let’s say you want to explode the A column. You want to turn every elements of the lists in A to a row. To do that you can use the explode() method in pandas.
df.explode('A')
### 2 . Multi-Column Explode –
You can also explode multiple columns together using the explode method in pandas. Let’s say you want to explode both the column A and C.
df.explode(list('AC'))
### 3 . Resetting the Index after explode –
To reset the index after explode set the ignore_index parameter to True.
df.explode(list('AC'), ignore_index=True)
Rating: 1 out of 5. | 2023-02-06 04:07:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1797419786453247, "perplexity": 3621.067145671027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500303.56/warc/CC-MAIN-20230206015710-20230206045710-00469.warc.gz"} |
https://www.sparrho.com/item/thermal-entanglement-and-teleportation-in-a-two-qubit-heisenberg-chain-with-dzyaloshinski-moriya-anisotropic-antisymmetric-interaction/959b62/ | # Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction
Research paper by Guo-Feng Zhang
Indexed on: 02 Mar '07Published on: 02 Mar '07Published in: Quantum Physics
#### Abstract
Thermal entanglement of a two-qubit Heisenberg chain in presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as quantum channel are investigated. It is found that the DM interaction can excite the entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of input one, its dependences on the temperature, DM interaction and spin coupling constant are given in detail. Entanglement teleportation will be better realized via antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of antiferromagnetic or ferromagnetic spin chains. | 2019-06-24 08:55:18 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8222208619117737, "perplexity": 1900.7892765300462}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999298.86/warc/CC-MAIN-20190624084256-20190624110256-00481.warc.gz"} |
https://laravelquestions.com/category/chart-js/ | #### Category : chart.js
Found in [consoletvschartssrcChartsServiceProvider.php] Error Found this error.. any ideas Sourc..
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I have a table showing branches expenses such as (branch: 1, total: 100)(branch: 2, total: 400) and it could be more than 2 branches and I would like to show them in a line chart with chart.js. my question here is how to have multi datasets based on how many branches the table has. I ..
This is my query to get the product name and total quantity sold. $prd = DB::table(‘order_details’) ->join(‘products’, ‘order_details.product_id’, ‘=’, ‘products.id’) ->select(‘products.name’, DB::raw(‘SUM(quantity) as quantity’)) ->groupBy(‘products.name’) ->orderBy(‘quantity’, ‘desc’) ->get(); return$prd; This is the output. [ { "name": "PINK", "quantity": "22" }, { "name": "WHITE", "quantity": "14" }, { "name": "RED", "quantity": "13" } ] But ..
I don’t know how to address this question properly but my problem is I can’t display my data in my chart using chart.js and laravel. To start with, I have a "sales" table in my database, and it has "total" and "created_at" fields which are the data that I wanted to reflect on my chart. ..
I’m using chart.js for showing statistics of reviews and messages of a user, but I’m getting problems with the scripts, now the stats are working but I got this error Cannot find element: #app and I don’t know how to manage that. If I use defer in this script (now I deleted it to see ..
I’m trying to create a statistics view, but chart.js gives me problems. I tried to delete defer from the app.js script tag and it works but it gave me problems on all the rest of the website. Here is the stats.view in which I’m trying to make work the scripts and the canvas, but with ..
Can someone direct me to example how can I use https://www.chartjs.org/chartjs-plugin-annotation/guide/usage.html with Laravel http://lavacharts.com/ Lavacharts package? I tried to add config to "annotations" array (as in example http://lavacharts.com/#chart-bar) but with no luck. which steps i need to reproduce to get this plugin to work with my existing charts? tnx! Y Sourc..
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I want to make a bar stacked graph with 2 datasets with Chartjs 6 – Laravel 8 $chart->labels($resultados1); $chart->dataset(‘Dataset1′,’bar’,$resultados2)->backgroundColor(collect([‘#7158e2’])); $chart->dataset(‘Dataset2′,’bar’,$resultados3)->backgroundColor(collect([‘#1158e2’])); //>>>>>>>>$chart->scales(‘xAxes’,’stacked’ => true , ‘yAxes’ => [‘stacked’ => true]);<<<<<<<<<<<<<<<<<<<<<< But obviously this last commented line is wrong I’ve found how to make this by javascript but I need to put this on laravel code easily .. Read more im trying to pass the content of the database to the dataset for the chartjs but the errors says UNEXPECTED TOKEN < IN JSON AT POSITION 0. this chartjs version is 7 samplechart.php <?php declare(strict_types = 1); namespace AppCharts; use ChartisanPHPChartisan; use ConsoleTVsChartsBaseChart; use IlluminateHttpRequest; class SampleChart extends BaseChart { /** * Handles the HTTP .. Read more I’m currently doing the dashboard in our project and can’t progress because of this error. Call to undefined method AppChartsSampleChart::labels(). I suspect that I missed some installation and configurations but I’ve done it several times now. SampleChart.php <?php declare(strict_types = 1); namespace AppCharts; use ChartisanPHPChartisan; use ConsoleTVsChartsBaseChart; use IlluminateHttpRequest; class SampleChart extends BaseChart { /** .. Read more I am new to laravel and with chart.js I did surf online but didn’t find the proper solution yet, Any help and suggestions would be great. Here is the link to a similar issue with some code overview. Please tell me if you need anything else. Hey guys,I need help to display datalabels from chartjs .. Read more So here I’ve called an array to display dates and their orders but I cannot see Data-labels, And this script is old but it works with hard written datasets and labels, Any ideas why it’s messed? Basically what the below code does is when you click the button it changes and calls that var to .. Read more so I’m trying to get data for my chart from the database and I want it to display a number of orders per day scenario well I tried this code and it gives me full unformatted dates from the database. Any ideas on how to change it to date/month??$data = DB::table(‘analytics’)->get(); $attrs = array(); .. Read more I don’t know, how much time I lost looking for solution for this issue. I wanted to use Chart.js in my Laravel project, so I followed instructions described here. composer require fx3costa/laravelchartjs (runned) Fx3costaLaravelChartJsProvidersChartjsServiceProvider::class (added in the right place) npm i chart.js (used to install chart.js) In my controller and blade I used code from .. Read more I am using chart.js, Laravel 5.4 and blade templates. I have to show doughnut chart and when user click on particular area then it should show the name of selected label and value belongs to it in the modal but firstly I am not able to get label name when user click on doughnut chart. .. Read more I´m traying to create a graphic in my app developed in Laravel 5.6. I´m sending all my data from my controller with one array.$callSend = array(); foreach($result as$call){ array_push($callSend, Cita::where(‘id_llamada’,$call->id) ->with("estado") ->get()); } Cita it´s my model to get all my data this return this: (754) [Array(1), Array(1), Array(1), Array(1), Array(1), Array(1), Array(1), ..
var ctx = document.getElementById("myLineChart").getContext(‘2d’); var myLineChart = new Chart(ctx, { type: ‘line’, data: { labels: [ @foreach($year as$year) "{{$year->year}}", @endforeach ], datasets: [ { label: ‘A’, data: [ @foreach($data1 as $dt1) {{$dt1->total}}, @endforeach ], borderColor: ‘rgba(75, 192, 192, 1)’, backgroundColor: ‘rgba(75, 192, 192, 0.2)’, }, { label: ‘B’, data: [ @foreach($data2 as$dt2) {{$dt2->total}}, .. Read more I am importing my chart js code from <script src="{{ asset(‘/css/tailwind/js/charts-bars.js’) }}" defer></script> I have some data from the controller and may I ask is it possible to pass the data to this script before the chart gets rendered? My charts-bars.js code const barConfig = { type: ‘bar’, data: { labels: [‘January’, ‘February’, ‘March’, ‘April’, .. Read more I’m currently working on a dashboard and im trying to display a score across a lot of people. Here is my chart.js code. <script> const labels = [ @foreach($all_staff as $staff) @php$i++; @endphp ‘{{ $i }}’, @endforeach ]; const data = { labels: labels, datasets: [{ label: ‘My First dataset’, backgroundColor: ‘rgb(255, 99, 132)’, .. Read more I would like to ask how install and integrate [email protected] with my laravel application. I use cdn links right now but later it wont be an option for me later. Used cdn links: <script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.22.2/moment.min.js"</script> <script src="https://cdnjs.cloudflare.com/ajax/libs/Chart.js/2.9.4/Chart.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/[email protected]"></script> Method I tried: Installing chartjs npm i [email protected] Add this line in webpack.mix.js: mix.copy(‘node_modules/chart.js/dist/chart.js’, ‘public/chart.js/chart.js’); Then .. Read more I’m using Chartisan with Chart.js & Laravel. How do I make use of these hooks to access the more complicated styling options in Chart.js? https://chartisan.dev/documentation/frontend/hooks#Custom-Hooks https://www.chartjs.org/docs/latest/samples/scale-options/grid.html <div x-data="{chart: null}" x-init="chart = new Chartisan({ el: ‘#{{$chartPath }}’, url: ‘@chart(\$chartPath)’, hooks: new ChartisanHooks() .datasets([{ type: ‘line’, fill: true, borderColor: ‘#BBE9DE’, tension: 0.1 }]) {{– .options({ title: .. | 2021-10-19 06:48:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2552759349346161, "perplexity": 7322.645108649697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585242.44/warc/CC-MAIN-20211019043325-20211019073325-00718.warc.gz"} |
https://www.vrcbuzz.com/standard-form-of-lpp/ | # Standard Form of LPP
## Standard form of LPP
In this tutorial, we will discuss about what is the standard form of linear programming problem?, what are the characteristics of standard form of linear programming problem?, how to convert LPP to its standard form?.
## Important Definitions
### Unrestricted Variables
Many times one encounter problems of the LPP in which some or all of the variables can have any sign. Variables which can be positive, negative or zero are called unrestricted variables.
Suppose that in a given LPP the variable $x_j$ is unrestricted in sign (i.e., it can take any value). Then $x_j$ can be written as
$$x_j = x^\prime_j - x^{\prime\prime}_j,$$
where $x^\prime_j,x^{\prime\prime}_j\geq 0$.
### Slack Variable
If a constraint has $\leq$ sign, then in order to make it an equality, we have to add something positive to the left hand side. The non-negative variable which is added to the left side of the constraint to convert it to equation is called slack variable.
e.g. Consider the constraint $x_1+3x_2 \leq 6$. We add a non-negative variable $s_1$ to the left side of the inequality to convert it into equation $x_1+3x_2 +s_1 =6$.
### Surplus Variable
If a constraint has $\geq$ sign, then in order to make it an equality, we have to subtract something positive from the left hand side. The non-negative variable which is subtracted from the left side of the constraint to convert it to equation is called surplus variable.
e.g. Consider the constraint $x_1+3x_2 \geq 6$. We subtract a non-negative variable $s_2$ from the left side of the inequality to convert it into equation $x_1+3x_2 - s_2 =6$
## What are the characteristics of Standard form of LPP?
The standard form of the LPP is used to develop the procedure for solving general linear programming problem. The characteristics of the standard form of a LPP are as follows :
• Objective function should be of maximization form. Minimization function is equivalent to maximization of negative expression of that function, i.e. $\min\; z = -\max\; [-z]$. e.g. $\min\; z =2x_1+3x_2$ is equivalent to $\max\; z^\ast=-2x_1-3x_2$.
• The right side elements of each constraint should be made non-negative (if not). The right side can always be made positive on multiplying both sides of the inequality by (-1) whenever it is necessary. e.g. $-3x_1+4x_2\leq -2$ can be written as $3x_1-4x_2\geq 2$.
• All the constraint should be converted to equations except for the non-negativity restrictions.
• Constraints of the inequality type can be changed to equality by adding or subtracting the left side of each such constraints by non-negative variables. For example
• The constrain $3x_1+2x_2 \leq 4$ can be written in equation form as $3x_1 +2x_2 +s_1 = 4$, where $s_1>0$. Here $s_1$ is called Slack Variable.
• The constraint $4x_1+3x_2 \geq 3$ can be written in equation form as $4x_1 +4x_2 -s_2 = 3$, where $s_2>0$. Here $s_2$ is called Surplus Variable.
• All the decision variables should be non-negative.
• Suppose that in a given LPP the decision variable $x_j$ is unrestricted in sign (i.e., it can take any value). Then $x_j$ can be written as
$$x_j = x^\prime_j - x^{\prime\prime}_j,$$
where $x^\prime_j,x^{\prime\prime}_j\geq 0$.
## Standard Form of General LPP
The standard form of General LPP with all $(\leq$) constraints can be obtained as follows :
$$\begin{equation*} \max z = c_1 x_1 + c_2 x_2 + \ldots + c_n x_n + 0x_{n+1} + \ldots + 0x_{n+m} \end{equation*}$$
subject to
$$\begin{eqnarray*} a_{11} x_1 + a_{12} x_2 + \ldots + a_{1j}x_j + \ldots + a_{1n}x_n + x_{n+1}& = & b_1 \\ a_{21} x_1 + a_{22} x_2 + \ldots + a_{2j}x_j + \ldots + a_{2n}x_n +x_{n+2} & =& b_2 \\ \vdots \qquad\qquad \vdots \qquad\qquad \vdots & = & \vdots \\ a_{i1} x_1 + a_{i2} x_2 + \ldots + a_{ij}x_j + \ldots + a_{in}x_n +x_{n+i} & = & b_i \\ \vdots \qquad\qquad \vdots \qquad\qquad \vdots & = & \vdots \\ a_{m1} x_1 + a_{m2} x_2 + \ldots + a_{mj}x_j + \ldots + a_{mn}x_n+x_{n+m} & = & b_m \end{eqnarray*}$$
and
$$\begin{equation*} x_j \geq 0,\; j = 1,2,\ldots,n+m \end{equation*}$$
In the objective function the coefficient of slack variables $x_{n+1}, x_{n+2}, \ldots, x_{n+m}$ are assumed to be zero so that conversion does not change the function to be optimized.
