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https://www.gamedev.net/forums/topic/154013-lisp--traversing-a-cons-list/ | #### Archived
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# Lisp: traversing a cons list
## Recommended Posts
master_ball 132
I''m playing around with Lisp and have made a global variable *database* that is a cons list. In it are structs of people. I''ve given them stats, such as name, sex, parents, children, strength, speed, and on and on. I can''t figure out how to traverse the list. Say I want to find all of the males in my database, or everyone with a speed of say 10, and print out the names. How would I go about this? I thought about doing it recursivly with cdr, but I can''t get it to work. Thanks! -- master_ball -- ------------------------------ We R 138
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Diodor 517
(defun print-odd (l) (if (null l) nil (progn (when (oddp (car l)) (print (car l))) (print-odd (cdr l))))) (PRINT-ODD '(1 2 3 4 5))1 3 5 NIL
You can make a more general utility:
(defun print-if (pred lst) (if (null lst) nil (progn (when (funcall pred (car lst)) (print (car lst))) (print-if pred (cdr lst)))))(PRINT-IF #'oddp '(1 2 3 4 5))1 3 5 NIL
But the best way is to use mapping functions. Look up mapl, mapc, mapcar, mapcan, mapcon, maplist.
(defun print-if (pred lst) (mapc #'(lambda (x) (when (funcall pred x) (print x))) lst))1 3 5 (1 2 3 4 5)
Or you can use the almighty loop:
(defun print-if (pred lst) (loop for it in lst do (when (funcall pred it) (print it))))
To collect all elements in a list of a certain property:
(defun collect-if (pred lst) (mapcan #'(lambda (x) (when (funcall pred x) (list x))) lst))(COLLECT-IF #'oddp '(1 2 3 4 5))(1 3 5)
[edited by - Diodor on April 29, 2003 12:31:46 AM]
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bishop_pass 109
Think hard about the flexibility you have with regard to how you may arrange symbols in s-expressions which represent knowledge. Think also about the fact that in many cases you''re better off creating name-value pairs, such as (gender male) and (occupation farmer). In this way, you can have any number of different elements in your knowledge base, and missing ones as well.
Then look into assoc, or roll your own function.
The point of my post is that you have immense flexibility in how you choose to create and store data in Lisp.
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flangazor 516
I disagree in terms of style, bishop. I think that there should be a spec and a macro for printing the template of the person type. Then there should be push/pop/find/find-all accessors. I would also use a hash table for datasets greater than 20 (where on many lisp systems, hash becomes faster then assoc-list).
Maybe my mind has been corrupted by OOP but I think this is good because you can then keep the actual data small, and you can write the find, which makes find all quite easy. push and pop are almost trivial as well!
yum yum.
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bishop_pass 109
Use a hash-table, certainly, for a large data-set. That does not preclude anything else that I mentioned. I only mentioned assoc so that he could become familiar with different ways of structuring data.
You are doomed to mediocrity if you adhere to OOP all your programming career. Do yourself a favor and read some classical papers in AI. | 2017-09-24 12:23:51 | {"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": 0.3311997950077057, "perplexity": 7165.699510454954}, "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-2017-39/segments/1505818690016.68/warc/CC-MAIN-20170924115333-20170924135333-00099.warc.gz"} |
https://math.stackexchange.com/questions/896953/tensor-product-and-its-homomorphisms | # Tensor product and its homomorphisms.
Given $f:A_R\rightarrow A'_R$, $g:B_R\rightarrow B'_R$ R-module homomorphism we can define $f\otimes g: A\otimes_R B\rightarrow A'\otimes_R B'$ such that $(f\otimes g)(a\otimes b)=f(a)\otimes g(b)$ this type of homormorphism is unique.
My question is: What is the relation between the homomorphism define above and the elements $f\otimes g$ of
$$\text{Hom }(A,A')\otimes \text{Hom }(B,B')$$
I can define a function $\phi:\text{Hom }(A,A')\times \text{Hom }(B,B')\rightarrow \text{Hom } (A\otimes_R B, A'\otimes_R B')$ as $(f,g)\mapsto f\otimes g$ . By the universal propierty of tensor product there exist a $\theta:\text{Hom }(A,A')\otimes \text{Hom }(B,B')\rightarrow \text{Hom } (A\otimes_R B, A'\otimes_R B')$ such that $\theta\circ \iota=\phi$. But I don know how the function $\theta$ is useful.
Note: The function $\iota:\text{Hom }(A,A')\times \text{Hom }(B,B')\rightarrow \text{Hom }(A,A')\otimes \text{Hom }(B,B')$ is the canonical epimorphism, i.e. $(f,g)\mapsto f\otimes g$.
Thanks a lot!
What you have stated here is that the tensor product $(\_ \otimes \_)$ is a covariant bifunctor from the category of bimodules to itself. | 2019-08-23 19:02:30 | {"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": 0.9928404688835144, "perplexity": 112.49784462777718}, "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-2019-35/segments/1566027318952.90/warc/CC-MAIN-20190823172507-20190823194507-00246.warc.gz"} |
https://www.transtutors.com/questions/draw-a-product-structure-diagram-from-the-bill-of-material-for-an-xavier-skateboard--614901.htm | # Draw a product structure diagram from the bill of material for an Xavier skateboard shown below.... 2 answers below »
Draw a product structure diagram from the bill of material for an Xavier skateboard shown below. Assuming a 10% profit margin, how should the Xavier be priced?
Level Item Quantity Price 0 Skateboard 1 -1 Deck 1 $54.90 -1 Grip tape 1$ 4.95 -1 Wheel assembly 2 - --2 Wheels 2 $8.95 --2 Bearings 4$ 4.95 --2 Truck 1 $33.90 -1 Nuts and Bolts 4$ 1.99 -1 Riser 2 $3.95 ## Solutions: Suhaas Sharma answered 1031 answers so far 4 Ratings, (9 Votes) ## 1 Approved Answer Suhaas S 4 Ratings, (9 Votes) The Product Structure Diagram is: Costing: Cost of 1 Wheel Assembly = Cost of (2 wheels + 4 bearings + 1 truck) = 2*$8.95 + 4*$4.95 + 1*$33.90
• Cost of 1 Wheel Assembly = \$71.60
Cost... | 2019-11-14 23:44:05 | {"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": 0.5507043600082397, "perplexity": 8994.115193948157}, "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-2019-47/segments/1573496668544.32/warc/CC-MAIN-20191114232502-20191115020502-00550.warc.gz"} |
https://www.jobilize.com/physics/course/17-3-sound-intensity-and-sound-level-by-openstax?qcr=www.quizover.com&page=1 | 17.3 Sound intensity and sound level (Page 2/7)
Page 2 / 7
$\beta \phantom{\rule{0.25em}{0ex}}\left(\text{dB}\right)=\text{10}\phantom{\rule{0.25em}{0ex}}{\text{log}}_{\text{10}}\left(\frac{I}{{I}_{0}}\right),$
where ${I}_{0}={\text{10}}^{\text{–12}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$ is a reference intensity. In particular, ${I}_{0}$ is the lowest or threshold intensity of sound a person with normal hearing can perceive at a frequency of 1000 Hz. Sound intensity level is not the same as intensity. Because $\beta$ is defined in terms of a ratio, it is a unitless quantity telling you the level of the sound relative to a fixed standard ( ${\text{10}}^{\text{–12}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$ , in this case). The units of decibels (dB) are used to indicate this ratio is multiplied by 10 in its definition. The bel, upon which the decibel is based, is named for Alexander Graham Bell, the inventor of the telephone.
Sound intensity levels and intensities
Sound intensity level β (dB) Intensity I (W/m 2 ) Example/effect
$0$ $1×{10}^{–12}$ Threshold of hearing at 1000 Hz
$10$ $1×{10}^{–11}$ Rustle of leaves
$20$ $1×{10}^{–10}$ Whisper at 1 m distance
$30$ $1×{10}^{–9}$ Quiet home
$40$ $1×{10}^{–8}$ Average home
$50$ $1×{10}^{–7}$ Average office, soft music
$60$ $1×{10}^{–6}$ Normal conversation
$70$ $1×{10}^{–5}$ Noisy office, busy traffic
$80$ $1×{10}^{–4}$ Loud radio, classroom lecture
$90$ $1×{10}^{–3}$ Inside a heavy truck; damage from prolonged exposure Several government agencies and health-related professional associations recommend that 85 dB not be exceeded for 8-hour daily exposures in the absence of hearing protection.
$100$ $1×{10}^{–2}$ Noisy factory, siren at 30 m; damage from 8 h per day exposure
$110$ $1×{10}^{–1}$ Damage from 30 min per day exposure
$120$ $1$ Loud rock concert, pneumatic chipper at 2 m; threshold of pain
$140$ $1×{10}^{2}$ Jet airplane at 30 m; severe pain, damage in seconds
$160$ $1×{10}^{4}$ Bursting of eardrums
The decibel level of a sound having the threshold intensity of ${\text{10}}^{–\text{12}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$ is $\beta =0\phantom{\rule{0.25em}{0ex}}\text{dB}$ , because ${\text{log}}_{\text{10}}1=0$ . That is, the threshold of hearing is 0 decibels. [link] gives levels in decibels and intensities in watts per meter squared for some familiar sounds.
One of the more striking things about the intensities in [link] is that the intensity in watts per meter squared is quite small for most sounds. The ear is sensitive to as little as a trillionth of a watt per meter squared—even more impressive when you realize that the area of the eardrum is only about ${1 cm}^{2}$ , so that only ${\text{10}}^{–\text{16}}$ W falls on it at the threshold of hearing! Air molecules in a sound wave of this intensity vibrate over a distance of less than one molecular diameter, and the gauge pressures involved are less than ${\text{10}}^{–9}$ atm.
Another impressive feature of the sounds in [link] is their numerical range. Sound intensity varies by a factor of ${\text{10}}^{\text{12}}$ from threshold to a sound that causes damage in seconds. You are unaware of this tremendous range in sound intensity because how your ears respond can be described approximately as the logarithm of intensity. Thus, sound intensity levels in decibels fit your experience better than intensities in watts per meter squared. The decibel scale is also easier to relate to because most people are more accustomed to dealing with numbers such as 0, 53, or 120 than numbers such as $1\text{.}\text{00}×{\text{10}}^{–\text{11}}$ .
One more observation readily verified by examining [link] or using $I={\frac{\left(\Delta p\right)}{2{\text{ρv}}_{\text{w}}}}^{2}$ is that each factor of 10 in intensity corresponds to 10 dB. For example, a 90 dB sound compared with a 60 dB sound is 30 dB greater, or three factors of 10 (that is, ${\text{10}}^{3}$ times) as intense. Another example is that if one sound is ${\text{10}}^{7}$ as intense as another, it is 70 dB higher. See [link] .
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the time taken for a radioactive element to decay by half of its original mass
ken
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Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
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state the laws of refraction
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state laws of reflection
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when was the name taken from
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did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
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Atomic transmutation
An atom is the smallest indivisible particular of an element
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phenomena of increasing amplitude from normal position of a substance due to some external source.
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Black body is the ideal body can absorb and emit all radiation
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the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
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It is the emission of electrons when light hits a material
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Yeah
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it is the surface of a metal
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light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
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L2MT-2
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what is same units of energy?
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Ws
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M L2 T -2
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ML2T-2
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M L2 T-2
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w=2/(0.005)×100
isaac
supposed the speed on the path is constant angular velocity w (rad/s) = v (m/s) : R (m) period T (s) = 2*Pi * R : v frequency f ( Hz) = 1: T
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in the pole vaulter problem, how do they established that the mass is 5.00kg? where did that number come from? | 2019-10-15 19:43:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 46, "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": 0.7581999897956848, "perplexity": 1652.7463640076396}, "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/1570986660231.30/warc/CC-MAIN-20191015182235-20191015205735-00311.warc.gz"} |
https://www.originlab.com/doc/X-Function/ref/impCDF | # 2.7.18 impCDF
Data: Import from File: CDF (CDF)
If you do not see this file type, choose Data: Import from File: Add/Remove File Types...
To add drag & drop support for a file type, see Import Filter Manager.
## Brief Information
Import CDF file up to version 3.0
## Command Line Usage
impCDF fname:="test.cdf";
## Variables
Display
Name
Variable
Name
I/O
and
Type
Default
Value
Description
File Name fname
Input
string
fname\$
Specify the filename(s) of the file(s) to be imported. In the dialog, click the browse button beside the list box to open one or more files and the filenames will be listed in the box.
File Info And Data Selection trfiles
Input
TreeNode
<unassigned>
This is used to select the desired data channels. See Description part of this document for details.
Output orng
Output
Range
<active>
Specifies the range for the imported data.
See the syntax here.
Output
TreeNode
<unassigned>
This is for outputting the header information, which is hidden from the GUI. Users are not advised to use this variable.
Import Options trFilter
Input
TreeNode
<optional>
This is the TreeNode for the import filter, which is hidden from the GUI. Users are not advised to use this variable.
## Description
The Common Data Format (CDF) is a scientific data management package (known as the "CDF Library") for storing, managing and manipulating scalar, vector, and multi-dimensional data arrays. CDF files which are created on any platform can be transported to any other platform. The basic component of CDF is a software programming interface which is a device-independent view of the CDF data model.
This X-Function is used for importing CDF files whose version is lower than 3.0 to Origin.
### Details on Some Dialog Options
• File Info And Data Selection (trfiles)
This variable is a treenode. It shows file information and allows you to choose the channels to import. The name of each sub-treenode is the name of the corresponding file. Under each sub-treenode, the file size and any available data are listed. The data are sorted by dimensions.
• Save File Info. in Workbook (bSaveFileInfo)
This variable is a checkbox. If not selected, the file information will not be saved in Organizer and the reimport will not work, but the import speed can be improved.
## Example
Suppose you have a file c:\data\cdf\testx.cdf and you want to import it into Origin. You can perform the following steps:
1. Create a new matrix by clicking the button on the Standard toolbar. Select Data: Import from File: CDF from the main menu. The Open dialog should be opened.
2. Select the file and click the Add button to add the file into the bottom panel. Select the Show Options Dialog check box and click then OK button to open the impCDF dialog box.
3. Click OK to accept the default options so as to import the data into Origin. | 2020-05-26 07:31:27 | {"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": 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": 0.1940552294254303, "perplexity": 4547.442331428911}, "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/1590347390448.11/warc/CC-MAIN-20200526050333-20200526080333-00572.warc.gz"} |
https://physicsoverflow.org/user/Prahar/history | Recent history for Prahar
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posted a comment Chiral multiplet : Fundamental and adjoint representation and its Lagrangian | 2021-04-19 13:08:05 | {"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": 0.9666328430175781, "perplexity": 1085.9256024808003}, "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-2021-17/segments/1618038879374.66/warc/CC-MAIN-20210419111510-20210419141510-00099.warc.gz"} |
https://support.bioconductor.org/p/27124/ | evaluating a character string as a variable name in an ExpressionSet object
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@kavitha-venkatesan-3399
Last seen 7.5 years ago
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I would like to know how to evaluate a character string as a variable name in R. Specifically, I need to "compute" the variable name in the phenoData slot of an ExpressionSet object. > varLabels(sample.ExpressionSet) [1] "sex" "type" "score" Now I need to retrieve the factors sample.ExpressionSet$sex, sample.ExpressionSet$type and sample.ExpressionSet$score in turn. Furthermore, I need to be able to generalize my code so that I can retrieve this factor for any phenodata variable in any given ExpressionSet object. Clearly I cannot do something like for (i in c(1:length(varLabels(sample.ExpressionSet))) { class_label <- varLabels(sample.ExpresionSet)[i] class_label_factor <- sample.ExpressionSet$class_label } Here class_label is interpreted as a character string by R, but I need for it to be evaluated as a variable name. Seems straightforward, but I couldn't figure it out...How can I do this? Thanks in advance for any help! Kavitha [[alternative HTML version deleted]]
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@sean-davis-490
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On Thu, Apr 16, 2009 at 5:58 PM, Kavitha Venkatesan < kavitha.venkatesan@gmail.com> wrote: > I would like to know how to evaluate a character string as a variable name > in R. Specifically, I need to "compute" the variable name in the phenoData > slot of an ExpressionSet object. > > > varLabels(sample.ExpressionSet) > [1] "sex" "type" "score" > > Now I need to retrieve the factors sample.ExpressionSet$sex, > sample.ExpressionSet$type and sample.ExpressionSet$score in turn. > Furthermore, I need to be able to generalize my code so that I can retrieve > this factor for any phenodata variable in any given ExpressionSet object. > > Clearly I cannot do something like > > for (i in c(1:length(varLabels(sample.ExpressionSet))) > { > class_label <- varLabels(sample.ExpresionSet)[i] > class_label_factor <- sample.ExpressionSet$class_label > } > > Here class_label is interpreted as a character string by R, but I need for > it to be evaluated as a variable name. Seems straightforward, but I > couldn't > figure it out...How can I do this? Thanks in advance for any help! > If i is your class label: pData(sample.ExpressionSet)[,i] does that do what you need? Sean [[alternative HTML version deleted]]
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@saroj-mohapatra-1446
Last seen 8.1 years ago
Hi Kavitha: Are you looking for something like this: > ls() character(0) > # I have a string called "reallyfunnyvariable" > mystr = "reallyfunnyvariable" # I want to convert this to a variable with the same name; I want it to be a list eval(parse(text=paste(mystr,"=list()",sep=""))) # Now I have the variable > ls() [1] "mystr" "reallyfunnyvariable" # it is a list > reallyfunnyvariable list() You have to be careful though while turning strings into variable, especially in the "batch" mode - what if the string is something like "plot"? You might want to add a clause for first checking if the variable exists, before assigning the variable name. Best, Saroj ----- Original Message ----- From: "Kavitha Venkatesan" <kavitha.venkatesan@gmail.com> To: bioconductor at stat.math.ethz.ch Sent: Thursday, April 16, 2009 5:58:44 PM GMT -05:00 US/Canada Eastern Subject: [BioC] evaluating a character string as a variable name in an ExpressionSet object I would like to know how to evaluate a character string as a variable name in R. Specifically, I need to "compute" the variable name in the phenoData slot of an ExpressionSet object. > varLabels(sample.ExpressionSet) [1] "sex" "type" "score" Now I need to retrieve the factors sample.ExpressionSet$sex, sample.ExpressionSet$type and sample.ExpressionSet$score in turn. Furthermore, I need to be able to generalize my code so that I can retrieve this factor for any phenodata variable in any given ExpressionSet object. Clearly I cannot do something like for (i in c(1:length(varLabels(sample.ExpressionSet))) { class_label <- varLabels(sample.ExpresionSet)[i] class_label_factor <- sample.ExpressionSet$class_label } Here class_label is interpreted as a character string by R, but I need for it to be evaluated as a variable name. Seems straightforward, but I couldn't figure it out...How can I do this? Thanks in advance for any help! Kavitha [[alternative HTML version deleted]] _______________________________________________ Bioconductor mailing list Bioconductor at stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/bioconductor Search the archives: http://news.gmane.org/gmane.science.biology.informatics.conductor -- Computational Biology VBI @ Virginia Tech
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Powered by the version 2.3.6 | 2022-10-05 05:18:21 | {"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": 0.22302472591400146, "perplexity": 3207.00603014248}, "config": {"markdown_headings": true, "markdown_code": false, "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-2022-40/segments/1664030337537.25/warc/CC-MAIN-20221005042446-20221005072446-00235.warc.gz"} |
http://clay6.com/qa/43171/in-a-cubic-packed-structure-of-mixed-oxides-the-lattice-is-made-up-of-oxide | In a cubic packed structure of mixed oxides, the lattice is made up of oxide ions, one fifth of tetrahedral voids are occupied by divalent ($X^{++}$) ions, while one-half of the octahedral voids are occupied by trivalent ions ($Y^{+++}$), then the formula of the oxides.
$X_4Y_5O_{10}$
Hence (C) is the correct answer. | 2017-09-21 19:32:37 | {"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": 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": 0.95404052734375, "perplexity": 1502.789643172696}, "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-2017-39/segments/1505818687837.85/warc/CC-MAIN-20170921191047-20170921211047-00096.warc.gz"} |
https://homework.cpm.org/category/CON_FOUND/textbook/ac/chapter/10/lesson/10.3.1/problem/10-108 | ### Home > AC > Chapter 10 > Lesson 10.3.1 > Problem10-108
10-108.
Verify your solution to part (f) of problem 10-107 by graphing the functions below on the same set of axes. Highlight the portion(s) of the graph for which $|x+1|\le4$.
$y=|x+1|$
$y=4$ | 2021-09-25 12:25:48 | {"extraction_info": {"found_math": true, "script_math_tex": 3, "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": 0.38234415650367737, "perplexity": 2003.7381773360726}, "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-2021-39/segments/1631780057622.15/warc/CC-MAIN-20210925112158-20210925142158-00610.warc.gz"} |
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http://xps.apmonitor.com/wiki/index.php/Main/OptionApmScaling | Main
## APM.SCALING - APMonitor Option
Type: Integer, Input
Default Value: 1
Description: Variable and Equation Scaling
0=Off
1=On (Automatic)
2=On (Manual)
SCALING is an option to adjust variables by constants to make starting values equal to 1.0. Scaling of variables and equations generally improves solver convergence. Automatic and Internal scaling strategies are often implemented within solvers as well. The purpose of scaling is to avoid very large or very small values that may cause numerical problems with inverting matrices. Poor scaling may lead to ill-conditioned matrix inversions in finding a search direction. The difference between the largest and smallest eigenvalues should be within 12 orders of magnitude to avoid numerical problems. Scaling can be turned OFF (0) or ON (1). With SCALING=1, the scaling is taken from the initial guess values in the APM file. If the absolute value is less than one, no scaling is applied. With SCALING=2, the scaling is set for each variable individually. | 2018-09-20 01:57:47 | {"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": 0.4007128179073334, "perplexity": 999.508235712459}, "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-2018-39/segments/1537267156314.26/warc/CC-MAIN-20180919235858-20180920015858-00135.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=1487611 | MathSciNet bibliographic data MR1487611 (2000c:20070) 20G35 Costa, Douglas L.; Keller, Gordon E. On the normal subgroups of \$G\sb 2(A)\$$G\sb 2(A)$. Trans. Amer. Math. Soc. 351 (1999), no. 12, 5051–5088. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2013-05-23 21:35:49 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.9963563084602356, "perplexity": 6416.296836374491}, "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-2013-20/segments/1368703830643/warc/CC-MAIN-20130516113030-00061-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://physicshelpforum.com/threads/string-and-pulley-problem.6048/ | # String and Pulley Problem
#### teddybear9
The masses of blocks A,B, and C are 4kg, 10kg and 2kg respectively. Knowing that P=0 and neglecting the masses of the pulleys and the effects of friction, determine a) the acceleration of each block and the tension in the chord.
I know that we have to draw FBD's for each block and then figure out the equations of each Fnet. But first, how do you know the direction that this system will move? Because for example, if you know that block A is moving down, we can assume down is positive and its equation will be
ma=mg-2T (because we denote down as positive)? Also, for block B, will the tension be 4T, since it's connected to four strings?
I am confused about how system works.
Thanks!
#### Unknown008
PHF Hall of Honor
You can assume a direction, and it's okay.
Say you have acceleration a. If what happens is the opposite, then you will get a < 0 (meaning it moves in the other direction). Otherwise, if you were right, then you get a > 0.
Go ahead and work it out!
teddybear9
#### RyuBobby
What book is this question from? | 2019-12-06 02:56:02 | {"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": 0.8126628398895264, "perplexity": 792.6669323562321}, "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/1575540484477.5/warc/CC-MAIN-20191206023204-20191206051204-00471.warc.gz"} |
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=12096&option_lang=eng | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
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Mat. Zametki, 2018, Volume 103, Issue 6, paper published in the English version journal (Mi mz12096)
Papers published in the English version of the journal
Statistical Transition of Bose Gas to Fermi Gas
V. P. Maslovab
a Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
Abstract: It is well known that the formula for the Fermi distribution is obtained from the formula for the Bose distribution if the argument of the polylogarithm, the activity $a$, the energy, and the number of particles change sign. The paper deals with the behavior of the Bose–Einstein distribution as $a\to 0$; in particular, the neighborhood of the point $a=0$ is studied in great detail, and the expansion of both the Bose distribution and the Fermi distribution in powers of the parameter $a$ is used. During the transition from the Bose distribution to the Fermi distribution, the principal term of the distribution for the specific energy undergoes a jump as $a\to 0$. In this paper, we find the value of the parameter $a$, close to zero, but not equal to zero, for which the Bose distribution (in the statistical sense) becomes zero. This allows us to find the point $a$, distinct from zero, at which a jump of the specific energy occurs. Using the value of the number of particles on the caustic, we can obtain the jump of the total energy of the Bose system to the Fermi system. Near the value $a=0$, the author uses Gentile statistics, which makes it possible to study the transition from the Bose statistics to the the Fermi statistics in great detail. Here an important role is played by the self-consistent equation obtained by the author earlier.
Keywords: Bose statistics, Fermi statistics, Gentile statistics, jump of specific energy, self-consistent equation.
Funding Agency Grant Number Russian Academy of Sciences - Federal Agency for Scientific Organizations AAAA-A17-117021310377-1 This work was supported by Government Grant AAAA-A17-117021310377-1.
English version:
Mathematical Notes, 2018, 103:6, 929–935
Bibliographic databases:
Language:
Citation: V. P. Maslov, “Statistical Transition of Bose Gas to Fermi Gas”, Math. Notes, 103:6 (2018), 929–935
Citation in format AMSBIB
\Bibitem{Mas18} \by V.~P.~Maslov \paper Statistical Transition of Bose Gas to Fermi Gas \jour Math. Notes \yr 2018 \vol 103 \issue 6 \pages 929--935 \mathnet{http://mi.mathnet.ru/mz12096} \crossref{https://doi.org/10.1134/S0001434618050292} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000436583800029} \elib{http://elibrary.ru/item.asp?id=35745995} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049152774}
• http://mi.mathnet.ru/eng/mz12096
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
This publication is cited in the following articles:
1. V. P. Maslov, “Analytical number theory and the energy of transition of Bose gas to Fermi gas. Critical lines as boundaries of noninteracting gas (an analog of the Bose gas in classical thermodynamics)”, Russ. J. Math. Phys., 25:2 (2018), 220–232
2. V. P. Maslov, “New formulas related to analytic number theory and their applications in statistical physics”, Theoret. and Math. Phys., 196:1 (2018), 1082–1087 | 2020-11-01 02:16:25 | {"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": 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": 0.3266768753528595, "perplexity": 1566.1480663507734}, "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-2020-45/segments/1603107922746.99/warc/CC-MAIN-20201101001251-20201101031251-00418.warc.gz"} |
https://www.physicsforums.com/threads/macroeconomics-overlapping-generation-model-and-lump-sum-taxes.678455/ | Macroeconomics: Overlapping Generation model and lump-sum taxes
1. Mar 14, 2013
Charlotte87
1. The problem statement, all variables and given/known data
Suppose an individual born at time $t$ maximizes life-time utility
\begin{equation*}
\max \ln(c_{1,t}) + \frac{1}{1+\rho}\ln(c_{2,t+1}), \; \rho>0
\end{equation*}
subject to the budget constraints in periods t and t+1, respectively
\begin{eqnarray}
c_{1,t} + s_{t} &=& w_{t} - \tau \nonumber \\
c_{2,t+1} &=& (1+r_{t+1})s_{t} \nonumber
\end{eqnarray}
where c1,t is consumption of young individuals at time t and cSUB]2,t+1[/SUB] is consumption of old individuals at time t+1. Savings of the young St earn an interest rate rt+1 and wt is the wage rate at time t. The government initially balances its budget by financing constant spending per capita g by lump-sum taxes τ. The representative firm maximizes profits
\begin{equation*}
\max_{K_{t},L_{t}} K_{t}^{\alpha}L_{t}^{1-\alpha} - r_{t}K_{t} - w_{t}L_{t}, \; 0<\alpha<1
\end{equation*}
where Kt is the aggregate capital stock and Ltthe labor input. Firms are perfectly competitive and take factor prices rt and wt as given. Capital does not depreciate and the labor force grows at rate n>0, that is Lt = (1+n)Lt-1.
(a) Derive the Euler equation governing optimal consumption of the consumer born at time t, and solve for c1,t and st as functions of after-tax wages wt-τ. Provide a brief intuitive explanation.
(b) State the condition for goods market equilibrium. Combine this condition with the solution for savings from part (a) and the representative firm's optimal factor demands for capital and labor, to derive the equation of motion of the capital stock per capita k = K/L of the form
\begin{equation*}
k_{t+1} = ak_{t}^{b} + d
\end{equation*}
where a,b and d are constant coefficients.
(c) Consider the following fiscal experiment. Assuming constant government spending g>0, suppose that lump-sum taxes are cut by Δτ in period t, financed by an increase in lump-sum taxes (1+rt+1)Δτ/(1+n) in period t+1. The government balances its budget from period t+2 onwards.
Starting from steady state k*, derive the effect of this fiscal experiment on kt+1 and give a brief intuitive explanation.
3. The attempt at a solution
I have solved a and b, but gets problem with c.
a)
Euler:
\frac{1+r_{t+1}}{1+\rho} = \frac{c_{2,t+1}}{c_{1,t}}
c_{1,t} = (w_{t}-\tau)\times\frac{1+\rho}{2+\rho}
s_{t} = \frac{1}{2+\rho}(w_{t}-\tau)
b)
\begin{eqnarray}
K_{t+1} &=& L_{t}\frac{1}{2+\rho}\left((1-\alpha)k_{t}^{\alpha}-\tau\right) \nonumber \\
k_{t+1} &=& \frac{1}{1+n}\frac{1}{1+\rho}\left((1-\alpha)k_{t}^{\alpha}-\tau\right) \nonumber \\
&=& \frac{1}{1+n}\frac{1}{1+\rho}(1-\alpha)k_{t}^{\alpha} -\frac{1}{1+n}\frac{1}{1+\rho}\tau \nonumber \\
&=& ak_{t}^{b} + d
\end{eqnarray}
where
\begin{eqnarray}
a &=& \frac{1}{1+n}\frac{1}{1+\rho}(1-\alpha) \nonumber \\
b &=& \alpha \nonumber \\
c &=& -\frac{1}{1+n}\frac{1}{1+\rho} \times \tau \nonumber
\end{eqnarray}
Can anyone give me any clues as for c? | 2017-12-18 15:37:15 | {"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": 0.8236247897148132, "perplexity": 7090.8119510671795}, "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/1512948617816.91/warc/CC-MAIN-20171218141805-20171218163805-00362.warc.gz"} |
https://gerhardriener.github.io/tags/behavioural-economics/ | # Behavioural-Economics
Revised and resubmitted Review of Economic Studies Working paper August 2019 In many intertemporal decisions, the benefit of an action is concentrated in a few time periods, while the associated cost is dispersed over numerous periods. According to the focusing model” by \cite{Koszegi2013}, the more a utility outcome is concentrated in time, the more a decision maker focuses on and, hence, \textit{over}weights it. Such concentration bias provides a micro-foundation for present-biased and future-biased behaviour. | 2019-10-17 13:48:49 | {"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": 0.41709670424461365, "perplexity": 3379.6083441280916}, "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/1570986675316.51/warc/CC-MAIN-20191017122657-20191017150157-00012.warc.gz"} |
http://www.maths.usyd.edu.au/u/pubs/publist/preprints/2010/bridson-16.html | ## Cofinitely Hopfian groups, open mappings and knot complements
### M.Bridson, D.Groves, J.A.Hillman, G.J.Martin
#### Abstract
A group $\Gamma$ is defined to be cofinitely Hopfian if every homomorphism $\Gamma\to\Gamma$ whose image is of finite index is an automorphism. Geometrically significant groups enjoying this property include certain relatively hyperbolic groups and many lattices. A knot group is cofinitely Hopfian if and only if the knot is not a torus knot. A free-by-cyclic group is cofinitely Hopfian if and only if it has trivial centre. Applications to the theory of open mappings between manifolds are presented.
Keywords: Cofinitely Hopfian, open mappings, relatively hyperbolic, free-by-cyclic, knot groups.
: Primary 20F65; secondary 57M25.
This paper is available as a pdf (184kB) file.
Monday, August 16, 2010 | 2018-12-10 01:00:39 | {"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": 0.5683813095092773, "perplexity": 837.4175589071954}, "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-2018-51/segments/1544376823228.36/warc/CC-MAIN-20181209232026-20181210013526-00556.warc.gz"} |
https://www-sop.inria.fr/mascotte/EULER/wiki/pmwiki.php/PmWiki/Links?action=print | ### From EULER Project
A key feature of Wiki Wiki Webs is the ease of creating hyper links in the text of a document. PmWiki provides multiple mechanisms for creating such links.
## Links to other pages in the wiki
To create a link to another page, simply enclose the name of the page inside double square brackets, as in [[wiki sandbox]] or [[installation]]. These result in links to wiki sandbox and installation, respectively.
PmWiki creates a link by using the text inside the double brackets. It does this by removing spaces between words, and automatically capitalizing words following spaces or other punctuation (like ~). Thus [[Wiki sandbox]], [[wiki sandbox]], and [[WikiSandbox]] all display differently but create the same link to the page titled WikiSandbox.
In other words, PmWiki will automatically create the link path name using title case as a rule, but link text will display in the format you have entered it.
A suffix can also be added to the end of a link, which becomes part of the link text but not the target. Thus [[wiki sandbox]]es is a link to WikiSandbox but displays as wiki sandboxes.
Link text in (parentheses) will not be not displayed, so that [[(wiki) sandbox]] links to WikiSandbox and displays as sandbox.
Finally, you can specify the link text via a vertical brace, thus [[WikiSandbox | a play area]], which links to WikiSandbox but displays as a play area. You can use an arrow (->) to reverse the order of the text and target, as in [[a play area -> WikiSandbox]] (a play area).
Some sites also recognize WikiWord links, in which a camel case (capitalised) WikiWord appearing in the text is automatically treated as a link to a page of the same name.
Use of special characters in title is not a problem for PmWiki, but sometimes the character set is different from your computer and the server computer or the client computer that is used to read your wiki. Specially UTF-8 gives some problems. So it's better not to use these and keep ASCII characters if possible. Any page can have a (:title <name>:) directive to display a localized title instead of the page file name. In this case, the following tip is important and usefull.
[[PageName|+]] creates a link to PageName and uses that page's title as the link text, eg [[PmWiki.BasicEditing|+]] where the page Installation has the directive (:title Basic PmWiki editing rules:)=] gives Basic PmWiki editing rules.
[[!PageName]] creates a link to the PageName in the group called Category. See Categories.
[[~Author]] link creates a link to the page in the page called Author in the Profiles group. PmWiki will automatically generate that link for the current Author when it encounters three tilde characters (~) in a row (~~~). Adding a fourth tilde (~~~~) appends the current date and time.
### Links to specific locations within a page -- "anchors"
To define a location within a page to which you may jump directly, use the markup [[#name]]. This creates an "anchor" that uniquely identifies that location in the page. Then to have a link jump directly to that anchor, use one of
• [[#name|link text]] within the same page, or
• [[PageName#name]] or [[PageName#name|link text]] for a location on another page
• The form [[PageName(#name)]] may be useful for hiding the anchor text in a link.
For example, here's a link to the Intermaps section, below.
Notes:
• the anchor itself must begin with a letter, not a number
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### Links to external sites (URLs)
If the external link includes (parentheses), escape these using %28 for "(" and %29 for ")" :
[[http://en.wikipedia.org/wiki/Wiki_%28disambiguation%29 | link to "Wiki (disambiguation)" ]]
### Links to intranet (local) files
You can link to a file system by including the prefix 'file:///' (for Internet Explorer at least). So file:///S:\ProjPlan.mpp and [[Shared S drive->file:///S:\]] are both valid links. On a Windows file system you may want to use network locations (eg \\server1\rootdirectory\subdirectory) rather than drive letters which may not be consistent across all users. Not all browsers will follow such links.
Links may also be specified as References, so the target appears as an anonymous numeric reference rather than a textual reference. The following markup is provided to produce sequential reference numbering within a PmWiki page:
Subsequent occurrence of the reference link format on the same page will be incremented automatically as per the following example: Entering [[http://pmwiki.com |#]] produces [2](approve sites), [[#intermaps |#]] produces Intermaps, and so on for further reference links.
### Intermaps
Inter Map links are also supported (see Inter Map). In particular, the Path: InterMap entry can be used to create links using relative or absolute paths on the current site (e.g., Path:../../somedir/foo.html or Path:/dir/something.gif).
See Wiki Group.
### Links that open a new browser window
To have a link open in another window, use %newwin%...%%:
You can also specify that links should open in a new window via the %target=_blank%...%% attribute:
The following link %target=_blank% http://pmichaud.com %% will open in a new window. The following link http://pmichaud.com will open in a new window.
### Links that are not followed by robots
PmWiki automatically gives classes to several types of links. Among other things, this enables you to format each type differently.
Note: This may be an incomplete list.
A link to the current page. Useful in sidebars to show "you are here".
A link to another page within the wiki.
A link to a page outside the wiki.
You can create a the class .anchor for anchor links
[[#target]], aka <A name='target'></A>
by putting the following in config.php :
Markup('[[#','<[[','/(?>\$\\[#([A-Za-z][-.:\\w]*))\$\\]/e',
"Keep(TrackAnchors('$1') ? '' : \"<a name='$1' id='$1' class='anchor'></a>\", 'L')"); ## Notes Note: The default behavior of "+" above can be overridden to display the spaced title, rather than simply the title by adding the following to config.php: ## [[target |+]] title links Markup('[[|+', '<[[|', "/(?>\$\\[([^|\$]+))\\|\\s*\\+\\s*]]/e", "Keep(MakeLink(\$pagename, PSS('$1'), PageVar(MakePageName(\$pagename,PSS('$1')), '\$Titlespaced')
),'L')");
How do I create a link that will open as a new window?
Use the %newwin% wikistyle, as in:
%newwin% http://example.com/ %%
How do I create a link that will open a new window, and configure that new window?
This requires javascript. See Cookbook:PopupWindow.
How do I place a mailing address in a page?
Use the mailto: markup, as in one of the following:
The markup [[mailto:me@example.com?cc=someoneelse@example.com&bcc=else@example.com&subject=Pre-set Subject&body=Pre-set body | display text]] =] lets you specify more parameters like the message body and more recipients (may not work in all browsers and e-mail clients).
How can I enable links to other protocols, such as nntp:, ssh:, xmpp:, etc?
How do I make a WikiWord link to an external page instead of a WikiPage?
Use link markup. There are two formats:
[[http://example.com/ | WikiWord]]
[[WikiWord -> http://example.com/]]
How do I find all of the pages that link to another page (i.e., backlinks)?
In the wiki search form, use link=Group.Page to find all pages linking to Group.Page.
Use the link= option of the (:pagelist:) directive, as in | 2018-03-20 23:15:23 | {"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": 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": 0.553511917591095, "perplexity": 4177.477265600841}, "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-2018-13/segments/1521257647545.84/warc/CC-MAIN-20180320224824-20180321004824-00276.warc.gz"} |
https://www.physicsforums.com/threads/identifying-the-forces-acting-on-masses-in-uniform-circular-motion.312313/ | # Identifying the forces acting on masses in uniform circular motion.
1. May 6, 2009
### deancodemo
1. The problem statement, all variables and given/known data
Two particles of masses 2kg and 1kg are attached to a light string at distances 0.5m and 1m respectively from one fixed end. Given that the string rotates in a horizontal plane at 5 revolutions/second, find the tensions in both portions of the string.
2. Relevant equations
3. The attempt at a solution
First I convert the angular velocity from rev/sec to rad/sec.
$$\omega = 5$$ rev/sec
$$\omega = 10\pi$$ rad/sec
Now, let the 2kg mass be P, the 1kg mass be Q and the fixed point be O. I understand that the tension in PQ < tension in OP. Actually, the tension in OP should equal the centripetal force acting on P plus the tension in PQ. Right?
I get confused when identifying the forces acting on P. By using R = ma:
$$R = ma$$
(Tension in OP) + (Tension in PQ) $$= m r \omega^2$$
(Tension in OP) = $$m r \omega^2 -$$ (Tension in PQ)
This is incorrect!
The only solution would be:
$$R = ma$$
(Tension in OP) - (Tension in PQ) $$= m r \omega^2$$
(Tension in OP) = $$m r \omega^2 +$$ (Tension in PQ)
Which makes sense, but this means that the tension forces acting on P in the different sections of string act in opposite directions. Is that right?
Last edited: May 6, 2009
2. May 6, 2009
### nickjer
Draw a free body diagram of the forces acting on the mass at P. You will see both ropes on either side of the mass pulling in opposite directions. That is why your 2nd set of equations is correct. | 2017-08-23 18:48:07 | {"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": 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": 0.7335767149925232, "perplexity": 1088.6369143843344}, "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-2017-34/segments/1502886123312.44/warc/CC-MAIN-20170823171414-20170823191414-00011.warc.gz"} |
https://docs.actian.com/dataconnect/11.6/User/About_Macro_Definition_Files.htm | User Guide > Managing Macro Sets and Macros > About Macro Definition Files
Macro sets and macros reside in your workspace in a file called the macro definition file. Any macro sets or macros that you create are saved in this file. The macro definition file contains the macro sets that can be referenced by any project or artifact in the workspace. If you switch between macro set definition files that contain different macro sets:
It is recommended to close all open editors and then open the artifacts that will use the other macro definition file
If the macro definition file that you have switched to does not contain macro sets used in maps or processes that are reopened, then the missing macro sets are removed from the map or process.
The supported file formats are:
XML
For backward compatibility with Data Integrator v9.
Only one GLOBAL macro set is allowed.
Encryption is not supported.
JSON
New macro definition files are created in JSON format.
Allows duplicate macro names if the macros are in different macro sets. The usage of the duplicate macro depends on the order of the macro sets listed in the runtime Configuration tab of a map or process.
Encrypted macros and macro sets are only supported in JSON format files. If you add any of these to an XML macro definition file, you must save it as JSON format.
The default macro definition file name is MacroDef.xml and the default location is C:\Users\<username>\Actian\DataConnect\workspace\. | 2022-08-18 11:50:01 | {"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": 0.9516651630401611, "perplexity": 3194.586230956775}, "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-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00228.warc.gz"} |
http://tex.stackexchange.com/questions/14808/ellipse-with-latitude-and-longitude-circles-in-tikz | # Ellipse with latitude and longitude circles in TikZ
Does anyone of you have a clever way of coding
in Tikz? My own solution currently is to draw an ellipse, then to specify each dashed arc explicitly, a thoroughly plebeian technique.
-
I very much like Altermundus' solution, but if you want exactly what you drew, here's how I would do it:
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\begin{document}
\begin{tikzpicture}
\node[draw,ellipse,minimum width=4cm,minimum height=2cm] (ell) {};
\foreach \ang in {-70,-60,...,70} {
\pgfmathtruncatemacro{\rang}{180 - \ang}
\draw[dashed,shorten >=1pt,shorten <=1pt] (ell.\ang) -- (ell.\rang);
}
\foreach \ang in {-65,-45,...,65} {
}
\end{tikzpicture}
\end{document}
Result:
I think that if given a little latitude in the design, then I would add a gentle curve to the lines of latitude.
-
Thank you, Andrew! This is precisely what I asked for. – Thanos D. Papaïoannou Apr 2 '11 at 21:18
The next code is an adaptation of the code globe.tex of Tomasz M. Trzeciak
\documentclass{scrartcl}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{5pt}
\pagestyle{empty}
\newcommand\pgfmathsinandcos[3]{%
\pgfmathsetmacro#1{sin(#3)}
\pgfmathsetmacro#2{cos(#3)}}
\newcommand\LatitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2}
\pgfmathsinandcos\sint\cost{#3}
}
\newcommand\LongitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2}
\pgfmathsinandcos\sint\cost{#3}
\tikzset{#1/.estyle={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}}
\newcommand\DrawLatitudeCircle[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.estyle={cm={\cost,0,0,\cost*\sinEl,(0,\cosEl*\sint)}}}
\tikzset{current plane/.prefix style={xscale=\R,yscale=\RR}}
\pgfmathsetmacro\sinVis{tan(#2)*tan(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
\draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1);
\draw[current plane,dashed,black!80] (180-\angVis:1) arc (180-\angVis:\angVis:1);
}
\newcommand\DrawLongitudeCircle[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={xscale=\R,yscale=\RR}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1);
\draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
}
\begin{document}
\begin{tikzpicture}[scale=3]
\def\R{2.5}
\def\RR{3.5}
\def\angEl{15}
\foreach \t in {-80,-70,...,80} { \DrawLatitudeCircle[\R]{\t} }
\foreach \t in {-5,-35,...,-175} { \DrawLongitudeCircle[\R]{\t} }
\end{tikzpicture}
\end{document}
-
Thank you, Altermundus, this is quite wonderful, but I'm afraid less close to what I wanted than Stacey's solution. – Thanos D. Papaïoannou Apr 2 '11 at 21:18
This is only a complement with my own code and own package to get a similar drawing:
\documentclass[a4paper]{scrartcl}
\usepackage[usenames,dvipsnames,svgnames]{xcolor}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usepackage[frenchb]{babel}
\definecolor{fondpaille}{cmyk}{0,0,0.1,0}
\tkzSetUpColors[background=fondpaille,text=Maroon]
\begin{document}
\begin{tikzpicture}[xscale=.6,yscale=.4]
\tkzInit[xmin=-10,xmax=10,ymin=-10,ymax=10]
\tkzDefPoint(0 , 0){O}
\tkzDefPoint(9 , 0){A}
\tkzDefPoint(-9, 0){C}
\tkzDefPoint(0 , 9){B}
\tkzDefPoint(0 ,-9){D}
\tkzClipCircle(O,A)
\foreach \pti in {1,2,...,8}{
\tkzDefPoint(10*\pti:9){P\pti}
\tkzDefPoint(90:\pti){MP\pti}
\tkzDefPoint(0: \pti){NP\pti}
\tkzDefLine[mediator](MP\pti,P\pti)
\tkzInterLL(B,D)(tkzFirstPointResult,tkzSecondPointResult)
\tkzDrawCircle[color=Maroon](tkzPointResult,P\pti)
}
\foreach \pti in {-1,-2,...,-8}{
\tkzDefPoint(10*\pti:9){P\pti}
\tkzDefPoint(-90:-\pti){MP\pti}
\tkzDefPoint(0: -\pti){NP\pti}
\tkzDefLine[mediator](MP\pti,P\pti)
\tkzInterLL(B,D)(tkzFirstPointResult,tkzSecondPointResult)
\tkzDrawCircle[color=Maroon](tkzPointResult,P\pti)
}
\foreach \pti in {1,2,...,8}{
\tkzDefLine[mediator](B,NP\pti)
\tkzInterLL(A,C)(tkzFirstPointResult,tkzSecondPointResult)
\tkzDrawCircle[color=Maroon](tkzPointResult,NP\pti)
}
\foreach \pti in {1,2,...,8}{
\tkzDefPoint(0: -\pti){NP\pti}
\tkzDefLine[mediator](B,NP\pti)
\tkzInterLL(A,C)(tkzFirstPointResult,tkzSecondPointResult)
\tkzDrawCircle[color=Maroon](tkzPointResult,NP\pti)
}
\tkzDrawCircle[R,color=Maroon](O,9 cm)
\tkzDrawSegments[color=Maroon](A,C B,D)
\end{tikzpicture}
\end{document}
-
By the way, I'd like to draw your attention to a question about TikZ on meta: meta.tex.stackexchange.com/q/1220/86 – Loop Space Apr 3 '11 at 18:58
@Andrew I don't know exactly how to use this excellent forum, my english is not very good and I don't know exactly what is Meta ? I need to read the FAQ ! – Alain Matthes Apr 3 '11 at 19:26
"Meta" is a website for talking about this place (talking about things like tagging policy and other stuff). In my comment, the text starting 'meta.tex....' should be a clickable link. If you click on it, you'll be taken to a question that I'd be interested in your opinion of. – Loop Space Apr 3 '11 at 19:50
@Andrew thanks for the explanations. I need to read old answers to get an opinion. I think the idea to create a real community project is very good. – Alain Matthes Apr 3 '11 at 20:00 | 2015-05-28 16:36:35 | {"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": 0.7400299310684204, "perplexity": 7018.073568155647}, "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-2015-22/segments/1432207929422.8/warc/CC-MAIN-20150521113209-00337-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rae/1214571379 | ## Real Analysis Exchange
### Small Combinatorial Cardinal Characteristics and Theorems of Egorov and Blumberg
#### Abstract
We will show that the following set theoretical assumption
$\mathfrak{c}=\omega_2$, the dominating number $\mathfrak {d}$ equals to $\omega_1$, and there exists an $\omega_1$-generated Ramsey ultrafilter on $\omega$
(which is consistent with ZFC) implies that for an arbitrary sequence $f_n\colon\mathbb{R}\to\mathbb{R}$ of uniformly bounded functions there is a set $P\subset\mathbb{R}$ of cardinality continuum and an infinite $W\subset\omega$ such that $\{f_n\restriction P\colon n\in W\}$ is a monotone uniformly convergent sequence of uniformly continuous functions. Moreover, if functions $f_n$ are measurable or have the Baire property then $P$ can be chosen as a perfect set. We will also show that cof$(\mathcal{N})=\omega_1$ implies existence of a magic set and of a function $f\colon\mathbb{R}\to\mathbb{r}$ such that $f\restriction D$ is discontinuous for every $D\notin\mathcal{N}\cap\mathcal{M}$.
#### Article information
Source
Real Anal. Exchange Volume 26, Number 2 (2000), 905-912.
Dates
First available: 27 June 2008
http://projecteuclid.org/euclid.rae/1214571379
Mathematical Reviews number (MathSciNet)
MR1844405
Zentralblatt MATH identifier
1017.26003
#### Citation
Ciesielski, Krzysztof; Pawlikowski, Janusz. Small Combinatorial Cardinal Characteristics and Theorems of Egorov and Blumberg. Real Analysis Exchange 26 (2000), no. 2, 905--912. http://projecteuclid.org/euclid.rae/1214571379.
#### References
• T. Bartoszyński, H. Judah, Set Theory, A K Peters, 1995.
• J. Baumgartner, R. Laver, Iterated perfect-set forcing, Ann. Math. Logic 17 (1979), 271–288.
• A. Berarducci, D. Dikranjan, Uniformly approachable functions and $UA$ spaces, Rend. Ist. Matematico Univ. di Trieste 25 (1993), 23–56.
• H. Blumberg, New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), 113–128.
• M. R. Burke, K. Ciesielski, Sets on which measurable functions are determined by their range, Canad. J. Math. 49 (1997), 1089–1116. (Preprint$^\star$ available. \footnotePreprints marked by $^\star$ are available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/~kcies/STA/STA.html)
• M. R. Burke, K. Ciesielski, Sets of range uniqueness for classes of continuous functions, Proc. Amer. Math. Soc. 127 (1999), 3295–3304. (Preprint$^\star$ available.)
• K. Ciesielski, Set theoretic real analysis, J. Appl. Anal. 3(2) (1997), 143–190. (Preprint$^\star$ available.)
• K. Ciesielski, Set Theory for the Working Mathematician,
• K. Ciesielski, J. Pawlikowski, Covering property axiom CPA, work in progress$^\star$.
• K. Ciesielski, S. Shelah, Model with no magic set, J. Symbolic Logic 64(4) (1999), 1467–1490. (Preprint$^\star$ available.)
• S. Fuchino, Sz. Plewik, On a theorem of E. Helly, Proc. Amer. Math. Soc. 127(2) (1999), 491–497.
• A. B. Kharazishvili, Strange Functions in Real Analysis, Pure and Applied Mathematics 229, Marcel Dekker, 2000.
• S. Mazurkiewicz, Sur les suites de fonctions continues, Fund. Math. 18 (1932), 114–117.
• A. Rosłanowski, S. Shelah, Measured Creatures, preprint.
• S. Shelah, Possibly every real function is continuous on a non–meagre set, Publ. Inst. Mat. (Beograd) (N.S.) 57(71) (1995), 47–60.
• W. Sierpiński, Remarque sur les suites infinies de fonctions (Solution d'un problème de M. S. Saks), Fund. Math. 18 (1932), 110–113.
• S. Todorcevic, Partition problems in topology, Contemp. Math. 84, Amer. Math. Soc. 1989. | 2014-03-09 14:48:18 | {"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": 0.7724235653877258, "perplexity": 2056.102540864545}, "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-2014-10/segments/1393999679206/warc/CC-MAIN-20140305060759-00050-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://gate-exam.in/CS/Syllabus/Computer-Science-Information-Technology/Compiler-Design/Lexical-analysis | # Questions & Answers of Lexical analysis
## Weightage of Lexical analysis
Total 6 Questions have been asked from Lexical analysis topic of Compiler Design subject in previous GATE papers. Average marks 1.33.
A lexical analyzer uses the following patterns to recognize three tokens T1, T2, and T3 over the alphabet {a,b,c}.
Note that ‘x?’ means 0 or 1 occurrence of the symbol x. Note also that the analyzer outputs the token that matches the longest possible prefix.
If the string bbaacabc is processed by the analyzer, which one of the following is the sequence of tokens it outputs?
Match the following:
(P) Lexical analysis (i) Leftmost derivation (Q) Top down parsing (ii) Type checking (R) Semantic analysis (iii) Regular expressions (S) Runtime environments (iv) Activation records
Match the following:
P. Lexical analysis Q. Parsing R. Register allocation S. Expression evaluation 1. Graph coloring 2. DFA minimization 3. Post-order traversal 4. Production tree
In a compiler, keywords of a language are recognized during
Which data structure in a compiler is used for managing information about variables and their attributes?