## Standard form of LPP Example 1
Convert the following LPP into standard form.
$$\begin{eqnarray*} Max\; z= 28x_1 +30x_2 & & \\ \mbox{s.t. } 6x_1+ 3x_2&\leq& 18 \\ 3x_1 +x_2 &\leq & 8 \\ 4x_1 +5x_2 &\leq & 30 \\ \mbox{and }x_1 , x_2 & \ge & 0 \end{eqnarray*}$$
#### Solution
The given LPP is
$$\begin{eqnarray*} Max\; z= 28x_1 +30x_2 & & \\ \mbox{s.t. } 6x_1+ 3x_2&\leq& 18 \\ 3x_1 +x_2 &\leq & 8 \\ 4x_1 +5x_2 &\leq & 30 \\ \mbox{and }x_1 , x_2 & \ge & 0 \end{eqnarray*}$$
Here the objective function is maximization type, all the constraints are of less than or equal to type and all the decision variables are non-negative.
Adding slack variable to the left side of each constraints, the standard form of given LPP is
$$\begin{eqnarray*} Max\; z= 28x_1 +30x_2 +0s_1 + 0 s_2 + 0s_3& & \\ \mbox{s.t. } 6x_1+ 3x_2+ s_1&=& 18 \\ 3x_1 +x_2 +s_2&= & 8 \\ 4x_1 +5x_2+s_3&= & 30 \\ \mbox{and }x_1 , x_2,s_1,s_2,s_3 & \ge & 0 \end{eqnarray*}$$
where $x_1,x_2$ are the decision variables and $s_1,s_2, s_3$ are the slack variables.
## Standard form of LPP Example 2
Convert the following LPP into standard form.
$$\begin{eqnarray*} Max\; z= 3x_1 +2x_2 & & \\ \mbox{s.t. } x_1 -x_2&\leq& 1 \\ x_1 +x_2 &\geq & 3 \\ \mbox{and }x_1 , x_2 & \ge & 0 \end{eqnarray*}$$
#### Solution
The given LPP is
$$\begin{eqnarray*} Max\; z= 3x_1 +2x_2 & & \\ \mbox{s.t. } x_1 -x_2&\leq& 1 \\ x_1 +x_2 &\geq & 3 \\ \mbox{and }x_1 , x_2 & \ge & 0 \end{eqnarray*}$$
Here the objective function is maximization type. First constraint is less than or equal to type. So to make the inequality constraint to equality, we add a slack variable $s_1$ to the left hand side of the inequality.
$$x_1 -x_2+s_1= 1$$
The the second constraint is greater than or equal to type. So to make the inequality constraint to equality, we subtract a surplus variable $s_2$ from the left hand side of the inequality.
$$x_1 +x_2 -s_2 = 3$$
The standard form of given LPP is
$$\begin{eqnarray*} Max\; z= 3x_1 +2x_2+0 s_1 +0 s_2 & & \\ \mbox{s.t. } x_1 -x_2+s_1&=& 1 \\ x_1 +x_2 -s_2 &=& 3 \\ \mbox{and }x_1 , x_2, s_1, s_2 & \ge & 0 \end{eqnarray*}$$
where $x_1,x_2$ are the decision variables and $s_1$ is slack variable and $s_2$ is surplus variables.
## Standard form of LPP Example 3
Convert the following LPP into standard form.
$$\begin{eqnarray*} Min\; z= 2x_1 -10x_2 & & \\ \mbox{s.t. } x_1 -x_2&\geq& 2 \\ x_1 -5x_2 &\geq & -5 \\ \mbox{and }x_1 , x_2 & \ge & 0 \end{eqnarray*}$$
#### Solution
The given LPP is
$$\begin{eqnarray*} Min\; z= 2x_1 -10x_2 & & \\ \mbox{s.t. } x_1 -x_2&\geq& 2 \\ x_1 -5x_2 &\geq & -5 \\ \mbox{and }x_1 , x_2 & \ge & 0 \end{eqnarray*}$$
Here the objective function is minimization type. Convert it to maximization type as
$$Max \quad z^\prime =-2x_1 + 10x_2$$
The first constraint is $\geq$ type. To convert this constraint to equality, subtract a surplus variable $s_1$ from the left hand side of the inequality.
$$-x_1-x_2 -s_1 =2$$
The right hand side of the second constraint is negative. To convert it to a positive quantity, multiply the constraint by (-1). That is $-x_1 +5x_2 \leq 5$. Now add slack variable $s_2$ to the left hand side of the constraint, we have
$$-x_1 +5x_2+s_2 = 5$$
Thus the standard form of the given LPP is
$$\begin{eqnarray*} Max\; z^\prime= -2x_1 +10x_2+0s_1 +0s_2 & & \\ \mbox{s.t. } -x_1 -x_2-s_1&=& 2 \\ -x_1 +5x_2 +s_2&= & 5 \\ \mbox{and }x_1 , x_2, s_1,s_2 & \ge & 0 \end{eqnarray*}$$
## Standard form of LPP Example 4
Convert the following LPP into standard form.
$$\begin{eqnarray*} Min\; z= -3x_1 -5x_2 & & \\ \mbox{s.t. } 2x_1 -3x_2&\leq& 15 \\ x_1 +x_2 &\leq & 3 \\ 4x_1+x_2 &\geq& 2\\ \mbox{and }x_1 & \ge & 0\\ x_2 & & \text{ unrestricted}. \end{eqnarray*}$$
#### Solution
The given LPP is
$$\begin{eqnarray*} Min\; z= -3x_1 -5x_2 & & \\ \mbox{s.t. } 2x_1 -3x_2&\leq& 15 \\ x_1 +x_2 &\leq & 3 \\ 4x_1+x_2 &\geq& 2\\ \mbox{and }x_1 & \ge & 0\\ x_2 & & \text{ unrestricted}. \end{eqnarray*}$$
Here the objective function is minimization type. Convert it to maximization type as
$$Max\quad z^\prime =3x_1 + 5x_2$$
The first constraint is $\leq$ type. To convert this constraint to equality, add a slack variable $s_1$ to the left hand side of the inequality.
$$2x_1-3x_2 +s_1 =15$$
The second constraint is $leq$ type. To convert it to equality add a slack variable $s_2$ to the left hand side of the constraint, we have
$$x_1 +x_2+s_2 = 3$$
The third constraint is $\geq$ type. To convert it to equality subtract a surplus variable $s_3$ from the left hand side of the constraint, we have
$$4x_1 +x_2-s_3 = 2$$
As the decision variable $x_2$ is unrestricted in sign, we introduce two extra non-negative variables $x_2^\prime$ and $x_2^{\prime\prime}$ such that
$$x_2 = x_2^\prime - x_2^{\prime\prime}$$
Thus the standard form of the given LPP is
$$\begin{eqnarray*} Max\; z^\prime= 3x_1 +5(x_2^\prime - x_2^{\prime\prime})+0s_1+0s_2+0s_3 & & \\ \mbox{s.t. } 2x_1 -3(x_2^\prime -x_2^{\prime\prime}) +s_1&=& 15 \\ x_1 +(x_2^\prime -x_2^{\prime\prime}) +s_2&= & 3 \\ 4x_1+(x_2^\prime -x_2^{\prime\prime}) -s_3&=& 2\\ \mbox{and }x_1,x_2^\prime,x_2^{\prime\prime},s_1,s_2,s_3 & \ge & 0 \end{eqnarray*}$$
## Important Definitions
The standard form of General LPP with all $(\leq$) constraints is as follows :
$$\begin{equation*} \max z = c_1 x_1 + c_2 x_2 + \ldots + c_n x_n + 0x_{n+1} + \ldots + 0x_{n+m} \end{equation*}$$
subject to
$$\begin{eqnarray*} a_{11} x_1 + a_{12} x_2 + \ldots + a_{1j}x_j + \ldots + a_{1n}x_n + x_{n+1}& = & b_1 \\ a_{21} x_1 + a_{22} x_2 + \ldots + a_{2j}x_j + \ldots + a_{2n}x_n +x_{n+2} & =& b_2 \\ \vdots \qquad\qquad \vdots \qquad\qquad \vdots & = & \vdots \\ a_{i1} x_1 + a_{i2} x_2 + \ldots + a_{ij}x_j + \ldots + a_{in}x_n +x_{n+i} & = & b_i \\ \vdots \qquad\qquad \vdots \qquad\qquad \vdots & = & \vdots \\ a_{m1} x_1 + a_{m2} x_2 + \ldots + a_{mj}x_j + \ldots + a_{mn}x_n+x_{n+m} & = & b_m \end{eqnarray*}$$
and
$$\begin{equation*} x_j \geq 0,\; j = 1,2,\ldots,n+m \end{equation*}$$
### Solution
A set of values $\{x_1, x_2, \ldots , x_{n+m}\}$ which satisfy the constraints of linear programming problem is called a solution of the LPP.
### Feasible Solution
A solution of a LPP which also satisfies the non-negativity restrictions of the problem is called its feasible solution.
### Basic Solution
A basic solution to the set of constraints is a solution obtained by setting any $n$ variables (among $n+m$ variables) equal to zero and solving for remaining $m$ variables, provided the determinant of the coefficient of these $m$ variables is non-zero. Such $m$ variables are called basic variables and remaining $n$ zero-valued variables are called non-basic variables.
The number of basic solutions thus obtained will be at the most $\binom{m+n}{n}$.
### Basic Feasible Solution
A basic solution which also satisfies the non-negativity restrictions of the problem is called basic feasible solution.
### Degenerate Basic Feasible Solution
If one or more of the basic variables are zero then such a basic feasible solution is called Degenerate Basic Feasible Solution.
### Non-degenerate Basic Feasible Solution
If all the basic variables are strictly greater than zero, then such basic feasible solution is called Non-degenerate Basic Feasible Solution.
### Optimal Solution
A feasible solution which optimizes (maximizes or minimizes) the objective function of a linear programming problem is called an optimal solution (i.e., maximal solution or minimal solution) of the LPP.
## Endnote
In this tutorial you learn about characteristics of standard form of LPP, some important terms related to linear programming problem and how to convert LPP to its standard form by illustrated examples. | 2022-10-05 19:00:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8159481883049011, "perplexity": 386.06116611114277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337663.75/warc/CC-MAIN-20221005172112-20221005202112-00279.warc.gz"} |
http://timescalewiki.org/index.php?title=Rd-continuous_implies_regulated&oldid=1512 | # Rd-continuous implies regulated
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. If $f$ is continuous, then $f$ is regulated. | 2019-10-23 15:21:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9638391733169556, "perplexity": 3976.6301384534877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987834649.58/warc/CC-MAIN-20191023150047-20191023173547-00523.warc.gz"} |
https://www.nag.com/numeric/nl/nagdoc_26.2/nagdoc_fl26.2/adhtml/d01/d01rg_ad_f.html | # NAG AD Library Routine Document
## d01rg_a1w_f (dim1_fin_gonnet_vec_a1w)
Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. The method of codifying AD implementations in routine name and corresponding argument types is described in the NAG AD Library Introduction.
## 1Purpose
d01rg_a1w_f is the adjoint version of the primal routine d01rgf .
## 2Specification
Fortran Interface
Subroutine d01rg_a1w_f ( ad_handle, a, b, f, epsabs, epsrel, dinest, errest, nevals, iuser, ruser, ifail)
Integer, Intent (Inout) :: iuser(*), ifail Integer, Intent (Out) :: nevals Type (nagad_a1w_w_rtype), Intent (In) :: a, b, epsabs, epsrel Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: dinest, errest Type (c_ptr), Intent (In) :: ad_handle External :: f
Subroutine f ( ad_handle, x, nx, fv, iflag, iuser, ruser)
Integer, Intent (In) :: nx Integer, Intent (Inout) :: iflag, iuser(*) Type (nagad_a1w_w_rtype), Intent (Inout) :: x(nx), ruser(*), fv(nx) Type (c_ptr), Intent (In) :: ad_handle
## 3Description
d01rgf is a general purpose integrator which calculates an approximation to the integral of a function $f\left(x\right)$ over a finite interval $\left[a,b\right]$:
$I= ∫ab fx dx .$
The routine is suitable as a general purpose integrator, and can be used when the integrand has singularities and infinities. In particular, the routine can continue if the subroutine f explicitly returns a quiet or signalling NaN or a signed infinity. For further information see Section 3 in the documentation for d01rgf .
None.
## 5Arguments
d01rg_a1w_f provides access to all the arguments available in the primal routine. There are also additional arguments specific to AD. A tooltip popup for each argument can be found by hovering over the argument name in Section 2 and a summary of the arguments are provided below:
• ad_handle – a handle to the AD configuration data object, as created by x10aa_a1w_f.
• a$a$, the lower limit of integration.
• b$b$, the upper limit of integration.
• ff must return the value of the integrand $f$ at a set of points.
• epsabs – the absolute accuracy required.
• epsrel – the relative accuracy required.
• dinest – on exit: the estimate of the definite integral f.
• errest – on exit: the error estimate of the definite integral f.
• nevals – on exit: the total number of points at which the integrand, $f$, has been evaluated.
• iuser – may be used to pass information to user-supplied argument(s).
• ruser – may be used to pass information to user-supplied argument(s).
• ifail – on entry: ifail must be set to $\mathrm{0}$, $-\mathrm{1}\text{ or }\mathrm{1}$. on exit: ifail = 0 unless the routine detects an error or a warning has been flagged (see Section 6).
## 6Error Indicators and Warnings
d01rg_a1w_f preserves all error codes from d01rgf and in addition can return:
$\mathbf{ifail}=-89$
See Section 5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 5.1 in the NAG AD Library Introduction for further information.
Not applicable.
## 8Parallelism and Performance
d01rg_a1w_f is not threaded in any implementation. | 2021-06-13 21:47:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8213886022567749, "perplexity": 7935.166936530218}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487610841.7/warc/CC-MAIN-20210613192529-20210613222529-00177.warc.gz"} |
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https://mathoverflow.net/questions/144069/topological-properties-of-k-orbits-in-g-b/144075 | # Topological properties of $K$ orbits in $G/B$
I'll be working over the complex numbers. Let $G$ be a connected reductive group, $\theta\colon G\to G$ an involution. Let $K=G^{\theta}$ be the fixed point subgroup. I am trying to track down references for some facts about $K$-orbits on the flag variety $G/B$.
Added later: to clarify, $G$ is a complex algebraic group, $\theta$ is an automorphism of group schemes over $Spec(\mathbb{C})$ of order $\leq 2$.
Added later: Here are some standard examples. The nicest one is as follows. Let $H$ be a connected reductive group and take $G=H\times H$. Define $\theta\colon G\to G$ by $\theta(x,y) = (y,x)$. So the fixed point group is just isomorphic to the original $H$. The flag variety of $G$ is the 2-fold product of the flag variety of $H$ and we are looking at $H$ acting on this diagonally. From the equivariant geometry point of view this is the same' as looking at Borel (of $H$) orbits on the flag variety of $H$. Note that in this case my questions are rather trivial, since all the orbits are linear affine spaces (in particular, they are contractible).
For a more interesting example, take $G=SL_2(\mathbb{C})$. For $\theta$ take conjugation by the matrix $\left( \begin{matrix} 1 & 0 \\ 0& -1\end{matrix} \right)$. Then $K$ is the usual (algebraic) torus. The flag variety is $\mathbb{P}^1 = \mathbb{C}\sqcup{\infty}$, and $K$ acts on it by $\lambda\cdot x = \lambda^2x$. So 3 orbits $0$, $\infty$ and $\mathbb{C}^*$. The component group of $\mathbb{C}^*$ is $\mathbb{Z}/2\mathbb{Z}$. And as soon as I write this I see that I messed up a bit with my question 3) and 3') and need to fix it.
The reason to use the symbol $K$ and evoke images of maximal compacts is as follows: with the above setup there is a real form $G_{\mathbb{R}}$ of $G$ such that $K_{\mathbb{R}}= K\cap G_{\mathbb{R}}$ is a maximal compact of both $G_{\mathbb{R}}$ and $K$. Once again I do not know of a reference for this fact', but I haven't really thought about it (so this might be quite simple).
Question 1) I have seen it stated in several places (for instance in Lusztig and Vogan's paper `Singularities of closures of $K$-orbits on flag manifolds') that the component group $K_x/K_x^0$ for any $x\in G/B$ has exponent $2$. Does anyone know a precise reference for this fact? Or better, have some intuition/argument why this is at least morally true?
Question 2) If $G$ is semisimple and simply connected, then $K$ is connected. Again this is supposedly true, but I would love a reference/argument/intuition.
Question 3) Assume to be in the situation of 2) so that $K$ is connected. Is it possible to find a covering group $K_1$ of $K$ Does the action of $K$ always factor through another group $K_1$ such that the component group $(K_1)_x/(K_1)_x^0$ is connected for all $x\in G/B$, and $K_1$-orbits coincide with $K$-orbits. Note: I am not saying that this is true. Just wondering if it's possible. But I have no intuition for this. The motivation for this is that I would like to untwist monodromy occuring in $K$-equivariant local systems by working with $K_1$ instead.
Question 3') Instead of $K$-orbits on $G/B$, I can instead work with $B$-orbits on $G/K$ (these have the benefit of being connected without any additional assumptions on $G$). Same sort of question as 3). Is it possible to find a covering group of $B$ Does the action of $B$ factor through a $B_1$ such that the component groups of the $B_1$-action at all points of $G/K$ are trivial, and the $B_1$-orbits coincide with $B$-orbits?
Yep, my knowledge of groups is weak!
• Do you assume some special hypothesis on the involution $\theta$ implying that $K$ is a maximal compact subgroup? – YCor Oct 6 '13 at 0:33
• @YvesCornulier: No additional hypothesis on $\theta$. But I am happy even with partial answers with additional hypothesis. My understanding is rather minimal at the moment, so anything would help! – Reladenine Vakalwe Oct 6 '13 at 0:36
• I'm not sure what do you mean by "$K$-orbits" here. If $G$ is complex semisimple and $K$ is the maximal compact subgroup, it is well-known that the $K$-action on $G/B$ is also transitive, hence the $K$-orbit is $G/B$ itself. Maybe what you really mean is the isotropy group of the $K$-action. – Zhaoting Wei Oct 6 '13 at 2:36
• But well, what is assumed on $\theta$? continuous/holomorphic/antiholomorphic involutive automorphism? – YCor Oct 6 '13 at 7:31
• @YvesCornulier: I have clarified in the question. Sorry for causing any confusion. I had assumed that since I was working with algebraic groups over $\mathbb{C}$, involution would automatically be understood to be in this category. – Reladenine Vakalwe Oct 6 '13 at 13:33
1. If $\theta$ is an involution of a complex linear algebraic group $G$ and if $K=G^\theta$ is its fixed-point set, then $K/K^0$ will always have exponent 2. This follows from a generalized "Cartan decomposition". The argument goes as follows. Let $\mathfrak p$ denote the (-1)-eigenspace of $d\theta$ on $\mathfrak g$. Then, morally at least, we ought to be able to express everything in $K$ as $k=k_0\exp X$, with $k_0 \in K^0$ and $X \in \mathfrak p$. But then $k^{-1} = (k_0\exp X)^{-1} = \exp(-X) k_0^{-1} = k' \exp(-X)$, for some $k' \in K^0$ (as $K^0$ is normal in $K$). On the other hand, $\exp(-X) = \exp(d\theta(X)) = \theta(\exp X) = \exp X$. Consequently, $k = k^{-1}$ in $K/K^0$, as desired. I've glossed over some details, which you can find in Loos, Symmetric Spaces, vol. 1, Benjamin (1969).
2. This follows from Theorem 8.1 in Steinberg, Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc. 80 (1968). An older reference---for compact Lie groups, at least---is Theorem 3.4 in Borel, Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes, Tôhoku Math. J. 13 (1961), 216–240.
For your question 2, the reason is in fact we can prove $$K\times \mathfrak{p}\xrightarrow{\sim} G\\ (k,p)\mapsto k\exp(p)$$ is an diffeomorphism. Here $\mathfrak{p}$ is the $-1$ eigen space of the involution $\theta$ on the Lie algebra $\mathfrak{g}$. Therefore $K$ is homotopic to $G$, hence connected.
You can see Section I.1 and I.2 of A. Knapp's book "Representation theory of Semisimple Groups".
By the way, I think there should be certain conditions on your involution $\theta$.
• I seem to have caused some confusion. I am working with algebraic groups over $\mathbb{C}$. The involution $\theta$ is a morphism of varieties. The subgroup $K$ is not a maximal compact. – Reladenine Vakalwe Oct 6 '13 at 13:26
From the top of my head: This has been studied in the more general context of connected linear reductive $k$-groups, for $k$ any field not in characteristic 2, in Helminck & Wang, On rationality properties of involutions of reductive groups, Adv. in Math. 99 (1993), 26-97 (freely available PDF version here).
But of course the case $k=\mathbb{C}$ (and also $k=\mathbb{R}$) has been well-known and studied long before, so this reference is certainly far from being "optimal". But then it also contains references to lots of previous work, which you can find by skimming its introduction, so it might still help you as a starting point for tracking down other / more / better references. Well, or perhaps somebody will just write up proofs and / or give better references... (in particular, somebody who is not in a hurry due to departing on a trip :-).
• The paper you mention has all sorts of interesting goodies, but from a quick skimming it doesn't seem to contain the sort of topological information I am after. It's a helpful starting point though. Thanks! – Reladenine Vakalwe Oct 6 '13 at 15:46
This is really a comment, but I want to have tex available. Perhaps this can clear up some of the confusion about involutions, and complex versus compact groups.
If $\theta$ is an arbitrary algebraic (i.e. holomorphic) involution of $G(\mathbb C)$ then $K(\mathbb C)=G(\mathbb C)^\theta$ is a complex, hence noncompact, reductive group. However there is a unique real form $G(\mathbb R)$ of $G(\mathbb C)$ so that $\theta$ normalizes $G(\mathbb R)$, and $K(\mathbb R)=G(\mathbb R)^{\theta}$ is compact. This is Cartan's classification of real groups in terms of their maximal compact subgroups., and accounts for some of the back and forth in the comments about complex versus compact groups.
For example the algebraic involution $\theta(g)={}^tg^{-1}$ of $GL(n,\mathbb C)$ has fixed points $O(n,\mathbb C)$. This is the complexification of $O(n)=GL(n,\mathbb R)^\theta$ - the maximal compact subgroup of $GL(n,\mathbb R)$. | 2019-12-11 00:08:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8923458456993103, "perplexity": 154.59532606857766}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540529516.84/warc/CC-MAIN-20191210233444-20191211021444-00069.warc.gz"} |
https://www.educative.io/answers/what-is-the-priorityqueuesize-method-in-java | Related Tags
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# What is the PriorityQueue.size() method in Java?
Harsh Jain
Ace your System Design Interview and take your career to the next level. Learn to handle the design of applications like Netflix, Quora, Facebook, Uber, and many more in a 45-min interview. Learn the RESHADED framework for architecting web-scale applications by determining requirements, constraints, and assumptions before diving into a step-by-step design process.
In this shot, we will learn how to use the PriorityQueue.size() method in Java.
### Introduction
The PriorityQueue.size() method obtains the number of elements present in the PriorityQueue.
The PriorityQueue.size() method is present in the PriorityQueue class inside the java.util package.
### Syntax
The syntax of the PriorityQueue.size() function is given below:
public int size();
### Parameters
The PriorityQueue.size() method does not accept any parameters.
### Return value
The PriorityQueue.size() method returns an integer value that denotes the number of elements in the PriorityQueue.
### Code
Let us have a look at the code below.
import java.util.*;class Main { public static void main(String[] args) { PriorityQueue<Integer> pq = new PriorityQueue<Integer>(); System.out.println("Number of elements in the priority queue are: " + pq.size()); pq.add(2); pq.add(28); pq.add(6); pq.add(80); pq.add(28); pq.add(7); pq.add(15); System.out.println("Number of elements in the priority queue are: "+pq.size()); }}
Using the PriorityQueue.size() method in Java
### Explanation
• In line 1, we import the required package.
• In line 2, we make a Main class.
• In line 4, we make a main() function.
• In line 6, we declare a PriorityQueue that consists of Integer type elements.
• In line 8, we print the current number of elements in the priority queue. Here, the output comes to $0$.
• From lines 10 to 16, we use the PriorityQueue.add() method to insert the elements in the PriorityQueue.
• In line 18, we use the PriorityQueue.size() method to display the number of elements present in the PriorityQueue.
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CONTRIBUTOR
Harsh Jain | 2022-10-01 04:09:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18394462764263153, "perplexity": 3729.1753505624247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335530.56/warc/CC-MAIN-20221001035148-20221001065148-00153.warc.gz"} |
https://proxieslive.com/how-can-one-measure-the-time-dependency-of-an-rnn/ | # How can one measure the time dependency of an RNN?
Most of the discussion about RNN and LSTM alludes to the varying ability of different RNNs to capture "long term dependency". However, most demonstrations use generated text to show the absence of long term dependency for vanilla RNN.
Is there any way to explicitly measure the term dependency of a given trained RNN, much like ACF and PACF of a given ARMA time series?
I am currently trying to look at the (Frobenius norm of) gradients of memories $$s_k$$ against inputs $$x_k$$, summed over training examples $$\{x^i\}_{i=1}^N$$$$\sum_{i=1}^N \big\|\frac{\partial s_k}{\partial x_k}(x^i)\big\|_F$$. I would like to know if there are more refined or widely-used alternatives.
Thank you very much! | 2020-09-27 16:15:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4202863276004791, "perplexity": 1220.6241080290552}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400283990.75/warc/CC-MAIN-20200927152349-20200927182349-00777.warc.gz"} |
https://newproxylists.com/nt-number-theory-continuing-an-analytic-continuation-of-the-dirichlet-eta-function/ | # nt.number theory – Continuing an analytic continuation of the Dirichlet \$eta\$-function?
The Dirichlet $$eta$$-function is defined as:
$$eta(s) = sum_{n=1}^infty frac{(-1)^{n+1}}{n^s} qquad Re(s) > 0$$
and has the full analytical continuation:
$$eta(s) = sum_{n=1}^N frac{(-1)^{n+1}}{n^s} + frac{(-1)^N}{2} int_{-infty}^{infty} frac{(N+1/2 +ix)^{-s}}{cosh(pi x)},dx qquad s in mathbb{C} tag{1}$$
valid for all integers $$N ge 0$$.
Wondered what would happen for negative $$N$$ and found numerically that:
$$eta(s) = sum_{n=1}^{-N-1} frac{(-1)^{n+1}}{n^s} + (-1)^{s+1},frac{(-1)^N}{2} int_{-infty}^{infty} frac{(N+1/2 +ix)^{-s}}{cosh(pi x)},dxqquad s in mathbb{Z} tag{2}$$
valid for all integers $$N < 0$$.
Note: assume the sums to be zero when their end values are $$< 1$$.