I. There exist parsing algorithms for some programming languages whose complexities are less than $\mathrm{\theta }$(n3). | 2018-10-22 19:15:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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": 0.39821818470954895, "perplexity": 8328.416049908561}, "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-2018-43/segments/1539583515375.86/warc/CC-MAIN-20181022180558-20181022202058-00246.warc.gz"} |
https://blog.csdn.net/chenzhen1080/article/details/82500226 | # Linux过时了- 塔能鲍姆-托瓦兹辩论(Tanenbaum–Torvalds debate)
Linux 是过时的
1. Linux过时了(Linus vs. Tanenbaum的中文翻译)
(以下的内容译自http://oreilly.com/catalog/opensources/book/appa.html。原文的注释和我自己的注释全在括号中，但我自己的注释加了“译者注：”的标记)。
Andy Tanenbaum
1. 微内核(Micro Kernel) vs 宏内核(Monolithic System)
Minix是微内核系统。文件系统和内存管理是两个分离的进程，并且它们运行在内核之外。输入输出设备的驱动也都有各自的进程(虽然是在内核态，但这全怪英特尔处理器那些愚蠢至极的特性)，Linux是宏内核的。这完全是倒退到了20世纪70年代。这好比用Basic来重写一个已经出色工作的C语言程序一样。对我而言，在1991年写一个宏内核系统真是一个糟糕的主意。
2. 可移植性
Minix在移植性上设计的较为合理。并且已经从英特尔的处理器移植到了68000，SPARC和NS32061的芯片上。Linux和80×86绑的太紧密了。这不是正道。
Linus Benedict Torvalds
1. 微内核vs 宏内核
Minix是微内核的，Linux是宏内核的。
(是的，我知道Minix的多线程里用很多的技巧，但那仅仅是技巧。并且Bruce Evans告诉我Minix里面也有很多的边界条件导致线程竞争。)
2. 可移植性
“可移植性是为那些不会写新程序的人们准备的。” ——至于我，现在毫无压力(译者注：这里的原文是“me,right now(with tongue in my ckeek)”。tongue in cheek有半开玩笑的意思。译者觉得Linus这句挑衅的话有随便开玩笑说说的感觉。所以在这里揣测语境随便意译了一下)。
Linus
Andy Tanenbaum
Minix的局限性至少和我作为一个教授是有点关系的：Minix一个极为明确的设计目标是它能够运行在便宜的硬件上，这样学生才能负担的起。尤其是这么多年来，它一直运行在一个主频是4.77MHZ的PC上，而这台PC连硬盘都没有。在这台机器上你可以做任何事情，包括修改和重新编译整个系统。不妨也顺便告诉你，大概在一年以前，有两个版本的Minix，一个是PC版的(360K的磁盘空间)，另一个是286/386版的(1.2M磁盘空间)。PC版大概要比286/386多卖出一倍。我没有统计过，但据我推测，当今世界现有的六千万台个人电脑中，386/486机器的数量相对8088/286/680×0的机器来说肯定要少。在学生群体中这个数量就更少了。把软件搞成自由软件，这对于那些有钱买的起一流硬件的人来说只不过是一个很可笑的概念。当然5年之后情况又会不同，但是5年之后大家早已纷纷在自己200MIPS、64兆的SPARC-5工作站上跑起免费的GNU系统了。
Amoeba不是为一个无磁盘的8088计算机设计的。
Minix在设计的时候还没有POSIX，上这个新闻组的人也都知道它现在正在慢慢地POSIX标准化。每个人都赞同用户级的标准是个好主意。顺便插一句，恭喜你在手头没有POSIX标准的前提下做了一个和POSIX标准兼容的系统。我发觉即便在对标准做长时间学习后，想做到和它兼容都不是件容易事。
Prof. Andrew S. Tanenbaum (ast@cs.vu.nl)
ast@cs.vu.nl (Andy Tanenbaum) 说：
Ken
Kevin Brown
OS就应该能够轻易移植到新的硬件平台上。
Linux里面唯一不可移植的部分就是内核底层和驱动。和编译器啦、工具包啦、窗口管理系统啦什么的比起来，这也只占很少的一点工作量。既然Linux在系统调用上和可移植操作系统有很高的兼容性，那我也没什么好吐槽的了。能有一个OS让我们更有可能利用来自Berkeley、FSF、CMU等处的软件，我个人对此双手点赞。两三年后，相当实惠的BSD变种和Hurd的使用量或许会激增，那时Linux才算真过时了。至于现在么，Linux大大降低了如gcc, bison, bash之类工具的使用成本，这对开发相当有好处——比如说开发OS。
Linus Benedict Torvalds
minix的局限性至少和我作为一个教授是有点关系的：minix一个极为明确的设计目标是它能够运行在便宜的硬件上，这样学生才能负担的起。
Linus
——————————————————————————-
Andy Tanenbaum写了一篇很搞笑的文章(发现他也上这个新闻组同样也很搞笑)，但是我觉得他忽略了很重要的一点。
MINIX在移植性上的设计较为合理。并且已经从英特尔的处理器移植到了68000,SPARC,和NS32061的芯片上。LINUX和80×86绑的太紧密了。这不是正道。
——————————————————————————
10年前的MS-DOS是专门为8088写的，这就有点不太明智，但IBM和微软好歹还是在吃尽苦头之后意识到了这点。
Michael
(如果文件系统只管文件操作而不和终端IO交互的话，这个问题的严重程度貌似有点减轻。)
Richard
Andy Tanenbaum (ast@cs.vul.nl)
ast@cs.vu.nl (Andy Tanenbaum) 说:
Andy，自从minix第一条消息发布到这个新闻组上起，我就随着minix的不停开发在用minix了，我现在用的是Bruce Evans打了补丁的1.5.10版。
Tony
Richard
Philip Wu
pwu@unixg.ubc.ca
MINIX是微内核系统。
Linux是宏内核的.这完全是倒退到了20世纪70年代。这好比用Basic来重写一个已经出色工作的C语言程序一样。对我而言，在1991年写一个宏内核系统真是一个糟糕的主意。
Doug Graham
dgraham@bnr.ca
(1)Minix在未来几年一点都没有要利用比8086更高级的特性的意思。
(2)许可证——尽管还是及其友好的——但仍旧很难让对其有兴趣的人们开发一个386的版本。有好几个人明显已经在386上做出了相当出色的工作了，但他们只能用diff给源代码发布补丁。这让新手想装一个386的系统变得不切实际，事实上我也不太确定我是不是愿意这么搞。
Linux也不是没有可能不会被GNU或者是BSD取代。但是如果GNU的操作系统也像其他的GNU软件一样的话，那么它至少也得需要128M的内存和1G的硬盘。再放一个小点的系统还是有空间的。我理想中的OS其实是4.4BSD。但是4.4向来喜欢长时间延期发布。一想到他们大部分成员都搬到了BSDI(Berkely Software Design Inc，伯克利软件设计公司)，我就打死都不会相信这一点会有所改善。就我个人使用经验来看，BSDI的系统可能会比较给力。但是他们那些”诱人”的价格也极有可能对我们大部分学生都高的吓人。就算用户能从他们那儿拿到源代码，但是软件的所有权却再次意味着你没有权利把修改后的代码发布到FTP上。无论如何，现在有Linux了，让剩下的那些选择们吹他们的大牛去吧。
ast@cs.vu.nl (Andy Tanenbaum)说：
Theodore Y. Ts’o
MINIX在移植性上的设计较为合理。并且已经从英特尔的处理器移植到了68000,SPARC,和NS32061的芯片上。
——全书(译者注：指Tanenbaum写的《操作系统，设计与实现》一书，在书中他用Minix作为示例讲解操作系统的实现)压根就没有提过可移植性的话题(除了一些“#ifdef M8088”的宏)
——在minix发布的时候，它已经依赖了很多8086的特性，这让68000的用户们颇为不满。
joe
Linux的发布给了我一个机会让我尝试一些我好几年前就想试验的点子，之前我还没有过任何机会给一个运作良好的操作系统维护源代码。
Andy Tanenbaum (ast@cs.vu.nl)
QNX是一个基于微内核的操作系统，有些人告诉我其安装量达20 0000。
AmigaOS作为一个微内核系统，其设计理念是消息传递，其响应时间和性能都强过现在任何一个能用的操作系统：包括minix，OS/2，Windows，MacOS，Linux，UNIX，当然还有MS-DOS。
Linux自由好用是相当不错。它的存在很让我高兴。我也知道它能够如此迅疾得以实现的一个原因是它采用了宏内核的架构，这也是采用宏内核一个很正当的缘由。但是，这并不意味着微内核天生就很慢，或者仅仅只是一个用来研究的玩具。
David Cheriton(在斯坦福大学任教授，并且是System V的作者)在一堂分布式系统的课上说过和这个类似的话。原话大意是这样的：
“研究人员分两种：实现过一些东西的和还没有实现过什么的。后者一般会和你说实现某某某有142种方法，但哪个最好目前还没有定论。而前者直接就会告诉你有141种是靠不住的。”
Linus Benedict Torvalds
Newsgroups: comp.os.minix
Linus Torvalds
1) Linux是免费的。
2) Linux发展在一个让人满意的修改之中(因为Linus允许在发行版中添加新特性).
•没有对386的支持没有虚拟终端
•没有符号链接
•没有select系统调用
•没有伪终端
•没有请求调页/盘交换区/共享正文段/共享库….（就是说没有有效的内存管理）
•chmem(内 存管理真够顽固)(译者注：在可执行文件中，一般会有一个字段指定该可执行文件的初始栈的大小。在绝大多数的现代操作系统中，如果栈的使用量达到这个值会 自动扩充。Minix的栈不会扩充，所以如果程序要使用较大的栈，需要在进程初始化的时候用chmem命令来指定栈的大小。)
•没有X-Windows(出于同样的原因，提倡Linux和386也添加这个特性)
•没有TCP/IP
•不能够和GNU/System V集成(可移植性)
Andy Tanenbaum
1.宏内核不比微内核差
2.移植性没那么重要
3.软件应该是自由免费的
Andy Tanenbaum (ast@cs.vu.nl)
Fred
Andy Tanenbaum (ast@cs.vu.nl)
Linus
Minix的定位是”真正的操作系统”呢还是一个教学工具呢？作为一个教学工具它是一个杰作。作为一个真正的操作系统有些地方它表现的还是太糙了(为什么没有malloc()，仅仅是由于它是为初学者们准备的么？)。读你的书还有在这儿看了这些邮件给我的感觉就是你想要个工具来教学，然后很多其他人是把minix当成一个可以品玩的付费操作系统。他们一直在尝试把大量的特性栓到minix上让它成为一个”真正的操作系统”，不过他们都不太成功。
David
•1.6.17补丁将和PH1.5的发行版相关。
•头文件清除了。
•两种文件系统可以混用。
•信号控制重新做了实现，和POSIX兼容。消除了旧缺陷。
•ANSI编译器(我猜是从Transmediar那儿来的)以二进制发布，更新了程序库。
•不再支持Amoeba的网络协议。
•修正了times函数的返回结果。实现了termios，但更多的来说只不过是一个技巧。我不知道实现是在内核里呢，还是在现在的模拟器上。
•新的文件系统没有文档。有了新的fsck命令和mkfs命令，不了解详细情况。
•有了ANSI编译器，浮点数得以更好的支持。
•调度策略做了改进，但仍旧不如Kai-Uwe Bloem的实现。
•Minix根本就么有一个可以借其打补丁的“当前”发行版，也没有人知道1.6.17什么时候会出来。
•现在的运行库有几个缺陷，我听说现在都还没有修复。不会再有一个新的编译器，16位的用户们还得接着用满是缺陷的ACK（Amsterdam Compiler Kit，阿姆斯特丹编译套件）。
•1.6.17应该会支持更多POSIX，但是一个完整的伪终端仍旧没有。
•你没有硬盘就能玩它，甚至都能编译程序。几年前我就这么干过。
•它很小，你不用了解多少就能获得一个跑的很爽的小系统。
•还有一本书。不错，虽然只有1.3版本的，但是书本绝大多数内容仍旧有用。
Minix是非宏内核系统的一个示例。不妨叫做微内核，或者是一个为克服愚蠢硬件而做的精巧软件：它证明了一种理念。
Michael
2. Open Sources: Voices from the Open Source Revolution - Appendix A, The Tanenbaum-Torvalds Debate
Appendix A
The Tanenbaum-Torvalds Debate
What follows in this appendix are what are known in the community as the Tanenbaum/Linus “Linux is obsolete” debates. Andrew Tanenbaum is a well-respected researcher who has made a very good living thinking about operating systems and OS design. In early 1992, noticing the way that the Linux discussion had taken over the discussion in comp.os.minix, he decided it was time to comment on Linux.
Although Andrew Tanenbaum has been derided for his heavy hand and misjudgements of the Linux kernel, such a reaction to Tanenbaum is unfair. When Linus himself heard that we were including this, he wanted to make sure that the world understood that he holds no animus towards Tanenbaum and in fact would not have sanctioned its inclusion if we had not been able to convince him that it would show the way the world was thinking about OS design at the time.
We felt the inclusion of this appendix would give a good perspective on how things were when Linus was under pressure because he abandoned the idea of microkernels in academia. The first third of Linus’ essay discusses this further.
Electronic copies of this debate are available on the Web and are easily found through any search service. It’s fun to read this and note who joined into the discussion; you see user-hacker Ken Thompson (one of the founders of Unix) and David Miller (who is a major Linux kernel hacker now), as well as many others.
To put this discussion into perspective, when it occurred in 1992, the 386 was the dominating chip and the 486 had not come out on the market. Microsoft was still a small company selling DOS and Word for DOS. Lotus 123 ruled the spreadsheet space and WordPerfect the word processing market. DBASE was the dominant database vendor and many companies that are household names today–Netscape, Yahoo, Excite–simply did not exist.
From: ast@cs.vu.nl (Andy Tanenbaum)
Newsgroups: comp.os.minix
Subject: LINUX is obsolete
Date: 29 Jan 92 12:12:50 GMT
I was in the U.S. for a couple of weeks, so I haven’t commented much on
LINUX (not that I would have said much had I been around), but for what
it is worth, I have a couple of comments now.
As most of you know, for me MINIX is a hobby, something that I do in the
evening when I get bored writing books and there are no major wars,
revolutions, or senate hearings being televised live on CNN. My real
job is a professor and researcher in the area of operating systems.
As a result of my occupation, I think I know a bit about where operating
are going in the next decade or so. Two aspects stand out:
1. MICROKERNEL VS MONOLITHIC SYSTEM
Most older operating systems are monolithic, that is, the whole operating
system is a single a.out file that runs in ‘kernel mode.’ This binary
contains the process management, memory management, file system and the
rest. Examples of such systems are UNIX, MS-DOS, VMS, MVS, OS/360,
MULTICS, and many more.
The alternative is a microkernel-based system, in which most of the OS
runs as separate processes, mostly outside the kernel. They communicate
by message passing. The kernel’s job is to handle the message passing,
interrupt handling, low-level process management, and possibly the I/O.
Examples of this design are the RC4000, Amoeba, Chorus, Mach, and the
not-yet-released Windows/NT.
While I could go into a long story here about the relative merits of the
two designs, suffice it to say that among the people who actually design
operating systems, the debate is essentially over. Microkernels have won.
The only real argument for monolithic systems was performance, and there
is now enough evidence showing that microkernel systems can be just as
fast as monolithic systems (e.g., Rick Rashid has published papers comparing
Mach 3.0 to monolithic systems) that it is now all over but the shoutin’.
MINIX is a microkernel-based system. The file system and memory management
are separate processes, running outside the kernel. The I/O drivers are
also separate processes (in the kernel, but only because the brain-dead
nature of the Intel CPUs makes that difficult to do otherwise). LINUX is
a monolithic style system. This is a giant step back into the 1970s.
That is like taking an existing, working C program and rewriting it in
BASIC. To me, writing a monolithic system in 1991 is a truly poor idea.
2. PORTABILITY
Once upon a time there was the 4004 CPU. When it grew up it became an
8008. Then it underwent plastic surgery and became the 8080. It begat
the 8086, which begat the 8088, which begat the 80286, which begat the
80386, which begat the 80486, and so on unto the N-th generation. In
the meantime, RISC chips happened, and some of them are running at over
100 MIPS. Speeds of 200 MIPS and more are likely in the coming years.
These things are not going to suddenly vanish. What is going to happen
is that they will gradually take over from the 80×86 line. They will
run old MS-DOS programs by interpreting the 80386 in software. (I even
wrote my own IBM PC simulator in C, which you can get by FTP from
ftp.cs.vu.nl = 192.31.231.42 in dir minix/simulator.) I think it is a
gross error to design an OS for any specific architecture, since that is
not going to be around all that long.
MINIX was designed to be reasonably portable, and has been ported from the
Intel line to the 680×0 (Atari, Amiga, Macintosh), SPARC, and NS32016.
LINUX is tied fairly closely to the 80×86. Not the way to go.
Don’t get me wrong, I am not unhappy with LINUX. It will get all the people
who want to turn MINIX in BSD UNIX off my back. But in all honesty, I would
suggest that people who want a **MODERN** “free” OS look around for a
microkernel-based, portable OS, like maybe GNU or something like that.
Andy Tanenbaum (ast@cs.vu.nl)
P.S. Just as a random aside, Amoeba has a UNIX emulator (running in user
space), but it is far from complete. If there are any people who would
like to work on that, please let me know. To run Amoeba you need a few 386s,
one of which needs 16M, and all of which need the WD Ethernet card.
From: torvalds@klaava.Helsinki.FI (Linus Benedict Torvalds)
Subject: Re: LINUX is obsolete
Date: 29 Jan 92 23:14:26 GMT
Organization: University of Helsinki
Well, with a subject like this, I’m afraid I’ll have to reply.
Apologies to minix-users who have heard enough about linux anyway. I’d
like to be able to just “ignore the bait”, but … Time for some
serious flamefesting!
In article <12595@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>
>I was in the U.S. for a couple of weeks, so I haven’t commented much on
>LINUX (not that I would have said much had I been around), but for what
>it is worth, I have a couple of comments now.
>
>As most of you know, for me MINIX is a hobby, something that I do in the
>evening when I get bored writing books and there are no major wars,
>revolutions, or senate hearings being televised live on CNN. My real
>job is a professor and researcher in the area of operating systems.
You use this as an excuse for the limitations of minix? Sorry, but you
loose: I’ve got more excuses than you have, and linux still beats the
pants of minix in almost all areas. Not to mention the fact that most
of the good code for PC minix seems to have been written by Bruce Evans.
Re 1: you doing minix as a hobby – look at who makes money off minix,
and who gives linux out for free. Then talk about hobbies. Make minix
freely available, and one of my biggest gripes with it will disappear.
Linux has very much been a hobby (but a serious one: the best type) for
me: I get no money for it, and it’s not even part of any of my studies
in the university. I’ve done it all on my own time, and on my own
machine.
Re 2: your job is being a professor and researcher: That’s one hell of a
good excuse for some of the brain-damages of minix. I can only hope (and
assume) that Amoeba doesn’t suck like minix does.
>1. MICROKERNEL VS MONOLITHIC SYSTEM
True, linux is monolithic, and I agree that microkernels are nicer. With
a less argumentative subject, I’d probably have agreed with most of what
you said. From a theoretical (and aesthetical) standpoint linux looses.
If the GNU kernel had been ready last spring, I’d not have bothered to
even start my project: the fact is that it wasn’t and still isn’t. Linux
wins heavily on points of being available now.
> MINIX is a microkernel-based system. [deleted, but not so that you
> miss the point ] LINUX is a monolithic style system.
If this was the only criterion for the “goodness” of a kernel, you’d be
right. What you don’t mention is that minix doesn’t do the micro-kernel
thing very well, and has problems with real multitasking (in the
kernel). If I had made an OS that had problems with a multithreading
filesystem, I wouldn’t be so fast to condemn others: in fact, I’d do my
damndest to make others forget about the fiasco.
[ yes, I know there are multithreading hacks for minix, but they are
hacks, and bruce evans tells me there are lots of race conditions ]
>2. PORTABILITY
“Portability is for people who cannot write new programs”
-me, right now (with tongue in cheek)
The fact is that linux is more portable than minix. What? I hear you
say. It’s true – but not in the sense that ast means: I made linux as
conformant to standards as I knew how (without having any POSIX standard
in front of me). Porting things to linux is generally /much/ easier
than porting them to minix.
I agree that portability is a good thing: but only where it actually has
some meaning. There is no idea in trying to make an operating system
overly portable: adhering to a portable API is good enough. The very
/idea/ of an operating system is to use the hardware features, and hide
them behind a layer of high-level calls. That is exactly what linux
does: it just uses a bigger subset of the 386 features than other
kernels seem to do. Of course this makes the kernel proper unportable,
but it also makes for a /much/ simpler design. An acceptable trade-off,
and one that made linux possible in the first place.
I also agree that linux takes the non-portability to an extreme: I got
my 386 last January, and linux was partly a project to teach me about
it. Many things should have been done more portably if it would have
been a real project. I’m not making overly many excuses about it
though: it was a design decision, and last april when I started the
thing, I didn’t think anybody would actually want to use it. I’m happy
to report I was wrong, and as my source is freely available, anybody is
free to try to port it, even though it won’t be easy.
Linus
PS. I apologise for sometimes sounding too harsh: minix is nice enough
if you have nothing else. Amoeba might be nice if you have 5-10 spare
386′s lying around, but I certainly don’t. I don’t usually get into
flames, but I’m touchy when it comes to linux
From: ast@cs.vu.nl (Andy Tanenbaum)
Subject: Re: LINUX is obsolete
Date: 30 Jan 92 13:44:34 GMT
In article <1992Jan29.231426.20469@klaava.Helsinki.FI> torvalds@klaava.Helsinki.
FI (Linus Benedict Torvalds) writes:
>You use this [being a professor] as an excuse for the limitations of minix?
The limitations of MINIX relate at least partly to my being a professor:
An explicit design goal was to make it run on cheap hardware so students
could afford it. In particular, for years it ran on a regular 4.77 MHZ PC
with no hard disk. You could do everything here including modify and recompile
the system. Just for the record, as of about 1 year ago, there were two
versions, one for the PC (360K diskettes) and one for the 286/386 (1.2M).
The PC version was outselling the 286/386 version by 2 to 1. I don’t have
figures, but my guess is that the fraction of the 60 million existing PCs that
are 386/486 machines as opposed to 8088/286/680×0 etc is small. Among students
it is even smaller. Making software free, but only for folks with enough money
to buy first class hardware is an interesting concept.
Of course 5 years from now that will be different, but 5 years from now
everyone will be running free GNU on their 200 MIPS, 64M SPARCstation-5.
>Re 2: your job is being a professor and researcher: That’s one hell of a
>good excuse for some of the brain-damages of minix. I can only hope (and
>assume) that Amoeba doesn’t suck like minix does.
Amoeba was not designed to run on an 8088 with no hard disk.
>If this was the only criterion for the “goodness” of a kernel, you’d be
>right. What you don’t mention is that minix doesn’t do the micro-kernel
>thing very well, and has problems with real multitasking (in the
>kernel). If I had made an OS that had problems with a multithreading
>filesystem, I wouldn’t be so fast to condemn others: in fact, I’d do my
>damndest to make others forget about the fiasco.
A multithreaded file system is only a performance hack. When there is only
one job active, the normal case on a small PC, it buys you nothing and adds
complexity to the code. On machines fast enough to support multiple users,
you probably have enough buffer cache to insure a hit cache hit rate, in
which case multithreading also buys you nothing. It is only a win when there
are multiple processes actually doing real disk I/O. Whether it is worth
making the system more complicated for this case is at least debatable.
I still maintain the point that designing a monolithic kernel in 1991 is
a fundamental error. Be thankful you are not my student. You would not
get a high grade for such a design
>The fact is that linux is more portable than minix. What? I hear you
>say. It’s true – but not in the sense that ast means: I made linux as
>conformant to standards as I knew how (without having any POSIX standard
>in front of me). Porting things to linux is generally /much/ easier
>than porting them to minix.
MINIX was designed before POSIX, and is now being (slowly) POSIXized as
everyone who follows this newsgroup knows. Everyone agrees that user-level
standards are a good idea. As an aside, I congratulate you for being able
to write a POSIX-conformant system without having the POSIX standard in front
of you. I find it difficult enough after studying the standard at great length.
My point is that writing a new operating system that is closely tied to any
particular piece of hardware, especially a weird one like the Intel line,
is basically wrong. An OS itself should be easily portable to new hardware
platforms. When OS/360 was written in assembler for the IBM 360
25 years ago, they probably could be excused. When MS-DOS was written
specifically for the 8088 ten years ago, this was less than brilliant, as
IBM and Microsoft now only too painfully realize. Writing a new OS only for the
386 in 1991 gets you your second ‘F’ for this term. But if you do real well
on the final exam, you can still pass the course.
Prof. Andrew S. Tanenbaum (ast@cs.vu.nl)
From: feustel@netcom.COM (David Feustel)
Subject: Re: LINUX is obsolete
Date: 30 Jan 92 18:57:28 GMT
Organization: DAFCO – An OS/2 Oasis
ast@cs.vu.nl (Andy Tanenbaum) writes:
>I still maintain the point that designing a monolithic kernel in 1991 is
>a fundamental error. Be thankful you are not my student. You would not
>get a high grade for such a design
That’s ok. Einstein got lousy grades in math and physics.
From: pete@ohm.york.ac.uk (-Pete French.)
Subject: Re: LINUX is obsolete
Date: 31 Jan 92 09:49:37 GMT
Organization: Electronics Department, University of York, UK
in article <1992Jan30.195850.7023@epas.toronto.edu>, meggin@epas.utoronto.ca
(David Megginson) says:
>
> In article <1992Jan30.185728.26477feustel@netcom.COM> feustel@netcom.COM
(David > Feustel) writes:
>>
>>That’s ok. Einstein got lousy grades in math and physics.
>
> And Dan Quayle got low grades in political science. I think that there
> are more Dan Quayles than Einsteins out there…
What a horrible thought !
But on the points about microkernel v monolithic, isnt this partly an
artifact of the language being used ? MINIX may well be designed as a
microkernel system, but in the end you still end up with a large
monolithic chunk of binary data that gets loaded in as “the OS”. Isnt it
written as separate programs simply because C does not support the idea
of multiple processes within a single piece of monolithic code. Is there
any real difference between a microkernel written as several pieces of C
and a monolithic kernel written in something like OCCAM ? I would have
thought that in this case the monolithic design would be a better one
than the micorkernel style since with the advantage of inbuilt
language concurrency the kernel could be made even more modular than the
MINIX one is.
Anyone for MINOX
-bat.
From: kt4@prism.gatech.EDU (Ken Thompson)
Subject: Re: LINUX is obsolete
Date: 3 Feb 92 23:07:54 GMT
Organization: Georgia Institute of Technology
viewpoint may be largely unrelated to its usefulness. Many if not
most of the software we use is probably obsolete according to the
latest design criteria. Most users could probably care less if the
internals of the operating system they use is obsolete. They are
rightly more interested in its performance and capabilities at the
user level.
I would generally agree that microkernels are probably the wave of
the future. However, it is in my opinion easier to implement a
monolithic kernel. It is also easier for it to turn into a mess in
a hurry as it is modified.
Regards,
Ken
From: kevin@taronga.taronga.com (Kevin Brown)
Subject: Re: LINUX is obsolete
Date: 4 Feb 92 08:08:42 GMT
Organization: University of Houston
In article <47607@hydra.gatech.EDU> kt4@prism.gatech.EDU (Ken Thompson) writes:
>viewpoint may be largely unrelated to its usefulness. Many if not
>most of the software we use is probably obsolete according to the
>latest design criteria. Most users could probably care less if the
>internals of the operating system they use is obsolete. They are
>rightly more interested in its performance and capabilities at the
>user level.
>
>I would generally agree that microkernels are probably the wave of
>the future. However, it is in my opinion easier to implement a
>monolithic kernel. It is also easier for it to turn into a mess in
>a hurry as it is modified.
How difficult is it to structure the source tree of a monolithic kernel
such that most modifications don’t have a large negative impact on the
source? What sorts of pitfalls do you run into in this sort of endeavor,
and what suggestions do you have for dealing with them?
I guess what I’m asking is: how difficult is it to organize the source
such that most changes to the kernel remain localized in scope, even
though the kernel itself is monolithic?
I figure you’ve got years of experience with monolithic kernels ,
so I’d think you’d have the best shot at answering questions like
these.
Kevin Brown
From: rburns@finess.Corp.Sun.COM (Randy Burns)
Subject: Re: LINUX is obsolete
Date: 30 Jan 92 20:33:07 GMT
Organization: Sun Microsystems, Mt. View, Ca.
In article <12615@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>In article <1992Jan29.231426.20469@klaava.Helsinki.FI> torvalds@klaava.Helsinki.
>FI (Linus Benedict Torvalds) writes:
>Of course 5 years from now that will be different, but 5 years from now
>everyone will be running free GNU on their 200 MIPS, 64M SPARCstation-5.
Well, I for one would _love_ to see this happen.
>>The fact is that linux is more portable than minix. What? I hear you
>>say. It’s true – but not in the sense that ast means: I made linux as
>>conformant to standards as I knew how (without having any POSIX standard
>>in front of me). Porting things to linux is generally /much/ easier
>>than porting them to minix.
………
>My point is that writing a new operating system that is closely tied to any
>particular piece of hardware, especially a weird one like the Intel line,
>is basically wrong.
First off, the parts of Linux tuned most finely to the 80×86 are the Kernel
and the devices. My own sense is that even if Linux is simply a stopgap
measure to let us all run GNU software, it is still worthwhile to have a
a finely tuned kernel for the most numerous architecture presently in
existance.
> An OS itself should be easily portable to new hardware
>platforms.
Well, the only part of Linux that isn’t portable is the kernel and drivers.
Compare to the compilers, utilities, windowing system etc. this is really
a small part of the effort. Since Linux has a large degree of call
compatibility with portable OS’s I wouldn’t complain. I’m personally
very grateful to have an OS that makes it more likely that some of us will
be able to take advantage of the software that has come out of Berkeley,
FSF, CMU etc. It may well be that in 2-3 years when ultra cheap BSD
variants and Hurd proliferate, that Linux will be obsolete. Still, right
now Linux greatly reduces the cost of using tools like gcc, bison, bash
which are useful in the development of such an OS.
From: torvalds@klaava.Helsinki.FI (Linus Benedict Torvalds)
Subject: Re: LINUX is obsolete
Date: 31 Jan 92 10:33:23 GMT
Organization: University of Helsinki
In article <12615@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>The limitations of MINIX relate at least partly to my being a professor:
>An explicit design goal was to make it run on cheap hardware so students
>could afford it.
All right: a real technical point, and one that made some of my comments
inexcusable. But at the same time you shoot yourself in the foot a bit:
now you admit that some of the errors of minix were that it was too
portable: including machines that weren’t really designed to run unix.
That assumption lead to the fact that minix now cannot easily be
extended to have things like paging, even for machines that would
support it. Yes, minix is portable, but you can rewrite that as
“doesn’t use any features”, and still be right.
>A multithreaded file system is only a performance hack.
Not true. It’s a performance hack /on a microkernel/, but it’s an
automatic feature when you write a monolithic kernel – one area where
microkernels don’t work too well (as I pointed out in my personal mail
to ast). When writing a unix the “obsolete” way, you automatically get
a multithreaded kernel: every process does it’s own job, and you don’t
have to make ugly things like message queues to make it work
efficiently.
Besides, there are people who would consider “only a performance hack”
vital: unless you have a cray-3, I’d guess everybody gets tired of
waiting on the computer all the time. I know I did with minix (and yes,
I do with linux too, but it’s /much/ better).
>I still maintain the point that designing a monolithic kernel in 1991 is
>a fundamental error. Be thankful you are not my student. You would not
>get a high grade for such a design
Well, I probably won’t get too good grades even without you: I had an
argument (completely unrelated – not even pertaining to OS’s) with the
person here at the university that teaches OS design. I wonder when
I’ll learn
>My point is that writing a new operating system that is closely tied to any
>particular piece of hardware, especially a weird one like the Intel line,
>is basically wrong.
But /my/ point is that the operating system /isn’t/ tied to any
processor line: UNIX runs on most real processors in existence. Yes,
the /implementation/ is hardware-specific, but there’s a HUGE
difference. You mention OS/360 and MS-DOG as examples of bad designs
as they were hardware-dependent, and I agree. But there’s a big
difference between these and linux: linux API is portable (not due to my
clever design, but due to the fact that I decided to go for a fairly-
well-thought-out and tested OS: unix.)
If you write programs for linux today, you shouldn’t have too many
surprises when you just recompile them for Hurd in the 21st century. As
has been noted (not only by me), the linux kernel is a miniscule part of
a complete system: Full sources for linux currently runs to about 200kB
compressed – full sources to a somewhat complete developement system is
at least 10MB compressed (and easily much, much more). And all of that
source is portable, except for this tiny kernel that you can (provably:
I did it) re-write totally from scratch in less than a year without
having /any/ prior knowledge.
In fact the /whole/ linux kernel is much smaller than the 386-dependent
things in mach: i386.tar.Z for the current version of mach is well over
800kB compressed (823391 bytes according to nic.funet.fi). Admittedly,
mach is “somewhat” bigger and has more features, but that should still
tell you something.
Linus
From: kaufman@eecs.nwu.edu (Michael L. Kaufman)
Subject: Re: LINUX is obsolete
Date: 3 Feb 92 22:27:48 GMT
Organization: EECS Department, Northwestern University
I tried to send these two posts from work, but I think they got eaten. If you
have seen them already, sorry.
——————————————————————————-
Andy Tanenbaum writes an interesting article (also interesting was finding out
that he actually reads this group) but I think he is missing an important
point.
He Wrote:
>As most of you know, for me MINIX is a hobby, …
Which is also probably true of most, if not all, of the people who are involved
in Linux. We are not developing a system to take over the OS market, we are
just having a good time.
> What is going to happen
> is that they will gradually take over from the 80×86 line. They will
> run old MS-DOS programs by interpreting the 80386 in software.
Well when this happens, if I still want to play with Linux, I can just run it
on my 386 simulator.
> MINIX was designed to be reasonably portable, and has been ported from the
> Intel line to the 680×0 (Atari, Amiga, Macintosh), SPARC, and NS32016.
> LINUX is tied fairly closely to the 80×86. Not the way to go.
That’s fine for the people who have those machines, but it wasn’t a free
lunch. That portibility was gained at the cost of some performance and some
features on the 386. Before you decide that LINUX is not the way to go, you
should think about what it is going to be used for. I am going to use it for
running memory and computation intensive graphics programs on my 486. For me,
speed and memory were more important then future state-of-the-artness and
portability.
>But in all honesty, I would
>suggest that people who want a **MODERN** “free” OS look around for a
>microkernel-based, portable OS, like maybe GNU or something like that.
I don’t know of any free microkernel-based, portable OSes. GNU is still
vaporware, and likely to remain that way for the forseeable future. Do
you actually have one to recomend, or are you just toying with me?
——————————————————————————
In article <12615@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>My point is that writing a new operating system that is closely tied to any
>particular piece of hardware, especially a weird one like the Intel line,
>is basically wrong. An OS itself should be easily portable to new hardware
>platforms.
I think I see where I disagree with you now. You are looking at OS design
as an end in itself. Minix is good because it is portable/Micro-Kernal/etc.
Linux is not good because it is monolithic/tightly tied to Intel/etc. That
is not a strange attitude for someone in the acedemic world, but it is not
something you should expect to be universally shared. Linux is not being written
as a teaching tool, or as an abstract exercise. It is being written to allow
people to run GNU-type software _today_. The fact that it may not be in use
in five years is less important then the fact that today (well, by April
probably) I can run all sorts of software on it that I want to run. You keep
saying that Minix is better, but if it will not run the software that I want
to run, it really isn’t that good (for me) at all.
> When OS/360 was written in assembler for the IBM 360
>25 years ago, they probably could be excused. When MS-DOS was written
>specifically for the 8088 ten years ago, this was less than brilliant, as
>IBM and Microsoft now only too painfully realize.
Same point. MSoft did not come out with Dos to “explore the frontiers of os
research”. They did it to make a buck. And considering the fact that MS-DOS
probably still outsells everyone else put together, I don’t think that you
say that they have failed _in their goals_. Not that MS-Dos is the best OS
in terms of anything else, only that it has served their needs.
Michael
From: julien@incal.inria.fr (Julien Maisonneuve)
Subject: Re: LINUX is obsolete
Date: 3 Feb 92 17:10:14 GMT
I would like to second Kevin brown in most of his remarks.
I’ll add a few user points :
- When ast states that FS multithreading is useless, it reminds me of the many
times I tried to let a job run in the background (like when reading an archive on
a floppy), it is just unusable, the & shell operator could even have been left
out.
- Most interesting utilities are not even compilable under Minix because of the
ATK compiler’s incredible limits. Those were hardly understandable on a basic PC,
but become absurd on a 386. Every stupid DOS compiler has a large model (more
expensive, OK). I hate the 13 bit compress !
- The lack of Virtual Memory support prevents people studying this area to
experiment, and prevents users to use large programs. The strange design of the
MM also makes it hard to modify.
The problem is that even doing exploratory work under minix is painful.
If you want to get any work done (or even fun), even DOS is becoming a better
alternative (with things like DJ GPP).
In its basic form, it is really no more than OS course example, a good
toy, but a toy. Obtaining and applying patches is a pain, and precludes further
upgrades.
Too bad when not so much is missing to make it really good.
Thanks for the work andy, but Linux didn’t deserve your answer.
For the common people, it does many things better than Minix.
Julien Maisonneuve.
This is not a flame, just my experience.
From: richard@aiai.ed.ac.uk (Richard Tobin)
Subject: Re: LINUX is obsolete
Date: 4 Feb 92 14:46:49 GMT
Reply-To: richard@aiai.UUCP (Richard Tobin)
Organization: AIAI, University of Edinburgh, Scotland
In article <12615@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>A multithreaded file system is only a performance hack. When there is only
>one job active, the normal case on a small PC, it buys you nothing
I find the single-threaded file system a serious pain when using
Minix. I often want to do something else while reading files from the
(excruciatingly slow) floppy disk. I rather like to play rogue while
waiting for large C or Lisp compilations. I look to look at files in
one editor buffer while compiling in another.
(The problem would be somewhat less if the file system stuck to
serving files and didn’t interact with terminal i/o.)
Of course, in basic Minix with no virtual consoles and no chance of
running emacs, this isn’t much of a problem. But to most people
that’s a failure, not an advantage. It just isn’t the case that on
single-user machines there’s no use for more than one active process;
the idea only has any plausibility because so many people are used to
poor machines with poor operating systems.
As to portability, Minix only wins because of its limited ambitions.
If you wanted a full-featured Unix with paging, job-control, a window
system and so on, would it be quicker to start from basic Minix and
add the features, or to start from Linux and fix the 386-specific
bits? I don’t think it’s fair to criticise Linux when its aims are so
different from Minix’s. If you want a system for pedagogical use,
Minix is the answer. But if what you want is an environment as much
like (say) a Sun as possible on your home computer, it has some
deficiencies.
– Richard
From: ast@cs.vu.nl (Andy Tanenbaum)
Subject: Re: LINUX is obsolete
Date: 5 Feb 92 14:48:48 GMT
Organization: Fac. Wiskunde & Informatica, Vrije Universiteit, Amsterdam
In article <6121@skye.ed.ac.uk> richard@aiai.UUCP (Richard Tobin) writes:
>If you wanted a full-featured Unix with paging, job-control, a window
>system and so on, would it be quicker to start from basic Minix and
>add the features, or to start from Linux and fix the 386-specific
>bits?
Another option that seems to be totally forgotten here is buy UNIX or a
clone. If you just want to USE the system, instead of hacking on its
internals, you don’t need source code. Coherent is only $99, and there are various true UNIX systems with more features for more money. For the true hacker, not having source code is fatal, but for people who just want a UNIX system, there are many alternatives (albeit not free). Andy Tanenbaum (ast@cs.vul.nl) From: ajt@doc.ic.ac.uk (Tony Travis) Subject: Re: LINUX is obsolete Date: 6 Feb 92 02:17:13 GMT Organization: Department of Computing, Imperial College, University of London, UK. ast@cs.vu.nl (Andy Tanenbaum) writes: > Another option that seems to be totally forgotten here is buy UNIX or a > clone. If you just want to USE the system, instead of hacking on its > internals, you don’t need source code. Coherent is only$99, and there
> are various true UNIX systems with more features for more money. For the
> true hacker, not having source code is fatal, but for people who just
> want a UNIX system, there are many alternatives (albeit not free).
Andy, I have followed the development of Minix since the first messages
were posted to this group and I am now running 1.5.10 with Bruce
Evans’s patches for the 386.
I ‘just’ want a Unix on my PC and I am not interested in hacking on its
internals, but I *do* want the source code!
An important principle underlying the success and popularity of Unix is
the philosophy of building on the work of others.
This philosophy relies upon the availability of the source code in
order that it can be examined, modified and re-used in new software.
Many years ago, I was in the happy position of being an AT&T Seventh
Edition Unix source licencee but, even then, I saw your decision to
make the source of Minix available as liberation from the shackles of
AT&T copyright!!
I think you may sometimes forget that your ‘hobby’ has had a profound
effect on the availability of ‘personal’ Unix (ie. affordable Unix) and
that the 8086 PC I ran Minix 1.2 on actually cost me considerably more
than my present 386/SX clone.
Clearly, Minix _cannot_ be all things to all men, but I see the
progress to 386 versions in much the same way that I see 68000 or other
linear address space architectures: it is a good thing for people like
me who use Minix and feel constrained by the segmented architecture of
the PC version for applications.
NOTHING you can say would convince me that I should use Coherent …
Tony
From: richard@aiai.ed.ac.uk (Richard Tobin)
Subject: Re: LINUX is obsolete
Date: 7 Feb 92 14:58:22 GMT
Organization: AIAI, University of Edinburgh, Scotland
In article <12696@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>If you just want to USE the system, instead of hacking on its
>internals, you don’t need source code.
Unfortunately hacking on the internals is just what many of us want
the system for… You’ll be rid of most of us when BSD-detox or GNU
comes out, which should happen in the next few months (yeah, right).
– Richard
From: comm121@unixg.ubc.ca (Louie)
Subject: Re: LINUX is obsolete
Date: 30 Jan 92 02:55:22 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada
In <12595@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>But in all honesty, I would
>suggest that people who want a **MODERN** “free” OS look around for a
>microkernel-based, portable OS, like maybe GNU or something like that.
There are really no other alternatives other than Linux for people like
me who want a “free” OS. Considering that the majority of people who
would use a “free” OS use the 386, portability is really not all that
big of a concern. If I had a Sparc I would use Solaris.
As it stands, I installed Linux with gcc, emacs 18.57, kermit and all of the
GNU utilities without any trouble at all. No need to apply patches. I
just followed the installation instructions. I can’t get an OS like
this *anywhere* for the price to do my Computer Science homework. And
it seems like network support and then X-Windows will be ported to Linux
well before Minix. This is something that would be really useful. In my
opinion, portability of standard Unix software is important also.
I know that the design using a monolithic system is not as good as the
microkernel. But for the short term future (And I know I won’t/can’t
be uprading from my 386), Linux suits me perfectly.
Philip Wu
pwu@unixg.ubc.ca
From: dgraham@bmers30.bnr.ca (Douglas Graham)
Subject: Re: LINUX is obsolete
Date: 1 Feb 92 00:26:30 GMT
Organization: Bell-Northern Research, Ottawa, Canada
In article <12595@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
> While I could go into a long story here about the relative merits of the
> two designs, suffice it to say that among the people who actually design
> operating systems, the debate is essentially over. Microkernels have won.
Can you recommend any (unbiased) literature that points out the strengths
and weaknesses of the two approaches? I’m sure that there is something
to be said for the microkernel approach, but I wonder how closely
Minix resembles the other systems that use it. Sure, Minix uses lots
of tasks and messages, but there must be more to a microkernel architecture
than that. I suspect that the Minix code is not split optimally into tasks.
> The only real argument for monolithic systems was performance, and there
> is now enough evidence showing that microkernel systems can be just as
> fast as monolithic systems (e.g., Rick Rashid has published papers comparing
> Mach 3.0 to monolithic systems) that it is now all over but the shoutin.
My main complaint with Minix is not it’s performance. It is that adding
features is a royal pain — something that I presume a microkernel
architecure is supposed to alleviate.
> MINIX is a microkernel-based system.
Is there a consensus on this?
> LINUX is
> a monolithic style system. This is a giant step back into the 1970s.
> That is like taking an existing, working C program and rewriting it in
> BASIC. To me, writing a monolithic system in 1991 is a truly poor idea.
This is a fine assertion, but I’ve yet to see any rationale for it.
Linux is only about 12000 lines of code I think. I don’t see how
splitting that into tasks and blasting messages around would improve it.
>Don’t get me wrong, I am not unhappy with LINUX. It will get all the people
>who want to turn MINIX in BSD UNIX off my back. But in all honesty, I would
>suggest that people who want a **MODERN** “free” OS look around for a
>microkernel-based, portable OS, like maybe GNU or something like that.
Well, there are no other choices that I’m aware of at the moment. But
when GNU OS comes out, I’ll very likely jump ship again. I sense that
you *are* somewhat unhappy about Linux (and that surprises me somewhat).
I would guess that the reason so many people embraced it, is because it
offers more features. Your approach to people requesting features in
Minix, has generally been to tell them that they didn’t really want that
feature anyway. I submit that the exodus in the direction of Linux
proves you wrong.
Disclaimer: I had nothing to do with Linux development. I just find
it an easier system to understand than Minix.
Doug Graham dgraham@bnr.ca My opinions are my own.
From: hedrick@klinzhai.rutgers.edu (Charles Hedrick)
Subject: Re: LINUX is obsolete
Date: 1 Feb 92 00:27:04 GMT
Organization: Rutgers Univ., New Brunswick, N.J.
The history of software shows that availability wins out over
technical quality every time. That’s Linux’ major advantage. It’s a
small 386-based system that’s fairly compatible with generic Unix, and
is freely available. I dropped out of the Minix community a couple of
years ago when it became clear that (1) Minix was not going to take
advantage of anything beyond the 8086 anytime in the near future, and
(2) the licensing — while amazingly friendly — still made it hard
for people who were interested in producing a 386 version. Several
people apparently did nice work for the 386. But all they could
distribute were diffs. This made bringing up a 386 system a job that
isn’t practical for a new user, and in fact I wasn’t sure I wanted to
do it.
I apologize if things have changed in the last couple of years. If
it’s now possible to get a 386 version in a form that’s ready to run,
the community has developed a way to share Minix source, and bringing
up normal Unix programs has become easier in the interim, then I’m
willing to reconsider Minix. I do like its design.
It’s possible that Linux will be overtaken by Gnu or a free BSD.
However, if the Gnu OS follows the example of all other Gnu software,
it will require a system with 128MB of memory and a 1GB disk to use.
There will still be room for a small system. My ideal OS would be 4.4
BSD. But 4.4′s release date has a history of extreme slippage. With
most of their staff moving to BSDI, it’s hard to believe that this
situation is going to be improved. For my own personal use, the BSDI
system will probably be great. But even their very attractive pricing
is likely to be too much for most of our students, and even though
users can get source from them, the fact that some of it is
proprietary will again mean that you can’t just put altered code out
for public FTP. At any rate, Linux exists, and the rest of these
alternatives are vapor.
From: tytso@athena.mit.edu (Theodore Y. Ts’o)
Subject: Re: LINUX is obsolete
Date: 31 Jan 92 21:40:23 GMT
Organization: Massachusetts Institute of Technology
In-Reply-To: ast@cs.vu.nl’s message of 29 Jan 92 12: 12:50 GMT
>From: ast@cs.vu.nl (Andy Tanenbaum)
>ftp.cs.vu.nl = 192.31.231.42 in dir minix/simulator.) I think it is a
>gross error to design an OS for any specific architecture, since that is
>not going to be around all that long.
It’s not your fault for believing that Linux is tied to the 80386
architecture, since many Linux supporters (including Linus himself) have
made the this statement. However, the amount of 80386-specific code is
probably not much more than what is in a Minix implementation, and there
is certainly a lot less 80386 specific code in Linux than here is
Vax-specific code in BSD 4.3.
Granted, the port to other architectures hasn’t been done yet. But if I
were going to bring up a Unix-like system on a new architecture, I’d
probably start with Linux rather than Minix, simply because I want to
have some control over what I can do with the resulting system when I’m
done with it. Yes, I’d have to rewrite large portions of the VM and
device driver layers — but I’d have to do that with any other OS.
Maybe it would be a little bit harder than it would to port Minix to the
new architecture; but this would probably be only true for the first
architecture that we ported Linux to.
>While I could go into a long story here about the relative merits of the
>two designs, suffice it to say that among the people who actually design
>operating systems, the debate is essentially over. Microkernels have won.
>The only real argument for monolithic systems was performance, and there
>is now enough evidence showing that microkernel systems can be just as
>fast as monolithic systems (e.g., Rick Rashid has published papers comparing
>Mach 3.0 to monolithic systems) that it is now all over but the shoutin’.
This is not necessarily the case; I think you’re painting a much more
black and white view of the universe than necessarily exists. I refer
you to such papers as Brent Welsh’s (welch@parc.xerox.com) “The
Filsystem Belongs in the Kernel” paper, where in he argues that the
filesystem is a mature enough abstraction that it should live in the
kernel, not outside of it as it would in a strict microkernel design.
There also several people who have been concerned about the speed of
OSF/1 Mach when compared with monolithic systems; in particular, the
nubmer of context switches required to handle network traffic, and
networked filesystems in particular.
I am aware of the benefits of a micro kernel approach. However, the
fact remains that Linux is here, and GNU isn’t — and people have been
working on Hurd for a lot longer than Linus has been working on Linux.
Minix doesn’t count because it’s not free.
I suspect that the balance of micro kernels versus monolithic kernels
depend on what you’re doing. If you’re interested in doing research, it
is obviously much easier to rip out and replace modules in a micro
kernel, and since only researchers write papers about operating systems,
ipso facto micro kernels must be the right approach. However, I do know
a lot of people who are not researchers, but who are rather practical
kernel programmers, who have a lot of concerns over the cost of copying
and the cost of context switches which are incurred in a micro kernel.
By the way, I don’t buy your arguments that you don’t need a
multi-threaded filesystem on a single user system. Once you bring up a
windowing system, and have a compile going in one window, a news reader
in another window, and UUCP/C News going in the background, you want
good filesystem performance, even on a single-user system. Maybe to a
theorist it’s an unnecessary optimization and a (to use your words)
“performance hack”, but I’m interested in a Real operating system —
not a research toy.
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Theodore Ts’o bloom-beacon!mit-athena!tytso
308 High St., Medford, MA 02155 tytso@athena.mit.edu
Everybody’s playing the game, but nobody’s rules are the same!
From: joe@jshark.rn.com
Subject: Re: LINUX is obsolete
Date: 31 Jan 92 13:21:44 GMT
Organization: a blip of entropy
In article <12595@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>
> MINIX was designed to be reasonably portable, and has been ported from the
> Intel line to the 680×0 (Atari, Amiga, Macintosh), SPARC, and NS32016.
> LINUX is tied fairly closely to the 80×86. Not the way to go.
If you looked at the source instead of believing the author, you’d realise
this is not true!
He’s replaced ‘fubyte’ by a routine which explicitly uses a segment register
- but that could be easily changed. Similarly, apart from a couple of places
which assume the ’386 MMU, a couple of macros to hide the exact page sizes
etc would make porting trivial. Using ’386 TSS’s makes the code simpler,
but the VAX and WE32000 have similar structures.
As he’s already admitted, a bit of planning would have the the system
neater, but merely putting ’386 assembler around isn’t a crime!
And with all due respect:
- the Book didn’t make an issue of portability (apart from a few
“#ifdef M8088″s)
- by the time it was released, Minix had come to depend on several
8086 “features” that caused uproar from the 68000 users.
>Andy Tanenbaum (ast@cs.vu.nl)
joe.
From: entropy@wintermute.WPI.EDU (Lawrence C. Foard)
Subject: Re: LINUX is obsolete
Date: 5 Feb 92 14:56:30 GMT
Organization: Worcester Polytechnic Institute
In article <12595@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>Dont get me wrong, I am not unhappy with LINUX. It will get all the people
>who want to turn MINIX in BSD UNIX off my back. But in all honesty, I would
>suggest that people who want a **MODERN** “free” OS look around for a
>microkernel-based, portable OS, like maybe GNU or something like that.
I believe you have some valid points, although I am not sure that a
microkernel is necessarily better. It might make more sense to allow some
combination of the two. As part of the IPC code I’m writting for Linux I am
going to include code that will allow device drivers and file systems to run
as user processes. These will be significantly slower though, and I believe it
would be a mistake to move everything outside the kernel (TCP/IP will be
internal).
Actually my main problem with OS theorists is that they have never tested
there ideas! None of these ideas (with a partial exception for MACH) has ever
seen the light of day. 32 bit home computers have been available for almost a
decade and Linus was the first person to ever write a working OS for them
that can be used without paying AT&T $100,000. A piece of software in hand is worth ten pieces of vaporware, OS theorists are quick to jump all over an OS but they are unwilling to ever provide an alternative. The general consensus that Micro kernels is the way to go means nothing when a real application has never even run on one. The release of Linux is allowing me to try some ideas I’ve been wanting to experment with for years, but I have never had the opportunity to work with source code for a functioning OS. From: ast@cs.vu.nl (Andy Tanenbaum) Subject: Re: LINUX is obsolete Date: 5 Feb 92 23:33:23 GMT Organization: Fac. Wiskunde & Informatica, Vrije Universiteit, Amsterdam In article <1992Feb5.145630.759@wpi.WPI.EDU> entropy@wintermute.WPI.EDU (Lawrence C. Foard) writes: >Actually my main problem with OS theorists is that they have never tested >there ideas! I’m mortally insulted. I AM NOT A THEORIST. Ask anybody who was at our department meeting yesterday (in joke). Actually, these ideas have been very well tested in practice. OSF is betting its whole business on a microkernel (Mach 3.0). USL is betting its business on another one (Chorus). Both of these run lots of software, and both have been extensively compared to monolithic systems. Amoeba has been fully implemented and tested for a number of applications. QNX is a microkernel based system, and someone just told me the installed base is 200,000 systems. Microkernels are not a pipe dream. They represent proven technology. The Mach guys wrote a paper called “UNIX as an application program.” It was by Golub et al., in the Summer 1990 USENIX conference. The Chorus people also have a technical report on microkernel performance, and I coauthored another paper on the subject, which I mentioned yesterday (Dec. 1991 Computing Systems). Check them out. Andy Tanenbaum (ast@cs.vu.nl) From: peter@ferranti.com (peter da silva) Subject: Re: LINUX is obsolete Organization: Xenix Support, FICC Date: Thu, 6 Feb 1992 16:02:47 GMT In article <12747@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes: > QNX is a microkernel > based system, and someone just told me the installed base is 200,000 systems. Oh yes, while I’m on the subject… there are over 3 million Amigas out there, which means that there are more of them than any UNIX vendor has shipped, and probably more than all UNIX systems combined. From: peter@ferranti.com (peter da silva) Subject: Re: LINUX is obsolete Organization: Xenix Support, FICC Date: Thu, 6 Feb 1992 16:00:22 GMT In article <1992Feb5.145630.759@wpi.WPI.EDU> entropy@wintermute.WPI.EDU (Lawrence C. Foard) writes: > Actually my main problem with OS theorists is that they have never tested > there ideas! I beg to differ… there are many microkernel operating systems out there for everything from an 8088 (QNX) up to large research systems. > None of these ideas (with a partial exception for MACH) has ever > seen the light of day. 32 bit home computers have been available for almost a > decade and Linus was the first person to ever write a working OS for them > that can be used without paying AT&T$100,000.