Question:
Is there a way to also expand equation (2) to $$s in mathbb{C}$$? If possible, I believe this would require some smart continuation of the $$(-1)^{s+1}$$ factor. Experimented with functions like $$cosleft(pi(s+1)right)$$, but no success yet. | 2021-02-26 12:32:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7105201482772827, "perplexity": 222.91464789666193}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357641.32/warc/CC-MAIN-20210226115116-20210226145116-00234.warc.gz"} |
https://www.sawaal.com/problems-on-trains-questions-and-answers/a-train-of-length-110-meter-is-running-at-a-speed-of-60-kmph-in-what-time-it-will-pass-a-man-who-is-_1653 | 84
Q:
# A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A) 10 B) 8 C) 6 D) 4
Explanation:
Distance = 110 m
Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= (66*5/18) m/sec = 55/3 m/sec
$\inline \fn_jvn \therefore$Time taken to pass the man = (100*3/55) = 6 s
Q:
The two trains leave Varanasi for Lucknow at 11:00 a.m. and at 11:30 a.m., respectively and travel at a speed of 110 km/h and 140 km/h, respectively. How many kilometers from Varanasi will both trains meet?
A) 255 1/3 km B) 238 2/3 km C) 246 1/3 km D) 256 2/3 km
Explanation:
0 118
Q:
The speed of a train is 72 km/hr and its length is 200 meters. What will be the time (in minutes) taken by the train to cross a pole?
A) 1/6 B) 3/5 C) 5 D) 10
Explanation:
0 190
Q:
Two stations L and M are 180 km apart from each other. A train leaves from L to M and simultaneously another train leaves from M to L. Both trains meet after 9 hours. If the speed of the first train is 10 km/hr more than the second train, then what is the speed (in km/hr) of the slower train?
A) 9 B) 5 C) 12 D) 15
Explanation:
0 200
Q:
X and Y are two stations which are 280 km apart. A train starts at a certain time from X and travels towards Y at 60 km/h. After 2 hours, another train starts from Y and travels towards X at 20 km/h. After how many hours does the train leaving from X meets the train which left from Y?
A) 2 hours B) 6 hours C) 3 hours D) 4 hours
Explanation:
1 173
Q:
A train travelling at constant speed crosses two persons walking in the same direction in 8 seconds and 8.4 seconds respectively. The first person was walking at the speed of 4.5 km/hr while the second was walking at the speed of 6 km/hr. What was the speed of the train in km/hr?
A) 42 B) 40 C) 32 D) 36
Explanation:
0 228
Q:
Train X travelling at 60 km/h overtakes another train Y, 225 m long, and completely passes it in 72 seconds. If the trains had been going in opposite directions, they would have passed each other in 18 seconds. The length (in m) of X and the speed (in km/h) of Y are, respectively:
A) 245 and 54 B) 255 and 40 C) 255 and 36 D) 245 and 45
Explanation:
0 281
Q:
A train moving with a uniform speed covers 338 m in 50 s. What is its speed?
A) 5.76 m/s B) 7.76 m/s C) 6.76 m/s D) 4.76 m/s
Explanation:
0 287
Q:
A train travelling at constant speed crosses two persons walking in the same direction in 4 seconds and 4.2 seconds, respectively. The first person was walking at the speed of 4.5 kmph while the second was walking at the speed of 6 kmph. What was the speed of the train in kmph?
A) 42 B) 36 C) 40 D) 32 | 2021-06-22 13:07:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.621189534664154, "perplexity": 818.1295905232698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488517820.68/warc/CC-MAIN-20210622124548-20210622154548-00510.warc.gz"} |
https://bornagainproject.org/git-main/py/sample/materials/ | ## Materials
The refractive properties of a homogeneous Material can be specified through two different functions:
• RefractiveMaterial, based on the refractive index,
• MaterialBySLD, based on the scattering length density (SLD).
RefractiveMaterial is equally suitable for X-rays or neutrons. However, it does not account for the wave-length dependence of the refractive index. This leads to incorrect results if there is too much spread in the incoming wavelength, as is regularly the case in neutron time-of-flight experiments.
MaterialBySLD is intended for neutron experiments with significant wavelength spread. Refractive indices as function of wavelength are computed internally from constant SLDs.
### Material by refractive index
A Material can be created through
magnetization = ba.kvector_t(1.0, 0.0, 0.0)
<material> = ba.RefractiveMaterial("name", delta, beta, magnetization)
where name is the arbitrary name of the material associated with its complex refractive index $n = 1 - \delta + i\beta$. The magnetization argument is a 3D vector (in A/m). The return value <material> is later used when referring to this particular material.
magnetization can be omitted in material construction. It is assumed to be zero then:
<material> = ba.RefractiveMaterial("name", delta, beta)
### Material by scattering length density
A Material can also be created through
<material> = ba.MaterialBySLD("name", sld_real, sld_imag, magnetization)
or, omitting magnetization again,
<material> = ba.MaterialBySLD("name", sld_real, sld_imag)
Here sld_real and sld_imag are the real and imaginary parts of the material scattering length density (SLD) according to the following convention:
$$SLD = sld_{real} - i \cdot sld_{imag}$$
SLD values for a wide variety of materials can be calculated with numerous online SLD-calculators, e.g. these ones:
The first of these returns values in inverse square angstroms, which are also the input units for MaterialBySLD. Thus the SLD values found with the calculator can be directly copied and pasted into a BornAgain script.
### Default = Vacuum
Both RefractiveMaterial and MaterialBySLD can be created with empty constructors:
<material> = ba.RefractiveMaterial()
<material2> = ba.MaterialBySLD()
In this case the “default” material is created, i.e. a material with the name vacuum, zero SLD/refractive index and zero magnetization. | 2022-09-26 00:01:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7651837468147278, "perplexity": 2935.3615961727355}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334620.49/warc/CC-MAIN-20220925225000-20220926015000-00246.warc.gz"} |
http://clay6.com/qa/24148/the-sum-of-n-terms-of-two-aps-is-in-the-ratio-5n-1-4n-10-find-the-ratio-of- | # The sum of n terms of two APs is in the ratio$\; 5n + 1: 4n+10$. Find the ratio of their $\;5^{th}$ terms.
$(a)\;\frac{47}{39}\qquad(b)\;1\qquad(c)\;\frac{6}{30}\qquad(d)\;\frac{5}{4}$
Explanation : $\frac{S_{1}}{S_{2}}=\frac{n/2\;[2a_{1}+(n-1)d_{1}]}{n/2\;[2a_{2}+(n-1)d_{2}]}$
$\frac{S_{1}}{S_{2}}=\frac{\;[2a_{1}+\frac{(n-1)}{2}d_{1}]}{\;[2a_{2}+\frac{(n-1)}{2}d_{2}]}=\frac{5n+1}{4n+10}$
For the ratio of the $\;5^{th}\;$ term , $\;\frac{a_{1}+4d_{1}}{a_{2}+4d_{2}}$
Let $\;\frac{n-1}{2}=4\quad\;then\;n=8+1=9$
Replacing the value of n in the ratio ,
$\frac{5*9+1}{4*9+10}=\frac{47}{47}=1.$ | 2017-12-14 17:13:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9467330574989319, "perplexity": 412.35545054197695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948545526.42/warc/CC-MAIN-20171214163759-20171214183759-00134.warc.gz"} |
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# At a fast food restaurant, Anas normally works 6.25 hours per day and
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At a fast food restaurant, Anas normally works 6.25 hours per day and [#permalink]
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Question Stats:
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At a fast food restaurant, Anas normally works 6.25 hours per day and earns $5.60 per hour. For each hour he works in excess of 6.25 hours on a given day, he is paid 1.25 times his regular rate. If Anas works 10.25 hours on a given day, how much does he earn for that day? A.$72
B. $63 C.$54
D. $48 E.$35
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Re: At a fast food restaurant, Anas normally works 6.25 hours per day and [#permalink]
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28 Sep 2017, 01:49
At a fast food restaurant, Anas normally works 6.25 hours per day and earns $5.60 per hour. For each hour he works in excess of 6.25 hours on a given day, he is paid 1.25 times his regular rate. If Anas works 10.25 hours on a given day, how much does he earn for that day? work = 6.25 hours salary per hour =$5.60
Total salary earned = 6.25 * 5.60 = 35
For each extra hour, rate = 1.25 * 5.60 = 7
Now total hours works = 10.25 = 6.25 + 4
So got salary at rate of 5.60/hour for initial 6.25 hours and at rate of 7/hour for last 4 hours.
Total salary = (6.25*5.6) +(4*7) = 35+28 = $63 Answer: B SC Moderator Joined: 22 May 2016 Posts: 1831 At a fast food restaurant, Anas normally works 6.25 hours per day and [#permalink] ### Show Tags 28 Sep 2017, 12:30 Bunuel wrote: At a fast food restaurant, Anas normally works 6.25 hours per day and earns$5.60 per hour. For each hour he works in excess of 6.25 hours on a given day, he is paid 1.25 times his regular rate. If Anas works 10.25 hours on a given day, how much does he earn for that day?
A. $72 B.$63
C. $54 D.$48
E. $35 Changing every decimal into a fraction makes arithmetic easier. Factors cancel. Regular hours for a workday = 6.25 hrs = $$6\frac{1}{4} = \frac{25}{4}$$ hours Regular pay:$5.60 per hr =
$$5\frac{3}{5} = \frac{28}{5}$$ per hour
Overtime: working > 6.25 hrs
Overtime rate of pay:
1.25 times regular rate =
$$1\frac{1}{4} = \frac{5}{4} * \frac{28}{5} = \frac{28}{4} = 7$$ per hour
If Anas works 10.25 hours, how much does he earn for that day?
Extra hours worked: 10.25 - 6.25 =
4 extra hours
Earnings for extra hrs=
(Overtime rate) * (# of hours)
$$(\frac{7}{hr}) * (4 hrs) = 28$$
Earnings for regular hours =
(Regular rate) * (Regular # of hrs)
$$\frac{28}{5hrs} * \frac{25}{4}hrs = 35$$
TOTAL earnings: $28 +$35 = $63 ANSWER B _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2679 Re: At a fast food restaurant, Anas normally works 6.25 hours per day and [#permalink] ### Show Tags 03 Oct 2017, 10:04 Bunuel wrote: At a fast food restaurant, Anas normally works 6.25 hours per day and earns$5.60 per hour. For each hour he works in excess of 6.25 hours on a given day, he is paid 1.25 times his regular rate. If Anas works 10.25 hours on a given day, how much does he earn for that day?
A. $72 B.$63
C. $54 D.$48
E. $35 Anas’ regular rate is$5.60 and his overtime rate is (1.25)(5.60), or \$7. We can create the following equation:
6.25(5.6) + 4(1.25 x 5.6)
35 + 4(7) = 35 + 28 = 63
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Re: At a fast food restaurant, Anas normally works 6.25 hours per day and &nbs [#permalink] 03 Oct 2017, 10:04
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Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2018-07-20 03:16:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.536512553691864, "perplexity": 11876.758776860686}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591481.75/warc/CC-MAIN-20180720022026-20180720042026-00287.warc.gz"} |
https://crypto.stackexchange.com/questions/34884/length-of-encryption-password-aes-256-cbc/58072 | # Length of encryption password aes-256-cbc
I'm encrypting a file with sensitive information with
cat secret | openssl aes-256-cbc -a -salt > secret.enc
I am choosing a random encryption password with openssl rand -base64 32 | head -c [password-length]
Is there any standard, how long it should be? Given the password length, how long would it take to crack and view the contents of the file?
Edit: I found this picture, which pretty much answers my question. Is it reliable?
• given the wording of the question, it appears you have a misunderstanding of how all this stuff works. AES-256 uses a 256-bit key, thats where the 256 comes from, and if you are choosing a random key, there is no password – Richie Frame Apr 27 '16 at 10:56
• @RichieFrame Sorry, mixed up key and password. I think I found the answer in the link. – user1506145 Apr 27 '16 at 11:57
Suppose you use 128 characters out of an alphabet (this is a large alphabet). To create a key you'd need about 37 fully random characters to create an AES key of 256 bit strength. Even you would create such a password, you'd have trouble encoding it over the required number of bits. You could either use a 44 character base 64 string or 64 character hex string as well - at least those would be easy to decode/encode to/from bytes. In general, people don't use those kind of passwords.
This is why password based key derivation functions such as bcrypt or PBKDF2 are being used. These strengthen the password using salt and a work factor (or iteration count for PBKDF2). Although still less then perfect, they allow you to use passwords relatively securely.
In general you should look up Password Based Encryption or PBE. This is for instance specified in the PKCS#5 standards (which defines PBKDF2).
The default OpenSSL implementation uses a scheme called EVP_BytesToKey. It uses an 8 byte salt and an "iteration count" set to 1. Due to the non-existent work factor you are best off specifying all 37 characters if you want to achieve such high level security.
In the end you're better off using e.g. PGP public / private key encryption. 128 bits of security is usually sufficient; the chance that your password is compromised is much larger than that anybody with a quantum computer tries to hack your file.
AES supports three key lengths. They are 128, 192 and 256 bits long. You chose to use the 256 bit algorithm that operates in CBC mode. It's a correct choice.
Now all you need is:
• key - 256 bits long
• initialization vector - 128 bits long
You can generate them using the command I found here:
openssl enc -aes-256-cbc -k secret -P -md sha1
I suggest not using a truly random key and IV, because you have to save them somewhere, and adversary can just read it from your hard drive. It's much better to use a long and complicated password that he has to read from a post-it-note glued to your monitor, and derive the key and IV from it.
As for security, let me put it this way. If I wanted to crack 256 bits long key and 128 bit long IV on my work laptop, I would probably be around a fifth of way done when the universe would collapse. It's much simpler to use rubber-hose cryptanalysis in this case.