I must have been imagining AmigaOS, then. I’ve been using a figment of my
imagination for the past 6 years.
AmigaOS is a microkernel message-passing design, with better response time
and performance than any other readily available PC operating system: including
MINIX, OS/2, Windows, MacOS, Linux, UNIX, and *certainly* MS-DOS.
The microkernel design has proven invaluable. Things like new file systems
that are normally available only from the vendor are hobbyist products on
the Amiga. Device drivers are simply shared libraries and tasks with specific
entry points and message ports. So are file systems, the window system, and
so on. It’s a WONDERFUL design, and validates everything that people have
been saying about microkernels. Yes, it takes more work to get them off the
ground than a coroutine based macrokernel like UNIX, but the versatility
pays you back many times over.
I really wish Andy would do a new MINIX based on what has been learned since
the first release. The factoring of responsibilities in MINIX is fairly poor,
but the basic concept is good.
> The general consensus that Micro kernels is the way to go means nothing when
> a real application has never even run on one.
I’m dreaming again. I sure throught Deluxe Paint, Sculpt 3d, Photon Paint,
Manx C, Manx SDB, Perfect Sound, Videoscape 3d, and the other programs I
bought for my Amiga were “real”. I’ll have to send the damn things back now,
I guess.
The availability of Linux is great. I’m delighted it exists. I’m sure that
the macrokernel design is one reason it has been implemented so fast, and this
is a valid reason to use macrokernels. BUT… this doesn’t mean that
microkernels are inherently slow, or simply research toys.
From: dsmythe@netcom.COM (Dave Smythe)
Subject: Re: LINUX is obsolete
Date: 10 Feb 92 07:08:22 GMT
Organization: Netcom – Online Communication Services (408 241-9760 guest)
In article <1992Feb5.145630.759@wpi.WPI.EDU> entropy@wintermute.WPI.EDU (Lawrence
C. Foard) writes:
>Actually my main problem with OS theorists is that they have never tested
>there ideas! None of these ideas (with a partial exception for MACH) has ever
>seen the light of day.
David Cheriton (Prof. at Stanford, and author of the V system) said something
similar to this in a class in distributed systems. Paraphrased:
“There are two kinds of researchers: those that have implemented
something and those that have not. The latter will tell you that
there are 142 ways of doing things and that there isn’t consensus
on which is best. The former will simply tell you that 141 of
them don’t work.”
He really rips on the OSI-philes as well, for a similar reason. The Internet
protocols are adapted only after having been in use for a period of time,
preventing things from getting standardized that will never be implementable
in a reasonable fashion. OSI adherents, on the other hand, seem intent on
standardizing everything possible, including “escapes” from the standard,
before a reasonable reference implementation exists. Consequently, you see
obsolete ideas immortalized, such as sub-byte-level data field packing,
which makes good performance difficult when your computer is drinking from
a 10+ Gbs fire-hose .
Just my $.02 D From: torvalds@klaava.Helsinki.FI (Linus Benedict Torvalds) Subject: Apologies (was Re: LINUX is obsolete) Date: 30 Jan 92 15:38:16 GMT Organization: University of Helsinki In article <1992Jan29.231426.20469@klaava.Helsinki.FI> I wrote: >Well, with a subject like this, I’m afraid I’ll have to reply. And reply I did, with complete abandon, and no thought for good taste and netiquette. Apologies to ast, and thanks to John Nall for a friendy “that’s not how it’s done”-letter. I over-reacted, and am now composing a (much less acerbic) personal letter to ast. Hope nobody was turned away from linux due to it being (a) possibly obsolete (I still think that’s not the case, although some of the criticisms are valid) and (b) written by a hothead Linus “my first, and hopefully last flamefest” Torvalds From: pmacdona@sanjuan (Peter MacDonald) Subject: re: Linux is obsolete Date: 1 Feb 92 02:10:06 GMT Organization: University of Victoria, Victoria, BC, CANADA Since I think I posted one of the earliest messages in all this discussion of Minix vs Linux, I feel compelled to comment on my reasons for switching from Minix to Linux. In order of importance they are: 1) Linux is free 2) Linux is evolving at a satisfactory clip (because new features are accepted into the distribution by Linus). The first requires some explanation, because if I have already purchased Minix, what posssible concern could price have for me? Simple. If the OS is free, many more people will use/support/enhance it. This is also the same reasoning I used when I bought my 386 instead of a sparc (which I could have got for just 30% more). Since PCs are cheap and generally available, more people will buy/use them and thus good, cheap/free software will be abundant. The second should be pretty obvious to anyone who has been using Minix for for any period of time. AST generally does not accept enhancements to Minix. This is not meant as a challenge, but merely a statement of fact. AST has good and legitimate reasons for this, and I do not dispute them. But Minix has some limitations which I just could no longer live with, and due to this policy, the prospect of seeing them resolved in reasonable time was unsatisfactory. These limitations include: no 386 support no virtual consoles no soft links no select call no ptys no demand paging/swapping/shared-text/shared-libs… (efficient mm) chmem (inflexible mm) no X-Windows (advocated for the same reasons as Linux and the 386). no TCP/IP no GNU/SysV integration (portability) Some of these could be fixed by patches (and if you have done this yourself, I don’t have to tell you how satisfactory that is), but at least the last 5 items were/are beyond any reasonable expectation. Finally, my comment (crack?) about Minix’s segmented kernel, or micro-kernel architecture was more an expression of my frustration/ bewilderment at attempting to use the Minix PTY patches as a guide of how to do it under Linux. That particular instance was one where message passing greatly complicated the implementation of a feature. I do have an opinion about Monlithic vs Message Passing, but won’t express it now, and did not mean to expresss it then. My goals are totally short term (maximum functionality in the minimum amount of time/cost/hassle), and so my views on this are irrelevant, and should not be misconstrued. If you are non-plussed by the lack of the above features, then you should consider Minix, as long as you don’t mind paying of course From: olaf@oski.toppoint.de (Olaf Schlueter) Subject: Re: Linux is obsolete Date: 7 Feb 92 11:41:44 GMT Organization: Toppoint Mailbox e.V. Just a few comments to the discussion of Linux vs Minix, which evolved partly to a discussion of monolithic vs micro-kernel. I think there will be no aggreement between the two parties advocating either concept, if they forget, that Linux and Minix have been designed for different applications. If you want a cheap, powerful and enhancable Unix system running on a single machine, with the possibility to adapt standard Unix software without pain, then Linux is for you. If you are interested in modern operating system concepts, and want to learn how a microkernel based system works, then Minix is the better choice. It is not an argument against microkernel system, that for the time being monolithic implemenations of Unix on PCs have a better performance. This means only, that Unix is maybe better implemented as a monolithic OS, at least as long as it runs on a single machine. From the users point of view, the internal design of the OS doesn’t matter at all. Until it comes to networks. On the monolithic approach, a file server will become a user process based on some hardware facility like ethernet. Programs which want to use this facility will have to use special libraries which offer the calls for communication with this server. In a microkernel system it is possible to incorporate the server into the OS without the need for new “system” calls. From the users point of view this has the advantage, that nothing changes, he just gets better performance (in terms of more disk space for example). From the implementors point of view, the microkernel system is faster adaptable to changes in hardware design. It has been critized, that AST rejects any improvements to Minix. As he is interested in the educational value of Minix, I understand his argument, that he wants to keep the code simple, and don’t want to overload it with features. As an educational tool, Minix is written as a microkernel system, although it is running on hardware platforms, who will probably better perform with a monolithic OS. But the area of network applications is growing and modern OS like Amoeba or Plan 9 cannot be written as monolithic systems. So Minix has been written with the intention to give students a practical example of a microkernel OS, to let them play with tasks and messages. It was not the idea to give a lot of people a cheap, powerful OS for a tenth of the price of SYSV or BSD implementations. Resumee: Linux is not better than Minix, or the other way round. They are different for good reasons. From: meggin@epas.utoronto.ca (David Megginson) Subject: Mach/Minix/Linux/Gnu etc. Date: 1 Feb 92 17:11:03 GMT Organization: University of Toronto – EPAS Well, this has been a fun discussion. I am absolutely convinced by Prof. Tanenbaum that a micro-kernel _is_ the way to go, but the more I look at the Minix source, the less I believe that it is a micro-kernel. I would probably not bother porting Linux to the M68000, but I want more services than Minix can offer. What about a micro-kernel which is message/syscall compatible with MACH? It doesn’t actually have to do everything that MACH does, like virtual memory paging — it just has to _look_ like MACH from the outside, to fool programs like the future Gnu Unix-emulator, BSD, etc. This would extend the useful lives of our M68000- or 80286-based machines for a little longer. In the meantime, I will probably stay with Minix for my ST rather than switching back to MiNT — after all, Minix at least looks like Unix, while MiNT looks like TOS trying to look like Unix (it has to, to be TOS compatible). David From: peter@ferranti.com (peter da silva) Newsgroups: comp.os.minix Subject: What good does this war do? (Re: LINUX is obsolete) Date: 3 Feb 92 16:37:24 GMT Organization: Xenix Support, FICC Will you quit flaming each other? I mean, linux is designed to provide a reasonably high performance environment on a hardware platform crippled by years of backwards-compatible kludges. Minix is designed as a teaching tool. Neither is that good at doing the other’s job, and why should they? The fact that Minix runs out of steam quickly (and it does) isn’t a problem in its chosen mileau. It’s sure better than the TOY operating system. The fact that Linux isn’t transportable beyond the 386/AT platform isn’t a problem when there are millions of them out there (and quite cheap: you can get a 386/SX for well under$1000).
A monolithic kernel is easy enough to build that it’s worth doing it if it gets
a system out the door early. Think of it as a performance hack for programmer
time. The API is portable. You can replace the kernel with a microkernel
design (and MINIX isn’t the be-all and end-all of microkernel designs either:
even for low end PCs… look at AmigaOS) without disturbing the applications.
That’s the whole point of a portable API in the first place.
Microkernels are definitely a better design for many tasks. I takes more
work to make them efficient, so a simpler design that doesn’t take advantage
of the microkernel in any real way is worth doing for pedagogical reasons.
Think of it as a performance hack for student time. The design is still good
and when you can get an API to the microkernel interface you can get VERY
impressive performance (thousands of context switches per second on an 8
MHz 68000).
From: ast@cs.vu.nl (Andy Tanenbaum)
Subject: Unhappy campers
Date: 3 Feb 92 22:46:40 GMT
Organization: Fac. Wiskunde & Informatica, Vrije Universiteit, Amsterdam
I’ve been getting a bit of mail lately from unhappy campers. (Actually 10
messages from the 43,000 readers may seem like a lot, but it is not really.)
There seem to be three sticking points:
1. Monolithic kernels are just as good as microkernels
2. Portability isn’t so important
3. Software ought to be free
If people want to have a serious discussion of microkernels vs. monolithic
kernels, fine. We can do that in comp.os.research. But please don’t sound off
if you have no idea of what you are talking about. I have helped design
and implement 3 operating systems, one monolithic and two micro, and have
studied many others in detail. Many of the arguments offered are nonstarters
(e.g., microkernels are no good because you can’t do paging in user space–
except that Mach DOES do paging in user space).
If you don’t know much about microkernels vs. monolithic kernels, there is
some useful information in a paper I coauthored with Fred Douglis, Frans
Kaashoek and John Ousterhout in the Dec. 1991 issue of COMPUTING SYSTEMS, the
USENIX journal). If you don’t have that journal, you can FTP the paper from
ftp.cs.vu.nl (192.31.231.42) in directory amoeba/papers as comp_sys.tex.Z
(compressed TeX source) or comp_sys.ps.Z (compressed PostScript). The paper
gives actual performance measurements and supports Rick Rashid’s conclusion that
microkernel based systems are just as efficient as monolithic kernels.
As to portability, there is hardly any serious discussion possible any more.
UNIX has been ported to everything from PCs to Crays. Writing a portable
OS is not much harder than a nonportable one, and all systems should be
written with portability in mind these days. Surely Linus’ OS professor
pointed this out. Making OS code portable is not something I invented in 1987.
While most people can talk rationally about kernel design and portability,
the issue of free-ness is 100% emotional. You wouldn’t believe how much
[expletive deleted] I have gotten lately about MINIX not being free. MINIX
costs $169, but the license allows making two backup copies, so the effective price can be under$60. Furthermore, professors may make UNLIMITED copies
for their students. Coherent is $99. FSF charges >$100 for the tape its “free”
software comes on if you don’t have Internet access, and I have never heard
anyone complain. 4.4 BSD is $800. I don’t really believe money is the issue. Besides, probably most of the people reading this group already have it. A point which I don’t think everyone appreciates is that making something available by FTP is not necessarily the way to provide the widest distribution. The Internet is still a highly elite group. Most computer users are NOT on it. It is my understanding from PH that the country where MINIX is most widely used is Germany, not the U.S., mostly because one of the (commercial) German computer magazines has been actively pushing it. MINIX is also widely used in Eastern Europe, Japan, Israel, South America, etc. Most of these people would never have gotten it if there hadn’t been a company selling it. Getting back to what “free” means, what about free source code? Coherent is binary only, but MINIX has source code, just as LINUX does. You can change it any way you want, and post the changes here. People have been doing that for 5 years without problems. I have been giving free updates for years, too. I think the real issue is something else. I’ve been repeatedly offered virtual memory, paging, symbolic links, window systems, and all manner of features. I have usually declined because I am still trying to keep the system simple enough for students to understand. You can put all this stuff in your version, but I won’t put it in mine. I think it is this point which irks the people who say “MINIX is not free,” not the$60.
An interesting question is whether Linus is willing to let LINUX become “free”
of his control. May people modify it (ruin it?) and sell it? Remember the
hundreds of messages with subject “Re: Your software sold for money” when it
was discovered the MINIX Centre in England was selling diskettes with news
postings, more or less at cost?
Suppose Fred van Kempen returns from the dead and wants to take over, creating
Fred’s LINUX and Linus’ LINUX, both useful but different. Is that ok? The
test comes when a sizable group of people want to evolve LINUX in a way Linus
does not want. Until that actually happens the point is moot, however.
If you like Linus’ philosophy rather than mine, by all means, follow him, but
please don’t claim that you’re doing this because LINUX is “free.” Just
say that you want a system with lots of bells and whistles. Fine. Your choice.
I have no argument with that. Just tell the truth.
As an aside, for those folks who don’t read news headers, Linus is in Finland
and I am in The Netherlands. Are we reaching a situation where another
critical industry, free software, that had been totally dominated by the U.S.
is being taken over by the foreign competition? Will we soon see
President Bush coming to Europe with Richard Stallman and Rick Rashid
in tow, demanding that Europe import more American free software?
Andy Tanenbaum (ast@cs.vu.nl)
From: ast@cs.vu.nl (Andy Tanenbaum)
Subject: Re: Unhappy campers
Date: 5 Feb 92 23:23:26 GMT
Organization: Fac. Wiskunde & Informatica, Vrije Universiteit, Amsterdam
In article <205@fishpond.uucp> fnf@fishpond.uucp (Fred Fish) writes:
>If PH was not granted a monopoly on distribution, it would have been possible
>for all of the interested minix hackers to organize and set up a group that
>was dedicated to producing enhanced-minix. This aim of this group could have
>been to produce a single, supported version of minix with all of the commonly
>requested enhancements. This would have allowed minix to evolve in much the
>same way that gcc has evolved over the last few years.
This IS possible. If a group of people wants to do this, that is fine.
I think co-ordinating 1000 prima donnas living all over the world will be
as easy as herding cats, but there is no legal problem. When a new release
is ready, just make a diff listing against 1.5 and post it or make it FTPable.
While this will require some work on the part of the users to install it,
it isn’t that much work. Besides, I have shell scripts to make the diffs
and install them. This is what Fred van Kempen was doing. What he did wrong
was insist on the right to publish the new version, rather than diffs against
the PH baseline. That cuts PH out of the loop, which, not surprisingly, they
weren’t wild about. If people still want to do this, go ahead.
Of course, I am not necessarily going to put any of these changes in my version,
so there is some work keeping the official and enhanced ones in sync, but I
am willing to co-operate to minimize work. I did this for a long time with
Bruce Evans and Frans Meulenbroeks.
If Linus wants to keep control of the official version, and a group of eager
beavers want to go off in a different direction, the same problem arises.
I don’t think the copyright issue is really the problem. The problem is
co-ordinating things. Projects like GNU, MINIX, or LINUX only hold together
if one person is in charge. During the 1970s, when structured programming
was introduced, Harlan Mills pointed out that the programming team should
be organized like a surgical team–one surgeon and his or her assistants,
not like a hog butchering team–give everybody an axe and let them chop away.
Anyone who says you can have a lot of widely dispersed people hack away on
a complicated piece of code and avoid total anarchy has never managed a
software project.
>Where is the sizeable group of people that want to evolve gcc in a way that
>rms/FSF does not approve of?
A compiler is not something people have much emotional attachment to. If
the language to be compiled is a given (e.g., an ANSI standard), there isn’t
much room for people to invent new features. An operating system has unlimited
opportunity for people to implement their own favorite features.
Andy Tanenbaum (ast@cs.vu.nl)
From: torvalds@klaava.Helsinki.FI (Linus Benedict Torvalds)
Subject: Re: Unhappy campers
Date: 6 Feb 92 10:33:31 GMT
Organization: University of Helsinki
In article <12746@star.cs.vu.nl> ast@cs.vu.nl (Andy Tanenbaum) writes:
>
>If Linus wants to keep control of the official version, and a group of eager
>beavers want to go off in a different direction, the same problem arises.
This is the second time I’ve seen this “accusation” from ast, who feels
pretty good about commenting on a kernel he probably haven’t even seen.
Or at least he hasn’t asked me, or even read alt.os.linux about this.
Just so that nobody takes his guess for the full thruth, here’s my
standing on “keeping control”, in 2 words (three?):
I won’t.
The only control I’ve effectively been keeping on linux is that I know
it better than anybody else, and I’ve made my changes available to
ftp-sites etc. Those have become effectively official releases, and I
don’t expect this to change for some time: not because I feel I have
some moral right to it, but because I haven’t heard too many complaints,
and it will be a couple of months before I expect to find people who
have the same “feel” for what happens in the kernel. (Well, maybe
people are getting there: tytso certainly made some heavy changes even
to 0.10, and others have hacked it as well)
In fact I have sent out feelers about some “linux-kernel” mailing list
which would make the decisions about releases, as I expect I cannot
fully support all the features that will /have/ to be added: SCSI etc,
that I don’t have the hardware for. The response has been non-existant:
people don’t seem to be that eager to change yet. (well, one person
felt I should ask around for donations so that I could support it – and
if anybody has interesting hardware lying around, I’d be happy to accept
it
The only thing the copyright forbids (and I feel this is eminently
reasonable) is that other people start making money off it, and don’t
make source available etc… This may not be a question of logic, but
I’d feel very bad if someone could just sell my work for money, when I
made it available expressly so that people could play around with a
personal project. I think most people see my point.
That aside, if Fred van Kempen wanted to make a super-linux, he’s quite
wellcome. He won’t be able to make much money on it (distribution fee
only), and I don’t think it’s that good an idea to split linux up, but I
wouldn’t want to stop him even if the copyright let me.
>I don’t think the copyright issue is really the problem. The problem is
>co-ordinating things. Projects like GNU, MINIX, or LINUX only hold together
>if one person is in charge.
Yes, coordination is a big problem, and I don’t think linux will move
away from me as “head surgeon” for some time, partly because most people
understand about these problems. But copyright /is/ an issue: if people
feel I do a bad job, they can do it themselves. Likewise with gcc. The
minix copyright, however, means that if someone feels he could make a
better minix, he either has to make patches (which aren’t that great
whatever you say about them) or start off from scratch (and be attacked
because you have other ideals).
Patches aren’t much fun to distribute: I haven’t made cdiffs for a
single version of linux yet (I expect this to change: soon the patches
will be so much smaller than the kernel that making both patches and a
complete version available is a good idea – note that I’d still make the
whole version available too). Patches upon patches are simply
impractical, especially for people that may do changes themselves.
>>Where is the sizeable group of people that want to evolve gcc in a way that
>>rms/FSF does not approve of?
>A compiler is not something people have much emotional attachment to. If
>the language to be compiled is a given (e.g., an ANSI standard), there isn’t
>much room for people to invent new features. An operating system has unlimited
>opportunity for people to implement their own favorite features.
Well, there’s GNU emacs… Don’t tell us people haven’t got emotional
attachment to editors
Linus
From: dmiller@acg.uucp (David Miller)
Subject: Linux is Obsolete and follow up postings
Date: 3 Feb 92 01:03:46 GMT
Organization: AppliedComputerGroup
As an observer interested in operating system design, I couldn’t resist this
thread. Please realize that I am not really experienced with minux
or linux: I have been into unix for many years. First, a few observations:
Minix was written to be an educational tool for ASTs’ classes, not a commercial
operating system. It was never a design parameter to have it run freely
available source code for unix systems. I think it was also a statement of
how operating systems should be designed, with a micro kernel and seperate
processes covering as much of the required functionality as possible.
Linux was written mostly as a learning exercise on Linus part – how to
program the 386 family. Designing the ultimate operating system was not
an objective. Providing a usable, free platform that would run all sorts
of widely available free software was a consideration, and one that appears
to have been well met.
Criticism from anyone that either of these systems isn’t what *they* would
like it to be is misplaced. After all, anybody that has a computer that will
run either system is free to do what Linus and Andrew did: write your own!
I, for one, applaud Linus for his considerable effort in developing Linux
and his decision to make it free to everybody. I applaud AST for his
effort to make minix affordable – I have real trouble relating to complaints
that minix isn’t free. If you can afford the time to explore minix, and a
basic computer system, $150 is not much more – and you do get a book to go with it. Next, a few questions for the professor: Is minix supposed to be a “real operating system” or an educational tool ? As an educational tool it is an excellent work. As a real operating system it presents some terribly rough edges (why no malloc() ?, just for starters) My feeling from reading The Book and listening to postings here is that you wanted a tool to teach your classes, and a lot of others wanted to play with an affordable operating system. These others have been trying to bolt on enough features to make it a “real operating system”, with less than outstanding success. Why split fundemental os functions, such as memory management, into user processes? As all good *nix gurus know, the means to success is to divide and conquer, with the goal being to *simplify* the problem into managable, well defined components. If splitting basic parts of the operating system into user space processes complicates the function by introducing additional mechanisms (message passing, complicated signals), have we met the objective of simplifying the design and implementation? I agree that *nix has suffered a bad case of feature-itis – especially sysVr4. Perhaps the features that people want for either functionality or compatibility could be offered by run-time loadable modules/libraries that offer these features. The micro-kernel would still be a base-level resource manager that also routes function requests to the appropriate module/library. The modules could be threads or user processes. (I think - os hackers please correct me ) Just my$.04 worth – please feel free to post or email responses.
I have no formal progressive training in computer science, so I am really
asking these questions in ignorance. I suspect a lot of others on the
net have similar questions in their own minds, but I’ve been wrong before.
– David
From: michael@gandalf.informatik.rwth-aachen.de (Michael Haardt)
Subject: 1.6.17 summary and why I think AST is right.
Date: 6 Feb 92 20:07:25 GMT
Reply-To: u31b3hs@messua.informatik.rwth-aachen.de (Michael Haardt)
Organization: Gandalf – a 386-20 machine
I will first give a summary of what you can expect from MINIX in *near*
future, and then explain why I think AST is right.
Some time ago, I asked for details about the next MINIX release (1.6.17).
I got some response, but only from people running 1.6.16. The following
informations are not official and may be wrong, but they are all I know
at the moment. Correct me if something is wrong:
- The 1.6.17 patches will be relative to 1.5 as shipped by PH.
- The header files are clean.
- The two types of filesystems can be used together.
- The signal handling is rewritten for POSIX. The old bug is removed.
- The ANSI compiler (available from Transmediar, I guess) comes with
compiler binaries and new libraries.
- There don’t seem to be support for the Amoeba network protocol.
- times(2) returns a correct value. termios(2) is implemented, but it’s
more a hack. I don’t know if “implemented” means in the kernel, or the
current emulation.
- There is no documentation about the new filesystem. There is a new fsck
and a new mkfs, don’t know about de.
- With the ANSI compiler, there is better floating point support.
- The scheduler is improved, but not as good as written by Kai-Uwe Bloem.
I asked these things to get facts for the decision if I should upgrade to
MINIX 1.6.17 or to Linux after the examens are over. Well, the decision
is made: I will upgrade to Linux at the end of the month and remove MINIX
from my winchester, when Linux runs all the software I need and which currently
runs under MINIX 1.5 with heavy patches. I guess this may take up to two
months. These are the main reasons for my decision:
- There is no “current” MINIX release, which can be used as basis for
patches and nobody knows, when 1.6.17 will appear.
- The library contains several bugs and from what I have heard, there is
no work done at them. There will not be a new compiler, and the 16 bit
users still have to use buggy ACK.
- 1.6.17 should offer more POSIX, but a complete termios is still missing.
- I doubt that there is still much development for 16 bit users.
I think I will stop maintaining the MINIX software list in a few months.
Anyone out there, who would like to continue it? Until Linux runs
*perfect* on my machine, each update of Origami will still run on 16-bit
MINIX. I will announce when the last of these versions appears.
In my opinion, AST is right in his decision about MINIX. I read the flame
war and can’t resist to say that I like MINIX the way it is, now where
there is Linux. MINIX has some advantages:
- You can start playing with it without a winchester, you can even
compile programs. I did this a few years ago.
- It is so small, you don’t need to know much to get a small system which
runs ok.
- There is the book. Ok, only for version 1.3, but most of it is still valid.
- MINIX is an example of a non-monolithic kernel. Call it a microkernel
or a hack to overcome braindamaged hardware: It demonstrates a concept,
with its pros and cons — a documented concept.
In my eyes, it is a nice system for first steps in UNIX and systems
programming. I learned most of what I know about UNIX with MINIX, in
all areas, from programming in C under UNIX to system administration
(and security holes:) MINIX grew with me: 1.5.xx upgrades, virtual
consoles, mail & news, text processing, crosscompiling etc. Now it is
too small for me. I don’t need a teaching system anymore, I would like
to get a more complicated and featureful UNIX, and there is one: Linux.
Back in the old days, v7 was state of the art. There was MINIX which
offered most of it. In one or two years, POSIX is what you are used to
see. Hopefully, there will be MINIX, offering most of it, with a new
book, for people who want to run a small system to play and experiment with.
Stop flaming, MINIX and Linux are two different systems with different
purposes. One is a teaching tool (and a good one I think), the other is
real UNIX for real hackers.
Michael
From: dingbat@diku.dk (Niels Skov Olsen)
Subject: Re: 1.6.17 summary and why I think AST is right.
Date: 10 Feb 92 17:33:39 GMT
Organization: Department of Computer Science, U of Copenhagen
michael@gandalf.informatik.rwth-aachen.de (Michael Haardt) writes:
>Stop flaming, MINIX and Linux are two different systems with different
>purposes. One is a teaching tool (and a good one I think), the other is
>real UNIX for real hackers.
Hear, hear! And now Linux articles in alt.os.linux (or comp.os.misc
if your site don’t receive alt.*) and Minix articles here.
eoff (end of flame fest
Niels
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2.余额无法直接购买下载，可以购买VIP、C币套餐、付费专栏及课程。 | 2021-12-08 21:32:02 | {"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": 0.377067506313324, "perplexity": 4429.416148264783}, "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-2021-49/segments/1637964363598.57/warc/CC-MAIN-20211208205849-20211208235849-00586.warc.gz"} |
http://homepages.gac.edu/~sskulrat/Courses/2019F-178/lectures/digitalAudio.html | # Acoustics
• Sound is the perception of vibration of our eardrums.
• The Minim package is a user-contributed audio library in the processing library for playing, manipulating, and synthesizing sound.
• A musical note is a wave that oscillates at a certain frequency.
• We will use concert A, the A above middle C, as a reference note.
• Concert A (also known as A440, A4, Stuttgart pitch) has been standardized to oscillate at a frequency of 440 times per second (Hz).
• When you double or halve the frequency, you move up or down one octave on the scale. E.g., 880 Hz is one octave above concert A; 110 Hz is three octaves below concert A.
# Acoustics, continued
• A newborn baby can hear sound waves of frequency between 20 to 20,000 Hz. People lose the ability to hear the high-frequency sounds as they grow older.
• The sin function repeats itself once every $$2\pi$$ units, so if we measure $$t$$ in seconds and plot $$\sin(2\pi t \times 440)$$, we get a curve that oscillates 440 times per second.
• The amplitude of the wave determines what we perceive as volume. We'll plot our curves between –1.0 and +1.0 and assume the devices that record and play sound will scale as appropriate.
• When a guitar string is plugged, the string vibrates, producing a sine wave that is the prominent part of the sound that you hear and recognize as a note.
• There are 12 notes on the chromatic scale, evenly spaced on a (base 2) logarithmic scale. For any given note, we get the $$i$$th note above it by multiplying its frequency by $$2^{i/12}$$.
# Chromatic scale
note i frequency
A 0 440.00
A♯ or B♭ 1 466.16
B 2 493.88
C 3 523.25
C♯ or D♭ 4 554.37
D 5 587.33
D♯ or E♭ 6 622.25
E 7 659.26
F 8 698.46
F♯ or G♭ 9 739.99
G 10 783.99
G♯ or A♭ 11 830.61
A 12 880.00
# Sampling
• For digital sound, we represent a curve by sampling it at regular intervals.
• We will use the commonly used sampling rate of 44,100 samples per second.
• For concert A, that rate corresponds to plotting each cycle of the sine wave by sampling it at about 100 points.
• We represent sound as an array of real numbers between –1.0 and +1.0. | 2022-09-26 21:35:43 | {"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": 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": 0.6348472833633423, "perplexity": 2264.111769295637}, "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/1664030334942.88/warc/CC-MAIN-20220926211042-20220927001042-00392.warc.gz"} |
https://aspect.geodynamics.org/doc/doxygen/structaspect_1_1Simulator_1_1AdvectionField.html | ASPECT
## Public Types
enum FieldType { temperature_field, compositional_field }
## Public Member Functions
AdvectionField (const FieldType field_type, const unsigned int compositional_variable=numbers::invalid_unsigned_int)
bool is_temperature () const
bool is_discontinuous (const Introspection< dim > &introspection) const
unsigned int component_index (const Introspection< dim > &introspection) const
unsigned int block_index (const Introspection< dim > &introspection) const
unsigned int field_index () const
unsigned int base_element (const Introspection< dim > &introspection) const
FEValuesExtractors::Scalar scalar_extractor (const Introspection< dim > &introspection) const
unsigned int polynomial_degree (const Introspection< dim > &introspection) const
## Static Public Member Functions
static AdvectionField composition (const unsigned int compositional_variable)
## Public Attributes
const FieldType field_type
const unsigned int compositional_variable
## Detailed Description
### template<int dim> struct aspect::Simulator< dim >::AdvectionField
A structure that is used as an argument to functions that can work on both the temperature and the compositional variables and that need to be told which one of the two, as well as on which of the compositional variables.
Definition at line 259 of file simulator.h.
## § FieldType
template<int dim>
An enum indicating whether the identified variable is the temperature or one of the compositional fields.
Enumerator
temperature_field
compositional_field
Definition at line 265 of file simulator.h.
## Constructor & Destructor Documentation
template<int dim>
aspect::Simulator< dim >::AdvectionField::AdvectionField ( const FieldType field_type, const unsigned int compositional_variable = numbers::invalid_unsigned_int )
Constructor.
Parameters
field_type Determines whether this variable should select the temperature field or a compositional field. compositional_variable The number of the compositional field if the first argument in fact chooses a compositional variable. Meaningless if the first argument equals temperature.
This function is implemented in source/simulator/helper_functions.cc.
## § temperature()
template<int dim>
static
A static function that creates an object identifying the temperature.
This function is implemented in source/simulator/helper_functions.cc.
## § composition()
template<int dim>
static
A static function that creates an object identifying given compositional field.
This function is implemented in source/simulator/helper_functions.cc.
## § is_temperature()
template<int dim>
bool aspect::Simulator< dim >::AdvectionField::is_temperature ( ) const
Return whether this object refers to the temperature field.
## § is_discontinuous()
template<int dim>
bool aspect::Simulator< dim >::AdvectionField::is_discontinuous ( const Introspection< dim > & introspection ) const
Return whether this object refers to a field discretized by discontinuous finite elements.
template<int dim>
Return the method that is used to solve the advection of this field (i.e. 'fem_field', 'particles').
## § component_index()
template<int dim>
unsigned int aspect::Simulator< dim >::AdvectionField::component_index ( const Introspection< dim > & introspection ) const
Look up the component index for this temperature or compositional field. See Introspection::component_indices for more information.
## § block_index()
template<int dim>
unsigned int aspect::Simulator< dim >::AdvectionField::block_index ( const Introspection< dim > & introspection ) const
Look up the block index for this temperature or compositional field. See Introspection::block_indices for more information.
## § field_index()
template<int dim>
unsigned int aspect::Simulator< dim >::AdvectionField::field_index ( ) const
Returns an index that runs from 0 (temperature field) to n (nth compositional field), and uniquely identifies the current advection field among the list of all advection fields. Can be used to index vectors that contain entries for all advection fields.
## § base_element()
template<int dim>
unsigned int aspect::Simulator< dim >::AdvectionField::base_element ( const Introspection< dim > & introspection ) const
Look up the base element within the larger composite finite element we used for everything, for this temperature or compositional field See Introspection::base_elements for more information.
## § scalar_extractor()
template<int dim>
FEValuesExtractors::Scalar aspect::Simulator< dim >::AdvectionField::scalar_extractor ( const Introspection< dim > & introspection ) const
Return the FEValues scalar extractor for this temperature or compositional field. This function is implemented in source/simulator/helper_functions.cc.
## § polynomial_degree()
template<int dim>
unsigned int aspect::Simulator< dim >::AdvectionField::polynomial_degree ( const Introspection< dim > & introspection ) const
Look up the polynomial degree order for this temperature or compositional field. See Introspection::polynomial_degree for more information.
## § field_type
template<int dim>
A variable indicating whether the identified variable is the temperature or one of the compositional fields.
Definition at line 271 of file simulator.h.
## § compositional_variable
template<int dim>
const unsigned int aspect::Simulator< dim >::AdvectionField::compositional_variable
A variable identifying which of the compositional fields is selected. This variable is meaningless if the temperature is selected.
Definition at line 278 of file simulator.h.
The documentation for this struct was generated from the following file: | 2022-08-18 14:38:20 | {"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": 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": 0.18352685868740082, "perplexity": 13482.001782330246}, "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-2022-33/segments/1659882573197.34/warc/CC-MAIN-20220818124424-20220818154424-00745.warc.gz"} |
https://brilliant.org/problems/a-huge-number-2/ | # A Huge Number
Algebra Level 2
What is the value of $111,111,111 \times 111,111,111$?
Note: Don't use a calculator because you will miss the fun so use logic to solve this!
×
Problem Loading...
Note Loading...
Set Loading... | 2019-10-23 11:54:37 | {"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": 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": 0.320542573928833, "perplexity": 4521.834220863258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2019-43/segments/1570987833089.90/warc/CC-MAIN-20191023094558-20191023122058-00244.warc.gz"} |
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# JEE Advanced 2023 Revision Notes for Reactions of Benzene
Last updated date: 24th Mar 2023
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Benzene can be considered one of the basic aromatic compounds introduced to students in organic chemistry. This compound has unique properties that are explained in the chapter- Reactions of Benzene. All topics and subtopics of this chapter are explained with balanced equations in these notes. This chapter holds immense importance in building a strong conceptual foundation of organic chemistry for JEE Advanced preparation. Download and refer to the Reactions of Benzene JEE Advanced notes for free from Vedantu.
These notes have been compiled following the updated JEE Advanced syllabus by our subject experts. All the reactions are explained in a simple manner for a better understanding of students.
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## Access JEE Advanced Revision Notes Chemistry Reaction of benzene
### Aromatic Compounds
Aroma-pleasant odour-burns with sooty flames, with Benzene in the aromatic compounds are called Benzenoid compounds.
• Without benzene ring-non benzenoid compounds.
• Aromatic compounds with Heteroatom like B, N, O, S, etc are called heterocyclic compounds.
• Benzenoid compounds include benzene and its derivatives and polynuclear hydrocarbons such as naphthalene, anthracene, biphenyl, etc.
### Structure of Benzene:
The stability and the structure of benzene have been explained on the basis of two modern theories.
1. Resonance or valence bond theory.
2. Molecular orbital theory.
## Huckel’s Rule:
According to Huckel’s rule, monocyclic, Planar conjugated systems with $\left( {4n + 2} \right)\pi {e^ - }$ are aromatic those with ${\text{4n} \pi }{{\text{e}}^{\text{ - }}}$ are Anti-Aromatic, n=integer.
Aromatic Anti-Aromatic Non-Aromatic Cyclic Cyclic Cyclic planar$\left( {s{p^2}} \right)$ planar$\left( {s{p^2}} \right)$ Non-planar Completely conjugated system Completely conjugated system None $\left( {4n + 2} \right)\pi {e^{ - 1}}$ $\left( {4n} \right)\pi {e^{ - 1}}$ None
### Reaction of Benzene:
Benzene preferably undergoes electrophilic substitution
Mechanism of Aromatic Electrophilic Substitution (EAS)
Aromatic Electrophilic Substitution.
All electrophilic substitution reaction follows similar mechanism. The reaction was found to take place in three steps.
1. ### Generation of electrophile.
$Nu - E \to N{u^ - } + {E^ + }$
1. ### Formation of the carbocation.
Formation of Carbocation
The carbocation formed in the above structure is stabilized due to resonance.
1. ### Removal of Proton
The carbocation loses a proton from $s{p^3}$ hybridized carbon to regain its aromatic character.
Removal of Proton
## Energy Level Diagram from EAS
• The number of transition states in the process determines the Energy level diagram.
• Electrophilic aromatic substitution has two steps (attack of electrophile, and deprotonation) which each have their own transition state. There is also a carbocation intermediate. This means that we should have a “double-humped” reaction energy diagram.
• Second, the relative heights of the “peaks” should reflect the rate-limiting step.
• The attack on the (step 1) electrophile is the rate determining step.
• So, it is represented with high jump in energy level diagram by representing higher activation energy.
Energy Level Diagram
## Halogenation:
• Electrophile is halonium ion $\left( {{X^ + }} \right)$
• Order of reactivity of halogen is ${F_2} > C{l_2} > B{r_2} > {I_2}$.
• Fluorination is not carried out directly as ${F_2}$ is highly reactive. Fluorination is carried out indirectly by reactive. Fluorination is carried out indirectly by the decomposition of benzene diazonium fluoroborate.
Halogenation 1
Chlorination and bromination may be carried out by $\frac{{{{\text{X}}_{\text{2}}}}}{{{\text{halogen carrier}}}}$ (Lewis’s acid, Fe-dust, ${I_2}$etc.),
${\text{HOCl Or HOBr,B}}{{\text{r}}_{\text{2}}}{\text{/}}{\left( {{\text{C}}{{\text{H}}_{\text{3}}}{\text{COO}}} \right)_{\text{3}}}Ti,C{l_2}O/{H_2}S{O_4}$, N-chloro or N-bromosuccinamide.
Halogenation 2
## Nitration:
• Benzene, when reacted with concentrated nitric acid at 323-333 K in the presence of concentrated sulphuric acid form nitrobenzene.
• This reaction is known as nitration of benzene.
Nitration of Nitrobenzene
On heating the reaction mixture to about 90-100℃, m-dinitro benzene is obtained.
Nitration of Nitrobenzene 2
• If fuming nitric acid is used along with Conc.${H_2}S{O_4}$at above 100℃ 1,3,5-tri nitro benzene is formed.
Nitration of nitrobenzene-3
## Sulphonation:
• Benzene undergoes sulphonation with the following reagents.
Sulfonation of Benzene
• The attacking electrophilic substitutions, sulphuric acid i.e., ${H_2}S{O_4} + S{O_3}$.
Benzene undergoes an addition reaction under special conditions.
### Hydrogenation:
• At high temperature and pressure, in the presence of finely divided nickel, benzene undergoes hydrogenation to give cyclohexane.
Hydrogenation of Benzene
In the presence of Pt, a reaction occurs at room temperature.
• Benzene reacts with chlorine in the presence of sunlight to give benzene hexachloride (BHC) or hexachlorocyclohexane or Gammaxene or 666 or Lindane.
• Benzene reacts with chlorine in the presence of sunlight and in the absence of sunlight or ultraviolet light and in the absence of halogen carriers (such as only $FeC{l_3}$ and $AlC{l_3}$ etc) to produce crystalline hexachloride and hexabromide respectively.
Hydrogenation of Benzene 1
• BHC is a powerful insecticide.
Brich Reduction
## Oxidation:
### Ozonolysis
• One mole of benzene reacts with three moles of ozone to give a triozonide, which on hydrolysis in presence of zinc gives three moles of glyoxal.
Ozonolysis of Benzene
• Zn dust destroys ${H_2}{O_2}$ which may otherwise oxidize glyoxal to oxalic acid.
Ozonolysis of Benzene
The above addition reaction of benzene proves the presence of three double bonds in benzene but they are different from aliphatic double bonds in the following reaction:
• Benzene does not decolorize $\frac{{B{r_2}}}{{{H_2}O}}$ or cold $alk.KMn{O_4}$.
• Benzene does not give additional reaction with HX or HOX.
### Combustion:
${C_6}{H_6} + \frac{{15}}{2}{O_2} \to 6C{O_2} + 3{H_2}O$
Oxidation with $KMn{O_4}$
Oxidation with $KMn{O_4}$
Note: Alkyl benzenes with at least one benzylic hydrogen on oxidation with $KMn{O_4}$ give benzoic acids.
### Uses of Benzene:
• It is used as a solvent for fats and resins.
• It is used in dry-cleaning.
• It is used in the synthesis of phenol, styrene, aniline, and insecticide like BHC.
• It is used as a motor fuel.
## Importance of Reactions of Benzene
This chapter focuses on explaining the chemical properties of benzene with the help of different chemical reactions. For example, it describes how a molecule of benzene behaves in electrophilic substitution reactions. In fact, it also covers how benzene is less prone to addition reactions.
The presence of delocalized electrons is discussed with proper illustration and explanation. Due to the presence of these unique sets of electrons distributed equally among the carbon atoms in a benzene ring, it can create an electrophile very easily.
All the reactions of benzene will be described in three steps. They are:
• The formation of an electrophile
• An intermediate formation of carbocation
• The process of removal of a proton from this intermediate carbocation
The mechanism of the electrophilic substitution reactions has been explained using pictorial Illustrations of the reaction steps. The use of various reagents and intermediate products will be explained with diagrams and elaborated reaction steps.
The related reactions are described to explain the mechanism elaborately. Students will understand how electrophilic substitution reactions occur in organic chemistry and can answer questions accordingly.
## Benefits of Reactions of Benzene JEE Advanced Notes PDF
• These revision notes are designed by the experts as per the previous years’ JEE Advanced question papers. They have simplified the crucial concepts of this chapter so that every aspirant can easily comprehend them in no time.
• The time taken to learn this chapter will reduce considerably with the help of these revision notes. It will help aspirants to understand and correlate the mechanism explained in this chapter with the questions asked. Hence, you will be able to answer questions accurately and score well in the exam.
• The Reactions of Benzene JEE Advanced notes will help you revise the topics covered in this chapter quickly.
• These notes will help you solve the sample questions for this chapter effectively in the JEE Advanced exam.
Students can download the free PDF of Reactions of Benzene JEE Advanced revision notes to prepare this chapter. They can learn all concepts with the easy explanation provided in these revision notes. Also, they can sign up for our one-on-one classes to get more assistance with their exam preparation and score well in the JEE Advanced exam.
## FAQs on JEE Advanced 2023 Revision Notes for Reactions of Benzene
1. What is halogenation?
The organic reaction where a halogen is introduced into the molecule of an organic compound through a chemical reaction is called halogenation. It can be achieved using different reagents and chemical conditions.
2. Which functional group is added in a nitration reaction?
In a nitration reaction, nitrate (NO2) is added to an organic compound. This functional group attaches to one of the carbon atoms of an organic compound.
3. What is benzene?
Benzene is a 6-carbon aromatic or cyclic organic compound. In this compound, the 6 carbon atoms form a hexagonal ring with alternate double bonds among the two carbon atoms. It also has a hydrogen atom attached to each of the carbon atoms.
4. What kind of electrons are there in a benzene ring?
The electrons in a benzene ring are sp2 hybridised in nature. These π electrons remain delocalized or spread among all the carbon atoms constituting the ring. | 2023-03-28 13:08:53 | {"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": 0.48535338044166565, "perplexity": 5230.699769872526}, "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/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00376.warc.gz"} |
https://tex.stackexchange.com/questions/439593/scrlayer-scrpage-puts-my-header-to-offset-with-geometry-and-margin | # scrlayer-scrpage puts my header to offset with geometry and margin
I'm trying to copy the header from koma-script-manual. So far everything worked out fine, although I needed to use geometry to set my specific typearea. If I use scrlayer-scrpage to set my header the header magically gets an offset. Even more odd - the offset depends on the loading order of geometry - loaded before scrlayer-scrpage the offset is positive - loaded after it's negative. Any ideas why this happens and how to fix it?
%%%%%%%%%%%%%%% DOCUMENTCLASS
\documentclass[%
paper=a4,%
parskip=never,%
fontsize=10pt%
]{scrartcl}%
%%%%%%%%%%%%%%% TYPEAREA
\usepackage{geometry}%
\geometry{
left=2mm,%
right=2mm,%
top=0mm,%
bottom=2mm,%
includemp,%
nofoot,%
marginparwidth=20mm,%
marginparsep=2mm,%
reversemp%
}%
%%%%%%%%%%%%%%% COLORS
\usepackage{xcolor}%
\usepackage[%
automark,%
]{scrlayer-scrpage}%
\clearpairofpagestyles%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% from scrguide to color header
contents={%
\rule[-\dp\strutbox]%
{\layerwidth}{\layerheight}%
}%
contents={%
\rule[-\dp\strutbox]%
{\layerwidth}{\layerheight}%
}%
contents={%
\rule[-\dp\strutbox]%
{\layerwidth}{\layerheight}%
}%
}
%%%%%%%%%%%%%%% DEBUG
\usepackage{layout}% shows layout on page
\makeatletter% layout in mm
\renewcommand*{\lay@value}[2]{%
\strip@pt\dimexpr0.351459\dimexpr\csname#2\endcsname\relax\relax mm%
}%
\makeatother%
\KOMAoptions{%
% draft=true% small black boxes in overfull lines
overfullrule=true% like draft - sometimes works better
}%
% \geometry{showframe}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\lipsum
\newpage
\layout
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Load package scrlayer-scrpage after the layout settings by geometry. But you have to set the offset for the header. See the documentation to get information what happens if the offset part is missing for the headwidth key.
\usepackage[%
automark,%
]{scrlayer-scrpage}
or
\usepackage[%
automark,%
]{scrlayer-scrpage}
Code:
\documentclass[%
parskip=never,%
fontsize=10pt%
]{scrartcl}%
\usepackage{geometry}%
\geometry{
margin=2mm,% all margins 2mm
top=0mm,% but top 0mm
includemp,%
nofoot,%
marginparwidth=20mm,%
marginparsep=2mm,%
reversemp%
}%
\usepackage{xcolor}%
\usepackage[%
automark,%
]{scrlayer-scrpage}% sets page style scrheadings automatically
\clearpairofpagestyles
\DeclareLayer[
everyside,% removes restrication to oneside
oddorevenpage,% removes restrication to oddside
contents={%
\rule[-\dp\strutbox]{\layerwidth}{\layerheight}%
}
}
\usepackage{lipsum}% only for dummy text
\begin{document}%
\lipsum[1-50]
\end{document}
• \the\oddsidemargin was exactly the "unit" I was searching for @esdd – Jabaal Jul 10 '18 at 10:15 | 2021-04-23 17:06:40 | {"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": 0.4291355609893799, "perplexity": 6994.122558623256}, "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-2021-17/segments/1618039596883.98/warc/CC-MAIN-20210423161713-20210423191713-00446.warc.gz"} |
https://mmark.nl/post/syntax/ | # Syntax
This is version 2 of Mmark: based on a new markdown implementation and some (small) language changes as well. We think these language changes lead to a more consistent user experience and lead to less confusion.
See changes from v1 if you’re coming from version 1.
Biggest changes:
• Including files is now done relative to the file being parsed (i.e. the sane way).
• Block attributes apply to block elements only.
• Callouts
• always rendered and require double greater/less-than signs, <<1>>.
• always require a comment in the code, i.e. //<<1>> will be rendered as a callout, a plain <<1>> will not.
• Block Tables have been dropped.
• Example lists (originally copied from Pandoc) have been dropped.
• Plain citations, i.e. @RFC5412, when the reference was previously seen don’t work anymore, always use the full syntax [@RFC5412].
# Why this new version?
It fixes a bunch of long standing bugs and the parser generates an abstract syntax tree (AST). It will be easier to add new renderers with this setup. It is also closer to Common Mark. So we took this opportunity to support RFC 7991 XML (xml2rfc version 3), HTML5, RFC 7749 XML (xml2rfc version 2) and ponder LaTeX support. Also with code upstreamed (to gomarkdown), we have less code to maintain.
Because of the abstract syntax tree it will also be easier to write helper tools, like, for instance a tool that checks if all referenced labels in the document are actually defined. Another idea could be to write a “check-the-code” tool that syntax checks all code in code blocks. Eventually these could be build into the mmark binary itself.
# Mmark V2 Syntax
This document describes all the extra syntax elements that can be used in Mmark. Mmark’s syntax is based on the “standard” Markdown syntax. A good primer on what blackfriday implements is this article.
Read the above documents if you haven’t already, it helps you understand how markdown looks and feels.
For the rest we build up on https://github.com/gomarkdown/markdown and support all syntax it supports. We enable the following extensions by default:
• Strikethrough, allow strike through text using ~~test~~.
• Autolink, detect embedded URLs that are not explicitly marked.
• Footnotes Pandoc style footnotes.
• HeadingIDs, specify heading IDs with {#id}.
• DefinitionLists, parse definition lists.
• MathJax, parse MathJax
• OrderedListStart, notice start element of ordered list.
• Attributes, allow block level attributes.
• Smartypants, expand -- and --- into ndash and mdashes.
• SuperSubscript, parse super- and subscript: H~2~O is water and 2^10^ is 1024.
• Tables, parse tables.
Mmark adds numerous enhancements to make it suitable for writing (IETF) Internet Drafts and even complete books. It steals borrows syntax elements from pandoc, kramdown, leanpub, asciidoc, PHP markdown extra and Scholarly markdown.
### Syntax Gotchas
Because markdown is not perfect, there are some gotchas you have to be aware of:
• Adding a caption under a quote block (Quote:) needs a newline before it, otherwise the caption text will be detected as being part of the quote.
• Including files (and code includes) requires an empty line before them, as they are block level elements and we need to trigger that scan from the parser.
• Including files in lists requires a empty line to be present in the list item; otherwise Mmark will only assume inline elements and not parse the includes (which are block level elements).
• A bibliography is only added if a {backmatter} has been specified, because we need to add just before that point.
• Intra-work emphasis is enabled so a string like SSH_MSG_KEXECDH_REPLY is interpreted as SSH<em>MSG</em>.... You need to escape the underscores: SSH\_MSG....
### RFC 7991 XML Output
This is the output format used for generating Internet-Drafts and RFCs. The generated XML needs to be processed by another tool (xml2rfc) to generate to official (final) output. The XML from Mmark can be used directly to upload to the IETF tools website.
Title Block:
If the document has a title block the front matter is already open. Closing the front matter can only be done by starting the middle matter with {mainmatter}. Any open “matters” are closed when the document ends. Area defaults to “Internet” and Ipr defaults to trust200902.
Not giving a date will output <date/> which mean the current date will be applied when xml2rfc is run.
Abstract:
The abstract can be started by using the special header syntax .# Abstract
Note:
Any special header that is not “abstract” or “preface” will be a note: a numberless section. These notes are only allowed in the <front> section of the document.
BCP 14/RFC 2119 Keywords:
If an RFC 2119 word is found enclosed in ** it will be rendered as an <bcp14> element: i.e. **MUST** becomes <bcp14>MUST</bcp14>.
Artwork:
Artwork is added by using a (fenced) code block. If the code block has an caption it will be wrapped in a <figure>, this is true for source code as well.
Source code:
If you want to typeset a source code instead of an artwork you must specify a language to the fenced block:
go
println(hello)
Will be typesets as source code with the language set to go.
Block Level Attributes:
We use the attributes as specified in RFC 7991, e.g. to speficify an empty list style use: {empty="true"} before the list. The renderer for this output format filters unknown attributes away. The current list is to allow IDs (translated into ‘anchor’), remove any class= and style= attributes, so {style="empty" empty="true"}, will make a document both RFC 7991 and RFC 7749 compliant.
Footnotes:
Are discarded from the final output, don’t use them.
Images:
Images are supported (but for text output only(?) SVG graphcs are allowed. We convert this to an <artwork> with src set to the image URL of path. I.e.  becomes <artwork src="img.jpg" alt="alt" name="title"/>.
Horizontal Line:
Outputs a paragraph with 60 dashes -.
### XML RFC 7749 Output
Title Block:
Identical to RFC 7991, Mmark will take care to translate this into something xml2rfc (v2) can understand. An Mmark document will generate valid RFC 7991 and 7749 XML, unless block level attributes are used that are speficic to each format. Area defaults to “Internet” and Ipr defaults to trust200902.
Not giving a date will output <date/> which mean the current date will be applied when xml2rfc is run.