EDIT:
Just for you to know you shouldn't use password as a key directly. You need to derive a key from a password. The command I pasted does exactly that. About the security of the password you already answered yourself. 9 characters is the absolute minimum (if there is at least one uppercase letter, one lowercase letter, one number and one symbol). But I strongly suggest using a passphrase instead of a password. They are vulnerable to dictionary hacking, but if you use enough words a dictionary hack also takes years to complete.
There are over a milion words in the English language.
If we use only lowercase letters in our four word passphrase, the dictionary hack has to do in the worst case $1000000^{4} = 10^{24}$ searches. In comparison, there are around 100 characters on the keyboard. A password of 12 of those characters will be cracked in less than $100^{12} = 10^{24}$ searches.
This mean that "singing retracted eleventh elephant" is an equivalent of a 12 character password, and also it's much easier to remember. And if we use a comma somewhere, uppercase letter, or use a word from a different language it gets much safer.
• Sorry @Filip Frank, I think I mixed up password and key. I ment the password length, how long would it take given a truly random password. I think I found it in the link, but would be great with some calculations as well. – user1506145 Apr 27 '16 at 12:01
• @user1506145 If the password is on a frequently used password list: not long enough. – zaph Apr 5 '18 at 15:32
• @FilipFranik The IV should be random and does not need to be secret so a common method is to prefix the encrypted data with the IV. – zaph Apr 5 '18 at 15:34
A collection of passwords and passphrases with a total of 100 characters results in a search space of 5.98 x 10^197. By comparison, there are roughly 10^80 atoms in the known universe.
If you want to super-secure your encrypted files, encrypt them first with Blowfish 448, then again with AES-256, both times using a different random password combined with a different long passphrase.
By encrypting it first with Blowfish, you're also randomizing the data, which makes even correctly decrypted AES-256 files appear as if they're still encrypted. Thus, no program or human can tell if a password guess was decrypted or not.
In this sense, you don't need a super-strong password for the Blowfish layer. A simple passphrase like "There ain't always nothing about Makia ain't what I swimmmingly done know." provides more than enough "security" for this randomizing layer. That's a keyspace of 6.06 x 10^142 in and of itself. Combined, you're looking at a level of complication on the order of 10^340.
In summary:
1. Encrypt with Blowfish 448 using a relatively simple passphrase mixed with a random password.
2. Encrypt with AES-256 using a different relatively simple passphrase mixed with a different random password.
1. Ensure that neither passphrases nor passwords will ever appear in any dictionary or body of literary work.
• No only is this questionable advice, but most of it has nothing to do with the question. – otus Apr 4 '18 at 4:35
• Also, your scheme is vulnerable to a MITM-attack allowing to find the keys using $2^{448}+2^{256}$ operations instead of the desired $2^{448} \cdot 2^{256}$ operations. – VincBreaker Apr 4 '18 at 9:44
• @VincBreaker True, but I would not like to buy the hardware for that :P, besides CPU it would also require a "few bits" of memory. – Maarten Bodewes Apr 4 '18 at 14:08
• My take is that Mugs is just trolling and knows full well that the answer is ridiculous. Note Mugs is a new user ID. – zaph Apr 5 '18 at 15:42 | 2020-08-12 10:11:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24856705963611603, "perplexity": 1554.1713479851778}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738888.13/warc/CC-MAIN-20200812083025-20200812113025-00482.warc.gz"} |
https://tardigrade.app/question/5yjkbnuw | # Q. The charge deposited on 4 $\mu$F capacitor in the circuit is
KCET KCET 2009Electrostatic Potential And Capacitance
Solution:
## $6 \mu$ F and 6 $\mu$ F are in series $\therefore$ Voltage ascross 4 $\mu$F = 6 V $\therefore$ Q $= 6\times 4 \times 10^{-6}$ $= 24 \times 10^{-6}$ C
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KCET 2019 Semiconductor Electronics: Materials Devices And Simple Circuits | 2020-08-07 18:19:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.365325927734375, "perplexity": 3925.0192678486387}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737206.16/warc/CC-MAIN-20200807172851-20200807202851-00085.warc.gz"} |
http://www.micans.org/zoem/doc/zoem.html | 15 Jun 2011 zoem 11-166
## NAME
zoem — macro processor for the Zoem macro/programming language.
## SYNOPSIS
zoem
(enter interactive mode - happens when none of -i, -I, -o is given)
## DESCRIPTION
Zoem is a macro/programming language. It is fully described in the Zoem User Manual , currently available in HTML only. This manual page documents the zoem processor, not the zoem language.
If the input file is specified using the -i option and is a regular file (i.e. not STDIN - which is specified by using a single hyphen), it must have the extension .azm. This extension can but need not be specified. The zoem key \__fnbase__ will be set to the file base name stripped of the .azm extension and any leading path components. If the input file is specified using the -I option, no extension is assumed, and \__fnbase__ is set to the file base name, period. The file base name is the file name with any leading path components stripped away.
If neither -i nor -o is specified, zoem enters interactive mode. Zoem should fully recover from any error it encounters in the input. If you find an exception to this rule, consider filing a bug report. In interactive mode, zoem start interpreting once it encounters a line containing a single dot. Zoem's input behaviour can be modified by setting the key \__parmode__. See the section SESSION MACROS for the details. In interactive mode, zoem does not preprocess the interactive input, implying that it does not accept inline files and it does not recognize comments. Both types of sequence will generate syntax errors. Finally, readline editing and history retrieval can be used in interactive mode provided that they are available on the system. This means that the input lines can be retrieved, edited, and discarded with a wide range of cursor positioning and text manipulation commands.
From within the entry file and included files it is possible to open and write to arbitrary files using the \write#3 primitive. Arbitrary files can be read in various modes using the \dofile#2 macro (providing four different modes with respect to file existence and output), \finsert#1, and \zinsert#1. Zoem will write the default output to a single file, the name of which is either specified by the -o option, or constructed as described below. Zoem can split the default output among multiple files. This is governed from within the input files by issuing \writeto#1 calls. Refer to the --split option and the Zoem User Manual.
If none of -i or -o is given, then zoem will enter interactive mode. In this mode, zoem interprets by default chunks of text that are ended by a single dot on a line of its own. This can be useful for testing or debugging. In interactive mode, zoem should recover from any failure it encounters. Interactive mode can also be accessed from within a file by issuing \zinsert{stdia}, and it can be triggered as the mode to enter should an error occur (by adding the -x option to the command line).
If -o is given and -i is not, zoem reads input from STDIN.
If -i is given and -o is not, zoem will construct an output file name as follows. If the -d option was used with argument <dev>, zoem will write to the file which results from expanding \__fnbase__.<dev>. Otherwise, zoem writes to (the expansion of) \__fnbase__.ozm.
For -i and -o, the argument - is interpreted as respectively stdin and stdout.
## OPTIONS
-i <file name>[.azm] (entry file name)
Specify the entry file name. The file must have the .azm extension, but it need not be specified.
-I <file name>[.azm] (entry file name)
Specify the entry file name, without restrictions on the file name.
-o <file name> (output file name)
Specify the output file name.
-d <device> (set key \__device__)
Set the key \__device__ to <device>.
-x (enter interactive mode on error)
The afterlife option. If zoem encounters an error during regular processing, it will emit error messages as usual, and then enter interactive mode. This allows you e.g. to inspect the values of keys used or defined within the problematic area.
-s <key>[=<val>] (set key to val)
Set the key \key to val if present, 1 otherwise. Any type of key can be set, including keys taking arguments and keys surrounded in quotes. Beware of the shell's quote and backslash interpolation. Currently val is not evaluated, so appending or prepending to a key is not possible.
-e <any> (evaluate any, exit)
This causes zoem to evaluate <any>, write any result text to stdout, and exit.
-E <any> (evaluate any, proceed)
This causes zoem to evaluate <any>, write any result text to stdout, and proceed e.g. with the entry file or an interactive session.
-chunk-size <num> (process chunks of size num)
Zoem reads its input in chunks. It fully processes a chunk before moving on with the next one. This option defines the (minimum) size of the chunks. The size or count of the chunks does not at all affect zoem's output. The default minimum chunk size equals one megabyte.
Zoem will read files in their entirety before further processsing if -chunk-size 0 is specified.
Zoem does not chunk input files arbitrarily. It will append to a chunk until it is in the outermost scope (not contained within any block) and the chunk will end with a line that was fully read.
Consequently, if e.g. a file contains a block (delimited by balanced curlies) spanning the entire file then zoem is forced to read it in its entirety.
--trace (trace mode, default)
Trace in default mode.
--trace-all-long (long trace mode)
Sets on most trace options in long mode. Trace options xxx not set have their own --trace-xxx entry (see below).
--trace-all-short (short trace mode)
Sets on most trace options in short mode. Trace options xxx not set have their own --trace-xxx entry (see below).
--trace-keys (trace keys)
Trace keys.
--trace-regex (trace regexes)
Trace regexes (i.e. the \inspect#4 primitive).
-trace k (trace mode, explicit)
Set trace options by adding their representing bits.
--stress-write (stress test using write)
This makes \write#3 recover from errors. It is a special purpose option used for creating zoem stress test suites, such as stress.azm in the zoem distribution /examples subdirectory.
--unsafe (prompt for \system#3)
--unsafe-silent (simply allow \system#3)
-allow cmd1[:cmdx]+ (allowable commands)
With --unsafe system calls are allowed but the user is prompted for each invocation. The command and its arguments (if any) are shown, but the STDIN information (if any) is withheld. With --unsafe-silent system calls are allowed and the user is never prompted.
Use -allow str or --allow=str to specify a list of allowable commands, as a string in which the commands are separated by colons.
--system-honor (require \system#3 to succeed)
With this option any \system#3 failure (for whatever reason, including safe behaviour) is regarded as a zoem failure. By default, failing system calls are ignored under either safe mode, unsafe mode (--unsafe), or silent unsafe mode (--unsafe-silent).
--split (assume split output)
This assumes zoem input that allows output to multiple files (e.g. chapters). It sets the default output stream to stdout (anticipating custom output redirection with \writeto#1) and sets the session macro \__split__ to 1.
--stats (show symbol table stats after run)
Show symbol table chacteristics. Symbol tables are maintained as hashes.
-tl k (set tab length)
Set the tab length. HTML output can be indented according to nesting structure, using tabs which are expanded to simple spaces. By default, the tab length is zero, meaning that no indent is shown. The maximum value the tab length can be set to is four.
-nsegment k (level of macro nesting allowed)
-nstack k (stack count)
-nuser k (user dictionary stack size)
-nenv k (environment dictionary stack size)
-buser k (initial user dict capacity)
-bzoem k (initial zoem dict capacity)
Probably needed only if you have some obscure and extreme use for zoem. The segment limit applies to simple nesting of macros. The stack limit applies to nesting of macros that evaluate an argument before use. Each such evaluation creates a new stack. The user limit applies to \push{user}, the env limit applies to the nesting level of environments (started with \begin#2). The user dict capacity pertains to the initial number of buckets allocated for user and environment dictionaries, and the zoem dict capacity pertains to the dictionary containing the zoem primitives.
-l <str> (list items)
List items identified by <str>. It can be any of all, filter. legend, builtin, session, trace, or zoem, Multiple identifiers can be joined in a string, e.g. -l legendzoem prints a legend followed by a listing of zoem primitives.
-h (show options)
Show short synopsis of options.
## SESSION MACROS
\__parmode__
This macro affects zoem's read behaviour in interactive mode. It can be set on the command line using the -s option. Bits that can be set:
1 chomp newlines (remove the newline character) 2 skip empty newlines 4 read paragraphs (an empty line triggers input read) 8 newlines can be escaped using a backslash 16 read large paragraphs (a single dot on a line triggers input read)
\__device__
The current output device, set by the command line option -d. The man and faq packages support html and roff as its values.
\__fnbase__
The base name of the input file name. Leading path components are stripped away. If the -i option is used the input file is required to have the .azm suffix. In that case the suffix is also stripped to obtain the base name.
\__fnentry__
The name of the entry file.
\__fnin__
The file currently being processed.
\__fnout__
The name of the default output file.
\__fnpath__
The leading component of the input file name, possibly empty.
\__fnup__
The file that included the current file, if applicable.
\__fnwrite__
This key is set by \write#3 to its first argument. It can be used by macros that are expanded during evaluation of the third argument. Possible usage is to branch on the name of the write output stream. For example a file called index.html may be treated differently from other files. The key is deleted afterwards. Nested invocations of \write#3 may corrupt the status of this key.
\__ia__
The input/output separator used in interactive mode.
\__line__
The line number in the file currently being processed. This number will be correct for any invocation outside the scope of a macro. For any invocation within a macro the result will be the line number of the closing curly of the outermost containing macro. The following
\__line__ \__line__ \__line__ \group{ \__line__ \group{\__line__} \__line__}
Results in
1 2 3 7 7 7
\__searchpath__
A vararg containing a list of paths to search when a file is to be included/imported/read/loaded. When you start zoem, this key should contain the location of the man.zmm and faq.zmm package files. It is advisable not to overwrite this key but to append to it instead.
\__zoemstat__
Set to one of ok, towel (that one is a bit lame), or error by either the interpreter, an occurrence of \catch#2, or \try#1.
\__zoemput__
Set by \try#1 to the possibly truncated result of processing its argument.
\__lc__
Expands to a left curly. It is hard to find a need for this — the zoem stress suite uses it to generate a particular syntax error at a deeper interpretation level.
\__rc__
Expands to a right curly.
## THE SET MODIFIERS
The \set#3 primitive allows a {modes}{<modifiers>} directive in its first argument. Here <modifiers> can be a combination of single-letter modifiers, each described below.
a
append to the key, do not overwrite, create if not existing.
c
conditionally; only set if not already defined.
e
existing; update existing key, possibly in lower dictionary.
g
global; set in the global (bottom) user dictionary.
u
unary; do not interpret vararg in <any> as key-value list (data keys only)
v
vararg; interpret vararg in <any> as key-value list (regular keys only).
w
warn if key exists (like \def#2 and \defx#2).
x
expand argument (like \setx#2 and \defx#2).
## THE INSPECT SUBLANGUAGE
The \inspect#4 primitive takes four arguments. The languages accepted by the first two arguments are described below. The third argument is a replacement string or a replacement macro accepting back-references (supplied as an anonymous macro). The fourth argument is the data to be processed.
arg 1
Is a vararg. Currently it accepts a single key mods for which the value should be a comma-separated list over the words posix, icase, dotall, iter-lines iter-args, match-once, discard-nmp, discard-nil-out, discard-miss, count-matches. Alternatively repeated use of mods is allowed.
arg 2
Is a regular expression. Tilde patterns are expanded according to all of the ZOEM, UNIX, and REGEX schemes. Refer to TILDE EXPANSION for these.
The third argument is a constant string or an anonymous key, the fourth argument is data.
## THE TR SUBLANGUAGE
The \tr#2 primitive takes two arguments. The first argument contains key-value pairs. The accepted keys are from and to which must always occur together, and delete and squash. The values of these keys must be valid translation specifications. This primitive transforms the data in the second argument by successively applying translation, deletion and squashing in that order. Only the transformations that are needed need be specified.
Translation specifications are subjected to UNIX tilde expansion as described below.
The syntax accepted by translation specifications is almost fully compliant with the syntax accepted by tr(1), with three exceptions. First, repeats are introduced as [*a*20] rather than [a*20]. Second, ranges can (for now) only be entered as X-Y, not as [X-Y]. X and Y can be entered in either octal or hexadecimal notation (see further below). As an additional feature, the magic repeat operator [*a#] stops on both class and range boundaries. Character specifications can be complemented by preceding them with the caret ^.
Specifications may contain ranges of characters such as a-z and 0-9. Posix character classes are allowed. The available classes are
[:alnum:] [:alpha:] [:cntrl:] [:digit:] [:graph:] [:lower:] [:print:] [:punct:] [:space:] [:upper:] [:xdigit:]
Characters can be specified using octal notation, e.g. \012 encodes the newline. Use \173 for the opening curly, \175 for the closing curly, \134 for the backslash, and \036 for the caret if it is the first character in a specification. DON'T use \\, \{, or \} in this case! Hexadecimal notation is written as \x7b (the left curly in this instance).
See EXAMPLES for an example of tr#2 usage.
## TILDE EXPANSION
Some primitives interface with UNIX libraries that require backslash escape sequences to encode certain tokens or characters. The backslash is special in zoem too and without further measures it can become very cumbersome to encode the correct escape sequences as it is not always clear which tokens should be escaped or unprotected at what point. It is especially difficult to handle the zoem characters with special meaning, {, } and \.
The two primitives under consideration are \inspect#4 and \tr#2. Both treat the tilde as an additional escape character for certain arguments (as documented in the user manual). These arguments are subjected to tilde expansion, where the tilde and the character it proceeds are translated to a new character or character sequence. There are three different sets of tilde escapes, ZOEM, UNIX and REGEX escapes. \tr#2 only accepts UNIX escapes, \inspect#4 accepts all. Tilde expansion is always the last processing step before strings are passed on to external libraries.
The ZOEM scheme contains some convenience escapes, such as ~E to encode a double backslash.
ZOEM tilde expansion
meta sequence replacement .-----------------------------. | ~~ | ~ | | ~E | \\ | | ~e | \ | | ~I | \{ | | ~J | \} | | ~x | \x | | ~i | { | | ~j | } | -----------------------------'
The zoem tr specification language accepts \x** as hexadecimal notation, e.g. \x0a denotes a newline in the ASCII character set
.
UNIX tilde expansion
meta sequence replacement .-----------------------------. | ~a | \a | | ~b | \b | | ~f | \f | | ~n | \n | | ~r | \r | | ~t | \t | | ~v | \v | | ~0 | \0 | | ~1 | \1 | | ~2 | \2 | | ~3 | \3 | -----------------------------'
REGEX tilde expansion
## AUTHOR
Stijn van Dongen. | 2015-01-27 14:18:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.553713858127594, "perplexity": 6594.943064538586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121981339.16/warc/CC-MAIN-20150124175301-00249-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://learn.careers360.com/ncert/question-show-that-f-defined-from-1-1-to-r-given-by-f-x-is-equal-to-x-over-x-plus-2-is-one-one-find-the-inverse-of-the-function-f-defined-from-1-1-to-range-f/ | Q
# Show that f : [–1, 1] → R, given by f (x) = x over (x + 2) is one-one. Find the inverse of the function f : [–1, 1] → Range f.
Q. 6 Show that $f : [-1, 1] \rightarrow R$, given by $f(x) = \frac{x}{(x + 2)}$ is one-one. Find the inverse of the function$f : [-1, 1] \rightarrow Range f$
Views
$f : [-1, 1] \rightarrow R$
$f(x) = \frac{x}{(x + 2)}$
One -one:
$f(x)=f(y)$
$\frac{x}{x+2}=\frac{y}{y+2}$
$x(y+2)=y(x+2)$
$xy+2x=xy+2y$
$2x=2y$
$x=y$
$\therefore$ f is one-one.
It is clear that $f : [-1, 1] \rightarrow Range f$ is onto.
Thus,f is one-one and onto so inverse of f exists.
Let g be inverse function of f in $Range f\rightarrow [-1, 1]$
$g: Range f\rightarrow [-1, 1]$
let y be an arbitrary element of range f
Since, $f : [-1, 1] \rightarrow R$ is onto ,so
$y=f(x)$ for $x \in \left [ -1,1 \right ]$
$y=\frac{x}{x+2}$
$xy+2y=x$
$2y=x-xy$
$2y=x(1-y)$
$x = \frac{2y}{1-y}$ ,$y\neq 1$
$g(y) = \frac{2y}{1-y}$
$f^{-1}=\frac{2y}{1-y},y\neq 1$
Exams
Articles
Questions | 2020-01-28 19:22:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.829649031162262, "perplexity": 1281.1311126697233}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251783000.84/warc/CC-MAIN-20200128184745-20200128214745-00436.warc.gz"} |
https://docs.derify.finance/whitepaper/mechanism/risk-factor/risk-exposure | Derify Protocol Documents
English
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⌃K
# Risk Exposure
When
$X+Y\neq0$
, the system has risk exposure because of the constant price fluctuation.
At any given moment
$t$
, we have the state of a derivative
$S_t$
, the sum of total long positions
$X_t$
, the sum of total short positions
$Y_t$
and the current price index
$I_t$
. Assuming that we have a new price
$I_{t+1}$
at the moment
$t+1$
, then the risk exposure
$V{exposure}$
can be calculated as follows:
$V_{exposure}=\sum\Big((X_t+Y_t)*(I_{t+1}-I_t)\Big)$
• $X_t$
is always positive and
$Y_t$
is always negative.
Consider that
$I_{t+1}-I_t$
from external markets is unpredictable and cannot be controlled, the only way to reduce the risk exposure is to restrict the value of
$X_t+Y_t$
.
Obviously, if
$X_t+Y_t=0$
, the risk exposure will not increase at moment
$t$
.
Thus, the hAMM system reaches a balanced state (i.e.
$X+Y=0$
), which is so called "risk exposure closed".
## Naked Position
At any moment, the value of
$X+Y$
means the "unhedged" or "naked" position
$N$
of a certain derivative at that moment:
$N=X+Y$
When
$N=0$
, the sum of total long positions equal to the sum of total short positions, and there are no naked positions.
When
$N>0$
, the sum of total long positions are greater than the sum of total short positions, and the naked positions are long positions.
When
$N<0$
, the sum of total short positions are greater than the sum of total long positions, and the naked positions are short positions.
$V_{exposure}$
can be simplified as follows:
$V_{exposure}=\sum\Big(N_t*(I_{t+1}-I_t)\Big)$
It can be concluded that:
When
$N=0$
, no matter how the index was fluctuated, the net profit/loss of all positions equals zero, and the net loss of the system will not increase.
When
$N\neq0$
, if the sign of
$I_{t+1}-I_t$
and
$N$
are the same (i.e., naked positions and the index fluctuation has the same direction), the net loss of the system may increase.
Thus, the balanced state of hAMM system equals to "zero naked position":
$N=X+Y=0$
The key to achieve the balance of hAMM system is to restrict naked position. | 2023-01-30 15:40:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 30, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.711017370223999, "perplexity": 2482.304197723516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499819.32/warc/CC-MAIN-20230130133622-20230130163622-00406.warc.gz"} |
https://mathoverflow.net/questions/121517/efficient-computation-of-discrete-infimal-convolution | # Efficient computation of “discrete infimal convolution”
This question arises from an application to graphical models in probability theory, but I have abstracted that part out so only algebra remains. Let $\mathbb{R}$ denote standard field of real numbers and $\mathcal{R} = (\mathbb{R}\cup\{\infty\},\min,+)$ the tropical semiring. Let $\mathbb{Z}_n$ denote the cyclic group of order $n$.
Elements of the group ring $\mathbb{R}\mathbb{Z}_n$ are tuples $(x_0,\ldots,x_{n-1})$ and multiplication of these corresponds to discrete cyclic convolution. The Fast Fourier Transform gives an embedding $\mathbb{R}\mathbb{Z}_n\to\mathbb{C}^n$ (with elementwise sum and product). The FFT and its inverse can be computed in $O(n\log n)$ arithmetic operations, so elements of $\mathbb{R}\mathbb{Z}_n$ can be multiplied in $O(n\log n)$ arithmetic operations.
Define the group semiring $\mathcal{R}\mathbb{Z}_n$ in an analogous way. The product of $x = (x_0,\ldots, x_{n-1})$ and $y = (y_0,\ldots,y_{n-1})$ in this semiring is given by $(x\cdot y)_k = \min _{j \in \mathbb{Z}_n} (x_j + y_{k-j})$. This operation could perhaps be called "discrete cyclic infimal convolution" by analogy with the notion of infimal convolution in convex analysis. I'm not sure whether there is a more standard name -- this one does not pop up in quick google searches.
The naive way of computing a discrete infimal convolution uses $O(n^2)$ operations, just as the naive method for computing a standard cyclic convolution. My question is: is there a way to compute this "discrete cyclic infimal convolution" in $O(n\log n)$ arithmetic operations?
In convex analysis, there is an analog of the Fourier transform which turns infimal convolution into pointwise addition: the convex conjugate (or Fenchel or Legendre transformation). However, this operation only behaves nicely for convex functions, so it is not clear to me how one would translate it to an equivalent tool for $\mathcal{R}\mathbb{Z}_n$, but perhaps there is something there.
I would be interested in answers to the question regardless of whether they go through some analog of the Fourier transform. Also, I don't mind various restrictions such as making $n$ a power of $2$, replacing $\mathbb{R}$ with $\mathbb{Q}$, removing $\infty$ from the definition of the semiring, etc. Really anything on this theme would be helpful. Also any suggestions for better tags would be appreciated; perhaps this is a well-studied area I'm not aware of.
You can approximate this using a fast numerical method (note this answer assumes you are performing max-convolution on an equivalent transformed problem on the ring $(\times, \max)$ rather than $(+, \min)$-- you can convert from this one to the one in the question using logarithms and negation if necessary):
If $M[m]$ is the exact result at index $m$ (i.e., $M = L ~*_\max~ R$), then consider every vector $u^{(m)}$ (for each index $m$ of the result, where $u^{(m)}[\ell] = L[\ell] R[{m-\ell}]$). When the vectors $L$ and $R$ are nonnegative (in my case, this was true because they are full of probabilities), then you can perform the $\max_\ell u^{(m)}_\ell$ with the Chebyshev norm:
$$M[m] = \max_\ell u^{(m)}_\ell \\ = \lim_{p \to \infty} \| u^{(m)} \|_p \\ = \lim_{p \to \infty} {\left( \sum_\ell {\left( u^{(m)}[\ell] \right)}^{p} \right)}^{\frac{1}{p}}\\ \approx {\left( \sum_\ell {\left( u^{(m)}[\ell] \right)}^{p^*} \right)}^{\frac{1}{p^*}}\\$$
(where $p^*$ is a large enough constant)
$$= {\left( \sum_\ell {L[\ell]}^{p^*} ~ {R[{m-\ell}]}^{p^*} \right)}^{\frac{1}{p^*}}\\ = {\left( \sum_\ell {\left(L^{p^*}\right)}[\ell] ~ {\left(R^{p^*}\right)}[{m-\ell}] \right)}^{\frac{1}{p^*}}\\ = {\left( L^{p^*} ~*~ R^{p^*} \right)}^{\frac{1}{p^*}}[m]$$
The standard convolution (denoted $*$) can be performed in $n \log(n)$ via FFT. A short paper illustrating the approximation for large-scale probabilistic inference problems is in press at the Journal of Computational Biology (Serang 2015 arXiv preprint).
Afterward a Ph.D. student, Julianus Pfeuffer, and I hacked out a preliminary bound on the absolute error ($p^*$-norm approximations of the Chebyshev norm are poor when $p^*$ is small, but on indices where the normalized result $\frac{M[m]}{\max_{m'} M[m']}$ is very small, large $p^*$ can be numerically unstable). Julianus and I worked out a modified method that is numerically stable in cases when the dynamic range of the result $M$ is very large (when the dynamic range is small, then the simple method from the first paper works fine). The modified method operates piecewise over $\log(\log(n))$ different $p^*$ values (including runtime constants, this amounts to $\leq 18$ FFTs even when $n$ is on the scale of particles in the observable universe, and those 18 FFTs can be done in parallel). (Pfeuffer and Serang arXiv link which has a link to a Python demonstration of the approach) The approach (and the Python demo code linked by the second paper) generalizes to tensors (i.e., numpy.arrays) by essentially combining the element-wise Frobenius norm with multidimensional FFT. There is no other known faster-than-naive method for matrices (and tensors).