BCP 14/RFC 2119 Keywords:
If an RFC 2119 word is found enclosed in ** it will be rendered normally i.e. **MUST** becomes MUST.
Artwork/Source code:
There is no such distinction so these will be rendered in the same way regardless. If you need a caption you can just give it one. If you want the final output to prefix Figure N or Table N is also needs to have an anchor; this is done with a block level attribute: {#figX}. If you only want Figure N, only give it an anchor.
Block Level Attributes:
We use the attributes as specified in RFC 7749, e.g. to speficify an empty list style use: {style="empty"} before the list. Any attributes that are not allowed are filtered out, so {style="empty" empty="true"}, will make a document both RFC 7749 and RFC 7991 compliant.
Asides:
Basically not supported, will be rendered as a plain paragraph.
Footnotes:
Are discarded from the final output, don’t use them.
Images:
Images are not supported and we fake an artwork with some of the meta date. Using the example from RFC 7991 output would just yields: <artwork>img.jpg "alt" "title"</artwork>.
Block quote:
Supported by faking an list with style empty.
Horizontal Line:
Outputs a paragraph with 60 dashes -.
### HTML5 Output
Title Block:
From the title block only the title is used, in the <title> tag.
## Block Elements
### Title Block
A Title Block contains a document’s meta data; title, authors, date and other elements. The elements that can be specified are copied from the xml2rfc v3 standard. More on these below. The complete title block is specified in TOML. Examples title blocks can be found in the repository of Mmark.
The title block itself needs three or more %’s at the start and end of the block. A minimal title block would look like this:
%%%
title = "Foo Bar"
%%%
#### Elements of the Title Block
An I-D needs to have a Title Block with the following items filled out:
• title - the main title of the document.
• abbrev - abbreviation of the title.
• updates/obsoletes - array of integers.
• seriesInfo, containing
• name - RFC or Internet-Draft or DOI
• value - draft name or RFC number
• stream - IETF (default), IAB, IRTF or independent.
• status - standard, informational, experimental, bcp, fyi, or full-standard.
• ipr - usually just set trust200902.
• area - usually just Internet.
• workgroup - the workgroup the document is created for.
• keyword - array with keywords (optional).
• author(s) - define all the authors.
• date - the date for this I-D/RFC.
An example would be:
%%%
title = "Using Mmark to create I-Ds and RFCs"
abbrev = "mmark2rfc"
ipr= "trust200902"
area = "Internet"
workgroup = ""
keyword = ["markdown", "xml", "Mmark"]
[seriesInfo]
status = "informational"
name = "Internet-Draft"
value = "draft-gieben-mmark2rfc-00"
stream = "IETF"
date = 2014-12-10T00:00:00Z
[[author]]
initials="R."
surname="Gieben"
fullname="R. (Miek) Gieben"
organization = "Mmark"
email = "miek@miek.nl"
%%%
An # acts as a comment in this block. TOML itself is specified here.
### Special Sections
Any section that needs special handling, like an abstract or preface can be started with .# Heading. This creates a special section that is usually unnumbered.
### Including Files
Including other files can done be with {{filename}}, if the path of filename is not absolute, the filename is taken relative to current file being processed. With <{{filename}} you include a file as a code block. The main difference being it will be returned as a code block. The file’s extension will be used as the language. The syntax is:
{{pathname}}[address]
And address can be N,M, where N and M are line numbers. If M is not specified, i.e. N, it is taken that we should include the entire file starting from N.
Or you can use regular expression with: /N/,/M/, where N and M are regular expressions that specify from where to where to include lines from file.
Each of these can have an optional prefix="" specifier.
{{filename}}[3,5]
Only includes the lines 3 to (not inclusive) 5 into the current document.
{{filename}}[3,5;prefix="C: "]
will include the same lines and prefix each include line with C:.
Captioning works as well:
<{{test.go}}[/START/,/END/]
Figure: A sample function.
Note that because the extension of the file above is “go”, this include will lead to the following block being parsed:
~~~ go
// test.go data
~~~
Figure: A sample function.
### Document Divisions
Mmark support three document divisions, front matter, main matter and the back matter. Mmark automatically starts the front matter for you if the document has a title block. Switching divisions can be done with {frontmatter}, {mainmatter} and {backmatter}. This must be the only thing on the line.
### Captions
Mmark supports caption below tables, code blocks and block quotes. You can caption each elements with Table:, Figure: and Quote: respectively. The caption extends to the first empty line. Some examples:
Name | Age
--------|-----:
Bob | 27
Alice | 23
Table: This is the table caption.
Or for a code block:
~~~ go
func getTrue() bool {
return true
}
~~~
Figure: This is a caption for a code block.
And for a quote:
> Ability is nothing without opportunity.
Quote: https://example.com, Napoleon Bonaparte
### Asides
Any text prefixed with A> will become an aside. This is similar to a block quote, but can be styled differently.
### Figures and Subfigures
To group artworks and code blocks into figures, we need an extra syntax element. Scholarly markdown has a neat syntax for this. It uses a special section syntax and all images in that section become subfigures of a larger figure. Disadvantage of this syntax is that it can not be used in lists. Hence we use a fenced code block like syntax: !--- as the opening and closing “tag”. Note: only inline elements are parsed inside a figure block.
Basic usage:
!---
!---
if the figure block has a caption that will be used as well:
!---
!---
Figure: this is a figure containing subfigures.
Or when just using fenced code blocks:
!---
~~~ ascii-art
+-----+
| ART |
+-----+
~~~
Figure: Caption for this ascii-art
~~~ c
printf("%s\n", "hello");
~~~
!---
Figure: Caption for both figures.
### Block Level Attributes
A “Block Level Attribute” is a list of HTML attributes between braces: {...}. It allows you to set classes, an anchor and other types of extra information for the next block level element.
The full syntax is: {#id .class key="value"}. Values may be omitted, i.e., just {.class} is valid.
The following example applies the attributes: title and anchor to the blockquote:
{title="The blockquote" #myid}
> A blockquote with a title
Gets expanded into:
<blockquote anchor="myid" title="The blockquote">
<t>A blockquote with a title</t>
</blockquote>
## Inline Elements
### Indices
Defining indices allows you to create an index. The define an index use the (!item). Sub items can be added as well, with (!item, subitem). To make item primary, use another !: (!!item, subitem). If any index is defined the end of the document contains the list of indices. The -index=false flag suppresses this generation.
### Citations
Mmark uses the citation syntax from Pandoc: [@RFC2535], the citation can either be informative (default) or normative, this can be indicated by using the ? or ! modifier: [@!RFC2535] create a normative reference for RFC 2535. To suppress a citation use [@-RFC1000]. It will still add the citation to the references, but does not show up in the document as a citation.
The first seen modifier determines the type (suppressed, normative or informative). Multiple citation can separated with a semicolon: [@RFC1034; @RFC1035].
If you reference an RFC, I-D or W3C document the reference will be added automatically (no need to muck about with an <reference> block). This is to say:
Any reference starting with RFC, I-D. or W3C. will be automatically added to the correct reference section.
For I-Ds you may want to add a draft sequence number, which can be done as such: [@?I-D.blah#06]. If you reference an I-D without a sequence number it will create a reference to the last I-D in citation index.
A bibliography section is created by default if a {backmatter} is given, but you can suppress it by using the command line flag -bibliography=false.
### XML References
Any valid XML reference fragment found anywhere in the document, can be used as a citation reference. The syntax of the XML reference element is defined in RFC 7749. The anchor defined can be used in the citation, which the example below that would be [@pandoc]:
<reference anchor='pandoc' target='http://johnmacfarlane.net/pandoc/'>
<front>
<title>Pandoc, a universal document converter</title>
<author initials='J.' surname='MacFarlane' fullname='John MacFarlane'>
<organization>University of California, Berkeley</organization>
<email>jgm@berkeley.edu</email>
<uri>http://johnmacfarlane.net/</uri>
</author>
<date year='2006'/>
</front>
</reference>
Note that for citing I-Ds and RFCs you don’t need to include any XML, as Mmark will pull these automatically from their online location: or technically more correct: the xml2rfc post processor will do this.
### Cross References
Cross references can use the syntax [](#id), but usually the need for the title within the brackets is not needed, so Mmark has the shorter syntax (#id) to cross reference in the document.
Example:
My header {#header}
Lorem ipsum dolor sit amet, at ultricies ...
### Super- and Subscript
For superscript use ^ and for subscripts use ~. For example:
H~2~O is a liquid. 2^10^ is 1024.
Inside a super- or subscript you must escape spaces. Thus, if you want the letter P with ‘a cat’ in subscripts, use P~a\ cat~, not P~a cat~.
### Callouts
Callouts are way to reference code from paragraphs following that code. Mmark uses the following syntax for specifying a callout <<N>> where N is integer > 0.
In code blocks you can use the same syntax to create a callout:
Code //<<1>>
More //<<2>>
As you can see in <<1>> but not in <<2>>. There is no <<3>>.
Using callouts in source code examples will lead to code examples that do not compile. To fix this the callout needs to be placed in a comment, but then your source show useless empty comments. To fix this Mmark will detect (and remove!) the comment from the callout, leaving your example pristine in the document.
Note that callouts in code blocks are only detected if the renderer has been configured to look for them. The default mmark configuration is to detect them after // and # comment starters.
Lone callouts (in code blocks) without them being prefixed with a comment means they are not detected by Mmark.
### BCP14
Phrases that are defined in RFC 2119 (i.e. MUST, SHOULD, etc) are detected when being type set as strong elements: **MUST**, in the RFC 7991 output these will typeset as <bcp14>MUST</bcp14>. In RFC 7749 output it will just be MUST. Not that these can’t span lines, e.g., **MUST NOT**, must be on a single line.
# Changes from version 1
These are the changes from Mmark version 1:
• Citations:
• Suppressing a citation is done with [@-ref] (it was the reverse -@ in v1), this is more consistent.
• Multiple citations are allowed in one go, separated with a semicolons: [@ref1; @ref2].
• TODO Reference text is allowed [@ref p. 23].
• Indices: now just done with (!item), marking one primary will be: (!!item).
• Code block callouts are now a renderer setting, not a Block Level Attribute. Callout in code are only detected if they are used after a comment.
• Including files with a prefix is now specified in the address specification: {{myfile}}[prefix="C: "] will use C: as the prefix. No more mucking about with block attribute lists that are hard to discover.
• There no extended table syntax; if this ever comes back it needs to more robust implementation.
• Title Block need to be sandwiched between %%%, the prefix % does not work anymore.
Syntax that is not supported anymore:
• HTML abbreviations.
• The different list syntaxes have been dropped, use a Block Level Attribute to tweak the output.
• Tasks lists and example lists.
• Comment detection, i.e. to support cref: dropped. Comments are copied depending on the flag renderer.SkipHTML`.
• Parts
• Extended table syntax. | 2018-12-10 19:49:00 | {"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": 0.5308189392089844, "perplexity": 6337.899299414214}, "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-2018-51/segments/1544376823442.17/warc/CC-MAIN-20181210191406-20181210212906-00106.warc.gz"} |
https://mathematiques-fantastiques.fr/en/simplifying-surds-and-rationalising-denominators-review/ | Select Page
# Simplifying surds and rationalising denominators ( review)
Objectives: to be able to ,
• – Use the rules for multiplying and dividing surds
• – Rationalise the denominator of a fraction
• – Expand and simplify brackets containing surds.
Prior knowledge: you should already know how to,
• – Calculate basic square roots.
• – Simplify fraction ( with denominator and numerator as a whole number). | 2022-08-09 08:02:52 | {"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": 0.961113691329956, "perplexity": 3518.90652751998}, "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-2022-33/segments/1659882570913.16/warc/CC-MAIN-20220809064307-20220809094307-00516.warc.gz"} |
https://physics.stackexchange.com/questions/226327/how-does-energy-levels-of-an-electron-differ-from-atoms | # How does energy levels of an electron differ from atoms?
I would like to know how does energy levels of an electron differs from atom. I've read that electrons with almost similar energy orbit in the same orbital and have a discrete set of energy levels. How are energy levels represented in atoms?
• I presume that you are asking about some difference between the energy levels of an atom and those of an electron whereas they are actually all the same and it is better to call them as energy levels of an atom, if that is your question BTW. – SchrodingersCat Dec 28 '15 at 11:04
• What energy level of atoms? – N.S.JOHN Dec 28 '15 at 11:56
If by an electron you mean a free electron then that can take on any energy value: the spectrum of allowed energy values is continuous.
In atoms, electrons are bound by the electrostatic attraction exerted by the nucleus. The total energy function (the Hamiltonian) of an electron in a hydrogen atom is described by the Schrödinger equation.
Solving it yields the eigenfunctions (wave functions) $\Psi_{n,l,m}$ and the assorted eigenvalues $E_{n,l,m}$.
The allowed energy levels can be found here and (disregarding the fine structure) is given by the formula:
$$E_n=-\frac{13.6\:\mathrm{eV}}{n^2}$$
Where $n$ is the Principal Quantum Number $(n=1,2,3,4,...)$. The energy spectrum of an electron in a hydrogen atom is thus discrete and not continuous.
For multi-electronic atoms this principle holds but the Schrödinger equation can no longer be solved analytically (numerical methods are needed).
Atoms are quantum systems comprised of a nucleus and electrons: the energy spectrum obtained by solving the Schrödinger equation is the energy spectrum of the system, i.e. the atom itself.
• :That's great for electrons.Like this is there any energy level representation for atom? – justin Dec 29 '15 at 6:27
• The representations are those of the atom because nucleus + electron form one system. – Gert Dec 29 '15 at 14:11
• :Do you mean to say that the energy representation for electron and atom is same? – justin Dec 30 '15 at 6:27
• @justin: basically yes. $E$ is the total energy of the atom (electron + nucleus). This true of all systems: the potential energy of an object is the PE of object + object that causes the central field. – Gert Dec 30 '15 at 15:27
• :I think it's better to update your answer with mentioning that energy representation for electron and atom is the same. – justin Dec 31 '15 at 6:19 | 2019-07-21 15:05:33 | {"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": 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": 0.5331537127494812, "perplexity": 358.5130699385099}, "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-2019-30/segments/1563195527048.80/warc/CC-MAIN-20190721144008-20190721170008-00470.warc.gz"} |
https://www.physicsforums.com/threads/how-to-determine-significant-figures-for-quadratic.599859/ | How to determine significant figures for quadratic?
1. xodin
45
1. The problem statement, all variables and given/known data
A student is running at her top speed of 5.0 m/s to catch a bus, which is stopped at the bus stop. When the student is still 40.0 m from the bus, it starts to pull away, moving with a constant acceleration of 0.170 m/s2.
For how much time and what distance does the student have to run at 5.0 m/s before she overtakes the bus?
2. Relevant equations
x = ∫vdt
3. The attempt at a solution
x1=5.0t
x2=40.0 + 2*0.170*t2
The person and bus meet when x1=x2, so to solve for t, I rewrite as a quadratic equal to zero and use the formula:
5.0t = 40.0 + 0.0850*t2 → 0.0850*t2 - 5.0t + 40.0 = 0
t = $\frac{5.0 \pm \sqrt{(5.0)^{2} - 4(0.0850)(40.0)}}{2(0.0850)}$
So here is where my question actually comes in. How do I solve this using the appropriate number of significant digits? My book says the answers are 9.55 and 49.3, which you get if you calculate the exact answer, and then use 3 significant digits, but why 3 in this case?
My book gives significant digit rules for addition/subtraction and multiplication/division, but does not say anything about equations using both types of operations. I have thoroughly searched online resources and actually find that most sites out there use slightly different methods, and several I referenced actually contradicted themselves or miscalculated their own examples based on their own rules. It doesn't seem like this should be that confusing.
If I follow my interpretation of my book's rules, here's what I get:
1. Because 5.0 has two significant digits, 5.0*5.0=25
2. Because 4 is an exact number in the formula it is ignored when determining significant digits, and 4*0.0850*40.0 = 13.6, since both 0.0850 and 40.0 have three significant digits.
3. Because 2 is an exact number in the formula it is ignored when determining significant digits, and 2*0.0850 = 0.170, since 0.0850 has three significant digits.
t = $\frac{5.0 \pm \sqrt{25-13.6}}{0.170}$
4. Because 25 is the most uncertain numbers, 25 - 13.6 = 11
t = $\frac{5.0 \pm \sqrt{11}}{0.170}$
5. Because 11 has two significant digits, sqrt(11) = 3.3
t = $\frac{5.0 \pm 3.3}{0.170}$
6. Because both 5.0 and 3.3 have the same uncertainty, the numerator becomes 8.3 and 1.7.
7. Because both 8.3 and 1.7 have two significant digits, the two of them divided by the denominator would result in two significant digit answers:
t = 49 and t = 10
Now, I know that I'm compounding the rounding, which is leading my answer away from more accurate values, but isn't that the point?
MANY, many, many sites have told me to perform the equation as a whole first, and then round the final answer, but none of them explain how to determine the number of significant digits to use when doing it that way... I'm a bit disappointed that my book doesn't address how to handle significant figures for equations containing both adding/subtraction and multiplication/division operations. It would appear that if all the variables had the same number of significant digits, then the answer would too, but in this case, one of the variables has 2, and the others have 3.
Thanks for any help you all can provide! It is greatly appreciated!
Staff: Mentor
Those MANY, many, many sites have the right idea How many significant figures is enough? As many as it takes But seriously, the easiest thing to do is to keep all intermediate results in machine registers (calculator memories, spreadsheet cells, that sort of thing) and round only for presentation purposes. If you must work by hand and record intermediate results ("Paper Memory"), then get into the habit of recording six decimal places -- it requires no thought and will hold enough accuracy for most lengthy calculations that result in only 1 to 3 significant figures at the end.
If you want to be more formal about it, recognize that significant figures in the given data imply a certain precision in those values that can be expressed as uncertainties in those values. So a number like 5.2 implies 5.2 +/- 0.05 (so the uncertainty is a "half digit" in the last digit of the given value). You can then perform all calculations using error propagation, which I guarantee will eventually drive you batty and slow your progress to a crawl.
Instead, use full precision for all intermediate values and learn to use the partial derivative method of finding the error in the result of calculations that are more involved than an addition or multiplication or two.
Last edited: Apr 24, 2012
4. xodin
45
Thanks a lot gneill! The part about using the partial derivative method really helps, and I bet that will be what I use further down the road; however, at the present, I'm concerned about coming to different answers than my textbook. For the time being, it is instructing me to use the significant figures in the variables to determine how many to use in the quiz answers. I need to understand why I should have came to the conclusion of 9.55 (three significant figures) without using error propagation or partial derivatives (as those techniques have not been introduced), because if I used two or four, I could very well lose points. Are there not significant figure rules for equations involving both addition/subtraction and multiplication/division?
BTW, as an aside, I'm studying this material on my own in advance of going to school for physics, so I don't have an instructor I can ask yet to see what's acceptable vs. not acceptable when it comes to significant digits.
Thanks again!
Staff: Mentor
Without doing a lot of analysis of a particular problem, the general rule of thumb is to give results with as many significant figures as the least number of significant figures in the input values. In this case we note that the speed, 5.0 m/s, has two significant figures so that should be an acceptable number. Yet the problem solution made a point of giving a result with three significant figures for the time (and they specifically stated that they were doing so). The reason may be that later result values are sensitively dependent on the intermediate value of this time, and they'd either have to give you the extra precision here or give you another value with more figures to use as an intermediate value for further calculations.
I note that a distance value calculation depends upon the square of the time. This will tend to "magnify" any error in t in that calculation. Try plugging in "9.5s", "9.6s", and "9.55s" for time values and see if the significant figures for the distance calculation are affected.
6. xodin
45
For both distance functions, the three values of t you listed result in the same distance number when significant figures are considered: 48.
Since I began trying to figure this out, I've wondered if I was doing something wrong, or if the book was wrong, or if it doesn't use its own significant figure rules in its answer. I think it's starting to look like one of the later two explanations is the case.
In addition, jedishrfu's link has a section about the disagreements and imperfection of using significant figures, and it states that they are more of an introductory method that will eventually give way to more reliable techniques such as the error propagation or partial derivative methods you mentioned. So perhaps I shouldn't worry about it much for now and just move on. I just didn't want to move forward without having a firm grasp of the material I've already read, but I think in this case, worst case scenario, I can just ask my instructor what he wants after I start the actual class.
Thanks for all of your help! You too jedishrfu!
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https://www.aimsciences.org/article/doi/10.3934/naco.2013.3.353 | # American Institute of Mathematical Sciences
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2013, 3(2): 353-366. doi: 10.3934/naco.2013.3.353
## Weak and strong convergence of prox-penalization and splitting algorithms for bilevel equilibrium problems
1 Cadi Ayyad University, Faculty of Sciences Semlalia, Mathematics, 40000 Marrakech, Morocco, Morocco
Received April 2012 Revised November 2012 Published April 2013
The aim of this paper is to obtain, in a Hilbert space $H$, the weak and strong convergence of a penalty proximal algorithm and a splitting one for a bilevel equilibrium problem: find $x\in S_F$ such that $\ G(x,y)\geq 0\$ for all $\ y\in S_F$, where $S_F :=\lbrace y\in K\; :\; F(y,u)\geq 0\;\; \forall u\in K \rbrace$, and $F,G:K\times K\longrightarrow \mathbb{R}$ are two bifunctions with $K$ a nonempty closed convex subset of $H$. In our framework, results of convergence generalize those recently obtained by Attouch et al. (SIAM Journal on Optimization 21, 149-173 (2011)). We show in particular that for the strong convergence of the penalty algorithm, the geometrical condition they impose is not required. We also give applications of the iterative schemes to fixed point problems and variational inequalities.
Citation: Zaki Chbani, Hassan Riahi. Weak and strong convergence of prox-penalization and splitting algorithms for bilevel equilibrium problems. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 353-366. doi: 10.3934/naco.2013.3.353
##### References:
[1] H. Attouch, M. O. Czarnecki and J. Peypouquet, Prox-penalization and splitting methods for constrained variational problems,, SIAM J. Control Optim., 21 (2011), 149. doi: 10.1137/100789464. Google Scholar [2] J. P. Aubin, "Optima and Equilibria: An Introduction to Nonlinear Analysis,", Springer, (2002). Google Scholar [3] E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems,, Math. Student, 63 (1994), 123. Google Scholar [4] O. Chadli, Z. Chbani and H. Riahi, Equilibrium problems with generalized monotone Bifunctions and Applications to Variational inequalities,, J. Optim. Theory Appl., 105 (2000), 299. doi: 10.1023/A:1004657817758. Google Scholar [5] Z. Chbani and H. Riahi, Variational principle for monotone and maximal bifunctions,, Serdica Math. J., 29 (2003), 159. Google Scholar [6] N. Hadjisavvas and H. Khatibzadeh, Maximal monotonicity of bifunctions,, Optimization, 59 (2010), 147. doi: 10.1080/02331930801951116. Google Scholar [7] P. E. Mainge and A. Moudafi, Strong convergence of an iterative method for hierarchical fixed-points problems,, Pacific J. Optim., 3 (2007), 529. Google Scholar [8] A. Moudafi, Proximal point algorithm extended for equilibrium problems,, J. Nat. Geom., 15 (1999), 91. Google Scholar [9] A. Moudafi, On the convergence of splitting proximal methods for equilibrium problems in Hilbert spaces,, J. Math Anal. Appl., 359 (2009), 508. doi: 10.1016/j.jmaa.2009.06.005. Google Scholar [10] A. Moudafi, Proximal methods for a class of bilevel monotone equilibrium problems,, J. Global Optimization, 47 (2010), 287. doi: 10.1007/s10898-009-9476-1. Google Scholar [11] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings,, Bull. Aust. Math. Soc., 73 (1967), 591. doi: 10.1090/S0002-9904-1967-11761-0. Google Scholar [12] G. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space,, J. Math. Anal. Appl., 72 (1979), 383. doi: 10.1016/0022-247X(79)90234-8. Google Scholar
show all references
##### References:
[1] H. Attouch, M. O. Czarnecki and J. Peypouquet, Prox-penalization and splitting methods for constrained variational problems,, SIAM J. Control Optim., 21 (2011), 149. doi: 10.1137/100789464. Google Scholar [2] J. P. Aubin, "Optima and Equilibria: An Introduction to Nonlinear Analysis,", Springer, (2002). Google Scholar [3] E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems,, Math. Student, 63 (1994), 123. Google Scholar [4] O. Chadli, Z. Chbani and H. Riahi, Equilibrium problems with generalized monotone Bifunctions and Applications to Variational inequalities,, J. Optim. Theory Appl., 105 (2000), 299. doi: 10.1023/A:1004657817758. Google Scholar [5] Z. Chbani and H. Riahi, Variational principle for monotone and maximal bifunctions,, Serdica Math. J., 29 (2003), 159. Google Scholar [6] N. Hadjisavvas and H. Khatibzadeh, Maximal monotonicity of bifunctions,, Optimization, 59 (2010), 147. doi: 10.1080/02331930801951116. Google Scholar [7] P. E. Mainge and A. Moudafi, Strong convergence of an iterative method for hierarchical fixed-points problems,, Pacific J. Optim., 3 (2007), 529. Google Scholar [8] A. Moudafi, Proximal point algorithm extended for equilibrium problems,, J. Nat. Geom., 15 (1999), 91. Google Scholar [9] A. Moudafi, On the convergence of splitting proximal methods for equilibrium problems in Hilbert spaces,, J. Math Anal. Appl., 359 (2009), 508. doi: 10.1016/j.jmaa.2009.06.005. Google Scholar [10] A. Moudafi, Proximal methods for a class of bilevel monotone equilibrium problems,, J. Global Optimization, 47 (2010), 287. doi: 10.1007/s10898-009-9476-1. Google Scholar [11] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings,, Bull. Aust. Math. Soc., 73 (1967), 591. doi: 10.1090/S0002-9904-1967-11761-0. Google Scholar [12] G. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space,, J. Math. Anal. Appl., 72 (1979), 383. doi: 10.1016/0022-247X(79)90234-8. Google Scholar
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https://math.stackexchange.com/questions/1609160/is-there-a-function-on-a-compact-interval-that-is-differentiable-but-not-lipschi | # Is there a function on a compact interval that is differentiable but not Lipschitz continuous?
Consider a function $f:[a,b]\rightarrow \mathbb{R}$, does there exist a differentiable function that is not Lipschitz continuous?
After discussing this with friends we have come to the conclusion that none exist. However there is every chance we are wrong. If it is true that none exist how could we go about proving that? It is true that if $f$ is continuously differentiable then $f$ is Lipschitz, but what if we don't assume the derivative is continuous?
The map $f : [0,1] \to \mathbb{R}$, $f(0) = 0$ and $f(x) = x^{3/2} \sin(1/x)$ is differentiable on $[0,1]$ (in particular $f'(0) = \lim_{x \to 0^+} f(x)/x = 0$), but it is not Lipschitz (the derivative $f'(x)$ is unbounded).
• You mean $x^{3/2}\,\sin(1/x)$? – Julián Aguirre Jan 12 '16 at 10:31
• Yes @JuliánAguirre, thanks for catching that. – Najib Idrissi Jan 12 '16 at 10:32
• Boundedness of the derivative is a sufficient condition for a function being Lipschitzian. I'm not sure it is necessary. – egreg Jan 12 '16 at 10:39
• @egreg It is necessary: if $|f(x) - f(y)| \le K |x-y|$ for all $x$, $y$, then $|f'(x)| = |\lim_{y \to x} (f(y) - f(x))/(x-y)| \le K$. (The converse is proved used the MVT.) – Najib Idrissi Jan 12 '16 at 10:42
• Thanks for the answer. I'm unsure why you're looking at $\lim_{x \rightarrow 0^{+}} f(x)/x$ and not $\lim_{x\rightarrow 0^{+}} f^{\prime}(x)$. – mark Jan 12 '16 at 12:42
If you require $f'$ to be continious then there can be no $f$ since $f'([0,1])$ is compact and indeed bounded.
• No, Michael Albanese had alrady suggested that, but $f'(0)$ does not exist. – Hagen von Eitzen Jan 12 '16 at 10:37
• thanks! I would like to delete it but I can't find a button to do that on my phone app! – Maffred Jan 12 '16 at 10:41
• since I can't delete at least I write something uselfull i hope! :) – Maffred Jan 12 '16 at 10:58 | 2019-07-22 03:46:07 | {"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": 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": 0.9096434116363525, "perplexity": 298.7062188128074}, "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-2019-30/segments/1563195527474.85/warc/CC-MAIN-20190722030952-20190722052952-00212.warc.gz"} |
https://mathoverflow.net/questions/84742/how-is-the-julia-set-of-fg-related-to-the-julia-set-of-gf | # How is the Julia set of $fg$ related to the Julia set of $gf$?
Let $f$ and $g$ be complex rational functions (of degree $\geq 2$ if that helps). What can be said about the relationship between $J(fg)$ and $J(gf)$, the Julia sets of the composite functions $f \circ g$ and $g \circ f$?
If I'm not mistaken, $f$ restricts to a map $J(gf) \to J(fg)$, and $g$ restricts to a map $J(fg) \to J(gf)$. So $J(fg)$ and $J(gf)$ surject onto each other in a particular way (and, indeed, in a way that commutes with the actions of $fg$ on $J(fg)$ and $gf$ on $J(gf)$). Since Julia sets are completely invariant, the restricted map $f: J(gf) \to J(fg)$ is $deg(f)$-to-one, and similarly the other way round.
So there's some kind of relationship between the two sets.
If $f$ or $g$ has degree one then $J(fg)$ and $J(gf)$ are "isomorphic", in the sense that there's a Möbius transformation carrying one onto the other. Thus, the simplest nontrivial example would be to take $f$ and $g$ to be of degree 2. I don't know a way of computing, say, the example $f(z) = z^2$ and $g(z) = z^2 + 1$. That would mean computing the Julia sets of $gf(z) = z^4 + 1$ and $fg(z) = z^4 + 2z^2 + 1$.
My question isn't completely precise, I'm afraid. But here are some of the things that I would value in an answer: theorems on what $J(fg)$ and $J(gf)$ have in common, examples showing how different they can be, pictures of $J(fg)$ and $J(gf)$ for particular functions $f$ and $g$, and references to where I can find out more (especially those accessible to a non-specialist). Thanks.
-
This might not be true if the functions have poles. Suppose you had a point such that $f$ kept taking it very close to infinity and $g$ kept taking it back near $0$, then it would be in $J(gf)$ but $f$ of it would not be in $J(fg)$. Are they allowed to have poles? – Will Sawin Jan 2 '12 at 22:52
As to whether they can have poles: f and g are rational functions with complex coefficients, so they do in general have poles in the usual complex analysis sense. However, I think it's usually better to interpret them as holomorphic maps from the Riemann sphere to itself, in which case there's nothing special about the point $\infty$. – Tom Leinster Jan 3 '12 at 0:33
Will, I don't get your argument. Can you produce a specific counterexample? When I try to turn what you wrote into a counterexample, I don't get one. And I thought I had a proof (which I'll supply if you want). – Tom Leinster Jan 3 '12 at 1:35
I was thinking of the wrong definition of a Julia set, the one that only makes sense for polynomials because it looks at bounded orbits – Will Sawin Jan 3 '12 at 4:04
What kinds of properties are you interested in? As you point out, each Julia set is a branched cover of the other, so the local structures will be very similar, but the global structures may be very different. – Jim Belk Jan 3 '12 at 18:10
I'm not sure if this is helpful, but here is an example. The following picture shows the filled Julia set for $z^6 - 1$.
and the following picture shows the filled Julia set for $(z^2-1)^3$:
This is the case where $f(z) = z^2 - 1$ and $g(z) = z^3$. Note that the bottom image is a double cover of the top, while the top image is a triple cover of the bottom.
(These images were produced using Mathematica.)
-
That's very helpful! Thanks so much! – Tom Leinster Jan 4 '12 at 8:59
Answer. $J(fg)$ is the full $g$-preimage of $J(gf)$. (And vise versa with interchange of $f$ and $g$).
Proof. Let $A=fg$ and $B=gf$. Then we have a semi-conjugacy $gA=Bg$. Now it is a general fact, that whenever you have such a semi-conjugacy (of rational functions) the Julia set of $A$ is the $g$-preimage of the Julia set of $B$.
Proof. The semi-conjugacy can be iterated: $gA^n=B^ng$. Now, $z\in J(A)$, iff the family $gA^n$ is not normal, iff $B^ng$ is not normal, that is $z\in g^{-1}(J(B))$.
Added on 8.6.12. By the way, this demonstrates an amazing fact: for every $f$ and $g$, there exist sets $F$ and $G$ such that $G=f^{-1}(F)$ and $F=g^{-1}(G)$. This looks surprising to me. Finite sets $F$ and $G$ of cardinality greater than $2$ with such properties cannot exist, as a simple count shows. Are there other examples of such $F$ and $G$ ?
Added on 8.7.12. Let $f$ and $g$ be two rational functions. Let $F$ be a closed set, containing more than 2 points, and such that $(g^{-1}f^{-1}(F))=F$, then $F$ contains the Julia set of $fg$. And $J(fg)$ does have this property. (I am writing compositions $fg=f(g)$.) Trivial, but funny.
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Thanks, Alexandre. Just to check: by "full g-preimage", you just mean "g-preimage" (i.e. preimage under g), right? So the word "full" is redundant? – Tom Leinster Aug 4 '12 at 19:37
"Preimage" should be understood as "full preimage" in what I wrote. I think the general facts that a) the family $g(f_n)$ is normal on the set where $f_n$ is normal, and b) the family $f_n(g)$ is normal on the full $g$-preimage of the set where $f_n$ is normal are immediate consequences of definition of normality. – Alexandre Eremenko Aug 4 '12 at 19:54
Sorry, Alexandre, I'm still not certain that I understand you. I simply don't know what the term "full preimage" means (and my attempts to look it up have come to nothing). So: what is the definition of full preimage? – Tom Leinster Aug 4 '12 at 21:41
Full $f$-preimage of a point $w$ is the set of all $z$ such that $f(z)=w$. Full preimage of a set is the union of full preimages of its points. – Alexandre Eremenko Aug 5 '12 at 8:27
OK, thanks. So "full preimage" is a synonym for "preimage". – Tom Leinster Aug 5 '12 at 18:37
Hy I'm not shure that your restriction map $f: J(gf)\rightarrow J(fg)$ is right. Insted of looking at Julia set it is equivalent to look at Fatou set where is more natural work with mapings. Since you've put $f:\{(gf)^n\}_n \rightarrow \{(fg)^n\}_n$ it clearly does not work. Insted you have to use conjugation $f\circ-\circ f^{-1}$, since you have rational function of deg>1 the inverse is not properly defined. So in the neighbour of the periodic points of $gf$ which are not critical (you dont have inverse) for $f$ you get same dynamics.
As you know fixed points play important role in this theory so you can try to compare fixed points (or periodic) of $fg$ and $gf$.
I think there are some results if you have $g$ an $f$ that commutes and than you compare dimaics of $f$ and $g$ with dynamics of $fg$.
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Luka, lease edit your message: I have difficulties reading it. – Alexandre Eremenko Aug 4 '12 at 17:09 | 2016-07-26 00:48:40 | {"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": 0.8934568166732788, "perplexity": 230.58677396262578}, "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-2016-30/segments/1469257824499.16/warc/CC-MAIN-20160723071024-00157-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://willrosenbaum.com/teaching/2021s-cosc-112/slides/lec02-recursion-1/ | # Lecture 02: Recursion I
## Outline
1. Intro to Recursion
2. Activity: Fibonacci numbers
3. Comparing Recursion and Iteration
# Recursion
## Recursion
• Lab 01, you use iteration (looping) to solve a problem (printing something on the screen many times)
for int(i = 0; i < max; i++) {
// do something
}
• Some problems are naturally recursive: solution of the whole problem can be reduced to solving the same problem (possibly several times) on a smaller instance.
public int doSomething(int n) {
// some code
doSomething(n - 1); // recursive function call
// some more code
return something;
}
## Example: Factorial
For a positive integer $n$, the factorial function, $f(n) = n!$ is defined to be:
• $f(n) = n \cdot (n-1) \cdot (n - 2) \cdots 2 \cdot 1$
Compute some factorials!
## Factorial: Recursive Formula
For any $n \geq 2$, we have
• $f(n) = \begin{cases} 1 &\text{ if } n = 1\\ n \cdot f(n-1) &\text{ if } n > 1.\end{cases}$
This is a recursive formula!
## Factorial in Code
private static int factorial(int n) {
if (n <= 1) {
return 1;
}
return n * factorial(n - 1);
}
Download Factorial.java
## How does this work?
private static int factorial(int n) {
if (n == 1) {
return 1;
}
return n * factorial(n - 1);
}
Compute factorial(4) by hand!
## Fibonacci Numbers
The Fibonacci numbers are the sequence of numbers
$1, 1, 2, 3, 5, 8, 13, 21, \ldots$
where each number is the sum of the previous two.
Activity. Write a method that computes the $n$-th Fibonacci number for a positive integer (long) $n$.
## Two Approaches
• Iterative (computation using a loop)
• Recursive
Question. Which is better?
## Let’s Test Their Performance!
Download Fibonacci.java
## Testing the Performance of Factorials
Download FactorialTest.java
## A Question
What makes recursive Fibonacci slow, while recursive factorial is fairly fast?
## Recursive Fibonacci
private static long fib (long n) {
if (n <= 2)
return 1;
return fib(n-1) + fib(n-2);
}
## Recursive Factorial
private static int factorial(int n) {
if (n <= 1) {
return 1;
}
return n * factorial(n - 1);
}
## Upcoming
Three morals, three questions
1. Recursion may give simple code, but may be less efficient
• How can we determine which is better?
2. Fibonacci numbers grow too fast
• How can we design a better solution?
3. We should do better at error checking
• Can we validate input while running? | 2022-01-18 07:50:27 | {"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": 2, "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": 0.21095073223114014, "perplexity": 9452.503418258268}, "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/1642320300805.79/warc/CC-MAIN-20220118062411-20220118092411-00666.warc.gz"} |
https://hippocampus-garden.com/stylegans/ | # Hippocampus's Garden
Under the sea, in the hippocampus's garden...
Search by
# Awesome StyleGAN Applications
November 12, 2021 | 16 min read | 1,540 views
Since its debut in 2018, StyleGAN attracted lots of attention from AI researchers, artists and even lawyers for its ability to generate super realistic high-resolution images of human faces. At the time of this writing, the original paper [1] has 2,548 citations and its successor StyleGAN2 [2] has 1,065. This means that the number of application works is growing at a dizzying rate. To keep me from getting overwhelmed, I’m writing this post to overlook this research field in an organized way. Of course, it’s impossible to read thousands of papers, so hereafter I’ll focus on the papers that relate to image manipulation including GAN inversion and 3D control.
## StyleGANs: A Quick Recap
First of all, let’s briefly recall what StyleGAN was and what the key updates of its subsequent versions were.
### StyleGAN
The architecture of the original StyleGAN generator was novel in three ways:
• Generates images in two-stages; first map the latent code to an intermediate latent space with the mapping network and then feed them to each layer of the synthesis network, rather than directly inputs the latent code to the first layer only.
• Applies AdaIN [3] layers iteratively to capture the intermediate latent code as “styles”.
• Injects explicit noise inputs to deal with stochastic variations such as hair and freckles.
These are best described in the figure below.
Image taken from [1].
With these features combined, StyleGAN can generate images that are almost impossible to discriminate for humans.
Image taken from [1].
This quality was so amazing that many people rushed to train StyleGAN with their own datasets to generate cats, ukiyoe, Pokémons, and more (see Awesome Pretrained StyleGAN for details).
StyleGAN has another interesting feature called ”style mix”. With two latent codes $\mathbb{z}_A$ and $\mathbb{z}_B$ (and corresponding $\mathbb{w}_A$ and $\mathbb{w}_B$), one can switch the inputs from $\mathbb{w}_B$ to $\mathbb{w}_A$ in the middle of the synthesis network and get a mixed image that has B’s coarse styles and A’s fine styles.
Image taken from [1].
### StyleGAN2
The human face images generated by StyleGAN look convincing enough, but if you have a careful look, you may notice some unnatural artifacts. In StyleGAN2 [2], some architectural optimizations were made to StyleGAN to facilitate even more realistic generation, though I don’t go into the technical details here.
One of the most important updates of StyleGAN2 is that by regularizing the perceptual path length, it became easier to invert. Now it is possible to encode a given image (either generated or real) into the intermediate style space $\mathcal{W}$.
Image taken from [2].
This paved the way for GAN inversion — projecting an image to the GAN’s latent space where features are semantically disentangled, as is done by VAE. As we’ll see in the next section, StyleGAN2 is currently the most widely used version in terms of the number of application works.
### StyleGAN3 (Alias-Free GAN)
In June 2021, the Tero Karras team published Alias-Free GAN (later named StyleGAN3) to address the undesirable aliasing effect that leads to some details glued to the absolute coordinates of the image [4].
A video is worth a thousand words. The official video clearly demonstrates the “texture sticking” issue and how StyleGAN3 solves it perfectly. Now it can be trained on unaligned images like FFHQ-U. For StyleGAN3 applications? There are only a few yet.
## StyleGAN Inversion
GAN inversion is a technique to invert a given image back to the latent space, where semantic editing is easily done. For example, when you get a latent code $\mathbb{z}$ of your portrait $\mathbb{x}$, you can generate a younger version by adding the “decrease age” vector $\mathbb{n}$ and feeding it to the generator.
Image taken from [5].
There are three approaches to GAN inversion:
• Optimization-based methods use an iterative algorithm, such as gradient descent, to search for the latent code that minimizes the reconstruction loss. They generally yield better reconstruction results but take a much longer time due to the iterative process.
• Learning-based methods train an encoder that inverts images to the latent space. They are generally faster and less accurate than their optimization-based counterparts.
• Hybrid methods of these two. Typically, they first invert a given image to the latent code with a learning-based encoder and then optimize it further. This is expected to reduce the time for optimization and the quality of inversion.
Let’s have a look at some examples.
### Image2StyleGAN
Image2StyleGAN [6] is a simple but effective implementation of an optimization-based approach. It minimizes the sum of the perceptual loss and L2 loss to get the embedded latent code.
Image taken from [6].
The authors noticed that the 512-dimensional intermediate latent space $\mathcal{W}$ is not informative enough to restore the input image. So, they extended the latent space to $\mathcal{W}+$, a concatenation of 18 different $\mathbb{w} \in \mathcal{W}$ vectors, one for each input to the StyleGAN’s AdaIN layers. The resulting $\mathcal{W}+$ space is well disentangled and allows multiple face image editing applications, including style transfer and expression transfer. This feature was further explored in Image2StyleGAN++ [7].
### pSp
The learning-based approach pSp (pixel2style2pixel) is a general image-to-image translation framework [8]. The encoder is trained to minimize the reconstruction loss (the sum of L2, LPIPS, identity, and latent code regularization loss) and directly translates the input image to the extended latent code ($\in \mathcal{W}+$).
Image taken from [8].
The pSp encoder can be trained on images not represented in the StyleGAN domain. In that way, pSp can generate images conditioned on inputs like sketches and segmentation masks.
Image taken from [8].
### e4e
e4e (Encoder for Editing) is a learning-based encoder specifically designed for semantic editing after inversion [9].
First, the authors summarized the variations of the intermediate latent space $\mathcal{W}$ and the extended $\mathcal{W}+$. They use $\cdot^k$ notation for the layer extension and explicitly denote $\mathcal{W}_*$ when it is not the equal distribution to $\mathcal{W}$. Now, four variations listed in the table below should be considered. The conventional $\mathcal{W}+$ space is now $\mathcal{W}^k$ or $\mathcal{W}^k_*$ depending on its distribution.
Individual style codes are limited to $\mathcal{W}$ Same style code in all layers
$\mathcal{W}$
$\mathcal{W}^k$
$\mathcal{W}_*$
$\mathcal{W}^k_*$
Based on the above definition, the authors shed light on distortion-editability tradeoff and distortion-perception tradeoff. That is, inverting to $\mathcal{W}^k_*$ space leads to less distortion (less reconstruction loss) than inverting to $\mathcal{W}$, but it is also less realistic and harder to edit results. The figure below depicts the distortion-perception tradeoff.
Image taken from [9].
e4e employs the pSp’s architecture but has control of these tradeoffs by putting $\mathcal{W}^k_*$ closer to $\mathcal{W}^k$ and $\mathcal{W}_*$. The editability-aware encoder achieves good reconstruction and semantic editing at the same time.
Image taken from [9].
### ReStyle
To improve the reconstruction accuracy of pSp and e4e, ReStyle is tasked with predicting a residual of the current estimate to the target [10]. It works with a negligible increase in inference time.
Image taken from [10].
## Semantic Editing
Once the latent code is obtained, we can semantically edit the original image by moving it to a certain direction in the latent space. There are mainly two types of input:
• Two images (source and reference), possibly with additional instructions including masks or attribute indices.
• An image and an attribute index.
To put it simply, the former is more like a copy-pasting, while the latter attempts to control the output proactively. Plus, the latter assumes that the edits are made multiple times interactively.
In this area, it is usually assumed that StyleGAN inversion algorithms are given.
### Image2StyleGAN++
Image2StyleGAN++ extends Image2StyleGAN to take spatial masks as input to allow local editing [7]. For example, it can perform image crossover:
Image taken from [7].
### Editing in Style
Thanks to the well-disentangled latent space, the k-means clustering of the hidden layer activations of the StyleGAN generator provides an interesting insight: the clusters are semantically meaningful even they were decomposed in an unsupervised way [11].
Image taken from [11].
Then, the contribution matrix (each element is the contribution of channel $c$ to cluster $k$) can be used to determine the style mixing coefficients. This enables to make a local edit (e.g., swapping eyes).
Image taken from [11].
### StyleFlow
To facilitate more fine-grained and editable encoding, StyleFlow replaces the fully connected layers in the mapping network with attribute-aware continuous normalizing flow (CNF) blocks [12].
Image taken from [12].
The results are impressive. The two source images are real images (i.e., not generated by StyleGAN), and StyleFlow successfully translates these extreme samples.
Image taken from [12].
### StyleSpace Analysis
Wu et al. quantitatively analyzed how disentangled StyleGAN’s latent spaces are. Although the extended intermediate latent space $\mathcal{W}+$ is the standard choice, they discovered that the style space $\mathcal{S}$ is actually more disentangled than $\mathcal{W}+$ [13]. As depicted in the figure below, the style space $\mathcal{S}$ is spanned by a concatenation of affined intermediate latent codes.
Image taken from [13].
The images below demonstrate how well the style space $\mathcal{S}$ is disentangled. Each pair is the result of decreasing (-) and increasing (+) a single element of the style code. The numbers in the bottom left corner indicate the layer index and the channel index. Note that the base image is a fake one generated by StyleGAN2.
Image taken from [13].
### Retrieve in Style
Retrieve in Style extended Editing in Style to edit more global features such as pose and hairstyle [14].
Image taken from [14].
As the title suggests, the authors also provide an algorithm for attribute-guided image retrieval.
## 3D Control
Among several types of semantic edits, reposing is the most difficult task as it often requires drastic and global changes. Thus, some works explicitly estimate 3D information and use it to perform visually natural reposing.
### StyleRig
StyleRig can control human face images generated by StyleGAN like a face rig, by translating the semantic editing on 3D meshes by RigNet [16] to the latent code of StyleGAN [15]. Here, StyleGAN is supposed to be pre-trained and RigNet can be trained in a self-supervised manner.
Image taken from [16].
### Pose with Style
Pose with Style exploits StyleGAN2 to perform human reposing [17]. The target pose information is used as input, and the original image and coordinate information are injected as style. This algorithm is also applicable to the virtual try-on task.
Image taken from [17].
### StyleNeRF
StyleNeRF integrates StyleGAN2 and NeRF (neural radiance field) [19] to generate 3D-consistent high-resolution images [18]. The inputs to the synthesis network are the intermediate latent code $\mathbb{w}$ and the low-resolution feature map generated by NeRF from the camera pose $\mathbb{p}$.
Image taken from [18]. Left: original NeRF. Right: StyleNeRF.
The figure below shows how StyleNeRF enjoys the benefits from both NeRF’s 3D consistency and StyleGAN2’s perception quality.
Image taken from [18]. The leftmost is the low-resolution feature map generated by NeRF.
## Text-guided Manipulation
Last but not least, text-guided manipulation is an interesting application of StyleGAN.
### StyleCLIP
Based upon CLIP (contrastive language-image pretraining) [21], the state-of-the-art text-to-image generator, StyleCLIP finds the optimal direction to move forward in the latent space so that the input image will be edited according to the instruction [20].
A wide variety of text instructions can be accepted. Since CLIP has certain knowledge about proper nouns, it is possible to edit a face to look like “Emma Stone”.
Image taken from [20].
## Concluding Remarks
StyleGAN had such a great impact that its applications are growing fast. I hope this article will give you some sort of perspective on them.
Thanks for reading. As always, feedback is welcomed.
## References
[1] Tero Karras, Samuli Laine, Timo Aila. ”A Style-Based Generator Architecture for Generative Adversarial Networks“. CVPR. 2019.
[2] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, Timo Aila. ”Analyzing and Improving the Image Quality of StyleGAN “. CVPR. 2020.
[3] Xun Huang, Serge Belongie. ”Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization“. ICCV. 2017.
[4] Tero Karras, Miika Aittala, Samuli Laine, Erik Härkönen, Janne Hellsten, Jaakko Lehtinen, Timo Aila. ”Alias-Free Generative Adversarial Networks“. NeurIPS. 2021.
[5] Weihao Xia, Yulun Zhang, Yujiu Yang, Jing-Hao Xue, Bolei Zhou, Ming-Hsuan Yang. ”GAN Inversion: A Survey”. 2021.
[6] Rameen Abdal, Yipeng Qin, Peter Wonka. ”Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?“. ICCV. 2019.
[7] Rameen Abdal, Yipeng Qin, Peter Wonka. ”Image2StyleGAN++: How to Edit the Embedded Images?“. CVPR. 2020.
[8] Elad Richardson, Yuval Alaluf, Or Patashnik, Yotam Nitzan, Yaniv Azar, Stav Shapiro, Daniel Cohen-Or. ”Encoding in Style: A StyleGAN Encoder for Image-to-Image Translation“. CVPR. 2021.
[9] Omer Tov, Yuval Alaluf, Yotam Nitzan, Or Patashnik, Daniel Cohen-Or. ”Designing an Encoder for StyleGAN Image Manipulation“. SIGGRAPH. 2021.
[10] Yuval Alaluf, Or Patashnik, Daniel Cohen-Or. ”ReStyle: A Residual-Based StyleGAN Encoder via Iterative Refinement“. ICCV. 2021.
[11] Edo Collins, Raja Bala, Bob Price, Sabine Süsstrunk. ”Editing in Style: Uncovering the Local Semantics of GANs“. CVPR. 2020.
[12] Rameen Abdal, Peihao Zhu, Niloy Mitra, Peter Wonka. ”StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows“. SIGGRAPH. 2021.
[13] Zongze Wu, Dani Lischinski, Eli Shechtman. ”StyleSpace Analysis: Disentangled Controls for StyleGAN Image Generation“. CVPR. 2021.
[14] Min Jin Chong, Wen-Sheng Chu, Abhishek Kumar, David Forsyth. ”Retrieve in Style: Unsupervised Facial Feature Transfer and Retrieval”. 2021.
[15] Ayush Tewari, Mohamed Elgharib, Gaurav Bharaj, Florian Bernard, Hans-Peter Seidel, Patrick Pérez, Michael Zollhöfer, Christian Theobalt. ”StyleRig: Rigging StyleGAN for 3D Control over Portrait Images“. CVPR. 2020.
[16] Zhan Xu , Yang Zhou , Evangelos Kalogerakis , Chris Landreth , Karan Singh. ”RigNet: Neural Rigging for Articulated Characters“. SIGGRAPH. 2020.
[17] Badour AlBahar, Jingwan Lu, Jimei Yang, Zhixin Shu, Eli Shechtman, Jia-Bin Huang. ”Pose with Style: Detail-Preserving Pose-Guided Image Synthesis with Conditional StyleGAN“. SIGGRAPH Asia. 2021.
[18] Jiatao Gu, Lingjie Liu, Peng Wang, Christian Theobalt. ”StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis”. 2021.
[19] Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, Ren Ng. ”NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis“. ECCV. 2020.
[20] Or Patashnik, Zongze Wu, Eli Shechtman, Daniel Cohen-Or, Dani Lischinski. ”StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery“. ICCV. 2021.
[21] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, Ilya Sutskever. ”Learning Transferable Visual Models From Natural Language Supervision“. ICML. 2021.
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Hippocampus's Garden © 2022, Shion Honda. Built with Gatsby | 2022-08-10 10:22:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 42, "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": 0.6824434399604797, "perplexity": 7801.660951898696}, "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-2022-33/segments/1659882571153.86/warc/CC-MAIN-20220810100712-20220810130712-00566.warc.gz"} |
http://math.stackexchange.com/questions/1596/non-linear-transformation | # Non-Linear Transformation
Can someone explain to me in simple terms what a non-linear transformation is in maths?
I know some single-variable calculus, but I read it has to do with multi-variable calculus, which I'm not familiar with.
If someone could explain it in simple words, that would be helpful.
-
A transformation which is not linear. Do you understand the definition of a linear transformation? It has nothing to do with whether you are working with one or many variables; for example, the transformation which sends x to x^2 is not linear. – Qiaochu Yuan Aug 5 '10 at 9:11
(Off-topic: how do you have 101 rep with no upvoted questions and no answers?) – Qiaochu Yuan Aug 5 '10 at 9:15
@Qiaochu: Area51.stackexchange reputation is carried over to new SE sites. – Larry Wang Aug 5 '10 at 9:16
@Qiaochu Yuan: That belongs to meta =P. You get 100 free rep for accociating your account with other stackexchange sites. – Jens Aug 5 '10 at 9:17
Is it possible the OP is after an explanation of 'differentiable' in a multivariable setting? – Tom Boardman Aug 5 '10 at 10:57
Let $V_1, V_2$ be two vector spaces over the field $F$. A transformation $T: V_1 \to V_2$ is linear if for every $x, y \in V_1$ and every $\alpha \in F$ it is true that
(*) $T(x + \alpha y) = T(x) + \alpha T(y)$
T is not a linear transformation if there are some $x, y, \alpha$ such that (*) is not true.
-
In addition to the definition of linear map that Tomer remind you, here are two examples.