Max-convolution is a very fun puzzle-- I'd be interested to hear about your specific application for this in comments (maybe the fast numerical method would work for you?).
Oliver Serang
• Thanks. This is one of the methods I thought about, but it seemed difficult to prove anything about in an appropriate computational model; I think this is related to the numerical instabilities. For example, if the data are all rational numbers, can we set $p^*$ appropriately and compute everything to some finite precision nicely bounded in terms of the data, then use some rounding scheme to recover the exact result? – Noah Stein Jun 29 '15 at 13:50
• For me the problem was mostly a curiosity. Some of my coworkers develop a software package (Dimple) that does belief propagation and other inference tasks, and it occurred to me that it was slightly strange that for the sum-product algorithm certain messages could be computed efficiently using FFT convolutions, but there wasn't a clear analog for the min-sum algorithm because that would require a fast, stable max-convolution algorithm. It's frustrating that numerical stability comes into it when the FFT is so nice on that front (as far as I know). – Noah Stein Jun 29 '15 at 13:53
• Hi Noah, faster max-product belief prop. (small world) is exactly why I created this trick. Note that the speed & novelty compared to extant methods lies in 1) not only using an approximation ($\| \cdot \|_{p^*}$), but also computing the $p^*$-approximation with ordinary FFT 2) it can be made numerically stable (see second paper); an error bound between $\|\cdot \|_\infty$ and $\| \cdot \|_{p^*}$ can be derived (and in practice, the error is very small). The code from the papers is brief and w/ Apache 2 license, so feel free to use it in Dimple (and enjoy a pastry from Flour bakery for me). -O – Oliver Jun 29 '15 at 21:40
Hi Noah,
Nice question! I tried thinking of the discrete fourier transform as a change of basis to the eigenbasis of a circulant matrix, but this did not generalize well tropically.
However, there are work on generalized Legendre-Fenchel transform to non convex/concave functions, including discrete ones, which preserves the convolution-to-sum property. See, for example
Characterization of a simple communication network using legendre transform
or
Slope transforms: theory and application to nonlinear signal processing
As to fast computation of the discrete Legendre-Fenchel transform, see Lucet's thesis:
La transformee de legendre-fenchel etla convexifiee d'une fonction: algorithmes rapides de calcul, analyse et regularite du second ordre
I haven't read the last two papers very carefully, but hopefully they're relevant. As a small observation, you can order either $y$ or $x$ in decreasing order, thus at least one of the Legendre transform is straight forward.
• Thank you for these references. However, looking through them, they all seem to work with versions of the Legendre transform $^\ast$ which retain the standard property that $f^{\ast\ast}$ is the convex hull of $f$ (the function whose epigraph is the convex hull of the epigraph of $f$). As such, there doesn't seem to be a way to go back from $f^\ast + g^\ast$ to the infimal convolution of $f$ and $g$ when $f$ and $g$ are not convex. Am I missing something? – Noah Stein Feb 13 '13 at 13:05
• I just noticed that you are at Berkeley and working with Bernd Sturmfels, so I should mention that I had already emailed him about this yesterday before you replied. Please let me know if you two have any further thoughts about this. – Noah Stein Feb 13 '13 at 16:06
• Good point. They did mention the extended inverse Legendre transform in the first paper (and generally searching for "slope transform deconvolution" returns some papers with claims that it is possible to deconvolve for non-convex/concave functions, but I have yet to find something explicit). There are nice pictures in www2.ensc.sfu.ca/~ljilja/cnl/presentations/takashi/seminar.ps which explain the intuition of the extended Lengedre transform. Given that it keeps the information on all slopes, I would expect deconvolution to be possible. – Ngoc Mai Tran Feb 13 '13 at 23:09
• Ah yes, I learned of this problem from Bernd. – Ngoc Mai Tran Feb 13 '13 at 23:52
After a bit more google searching, I found the 2006 paper Necklaces, Convolutions, and X+Y, which addresses this problem. The nine authors give an $O(n\sqrt{n})$ algorithm in the nonuniform linear decision tree model (I'm having little trouble pinning down the details of this computational model) and an $O\left(\frac{n^3(\log \log n)^3}{(\log n)^2}\right)$ algorithm in the real RAM model. I haven't found any newer results, so it seems that the problem I posed is open.
• Regarding the etiquette of answering my own question in this way: do I accept this answer because it shows the problem is considered open, which is as far as MO is intended to go? Or not because I would still be happy for someone to answer it? – Noah Stein Feb 18 '13 at 15:03
• Here's a paper on infimal convolution with a pretty excellent review of the literature, asserting that the problem is open (as of 2015). (The paper's actual contribution is the same $p$-norm convolution trick that Oliver and others have suggested.) – Bill Bradley Feb 24 '16 at 4:16
• @BillBradley: Thanks. By the way, that paper is by the same Oliver. :-) – Noah Stein Feb 24 '16 at 17:07 | 2019-05-19 17:32:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8007388114929199, "perplexity": 465.2981157083912}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255071.27/warc/CC-MAIN-20190519161546-20190519183546-00399.warc.gz"} |
https://solvedlib.com/n/two-sides-and-an-angle-ssa-ot-amp-triarigle-are-given-deterrine,14845662 | # Two sides and an angle (SSA) ot & triarigle are given. Deterrine whether the given measurements produce one triangle, two
###### Question:
Two sides and an angle (SSA) ot & triarigle are given. Deterrine whether the given measurements produce one triangle, two triangles or no triangle at all_ Solve each triangl that resulls a =13, c=15.2 A =53" Select the correct choice below and, if necessary fill in the answer boxes t0 complete your choice. (Round side lengths t0 the nearest tenth and angle measurements l0 lhe nearest degree as needed 0AJ There i5 only one possible solution for the triangle_ The measurements tor the remaining side b and angles B and € are as follows B ~ There are tWO possible solutions for the triangle The measurements for the solution with Ine the smaller angle C are as follows The measurements for the solution With the Ihe larger angle € are as follows There are no possible solulions tor this triangie Click to select and enter your answer(s) and then click Check Answer Clear AI Check Ansie
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Consider the unit cube with vertices (corner points) (0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1). Let S be the boundary of the cube minus (i.e. not including) the bottom square (the side which lies in the xy plane). Orient S with the normal which points out...
##### Answer_the following questions ftom E the table summarizing variable radius cruise. Plot Count 4) Calculate the mean and standard deviation of basal area per acre assuming the cruise was done with a 30 BAF prismE 1 b) Calculate the mean and standard deviation of basal area per acre assuming the cruise was done with 20 BAF prism
Answer_the following questions ftom E the table summarizing variable radius cruise. Plot Count 4) Calculate the mean and standard deviation of basal area per acre assuming the cruise was done with a 30 BAF prism E 1 b) Calculate the mean and standard deviation of basal area per acre assuming the cru...
##### Usc thc power scrics2" Ix<i etctninc PoYYCiET1O) Cenict 0 foruk funuonlx) = (1-Sx}6 n(srr" En(sr+' 2n(-1(s.r" En(srr" - 5 n( - Iy(sr+1chark for convcrgence = thc endpoints of the (Be surc incluk= Find the interval of convergence of thc porcr seres: interval:)2k7405 10'-[(-20, 20) (10, 20) (-10, 10) d. (0, 10) (0, 20)
Usc thc power scrics 2" Ix<i etctninc PoYYCiET1O) Cenict 0 foruk funuon lx) = (1-Sx} 6 n(srr" En(sr+' 2n(-1(s.r" En(srr" - 5 n( - Iy(sr+1 chark for convcrgence = thc endpoints of the (Be surc incluk= Find the interval of convergence of thc porcr seres: interval:) 2k7405 1...
##### A rocket is fired tom rest at z -0 and travels along a parabolic trajectory described...
A rocket is fired tom rest at z -0 and travels along a parabolic trajectory described by y 160(103)x] m Part A I the z component of acceleration is a ms2 whore t is in seconds, determine the magnitude of the rocket's velocily when t Express your answer using three significant figures and include...
##### Draw the major organic product(s) of the following reaction. CHE NaNH / NH (0) HyC-C-CEC-H CH,CH2-...
Draw the major organic product(s) of the following reaction. CHE NaNH / NH (0) HyC-C-CEC-H CH,CH2- CHE...
##### A pentagon with sides $3 \mathrm{m}, 4 \mathrm{m}, 5 \mathrm{m} .6 \mathrm{m},$ and 7 $\mathrm{m}$ has area 48 $\mathrm{m}^{2}$ . Find the perimeter of a similar pentagon whose area is 27 $\mathrm{m}^{2}$ .
A pentagon with sides $3 \mathrm{m}, 4 \mathrm{m}, 5 \mathrm{m} .6 \mathrm{m},$ and 7 $\mathrm{m}$ has area 48 $\mathrm{m}^{2}$ . Find the perimeter of a similar pentagon whose area is 27 $\mathrm{m}^{2}$ ....
##### Question 2: Indicate whether the following statements are True or False: a) If time to maturity,...
Question 2: Indicate whether the following statements are True or False: a) If time to maturity, is greater than time to maturity2 then American call optionis less than American call option2 b) If volatility, is greater than volatility2 then European call option; is greater than European call option...
##### 12.~/0.1 POINTS0/4 Submissions UsedChoose all of the processes from below which describe changes which are independent of the path by which the change occurs:the elevation increase experienced by traveller travelling from Grand Isle, LA to Denver, Coloradothe effort required to capture tiger in the wildthe longitude decrease experienced by traveller travelling from Baton Rouge, LA to London, Englandthe energy released by the combustion of a gallon of gasolinethe amount of work required to build
12. ~/0.1 POINTS 0/4 Submissions Used Choose all of the processes from below which describe changes which are independent of the path by which the change occurs: the elevation increase experienced by traveller travelling from Grand Isle, LA to Denver, Colorado the effort required to capture tiger in...
##### Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it Suppose also that we choose random sample of J0 Colonials games Answer the following. (If necessary, consult Ist_of formulas. )Estimatc tnc numocr onmcs tho samplc that thc Colonlals win slvlng thc mcan of thc relevant distnbut on Tlal 4tne exatcaton Ortn teleVunt TArldom arinbld)_ nol rounu Your [undnttQu Illy (G unceteanly Houtumi at least trree decimnal Glacesgwlrg the standurd H
Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it Suppose also that we choose random sample of J0 Colonials games Answer the following. (If necessary, consult Ist_of formulas. ) Estimatc tnc numocr onmcs tho samplc that thc Colonlals w...
##### The number 8127.3 expressed in scientific notation tothree significant figures isThe number 0.00123 expressed in scientific notation tothree significant figures is The number 47828 expressed in scientific notation to twosignificant figures isThe number 500.03 expressed in scientific notation tofour significant figures is The number 9104.98 expressed in scientific notation tothree significant figures is
The number 8127.3 expressed in scientific notation to three significant figures is The number 0.00123 expressed in scientific notation to three significant figures is The number 47828 expressed in scientific notation to two significant figures is The number 500.03 expressed in scientific notati...
##### There is a group of people. The average height of these people is 67 inches. Is...
There is a group of people. The average height of these people is 67 inches. Is it more likely to pick an individual who is more than 68 inches tall or a sample of four people who average more than 68 inches tall? Or are they probabilities equal? Or is it impossible to tell? You do not have to expla...
##### (Round to three decimal places or leave exact)a) Find the area under the curve f(x)=3x+2x^3 on theinterval [0,4] ∫04 (3x+2x3)dx=b) Find the area under the curve f(x)=7x^2+2 over the interval[0,4] ∫04 (7x2+2)dx=c) Find the area under the curve 4x^-1 on the interval[1,2.5]∫12.5 4x-1dx=d) Find the area under the curve f(x)=4xe^x on the interval[-5,3]∫-53 (4x-ex)dx=
(Round to three decimal places or leave exact) a) Find the area under the curve f(x)=3x+2x^3 on the interval [0,4] ∫04 (3x+2x3)dx= b) Find the area under the curve f(x)=7x^2+2 over the interval [0,4] ∫04 (7x2+2)dx= c) Find the area under the curve 4x^-1 on the interval [1,2.5] âË...
##### 14) Fill in the Blank. You run a regression analysis on a bivariate set of data...
14) Fill in the Blank. You run a regression analysis on a bivariate set of data (n=25). With x(x-bar) -58.2 and "y=42.5 (y- bar), you obtain the regression equation yly-hat) - 3.111x-23.245 with a correlation coefficient of r=-0.095. You want to predict what value (on average) for the response v...
##### The past , trout Cleanxater Creck were inches ong On averase with a 2.5 inch standard devlation ncecht <innie trout from the creek fowingBuildEne Cunrent Mean lenathtrouteun ate Lreek usine tc old standard dt alionRound all intermaxlate calculations txo decimals, chen constnuct the Cl and enter like this: (min,maxlNote; Ifyou [ built-In comund on calculatonicomnduic roundlng Use the formulas given che textnotesmight get Marked wrong dueUse your inchesdecide GhetheMean ienetLoulClearwater cret
the past , trout Cleanxater Creck were inches ong On averase with a 2.5 inch standard devlation ncecht <innie trout from the creek fowing Build Ene Cunrent Mean lenath trout eun ate Lreek usine tc old standard dt alion Round all intermaxlate calculations txo decimals, chen constnuct the Cl and en...
##### How does initial speed, angle, height, Gravity, and air resistance affect the time, range, and max...
How does initial speed, angle, height, Gravity, and air resistance affect the time, range, and max height of a projectile?...
##### Chapter 2 Forecasting13 . quality control analyst has kept a record of the defective rate of a process he has been trying to improve during period of about four weeks The following data (percent- ages) were recorded: WeekMonday 10.2 94 8.4 7.8 Tuesday 8.2 73 7.0 6.5 Wednesday 7.2 6.8 6.3 5.0 Thursday 6.8 6.0 5.4 4.8 Friday 94 9.0 8.2 Determine daily relatives for the defective rate: Compute a linear trend equation for the defective rate: Use your answers from the preceding two parts to 'pre
chapter 2 Forecasting 13 . quality control analyst has kept a record of the defective rate of a process he has been trying to improve during period of about four weeks The following data (percent- ages) were recorded: Week Monday 10.2 94 8.4 7.8 Tuesday 8.2 73 7.0 6.5 Wednesday 7.2 6.8 6.3 5.0 Thurs...
##### Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x,...
Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x, 0) =1 + x2 using the method of characteristics. Find the u(x, y). Substitute your found solution u(x, y) in the equation and verify that it satisfies the equation. solution explicitly in the form u =...
##### A small candy shop is preparing for the holiday season. The owner must decide how many...
A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut/Raisin Delite to put up. The deluxe mix has .66 pound raisins and .34 pound peanuts, and the standard mix has .48 pound raisins and .52 pound peanuts ...
##### Regarding nutrients, which ones only serve as "building blocks", contributing to and maintaining the structure of...
Regarding nutrients, which ones only serve as "building blocks", contributing to and maintaining the structure of the body? What is the function that all the others also have or have instead? A drug is defined by most experts as "any substance ingested or put in the body other than food ...
##### At noon, ship A is 50 nautical miles due west of ship B. Ship A is...
At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)...
##### Carrie Williams has been admitted to the Psychiatric Unit at Bayshores Treatment Facility. She is eight-and-one-half...
Carrie Williams has been admitted to the Psychiatric Unit at Bayshores Treatment Facility. She is eight-and-one-half months pregnant and in a manic state. She has not slept for three days, is hyperactive and hypervoluble. When you come on duty, she is running all over the Day Room, jumping from chai...
##### SccionExercisePert zFrontal ScctionCenx Vestibular Glandt Grcatet InfundibulumOvanOviduct Utenus VaginaInferior View ClitorisHymen Labium Majus Labium Minus Mons PubisPerineum Posterior Fourchet Prepuce of Clitoris Urethral Orifice Vaginal Orifice
Sccion Exercise Pert z Frontal Scction Cenx Vestibular Glandt Grcatet Infundibulum Ovan Oviduct Utenus Vagina Inferior View Clitoris Hymen Labium Majus Labium Minus Mons Pubis Perineum Posterior Fourchet Prepuce of Clitoris Urethral Orifice Vaginal Orifice...
##### Dummy Variable Refer to Data Set 9 "Bear Measurements" in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response $(y)$ variable represent weight, use the variable of age and the dummy variable of sex to find the multiple regression equation. Use the equation to find the predicted weight of a bear with the characteristics given below. Does sex appear to have much of an effect on the weight of a bear?a. Fem
Dummy Variable Refer to Data Set 9 "Bear Measurements" in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response $(y)$ variable represent weight, use the variable of age and the dummy variable of sex to find ...
##### QUESTION 3ball is thrown directly upward and then caught at the same height was leased 1.67 Iater. what is the initial velocity of the ball in SI units? Assume air resistance negligible: Take the upward direction t0 be positive: Dont forget include the unitsl
QUESTION 3 ball is thrown directly upward and then caught at the same height was leased 1.67 Iater. what is the initial velocity of the ball in SI units? Assume air resistance negligible: Take the upward direction t0 be positive: Dont forget include the unitsl...
##### Classily the items as components of a melabolic pathwaymultienzyme complex:group of enzymes physically attached each otherThe product Irom one chomical roacion immodialely bound Ihe naxt enzymeMultienzyme ComplexMetabolic PathwayThe product trom reactons acts as an alloslerc inhibibrSeries 0l enzymes that help conver a specifc substrate Ihe Iinal productThe product of one enzyme Ihe substrate Ior the next OlymneRegot
Classily the items as components of a melabolic pathway multienzyme complex: group of enzymes physically attached each other The product Irom one chomical roacion immodialely bound Ihe naxt enzyme Multienzyme Complex Metabolic Pathway The product trom reactons acts as an alloslerc inhibibr Series 0... | 2023-03-20 10:35:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5894519090652466, "perplexity": 4318.542985085023}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00157.warc.gz"} |
https://www.semanticscholar.org/paper/A-study-of-Bhabha-scattering-at-PETRA-energies-Braunschweig-Gerhards/85a550b3c0cfb3894eb7cb4a4815ca198dc5b062 | # A study of Bhabha scattering at PETRA energies
@article{Braunschweig1988ASO,
title={A study of Bhabha scattering at PETRA energies},
author={Wolfgang Braunschweig and Roland Gerhards and F. J. Kirschfink and H. -U. Martyn and P. Rosskamp and B. Bock and H. M. Fischer and Helvi Hartmann and J. L. Hartmann and E. Hilger and Andreas Jocksch and Volker Mertens and R. Wedemeyer and Brian Foster and A. J. Martin and A. J. Sephton and F. Barreiro and E. Bernardi and Janusz Chwastowski and Yehuda Eisenberg and Andrzej Eskreys and Kirsten Gather and Krzysztof Genser and H. Hultschig and P. Joos and Henri Kowalski and Aaron Ladage and B. L{\"o}hr and D. L{\"u}ke and P. M{\"a}ttig and Avram Montag and Dieter Notz and J. M. Pawlak and Evelyne Ronat and Eduardo Ros and Dieter Trines and Teresa Tymieniecka and Roman Walczak and Guenter Wolf and Wolfram Dietrich Zeuner and Hermann Kolanoski and T. Kracht and J. Kr{\"u}ger and Erich Lohrmann and G. Poelz and K. U. P{\"o}snecker and David M. Binnie and J. K. Sedgbeer and J. Shulman and D. Su and A.T. Watson and J Perez Cerezo and M. A. Valdivia Garc{\'i}a and A. Leites and J. Del Peso and J. F. Troc{\'o}niz and C. J. Balkwill and Michael G. Bowler and Philip Nicholas Burrows and Roger J. Cashmore and P. D. Dauncey and Greg P. Heath and Douglas J. Mellor and Peter Ratoff and I. R. Tomalin and J. Yelton and S. L. Lloyd and Geoffrey Ethan Forden and J. C. Hart and D. H. Saxon and Stephanie Brandt and Mark T. Holder and Luis Labarga and Uri Karshon and Giora Mikenberg and Didier Revel and Asaf Shapira and Naor Wainer and G. Yekutieli and Gregory J. Baranko and Allen Caldwell and J. M. Izen and David Robert Muller and Steven M. Ritz and D Strom and M. Takashima and Eric Wicklund and Sau Lan Wu and G. Zobernig and Tasso Collaboration},
journal={Zeitschrift f{\"u}r Physik C Particles and Fields},
year={1988},
volume={37},
pages={171-177}
}
We report on high statistics Bhabha scattering data taken with the TASSO experiment at PETRA at center of mass energies from 12 GeV to 46.8 GeV. We present an analysis in terms of electroweak parameters of the standard model, give limits on QED cut-off parameters and look for possible signs of compositeness.
12 Citations
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We examine the phenomenological consistency of composite-model pictures for the llγγ events at LEP: the picture with an extra boson and that with an excited lepton. It turns out that the former isExpand
Electron-positron annihilation at high energies
The experimental physics programme of PEP and PETRA is presented. The data from 11 independent experiments are collated according to subject matter and compared with theory. The author starts with aExpand
Search for the substructure of leptons in high energy QED processes at tristan
Abstract QED processes up to O(α 4 ) have been studied at center-of-mass energies between 50 and 57 GeV using the AMY detector at TRISTAN. A possible substructure of the electron and muon isExpand
A measurement of electroweak effects in the reactione+e− → τ+τ− at 35.0 and 42.4 GeV
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First observation of the Top Quark at the Large Hadron Collider
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Experimental constraints on extra dimensions
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Abstract We investigate the implications for experiment of the existence of compactified dimensions with a scale much larger than the Planck length. Such manifolds might occur in certain stringExpand
A measurement of muon pair production ine+e− annihilation at centre of mass energies 35.0≤ $$\sqrt s$$ ≤46.8 GeV
The reactione+e−→µ+µ− has been studied at centre of mass energies between 35.0 and 46.8 GeV using the TASSO detector at PETRA. We present measurements of the forward-backward charge asymmetry (Aμμ)Expand
Limits on extra dimensions in orbifold compactifications of superstrings
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Abstract Perturbative breaking of supersymmetry in four-dimensional string theories predict in general the existence of new large dimensions at the TeV scale. Such dimensions can be consistent withExpand
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Weak and electromagnetic interactions of the leptons are examined under the hypothesis that the weak interactions are mediated by vector bosons. With only an isotopic triplet of leptons coupled to aExpand | 2021-10-26 18:09:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6842892169952393, "perplexity": 6241.284804357222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587915.41/warc/CC-MAIN-20211026165817-20211026195817-00572.warc.gz"} |
https://wiki.math.ntnu.no/ma8103/2016v/start | # MA8103 Non-Linear Hyperbolic Conservation Laws
### General information
Background: In the course we study a class of nonlinear partial differential equation called hyperbolic conservation laws. These equations are fundamental in our understanding of continuum mechanical systems, and can be used to describe mass, momentum and enery conservation in mechanical systems. Examples of the use of conservation laws you may have seen in TMA4305 Partial differential equations and TMA4195 Mathematical modeling as well as in courses in physics and fluid mechanics. The equations share many properties that make numerical computations difficult. The equations may, for instance, develop singularities in finite time from smooth initial data. These equations have been extensively studied due to their importance in applications. Examples of applications include weather forecasting, flow of oil in a petroleum reservoir, waves breaking at a shore, and in gas dynamics.
Lecturer: Helge Holden Email: holden [at] math [dot] ntnu [dot] no
Textbook: H. Holden and N. H. Risebro: Front Tracking for Hyperbolic Conservation Laws, Springer, Second edition 2015. The book exists as an eBook, and NTNU students can read and download it freely. There will be an inexpensive paperback edition called "MyCopy" that sells for EUR 24.95 (incl. shipping).
### Time and place
For regular weeks the lectures are
Wednesday at 14:15-16 in room 656, Sentralbygg 2
Thursday at 10:15-12 in room 922, Sentralbygg 2
The lectures will be in English, and there will be an oral exam at the end of the semester.
### Lecture plan
• Tue, Jan. 12 at 8:15-10:00 (room 922): p. 1-6.
• Wed, Jan. 20: p. 6-9, 53-56. Exercises 1.8 and 1.9 (p. 48-49) are strongly recommended.
• Thu, Jan. 21: p. 56-60.
• Wed, Jan. 27: p. 60-65.
• Thu, Jan. 28: p. 65-73.
• Wed, Feb. 3: p. 73-78.
• Thu, Feb. 4: p. 78-84.
• Wed, Feb. 10: p. 84-88.
• Thu, Feb. 11: p. 95-105.
• Wed, Feb. 17: p. 105-110.
• Fri, Feb. 19 at 8:15-10:00 (room 656, Simastuen): p. 110-115 (the proof of Thm. 3.10 not presented).
• Wed, Feb. 24: p. 115-119.
• Thu, Feb. 25: p. 119-126.
• Wed, Mar. 2: p. 171-175.
• Fri, Mar. 4 at 8:15-10:00 (rom 656, Simastuen): p. 175-180.
• Wed, Mar. 9: NO lecture
• Thu, Mar. 10: p. 180-185.
• Fri, Mar. 11 at 8:15-10:00 (rom 656, Simastuen): p. 185-189.
• Wed, Mar. 16: p. 223-231 (the derivation of the shallow water equations from the Navier-Stokes equations not presented).
• Fri, Mar. 18 at 8:15-10:00 (rom 656, Simastuen): p. 232-235.
• Wed, Mar. 30: NO lecture.
• Thu, Mar. 31: NO lecture.
• Wed, Apr. 6: NO lecture.
• Thu, Apr. 7 (rom 734): p. 235-244.
• Wed, Apr. 13: p. 244-249.
• Fri, Apr. 15 at 8:15-10:00 (rom 656, Simastuen): p. 249-253.
• Wed, Apr. 20: p. 254-260.
• Fri, Apr. 22 at 8:15-10:00 (rom 656, Simastuen): Exercises 2.17-2.19, 5.8
• Fri, Apr. 29 at 13:15-16:00 (rom 656, Simastuen): A brief introduction to Ch. 6. Then Sects. 4.4 and 4.5.
Exam: The exam is oral. At the day of the exam you meet at 9:00 am in my office. The time for each candidate will be decided then.
Curriculum: Ch. 1, p. 1-16; Ch. 2; Ch. 3, p. 91-126; Ch. 4, p. 171-188, 205-216; Ch. 5, p. 223-259; Ch. 6, just the general construction of the front tracking approximation.
Regulations concerning the exam: For the first 20 min the candidate presents a lecture using blackboard only on one of the topics given below. Notes are allowed. It should be a lecture presenting the main parts of the topic, or if the topic is big, a selected part of it. Proofs are encouraged. After that, and for approximately 25 min the candidate will be asked questions about all of the curriculum. Here there will of course be no notes. The topic is decided at the beginning of the exam.
Topics: (A): Ch 2; (B): Ch 3; (C): Ch 4; (D): Ch. 5. | 2022-09-25 19:58:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2607116103172302, "perplexity": 8532.570574810954}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334596.27/warc/CC-MAIN-20220925193816-20220925223816-00652.warc.gz"} |