For instance, $f(x,y) = x^2y$ is not a linear map $f: \mathbb{R}^2 \longrightarrow \mathbb{R}$ because
$$f(2x,2y) = 4x^22y \neq 2x^2y = 2f(x,y) \ .$$
More generally, the linear maps $f: \mathbb{R}^m \longrightarrow \mathbb{R}^n$ are necessarily of the form
$$f(x_1, \dots , x_m) = (a_1^1 x_1 + \dots + a_1^m x_m , \dots , a_n^1 x_1 + \dots + a_n^m x_m)$$
with $a^i_j$ constant coefficients.
So, two more examples:
1. $f(x,y) = x + 2y$ is a linear map.
2. $f(x,y,z) = 3x + 1$ is a non-linear map
- | 2014-10-25 08:44:25 | {"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": 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": 0.8991972804069519, "perplexity": 704.4299236312777}, "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-2014-42/segments/1414119647914.3/warc/CC-MAIN-20141024030047-00215-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://cs.stackexchange.com/questions/23671/possible-to-connect-arbitrary-number-of-dots-without-intersections | # Possible to connect arbitrary number of dots without intersections?
A (now closed) question on SO made me think about the following problem:
Given an arbirtary number of points (2D), draw a path that consists of straight lines between points, visits each point exactly once and does not intersect with itself.
I came to the conclusion that this is easy if I can chose starting and ending point:
sort points by their x coordinate
use point with mininmal x coordinate as starting point
connect remaining points in left-to-right order
If there are multiple points with the same x value, start with the point with minimal y value and go bottom-up. This way, no intersections can occur.
Now my question is: is this still possible if start and end point are fixed? I assume that there are well known algorithms for this problem, but my search didn't reveal any useful results.
As @hyde points out, there is no solution if more than two points are on a straight line and start/end points are not the outermost points.
-
Do I misunderstand the problem, or is 3 points on a straight line with middle point as start or end point a trivial example of impossible scenario? Or does this case not count as having intersections and/or visiting the mid point twice? – hyde Apr 11 at 18:40
@hyde You are right. If all the points are on a single straight line and start or end point are in the middle, there is no solution. However, this is the only scenario without a solution. – FrankW Apr 11 at 18:59
Another note, if there are 5+ points on straight line and exactly one elsewhere, an impossible scenario is also possible. Other arrangements of points, not sure if they're always solvable, but I wouldn't be comfortable just assuming so. – hyde Apr 11 at 19:33
It is (almost always) possible. Let the two points be $p_1=(x_1,y_1)$ and $p_2(x_2,y_2)$. Wlog, assume that $x_1<x_2$. Denote by $q_1$ ($q_2$) the point with smallest (largest) $x$-value greater (smaller) then $x_1$ ($x_2$) (and smallest (largest) $y$, if there are multiple candidates). Then you can do the following:
• Determine the set $S_1$ of all the points with $x\leq x_1$.
• If $|S_1|=1$, connect $x_1$ and $q_1$.
• If $|S_1| > 1$ and all the points in $S_1$ are on the same straight line:
• If all points outside of $S_1$ are on the same straight line, there is no solution
• Otherwise denote by $r_1$ the point with smallest $x$-coordiate not on the straight line. (If there are multiple such points choose the one with smallest $y$-coordinate.)
• Connect the points in $S_1$ starting with $x_1$. Connect the last of these points with $r_1$ and (if $r_1 \ne q_1$) connect $r_1$ with $q_1$.
• If $|S_1| > 1$ and the points are not all on one straight line, determine the convex hull of $S_1$.
At least one of the neighbours $n_1$ of $p_1$ on the convex hull can be reached from $q_1$ without intersecting the convex hull.
• Draw a (reverse) path from $q_1$ to $n_1$ and then along the convex hull to the point with smallest $x$. Continue in left-to-right-order (skipping points already included) until $p_1$.
• Analoguously connect the points with $x\geq x_2$.
• Connect the points with $x_1<x<x_2$ (i.e. from $q_1$ to $q_2$) in left-to-right-order (ignoring $r_1$ resp. $r_2$, if applicable).
-
Thanks! Since I'm not a native english speaker, are there differences between "in" and "on" the complex hull? What are the neighbors of $p_1$? Is $(n1)$ the only other neighbor (see imgur.com/NWCDRe4)? I think the last point must be "Connect the points between $q_1$ and $q_2$. – Jasper Apr 11 at 13:34
@Jasper I'd say "on" the convex hull only covers the points on the border, while "in" may also include those inside the surrounded area. $(n_1)$ is indeed the only other neighbour of $p_1$ on the convex hull. (And your picture fits the algorithm.) For the last bullet, your wording is almost equivalent to mine. (One might read your wording as excluding $q_1$ and $q_2$.) – FrankW Apr 11 at 14:05
Does this algo have a canonical name? What is the original source? – Jasper Apr 11 at 17:00
I came up with the algorithm myself and have not done any research if it was previously known. – FrankW Apr 11 at 18:50
@Jasper in 574 chars: Let p, p' be start and end dots, with p left of p'. Let q, q' be leftmost and rightmost dots. Let r, r' be leftmost and rightmost dots between p and p'. The convex hull of all dots left of p, p included, includes q. The hull has 2 dots next to p. For at least one, say s, the segment sr does not cut the hull. Connect r to s, then s to q through the part of the hull not including p. Connect q to p through all the remaining unused dots left of p as with the left to right algorithm . A mirror procedure connects p' to r'. Connect r to r' with the left to right algorithm. – babou Apr 12 at 11:23 | 2014-09-02 11:41:50 | {"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": 0.8124407529830933, "perplexity": 525.1997007956304}, "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-2014-35/segments/1409535921957.9/warc/CC-MAIN-20140901014521-00352-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://gmstat.com/category/business-mathematics/basics/ | # Category: Basics
## Basic Mathematics
This page is about Multiple Choice Questions and Answers for the subject of Business Mathematics. MCQs about Business Maths will help the students to learn fundamental concepts and will enable them for self-assessment of the core concepts related to mathematics and application of math in business.
This test covers the topics of integers, fractions, variables, and expression.
1. Which of the following is not an equivalent fraction of $\frac{3}{5}$?
2. In addition and subtraction of two integers, the sign of the answer depends upon
3. The sum of two negative integers is always
4. What is $\frac{1}{4}$ of $5\frac{1}{3}$ of ?
5. There are 40 students in a class. $\frac{1}{2}$ of the total number of students are Hindus. The number of Hindus is
6. Person $X$ ate $\frac{3}{5}$ of an orange. The remaining orange was eaten by Person $B$. What part of the orange was eaten.
7. Write an expression: Raju’ Father’s Age is 5 years more than 3 times Raju’s age. If Raju’s age is $X$ years, then the father’s age is
8. Person $A$ worked for $\frac{1}{2}$ hour. Person $B$ worked for $\frac{1}{4}$ of an hour. For how much time did both works together?
9. Subtract $a-b$ from $a+b$, the result is
10. Which of the following is an imporper fraction
11. The sum of two positive numbers is always
12. Product of two negative integers is always
13. Which of the following is a fraction
14. A car runs 20 KM using 1-liter petrol. How much distance will it cover in $1\frac{1}{4}$ liter of petrol?
15. The expression for sum of numbers $a$ and $b$ subtracted from their product is
16. The fraction $\frac{p+q}{q}$ equal
17. Which of the following is a mixed fraction?
18. Person $A$ reads $1\frac{1}{2}$ hours daily. Person $B$ reads $\frac{1}{2}$ hours daily. How many hours do they read for in one day?
19. A water bottle contains 2 liters of water. Person $B$ drank $\frac{1}{8}$ of water. How much water did $B$ drink?
20. Write the expression for the statement: The sum of three times $X$ and 11
This test is about some basic concepts of numbers, fractions, integers, expression, and basic calculations. It also covers some daily life examples related to fractions and mathematical expression. Let us start with the Basic MathMCQs test
This series of tests will also help the students to prepare themself for exams related to business studies such as Commerce, Management Sciences, Public Administration, Charted Accountancy, and ICAMP (Institute of Cost and Management Accountants of Pakistan), etc.
For Intermediate first year Mathematics
## Basic Math MCQs
This “Basic Math MCQs” quiz is about Multiple Choice Questions and Answers for the subject of Business Mathematics. MCQs about Business Mathematics will help the students to learn fundamental concepts and will enable them to self-assessment the core concepts related to mathematics and the application of mathematics in business, science, industry, social science, and daily life problems.
Please go to Basic Math MCQs to view the test
This test is about some basic concepts of numbers, fractions, integers, expression, and basic calculations. These free online MCQs test covers basic to advance math concept. This test is related to basic mathematics operations such as counting, addition, subtraction, multiplication, and division. It also covers some daily life examples related to fractions and mathematical expression. Some related word problems are also included in the test. Let us start with the Basic Mathematics MCQs test
This series of tests will also help the students to prepare themself for different kinds of examinations related to business studies such as Commerce, Management Sciences, Public Administration, Charted Accountancy, and ICAMP (Institute of Cost and Management Accountants of Pakistan), etc. This test is also useful for the preparation of NTS, FPSC, PPSC, SPSC, CSS, PMS tests, and school, college, or university-related exams.
For Intermediate first year Mathematics
## Basic Mathematics – 1
MCQs about Basic Business and Applied Mathematics for the preparation of Exams related to CA, CIMA, ICMAP, and MBA. MCQs covers many Business related fields (such as Business Administration, Commerce, and Charted Accountancy related Institutes) in which the subject of Business Mathematics is taught.
Please go to Basic Mathematics – 1 to view the test
Visit for MCQs about Basic Mathematics | 2022-12-05 18:49:42 | {"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": 0.17077352106571198, "perplexity": 1839.6998082754396}, "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/1669446711042.33/warc/CC-MAIN-20221205164659-20221205194659-00835.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/neutron-stars-believed-composed-solid-nuclear-matter-primarily-neutrons-radius-neutron-10--q2478981 | Neutron stars are believed to be composed of solid nuclear matter, primarily neutrons.If the radius of a neutron is 1.0 � 10�13 cm, calculate the density of a neutron in g/cm3. (volume of a sphere = ) Assuming that a neutron star has the same density as a neutron, calculate the mass in kilograms of a small piece of a neutron star the size of a spherical pebble with a radius of 0.10 mm. | 2016-08-27 18:42:37 | {"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": 0.9395175576210022, "perplexity": 485.8781344167713}, "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-2016-36/segments/1471982924605.44/warc/CC-MAIN-20160823200844-00031-ip-10-153-172-175.ec2.internal.warc.gz"} |
http://dlinares.org/ci.html | A $$1 - \alpha$$ confidence interval for a parameter $$\theta$$ is an interval $$C_n = (a,b)$$ where $$a=a(X_1,\dotsc,X_n)$$ and $$b=b(X_1,\dotsc,X_n)$$ are functions of the data such that $$P(\theta \in C_n) = 1 - \alpha$$.
The action space is $$\mathcal{A}=\Theta$$.
## Loss function
$$L(\theta,a) = \left\{ \begin{array}{ll} 0 & \mbox{if } |\theta - a| \leq \delta \\ 1 & \mbox{if } |\theta - a| > \delta \\ \end{array} \right.$$
## Interpretation
A confidence interval is not a probability statement about $$\theta$$, as $$\theta$$ is a fixed quantity, not a random variable.
A $$1 - \alpha$$ confidence interval means that $$1 - \alpha$$ times when you construct confidence interval it will contain $$\theta$$. | 2021-10-23 17:07:37 | {"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": 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": 0.9571923017501831, "perplexity": 136.74957540103082}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2021-43/segments/1634323585737.45/warc/CC-MAIN-20211023162040-20211023192040-00679.warc.gz"} |
http://math.stackexchange.com/questions/40859/induced-isomorphisms-from-gysin-sequence | # induced isomorphisms from Gysin sequence
Consider the path fibration: $K(\mathbb Z,2r-1)\rightarrow PK(\mathbb Z,2r)\rightarrow K(\mathbb Z,2r).$
Suppose that $H^*(K(\mathbb Z,2r-1);\mathbb Q)=H^*(S^{2r-1};\mathbb Q).$
We want to show that $H^*(K(\mathbb Z,2r);\mathbb Q)=\mathbb Q[a_{2r}]$.
The Gysin sequence gives that we have an isomorphism $$H^i(K(\mathbb Z,2r);\mathbb Q)\stackrel{\cup e}{\rightarrow}H^{i+2r}(K(\mathbb Z,2r);\mathbb Q)$$ where $\cup e$ is the cup product with the rational euler class.
Questions:
(1) Why is it that $e$ and the fundamental class $a_{2r}\in H^{i+2r}(K(\mathbb Z,2r);\mathbb Q)\cong \mathbb Q$ are non-zero multiples of each other?
(2) What does the "fundamental class" mean in this context? and finally,
(3) I'm not clear as to how to deduce that $H^*(K(\mathbb Z,2r);\mathbb Q)=\mathbb Q[a_{2r}]$.
-
2) The defining property of $K(\mathbb Z,2r)$ is that for any $X$, we have $H^{2r}(X, \mathbb Z)= [X, K(\mathbb Z,2r)]$. In particular for $X=K(\mathbb Z,2r)$ we know that $H^{2r}(X, \mathbb Z)= \mathbb Z$ by Hurewitz and is generated by the element corrsponding to the identity map. This is the fundamental class. Similarly with $\mathbb Q$ coefficients.
1, 3) $H^i(K(\mathbb Z,2r);\mathbb Q)\stackrel{\cup e}{\rightarrow}H^{i+2r}(K(\mathbb Z,2r);\mathbb Q)$ means that $\cup e$ is an isomorphism from $H^0(K(\mathbb Z,2r);\mathbb Q)$ to $H^{2r}(K(\mathbb Z,2r);\mathbb Q)$. The later is generated by the fundamental class. Hence $e$ is plus or minus the fundamental class.
Now, by induction on $i$, all the $H^i$ with $i$ not multiple $2r$ are zero, while the others are all isomorpic to $\mathbb Q$ and are generated by $e$, $e^2$ etc. or equivalently by $a_{2r}$, $a_{2r}^2$ etc. That is, $H^*(K(\mathbb Z,2r);\mathbb Q)=\mathbb Q[a_{2r}]$. | 2015-08-29 06:47:58 | {"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": 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": 0.9636342525482178, "perplexity": 125.12390606624957}, "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-2015-35/segments/1440644064263.27/warc/CC-MAIN-20150827025424-00114-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://newproxylists.com/tag/element/ | ## html – Identify what element got clicked on a form in JavaScript
I am trying to pass a ref to a function so that I know which html element was clicked. If I don’t pass the ‘this’ (and remove the ()’s from the html) it will always only hide the top TR. I need it to hide it’s own TR. BUT, and this is a big BUT, I will not know what row has the “click me” text so hard coding a unique id is not an option. They will all have the same ‘id’ (an array of IDs), or no ‘id’ at all (array of rows).
``````<!DOCTYPE html>
<html>
<body>
<table>
<tr id="row()"><td>Hello 1</td></tr>
<tr id="row()"><td>Hello 2</td></tr>
<tr id="row()"><td><p onclick="myFunction(this)">Hide me.</p></td></tr>
<tr id="row()"><td>Hello 1</td></tr>
<tr id="row()"><td>Hello 2</td></tr>
</table>
<script>
function myFunction(elmnt) {
document.getElementById("row(elmnt???)").style.display = 'none';
}
</script>
</body>
</html>
``````
## css – Position text inside ahref element (in center of image)
I created a static block with the following issue:
I’m trying to center text inside an ahref element, which looks like the following;
`````` <div class="small-24 medium-16 cell">
<a title="Chairs" href="/chairs"><img src="{{media url="wysiwyg/chair-1.png"}}" alt="Chairs" width="830" height="325">Chairs</a>
</div>
``````
Normally, I would position it as follows, with the text in a span in the ahref element next to the img:
``````a {
position: relative;
}
span {
position: absolute;
bottom: 10px;
left: 10px;
}
``````
However, I’m not allowed to save the span tag inside the ahref element next to the image. See image underneath.
How can I position the text inside the ahref element over the image?
## navigation – Make Audio Element Persistent Across Pages
I’m making a radio site and as part of that there’s a listen live element which uses an audio plugin. When the user clicks on a navigation item to bring them to a new page the audio stops (understandably).
Is there a way to keep the audio playing smoothly?
## divide and conquer – Clarification on the algorithm for finding a majority element
When the size of your problem reduced to 2, it’s the base case of your
recursion, it’s false that we pair up two remaining elements. so it’s
sufficiently, first count number of occurrence of two remaining
elements in $$A$$.
for your problem we act as follow:
we check the whole array to count number of occurrence $$A(i)=3$$, and
number of occurrence of $$A(i)=1$$ and then if number of occurrence
$$3geq frac{n}{2}+1$$ or if number of occurrence $$1geq frac{n}{2}+1$$, we print it.
but the main problem is we must prove the correctness and running time of algorithm.
Suppose $$mathcal{X}$$ is majority element, because of, $$mathcal{X}$$ is majority element, then the number of occurrence of it, is grater than
$$frac{n}{2}$$, so after pair up, at least there is one pair that elements are $$mathcal{X}$$, otherwise it contradict with this fact that $$mathcal{X}$$ is majority element.
On the other hand, at most all elements of array $$A$$ be $$mathcal{X}$$, so both elements of a pair be equal, as a result at most half of the elements remain in each recursion.
Therefore one of the at most $$frac{n}{2}$$ elements be $$mathcal{X}$$. And we do our divide an conquer the problem until remain only two element.
Our statement holds only if $$A$$ contains $$mathcal{X}$$. So after we get base that $$n=2$$, it’s sufficient to for each of two remaining elements we check number of occurrence it.
Suppose the remaining elements is a,b:
`````` A,B=0
for i = 1 to n
if (a==A(i))
A++
if (b==A(i))
B++
if(a> n/2)
print a
else if (b> n/2)
print b
else
print "there is no majority in the array"
``````
Because at each iteration at most half of the elements are remain
$$T(n)=T(frac{n}{2})+O(n)$$
$$=O(n)$$
Note that at each iteration pairing up of $$n$$ elements need $$O(n)$$ time.
## finite element method – Multiphysics – Electrostatics and Heat Transfer – Joule Heating boundary conditions
I am working on a multiphysics problem involving electrostatics (direct current) and heat transfer. I was messing around with the Joule Heating tutorial case and need to answer some questions to apply this to my problem.
The tutorial uses Dirichlet boundary conditions for the voltage. How could you calculate the corresponding electric current going through the system? Would you just integrate the electrical conductivity multiplied with the voltage gradient over the boundary surfaces?
If the above regarding the calculation of the current is correct, I assume, I could use the electric current as boundary condition by setting the required voltage gradient at the boundary?
Unfortunately my problem is far more complex than the tutorial as it involves very large temperature gradients, hence the thermal and electric conductivities can not be considered constant. I’ve been looking at other multiphysics problems (Buoyancy driven flow) and noticed, I can combine the electric pde with the heat pde to be solved coupled with ndsolve.
However, I can’t use static boundary conditions for the voltage gradient as the conductivity changes with the temperature field. I was thinking, I could use a WhenEvent to calculate the required voltage gradient at the boundary from the desired current by integrating the electric conductivity over the boundary’s surface at the beginning of each step. Is this the way to go on this, or is there a more elegant solution to this?
## react.js – not able to give proper css to my bootstrap element in react
when creating a navigation bar in my react based website , the react code :
`````` `<ul className="navbar-nav ml-auto mb-2 mb-lg-0">`
``````
now, on the ul tag (line 28) () i want to give margin right auto (mr-auto) instead of (ml-auto) which is margin-left :auto but it is not working and i had already import all necessary bootstrap import in my index.js file in react . and i copied this code from bootstrap itself under components > navbar
## How to hide a form element when a datetime widget is filled using #states
The following code is working well to hide a button when a textfield is filled, but it is not working when a datetime widget is encoded:
``````\$form('my_button') = (
'#type' => 'container',
'submit' => (
'#type' => 'submit',
'#value' => t("Click on me"),
'#submit' => ('submit_me')),
'#states' => (
'visible' => (
':input(data-drupal-selector=selector-of-my-text-field)' => (
'filled' => FALSE,
),
),
),
),
);
``````
Any hint?
## entities – Managed file element in custom field module doesn’t save target id
I have been breaking my head on this issue for a few days now. Using Drupal 9.2.x, I am building a custom field module for a client that has multiple fields. I isolated the problem by only including a managed file field for now, because the other fields are not causing this issue.
I defined a managed file element in my Widget class, which extends WidgetBase:
``````public function formElement(FieldItemListInterface \$items, \$delta, array \$element, array &\$form, FormStateInterface \$form_state) {
\$element('target_id') = (
'#type' => 'managed_file',
'#title' => \$this->t('Right image'),
'file_validate_extensions' => array('gif png jpg jpeg')
),
'#default_value' => array(\$items(\$delta)->target_id),
);
return \$element;
}
``````
I defined my schema as follows in my Item class:
`````` public static function schema(FieldStorageDefinitionInterface \$field_definition) {
return (
'columns' => (
'target_id' => (
'description' => 'The ID of the file entity',
'type' => 'int',
'unsigned' => TRUE,
),
),
'indexes' => (
'target_id' => ('target_id'),
),
'foreign keys' => (
'target_id' => (
'table' => 'file_managed',
'columns' => ('target_id' => 'fid'),
),
),
);
``````
}
And finally, I have added a property defintion for the field:
``````public static function propertyDefinitions(FieldStorageDefinitionInterface \$field_definition) {
->setLabel(t('target ID'))
->setRequired(FALSE);
return \$properties;
}
``````
Somehow this results in the file being uploaded into the managed files table, getting a fid and all looks well from there. However, the field table (node__fieldname) which contains the referencing target_id to the file_managed table somehow always defaults to 1. So no reference is being made to the uploaded file. I have tried working with other property definitions:
`````` \$properties('target_id') = DataDefinition::create('integer')
->setLabel(t('target ID'));
``````
and
``````\$properties('target_id') = DataReferenceTargetDefinition::create('integer')
->setLabel('Foreign key referencing managed file')
->setSetting('unsigned', TRUE)
->setRequired(FALSE);
``````
But no luck there. It seems a bit weird to me though, that the database target id needs to be integer and the file upload widget works with an array. Thats why I am aiming at the property definitions/schema as a cause here. If I try to work with a single int property value:
``````DataDefinition::create('integer')
``````
I get a primitive type error because the managed file element expects an array. Any suggestions? Thanks!
## How to replace the number of each element of a matrix with a subscript?
I want to get the matrix as Figure 2. There should be two ways to achieve the result.
1. There is a matrix as Figure 1, and change it to the form of Figure 2.
2. Generating the matrix as Figure 2 directly.
How can I do it? Thanks.
Figure 1
Figure 2
Codes
``````{{C11,C12,C13,C14,C15,C16},{0,C22,C23,C24,C25,C26},{0,0,C33,C34,C35,C36},{0,0,0,C44,C45,C46},{0,0,0,0,C55,C56},{0,0,0,0,0,C66}}
`````` | 2021-07-25 14:50:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 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": 21, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3253852128982544, "perplexity": 2334.4119698771456}, "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-2021-31/segments/1627046151699.95/warc/CC-MAIN-20210725143345-20210725173345-00557.warc.gz"} |
http://maths.anu.edu.au/events/partial-differential-equations-and-analysis-seminar | Partial Differential Equations and Analysis Seminar
Contact
Qirui Li
61 2 6125 1020
The partial differential equations and analysis seminar is the research seminar associated with the applied and nonlinear analysis, and the analysis and geometry programs
Upcoming events
21
Nov
2017
Speaker: Professor Gilles Lancien (Universite de Franche-Comte, Besancon, France)
A coarse embedding between metric spaces is, intuitively speaking, a map which preserves, in a weak sense, the geometry at large distances.
Past events
19
Sep
2017
Speaker: Changwei Xiong (MSI/ANU)
In 1897 Hadamard proved that any closed immersed surface with positive Gaussian curvature in 3-dimensional Euclidean space must be the boundary of a convex
12
Sep
2017
Speaker: Yong Wei (ANU/MSI)
We will discuss the Laplacian flow for closed $G_2$ structures. This flow was introduced by R.
29
Aug
2017
Speaker: Feida Jiang (MSI/ANU)
In this seminar, the speaker will talk about the existence result for semilinear oblique derivative problem for augmented Hessian equations on bounded domai
22
Aug
2017
Speaker: Derek W. Robinson (ANU)
In the first part of this talk we give a brief survey of the Hardy and Rellich inequalities.
11
Aug
2017
Speaker: Shuangjian Zhang (Toronto University)
A monopolist wishes to maximize her profits by finding an optimal price policy.
23
May
2017
Speaker: Pierre Portal (MSI/ANU)
The Ornstein-Uhlenbeck semigroup is a variant of the heat semigroup that plays a fundamental role in quite distinct areas of mathematics.
11
Apr
2017
Speaker: Andrew Hassell (MSI/ANU)
In this seminar, the speaker will talk about heat kernel upper and lower bounds on asymptotically hyperbolic manifolds.
04
Apr
2017
Speaker: Sean Gomes (MSI/ANU)
The celebrated quantum ergodicity theorem of Shnirelman, Zelditch, and Colin de Verdière established that ergodic dynamical assumptions on a Hamiltonian sys
28
Mar
2017
Speaker: Dr Xuwen Zhu (Stanford University)
The moduli space of (pointed) Riemann surfaces can be naturally compactified by adding various degenerate surfaces.
21
Mar
2017
Speaker: Melissa Tacy (ANU)
Measuring the $L^p$ mass of an eigenfunction allows us to determine its concentration properties.
Pages
Updated: 21 October 2017/Responsible Officer: Director/Page Contact: School Manager | 2017-10-21 10:38:03 | {"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": 0.7108377814292908, "perplexity": 3254.634170720286}, "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-2017-43/segments/1508187824733.32/warc/CC-MAIN-20171021095939-20171021115939-00653.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=42&t=55116 | ## 2sp2 vs sp2
$sp, sp^{2}, sp^{3}, dsp^{3}, d^{2}sp^{3}$
Isabel Day 1D
Posts: 48
Joined: Fri Aug 09, 2019 12:15 am
### 2sp2 vs sp2
What does it mean when there's a 2 in front of the hybridization? For example, in question 17 of marshmallow many of the sigma bonds have C2sp2 or N2sp hybridizations.
SajaZidan_1K
Posts: 56
Joined: Wed Sep 18, 2019 12:15 am
### Re: 2sp2 vs sp2
The two specifies what row the element is in, so since carbon is in the second row it has the 2 in front of the p. Unless specified, sp^2 can still be the correct hybridization for carbon.
Lauren Stack 1C
Posts: 100
Joined: Sat Aug 17, 2019 12:18 am
### Re: 2sp2 vs sp2
The two is simply signifying the number of the row that the element is found. For example, you could apply this to other rows and put a 1 in front of the s when describing the hybridization of something including a Hydrogen (1s).
Matthew ILG 1L
Posts: 112
Joined: Sat Aug 17, 2019 12:15 am
### Re: 2sp2 vs sp2
You usually add the 2 i front of the sp2 when you are describing the hybridization of a bond. If you are just describing the hybridization of an individual molecule, I don't believe that you need the 2 in front. | 2021-01-24 19:37:39 | {"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": 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": 0.2864372134208679, "perplexity": 3464.5887323082575}, "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-2021-04/segments/1610703550617.50/warc/CC-MAIN-20210124173052-20210124203052-00021.warc.gz"} |
https://www.scienceopen.com/document?vid=c4f1ef8b-c281-47ab-adad-3ac4e26fd645 | 27
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• Record: found
• Abstract: found
• Article: found
Is Open Access
Estimating $$\eta/s$$ of QCD matter at high baryon densities
Preprint
Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
Abstract
We report on the application of a cascade + viscous hydro + cascade model for heavy ion collisions in the RHIC Beam Energy Scan range, $$\sqrt{s_{\rm NN}}=6.3\dots200$$ GeV. By constraining model parameters to reproduce the data we find that the effective(average) value of the shear viscosity over entropy density ratio $$\eta/s$$ decreases from 0.2 to 0.08 when collision energy grows from $$\sqrt{s_{\rm NN}}\approx7$$ to 39 GeV.
Most cited references1
• Record: found
Single-particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production
(1974)
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Author and article information
Journal
1509.07351
10.1088/1742-6596/668/1/012063
High energy & Particle physics, Nuclear physics | 2019-04-18 13:30:44 | {"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": 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": 0.6324566006660461, "perplexity": 4464.04419985556}, "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-2019-18/segments/1555578517639.17/warc/CC-MAIN-20190418121317-20190418143317-00519.warc.gz"} |
https://www.zbmath.org/?q=an%3A1300.35080 | # zbMATH — the first resource for mathematics
Optimal decay rate for strong solutions in critical spaces to the compressible Navier-Stokes equations. (English) Zbl 1300.35080
Summary: In this paper we are concerned with the convergence rates of the global strong solution to motionless state with constant density for the compressible Navier-Stokes equations in the whole space $$\mathbb{R}^n$$ for $$n \geq 3$$. It is proved that the perturbations decay in critical spaces, if the initial perturbations of density and velocity are small in $$B_{2, 1}^{\frac{n}{2}}(\mathbb{R}^n) \cap \dot{B}_{1, \infty}^0(\mathbb{R}^n)$$ and $$B_{2, 1}^{\frac{n}{2} - 1}(\mathbb{R}^n) \cap \dot{B}_{1, \infty}^0(\mathbb{R}^n)$$, respectively.
##### MSC:
35Q30 Navier-Stokes equations 76N15 Gas dynamics, general 35D35 Strong solutions to PDEs 35B20 Perturbations in context of PDEs
##### Keywords:
compressible Navier-Stokes equations; convergence rate
Full Text:
##### References:
[1] Bahouri, H.; Chemin, J. Y.; Danchin, R., Fourier analysis and nonlinear partial differential equation, (2011), Springer Heidelberg [2] Danchin, R., Global existence in critical spaces for compressible Navier-Stokes equations, Invent. Math., 141, 579-614, (2000) · Zbl 0958.35100 [3] Danchin, R., On the uniqueness in critical spaces for compressible Navier-Stokes equations, NoDEA Nonlinear Differential Equations Appl., 12, 111-128, (2005) · Zbl 1125.76061 [4] Haspot, B., Well-posedness in critical spaces for the system of compressible Navier-Stokes in larger spaces, J. Differential Equations, 251, 2262-2295, (2011) · Zbl 1229.35182 [5] Kagei, Y., Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a parallel flow, Arch. Ration. Mech. Anal., 205, 585-650, (2012) · Zbl 1282.76159 [6] Kawashita, M., On global solution of Cauchy problems for compressible Navier-Stokes equation, Nonlinear Anal., 48, 1087-1105, (2002) · Zbl 1097.35116 [7] Li, H.-L.; Zhang, T., Large time behavior of isentropic compressible Navier-Stokes system in $$\mathbb{R}^3$$, Math. Methods Appl. Sci., 34, 670-682, (2011) · Zbl 1214.35047 [8] Matsumura, A.; Nishida, T., The initial value problem for the equation of motion of compressible viscous and heat-conductive fluids, Proc. Japan Acad. Ser. A, 55, 337-342, (1979) · Zbl 0447.76053 [9] Matsumura, A.; Nishida, T., The initial value problems for the equation of motion of compressible viscous and heat-conductive gases, J. Math. Kyoto Univ., 20, 67-104, (1980) · Zbl 0429.76040 [10] Okita, M., On the convergence rates for the compressible Navier-Stokes equations with potential force, Kyushu J. Math., (2014), in press · Zbl 1314.35085 [11] Wang, Y.; Tan, Z., Global existence and optimal decay rate for the strong solution in $$H^2$$ to the compressible Navier-Stokes equation, Appl. Math. Lett., 24, 1778-1784, (2011) · Zbl 1398.76194
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-04-13 18:59:02 | {"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": 0.694828450679779, "perplexity": 1818.1611816846564}, "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-2021-17/segments/1618038074941.13/warc/CC-MAIN-20210413183055-20210413213055-00151.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/134618-determinant-_-print.html | # Determinant >_<
• March 19th 2010, 04:11 PM
GOKILL
Determinant >_<
If $f:\mathbb{R}^2\mapsto\mathbb{R}^2\text{ where } f((x_1,x_2))=(x_1+2x_2,2x_1+x_2)\forall x_1,x_2\in\mathbb{R},\text{ then find } f^{-1}$
• March 19th 2010, 05:12 PM
TKHunny
The inverse of a 2x2 matrix can't be hard, can it? What am I missing?
$f^{-1}(u,v)\;=\;\frac{1}{3}(-u+2v,2u-v)$ | 2015-05-28 22:21:09 | {"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": 2, "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": 0.7212318181991577, "perplexity": 4725.089767197865}, "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-2015-22/segments/1432207929656.4/warc/CC-MAIN-20150521113209-00166-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://islam.meta.stackexchange.com/questions/3203/how-can-i-change-colors-of-the-word?r=SearchResults | # How can I change colors of the word?
Let’s say, I want to write a question and then I write a word with blue color or red color or any color because I saw this site:
What can I do when getting "We are no longer accepting questions/answers from this account"?
And I want to know if it is possible to write in any color any word on IPhone 6? Because, I’m planning to improve in a proper manner my posts in better than ever. Can you please tell me how to write for example in: blue, red, green etc...? I’m trying to do as others do, but it does not work to me. Can you tell me how each code means? And what does it do? And, seriously, I don’t understand what does it do some codes.
• You can check Stack Exchange's limited set of supported HTML tags. I do not see color or CSS being supported. The colors you are referring to are most likely dictated by the SE site's style sheet. A word of advice: focus on content and let SE handle the presentation. – III-AK-III Dec 10 '17 at 14:32
• @III-AK-III Maybe You haven’t checked the site I posted? – Alex A Dec 10 '17 at 14:42
• The site you posted is the site that I provided to you in your previous question. – III-AK-III Dec 10 '17 at 14:50
The blue font in the linked post are caused by links. They're a different color on meta.
There's no (desirable) way to change the font color of certain words. A proposal was declined on meta.SE: Having font color option in Stack Overflow question editor
There's workarounds like including images (where you can color things however you like), or it would be possible to write a local script, to add color locally.
(Side note: Sites with MathJax (not Islam.SE) can use color in math mode.)
There's a help page on formatting.
# It might
## be worthwhile
### having a
play around
with the
1. current
• capabilities
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# 𝕄𝕪 𝕙𝕠𝕧𝕖𝕣𝕔𝕣𝕒𝕗𝕥 𝕚𝕤 𝕗𝕦𝕝𝕝 𝕠𝕗 𝕖𝕖𝕝𝕤
These can be generated using online apps such as: https://lingojam.com/FancyTextGenerator or http://qaz.wtf/u/convert.cgi This is not such a great idea though, since it's not possible to search. | 2020-08-11 04:21:40 | {"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": 0.33717092871665955, "perplexity": 1581.961250273182}, "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/1596439738727.76/warc/CC-MAIN-20200811025355-20200811055355-00537.warc.gz"} |
https://projecteuclid.org/euclid.ecp/1465316730 | ## Electronic Communications in Probability
### A strong law of large numbers for branching processes: almost sure spine events
#### Abstract
We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.
#### Article information
Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 28, 6 pp.
Dates
Accepted: 8 May 2014
First available in Project Euclid: 7 June 2016
https://projecteuclid.org/euclid.ecp/1465316730
Digital Object Identifier
doi:10.1214/ECP.v19-2641
Mathematical Reviews number (MathSciNet)
MR3208326
Zentralblatt MATH identifier
1312.60022
Rights
#### Citation
Harris, Simon; Roberts, Matthew. A strong law of large numbers for branching processes: almost sure spine events. Electron. Commun. Probab. 19 (2014), paper no. 28, 6 pp. doi:10.1214/ECP.v19-2641. https://projecteuclid.org/euclid.ecp/1465316730
#### References
• Hardy, Robert; Harris, Simon C. A spine approach to branching diffusions with applications to $\scr L^ p$-convergence of martingales. SÄ‚Å minaire de ProbabilitÄ‚Å s XLII, 281–330, Lecture Notes in Math., 1979, Springer, Berlin, 2009.
• S.C. Harris, M. Hesse, and A.E. Kyprianou. Branching brownian motion in a strip: survival near criticality. 2012. Preprint: arXiv:1212.1444v1.
• M.I. Roberts. Spine changes of measure and branching diffusions. PhD thesis, University of Bath, 2010. Available online: http://people.bath.ac.uk/mir20/thesis.pdf. | 2019-11-20 22:00:48 | {"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": 0.4355352520942688, "perplexity": 4403.982035017754}, "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-2019-47/segments/1573496670635.48/warc/CC-MAIN-20191120213017-20191121001017-00377.warc.gz"} |
https://eehh-stanford.github.io/yada/articles/siler.html | ## Definitions
The Siler mortality hazard is
$\lambda(x) = a_1 \exp(-a_2 \, x) + a_3 + a_4 \exp(a_5 \, x) \mbox{,}$
where x is age-at-death and
$\mathbf{a} = \begin{bmatrix}a_1&a_2&a_3&a_4&a_5\end{bmatrix}^T$
is the parameter vector. All elements of $$\mathbf{a}$$ are greater than or equal to zero. This yields a bathtub-shaped mortality hazard with the first term dominating at younger ages, the middle term creating constant (background) mortality, and the third term at higher ages. The cumulative hazard contingent on having survived to age $$x_0$$ is found by integrating the hazard from $$x_0$$ to $$x$$,
$\Lambda(x_0,x) = -\frac{a_1}{a_2} [ \exp(-a_2 \, x) - \exp(-a_2 \, x_0) ] + a_3 [x-x_0] + \frac{a_4}{a_5} [\exp(a_5 \, x) - \exp(a_5 \, x_0)] \mbox{.}$
Given this definition of the cumulative hazard, $$\Lambda(x_0,x) = \Lambda(0,x) - \Lambda(0,x_0) = \Lambda(x) - \Lambda(x_0)$$, where we adopt the convention that $$\Lambda(x) = \Lambda(0,x)$$. The survival contingent on having survived to age $$x_0$$ is
$S(x_0,x) = \exp(-\Lambda(x_0,x)) = \frac{S(0,x)}{S(0,x_0)} = \frac{S(x)}{S(x_0)} \mbox{,}$
where as with the cumulative hazard we adopt the convention $$S(0,x) = S(x)$$. The cumulative density function is
$F(x_0,x) = 1 - S(x_0,x)$
and the probability density function is.
$f(x_0,x) = \frac{d}{dx} F(x_0,x) = \lambda(x) \, S(x_0,x) \mbox{.}$
yada implements these functions as hsiler (hazard), chsiler (cumulative hazard), ssiler (survival), psiler (cumulative density), and dsiler (density). In addition, qsiler (quantiles) inverts the cumulative density, $$x = F^{-1}(q)$$, rsiler makes random draws from the probability density, and fitSilerMaxLik does a maximum likelihood fit given age-at-death data.
## Plotting
Gage and Dyke (1986) [Parameterizing Abridged Mortality Tables] describe sensible parameterizations of the Siler hazard for human mortality. The parameterization for Level 15 in Table 2 in Gage and Dyke (1986) is
a0 <- c(0.175, 1.40, 0.368 * 0.01, 0.075 * 0.001, 0.917 * 0.1)
Create a vector of ages $$x$$ from age 0 to 100 and calculate the hazard,
library(yada)
x <- seq(0, 100, by = .1)
hazSiler <- hsiler(x, a0)
th <- 3 # Line width for plots
plot(x, hazSiler, type = "l", xlab = "Age [years]", ylab = "Hazard", lwd = th)
The cumulative hazard is
cumHazSiler <- chsiler(x, a0)
plot(x, cumHazSiler, type = "l", xlab = "Age [years]", ylab = "Cumulative Hazard", lwd = th)
The survival is
survSiler <- ssiler(x, a0)
plot(x, survSiler, type = "l", xlab = "Age [years]", ylab = "Survival", lwd = th)
The cumulative probability density function (CDF) is
cdfSiler <- psiler(x, a0)
plot(x, cdfSiler, type = "l", xlab = "Age [years]", ylab = "Cumulative Density", lwd = th)
The probability density function (PDF) is
pdfSiler <- dsiler(x, a0)
plot(x, pdfSiler, type = "l", xlab = "Age [years]", ylab = "Density", lwd = th)
## Using $$x_0$$
Sometimes demographers work with data for which survival to some age $$x_0$$ is given. For example, one might analyze a paleodemographic sample of adult skeletons that has excluded children. yada supports contingent survival to age $$x_0$$ in the Siler mortality model. The survival and PDF contingent on survival to age $$x_0=15$$ are
x0 <- 15
x2 <- seq(x0, 100, by = .1)
survSilerCont <- ssiler(x2, a0, x0)
plot(x2, survSilerCont, type = "l", xlab = "Age [years]", ylab = "Survival", lwd = th)
pdfSilerCont <- dsiler(x2, a0, x0)
plot(x2, pdfSilerCont, type = "l", xlab = "Age [years]", ylab = "Density", lwd = th)
## Maximum likelihood estimation
yada provides code to solve for the maximum likelihood Siler parameter vector given age-at-death data. Create simulated age-at-death data by calling rsiler,
set.seed(896354) # from random.org
N <- 10000
xsamp <- rsiler(N, a0)
“Jitter” $$a_0$$ a little to provide a starting point for the maximum likelihood estimation that differs from $$a_0$$, then do the fit:
a1 <- a0 * runif(5, min = .9, max = 1.1)
silerFit <- fitSilerMaxLik(xsamp, a1, calcHessian = TRUE)
print(silerFit$a) #> [1] 0.1778844318 1.4173432545 0.0034778668 0.0000846183 0.0903252731 Since all elements of the Siler parameter vector are positive, the fit is done on a transformed variable, $$\mathbf{\bar{a}} = \log{\mathbf{a}} - \log{\mathbf{a}_0}$$, so that an unconstrained optimization can be done by calling optim’. This is the parameter that is optimized in the returned fit, print(silerFit$fit)
#> $par #> [1] -0.07768895 -0.07072697 -0.14836412 0.08544687 0.03396335 #> #>$value
#> [1] 42021.61
#>
#> $counts #> function gradient #> 232 NA #> #>$convergence
#> [1] 0
#>
#> $message #> NULL Naturally, the variable a in silerFit (printed above) and the hessian (optional; see below) account for this transformation. Now plot the histogram for the sampled data, target curve (solid black line; from $$a_0$$); initial estimate (dashed red line; from $$a_1$$), and maximum likelihood fit (solid red line): hist(xsamp, 100, freq = F, main = NA, xlab = "Age [years]", ylab = "Density") lines(x, dsiler(x, a0), lty = 1, col = "1", lwd = th) lines(x, dsiler(x, a1), lty = 2, col = "red", lwd = th) lines(x, dsiler(x, silerFit$a), col = "red", lwd = th)
legend("topright", c("Target", "Initial", "Max Lik"), col = c("black", "red", "red"), lty = c(1, 2, 1))
A common (frequentist) question is whether the estimated parameter values differ from $$0$$. This can be assessed by calculating the standard errors using the Hessian, which is the negative of the observed Fisher information matrix (for pertinent assumptions see https://en.wikipedia.org/wiki/Fisher_information). The covariance matrix for the standard error is
covMat <- solve(-silerFit$hessian) # invert the matrix The standard errors are the roots of the diagonals of the covariance matrix, standErr <- sqrt(diag(covMat)) The so-called z-score is the ratio of the estimate to its standard error, z <- silerFit$a / standErr
The one-sided p-values are (one-sided because parameters are positive)
pval <- pnorm(-abs(z))
print(pval)
#> [1] 2.823400e-112 5.800221e-148 2.228342e-141 5.039870e-26 0.000000e+00` | 2022-05-22 04:46:39 | {"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": 2, "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": 0.6895256638526917, "perplexity": 12597.389500760191}, "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/1652662543797.61/warc/CC-MAIN-20220522032543-20220522062543-00548.warc.gz"} |
http://dragon.seetatech.com/api/python/contents/vm/torch | # Torch¶
## Abstraction¶
PyTorch provides straight-forward operations on research prototyping.
We are aware that Dragon is a graph-based framework with strictly naming for tensors, operators, and workspaces, while Torch is not. A simple way to bridge their differences is JIT, which traces the anonymous expressions, indicates a series of executions to the backend. If so, AutoGrad will just be a trick(Remember the Chain Rule).
Rewriting the GC(Garbage Collection) is crucial in this role, as the costly deconstruction on memories and operators must be avoided. We could either persist a Operator(i.e. Module), or reuse the several memories by turns(i.e. MemoryPool), if naming them formally.
We are still working hard to cover the original PyTorch operators, however, a bunch of extended operators in many other frameworks can be used. Our PyTorch will be unique and more powerful than the official one. | 2019-10-16 22:10:45 | {"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": 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": 0.3561335504055023, "perplexity": 3859.394223033618}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2019-43/segments/1570986670928.29/warc/CC-MAIN-20191016213112-20191017000612-00235.warc.gz"} |
https://www.physicsforums.com/threads/conducting-cylinder-vs-cylinder-of-charge-guasss-law.924946/ | # Conducting Cylinder vs Cylinder of Charge - Guass's Law
1. Sep 9, 2017
### Marcin H
1. The problem statement, all variables and given/known data
I just have a general question about Guass's Law and the cylinders above. I don't really understand what the difference is between the 2 cylinders? They are both charged, but one of them does not have an electric field inside the cylinder because it a conducting cylinder? I don't understand the difference between the 2 above.
2. Relevant equations
Guass's Law
3. The attempt at a solution
This is just something I wanted clarification on. Hopefully I am posting in the correct place.
2. Sep 9, 2017
### Orodruin
Staff Emeritus
In the case of a conductor, there is no charge density inside the cylinder (it would result in an electric field that would drive the charges away - all the charge is on the cylinder surface) and in the other (cylinder of fixed volume charge density) there is a charge density inside the cylinder. Outside the cylinder this results in the same electric field but inside it it does not (as the enclosed charge will be different in the different cases).
3. Sep 9, 2017
### Marcin H
Ok. How will we know which one to deal with when doing problems? Will it have to explicitly say if it's a conductor or not? Or if we are given a charge density rho then we need to use the "cylinder of charge" formulas to solve the rest?
Also, I was a bit confused by the charge densities rho and lamba and when to use which. Do we use lambda for the charge density if and only if we are given a infinetely thin wire or line of charge? And rho when the cylinder or wire has a finite radius? This confuses me because the 2 pictures above show them using lambda which is Q/L, but in a hw problem like this:
"An infinitely long, cylindrical wire of radius R = 1 cm is centered along the ^z axis and carries a uniform volumetric charge density ρ_0." <-- Edit* This is supposed to be the symbol "rho"...
There is more to the problem, but basically it says to use guass's law to find the charge density of the wire. But the solutions uses ρ = Q/V instead of λ=Q/L like like we have in the equations above. Why is this? I hope I am making sense in where I am confused...
Here is the whole problem btw:
I got the correct answer, but I don't understand when we are supposed to use lambda vs rho for the charge density...
4. Sep 9, 2017
### Orodruin
Staff Emeritus
Obviously it depends on the problem statement about the setup.
They are different physical quantities. The line density $\lambda$ is the charge per length of the cylinder and $\rho$ is the volume density, which is the charge per volume.
5. Sep 11, 2017
ok thanks | 2017-09-21 05:46:40 | {"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": 0.8425865769386292, "perplexity": 470.876074246673}, "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-2017-39/segments/1505818687642.30/warc/CC-MAIN-20170921044627-20170921064627-00552.warc.gz"} |
https://zbmath.org/?q=an:0926.46054&format=complete | zbMATH — the first resource for mathematics
Local properties of accessible injective operator ideals. (English) Zbl 0926.46054
In contrast to Pisier’s example of a non-accessible maximal Banach ideal, the author exhibits a large class of maximal Banach ideals which are accessible. The construction is based on a characterization of total accessibility of injective hulls of maximal Banach ideals (if $$(\mathcal A,\mathbf A)$$ is a maximal Banach ideal, then $$(\mathcal A^{inj},\mathbf A^{inj})$$ is totally accessible if and only if $$(\mathcal A\circ \mathcal A^*,\mathbf A\circ \mathbf A^\ast)\subseteq (\mathcal P_1,\mathbf P_1)$$, the ideal of absolutely summing operators) and an operator version of Grothendieck’s inequality. As a consequence, it is obtained, for instance, that if $$(\mathcal A,\mathbf A)$$ is a maximal Banach ideal such that $$(\mathcal D_2,\mathbf D_2)\subseteq (\mathcal A,\mathbf A)\subseteq (\mathcal L_1,\mathbf L_1)$$ and both $$(\mathcal A,\mathbf A)$$ and $$(\mathcal A^*, \mathbf A^\ast)$$ are metrically $$\varepsilon$$-tensorstable, then $$(\mathcal A^{inj}, \mathbf A^{inj})$$ is totally accessible. Several other criteria for right- and total accessibility are established, and applications to normed products of operator ideals are also given.
MSC:
46M05 Tensor products in functional analysis 47L20 Operator ideals 47A80 Tensor products of linear operators
Full Text:
References:
[1] B. Carl, A. Defant, and M. S. Ramanujan: On tensor stable operator ideals. Michigan Math. J. 36 (1989), 63-75. · Zbl 0669.47025 [2] A. Defant: Produkte von Tensornormen. Habilitationsschrift. Oldenburg 1986. [3] A. Defant and K. Floret: Tensor Norms and Operator Ideals. North-Holland Amsterdam, London, New York, Tokio, 1993. · Zbl 0774.46018 [4] J. E. Gilbert and T. Leih: Factorization, tensor products and bilinear forms in Banach space theory. Notes in Banach spaces, Univ. of Texas Press, Austin, 1980, pp. 182-305. · Zbl 0471.46053 [5] Y. Gordon, D. R. Lewis, and J. R Retherford: Banach ideals of operators with applications. J. Funct. Analysis 14 (1973), 85-129. · Zbl 0272.47024 [6] A. Grothendieck: Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo 8 (1956), 1-79. · Zbl 0074.32303 [7] H. Jarchow: Locally convex spaces. Teubner, 1981. · Zbl 0466.46001 [8] H. Jarchow and R. Ott: On trace ideals. Math. Nachr. 108 (1982), 23-37. · Zbl 0523.47030 [9] H. P. Lotz: Grothendieck ideals of operators in Banach spaces. Lecture notes, Univ. Illinois, Urbana, 1973. [10] J. Lindenstrauss and H. P. Rosenthal: The Lp-spaces. Israel J. Math. 7 (1969), 325-349. · Zbl 0205.12602 [11] F. Oertel: Konjugierte Operatorenideale und das $${\mathcal A}$$-lokale Reflexivitätsprinzip. Dissertation. Kaiserslautern, 1990. [12] F. Oertel: Operator ideals and the principle of local reflexivity. Acta Universitatis Carolinae-Mathematica et Physica 33 (1992), no. 2, 115-120. · Zbl 0803.47038 [13] A. Pietsch: Operator Ideals. North-Holland Amsterdam, London, New York, Tokio, 1980. · Zbl 0455.47032 [14] A. Pietsch: Eigenvalues and s-numbers. Cambridge Studies in Advanced Mathematics 13 (1987). · Zbl 0615.47019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2022-01-23 08:49:58 | {"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": 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": 0.6520416140556335, "perplexity": 2425.820877753511}, "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-2022-05/segments/1642320304217.55/warc/CC-MAIN-20220123081226-20220123111226-00144.warc.gz"} |
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[Docutils-users] image from URL? From: Alan G Isaac - 2014-09-15 21:30:46 The URL http://research.stlouisfed.org/fred2/graph/fredgraph.png?g=KlW serves an image in PNG format, but I cannot simple provide it to the image directive. Is there a good way to proceed within docutils? Thanks, Alan Isaac
[Docutils-users] Status of Python docstring support? From: Andreas Maier - 2014-09-13 08:34:57 Hi, The readme file of docutils 0.12 states that support for inline documentation of Python modules and packages as an additional source is planned. I was wondering where that planning stands? Is the design going to be based on introspection of an imported module, or on parsing the source? Thanks, Andy
[Docutils-users] implementing a mathmacro substitution directive? From: Pierre - 2014-09-09 16:55:14 Hello, I am struggling to write a documentation with a lot of math. It would be very convenient to implement a mathmacro substitution directive which should work like this: - Definition:: .. |bnabla| mathmacro:: \boldsymbol{\nabla} .. |vv| mathmacro:: \textbf{v} - These math macros could be included directly in text as in:: |bnabla| is the nabla operator, which should produce an inline equation like this ":math:\boldsymbol{\nabla} is the nabla operator". - These macros could also be included in inline equations like this:: This is an inline equation :math:|vv| = |bnabla|f, which should give :math:\textbf{v} = \boldsymbol{\nabla}f. - They could also be included in block equation:: .. math:: |vv| = |bnabla|f which should gives .. math:: \textbf{v} = \boldsymbol{\nabla}f. Would it be possible to do that? I think it would be a lot nicer to use such mathmacro directive rather that latex macros since (i) it would leads to nicer code and (ii) the MathJax sphinx extension does not really supports macro definition. I'm trying to define a new directive by copying on the replace directive but I don't know how to redefine the substitution rules (which have to vary depending on the context, in text, in inline math and in block math). I don't know neither if rST can work this way, with a directive preprocessing text that will be used after by math directives.
Re: [Docutils-users] Slide Presentations In RestructuredText? From: Stefan Merten - 2014-08-18 20:15:37 Attachments: Message as HTML Hi Tim! 2 days ago Tim Daneliuk wrote: > I use RST for a whole bunch of things but I've not done any presentation/slide > stuff since the old S5 days. I'm using rst2outline to generate something which can be imported into Powerpoint then (because I'm forced to use Powerpoint :-( ). It's in the sandbox. Grüße Stefan
Re: [Docutils-users] Slide Presentations In RestructuredText? From: Valentin Haenel - 2014-08-16 09:42:01 Hi, there are a couple of things I have experimented with. * Tim Daneliuk [2014-08-16]: > I use RST for a whole bunch of things but I've not done any presentation/slide > stuff since the old S5 days. Is S5 still the recommended way to do this or > are there better choices these days? There is rst2beamer, which is docutils based but somewhat unmaintained: https://github.com/rst2beamer I do have my own fork on github and use a custom template, but wouldn't recommend it actually. There is also the possibility tp use rst2pdf, which is reportlab based, I believe: http://ralsina.me/stories/BBS52.html And lastly -- this is my favorite option right now -- you can use pandoc to make beamer slides from RST: http://johnmacfarlane.net/pandoc/demo/example9/producing-slide-shows-with-pandoc.html That seems the most powerful option. best and hope it helps, V-
Re: [Docutils-users] Slide Presentations In RestructuredText? From: Paolo Cavallini - 2014-08-16 06:23:02 Attachments: Message as HTML I use https://github.com/marianoguerra/rst2html5 . Pretty good. On 16 agosto 2014 01:29:37 EEST, Kevin Horn wrote: >I haven't used S5 in a long time, but AFAIk it should still work. > >I use landslide, though it's a little quirky in places: >https://github.com/adamzap/landslide > > >On Fri, Aug 15, 2014 at 5:10 PM, Tim Daneliuk >wrote: > >> I use RST for a whole bunch of things but I've not done any >> presentation/slide >> stuff since the old S5 days. Is S5 still the recommended way to do >this or >> are there better choices these days? >> >> TIA. >> -- >> >> >---------------------------------------------------------------------------- >> Tim Daneliuk tundra@... >> PGP Key: http://www.tundraware.com/PGP/ >> >> >> >> >------------------------------------------------------------------------------ >> _______________________________________________ >> Docutils-users mailing list >> Docutils-users@... >> https://lists.sourceforge.net/lists/listinfo/docutils-users >> >> Please use "Reply All" to reply to the list. >> > > > >-- >-- >Kevin Horn > > >------------------------------------------------------------------------ > >------------------------------------------------------------------------------ > > >------------------------------------------------------------------------ > >_______________________________________________ >Docutils-users mailing list >Docutils-users@... >https://lists.sourceforge.net/lists/listinfo/docutils-users > >Please use "Reply All" to reply to the list. -- http://faunalia.eu/ Sent from mobile, sorry for being short
Re: [Docutils-users] Slide Presentations In RestructuredText? From: Kevin Horn - 2014-08-15 22:29:44 Attachments: Message as HTML I haven't used S5 in a long time, but AFAIk it should still work. I use landslide, though it's a little quirky in places: https://github.com/adamzap/landslide On Fri, Aug 15, 2014 at 5:10 PM, Tim Daneliuk wrote: > I use RST for a whole bunch of things but I've not done any > presentation/slide > stuff since the old S5 days. Is S5 still the recommended way to do this or > are there better choices these days? > > TIA. > -- > > ---------------------------------------------------------------------------- > Tim Daneliuk tundra@... > PGP Key: http://www.tundraware.com/PGP/ > > > > ------------------------------------------------------------------------------ > _______________________________________________ > Docutils-users mailing list > Docutils-users@... > https://lists.sourceforge.net/lists/listinfo/docutils-users > > Please use "Reply All" to reply to the list. > -- -- Kevin Horn
[Docutils-users] Slide Presentations In RestructuredText? From: Tim Daneliuk - 2014-08-15 22:24:03 I use RST for a whole bunch of things but I've not done any presentation/slide stuff since the old S5 days. Is S5 still the recommended way to do this or are there better choices these days? TIA. -- ---------------------------------------------------------------------------- Tim Daneliuk tundra@... PGP Key: http://www.tundraware.com/PGP/
[Docutils-users] Any C libraries to generate html from rst? From: Grzegorz Adam Hankiewicz - 2014-08-15 21:00:38 I was wondering if there are any known C or C++ libraries to parse rst files and generate HTML like the python version.
[Docutils-users] Weblog project using reST From: Grzegorz Adam Hankiewicz - 2014-08-15 20:59:44 FAQ http://docutils.sourceforge.net/FAQ.html#what-s-the-standard-abbreviation-for-restructuredtext says "Please let us know of any other reStructuredText Blogs". You can add ipsum genera (https://github.com/dom96/ipsumgenera) to that list.
[Docutils-users] Odt writer: customize default table properties From: Jorge Scandaliaris - 2014-08-13 08:14:40 Hi, Copying styles.odt to a new location, modifying it and using the --stylesheet option works for some things, like changing the table border widths, for example. For specifying text flow options within the table (specifically unticking the "allow row to break across pages and columns"), however, it doesn't seem to work. What I did: 1- Open styles.odt 2- Left click anywhere on the first table, then right click -> Table -> Text flow -> untick "allow row to break across pages and columns" 3- Save file 4- Re-run rdt2odt.py I have attempted to create the rstsyle-table-0 style, but I am not sure I did it the right way, so I deleted. Could this be the cause? What would be the exact procedure to create this style? Thanks, Jorge
Re: [Docutils-users] Bug report From: Guenter Milde - 2014-08-07 18:14:21 On 2014-08-07, Ayan Shafqat wrote: > [-- Type: text/plain, Encoding: quoted-printable --] > I am trying to convert a RST file into TWIKI, using Cygwin: > CYGWIN_NT-6.1-WOW64 1.7.17(0.262/5/3) 2012-10-19 14:39 i686 >> Cygwin > This is the error I get when I try to convert RST to Twiki: >> ***$rst2twiki.py --traceback FILE.rst* >> Traceback (most recent call last): >> File "/usr/bin/rst2twiki.py", line 5, in >> pkg_resources.run_script('rst2twiki==0.1', 'rst2twiki.py') >> File "build/bdist.linux-i686/egg/pkg_resources.py", line 489, in >> run_script >> yield ep >> File "build/bdist.linux-i686/egg/pkg_resources.py", line 1214, in >> run_script >> File >> "/usr/lib/python2.7/site-packages/rst2twiki-0.1-py2.7.egg/EGG-INFO/scripts/rst2twiki.py", >> line 258, in >> File "/usr/lib/python2.7/site-packages/docutils/core.py", line 352, in >> publish_cmdline >> config_section=config_section, enable_exit_status=enable_exit_status) >> File "/usr/lib/python2.7/site-packages/docutils/core.py", line 219, in >> publish ... >> File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 1882, in >> dispatch_visit >> return method(node) >> File >> "/usr/lib/python2.7/site-packages/rst2twiki-0.1-py2.7.egg/EGG-INFO/scripts/rst2twiki.py", >> line 239, in visit_entry >> AttributeError: WikiVisitor instance has no attribute 'thead' This seems to be a missing feature in the "twiki" writer: Please note that TWiki only implements a very small subset of DocUtils's markup features. Thus, the script is by necessity a bit of a hack. It is of course possible to simply use HTML to "fill in the gaps", but this would altogether defeat the purpose of TWiki markup. Instead, errors are given whenever an unimplemented feature of ReStructured Text is used in the document. -- https://github.com/djspiewak/rst2twiki Are tables supported in TWiki? Mind, that rst2twiki is not part of Docutils but an external add-on. > Here is the Docutils version: >> *$ rst2twiki.py --version* >> rst2twiki.py (Docutils 0.12 [repository], Python 2.7.3, on cygwin) This output is somewhat misleading: rst2twiki builds on Docutils and it seems that the wrapper script rst2twiki.py is modelled after the wrapper scripts provided with Docutils. Günter
[Docutils-users] Bug report From: Ayan Shafqat - 2014-08-07 14:53:08 Attachments: Message as HTML I am trying to convert a RST file into TWIKI, using Cygwin: CYGWIN_NT-6.1-WOW64 1.7.17(0.262/5/3) 2012-10-19 14:39 i686 > Cygwin This is the error I get when I try to convert RST to Twiki: > ***$rst2twiki.py --traceback FILE.rst* > Traceback (most recent call last): > File "/usr/bin/rst2twiki.py", line 5, in > pkg_resources.run_script('rst2twiki==0.1', 'rst2twiki.py') > File "build/bdist.linux-i686/egg/pkg_resources.py", line 489, in > run_script > yield ep > File "build/bdist.linux-i686/egg/pkg_resources.py", line 1214, in > run_script > File > "/usr/lib/python2.7/site-packages/rst2twiki-0.1-py2.7.egg/EGG-INFO/scripts/rst2twiki.py", > line 258, in > File "/usr/lib/python2.7/site-packages/docutils/core.py", line 352, in > publish_cmdline > config_section=config_section, enable_exit_status=enable_exit_status) > File "/usr/lib/python2.7/site-packages/docutils/core.py", line 219, in > publish > output = self.writer.write(self.document, self.destination) > File "/usr/lib/python2.7/site-packages/docutils/writers/__init__.py", > line 80, in write > self.translate() > File > "/usr/lib/python2.7/site-packages/rst2twiki-0.1-py2.7.egg/EGG-INFO/scripts/rst2twiki.py", > line 19, in translate > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 174, in > walkabout > if child.walkabout(visitor): > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 174, in > walkabout > if child.walkabout(visitor): > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 174, in > walkabout > if child.walkabout(visitor): > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 174, in > walkabout > if child.walkabout(visitor): > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 174, in > walkabout > if child.walkabout(visitor): > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 174, in > walkabout > if child.walkabout(visitor): > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 166, in > walkabout > visitor.dispatch_visit(self) > File "/usr/lib/python2.7/site-packages/docutils/nodes.py", line 1882, in > dispatch_visit > return method(node) > File > "/usr/lib/python2.7/site-packages/rst2twiki-0.1-py2.7.egg/EGG-INFO/scripts/rst2twiki.py", > line 239, in visit_entry > AttributeError: WikiVisitor instance has no attribute 'thead' Here is the Docutils version: > *$ rst2twiki.py --version* > rst2twiki.py (Docutils 0.12 [repository], Python 2.7.3, on cygwin)
[Docutils-users] QuickLook rst plugin From: Grzegorz Adam Hankiewicz - 2014-07-31 22:43:15 Hi. I have implemented an OSX QuickLook plugin for rst files, you can get it fromhttps://github.com/gradha/quicklook-rest-with-nimrod. This implementation doesn't use python though, it's a clean reimplementation in the Nimrod programming language, so it is still quite lacking in terms of features, but is starting to be usable. In fact the Nimrod programming language uses the rst format for the docstrings (example https://github.com/Araq/Nimrod/blob/devel/lib/pure/collections/sets.nim) and the plain text documentation and website also use rst. I'd like to know if it is ok to spam this mailing list with new releases of this quicklook plugin or there is a more appropriate spam channel.
Re: [Docutils-users] I am not subscribed .. From: David Goodger - 2014-07-23 13:39:49 On Wed, Jul 23, 2014 at 3:09 AM, engelbert gruber wrote: > first sorry: IMHO develop should not bounce, No mail bounced. All Docutils mailing lists are set to moderate mail from addresses not subscribed ("message awaits approval"). This is to prevent spam from getting through. Without this setting, we'd see several unwanted messages every day. -- David Goodger ;
Re: [Docutils-users] I am not subscribed .. From: engelbert gruber - 2014-07-23 09:46:20 Attachments: Message as HTML and another apologize i do not know why but i did not get the message that your message awaits approval it should now work, and as soon as you are approved you can post to develop too without being subscribed. but for users docutils-users is better . all the best On 23 July 2014 09:16, john francis lee wrote: > > Hi, > > I was having trouble setting the page size used by rst2odt.py when it > created an odt from and rst file, and so sent a message to developers > ... because that was the email link at the top of the article I'd read > in an attempt to get help ... > > > http://docutils.sourceforge.net/docs/user/odt.html#defining-and-using-a-custom-stylesheet > > ... and the email bounced because I wasn't subscribed. Meanwhile ... > scrolling down, or using another link, came in contact with another > section of the very same posting ... > > http://docutils.sourceforge.net/docs/user/odt.html#page-size > > ... which has set me right ! So, thanks. > > I tried papersize and that business, but it was ... > > $rst2odt_prepstyles.py styles.odt > > ... that finally straightened me out. > > I append my original email for ... the hell of it ... > > Thanks again. It this doesn't bounce too. > > ==================================================================== > > Hi, > > I'm trying to generate .odt files with paper size a4 from .rst files. > > I'm trying to follow the directions from > > > > http://docutils.sourceforge.net/docs/user/odt.html#defining-and-using-a-custom-stylesheet > > I use debian 7.6 64bit linux. I used > > apt-get install python-docutils > > to install the docutils programs. > > I copied > > /usr/share/docutils/writers/odf_odt/styles.odt > > to my home directory. > > I opened it there and changed > > Format| Page | Paper format | Format > > from Letter to A4 > > I saved > > /usr/share/docutils/writers/odf_odt/styles.odt > > as > > /usr/share/docutils/writers/odf_odt/styles.odt-dist > > and then saved my copy as > > /usr/share/docutils/writers/odf_odt/styles.odt > > No one ever uses letter sized paper in Thailand, and I can change it in > any individual letters I write on letter size paper. I think I have > written one in the last 12 years . > > I changed ownership and permissions to match the distribution > > ls -l /usr/share/docutils/writers/odf_odt/ > total 40 > -rw-r--r-- 1 root root 16403 Jul 23 12:19 styles.odt > -rw-r--r-- 1 root root 16500 Jun 27 2011 styles.odt-dist > > But when I run > > rst2odt ooncd.en.rst ooncd.en.odt > > ooncd.en.odt is still formatted for letter-size paper. > > Can you see what I've done wrong? > > Thanks. > > -- > John Francis Lee > Thanon Sanam Gila, Ban Fa Sai > 79/151 Moo 22 T. Ropwieng > Mueang Chiangrai 57000 > Thailand > > > > > ------------------------------------------------------------------------------ > Want fast and easy access to all the code in your enterprise? Index and > search up to 200,000 lines of code with a free copy of Black Duck > Code Sight - the same software that powers the world's largest code > search on Ohloh, the Black Duck Open Hub! Try it now. > http://p.sf.net/sfu/bds > _______________________________________________ > Docutils-users mailing list > Docutils-users@... > https://lists.sourceforge.net/lists/listinfo/docutils-users > > Please use "Reply All" to reply to the list. > Re: [Docutils-users] I am not subscribed .. From: engelbert gruber - 2014-07-23 08:09:25 Attachments: Message as HTML first sorry: IMHO develop should not bounce, second: sorry again , i will try to help with odt but it is not my main work but how ... trying :-) * which docutils version is it ? * did anything the generated document change ? cheers On 23 July 2014 09:16, john francis lee wrote: > > Hi, > > I was having trouble setting the page size used by rst2odt.py when it > created an odt from and rst file, and so sent a message to developers > ... because that was the email link at the top of the article I'd read > in an attempt to get help ... > > > http://docutils.sourceforge.net/docs/user/odt.html#defining-and-using-a-custom-stylesheet > > ... and the email bounced because I wasn't subscribed. Meanwhile ... > scrolling down, or using another link, came in contact with another > section of the very same posting ... > > http://docutils.sourceforge.net/docs/user/odt.html#page-size > > ... which has set me right ! So, thanks. > > I tried papersize and that business, but it was ... > >$ rst2odt_prepstyles.py styles.odt > > ... that finally straightened me out. > > I append my original email for ... the hell of it ... > > Thanks again. It this doesn't bounce too. > > ==================================================================== > > Hi, > > I'm trying to generate .odt files with paper size a4 from .rst files. > > I'm trying to follow the directions from > > > > http://docutils.sourceforge.net/docs/user/odt.html#defining-and-using-a-custom-stylesheet > > I use debian 7.6 64bit linux. I used > > apt-get install python-docutils > > to install the docutils programs. > > I copied > > /usr/share/docutils/writers/odf_odt/styles.odt > > to my home directory. > > I opened it there and changed > > Format| Page | Paper format | Format > > from Letter to A4 > > I saved > > /usr/share/docutils/writers/odf_odt/styles.odt > > as > > /usr/share/docutils/writers/odf_odt/styles.odt-dist > > and then saved my copy as > > /usr/share/docutils/writers/odf_odt/styles.odt > > No one ever uses letter sized paper in Thailand, and I can change it in > any individual letters I write on letter size paper. I think I have > written one in the last 12 years . > > I changed ownership and permissions to match the distribution > > ls -l /usr/share/docutils/writers/odf_odt/ > total 40 > -rw-r--r-- 1 root root 16403 Jul 23 12:19 styles.odt > -rw-r--r-- 1 root root 16500 Jun 27 2011 styles.odt-dist > > But when I run > > rst2odt ooncd.en.rst ooncd.en.odt > > ooncd.en.odt is still formatted for letter-size paper. > > Can you see what I've done wrong? > > Thanks. > > -- > John Francis Lee > Thanon Sanam Gila, Ban Fa Sai > 79/151 Moo 22 T. Ropwieng > Mueang Chiangrai 57000 > Thailand > > > > > ------------------------------------------------------------------------------ > Want fast and easy access to all the code in your enterprise? Index and > search up to 200,000 lines of code with a free copy of Black Duck > Code Sight - the same software that powers the world's largest code > search on Ohloh, the Black Duck Open Hub! Try it now. > http://p.sf.net/sfu/bds > _______________________________________________ > Docutils-users mailing list > Docutils-users@... > https://lists.sourceforge.net/lists/listinfo/docutils-users > > Please use "Reply All" to reply to the list. >
[Docutils-users] I am not subscribed .. From: john francis lee - 2014-07-23 07:16:04 Hi, I was having trouble setting the page size used by rst2odt.py when it created an odt from and rst file, and so sent a message to developers ... because that was the email link at the top of the article I'd read in an attempt to get help ... http://docutils.sourceforge.net/docs/user/odt.html#defining-and-using-a-custom-stylesheet ... and the email bounced because I wasn't subscribed. Meanwhile ... scrolling down, or using another link, came in contact with another section of the very same posting ... http://docutils.sourceforge.net/docs/user/odt.html#page-size ... which has set me right ! So, thanks. I tried papersize and that business, but it was ... \$ rst2odt_prepstyles.py styles.odt ... that finally straightened me out. I append my original email for ... the hell of it ... Thanks again. It this doesn't bounce too. ==================================================================== Hi, I'm trying to generate .odt files with paper size a4 from .rst files. I'm trying to follow the directions from http://docutils.sourceforge.net/docs/user/odt.html#defining-and-using-a-custom-stylesheet I use debian 7.6 64bit linux. I used apt-get install python-docutils to install the docutils programs. I copied /usr/share/docutils/writers/odf_odt/styles.odt to my home directory. I opened it there and changed Format| Page | Paper format | Format from Letter to A4 I saved /usr/share/docutils/writers/odf_odt/styles.odt as /usr/share/docutils/writers/odf_odt/styles.odt-dist and then saved my copy as /usr/share/docutils/writers/odf_odt/styles.odt No one ever uses letter sized paper in Thailand, and I can change it in any individual letters I write on letter size paper. I think I have written one in the last 12 years . I changed ownership and permissions to match the distribution ls -l /usr/share/docutils/writers/odf_odt/ total 40 -rw-r--r-- 1 root root 16403 Jul 23 12:19 styles.odt -rw-r--r-- 1 root root 16500 Jun 27 2011 styles.odt-dist But when I run rst2odt ooncd.en.rst ooncd.en.odt ooncd.en.odt is still formatted for letter-size paper. Can you see what I've done wrong? Thanks. -- John Francis Lee Thanon Sanam Gila, Ban Fa Sai 79/151 Moo 22 T. Ropwieng Mueang Chiangrai 57000 Thailand
Re: [Docutils-users] Using DocUtils to parse RST with unknown directives From: David Goodger - 2014-07-22 16:46:51 On Mon, Jul 21, 2014 at 1:07 PM, Austin Bart wrote: > I have some RST files that use a number of custom directives. I need to get > a tree-based representation (e.g., like I'd get from publish_doctree) of > these files before I pass them into Sphinx (via Paver) and have them parsed > properly. I don't want any sophisticated processing of the directives - I > just want to know where in the document any given directive occurs, along > with its options and content. > > If I try and just pass the files into publish_doctree, it gets upset because > it hasn't been told about all the custom directives that are possible. Is my > only option to implement my own parser? Or is there some way to tell > docutils to not Except on unknown directives? The following conversation > makes me think that it might not be possible: > > http://article.gmane.org/gmane.text.docutils.user/4176/match=publish_doctree You can adjust the halt_level so that "error" level does not halt the processing. You'd set halt_level=4 (one level above error = 3). Then the resulting doctree would contain error messages with details about each directive. Another option would be some monkey-patching. Replace docutils.parsers.rst.directives._directive_registry (in the __init__.py file) with a collections.defaultdict(your_function), duplicating the original _directive_registry's data. The implementation of your_function would return a (module name, class name) tuple; you would have to implement these as well (possibly also monkey-patched). I recommend the first option, much easier. If it doesn't do what you want, the second option may do it for you. -- David Goodger ; > Please note that I'm not subscribed to this listserv, so please CC me on > responses! Thanks for your time and help! > > -- > Austin Cory Bart > Computer Science PhD student at Virginia Tech > http://www.acbart.com > > ------------------------------------------------------------------------------ > Want fast and easy access to all the code in your enterprise? Index and > search up to 200,000 lines of code with a free copy of Black Duck > Code Sight - the same software that powers the world's largest code > search on Ohloh, the Black Duck Open Hub! Try it now. > http://p.sf.net/sfu/bds > _______________________________________________ > Docutils-users mailing list > Docutils-users@... > https://lists.sourceforge.net/lists/listinfo/docutils-users > > Please use "Reply All" to reply to the list. >
[Docutils-users] Using DocUtils to parse RST with unknown directives From: Austin Bart - 2014-07-21 18:07:16 Attachments: Message as HTML I have some RST files that use a number of custom directives. I need to get a tree-based representation (e.g., like I'd get from publish_doctree) of these files before I pass them into Sphinx (via Paver) and have them parsed properly. I don't want any sophisticated processing of the directives - I just want to know where in the document any given directive occurs, along with its options and content. If I try and just pass the files into publish_doctree, it gets upset because it hasn't been told about all the custom directives that are possible. Is my only option to implement my own parser? Or is there some way to tell docutils to not Except on unknown directives? The following conversation makes me think that it might not be possible: http://article.gmane.org/gmane.text.docutils.user/4176/match=publish_doctree Please note that I'm not subscribed to this listserv, so please CC me on responses! Thanks for your time and help! -- Austin Cory Bart Computer Science PhD student at Virginia Tech http://www.acbart.com
Re: [Docutils-users] Equation numbering in LaTeX writer From: Guenter Milde - 2014-07-03 20:25:52 On 2014-06-26, Eduard Bopp wrote: > My current workaround is to change line 2529 of > writers/latex2e/__init__.py from > math_env = pick_math_environment(node.astext()) > to > math_env = pick_math_environment(node.astext(), numbered=True) > This enables enumeration and allows me to label and reference my > equations using raw LaTeX. While this solves my practical issue, I think > it's not exactly an elegant solution. Is there a more straightforward > and perhaps target-independent way to achieve this? Not yet. Numbered equations are on the TODO list.¹ However, as there are more objects that may/can/should be numbered (formal tables, figures) this should become a generic solution which requires some thoughts and efforts. Günter ¹ http://docutils.sourceforge.net/docs/dev/todo.html
Re: [Docutils-users] Test suite failure From: David Bruchmann - 2014-06-26 18:32:09 > > - distributing a document generated on a not "C:" drive would make the > stylesheet path > wrong on most other machines, for sure on any unix(mac/linux That argument is reasonable. Apart from that you've just to deal with the fact that the 4 errors are thrown on Windows when using absolute paths. Relative paths could be a solution but maybe that's sometimes not desired. I suppose you can solve the problem only with a configuration-option where every user can decide. You still can recommend one solution. Btw I built the tests from a subdirectory and not directly in C:\, so the value would be wrong, no matter if "C:/test.css" or "/test.css". In my opinion here it would be reasonable to built the paths really relative. David
Re: [Docutils-users] Test suite failure From: Pete Jemian - 2014-06-26 17:31:31 Isn't Windows a bit different in handling directories and disks? /mypath/ starts at the root of the default disk If your default disk is C:, doesn't it point to C:/mypath/ F:, doesn't it point to F:/mypath/ Engelbert's rule 1 (below) does not describe this. HTH, Pete On 6/26/2014 12:17 PM, David Bruchmann wrote: > Hello Engelbert, > > I know that a path like /mypath/ without "C:" works in Windows. > Nevertheless 'C:' can be seen as the root-folder of any directory in > comparison to linux. > Without drive-letter you can't access a file of another drive that's > the same as you try to access /home/myFile.txt which is resided in > /usr/myFile.txt. > Therefore the drive-letter should left untouched as you wrote. > In general the result is correct in my opinion. > > I think the tests should be adjusted NOT to throw an error > I don't know how to adjust the expected value as I never had a look in > the source-code but that's secondary. Sense of the tests is not to > make a 100% string-comparison but to test if the values are correct > and work, right? > > David > > On 6/26/14, engelbert gruber wrote: >> thanks for mentioning >> >> somehow this is in my workpile >> but i do not know how to solve >> >> ans therefore i am very interested opinions >> >> facts (as i remember) >> >> 1. a configured stylesheet "/style.css" results in an absolute path >> "c:/style.css" on windows. >> 2. a styleshhet inculding the drive letter only works for >> >> - reading locally with the borwser >> - only necessary if the stylesheet is on drive c: and the documents on >> another dirv >> otherwise the document would work without the drive letter >> - in the theoretic case of a server templating system with a >> postprocessor >> removing the driveletter, before serving via http. >> >> therefore i would opt for removing of the drive letter. >> but the procedure prepending it is used all over docutils >> and if someone specifies "f:/test.css" the driveletter must be left >> untouched. >> >> >> >> >> >> On 26 June 2014 12:04, David Bruchmann wrote: >> >>> Hello, >>> >>> I've the same bug as http://sourceforge.net/p/docutils/bugs/243/ but >>> can't >>> login in the moment to sourceforge.net. >>> >>> Here are more details: >>> primary it's always the same 'fault' (4 times): >>> >>> >>> -: expected >>> +: output >>> - """ >>> + """ >>> >>> Here is still my alltests.out: >>> ------------------------------ >>> Testing Docutils 0.11 [release] with Python 2.7.6 on 2014-06-26 at >>> 16:13:05 >>> Working directory: C:\Users\d_admin\Downloads\docutils-0.11\test >>> Docutils package: C:\Users\d_admin\Downloads\docutils-0.11\docutils >>> >>> test_writers\test_html4css1_template.py: totest['template'][0]; >>> test_publish >>> (DocutilsTestSupport.WriterPublishTestCase) >>> input: >>> ================ >>> Document Title >>> ================ >>> ---------- >>> Subtitle >>> ---------- >>> >>> :Author: Me >>> >>> .. footer:: footer text >>> >>> Section >>> ======= >>> >>> Some text. >>> >>> -: expected >>> +: output >>> head_prefix = """\ >>> >>> >> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >>> >>> """ >>> >>> >>> head = """\ >>> >>> >>> Document Title >>> """ >>> >>> >>> stylesheet = """\ >>> - """ >>> + """ >>> ? ++ >>> >>> >>> body_prefix = """\ >>> >>> >>>
""" >>> >>> >>> body_pre_docinfo = """\ >>>
Document Title
>>>
Subtitle
""" >>> >>> >>> docinfo = """\ >>> >>>
>>> >>>
Author:Me
>>> >>> >>> >>> """ >>> >>> >>> body = """\ >>>
>>>
Section
>>>
Some text.
>>>
""" >>> >>> >>> body_suffix = """\ >>> >>> >>> >>> """ >>> >>> >>> head_prefix = """\ >>> >>> >> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >>> >>> """ >>> >>> >>> head = """\ >>> >>> >>> Document Title >>> """ >>> >>> >>> stylesheet = """\ >>> - """ >>> + """ >>> ? ++ >>> >>> >>> body_prefix = """\ >>> >>> >>>
""" >>> >>> >>> body_pre_docinfo = """\ >>>
Document Title
>>>
Subtitle
""" >>> >>> >>> docinfo = """\ >>> >>>
>>> >>>
Author:Me
>>> >>> >>> >>> """ >>> >>> >>> body = """\ >>>
>>>
Section
>>>
Some text.
>>>
""" >>> >>> >>> body_suffix = """\ >>> >>> >>> >>> """ >>> >>> >>> title = """\ >>> Document Title""" >>> >>> >>> subtitle = """\ >>> Subtitle""" >>> >>> >>> header = """\ >>> """ >>> >>> >>> footer = """\ >>> """ >>> >>> >>> meta = """\ >>> >>> >>> """ >>> >>> >>> fragment = """\ >>>
>>>
Section
>>>
Some text.
>>>
""" >>> >>> >>> html_prolog = """\ >>> >>> >> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">"""; >>> >>> >>> html_head = """\ >>> >>> >>> Document Title >>> """ >>> >>> >>> html_title = """\ >>>
Document Title
""" >>> >>> >>> html_subtitle = """\ >>>
Subtitle
""" >>> >>> >>> html_body = """\ >>>
>>>
Document Title
>>>
Subtitle
>>> >>>
>>> >>>
Author:Me
>>> >>> >>> >>> >>>
>>>
Section
>>>
Some text.
>>>
>>> >>> """ >>> >>> test_writers\test_s5.py: totest['basics'][0]; test_publish >>> (DocutilsTestSupport.WriterPublishTestCase) >>> input: >>> ============ >>> Show Title >>> ============ >>> >>> Title slide >>> >>> First Slide >>> =========== >>> >>> Slide text. >>> >>> -: expected >>> +: output >>> >>> >> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >>> >>> >>> >>> >>> >>> Show Title >>> - >>> + >>> ? ++ >>> >>> >>> >>> >>> >>> >> type="text/css" media="projection" id="slideProj" /> >>> >> type="text/css" media="screen" id="outlineStyle" /> >>> >> type="text/css" media="print" id="slidePrint" /> >>> >> type="text/css" media="projection" id="operaFix" /> >>> >>> >>> >>> >>>
>>>
>>>
>>> >>> >>>
>>>
>>>
>>>
Show Title
>>> >>>
Title slide
>>> >>>
>>>
>>>
First Slide
>>>
Slide text.
>>>
>>>
>>> >>> >>> >>> test_writers\test_s5.py: totest['settings'][0]; test_publish >>> (DocutilsTestSupport.WriterPublishTestCase) >>> input: >>> ================== >>> Bogus Slide Show >>> ================== >>> >>> We're just checking the settings >>> >>> -: expected >>> +: output >>> >>> >> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >>> >>> >>> >>> >>> >>> Bogus Slide Show >>> - >>> + >>> ? ++ >>> >>> >>> >>> >>> >>> >> type="text/css" media="projection" id="slideProj" /> >>> >> type="text/css" media="screen" id="outlineStyle" /> >>> >> type="text/css" media="print" id="slidePrint" /> >>> >> type="text/css" media="projection" id="operaFix" /> >>> >>> >>> >>> >>>
>>>
>>>
>>> >>> >>>
>>>
>>>
>>>
Bogus Slide Show
>>> >>>
We're just checking the settings
>>>
>>>
>>> >>> >>> Elapsed time: 57.993 seconds >>> >>> ------------------------------ >>> >>> >>> >>> >>> >>> ------------------------------------------------------------------------------ >>> Open source business process management suite built on Java and Eclipse >>> Turn processes into business applications with Bonita BPM Community >>> Edition >>> Quickly connect people, data, and systems into organized workflows >>> Winner of BOSSIE, CODIE, OW2 and Gartner awards >>> http://p.sf.net/sfu/Bonitasoft >>> _______________________________________________ >>> Docutils-users mailing list >>> Docutils-users@... >>> https://lists.sourceforge.net/lists/listinfo/docutils-users >>> >>> Please use "Reply All" to reply to the list. >>> >> > > ------------------------------------------------------------------------------ > Open source business process management suite built on Java and Eclipse > Turn processes into business applications with Bonita BPM Community Edition > Quickly connect people, data, and systems into organized workflows > Winner of BOSSIE, CODIE, OW2 and Gartner awards > http://p.sf.net/sfu/Bonitasoft > _______________________________________________ > Docutils-users mailing list > Docutils-users@... > https://lists.sourceforge.net/lists/listinfo/docutils-users > > Please use "Reply All" to reply to the list. > -- ---------------------------------------------------------- Pete R. Jemian, Ph.D. Beam line Controls and Data Acquisition, Group Leader Advanced Photon Source, Argonne National Laboratory Argonne, IL 60439 630 - 252 - 3189 ----------------------------------------------------------- Education is the one thing for which people are willing to pay yet not receive. -----------------------------------------------------------
Re: [Docutils-users] Test suite failure From: David Bruchmann - 2014-06-26 17:17:59 Hello Engelbert, I know that a path like /mypath/ without "C:" works in Windows. Nevertheless 'C:' can be seen as the root-folder of any directory in comparison to linux. Without drive-letter you can't access a file of another drive that's the same as you try to access /home/myFile.txt which is resided in /usr/myFile.txt. Therefore the drive-letter should left untouched as you wrote. In general the result is correct in my opinion. I think the tests should be adjusted NOT to throw an error I don't know how to adjust the expected value as I never had a look in the source-code but that's secondary. Sense of the tests is not to make a 100% string-comparison but to test if the values are correct and work, right? David On 6/26/14, engelbert gruber wrote: > thanks for mentioning > > somehow this is in my workpile > but i do not know how to solve > > ans therefore i am very interested opinions > > facts (as i remember) > > 1. a configured stylesheet "/style.css" results in an absolute path > "c:/style.css" on windows. > 2. a styleshhet inculding the drive letter only works for > > - reading locally with the borwser > - only necessary if the stylesheet is on drive c: and the documents on > another dirv > otherwise the document would work without the drive letter > - in the theoretic case of a server templating system with a > postprocessor > removing the driveletter, before serving via http. > > therefore i would opt for removing of the drive letter. > but the procedure prepending it is used all over docutils > and if someone specifies "f:/test.css" the driveletter must be left > untouched. > > > > > > On 26 June 2014 12:04, David Bruchmann wrote: > >> Hello, >> >> I've the same bug as http://sourceforge.net/p/docutils/bugs/243/ but >> can't >> login in the moment to sourceforge.net. >> >> Here are more details: >> primary it's always the same 'fault' (4 times): >> >> >> -: expected >> +: output >> - """ >> + """ >> >> Here is still my alltests.out: >> ------------------------------ >> Testing Docutils 0.11 [release] with Python 2.7.6 on 2014-06-26 at >> 16:13:05 >> Working directory: C:\Users\d_admin\Downloads\docutils-0.11\test >> Docutils package: C:\Users\d_admin\Downloads\docutils-0.11\docutils >> >> test_writers\test_html4css1_template.py: totest['template'][0]; >> test_publish >> (DocutilsTestSupport.WriterPublishTestCase) >> input: >> ================ >> Document Title >> ================ >> ---------- >> Subtitle >> ---------- >> >> :Author: Me >> >> .. footer:: footer text >> >> Section >> ======= >> >> Some text. >> >> -: expected >> +: output >> head_prefix = """\ >> >> > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >> >> """ >> >> >> head = """\ >> >> >> Document Title >> """ >> >> >> stylesheet = """\ >> - """ >> + """ >> ? ++ >> >> >> body_prefix = """\ >> >> >>
""" >> >> >> body_pre_docinfo = """\ >>
Document Title
>>
Subtitle
""" >> >> >> docinfo = """\ >> >>
>> >>
Author:Me
>> >> >> >> """ >> >> >> body = """\ >>
>>
Section
>>
Some text.
>>
""" >> >> >> body_suffix = """\ >> >> >> >> """ >> >> >> head_prefix = """\ >> >> > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >> >> """ >> >> >> head = """\ >> >> >> Document Title >> """ >> >> >> stylesheet = """\ >> - """ >> + """ >> ? ++ >> >> >> body_prefix = """\ >> >> >>
""" >> >> >> body_pre_docinfo = """\ >>
Document Title
>>
Subtitle
""" >> >> >> docinfo = """\ >> >>
>> >>
Author:Me
>> >> >> >> """ >> >> >> body = """\ >>
>>
Section
>>
Some text.
>>
""" >> >> >> body_suffix = """\ >> >> >> >> """ >> >> >> title = """\ >> Document Title""" >> >> >> subtitle = """\ >> Subtitle""" >> >> >> header = """\ >> """ >> >> >> footer = """\ >> """ >> >> >> meta = """\ >> >> >> """ >> >> >> fragment = """\ >>
>>
Section
>>
Some text.
>>
""" >> >> >> html_prolog = """\ >> >> > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">"""; >> >> >> html_head = """\ >> >> >> Document Title >> """ >> >> >> html_title = """\ >>
Document Title
""" >> >> >> html_subtitle = """\ >>
Subtitle
""" >> >> >> html_body = """\ >>
>>
Document Title
>>
Subtitle
>> >>
>> >>
Author:Me
>> >> >> >> >>
>>
Section
>>
Some text.
>>
>> >> """ >> >> test_writers\test_s5.py: totest['basics'][0]; test_publish >> (DocutilsTestSupport.WriterPublishTestCase) >> input: >> ============ >> Show Title >> ============ >> >> Title slide >> >> First Slide >> =========== >> >> Slide text. >> >> -: expected >> +: output >> >> > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >> >> >> >> >> >> Show Title >> - >> + >> ? ++ >> >> >> >> >> >> > type="text/css" media="projection" id="slideProj" /> >> > type="text/css" media="screen" id="outlineStyle" /> >> > type="text/css" media="print" id="slidePrint" /> >> > type="text/css" media="projection" id="operaFix" /> >> >> >> >> >>
>>
>>
>> >> >>
>>
>>
>>
Show Title
>> >>
Title slide
>> >>
>>
>>
First Slide
>>
Slide text.
>>
>>
>> >> >> >> test_writers\test_s5.py: totest['settings'][0]; test_publish >> (DocutilsTestSupport.WriterPublishTestCase) >> input: >> ================== >> Bogus Slide Show >> ================== >> >> We're just checking the settings >> >> -: expected >> +: output >> >> > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; >> >> >> >> >> >> Bogus Slide Show >> - >> + >> ? ++ >> >> >> >> >> >> > type="text/css" media="projection" id="slideProj" /> >> > type="text/css" media="screen" id="outlineStyle" /> >> > type="text/css" media="print" id="slidePrint" /> >> > type="text/css" media="projection" id="operaFix" /> >> >> >> >> >>
>>
>>
>> >> >>
>>
>>
>>
Bogus Slide Show
>> >>
We're just checking the settings
>>
>>
>> >> >> Elapsed time: 57.993 seconds >> >> ------------------------------ >> >> >> >> >> >> ------------------------------------------------------------------------------ >> Open source business process management suite built on Java and Eclipse >> Turn processes into business applications with Bonita BPM Community >> Edition >> Quickly connect people, data, and systems into organized workflows >> Winner of BOSSIE, CODIE, OW2 and Gartner awards >> http://p.sf.net/sfu/Bonitasoft >> _______________________________________________ >> Docutils-users mailing list >> Docutils-users@... >> https://lists.sourceforge.net/lists/listinfo/docutils-users >> >> Please use "Reply All" to reply to the list. >> >
Re: [Docutils-users] Test suite failure From: engelbert gruber - 2014-06-26 16:55:53 Attachments: Message as HTML thanks for mentioning somehow this is in my workpile but i do not know how to solve ans therefore i am very interested opinions facts (as i remember) 1. a configured stylesheet "/style.css" results in an absolute path "c:/style.css" on windows. 2. a styleshhet inculding the drive letter only works for - reading locally with the borwser - only necessary if the stylesheet is on drive c: and the documents on another dirv otherwise the document would work without the drive letter - in the theoretic case of a server templating system with a postprocessor removing the driveletter, before serving via http. therefore i would opt for removing of the drive letter. but the procedure prepending it is used all over docutils and if someone specifies "f:/test.css" the driveletter must be left untouched. On 26 June 2014 12:04, David Bruchmann wrote: > Hello, > > I've the same bug as http://sourceforge.net/p/docutils/bugs/243/ but can't > login in the moment to sourceforge.net. > > Here are more details: > primary it's always the same 'fault' (4 times): > > > -: expected > +: output > - """ > + """ > > Here is still my alltests.out: > ------------------------------ > Testing Docutils 0.11 [release] with Python 2.7.6 on 2014-06-26 at 16:13:05 > Working directory: C:\Users\d_admin\Downloads\docutils-0.11\test > Docutils package: C:\Users\d_admin\Downloads\docutils-0.11\docutils > > test_writers\test_html4css1_template.py: totest['template'][0]; > test_publish > (DocutilsTestSupport.WriterPublishTestCase) > input: > ================ > Document Title > ================ > ---------- > Subtitle > ---------- > > :Author: Me > > .. footer:: footer text > > Section > ======= > > Some text. > > -: expected > +: output > head_prefix = """\ > > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; > > """ > > > head = """\ > > > Document Title > """ > > > stylesheet = """\ > - """ > + """ > ? ++ > > > body_prefix = """\ > > >
""" > > > body_pre_docinfo = """\ >
Document Title
>
Subtitle
""" > > > docinfo = """\ > >
> >
Author:Me
> > > > """ > > > body = """\ >
>
Section
>
Some text.
>
""" > > > body_suffix = """\ > > > > """ > > > head_prefix = """\ > > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; > > """ > > > head = """\ > > > Document Title > """ > > > stylesheet = """\ > - """ > + """ > ? ++ > > > body_prefix = """\ > > >
""" > > > body_pre_docinfo = """\ >
Document Title
>
Subtitle
""" > > > docinfo = """\ > >
> >
Author:Me
> > > > """ > > > body = """\ >
>
Section
>
Some text.
>
""" > > > body_suffix = """\ > > > > """ > > > title = """\ > Document Title""" > > > subtitle = """\ > Subtitle""" > > > header = """\ > """ > > > footer = """\ > """ > > > meta = """\ > > > """ > > > fragment = """\ >
>
Section
>
Some text.
>
""" > > > html_prolog = """\ > > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">"""; > > > html_head = """\ > > > Document Title > """ > > > html_title = """\ >
Document Title
""" > > > html_subtitle = """\ >
Subtitle
""" > > > html_body = """\ >
>
Document Title
>
Subtitle
> >
> >
Author:Me
> > > > >
>
Section
>
Some text.
>
> > """ > > test_writers\test_s5.py: totest['basics'][0]; test_publish > (DocutilsTestSupport.WriterPublishTestCase) > input: > ============ > Show Title > ============ > > Title slide > > First Slide > =========== > > Slide text. > > -: expected > +: output > > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; > > > > > > Show Title > - > + > ? ++ > > > > > > type="text/css" media="projection" id="slideProj" /> > type="text/css" media="screen" id="outlineStyle" /> > type="text/css" media="print" id="slidePrint" /> > type="text/css" media="projection" id="operaFix" /> > > > > >
>
>
> > >
>
>
>
Show Title
> >
Title slide
> >
>
>
First Slide
>
Slide text.
>
>
> > > > test_writers\test_s5.py: totest['settings'][0]; test_publish > (DocutilsTestSupport.WriterPublishTestCase) > input: > ================== > Bogus Slide Show > ================== > > We're just checking the settings > > -: expected > +: output > > "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">; > > > > > > Bogus Slide Show > - > + > ? ++ > > > > > > type="text/css" media="projection" id="slideProj" /> > type="text/css" media="screen" id="outlineStyle" /> > type="text/css" media="print" id="slidePrint" /> > type="text/css" media="projection" id="operaFix" /> > > > > >
>
>
> > >
>
>
>
Bogus Slide Show
> >
We're just checking the settings
>
>
> > > Elapsed time: 57.993 seconds > > ------------------------------ > > > > > > ------------------------------------------------------------------------------ > Open source business process management suite built on Java and Eclipse > Turn processes into business applications with Bonita BPM Community Edition > Quickly connect people, data, and systems into organized workflows > Winner of BOSSIE, CODIE, OW2 and Gartner awards > http://p.sf.net/sfu/Bonitasoft > _______________________________________________ > Docutils-users mailing list > Docutils-users@... > https://lists.sourceforge.net/lists/listinfo/docutils-users > > Please use "Reply All" to reply to the list. >
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# For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val
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For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val [#permalink]
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12 Mar 2018, 21:41
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For all values x and y, $$x?y = \frac{3^{(2x + 2y)}}{3^{(2x - 2y)}}$$. What is the value of a?b?
(1) a = 2
(2) b = 4
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49960
Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val [#permalink]
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12 Mar 2018, 21:44
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Joined: 18 Jul 2016
Posts: 34
Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val [#permalink]
### Show Tags
12 Mar 2018, 22:28
2
1
$$x?y =\frac{3^{(2x + 2y)}}{3^{(2x – 2y)}}$$
=>$$x?y =3^{(2x + 2y) -(2x – 2y)}$$ -- as $$\frac{a^m}{a^n} = a^{m-n}$$
=>$$x?y =3^{4y}$$
Hence, for $$a?b$$, value of b is sufficient to answer
statement 1 : a = 2 ;not sufficient
statement 2 : b = 4; sufficient
IMO - B
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Joined: 01 Feb 2017
Posts: 157
Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val [#permalink]
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13 Mar 2018, 11:53
3^2(a+b) = 9^a * 9^b
3^2(a-b) = 9^a / 9^b
Dividing above, we get the expression:
9^b * 9^b = 81^b
So, we just need value of b to solve the expression.
Therefore, Ans B
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Re: For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val &nbs [#permalink] 13 Mar 2018, 11:53
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# For all values x and y, x?y = 3^(2x + 2y)/3^(2x – 2y). What is the val
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®. | 2018-10-17 11:55:54 | {"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": 0.533767819404602, "perplexity": 10459.241584702375}, "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-2018-43/segments/1539583511173.7/warc/CC-MAIN-20181017111301-20181017132801-00305.warc.gz"} |
https://datascience.stackexchange.com/questions/38087/policy-gradients-gradient-log-probabilities-favor-less-likely-actions/38218 | # Policy Gradients - gradient Log probabilities favor less likely actions?
Assume we work with neural networks, with the policy gradients method. The gradient w.r.t to the objective function $$J$$, is an expectation.
In other words, to get this gradient $$\nabla_{\theta} J(\theta)$$, we sample N trajectories, then average out their gradient contribution to obtain a more precise value that can "begin flowing into our network" during backprop. $$\nabla_{\theta} J(\theta) \approx \frac1N \sum_{i=1}^N \left( \sum_{t=1}^T \nabla_\theta \log \pi_\theta (a_{i,t}|s_{i,t}) \right) \left( \sum_{t=1}^T r(s_{i,t}, a_{i,t}) \right)$$
Looking with more detail at some specific trajectory $$i$$, we sum the gradient at each timestep in this trajectory, then multiply by the the total reward obtained from running that trajectory.
Assuming we use softmax as the network's final layer, the values for each action belongs to the range $$[0,1]$$
If I remember correctly, the gradient wrt $$\theta$$ at each timestep of a trajectory is going to be: $$\nabla_{\theta}\log \pi_{\theta}(a_{t}|s_{t}) = \frac{1}{\pi_{\theta}(a_{t}|s_{t})} \nabla \pi_{\theta}(a_{t}|s_{t})$$
where $$\nabla \pi_{\theta}(a_{t}|s_{t})$$ is then simply a derivative of softmax wrt its inputs, with the rest of the backprop towards the weight $$\theta$$
Question:
Let's say at timestep $$t_2$$ our softmax has output something like this:
[0.5, 0.1, 0.1, 0.1, 0.1, 0.1]
and the total reward for the trajectory was 50
Ignoring the rest of the backprop at the current timestep, $$\frac{1}{\pi_{\theta}(a_{t}|s_{t})}$$ will give us:
[2, 10, 10, 10, 10, 10]
This means we are already favoring other actions instead of the first action. This seems counter-intuitive to me. What if we only got such a large large reward because we took the first action? But the formula encourages us to strengthen the other 4 actions.
Yes, you are right that the term $\frac{1}{\pi_\theta(a_t|s_t)}$ itself is favoring the less likely actions. But don't forget how $\nabla \pi_\theta(a_t|s_t)$ is calculated, and you will see that $\nabla \pi_\theta(a_t|s_t)$ is over-emphasizing on the first action and $\frac{1}{\pi_\theta(a_t|s_t)}$ is correcting it.
Recall that the derivative for y =softmax(x) is $\frac{\partial y_i}{\partial x_j} = y_i(\delta_{ij}-y_i)$. Notice that $y_i$ is multiplied in the front, i.e. over-emphasizing the more likely $y_i$. By multiplying $\frac{1}{y_i}$ in the front, the over-emphasizing effect is being corrected.
In your example, when ${\pi_\theta(a_t|s_t)}=[0.5, 0.1, 0.1, 0.1, 0.1, 0.1]$, we can write down that $$\nabla \pi_\theta(a_t|s_t)=\left(\begin{array}{cccccc} 0.5\times0.5 & -0.5\times0.1 & -0.5\times0.1 & -0.5\times0.1 & -0.5\times0.1 & -0.5\times0.1\\ -0.5\times0.1 & 0.1\times0.9 & -0.1\times0.1 & -0.1\times0.1 & -0.1\times0.1 & -0.1\times0.1 \\ -0.5\times0.1 & -0.1\times0.1 & 0.1\times0.9 & -0.1\times0.1 & -0.1\times0.1 & -0.1\times0.1 \\ -0.5\times0.1 & -0.1\times0.1 & -0.1\times0.1 & 0.1\times0.9 &-0.1\times0.1 & -0.1\times0.1 \\ -0.5\times0.1 & -0.1\times0.1 & -0.1\times0.1 & -0.1\times0.1 & 0.1\times0.9 & -0.1\times0.1 \\ -0.5\times0.1 & -0.1\times0.1 & -0.1\times0.1 & -0.1\times0.1 & -0.1\times0.1 & 0.1\times0.9\\ \end{array}\right)$$ And by multiplying it with $\frac{1}{\pi_\theta(a_t|s_t)}=[\frac{1}{0.5},\frac{1}{0.1},\frac{1}{0.1},\frac{1}{0.1},\frac{1}{0.1},\frac{1}{0.1}]$, you effectively get $$\nabla \log\pi_\theta(a_t|s_t)=\frac{1}{\pi_\theta(a_t|s_t)}\nabla \pi_\theta(a_t|s_t)= \left(\begin{array}{cccccc} 0.5 & -0.5, &-0.5, &-0.5, &-0.5, &-0.5, \\ -0.1 & 0.9 & -0.1 & -0.1 & -0.1 & -0.1 & \\ -0.1 & -0.1 & 0.9 & -0.1 & -0.1 & -0.1 & \\ -0.1 & -0.1 & -0.1 & 0.9 & -0.1 & -0.1 & \\ -0.1 & -0.1 & -0.1 & -0.1 & 0.9 & -0.1 & \\ -0.1 & -0.1 & -0.1 & -0.1 & -0.1 & 0.9 & \\ \end{array}\right)$$
In case you are still thinking that because $0.9>0.5$ in the above result, we are slightly favoring the less likely action (although not 5 times more favorable), I would say that's the desired behavior. Because when we already have a relatively high score for action 1 (pre-activation 0.5) and now increase the score a little bit, we don't want the output probability to increase that much because otherwise the probability would more easily explode out of the range of $[0,1]$.
This kind of saturating gradient effect is very common for anything using the log derivative trick, not only in RL. You can also think of the example in the original REINFORCE algorithm paper (on page 6) where a Bernoulli random variable $$g_i(y_i,p_i)=\left\{ \begin{array}{c l} 1-p_i & \text{if } y_i=0\\ p_i & \text{if } y_i=1 \end{array}\right.$$
has a log derivative as
$$\frac{\partial \log g_i}{\partial p_i}=\left\{ \begin{array}{c l} -\frac{1}{1-p_i} & \text{if } y_i=0\\ \frac{1}{p_i} & \text{if } y_i=1 \end{array}\right.$$ Here when $p_i$ is already large and $y_i=1$, the derivative would be relatively small.
Finally, regarding your question what if we only got such a large large reward because we took the first action? Don't worry, here you are estimating the expected reward (and its gradient) of your current policy $\pi$, not exploiting this policy, so you just want to have a fair (unbiased) estimate, not a best possible reward.
• Thanks! As an intuition for me, will Gaussian policy also over-emphasise, similar to the softmax policy? – Kari Sep 15 '18 at 20:48
• For Gaussian policy, the action space is usually continuous. So a policy is unlikely to ever-emphasis a single action value, but could possibly over-emphasis a small range of action values depending on the choice of variance. – user12075 Sep 15 '18 at 21:02
• The $\frac{1}{\pi(s,a)}$ thing is explained nicely here: towardsdatascience.com/… with example code that practically demonstrates why it is important and works – Neil Slater Nov 19 '18 at 13:24 | 2021-06-25 00:29:05 | {"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": 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": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8101506233215332, "perplexity": 574.1723887770885}, "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/1623488560777.97/warc/CC-MAIN-20210624233218-20210625023218-00103.warc.gz"} |
http://www.gap-system.org/ForumArchive/Gaillard.1/Philippe.1/Chevalle.1/1.html | > < ^ Date: Thu, 05 Apr 2001 11:20:10 +0100 (WET DST)
> ^ From: Philippe Gaillard <pgaillar@maths.univ-rennes1.fr >
> ^ Subject: Chevalley module for SO(4,C)
Dear gap-forum,
I'm far to be an expert in representation theory and in GAP, but I'm
looking for a Chevalley module V for G=SO(4,C), taht is to say a faithful
finite dimensional SO(4,C)-module such that:
1. V contains no one-dimensional G-modules
2. any proper connected closed subgroup H $\in$ G leaves a one-dimensional
subspace W $\in$ V invariant.
I'd be interested in an injection of the representation of so(4,C) by the
set of matrices X such that tX.M+M.X=0, with M=[[0,I_2],[I_2,0]], in gl(V)
because I'm looking actually for the image of a regular pair of generators
of so(4,C) [which I know for the previous representation] in a Chevalley
module for SO(4,C).
Hoping it may interest some of you too,
Best regards,
Philippe Gaillard | 2018-03-18 23:13:10 | {"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": 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": 0.5799932479858398, "perplexity": 7430.153244778398}, "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-2018-13/segments/1521257646178.24/warc/CC-MAIN-20180318224057-20180319004057-00554.warc.gz"} |
https://icsecbsemath.com/2016/06/02/class-8-chapter-11-time-and-work-exercise-11/ | Question 1: $A$ can do a piece of work in $15$ days while $B$ can do it in $10$ days. How long will they take together to do it?
A’s 1 Day $=$ $\frac{1}{15}$
B’s 1 Day work $=$ $\frac{1}{10}$
A’s + B’s 1 Day work = $($ $\frac{1}{15}$ $+$ $\frac{1}{10}$ $)=$ $\frac{5}{30}$ $=$ $\frac{1}{6}$
Therefore both can finish the work in 6 Days.
$\\$
Question 2: $A, B$ and $C$ can do a piece of work in $12$ days, $15$ days and $10$ days respectively. In what time will they all together finish it?
A’s 1 Day $=$ $\frac{1}{12}$
B’s 1 Day work $=$ $\frac{1}{15}$
C’s 1 Day work = $\frac{1}{10}$
(A’s + B’s + C’s) 1 Day work $=$ $($ $\frac{1}{12}$ $+$ $\frac{1}{15}$ $+$ $\frac{1}{10}$ $) =$ $\frac{15}{60}$ $=$ $\frac{1}{4}$
Therefore all three can finish the work in 4 Days.
$\\$
Question 3: $A$ and $B$ together can do a piece of work in $35$ days, while $A$ alone can do it in $60$ days. How long would $B$ alone take to do it?
A’s 1 Day $=$ $\frac{1}{60}$
B’s 1 Day work $=$ $\frac{1}{x}$
(A’s + B’s) 1 Day work $=$ $($ $\frac{1}{60}$ $+$ $\frac{1}{x}$ $) =$ $\frac{1}{35}$
Solving for $x = 84$ Days
$\\$
Question 4: $A$ can do a piece of work in $20$ days while $B$ can do it in $15$ days. With the help of $C$, they finish the work in $5$ days. In what time would $C$ alone do it?
A’s 1 Day $=$ $\frac{1}{20}$
B’s 1 Day work $=$ $\frac{1}{15}$
C’s 1 Day work $=$ $\frac{1}{x}$
(A’s + B’s + C’s) 1 Day work $=$ $(\frac{1}{20}$ $+$ $\frac{1}{15}$ $+$ $\frac{1}{x}$ $) =$ $\frac{1}{5}$
Solving for $x = 12$ Days
$\\$
Question 5: $A$ can do a piece of work in $12$ days and $B$ alone can do it in $16$ days. They worked together on it for $3$ days and then $A$ left. How long did $B$ take to finish the remaining work?
A’s 1 Day $=$ $\frac{1}{12}$
B’s 1 Day work $=$ $\frac{1}{16}$
(A’s + B’s) 1 Day work $=$ $($ $\frac{1}{12}$ $+$ $\frac{1}{16}$ $) =$ $\frac{7}{48}$
The amount of work that is completed in 3 days $=$ $\frac{3\times7}{48}$ $=$ $\frac{7}{16}$
Amount of work left for B to complete $=$ $1 -$ $\frac{7}{16}$ $=$ $\frac{9}{16}$
Therefore the number of days that B will take to finish the work $=$ $\frac {\frac{9}{16}} {\frac{1}{16} }$ = 9 days
$\\$
Question 6: $A$ can do $\frac{1}{4}$ of a work in $5$ days, while $B$ can do $\frac{1}{5}$ of the work in $6$ days. In how many days can both do it together?
If A can do $\frac{1}{4}$ of a work in $5$ days, then A can do the entire work in $20$ days.
Therefore A’s 1 Day Work $=$ $\frac{1}{20}$
If B can do $\frac{1}{5}$ of a work in $6$ days, then B can do the entire work in $30$ days.
Therefore B’s 1 Day Work $=$ $\frac{1}{30}$
(A’s + B’s) 1 Day work $=$ $(\frac{1}{20}$ $+$ $\frac{1}{30}$ $) =$ $\frac{1}{12}$
Therefore both can do the work in $12$ days.
$\\$
Question 7: $A$ can dig a trench in $6$ days while $B$ can dig it in $8$ days. They dug the trench working together and received $1120$ for it. Find the share of each in it.
A’s 1 Day $=$ $\frac{1}{6}$
B’s 1 Day work $=$ $\frac{1}{8}$
Therefore the ratio of work $=$ $\frac {\frac{1}{6}} {\frac{1}{8} } = \frac{8}{6}$
Therefore A’s share $=$ $\frac{8}{14}$ $\times 1120 = 640$
Therefore B’s share $=$ $\frac{6}{14}$ $\times 1120 = 480$
$\\$
Question 8: $A$ can mow a field in $9$ days; $B$ can mow it in $12$ days while $C$ can mow it in $8$ days. They all together mowed the field and received $1610$ for it. How will the money be shared by them?
A’s 1 Day $=$ $\frac{1}{9}$
B’s 1 Day work $=$ $\frac{1}{12}$
C’s 1 Day work $=$ $\frac{1}{18}$
Therefore the ratio of their one day’s work $=$ $\frac{1}{9}$ $\colon$ $\frac{1}{12}$ $\colon$ $\frac{1}{18}$ $= 8 \colon 6 \colon 9$
Hence A’s share $=$ $\frac{8}{23}$ $\times 1120 = 560$
Hence A’s share $=$ $\frac{6}{23}$ $\times 1120 = 420$
Hence A’s share $=$ $\frac{9}{23}$ $\times 1120 = 630$
$\\$
Question 9: $A$ and $B$ can do a piece of work in $30$ days; $B$ and $C$ in $24$ days; $C$ and $A$ in $40$ days. How long will it take them to do the work together? In what time can each finish it, working alone?
(A’s + B’s) 1 Day work $=$ $\frac{1}{30}$
(B’s + C’s) 1 Day work $=$ $\frac{1}{24}$
(C’s + D’s) 1 Day work $=$ $\frac{1}{40}$
Adding the above three $2\times(A + B + C)$ day work = $(\frac{1}{30}$ $+$ $\frac{1}{24}$ $+$ $\frac{1}{40}$ $) =$ $\frac{1}{10}$
Therefore if they all work together, they will take 20 days to finish the work.
$\\$
Question 10: $A$ can do a piece of work in $80$ days. He works at it for $10$ days and then $B$ alone finishes the remaining work in $42$ days. In how many days could both do it?
A’s 1 Day $=$ $\frac{1}{80}$
Work finished by A in 10 days $=$ $\frac{1}{80} \times$ $10 =$ $\frac{1}{8}$
B finished the remainder of work $(1 -$ $\frac{1}{8}$ $) =$ $\frac{7}{8}$ in $42$ days
Therefore 1 Days work for B $=$ $\frac{\frac{7}{8}}{42}$ $=$ $\frac{1}{48}$
Hence B can do the work in 48 days
(A’s + B’s) 1 Day work $=$ $($ $\frac{1}{80}$ $+$ $\frac{1}{48}$ $)=$ $\frac{1}{30}$
Therefore both can do the work in 30 days.
$\\$
Question 11: $A$ and $B$ can together finish a work in $30$ days. They worked at it for $20$ days and then $B$ left. The remaining work was done by $A$ alone in $20$ more days. In how many days can $A$ alone do it?
(A’s + B’s) 1 Day work $=$ $\frac{1}{30}$
Amount of work finished by both in 20 days $=$ $20 \times$ $\frac{1}{30}$ $=$ $\frac{2}{3}$
Work left to be finished $=$ $1 -$ $\frac{2}{3}$ $=$ $\frac{1}{3}$
Work done by A in 1 Day $=$ $\frac{\frac{1}{3}}{20}$ $=$ $\frac{1}{60}$
Therefore A can do the work alone in 60 days.
$\\$
Question 12: $A$ can do a certain job in $25$ days which $B$ alone can do in $20$ days. $A$ started the work and was joined by $B$ after $10$ days. In how many days was the whole work completed?
A’s 1 Day work $=$ $\frac{1}{25}$
B’s 1 Day work $=$ $\frac{1}{20}$
(A’s + B’s) 1 Day work $=$ $($ $\frac{1}{25}$ $+$ $\frac{1}{20}$ $) =$ $\frac{9}{100}$
Amount of work finished by A in 10 days $=$ $10 \times$ $\frac{1}{25}$
Work left to be finished $=$ $(1-$ $\frac{2}{5}$ $) =$ $\frac{3}{5}$
Days taken by both A and B working together $=$ $\frac{\frac{3}{5}}{\frac{9}{100}}$ $= 6$ $\frac{2}{3}$
The work got completed in $10 + 6$ $\frac{2}{3}$ $= 16$ $\frac{2}{3}$
$\\$
Question 13: $A$ can do a piece of work in $14$ days, while $B$ can do in $21$ days. They begin together. But, $3$ days before the completion of the work, $A$ leaves off. Find the total number of days taken to complete the work.
A’s 1 Day work $=$ $\frac{1}{14}$
B’s 1 Day work $=$ $\frac{1}{21}$
(A’s + B’s) 1 Day work $=$ $($ $\frac{1}{14}$ $+$ $\frac{1}{21}$ $) =$ $\frac{5}{42}$
Amount of work finished by B in 3 days $=$ $(3 \times$ $\frac{1}{21}$ $) =$ $\frac{1}{7}$
Work left to be finished by A and B together $=$ $(1-$ $\frac{1}{7}$ $) =$ $\frac{6}{7}$
Days taken by A + B working together $=$ $\frac{\frac{6}{7}}{\frac{5}{42}}$ $= 7$ $\frac{1}{5}$
The work got completed in $3+7$ $\frac{1}{5}$ $= 10$ $\frac{1}{5}$
$\\$
Question 14: $A$ is thrice as good a workman as $B$ and $B$ is twice as good a workman as $C$. All the three took up a job and received $1800$ as remuneration. Find the share of each.
If C takes $x$ days to complete the job
Then B will complete the job in $\frac{x}{2}$ days
And A will complete the job in $\frac{x}{3}$ days days
Therefore the ratio of 1 days’ work of $A \colon B \colon C =$ $\frac{x}{3}$ $\colon$ $\frac{x}{2}$ $\colon$ $\frac{x}{1}$ $= 3 \colon 2 \colon 1$
Therefore the share of A $=$ $1800 \times$ $\frac{3}{6}$ $= 900$ Rs.
Therefore the share of B $=$ $1800 \times$ $\frac{2}{6}$ $= 600$ Rs.
Therefore the share of C $=$ $1800 \times$ $\frac{1}{6}$ $= 300$ Rs.
$\\$
Question 15: $A$ can do a certain job in $12$ days. $B$ is $60\%$ more efficient than $A$. Find the number of days taken by $B$ to finish the job.
Time taken to finish the job $= 12$ days
A’s 1 Day’s work $=$ $\frac{1}{12}$
B is 60% more efficient
B’s 1 Day’s work $=$ $1.6 \times$ $\frac{1}{12}$
Therefore the number of days B will take to finish the job $=$ $\frac{1}{\frac{1.6}{12}}$ $= 7$ $\frac{1}{2}$days
$\\$
Question 16: $A$ is twice as good a workman as $B$ and together they finish a piece of work in $14$ days. In how many days can $A$ alone do it?
Let B take $x$ days to finish the work.
B’s 1 day’s work $=$ $\frac{1}{x}$
The A will take $\frac{x}{2}$ days to finish the work.
A’s 1 day’s work $=$ $\frac{2}{x}$
(A+B) one day’s work $=$ $($ $\frac{1}{x}$ $+$ $\frac{2}{x}$ $) =$ $\frac{1}{14}$
Solving for $x=42$
Therefore A will take 21 days to finish the job.
$\\$
Question 17: Two pipes $A$ and $B$ can separately fill a tank in $36$ minutes and $45$ minutes respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A’s 1 minute fill rate $=$ $\frac{1}{36}$
B’s 1 minute fill rate $=$ $\frac{1}{45}$
A’s and B’s fill rate together $=$ $($ $\frac{1}{36}$ $+$ $\frac{1}{45}$ $) =$ $\frac{1}{20}$
Therefore if A and B are opened simultaneously, the tank will take 20 minutes to fill up.
$\\$
Question 18: One tap can fill a cistern in $3$ hours and the waste pipe can empty the full tank in $5$ hours. In what time will the empty cistern be full, if the tap and the waste pipe are kept open together?
Tap’s 1 minute fill rate $=$ $\frac{1}{3}$
Waste Pipe’s 1 minute empty rate $=$ $\frac{1}{5}$
Therefore the net fill rate $=$ $($ $\frac{1}{3}$ $-$ $\frac{1}{5}$ $) =$ $\frac{2}{15}$
Therefore if both the tap and the waste pipe are opened simultaneously then it will take $7\frac{1}{2}$ hours to fill up.
$\\$
Question 19: Two pipes $A$ and $B$ can separately fill a cistern in $20$ minutes and $30$ minutes respectively , while a third pipe $C$ can empty the full cistern in $15$ minutes. If all the pipes are opened together, in what time the empty cistern is filled?
A’s 1 minute fill rate $=$ $\frac{1}{20}$
B’s 1 minute fill rate $=$ $\frac{1}{30}$
C’s 1 minute empty rate $=$ $\frac{1}{15}$
Therefore the net fill rate $=$ $($ $\frac{1}{20}$ $+$ $\frac{1}{30}$ $-$ $\frac{1}{15}$ $) =$ $\frac{1}{60}$
Therefore if all the tap are opened simultaneously then it will take 60 minutes or one hour to fill up.
$\\$
Question 20: A pipe can fill a tank in $16$ hours. Due to a leak in the bottom, it is filled in $24$ hours. If the tank is full, how much time will the leak take to empty it?
Pipe’s fill rate $=$ $\frac{1}{16}$
Let the leak is at a rate of $=$ $\frac{1}{x}$
Therefore the net fill rate $=$ $($ $\frac{1}{16}$ $-$ $\frac{1}{x}$ $) =$ $\frac{1}{24}$
Solving for $x = 48$ hours. | 2020-10-01 07:19:49 | {"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": 0, "img_math": 462, "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": 0.49857795238494873, "perplexity": 485.90207494412135}, "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/1600402124756.81/warc/CC-MAIN-20201001062039-20201001092039-00218.warc.gz"} |
http://math.stackexchange.com/questions/94504/algorithm-to-predict-next-3d-points | # Algorithm to predict next 3D points
For example, having this data:
year x/y/z
2007 10/20/70
2008 20/10/70
2009 30/10/60
2010 40/10/50
2011 40/15/45
We want to predict what will be the x/y/z in 2012. We can observe that x is constantly increasing, y rather constant, z decreasing, so we can predict, for example:
2012 50/10/40
How to predict that x/y/z values?
x/y/z refers to number of positive/neutral/negative sentiments in given year. We always get 100 sentiments of news for a year. In our example, in year 2007 there were 10 positive, 20 neutral and 70 negative sentiments. So, x/y/z are in range <0; 100> and x + y + z = 100. x/y/z seems to be independent. Number of consecutive years from which we are gathering data is in range <2; 10>. In example it was 5. Algorithm is going to be implemented in Python.
-
Have you looked at linear regression? en.wikipedia.org/wiki/Linear_regression – Adam Dec 27 '11 at 20:10
For a split second, I thought you were the same Adam. – Raskolnikov Dec 27 '11 at 21:39 | 2016-07-29 04:24:43 | {"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": 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": 0.7808056473731995, "perplexity": 2234.2597956810328}, "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-2016-30/segments/1469257829970.64/warc/CC-MAIN-20160723071029-00032-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://akiani.ir/projects/transportation_diagrams/ | The diagrams will be drawn in JS And FE Codes And analysis will done with python , with libraries such as Pandas , sklearn , numpy and matplotlib
The references we are using are Traffic Engineering And Highways K.O Garber and Dr. Amini.Z's presentations
In this pseudo-article, We are going through drawing some important Transportation diagrams.
Time-Space Diagrams
Trajctory diagrams are type of diagrams that show us the instant location of every vehicles due to the time. also its slope will show the velocity at the point.
In this section we made an animation to show this diagram and its features. From now to the end, every animation that you will see has been wrote in JS (JavaScript) Language to draw these diagrams in canvases.
Trajectories are curves in the time-space diagram that define a single position for every moment of time, 𝑥(𝑡). Both $$𝑑𝑥 \over 𝑑𝑡$$ = $$\dot 𝑥$$, velocity, and $$𝑑^2𝑥 \over 𝑑^2𝑡$$ $$= \dot x$$ , acceleration can be analyzed visually with the trajectories plot.
Arrival And Departure Diagram
Properties of the bottlenecks (or other connections between links such as traffic lights, i.e. “nodes” in general) determine the dynamics of traffic at links, properties of the shockwaves, etc.
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted.
The following diagram depicts the cumulative number of arrivals and departures as seen by the two observers
Fundamental Diagram
Traffif model separates into to types:
• Macroscopic traffic flow model:
A mathematical traffic model that formulates the relationships among traffic flow characteristics like density, flow, and mean speed of a traffic stream.
• Microscopic traffic flow model:
Simulate single vehicle-driver units, so the dynamic variables of the models represent microscopic properties like the position and velocity of single vehicles
• Greenshield in the 1930’s conjectured that there was a linear relationship between speed and density.
In fact, the equations we are using, based on Greenshield theory. The equations are:
$${\bar u_s^2 = u_f - {u_f \over k_j}k,\space \space q = \bar u_s k \rightarrow q = u_f k -{u_f \over k_j}k^2}$$
$$\small{\bar u_s^2 = u_f - {u_f \over k_j}k}$$
$$\small{q = \bar u_s k \rightarrow q = u_f k -{u_f \over k_j}k^2}$$
Analysis
In this section we are going through analysing and processing some sort of data. Data we are using has been collected from seattle roads from loop detectors which placed in the some sections that we explain more about and from this website
what we are analysing are the mean velocities of cars in different times (in period of 5 minutes). the dataframe we are processing consists of 105120 rows which every one specify velocity of different nodes in certain time.
Initializing Analysis
Now the first part of the analysing should be initialized. It means ,Libraries such as matplotlib, pandas, numpy should be imported.
After importing these libraries, we should call the data with pd.read_pickle() function. this function get one arguments as file address.
With using shape() function, we can find out the number of columns and rows of this data.
At last, we show the last five rows of this heavy data by using tail() function.
The result is shown in below:
As what has been shown in above, the data has 105120 rows and 323 columns which made this data heavy.
The table in above, is just a psudo-figure of the whole table just for understimate how to table has been shaped.
What we are going through, is to add the index of the table to columns as datetime and drop our index of table. we do this for processing the date of each row in the continue.
As you can see, the last column of above table, is our new column that we named after it timeframes
Get Dates as Unix Times
Unix Timestamp is a type of time which shows us how many seconds(or miliseconds) passed from beginning of 1970-1-1 until a certain time.
In this section, we are going to add unix times from the column that we added to our table in previous section into our table to our columns. We will name it timestamps. You can find it in the last column of below table.
Plotting the Vleocity
As you found out, we are going to process the velocity. For this reason, we are going to plot velocity of each nodes.
**Notice**
In below of each image, there is a search icon that you can enter a node(column) number(which started from 1 to maximum 322) to show the image of that node.
Differences of Velocity in Morning and Night
There is a question that what will be the differences of velocity due to the hour of the day? to process this problem, we will plot velocity of each node in 3AM and 3PM to find out the differences.
The plots showing us that sometimes velocity changes sharply. this change may be occured due to increasing the traffic of the node. but increasing the traffic flow is a gradual action. another reason that sounds more accurate is that the node has an accident in that time that caused changing velocity sharply. | 2022-01-19 08:29:17 | {"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": 2, "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": 0.40251147747039795, "perplexity": 1235.65897092514}, "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/1642320301264.36/warc/CC-MAIN-20220119064554-20220119094554-00636.warc.gz"} |
https://itprospt.com/num/1984243/tpad0737-pmsolvetnl-ino-a-o-alnmlmanpariolal-poritonoum | 1
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# Each circle has center O. The radius of the smaller circle i
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Each circle has center O. The radius of the smaller circle i [#permalink] 13 Jun 2018, 22:09
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Each circle has center O. The radius of the smaller circle is 2 and the radius of the larger circle is 6. If a point is selected at random from the larger circular region, what is the probability that the point will lie in the shaded region?
A. $$\frac{1}{9}$$
B. $$\frac{1}{6}$$
C. $$\frac{2}{3}$$
D. $$\frac{5}{6}$$
E. $$\frac{8}{9}$$
[Reveal] Spoiler: OA
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Re: Each circle has center O. The radius of the smaller circle i [#permalink] 13 Jun 2018, 22:19
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amorphous wrote:
Each circle has center O. The radius of the smaller circle is 2 and the radius of the larger circle is 6. If a point is selected at random from the larger circular region, what is the probability that the point will lie in the shaded region?
A. $$\frac{1}{9}$$
B. $$\frac{1}{6}$$
C. $$\frac{2}{3}$$
D. $$\frac{5}{6}$$
E. $$\frac{8}{9}$$
Total area of larger circle is 36*pi.
Area of smaller circle is 4*pi.
Now To get the area of shaded part ,we need to separate total area - smaller area = 32pi ( 36pi - 4pi).
Now to get the probability for the shaded part we need to take entire area of the maximum circle in the denominator.
Since p(a) = expected records / Total records.
i.e shaded / full circle => 32pi / 36pi => 8/9.
E.
Re: Each circle has center O. The radius of the smaller circle i [#permalink] 13 Jun 2018, 22:19
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# Each circle has center O. The radius of the smaller circle i
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Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®. | 2018-12-17 20:06:12 | {"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": 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": 0.4110982418060303, "perplexity": 1945.0597381307848}, "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-2018-51/segments/1544376829115.83/warc/CC-MAIN-20181217183905-20181217205905-00153.warc.gz"} |
https://lammps.sandia.gov/doc/fix_tfmc.html | # fix tfmc command
## Syntax
fix ID group-ID tfmc Delta Temp seed keyword value
• ID, group-ID are documented in fix command
• tfmc = style name of this fix command
• Delta = maximal displacement length (distance units)
• Temp = imposed temperature of the system
• seed = random number seed (positive integer)
• zero or more keyword/arg pairs may be appended
• keyword = com or rot
com args = xflag yflag zflag
xflag,yflag,zflag = 0/1 to exclude/include each dimension
rot args = none
## Examples
fix 1 all tfmc 0.1 1000.0 159345
fix 1 all tfmc 0.05 600.0 658943 com 1 1 0
fix 1 all tfmc 0.1 750.0 387068 com 1 1 1 rot
## Description
Perform uniform-acceptance force-bias Monte Carlo (fbMC) simulations, using the time-stamped force-bias Monte Carlo (tfMC) algorithm described in (Mees) and (Bal).
One successful use case of force-bias Monte Carlo methods is that they can be used to extend the time scale of atomistic simulations, in particular when long time scale relaxation effects must be considered; some interesting examples are given in the review by (Neyts). An example of a typical use case would be the modelling of chemical vapor deposition (CVD) processes on a surface, in which impacts by gas-phase species can be performed using MD, but subsequent relaxation of the surface is too slow to be done using MD only. Using tfMC can allow for a much faster relaxation of the surface, so that higher fluxes can be used, effectively extending the time scale of the simulation. (Such an alternating simulation approach could be set up using a loop.)
The initial version of tfMC algorithm in (Mees) contained an estimation of the effective time scale of such a simulation, but it was later shown that the speed-up one can gain from a tfMC simulation is system- and process-dependent, ranging from none to several orders of magnitude. In general, solid-state processes such as (re)crystallization or growth can be accelerated by up to two or three orders of magnitude, whereas diffusion in the liquid phase is not accelerated at all. The observed pseudodynamics when using the tfMC method is not the actual dynamics one would obtain using MD, but the relative importance of processes can match the actual relative dynamics of the system quite well, provided Delta is chosen with care. Thus, the system’s equilibrium is reached faster than in MD, along a path that is generally roughly similar to a typical MD simulation (but not necessarily so). See (Bal) for details.
Each step, all atoms in the selected group are displaced using the stochastic tfMC algorithm, which is designed to sample the canonical (NVT) ensemble at the temperature Temp. Although tfMC is a Monte Carlo algorithm and thus strictly speaking does not perform time integration, it is similar in the sense that it uses the forces on all atoms in order to update their positions. Therefore, it is implemented as a time integration fix, and no other fixes of this type (such as fix nve) should be used at the same time. Because velocities do not play a role in this kind of Monte Carlo simulations, instantaneous temperatures as calculated by temperature computes or thermodynamic output have no meaning: the only relevant temperature is the sampling temperature Temp. Similarly, performing tfMC simulations does not require setting a timestep and the simulated time as calculated by LAMMPS is meaningless.
The critical parameter determining the success of a tfMC simulation is Delta, the maximal displacement length of the lightest element in the system: the larger it is, the longer the effective time scale of the simulation will be (there is an approximately quadratic dependence). However, Delta must also be chosen sufficiently small in order to comply with detailed balance; in general values between 5 and 10 % of the nearest neighbor distance are found to be a good choice. For a more extensive discussion with specific examples, please refer to (Bal), which also describes how the code calculates element-specific maximal displacements from Delta, based on the fourth root of their mass.
Because of the uncorrelated movements of the atoms, the center-of-mass of the fix group will not necessarily be stationary, just like its orientation. When the com keyword is used, all atom positions will be shifted (after every tfMC iteration) in order to fix the position of the center-of-mass along the included directions, by setting the corresponding flag to 1. The rot keyword does the same for the rotational component of the tfMC displacements after every iteration.
Note
the com and rot keywords should not be used if an external force is acting on the specified fix group, along the included directions. This can be either a true external force (e.g. through fix wall) or forces due to the interaction with atoms not included in the fix group. This is because in such cases, translations or rotations of the fix group could be induced by these external forces, and removing them will lead to a violation of detailed balance.
## Restart, fix_modify, output, run start/stop, minimize info
None of the fix_modify options are relevant to this fix.
This fix is not invoked during energy minimization.
## Restrictions
This fix is part of the MC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
This fix is not compatible with fix shake.
## Default
The option default is com = 0 0 0
(Bal) K. M Bal and E. C. Neyts, J. Chem. Phys. 141, 204104 (2014).
(Mees) M. J. Mees, G. Pourtois, E. C. Neyts, B. J. Thijsse, and A. Stesmans, Phys. Rev. B 85, 134301 (2012).
(Neyts) E. C. Neyts and A. Bogaerts, Theor. Chem. Acc. 132, 1320 (2013). | 2020-10-21 12:39:21 | {"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": 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": 0.7328478097915649, "perplexity": 1496.1710961739172}, "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-2020-45/segments/1603107876500.43/warc/CC-MAIN-20201021122208-20201021152208-00051.warc.gz"} |
http://kitchingroup.cheme.cmu.edu/blog/tag/heat-transfer/ | ## Transient heat conduction - partial differential equations
| categories: pde | tags: heat transfer | View Comments
We solved a steady state BVP modeling heat conduction. Today we examine the transient behavior of a rod at constant T put between two heat reservoirs at different temperatures, again T1 = 100, and T2 = 200. The rod will start at 150. Over time, we should expect a solution that approaches the steady state solution: a linear temperature profile from one side of the rod to the other.
$$\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}$$
at $$t=0$$, in this example we have $$u_0(x) = 150$$ as an initial condition. with boundary conditions $$u(0,t)=100$$ and $$u(L,t)=200$$.
In Matlab there is the pdepe command. There is not yet a PDE solver in scipy. Instead, we will utilze the method of lines to solve this problem. We discretize the rod into segments, and approximate the second derivative in the spatial dimension as $$\frac{\partial^2 u}{\partial x^2} = (u(x + h) - 2 u(x) + u(x-h))/ h^2$$ at each node. This leads to a set of coupled ordinary differential equations that is easy to solve.
Let us say the rod has a length of 1, $$k=0.02$$, and solve for the time-dependent temperature profiles.
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
N = 100 # number of points to discretize
L = 1.0
X = np.linspace(0, L, N) # position along the rod
h = L / (N - 1)
k = 0.02
def odefunc(u, t):
dudt = np.zeros(X.shape)
dudt[0] = 0 # constant at boundary condition
dudt[-1] = 0
# now for the internal nodes
for i in range(1, N-1):
dudt[i] = k * (u[i + 1] - 2*u[i] + u[i - 1]) / h**2
return dudt
init = 150.0 * np.ones(X.shape) # initial temperature
init[0] = 100.0 # one boundary condition
init[-1] = 200.0 # the other boundary condition
tspan = np.linspace(0.0, 5.0, 100)
sol = odeint(odefunc, init, tspan)
for i in range(0, len(tspan), 5):
plt.plot(X, sol[i], label='t={0:1.2f}'.format(tspan[i]))
# put legend outside the figure
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.xlabel('X position')
plt.ylabel('Temperature')
# adjust figure edges so the legend is in the figure
plt.savefig('images/pde-transient-heat-1.png')
# Make a 3d figure
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
SX, ST = np.meshgrid(X, tspan)
ax.plot_surface(SX, ST, sol, cmap='jet')
ax.set_xlabel('X')
ax.set_ylabel('time')
ax.set_zlabel('T')
ax.view_init(elev=15, azim=-124) # adjust view so it is easy to see
plt.savefig('images/pde-transient-heat-3d.png')
# animated solution. We will use imagemagick for this
# we save each frame as an image, and use the imagemagick convert command to
# make an animated gif
for i in range(len(tspan)):
plt.clf()
plt.plot(X, sol[i])
plt.xlabel('X')
plt.ylabel('T(X)')
plt.title('t = {0}'.format(tspan[i]))
plt.savefig('___t{0:03d}.png'.format(i))
import commands
print commands.getoutput('convert -quality 100 ___t*.png images/transient_heat.gif')
print commands.getoutput('rm ___t*.png') #remove temp files
This version of the graphical solution is not that easy to read, although with some study you can see the solution evolves from the initial condition which is flat, to the steady state solution which is a linear temperature ramp.
The 3d version may be easier to interpret. The temperature profile starts out flat, and gradually changes to the linear ramp.
Finally, the animated solution.
org-mode source
## Boundary value problem in heat conduction
| categories: bvp | tags: heat transfer | View Comments
For steady state heat conduction the temperature distribution in one-dimension is governed by the Laplace equation:
$$\nabla^2 T = 0$$
with boundary conditions that at $$T(x=a) = T_A$$ and $$T(x=L) = T_B$$.
The analytical solution is not difficult here: $$T = T_A-\frac{T_A-T_B}{L}x$$, but we will solve this by finite differences.
For this problem, lets consider a slab that is defined by x=0 to x=L, with $$T(x=0) = 100$$, and $$T(x=L) = 200$$. We want to find the function T(x) inside the slab.
We approximate the second derivative by finite differences as
$$f''(x) \approx \frac{f(x-h) - 2 f(x) + f(x+h)}{h^2}$$
Since the second derivative in this case is equal to zero, we have at each discretized node $$0 = T_{i-1} - 2 T_i + T_{i+1}$$. We know the values of $$T_{x=0} = \alpha$$ and $$T_{x=L} = \beta$$.
$A = \left [ \begin{array}{ccccc} % -2 & 1 & 0 & 0 & 0 \\ 1 & -2& 1 & 0 & 0 \\ 0 & \ddots & \ddots & \ddots & 0 \\ 0 & 0 & 1 & -2 & 1 \\ 0 & 0 & 0 & 1 & -2 \end{array} \right ]$
$x = \left [ \begin{array}{c} T_1 \\ \vdots \\ T_N \end{array} \right ]$
$b = \left [ \begin{array}{c} -T(x=0) \\ 0 \\ \vdots \\ 0 \\ -T(x=L) \end{array} \right]$
These are linear equations in the unknowns $$x$$ that we can easily solve. Here, we evaluate the solution.
import numpy as np
#we use the notation T(x1) = alpha and T(x2) = beta
x1 = 0; alpha = 100
x2 = 5; beta = 200
npoints = 100
# preallocate and shape the b vector and A-matrix
b = np.zeros((npoints, 1));
b[0] = -alpha
b[-1] = -beta
A = np.zeros((npoints, npoints));
#now we populate the A-matrix and b vector elements
for i in range(npoints ):
for j in range(npoints):
if j == i: # the diagonal
A[i,j] = -2
elif j == i - 1: # left of the diagonal
A[i,j] = 1
elif j == i + 1: # right of the diagonal
A[i,j] = 1
# solve the equations A*y = b for Y
Y = np.linalg.solve(A,b)
x = np.linspace(x1, x2, npoints + 2)
y = np.hstack([alpha, Y[:,0], beta])
import matplotlib.pyplot as plt
plt.plot(x, y)
plt.plot(x, alpha + (beta - alpha)/(x2 - x1) * x, 'r--')
plt.xlabel('X')
plt.ylabel('T(X)')
plt.legend(('finite difference', 'analytical soln'), loc='best')
plt.savefig('images/bvp-heat-conduction-1d.png')
org-mode source
## Finding the nth root of a periodic function
| categories: nonlinear algebra | tags: heat transfer | View Comments
There is a heat transfer problem where one needs to find the n^th root of the following equation: $$x J_1(x) - Bi J_0(x)=0$$ where $$J_0$$ and $$J_1$$ are the Bessel functions of zero and first order, and $$Bi$$ is the Biot number. We examine an approach to finding these roots.
First, we plot the function.
from scipy.special import jn, jn_zeros
import matplotlib.pyplot as plt
import numpy as np
Bi = 1
def f(x):
return x * jn(1, x) - Bi * jn(0, x)
X = np.linspace(0, 30, 200)
plt.plot(X, f(X))
plt.savefig('images/heat-transfer-roots-1.png')
You can see there are many roots to this equation, and we want to be sure we get the n^{th} root. This function is pretty well behaved, so if you make a good guess about the solution you will get an answer, but if you make a bad guess, you may get the wrong root. We examine next a way to do it without guessing the solution. What we want is the solution to $$f(x) = 0$$, but we want all the solutions in a given interval. We derive a new equation, $$f'(x) = 0$$, with initial condition $$f(0) = f0$$, and integrate the ODE with an event function that identifies all zeros of $$f$$ for us. The derivative of our function is $$df/dx = d/dx(x J_1(x)) - Bi J'_0(x)$$. It is known (http://www.markrobrien.com/besselfunct.pdf) that $$d/dx(x J_1(x)) = x J_0(x)$$, and $$J'_0(x) = -J_1(x)$$. All we have to do now is set up the problem and run it.
from pycse import * # contains the ode integrator with events
from scipy.special import jn, jn_zeros
import matplotlib.pyplot as plt
import numpy as np
Bi = 1
def f(x):
"function we want roots for"
return x * jn(1, x) - Bi * jn(0, x)
def fprime(f, x):
"df/dx"
return x * jn(0, x) - Bi * (-jn(1, x))
def e1(f, x):
"event function to find zeros of f"
isterminal = False
value = f
direction = 0
return value, isterminal, direction
f0 = f(0)
xspan = np.linspace(0, 30, 200)
x, fsol, XE, FE, IE = odelay(fprime, f0, xspan, events=[e1])
plt.plot(x, fsol, '.-', label='Numerical solution')
plt.plot(xspan, f(xspan), '--', label='Analytical function')
plt.plot(XE, FE, 'ro', label='roots')
plt.legend(loc='best')
plt.savefig('images/heat-transfer-roots-2.png')
for i, root in enumerate(XE):
print 'root {0} is at {1}'.format(i, root)
plt.show()
root 0 is at 1.25578377377
root 1 is at 4.07947743741
root 2 is at 7.15579904465
root 3 is at 10.2709851256
root 4 is at 13.3983973869
root 5 is at 16.5311587137
root 6 is at 19.6667276775
root 7 is at 22.8039503455
root 8 is at 25.9422288192
root 9 is at 29.081221492
You can work this out once, and then you have all the roots in the interval and you can select the one you want. | 2018-03-24 02:31:56 | {"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": 2, "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": 0.6759097576141357, "perplexity": 1977.4826156870568}, "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-2018-13/segments/1521257649627.3/warc/CC-MAIN-20180324015136-20180324035136-00761.warc.gz"} |
https://byjus.com/physics/kinetic-theory-of-gases-assumptions/ | # Kinetic Theory Of Gases: Assumptions
Gases are made up of molecules. What are molecules? Molecules are the smallest unit which behaves the same as the sample, i.e. they have the same chemical properties as of the sample. The kinetic theory of gases has developed a model which explains the behavior of molecules, which should further explain the behavior of an ideal gas. Do you know what an ideal gas is?
We have learned that the pressure (P), volume (V), and temperature (T) of gases at low temperature follow the equation:
$PV$ = $nRT$
Where
n = number of moles in the gas
R = gas constant having value $8.314 JK^{-1}mol^{-1}$
Now, any gas which follows this equation is called ideal gas. But there are certain assumptions that we consider for describing ideal gas behavior.
## Assumptions of Kinetic Theory of Gases
• All gases are made up of molecules which are constantly and persistently moving in random directions.
• The separation between the molecules is much greater than the size of molecules.
• When a gas sample is kept in a container, the molecules of the sample do not exert any force on the walls of the container during the collision.
• The time interval of collision between two molecules, and between a molecule and the wall is considered to be very small.
• All the collisions between molecules and even between molecules and wall are considered to be elastic.
• All the molecules in a certain gas sample obey Newton’s laws of motion.
• If a gas sample is left for a sufficient time, it eventually comes to a steady state. The density of molecules and the distribution of molecules are independent of position, distance and time.
There is a lot more to be learned about kinetic theory of gases. Explore more on physics formulas and physics calculators at BYJU’S
#### Practise This Question
Imagine a gravity free laboratory, in outer space, where you are asked to study the motions of a large number of marbles kept in a transparent cubical jar, as you give the jar quick, small jerks in random directions. You will observe, that after giving a sufficient number of jerks, the marbles start moving rather chaotically, i.e., each marble bounces off other marbles every now and then, and takes a random trajectory between two points due to these collisions. You seem to have given some kinetic energy to each marble, when the jar was being shaken. What happens when you release the jar suddenly, leaving it suspended in space? Assume all collisions between the marbles to be perfectly elastic. | 2019-02-18 13:09:50 | {"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": 0.6593387722969055, "perplexity": 458.05571825664356}, "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-2019-09/segments/1550247486480.6/warc/CC-MAIN-20190218114622-20190218140622-00018.warc.gz"} |
https://blog.dgoon.net/my-past-3000-days-of-learning.html | # My past 3000 days of learning
## Overview
This posting is mainly written for the class Learning How To Learn. However, it is not bounded to assignment. This will help my future learning, and I hope this will help you to learn from examples, or my cases.
This will embed some code snippets, but you can safely ignore them. They’re only to draw or calculate some numbers.
I’ve learned many learning methodologies, techniques and underlying researches in the class. Now, I’ll use them to analyze my past 3000 days’ learning trials. They are related to the topics:
• Teamwork
• Practice, Illusion of competence of learning
• Process, not Product
• Repeat in spaced manner, to form chunks
• Action: Journaling, Pomodoro
## My Trials
I finished mandatory military service at 2006. Since then, I’ve been trying various things. Some are for work, and some not.
I collected somewhat big learning trials for almost 8 years, approximately 3000 days.
Sorry for the big drawing. You can see the full picture at flickr page. I’ll list them up here in plaintext:
In [5]:
for trial in Trials:
print('%-30s\t%s ~ %s' % (trial['name'], trial['start'], trial['end']))
Study Ruby 2006-1 ~ 2008-1
Study Japanese 2006-2 ~ 2007-2
Study RoR 2007-1 ~ 2008-1
Study Python 2008-2 ~ 2014-2
Study Erlang 2010-1 ~ 2010-2
Korean brush painting 2010-1 ~ 2010-2
Study basic statistics 2011-1 ~ 2011-2
Writing journal 2011-2 ~ 2014-2
Using pomodoro 2013-2 ~ 2014-2
Korean traditional archery 2014-1 ~ 2014-2
Study Dot Language 2014-2 ~ 2014-2
SICP 2008-1 ~ 2011-1
HTDP 2011-1 ~ 2012-1
Aosabook 2012-1 ~ 2012-2
JMBook 2012-2 ~ 2013-2
MMIX 2013-2 ~ 2014-1
IPSC 2014-1 ~ 2014-2
PCI 2014-1 ~ 2014-2
MIA 2014-2 ~ 2014-2
Murphy 2014-2 ~ 2014-2
Coursera ML 2013-2 ~ 2014-1
Coursera compdata 2014-1 ~ 2014-2
Coursera ModelThinking 2014-1 ~ 2014-2
Coursera getdata 2014-2 ~ 2014-2
Coursera learning 2014-2 ~ 2014-2
Following number 1 or 2 means, first half or second half of the year. For example, 2006-1 means second half of the year 2006.
## Trial features
For each trial, I assigned simple meta information. Meta info has 5 categories, each has boolean(True/False) value.
1. Teamed: With team or not?
2. Practiced: Did practice in extra time?
3. Regular: Was it regular?
4. Paid: Was it paid course?
5. Success: Successful?
This is the complete table:
In [6]:
pd.DataFrame(M, columns=names, index=[x['name'] for x in Trials])
Out[6]:
teamed practiced regular paid success
Study Ruby False False False False False
Study Japanese False True True True True
Study RoR False False False True False
Study Python False True False True True
Study Erlang False False False False False
Korean brush painting True True True True False
Study basic statistics False False False False False
Writing journal False False False False True
Driver license True False True True True
Using pomodoro False False True False True
Korean traditional archery False True True True True
Study Dot Language False True False False True
SICP True True True False True
HTDP True True True False True
Aosabook True True True False True
JMBook True True True False True
MMIX True False True False False
IPSC True False True False True
PCI True True True False True
MIA True True True False True
Murphy True False True False False
Coursera ML False True True False True
Coursera compdata True True True True True
Coursera ModelThinking True False True True True
Coursera getdata True True True True True
Coursera learning True False True True True
In the course, I’ve learned:
• Learn with team, it works better
• Practice makes permanent
• Spaced repetition is important
I have teamed, practiced and regular features on each trials. Are they related to the results? I also have paid info, which is not covered in the course. But I feel it has affected my learning. How much? Let’s calculate conditional probabilities and correlation coefficients for each columns.
In [7]:
for name in names[:-1]:
pp, pn, np, nn = 0, 0, 0, 0
for n, r in zip(X[name], X['success']):
if n==1 and r==1:
pp += 1
elif n==1 and r==-1:
pn += 1
elif n==-1 and r==1:
np += 1
else:
nn += 1
print 'p(success | %s) = %.3f' % (name, float(pp)/(pp+pn))
print 'p(success) = %.3f' % (float(pp+np)/(pp+pn+np+nn))
p(success | teamed) = 0.800
p(success | practiced) = 0.929
p(success | regular) = 0.842
p(success | paid) = 0.900
p(success) = 0.769
In [8]:
from sklearn.metrics import matthews_corrcoef
for name in names[:-1]:
print('Matthew correlation coefficient between %s and success: %.3f' % (name, matthews_corrcoef(X[name], X['success'])))
Matthew correlation coefficient between teamed and success: 0.085
Matthew correlation coefficient between practiced and success: 0.408
Matthew correlation coefficient between regular and success: 0.285
Matthew correlation coefficient between paid and success: 0.245
Actually, each columns are not independent, but I’ll ignore it. (Wrong, but not TOO wrong, I guess.)
Base success ratio is about 0.77, and each condition increases the success probabilty a litte bit. It becomes much clearer when calculate matthew correlation coefficients. All 4 features have positive relations, although their strengths vary.
We cannot say it has causality, but at least there must be correlations. And, among those four, practicing was the most important factor for me.
## Habits
Among 26 items in the list, there are two special trials.
1. Writing journal
2. Using Pomodoro
These are not direct learning challenge, but a meta-learning try: creating habits. I can say, these two habits creations are successful, because I’ve been writing journals and using pomodoro techniques for more than a year comfortably. This is more detail how I did.
In the course, pomodoro technique is introduced as a tool to tackle procrastination problem. But my reason to adapt pomodoro is to use pomodoro as a unit of works. In other words, it’s the concept of Process oriented, not product.
• Journal (In Evernote)
• Write down next week’s major goals on Sunday night, before sleep
• Every morning, I declare the things to do
• Every night before sleep, I wrote retrospection on the day
• Pomodoro
• When write down todo list, set a goal of pomodoros. (Example: Study on Coursera for 4 pomodoros, Read books for 6 pomodoros)
• In the end of the week, check the number of pomodoros and adjust the number of pomodoro for the next week.
Shortly, the chart looks:
After journaling, I did more and more succeeded.
Is is true? I split the whole period into 3 segments and calculate the average number of learning activities(activities per halfyear) and success ratio. Intuitively, Learning activities times success ratio seems a reasonable score value, so I calculcated it also.
Out[9]:
Before_journaling After_journaling,before_pomodoro After_pomodoro LearningActivities 0.7500 0.8000 4.3333 SuccessRatio 0.5556 1.0000 0.8462 Score 0.4167 0.8000 3.6667
Let’s interpret the table.
• Writing journal: It increased success ratio.
• Using pomodoro: It increased the number of learning activities.
I concluded that: Both Journal and Pomodoro boost my overall learning efficiency.
## Teams
I grouped some learning activities in the chart. There are 3 groups. I’ll explain them briefly.
#### TSG
At first, it was “SICP Study Group”. After almost 4 years of SICP Problem Solving(code, personalwiki), we decided to continue the group as Tuesday Study Group. The main purpose is to spend hours together regulary.
#### MLDSS
Machine learning and Data Science Study group. Most members are(or were) SNUCSE students. One core man started the group, and currently in Season 3, reading “Machine Learning: A Probabilistic Perspective”. Nowaday, I have troubles in following the study. The book seems a little bit difficult for me. So I’m trying to find a way to overcome this hardship in the course materials.
#### Coursera
In the company, there are several people to keep learning something. Mainly we’ve been taking coursera classes. It’s like a game to collect certificates. ;-)
I already stated that, With team, learning results better above. Actually, these 3 groups’s results are much better than the total average. Ok, team works. Now, I’m saying about How to maintain the team. Before the course, I had a little bit vague ideas in my mind. While watching the class videos, I realized that,
Process, not product
This concept can be applied to team creation and maintenance.
The Team, especially if the team is for learning, must focus on process, not product. Of course, it is good to have concrete output from learning activities. But if the study group start to focus on generating output - Presentation, Code, Seminar, Finish materials in limited time … -, members are getting stressful. Product is automagically generated as long as study group keeps going on.
In a single task, process oriented goal is preferred because we can start it with easy mind. For instance, Spend 2 pomodoros on physic homework is better than Finish physics homework. This simple policy greatly works on study group. Spend every tuesday evening on solving SICP problems is (usually) better than Finish solving problems in SICP Chapter 2 until next month.
If output is considered more important, questions are skipped. Sometimes, members feel guilty to give easy questions. But they shouldn’t. If all the other know the correct and rich answers for these easy questions, they don’t need the study group. Teaching is (one of) the best learning skill.
So, in my opinion, the team should focus on the learning process, not the product of learning, for long-run.
## Why So Many Failures in Programming?
My major is Computer Science and Engineering and I’ve been a professional programmer since 2006. However, you can see many(more than avg) failures in learning programming languages. Why so many, especially programming languages? It’s my field!
While watching the video, I catched the term, Illustions of competence of learning. Immediately, I understand why I failed so many in my field.
#### I Failed because I was experienced.
I learned new programming languages, frameworks or platforms quickly at first, because I had similar experience and knowledge in my brain. And I began to think, “I understand it. I know it enough for now”. I stopped to code, read and study and feel satisfied. That was a TRAP. Actually, at that time the knowledge and understanding were only in my working memory and NOT CONSOLIDATED YET. Because I stopped further practice, the longterm memory cannot have newly learned materials. This is typical working example of Illusions of competence of learning.
In real learning, the first understanding is just a small bit. Especially about the programming language, you must be able to write the code in the language if you learned it correctly. Understanding the syntax is nothing. Repetitive practice(=Coding) must be followed after understanding to master new languages, in spaced duration.
All successfull learning challenges involved continuous practice sessions, even though it’s not intended.
From now on, I’ll challenge to learn a new programming language(rust) with carefully scheduled repeating coding sessions.
## Conclusion
I already listed some topic in the overview. (Repeat!)
• Study together, it works.
• Focus on process. Also, I think it can be applied to team activities.
• Practice is not optional. It is the key to mastering anything.
• My learning efficiency increased a lot by writing journal and using pomodoro. I hope you also try!
The course doesn’t cover the effect of paid learning. In my case, it results better. ;-) | 2023-03-29 06:48:23 | {"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": 0.24310876429080963, "perplexity": 4829.970912448305}, "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/1679296948951.4/warc/CC-MAIN-20230329054547-20230329084547-00726.warc.gz"} |
https://jpmccarthymaths.com/ | ## Assignment 1
Assignment 1 has a hand-in time and date of 12:00 Friday 1 March (Week 5). Submit in class or to A283.
Read the P.51 and P.52 instructions carefully. You will be submitting an Excel file, and written work, including a print out of your Excel work.
Note in particular:
• Work submitted after the deadline will be assigned a mark of ZERO. Hand up whatever you have on time.
• Only Partial Pivoting has to be done using Excel.
• Note that if you are doing Gaussian Elimination by hand you must use exact fractions and square roots rather a decimal approximation.
• I advise that you do the questions out roughly first because small mistakes are inevitable.
The files you need to complete this assignment have been emailed to you. If you don’t want to calculate your $c_i$ and $P$ they are calculated in MATH7021A1 – Student Data.
We have now covered enough in class for you to do all of the Assignment. I recommend that you start ASAP.
WARNING!
This gives a good opportunity for collaboration but remember collaboration does not mean one student solving the problem and everyone else copying that student’s work. I demand originality of presentation here and you should at least understand what you hand up. If you are unsure of what I mean by this please email me immediately as if I have students who have clearly copied the answer word-for-word from another student they will all be sharing the marks.
Start early so you have enough time to complete the assignment properly and get good learning from it.
THIS IS A LEARNING ACTIVITY NOT JUST A GRADED ACTIVITY. THE CHAPTER ONE EXAM QUESTION IS WORTH 24.5% OF YOUR FINAL GRADE WHILE THIS ASSIGNMENT IS WORTH JUST 15%. THINK ABOUT WHAT THIS MEANS.
Regarding Q. 1.3.5, Assignment 1, on P.62 of the manual. The intention with Q. 1.3.5 (b) really is for you to engage in some problem solving skills to come up with a clever way of implementing the Jacobi Method in Excel.
It should still be doable by hand but if it takes a large number of iterations to converge (to two significant figures), Excel is far more suitable.
It is possible that it could take a small number of iterations to converge to two significant figures (say two or three iterations) — which is no problem by hand — but potentially it could take more (at least six). I don’t really want people spending loads of time doing iterations by hand, so I will give 3/4 marks for part (b) if you do six iterations by hand. If you want to keep going – by hand – until convergence (to two significant figures) you can of course get the 4/4 marks – but you need to ask yourself is it worth your time to keep going for the sake of one mark (out of 60… out of 15% —- that is 0.25% of your final grade).
If it converges with fewer than six iterations then happy days for you, you can get 4/4.
If it doesn’t, you might be better off trying to come up with a way of doing the question in Excel if you really want all the marks.
You can still answer part (c) if you do six iterations and do not yet have convergence.
## Test 1
Test 1, worth 15%, takes place from 19:00 to 20:05 sharp, Tuesday 26 February in the usual lecture venue. There is a sample on P.45 of the notes to give you an idea of the length and layout only.
Almost everything in Chapter 1 is examinable. This means:
• P.23, Q.1-10
• P.32, Q.1-8 [Q.9 is too long and Q.10 is not examinable]
• P.39, Q.1-11
Additional practise questions may be found by looking at past exam papers (usually vectors are Q. 1, sometimes Q. 2).
You will want to be familiar with all the concepts in the Vector Summary, P. 41-44.
If you want questions answered you have two options:
• ask me questions via email, perhaps with a photo to show your work
• ask me questions via the comment function on this website
## Week 4
We had Concept MCQ about vectors and then we started looking at Chapter 2: Matrices. We did some examples of matrix arithmetic and looked at Matrix Inverses — “dividing” for Matrices. This will allow us to solve matrix equations. Here find a note that answers the question: why do we multiply matrices like we do?
## VBA Assessment 1
VBA Assessment 1 will take place in Week 6 (5 & 8 March) in your usual lab time. You will not be allowed any resources – but the library of code (p.148) and these formulae will appear on the assessment:
The following is the proposed layout of the assessment:
### Q. 1: Numerical Solution of Initial Value Problem [80%]
Examples of initial value problems that might be arise include:
• Damping
$\displaystyle \frac{dv}{dt}=-\frac{\lambda}{m}v(t)$; $v(0)=u$
• The motion of a free-falling body subject to quadratic drag:
$\displaystyle \frac{dv}{dt}=g-\frac{c}{m}v(t)^2$; $v(0)=u$
• Newton Cooling
$\displaystyle \frac{d\theta}{dt}=-k\cdot (\theta(t)-\theta_R)$; $\theta(0)=\theta_0$
• The charge on a capacitor
$\displaystyle \frac{dq}{dt}=\frac{E}{R}-\frac{1}{RC}q(t)$; $q(0)=0$
Students have a choice of how to answer this problem:
• The full, 80 Marks are going for a VBA Heun’s Method implementation (like Lab 3).
• An Euler Method implementation (like Lab 2), gets a maximum of 60 Marks.
You will be asked to write a program that takes as input all the problem parameters, perhaps some initial conditions, a step-size, and a final time, and implements Heun’s Method (or possibly Euler’s Method): similar to Exercise 1 on p. 122 (except possibly implementing Heun’s Method) and also Exercise 1 on p.128 (except without the “conditional” derivative).
If you can write programs for each of the four initial value problems above you will be in absolutely great shape for this assessment.
### Q. 2: Using your Program [20%]
You will then be asked to use your program to answer a number of questions about your model. For example, assuming Heun’s Method is used, consider the initial value problem (3.7) on p. 119.
1. Given, $v_0=0.2$, $m=3$, $\lambda=1.5$, $h=0.01$, approximate $v(0.3)$.
2. Given, $v_0=0.4$, $m=30$, $\lambda=1.5$, $h=0.1$, investigate the behaviour of $v(t)$ for large $t$.
3. Given $v_0=0.2$, $m=0.1$, $\lambda=1.5$, $h=0.5$, $T=10$, run the Heun program. Comment on the behaviour of $v(t)$. Run the same program except with $h=0.05$. Comment on the behaviour of $v(t)$.
4. Given, $v_0=0$, $m=3$, $\lambda=1.5$, $h=0.1$, $T=2$, run the Heun program. Comment on the behaviour of $v(t)$.
## Week 4
We finished off a Three Term Taylor Method example and spoke again about Heun’s Method.
We also introduced second order differential equations and saw how to attack them numerically. In particular we looked at a real pendulum.
In VBA we worked on Lab 3. Those of us who did not finish the lab are advised to finish it outside class time, and are free to email me on their work if they are unsure if they are correct or not.
## Week 5
In the morning class we will finish looking at second order differential equations.
In the afternoon we will begin a quick study of Runge-Kutta Methods.
In VBA we have MCQ III and look at Lab 4, on Second Order Differential Equations.
## Assessment
The following is a proposed assessment schedule:
1. Week 6, 20% First VBA Assessment, Based (roughly) on Weeks 1-4
2. Week 7, 20 % In-Class Written Test, Based (roughly) on Weeks 1-5
3. Week 11, 20% Second VBA Assessment, Based (roughly) on Weeks 6-9
4. Week 12, 40% Written Assessment(s), Based on Weeks 1-11
## Study
Study should consist of
• doing exercises from the notes
• completing VBA exercises
## Ungraded Concept MCQ League Table
To add a bit of interest to the Ungraded Concept MCQs, I will keep a league table.
Unless you are excelling, you are identified by the last five digits of your student number. AW is the number of attendance warnings received.
## Assignment 1
Assignment 1 has a hand-in time and date of 12:00 Friday 1 March (Week 5).
Read the P.51 and P.52 instructions carefully. You will be submitting an Excel file, and written work, including a print out of your Excel work.
Note in particular:
• Work submitted after the deadline will be assigned a mark of ZERO. Hand up whatever you have on time.
• Only Partial Pivoting has to be done using Excel.
• Note that if you are doing Gaussian Elimination by hand you must use exact fractions and square roots rather a decimal approximation.
• I advise that you do the questions out roughly first because small mistakes are inevitable.
The files you need to complete this assignment have been emailed to you. If you don’t want to calculate your $c_i$ and $P$ they are calculated in MATH7021A1 – Student Data.
We have now covered enough in class for you to do all of the Assignment. I recommend that you start ASAP.
WARNING!
This gives a good opportunity for collaboration but remember collaboration does not mean one student solving the problem and everyone else copying that student’s work. I demand originality of presentation here and you should at least understand what you hand up. If you are unsure of what I mean by this please email me immediately as if I have students who have clearly copied the answer word-for-word from another student they will all be sharing the marks.
Start early so you have enough time to complete the assignment properly and get good learning from it.
THIS IS A LEARNING ACTIVITY NOT JUST A GRADED ACTIVITY. THE CHAPTER ONE EXAM QUESTION IS WORTH 24.5% OF YOUR FINAL GRADE WHILE THIS ASSIGNMENT IS WORTH JUST 15%. THINK ABOUT WHAT THIS MEANS.
## Week 3
On Monday, we looked at applications to temperature distribution, where the Jacobi Method is used to find approximate solutions to a diagonally dominant linear system. We also had about ten minutes of tutorial time with this.
On Wednesday we showed the following video, which shows how the approximations to the solution iterate:
## Test 1
Test 1, worth 15%, takes place from 19:00 to 20:05 sharp, Tuesday 26 February in the usual lecture venue. There is a sample on P.45 of the notes to give you an idea of the length and layout only.
Almost everything in Chapter 1 is examinable. This means:
• P.23, Q.1-10
• P.32, Q.1-8 [Q.9 is too long and Q.10 is not examinable]
• P.39, Q.1-11
Additional practise questions may be found by looking at past exam papers (usually vectors are Q. 1, sometimes Q. 2).
You will want to be familiar with all the concepts in the Vector Summary, P. 41-44.
If you want questions answered you have three options:
• hand me up written work next week, which I will correct, scan, and email back to you
• ask me questions via email, perhaps with a photo to show your work
• ask me questions via the comment function on this website
## Week 3
We start working with the cross product and looked at the applications of vectors to work and moments.
We had no tutorial time but have some active learning time with a Concept MCQ: Vector or Scalar?
## Week 3
We backtracked a little and found the Maclaurin Series
$\displaystyle \ln(\sec x)\approx \frac{1}{2}x^2+\frac{1}{12}x^4$.
We then did some further study on the Euler Method. The global error with the Euler Method is $\mathcal{O}(h)$ and we need to reduce this by coming up with a better method or adjusting the Euler Method.
We looked at the Three Term Taylor Method as a better method. To employ the Three Term Taylor Method we need implicit differentiation, which means more pen-and-paper work.
We could avoid implicit differentiation by looking at Huen’s Method, which is an adjustment of Euler’s Method in that it uses lines.
In VBA we finished off the Euler Method Lab 2 and looked at P. 122, Exercise 1. The first group also started P. 123, Exercise 2, but the later groups instead used the time for some theory revision.
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
## Assignment 1
Assignment 1 has a hand-in time and date of 12:00 Friday 1 March (Week 5).
Read the P.51 and P.52 instructions carefully. You will be submitting an Excel file, and written work (including a print out of your Excel work).
Note in particular:
• Work submitted after the deadline will be assigned a mark of ZERO. Hand up whatever you have on time.
• Only Partial Pivoting has to be done using Excel.
• Note that if you are doing Gaussian Elimination by hand you must use exact fractions and square roots rather a decimal approximation.
• I advise that you do the questions out roughly rst because small mistakes are inevitable.
The files you need to complete this assignment have been emailed to you. If you don’t want to calculate your $c_i$ and $P$ they are calculated in MATH7021A1 – Student Data.
We have now covered enough in class for you to do all of the Assignment except for Q. 1.3.5. After Monday we will have enough covered in class.
WARNING!
This gives a good opportunity for collaboration but remember collaboration does not mean one student solving the problem and everyone else copying that student’s work. I demand originality of presentation here and you should at least understand what you hand up. If you are unsure of what I mean by this please email me immediately as if I have students who have clearly copied the answer word-for-word from another student they will all be sharing the marks.
Start early so you have enough time to complete the assignment properly and get good learning from it.
THIS IS A LEARNING ACTIVITY NOT JUST A GRADED ACTIVITY. THE CHAPTER ONE EXAM QUESTION IS WORTH 24.5% OF YOUR FINAL GRADE WHILE THIS ASSIGNMENT IS WORTH JUST 15%. THINK ABOUT WHAT THIS MEANS.
## Week 2
We started Monday with some Gaussian Elimination Concept MCQs. We probably should have waited until we finished the Gaussian Elimination examples, which we did straight afterwards.
Wednesday am we had some tutorial time — and then Wednesday pm began to look at applications of linear systems to traffic and pipe flow.
On Thursday we finished the section on pipe flow and had a little more tutorial time.
## Week 3
On Monday, we will look at applications to temperature distribution, where the Jacobi Method is used to find approximate solutions to a diagonally dominant linear system.
Wednesday am we will finish looking at Chapter 1, and hopefully have another Concept MCQ. Wednesday pm we will have more tutorial time (and do the Concept MCQ if necessary).
On Thursday we will start work on Chapter 2 — the method of undetermined coefficients for solving linear odes.
## Study
Please feel free to ask me questions about the exercises via email or even better on this webpage.
## Exam Papers
These are not always found in your programme selection — most of the time you will have to look here.
## Student Resources
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
If you are a little worried about your maths this semester, perhaps after the Quick Test or in general, I would just like to remind you about the Academic Learning Centre. Most students received slips detailing areas of maths that they should brush up on. The timetable is here: there is some availability after 16:00 on Mondays and Tuesdays.
## Week 2
We finished the dot product examples.
Then we had extensive tutorial time in which we worked on:
• P.23, Q.1-10
• P.45, Sample Test, Q. 1, 2, 4
• P. 203, Winter 2018, Q. 1 (a), (b)
Then we started talking about the cross product.
## Homework Exercises
If you do any of the suggested exercises you can give them to me for correction. Please feel free to ask me questions about the exercises via email or even better on this webpage.
• P.23, Q.1-10
• P.45, Sample Test, Q. 1, 2, 4
• P. 203, Winter 2018, Q. 1 (a), (b)
• I also handed out an older exam paper: you might be able to do some of Q. 1 (a).
## Week 3
We will start working with the cross product and begin to look at the applications of vectors to work and moments. There will be no tutorial time.
## Test 1
If we finish the Vectors chapter the test will be in Week 5: otherwise we will push this out to Week 6. Official notice will be given in Week 3 (or Week 4 if necessary). There is a sample test in the notes.
## CIT Mathematics Exam Papers
These are not always found in your programme selection — most of the time you will have to look here.
## Student Resources
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
## Week 2
We developed the Euler Method for approximating the solution of differential equations. As we will need Taylor Series to analyse the error in this approximation — and improve Euler’s Method — we started looking at that. We kind of rushed it, but we used it to analyse the Euler Method.
In VBA we started programming the Euler Method to solve the problem of a damper. We did MCQ 1.
I am emailing a link of this to everyone on the class list every week. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.com and I will add you to the mailing list.
## Timetable
The Geotech Tutorial Groups are determined by whether or not you are taking MATH7021.
If you are taking MATH7021 your Geotech tutorial is Wednesday 12:00 and you attend the 14:00 MATH7021 class in A243L.
## Week 1
We started the first chapter on Linear Algebra. Essentially, for us, simultaneous equations. We looked at Gaussian Elimination including Partial Pivoting, which is required in the presence of rounding. We were a little disrupted by snow on Wednesday, effectively costing us 0.5 – 1 hours.
## Week 2
We will finish the Gaussian Elimination examples on Monday — then have some tutorial time — and then Wednesday pm begin to look at applications of linear systems to traffic and pipe flow.
## Assignment 1 – Warning
Assignment 1 has a hand-in date of Friday 1 March (Week 5). More information next week.
## Study
Please feel free to ask me questions about the exercises via email or even better on this webpage.
## CIT Mathematics Exam Papers
These are not always found in your programme selection — most of the time you will have to look here. | 2019-02-24 02:16:51 | {"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": 41, "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": 0.30962756276130676, "perplexity": 1281.2743533348216}, "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-2019-09/segments/1550249569386.95/warc/CC-MAIN-20190224003630-20190224025630-00398.warc.gz"} |
https://mc-stan.org/docs/2_18/reference-manual/increment-log-prob-section.html | This is an old version, view current version.
## 7.3 Increment Log Density
The basis of Stan’s execution is the evaluation of a log probability function (specifically, a probability density function) for a given set of (real-valued) parameters; this function returns the log density of the posterior up to an additive constant. Data and transformed data are fixed before the log density is evaluated. The total log probability is initialized to zero. Next, any log Jacobian adjustments accrued by the variable constraints are added to the log density (the Jacobian adjustment may be skipped for optimization). Sampling and log probability increment statements may add to the log density in the model block. A log probability increment statement directly increments the log density with the value of an expression as follows.6
target += -0.5 * y * y;
The keyword target here is actually not a variable, and may not be accessed as such (though see below on how to access the value of target through a special function).
In this example, the unnormalized log probability of a unit normal variable $$y$$ is added to the total log probability. In the general case, the argument can be any expression.7
An entire Stan model can be implemented this way. For instance, the following model will draw a single variable according to a unit normal probability.
parameters {
real y;
}
model {
target += -0.5 * y * y;
}
This model defines a log probability function
$\log p(y) = - \, \frac{y^2}{2} - \log Z$
where $$Z$$ is a normalizing constant that does not depend on $$y$$. The constant $$Z$$ is conventionally written this way because on the linear scale, $p(y) = \frac{1}{Z} \exp\left(-\frac{y^2}{2}\right).$ which is typically written without reference to $$Z$$ as $p(y) \propto \exp\left(-\frac{y^2}{2}\right).$
Stan only requires models to be defined up to a constant that does not depend on the parameters. This is convenient because often the normalizing constant $$Z$$ is either time-consuming to compute or intractable to evaluate.
#### Relation to compound addition and assignment
The increment log density statement looks syntactically like compound addition and assignment (see the compound arithmetic/assignment section, it is treated as a primitive statement because target is not itself a variable. So, even though
target += lp;
is a legal statement, the corresponding long form is not legal.
target = target + lp; // BAD, target is not a variable
#### Vectorization
The target += ... statement accepts an argument in place of ... for any expression type, including integers, reals, vectors, row vectors, matrices, and arrays of any dimensionality, including arrays of vectors and matrices. For container arguments, their sum will be added to the total log density.
### Accessing the Log Density
To access accumulated log density up to the current execution point, the function target()() may be used.
1. The current notation replaces two previous versions. Originally, a variable lp__ was directly exposed and manipulated; this is no longer allowed. The original statement syntax for target += u was increment_log_prob(u), but this form has been deprecated and will be removed in Stan 3.
2. Writing this model with the expression -0.5 * y * y is more efficient than with the equivalent expression y * y / -2 because multiplication is more efficient than division; in both cases, the negation is rolled into the numeric literal (-0.5 and -2). Writing square(y) instead of y * y would be even more efficient because the derivatives can be precomputed, reducing the memory and number of operations required for automatic differentiation. | 2021-10-22 15:59:31 | {"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": 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": 0.6167044043540955, "perplexity": 934.9129257031046}, "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/1634323585516.51/warc/CC-MAIN-20211022145907-20211022175907-00089.warc.gz"} |
https://www.bankruptcyblogcontent.com/vmdydbi/sunrise-direction-in-summer-and-winter.html | Really cool map! Sunrise and sunset times in Sunrise, December 2022 To find true-east more accurately in summer and winter, you'll have to adjust your direction slightly. This is the one other day of the year when you can see the sunrise due east and the sunset due west. Rays of sunlight strike the globe perpendicularly at 23.5 N latitude, the Tropic of Cancer, at noon on the summer solstice. Around September 21, the sun has made its way back to the equator moving south. Minare soon becomes a late-night talk show host under Matou's direction, covering amusing narratives set in Sapporo, all while balancing her day job and personal life to make ends meet. According to this table, at latitude 30 degrees (North or South) the sun will rise and set 27 degrees away from due east and due west on both solstices, the dates of maximum amplitude. Note (Oct 2018): I'm aware of the broken map (see this article for more context). SunCalc is a little app that shows sun movement and sunlight phases during the given day at the given location.. You can see sun positions at sunrise, specified time and sunset.The thin orange curve is the current sun trajectory, and the yellow area around is … Winter w.vuyk where I come from, sunrise in the winter is much darker than sunrise in the summer. Directions of sunsets and sunrises at the solstices The answer is that the degree of the sun’s movement along the horizon depends on two things: 1) the time of year. Winter From 35° S latitude, the winter Sun would rise at $\theta=119$ from If you watch sunrise and sunset locations over a year, you will also note that the location of where the Sun rises and sets changes. sunrise turkey weather in january 2021 Sunrise and sunset times in Honolulu - Time and Date The winter solstice is the shortest day and longest night of … Sun direction vest you calculate sun orientation in Sydney throughout the day, optimize your orientation and sun exposure and get orientation in summer, winter and more. Sun path refers to the daily and seasonal arc-like path that the Sun appears to follow across the sky as the Earth rotates and orbits the Sun. The Sun always rises in the east. The only complaint I have is the "<14:30" and ">10:30". + 18morecheap eatsraw for you, avantgardino express, and more; difference between mandibular first and second premolar; moishes catering menu; water park zombies release date Relatively high in the north the days in summer are long and short in winter. Longer and thinner lines mean the sun is closer to the horizon. Winter Solstice. Click on the map or search to choose a new location. Polar nights are long, but they get shorter as you go farther north. The mix of time zones, seasonal clock changes, and earthly incline all make this a very complex and beautiful picture. You must turn to the north. Having never act to Australia or rack the equator, I have … You must turn to the north. In the summer, it will be somewhat north of east, and in the winter somewhat SOUTH of east, but the … As we orbit the Sun, the rising and setting points are further north in the summer and further south in the winter. In the Northern Hemisphere, where it is the year's longest day in terms of daylight, the June solstice is also called the summer solstice. With her energetic voice, she delivers a smooth dialogue with no hesitation, which Matou recognizes as raw talent. Hint; The first set of azimuth/altitude data represents sunrise. The horizontal line signifies the horizon, the vertical lines … Longer and thinner lines mean the sun is closer to the horizon. In the Northern Hemisphere, in summer, the sun will rise and set north of 90/270, and in the winter it rises and sets south of 90/270. This results in many hours of daylight, and summer. The Summer Solstice is the longest day of the year and gets longer as you go further north. The sun rising in extreme northeast and setting in the extreme northwest is observed during the summer solstice. Most people, I suppose, think the sun rises in the east and sets in the west. Answer (1 of 6): Sun rises in the east and sets in the west. 1. You don’t get a ray of daylight on the winter solstice until you get north of the Antarctic Circle. The solar day over the course of the Winter of 2020. (40.8°) 91.409. In fact, the word solstice means 'standstill of the Sun'. Enjoy ! 2) Duration of Daylight – state the time at which the sun rises, and sets for each of the given days. Sun Direction : direction of the sun throughout the day. The time and direction of sunset, noon, and sunrise for any location. Beauty of a Winter Sunrise . Accurate location-specific knowledge of sun path and climatic conditions is essential for economic decisions about solar collector area, orientation, landscaping, summer shading, and the cost-effective use of solar trackers. It’s known as the Autumnal Equinox. If you don't have a compass or can't visit the property, street maps, council geo-search websites, and Google Maps are all displayed with North up; use this to orientate yourself & work out when and how sun will come into a house. The … For an observer in the Northern hemisphere, this means that in summer, the sun rises in the northeast and sets in the northwest, while in winter, it rises in the southeast and sets in the southwest. Likewise is the difference in direction of sunrise and sunset. Use these numbers to determine the duration of sunlight on each day. The sun's position will be on the far side of the equator for the autumn and winter months, and on the close side in the spring and summer. Around September 21, the sun has made its way back to the equator moving south. Around September 21, the sun has made its way back to the equator moving south. This is the one other day of the year when you can see the sunrise due east and the sunset due west. * All times are local time for Sunrise. 2. Times for sunrise and sunset in the Philippines won’t differ much all over the year. On the model, summer solstice is represented by the longest cord. Vicki, the Sun’s position on the horizon at sunrise is furthest north on the winter solstice (62-degrees of azimuth as measured from due North, or 28-degrees north of due East) and furthest south on the summer solstice (at 119-degrees of azimuth or 29-degrees south of due East). Winter is the coldest season of the year in polar and temperate zones.It occurs between autumn and spring.The tilt of Earth's axis causes seasons; winter occurs when a hemisphere is oriented away from the Sun.Different cultures define different dates as the start of winter, and some use a definition based on weather. In the Northern Hemisphere, in summer, the sun will rise and set north of 90/270, and in the winter it rises and sets south of 90/270. The reason is the only fair proximity to the equator. Only on the equinoxes (Sept/Mar 21st) does the Sunrise/set at due East/West. The Solstices (Summer & Winter) The summer solstice occurs at the moment the earth's tilt toward from the sun is at a maximum. Vicki, the Sun’s position on the horizon at sunrise is furthest north on the winter solstice (62-degrees of azimuth as measured from due North, or 28-degrees north of due East) and furthest south on the summer solstice (at 119-degrees of azimuth or 29-degrees south of due East). The motion of the sun is symmetric across the horizon, so these values are the same on a given day. However, because the Earth is inclined at an angle (23.5 degrees), its poles tilt towards or away from the sun depending on the time of year. For an observer in the Northern hemisphere, this means that in summer, the sun rises in the northeast and sets in the northwest, while in winter, it rises in the southeast and sets in the southwest. Now the situation in Tucson on the summer solstice compared to the equinoxes. On a standard meridian at the equator one might expect the Sun to rise at 6:00 A.M. and set at 6:00 P.M., but the Sun rises at 6:03 A.M. in July, a summer month, and also rises late, at 6:11 A.M. in February, a winter month. The angle of the Earth’s axis means that sunrise is later in the southern hemisphere in June, and sunset’s earlier. In the Southern Hemisphere, on the other hand, it is the shortest day of the year and is known as the winter solstice. The lines on the drawing show the direction and height (altitude) of the sun throughout the day. Thus, the Sun will rise north of true East and set north of true West during summer whereas during winter, the Sun will rise south of true East and set south of true West. Lastly, December 21 brings the winter solstice which is popularly known as “the shortest day of the year.” If the sun rises 20° south of east, it will set 20° south of west. The answer is: at all latitudes of the earth between the polar circles (it means between 66° 33’ N and 66° 33’ S of Latitude) the line indicating the direction of the sunrise at summer begin is the same as the sunset at winter begin, in opposite side. On summer solstice, the Sun rises as far northeast as it ever gets, and sets as far northwest as it gets. Like a pendulum, the sunrise direction changes from NE @ summer solstice to SE @ winter solstice, and back to NE, completing one full swing back and forth, or one full cycle, each year. What time does the sunrise in summer in England? So in summer the sun moves slightly to the north and in the winter slightly back to south, but without much change in the distance. It rises seven minutes before 6:00 A.M. in mid-May, and 20 minutes before 6:00 A.M. at the end of October. It can help you track the sun in your yard to choose optimal planting locations for your plants depending on what kind of light they need. Thicker and shorter lines mean the sun is higher in the sky. declination ranges between approximately +23.5 and -23.5 degrees for the Sun during 6 months (southern hemisphere winter to summer) and then from -23.5 to +23.5 during the next 6 months. On the day of the summer or winter solstice, the sun rises and sets at its most northern or southern location. The colors of a sunrise or sunset are based on how light is entering and traveling through the atmosphere. The passage tomb at Newgrange in Ireland may be the most impressive winter solstice monument on Earth. Today’s and tonight’s Fort Wayne, IN weather forecast, weather conditions and Doppler radar from The Weather Channel and Weather.com Also like a pendulum, there is a stopping or 'standstill' at the extremes, or solstices. Rays of sunlight strike the globe perpendicularly at 23.5 N latitude, the Tropic of Cancer, at noon on the summer solstice. Notice also how much higher in the sky the sun appears in summer than in winter - approximately 47° higher - which is double the angle of the tilt. Sunrise and sunset in Sweden. This year it falls on Monday, June 21 – when the UK will enjoy 16 hours and 38 minutes of daylight. And the same for sunset in the winter is much darker earlier than sunset in the winter. What direction the sun rise? In fact, the word solstice means 'standstill of the Sun'. Summer & Winter Solstice. You can display here the sun direction and the sunny hours in Sydney (Australia. Sunrise at equinox at latitude 37 degrees facing due east SunCalc is a little app that shows sun movement and sunlight phases during the given day at the given location.. You can see sun positions at sunrise, specified time and sunset.The thin orange curve is the current sun trajectory, and the yellow area around is … So its ‘swing’ is 57-degrees. At the summer solstice, the Sun rises as far to the northeast as it ever does, and sets as far to the northwest. Sunrise at equinox at latitude 37 degrees facing due east There is a time gap of around 2 hours in terms of … The time and direction of sunset, noon, and sunrise for any location. The Sun's path affects the length of daytime experienced and amount of daylight received along a certain latitude during a given season. Lastly, December 21 brings the winter solstice which is popularly known as “the shortest day of the year.” Thus, the Sun will rise north of true East and set north of true West during summer whereas during winter, the Sun will rise south of true East and set south of true West. It blows my mind that Scotland and Spain can share a sunrise time in winter, but sunset time is approximately 4 hours different. In the summer, it will be somewhat north of east, and in the winter somewhat SOUTH of east, but the direction of the sunrise is always more-or-less east. On June 21 the sun rises in the NE and sets in the NW. This is because the equinox marks the point where the sun passes the celestial equator. Every day after that, the Sun rises a tiny bit further south. How the Date Affects the Direction of Sunrise and Sunset. Note (Oct 2018): I'm aware of the broken map (see this article for more context). And it does--for two days out of the year. The precise direction of sunrise depends on your location and the date; the further south you are, the more northerly the direction of the sunrise. What is the direction of sunrise? The direction of the sunrise is east, because the Sun rises in the east and sets in the west, due to the Earth turning on it's axis. Therefore, I have to adjust the +/- times as the year goes on to adjust for the lightness and darkness of the seasons. Today is highlighted. The sun will rise at 4.52am and set at 9.26pm. Stay tuned — I'm working on a new version! The shortest day of the year is called the winter solstice. Winter Solstice. In the summer you should adjust a little to the right, and in winter a little to the left. This results in many hours of daylight, and summer. Sun Direction: ↑ 255° West: Sun Altitude: -26.3° Sun Distance: 91.408 million mi: Next Equinox: Mar 20, 2022 5:33 am (Vernal) Sunrise Today: 7:10 am ↑ … Example. The day, twilights (civil, nautical, and astronomical), and night are indicated by the color bands from yellow to … The exact location where the Sun will rise and set will vary widely depending on the place. Answer (1 of 4): “Why does the sun rise at different horizons during winter versus summer?” It has to do with the axis (tilt) of the earth in relation to the sun and where the sun is in it’s orbit around the earth. Of course, in the same way that the reverse direction of the Summer Sunrise is the Winter Sunset, the reverse of the Winter Sunrise is the Summer Sunset as shown left. Now the situation in Tucson on the summer solstice compared to the equinoxes. This is our final weekend of Summer and we will be open Thursday through Monday (Sep. 6) from 9am to 4pm.We have two bonus weekends this summer: October 1-2 and October 9-10. The difference in the length of the day between summer and winter, from here to the north, begin to be striking – slightly more than 8 hours at winter solstice, to more than 16 hours during the summer solstice. On summer solstice, the Sun rises as far northeast as it ever gets, and sets as far northwest as it gets. Sunrise and sunset in the most important cities of Sweden. The cities are ordered by their geographic position from east to west, so in an approximate direction of the sun course. Since the orbit of the sun is elliptical, sunrise or sunset never happen on a whole longitude at the same time. In winter solstice, the sun rises in farthest southeast and sets in the furthest southwest. Also like a pendulum, there is a stopping or 'standstill' at the extremes, or solstices. They take into account refraction. It shows the sun’s hourly direction intervals, its equinox, winter & summer solstice paths, sunrise sunset times, twilight times, sun shadow, the golden hour & more. The sun rises in the NE on the summer solstice and sets in the NW. The Sun's path affects the length of daytime experienced and amount of daylight received along a certain latitude during a given season. Therefore, on the day of the summer solstice, the sun appears at its highest elevation with a noontime position that changes very little for several days before and after the summer solstice. Like a pendulum, the sunrise direction changes from NE @ summer solstice to SE @ winter solstice, and back to NE, completing one full swing back and forth, or one full cycle, each year. First Solstice of the Year What direction does the sunrise in the Philippines? Stay tuned — I'm working on a new version! The sun’s movement along your horizon – … hgOr, kAFRCS, vwTqO, Zpcisr, WVb, kIvVLWc, xJTQh, pyviIM, KjJS, pCY, CDB,
Healthcare Definition, Northern Lights Resort Wisconsin, Xerox Workcentre 3325 Ip Address, Technoblade Axe Of Peace Enchantments, Moroccan Salmon With Couscous, Silver Birch Tree Lifespan, Easton Ea70 Ax Wheel Rear, Harvard-westlake Handbook, Granite School District Hr, American Muscle Grill, ,Sitemap,Sitemap | 2022-10-04 12:34:07 | {"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": 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": 0.2658834457397461, "perplexity": 1450.2669081606493}, "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-2022-40/segments/1664030337504.21/warc/CC-MAIN-20221004121345-20221004151345-00269.warc.gz"} |
https://www.physicsforums.com/threads/windows-vista-website.105849/page-2 | # Windows Vista Website
Anttech said:
That's unfair.. considering the first M$windows was made for IBM, and not to mention DOS How is that unfair? Name one instance where good engineering won out over good marketeering in MS history. Not one where they coincided, but where good engineering sense clearly trumped the marketers. I can't think of any. In every case MS has acted in the interests of money first, not quality. And it has made them billions upon billions. Kudos to them for that. But my statement is hardly unfair. #### Anttech Ermm it is totally unfair, you are 100% biased, and by your own admitance you know zip about M$ technologies...
The development of .NET by M$is by no means a "marketing" ploy. If you think it is then any technology done for Susi is also.. M$ also developed Dos for IBM on IBM's payrole, hardly a "marketing" ploy.
If you want more I will find more...
Just cause you dont like the OS means jack sh@t
#### franznietzsche
Anttech said:
Ermm it is totally unfair, you are 100% biased, and by your own admitance you know zip about M$technologies... Being unfamiliar with due to lack of use, is not knowing "zip about." 100% biased? Not so bad. I will admit to heavy bias, of course I'm also heavily biased in favour of General Relativity over Newtonian gravity, and in favor of quantum mechanics over classical mechanics for describing the behavoir of electrons in an atom, if being biased means I've made my judgements based on the evidence I've seen. Show me clear evidence, and I'll accept that. The development of .NET by M$ is by no means a "marketing" ploy. If you think it is then any technology done for Susi is also..
.NET was an effort to keep people using MS only products (as opposed to using Java). MS is company that believes very strongly in its monoculture, and that people shouldn't use a single piece of software not made by them, including programming languages. Its about mindshare, which comes down to marketing. If applications are written for Java, then you don't necessarily need Windows to run them (this was of course the point of a write once run anywhere language). .NET was/is an effort to prevent that.
#### Anttech
I said MS acts in the interests of money first, not quality engineering first, yes? This is a counterpoint how? How is this even relevant?
edit: And MS didn't develop DOS. Depending on who you talk to, they bought it or stole it from SCP and licensed it to IBM.
Not biased?
#### Anttech
Show me clear evidence, and I'll accept that.
MS never did anything because it was good technology, they did it because it made money for them and intel.
You made the statement not me, u back it up. I said it is unfair, and already showed you that M$worked for IBM not Intel... You have self admittedly stated you are "unfamiliar with due to lack of use," how can you possible then try and state what you did, when you know nothing about the technologies that M$ have made over the years?
Look, I am not an M$biggit, I would just prefer that you wouldnt slant arguements for the sake of a dig at M$, if you could show you knew about the technologies then fine, but you cant.. If we were talking about something that you use daily and have experience with then fine...
Anyway as I said I am not an M$Biggit, I use a varitity of Opperating systems, the one I use most and are most familure with is IOS... #### sid_galt franznietzsche said: I said MS acts in the interests of money first, not quality engineering first, yes? If MS didnt do quality enginnering, it would lose money and reputation as it is. quality engineering = making money in a free economy. I am not a fan of Microsoft but the thing is that some their products are quality engineered because they work. Windows works because it is very user friendly so it is quality engineered in that area. These days they have been lagging behind in several areas which has predictably led people to other products and reduced income for microsoft. Last edited: #### franznietzsche Anttech said: LOL... Do you even know what .net is? And you can run .NET on Linux so it isnt just for windows You're not even arguing my point now. You're just trying to come up with stuff to say. Mono is not a Microsoft project. The purpose of .NET was and remains to prevent Windows from being marginalized by a middleware API not produced by Microsoft. Anttech said: Irrelivent to this debate... GR and Microsoft windows really dont have anything in common, and by stating you are on the side of general scientific thinking, is nothing to do with wheather you know anything about M$ technology or not... Please dont try and obscure this point.
Not irrelevant. You accused me of being unfairly biased. I replied by stating that my opinion is based on the evidence I've seen.
Anttech said:
Not biased?
SCP sued MS for patent infringement. In their opinion, MS stole it. So yes, that was not a biased statement. But you, being so much more knowledgeable about MS than me, would have known that right? So i have to assume that either, you have no case, and you know it, or you don't know as much as you like to pretend.
Anttech said:
You made the statement not me, u back it up. I said it is unfair, and already showed you that M$worked for IBM not Intel... You have self admittedly stated you are "unfamiliar with due to lack of use," how can you possible then try and state what you did, when you know nothing about the technologies that M$ have made over the years?
Again you are twisting my words. Unfamiliar does not equal 'knows nothing about." But since you can't come up with anything other than that, i can understand why you keep repeating it. If it makes you feel better, I've used every version of windows in the home line since 3.1 (3.1, 95, 98, 98SE, ME, XP) as well as the more recent 'professional' ones (2000, XP Pro (not that there is a big difference between XP home and XP pro)). I've used Office 97/2000/XP. I've seen first hand what their decades of a lack of security policy has done (Word Macro that self-propagates through Email and does various nasties to your computer anyone?), and it can hardly be called 'quality.'
Look, I am not an M$biggit, I would just prefer that you wouldnt slant arguements for the sake of a dig at M$, if you could show you knew about the technologies then fine, but you cant.. If we were talking about something that you use daily and have experience with then fine...
And you can't show that you know anything about the history of MS or the development of their products. You actually thought they developed MS-DOS before they licensed it to IBM (granted, large portions of it were rewritten by 2.0).
We're not talking about their technologies, we're talking about why they've developed them. This is a discussion of motive. And quality has never been a goal in its own right for them. Quality has been something where they have consistently aimed for the lowest mark that would still make them money.
Anttech said:
Anyway as I said I am not an M$Biggit, I use a varitity of Opperating systems, the one I use most and are most familure with is IOS... Me thinks the lady doth protest too much. sid_galt said: If MS didnt do quality enginnering, it would lose money and reputation as it is. quality engineering = making money in a free economy. I am not a fan of Microsoft but the thing is that some their products are quality engineered because they work. Windows works because it is very user friendly so it is quality engineered in that area. These days they have been lagging behind in several areas which has predictably led people to other products and reduced income for microsoft. Read the findings of fact from the DOJ trial. You'll find quite a different story. Monopoly control = making money in a free economy. MS won out early on, not because their products were superior, but because they were far cheaper. CP/M was much better than QDOS/MS-DOS, but it cost$249 as opposed to $69 (IIRC). Once MS-DOS was firmly established on PCs, that was that. Then, when MS split from IBM, taking NT with them. Their popularity skyrocketed with Windows 95. Then begins the illegal monopolizing, forced upgrades, bullying of OEMs, and so on and so forth. #### sid_galt franznietzsche said: MS won out early on, not because their products were superior, but because they were far cheaper. From a user's perspective, for ordinary day to day work I find Windows easier to use than either Mac or Linux. But even if their products won out because they were cheaper, they couldn't have won out if they had built poor products. franznietzsche said: CP/M was much better than QDOS/MS-DOS, but it cost$249 as opposed to \$69 (IIRC).
Possibly. But even if CP/M was much better, you can't say that DOS was bad and not a quality product. If it served the purpose of the user and cost less than CP/M, then for the user it was a quality product.
franznietzsche said:
Then begins the illegal monopolizing, forced upgrades, bullying of OEMs, and so on and so forth.
1) Being illegal does not make it automatically wrong.
2) Forced upgrades??? What do you mean? MS didn't force anyone to upgrade their software.
3) As to the bullying of OEMs, did MS violate the patents of the OEMs? If it did, then it was wrong.
But if it didn't then that is not bullying. Whatever happened to the OEMs then was not MS's fault.
#### franznietzsche
sid_galt said:
From a user's perspective, for ordinary day to day work I find Windows easier to use than either Mac or Linux. But even if their products won out because they were cheaper, they couldn't have won out if they had built poor products.
You don't seem to understand how a free market actually works. The best marketed product, not the best product is what wins. MS has one of the world's best marketing dpmts.
Computers are not furniture. The majority of consumers do not know what poor quality software is, because they do not understand software. If a chair breaks on them, they know it was poorly made. If their computer can't run for more than a few days at a time without problems, or if they're constantly fighting to hold back malware, they think that's just how computers are, they don't realize that the software is poorly made. A poor product only hurts you if people can tell its a poor product. With computers, the average joe doesn't even know the difference between hardware and software.
Possibly. But even if CP/M was much better, you can't say that DOS was bad and not a quality product. If it served the purpose of the user and cost less than CP/M, then for the user it was a quality product.
Have you ever used DOS? As a CLI, it was abysmal when it was invented. Bash, the standard shell prompt in linux, has not changed much since 1987, when it was released. DOS-Prompt has never ever been as useful or functional (MS is just starting to try to catch up on that with MSH i.e. Monad).
1) Being illegal does not make it automatically wrong.
2) Forced upgrades??? What do you mean? MS didn't force anyone to upgrade their software.
3) As to the bullying of OEMs, did MS violate the patents of the OEMs? If it did, then it was wrong.
But if it didn't then that is not bullying. Whatever happened to the OEMs then was not MS's fault.
Do you know what OEMs are? Or did you ignore what I said about reading the Findings of Fact from the DOJ trial? OEMs are companies like Dell, Gateway, Compaq, HP, who sell computer systems. MS used punitive pricing to punish any OEMs who offered computers with anything other than Windows on them. They threatened to pull licenses to sell windows on some of them if they sold competing products. That is not only illegal, its wrong. Unless of course you want to say that's not MS's fault?
Monopolizing is illegal for a reason, it destroys the free market. That is bad.
Have you ever tried to open an Office document from a later version of Office in an older one? Forced upgrades. See my above post.
#### Anttech
Monopolizing is illegal for a reason, it destroys the free market. That is bad.
I aggree with this.
The rest of what you say is in the majority just your oppinion. I wont debate with someone who is not mature (and you arent) enough to not patronise.
#### Sprinter
anyway, microsoft does really produce good products.
easy to use, easy to update, easy to find reference books for learning.
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• Solo and co-op problem solving | 2019-10-22 18:42:01 | {"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": 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": 0.38251572847366333, "perplexity": 2469.7021486739286}, "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/1570987823061.83/warc/CC-MAIN-20191022182744-20191022210244-00239.warc.gz"} |
http://www.flyingcoloursmaths.co.uk/tactical-voting/ | # Tactical Voting
As a progressively more adamant Europhile, I was pleased to learn that the UK would take part in next month’s European Parliament elections1. As an amateur psephologist, I was delighted.
Rather glibly, I responded to someone asking whether one needed to vote tactictally in these elections by saying “no, it’s PR, vote for who you want to get in”. But then I read a tweet thread explaining that that’s not quite true: because of the way regions are arranged, it’s not always the case that all votes are equal.
### A poll
I’ve only been able to find one recent poll for the elections - perhaps unsurprisingly, since everyone was insisting they couldn’t possibly take place. Let’s make the entirely unreasonable assumption that the numbers Hanbury have reported are absolutely bang on, and see how the system would work in my region, the South West.
Hanbury has the numbers as:
LAB: 28.4%
CON: 25.5%
BRX: 16.8%
LD: 13.4%
TIG: 5.4%
(5% bar)
… and the South West elects 6 MEPs.
The D’Hondt system takes the following steps:
1. Divide each party’s vote share by one more than the number of seats so far allocated to it to get a dividend
2. Allocate the next seat to the party with the highest dividend.
3. Repeat steps 1 and 2 until you run out of seats.
In this (and pretty much every) case, we start with no seats allocated, so we divide everybody’s percentage by 1. The leading party is LAB, who take the first seat.
For the second seat, the dividends for everyone except LAB remain the same, but Labour’s dividend drops to 14.2% (putting them, for the moment, third). Since CON now has the biggest dividend (25.5%), they take the second seat.
For the third seat, the Conservative dividend drops to 12.75%, putting them temporarily in fourth. The dividends are now:
BRX (0): 16.8
LAB (1): 14.2
LD (0): 13.4
CON (1): 12.75
TIG (0): 5.4
The Brexit Party takes the third seat, and their dividend drops to 8.4% and fourth place. Labour’s dividend for the fourth seat is highest, so they take it, dropping to 9.47% (and third place). After four seats being allocated, we have:
LD (0): 13.4
CON (1): 12.75
LAB (2): 9.5
BRX (1): 8.4
TIG (0): 5.4
The penultimate seats will fall to the Liberal Democrats (dropping to 6.7%) and to the Conservatives (dropping to 8.5%). The final result would be:
LAB: 28.4% - 2 seats
CON: 25.5% - 2 seats
BRX: 16.8% - 1 seat
LD: 13.4% - 1 seat
TIG: 5.4% (5% bar)
… which looks pretty fair: Labour and the Conservatives have roughly double the support of the Brexit Party and the LibDems. Each seat, in the end, required 12.75% of the votes.
### Deeper analysis?
To think about voting tactically, it’s worth thinking about “wasted” votes. How far away was each party from winning the final seat?
To work this out, we can divide each party’s vote share by the number of seats it ‘deserved’ - how many 12.75%s go into their polling numbers?
LAB: 2.23
CON: 2.00
BRX: 1.32
LD: 1.05
TIG: 0.42
The higher the decimal part of this, the closer you are to winning an extra seat.
In raw percentage point terms, The Independent Group2 are closest to winning an extra seat: they would require an extra 7.45 points to take the final seat from the Tories. I haven’t listed the Green and UKIP, who are both on 5%; they are next in line (7.75 extra points), followed by Brexit (8.7), Labour (9.85), the Lib Dems (12.1) and the Conservatives (12.75).
You can also consider a defensive strategy, looking at how far each party is from losing a seat, by comparing how many 9.47%s go into each party’s share. (That’s the leading remaining dividend).
LAB: 3.00
CON: 2.69
BRX: 1.77
LD: 1.42
Here, the lower the decimal part, the closer you are to losing a seat. The Lib Dems are most at risk here; a drop of 4 points or so would see them lose the last seat to Labour. The Conservatives would need to drop about 6.5% to lose their second seat, and Brexit a bit more than seven points.
### How to vote tactically
Depending on how your affiliation lies, you might choose to express a preference between two parties vying for the last seat rather than voting for a party some way behind (or ahead) - in the South West, the battle is between the Lib Dems and Labour (between whom I don’t have a strong preference), and it’s hardly marginal in any case.
In Scotland, by contrast, the three major parties are split 32.2-24.3-21.7 - and the system gives them two seats apiece. The last seat became Labour’s second rather than the SNP’s third by fractions of a percent - 0.35 more points for the SNP or 0.24 less for Labour would have seen a 3-2-1 split.
Voting for the party you like best is an absolutely fine strategy for elections - but if you want to vote in a way that maximises your chances of affecting the result, it pays to study the system and - in the Euros - choose between the two parties most likely to win the final seat.
## Colin
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.
1. Apparently, this is an undemocratic thing, and the EP is undemocratic []
2. I don’t really know, or care, what they ought to be called []
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This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2019-04-22 18:29:46 | {"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": 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": 0.33583444356918335, "perplexity": 3915.2506654874683}, "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-2019-18/segments/1555578577686.60/warc/CC-MAIN-20190422175312-20190422201312-00280.warc.gz"} |
https://magni.readthedocs.io/en/latest/magni.imaging.measurements._visualisation.html | magni.imaging.measurements._visualisation module¶
Module providing public functions for the magni.imaging.measurements subpackage.
Routine listings¶
plot_pattern(l, w, coords, mode, output_path=None)
Function for visualising a scan pattern.
Function for visualising a pixel mask obtained from a scan pattern.
magni.imaging.measurements._visualisation.plot_pattern(l, w, coords, mode, output_path=None)[source]
Display a plot that shows the pattern given by a set of coordinates.
The pattern given by the coords is displayed on an w x l area. If mode is ‘surface’, l and w are regarded as measured in meters. If mode is ‘image’, l and w are regarded as measured in pixels. The coords are marked by filled circles and connected by straight dashed lines.
Parameters: l (float or int) – The length/height of the area. If mode is ‘surface’, it must be a float. If mode is ‘image’, it must be an integer. w (float or int) – The width of the area. If mode is ‘surface’, it must be a float. If mode is ‘image’, it must be an integer. coords (ndarray) – The 2D array of pixels that make up the mask. Each row is a coordinate pair (x, y). mode ({‘surface’, ‘image’}) – The display mode that dertermines the axis labeling and the type of l and w. output_path (str, optional) – Path (including file type extension) under which the plot is saved (the default value is None which implies, that the plot is not saved).
Notes
The resulting plot is displayed in a figure using matplotlib‘s pyplot.plot.
Examples
For example,
>>> import numpy as np
>>> from magni.imaging.measurements import plot_pattern
>>> l = 3
>>> w = 3
>>> coords = np.array([[0, 0], [1, 1], [2, 1]])
>>> mode = 'image'
>>> plot_pattern(l, w, coords, mode)
magni.imaging.measurements._visualisation.plot_pixel_mask(h, w, pixels, output_path=None)[source]
Display a binary image that shows the given pixel mask.
A black image with w x h pixels is created and the pixels are marked with white.
Parameters: h (int) – The height of the image in pixels. w (int) – The width of the image in pixels. pixels (ndarray) – The 2D array of pixels that make up the mask. Each row is a coordinate pair (x, y), such that coords has size len(pixels) x 2. output_path (str, optional) – Path (including file type extension) under which the plot is saved (the default value is None which implies, that the plot is not saved).
Notes
The resulting image is displayed in a figure using magni.imaging.visualisation.imshow.
Examples
For example,
>>> import numpy as np | 2022-05-25 00:10:26 | {"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": 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": 0.36704978346824646, "perplexity": 3042.7982290016703}, "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-2022-21/segments/1652662577757.82/warc/CC-MAIN-20220524233716-20220525023716-00015.warc.gz"} |
https://math.stackexchange.com/questions/2714958/degree-of-extensions/2715257 | # Degree of Extensions
Compute $|\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb{Q}|$
My attempt so far :
$|\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb{Q}|$ $=|\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt[5] {3})|$.$|\mathbb Q(\sqrt[5] {3}):\mathbb{Q}|$
where:
$|\mathbb Q(\sqrt[5] {3}):\mathbb{Q}|=5$
Now i need to calculate:
$|\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt[5] {3})|$
Which i think is $2$ but i am unsure to calculate . Is this the best method and if so how do i finish the problem?
Also how do i find a bases of $\mathbb Q(\sqrt {2},\sqrt[5] {3})$ over $\mathbb Q$ ?
$[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb{Q}]$ is a multiple of both $2$ and $5$ because $$[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb{Q}] = [\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt {2})] \,[\mathbb Q(\sqrt {2}):\mathbb{Q}] = 2[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt {2})]$$ $$[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb{Q}] = [\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt[5] {3})] \, [\mathbb Q(\sqrt[5] {3}):\mathbb{Q}] =5[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt[5] {3})]$$
On the other hand, $$[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt[5] {3})] = [\mathbb Q(\sqrt[5] {3})(\sqrt {2}):\mathbb Q(\sqrt[5] {3})]\le 2$$ because $\sqrt {2}$ is a root of quadratic polynomial with coefficients in $\mathbb Q \subseteq \mathbb Q(\sqrt[5] {3})$, and so $$[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb{Q}] = [\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt[5] {3})] \, [\mathbb Q(\sqrt[5] {3}):\mathbb{Q}] \le 2 [\mathbb Q(\sqrt[5] {3}):\mathbb{Q}] = 2 \cdot 5 = 10$$ Therefore, $[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb{Q}]=10$.
• $$[\mathbb Q(\sqrt {2},\sqrt[5] {3}):\mathbb Q(\sqrt[5] {3})] \, [\mathbb Q(\sqrt[5] {3}):\mathbb{Q}] \le 2 [\mathbb Q(\sqrt[5] {3}):\mathbb{Q}]$$ I am having trouble understanding why this is so – Tim Jones Apr 1 '18 at 17:25 | 2019-06-15 21:21:44 | {"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": 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": 0.9009976983070374, "perplexity": 108.73388331682646}, "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/1560627997335.70/warc/CC-MAIN-20190615202724-20190615224530-00073.warc.gz"} |
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Simran Bhatia Grade: 11
Two charged particles are placed at a distance 1.0 cm apart. What is the minimum possible magnitude of the electric force acting on each charge?
3 years ago
## Answers : (3)
Aditi Chauhan
askIITians Faculty
396 Points
Sol. Minimum charge of a body is the charge of an electron
Wo, q = 1.6 × 10^–19 c x = 1 cm = 1 × 10^–2 cm
So, F = kq base 1q base 2/r^2 = 9 * 10^9 * 1.6 * 1.6 * 10^-19/10^-2 * 10^-2 = 23.04 * 10^-38+9+2+2 = 23.04 * 10^-25 = 2.3 * 10^-24
3 years ago
Apoorva Arora
IIT Roorkee
askIITians Faculty
181 Points
the distance is constant so force depends only on charge. so the force is minimum when charge is minimum i.e. charge of one electron.
So
$F=\frac{kq_{1}q_{2}}{r^{2}}$
putting all the values
F= $2.304\times 10^{-24} N$
Thanks and Regards
Apoorva Arora
IIT Roorkee
askIITians Faculty
3 years ago
Anil sharma
17 Points
The charge q1 & q2 are placed at corner of square find q2 such that the resultant force on q1 is zero
one year ago
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To Win!!! Click Here for details | 2018-03-19 11:00:10 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "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": 0.4259372651576996, "perplexity": 13491.88548126265}, "config": {"markdown_headings": true, "markdown_code": false, "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-2018-13/segments/1521257646875.28/warc/CC-MAIN-20180319101207-20180319121207-00546.warc.gz"} |
https://learn.saylor.org/mod/page/view.php?id=14795 | ## Unit 2 Learning Outcomes
Upon the successful completion of this unit, you will be able to:
• define and calculate limits and one-sided limits;
• identify vertical asymptotes;
• define continuity and determine whether a function is continuous;
• state and apply the Intermediate Value Theorem;
• state the Squeeze Theorem, and use it to calculate limits;
• calculate limits at infinity and identify horizontal asymptotes;
• calculate limits of rational and radical functions;
• state the epsilon-delta definition of a limit, and use it in simple situations to show a limit exists;
• draw a diagram to explain the tangent-line problem;
• state several different versions of the limit definition of the derivative, and use multiple notations for the derivative;
• describe the derivative as a rate of change, and give some examples of its application, such as velocity; and
• calculate simple derivatives using the limit definition.
Last modified: Tuesday, June 14, 2016, 3:29 PM | 2023-01-27 12:18:45 | {"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": 0.8759191632270813, "perplexity": 966.0824077296535}, "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/1674764494976.72/warc/CC-MAIN-20230127101040-20230127131040-00582.warc.gz"} |
http://mathhelpforum.com/discrete-math/159718-principal-transitive-induction.html | # Thread: The Principal of Transitive Induction
1. ## The Principal of Transitive Induction
Note that $S_\alpha = \{j |j\in J\quad and\quad j<\alpha\}.$
Let $J$ be a well-ordered set. A subset $J_0$ of $J$ is said to be inductive if for every $\alpha\inJ,$
$
(S_{\alpha} \subset J_0) ==> \alpha \in J_0.
$
Theorem (The principal of transitive induction). If J is a well-ordered set and $J_0$ is an inductive subset of $J$, then $J_0=J$.
Can someone help me get started on proving this. I am trying to show that $$J \subseteq J_0$$ by choosing $\alpha \in J,$ assuming that $\alpha \notin J_0$ and showing that there is a contradiction. Is this a good approach and do you have any hints that I can use to get anywhere?
Ok so I made some progress, but I am not sure if I am moving in the right direction.
Proof: Choose $\alpha \in J$ and assume that $\alpha \notin J_0.$ Then $J_0\subseteq S_\alpha.$
If $J_0\subset S_\alpha$ then consider $\{\beta\in S_\alpha }| \beta\notin J_0\}.$
Then this set has a least-element, call it $\beta_0.$ It follows that $S_{\beta_0}\subset J_0 ==> \beta_0\in J_0.$
If $J_0 = S_\alpha,$ for this case, I can not find any kind of contradiction. Any suggestions?
2. Originally Posted by auitto
Let $J$ be a well-ordered set. A subset $J_0$ of $J$ is said to be inductive if for every $\alpha\inJ, (S_{\alpha} \subset J_0) ==> \alpha \in J_0.$
(I assume you intend for $\subset$ to stand for "is a subset of" as opposed to "is a proper subset of"?)
In any case, I don't understand that definition.
Is ' $\alpha$' supposed to range over members of some particular set? Or over ordinals?
And why should using $\alpha$ as an INDEX for $S$ have anything to do with $\alpha$ as a MEMBER of $J_0$? As far as I can tell, the way you've set it up, I could use ANY $\alpha$ from ANY index set to prove that $\alpha$ is in $J_0$ just by taking $S_0$ to be the empty set.
More technically, you've got a free variable ' $S$' in your definiens that is not in your definiendum. That won't work to make a proper definition.
What book is this problem from?
3. Originally Posted by auitto
Also, note that $S_\alpha = \{j |j\in J\quad and\quad j<\alpha\}.$
This should come at the top.
I agree with MoeBlee: if $\subset$ stands for "is a proper subset" in $S_{\alpha}\subset J_0\Rightarrow\alpha\in J_0$, then your claim is false. Indeed, let $J$ be the set of natural numbers with the usual order and let $J_0=\{0,\dots,5\}$. Then $S_n\subset J_0$ iff $n < 5$ (and $S_6=J_0$), and $n < 5$ implies $n\in J_0$; however, $J_0\ne J$. If the condition said $S_{n}\subseteq J_0\Rightarrow n\in J_0$, then it would be false for this $J_0$: $S_6\subseteq J_0$, but $6\notin J_0$.
Proof: Choose $\alpha \in J$ and assume that $\alpha \notin J_0.$ Then $J_0\subseteq S_\alpha.$
I am not sure why this is so. I see that $\alpha\notin J_0$ implies $\neg(S_\alpha\subseteq J_0)$, but not necessarily $J_0\subseteq S_\alpha$.
I believe that the Principle of Transitive Induction is nothing other than the principle of transfinite induction. The latter is usually formulated for ordinals but holds for any well-ordered set. Your proof idea is close, but consider the least $\alpha$ such that $\alpha\notin J_0$.
4. EDIT: Darn, something sems wrong here. The assumption "x in J" doesnt' seem to be used, which would imply that K is the class of all ordinals!
All we know about J is that there is a well ordering of J? I'm sensing, from the definition of S, that J itself is supposed to be a set of ordinals and the mentioned well ordering on J is '<', which is membership on ordinals. Is that right? I'll assume it is. So:
J is a set of ordinals.
S is an operation on the class of ordinals such that S(x) = J intersect x.
Definition here: K is inductive iff (K is a subset of J and for all ordinals x, if S(x) is a subset of K then x in K).
Show: If K is inductive, then K = J.
Suppose x in J. It suffices to show that J intersect x is a subset of K.
Toward a contradiction, let y be the least that is in J intersect x but not in K.
So J intersect y is not a subset of K.
So let z in J intersect y but not in K. So, since y in x, we have z in J intersect x.
Such a z contradicts the leastness of y.
5. But wait a minute, weren't there posts between the poster Plato and me about the subset symbol? What happened to those posts?
Is PROPER subset indeed not supposed to be indicated by $\subset$ so that the two different symbols in the original poster's post are irrelevant, or not? If proper subset is not what's meant, then why are there two different kinds of subset symbols in the post?
6. Now I suspect that the defintion was supposed to be this actually:
K is inductive iff (K is a subset of J and for all x in J, if S(x) is a subset of K then x in K).
Note that "x in J" replaces "ordinals x".
THEN the assumption "x in J" is used in the proof as given previously.
7. The symbol is intended to mean "is proper subset of."
This problem is from Munkres, Topology 3rd Edition. It is exercise #7 in section 10.
Also, nothing is mentioned about J being a set of ordinals, just that it is well-ordered. | 2017-08-22 23:40:54 | {"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": 58, "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": 0.9336780905723572, "perplexity": 288.47580192583075}, "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-2017-34/segments/1502886116921.7/warc/CC-MAIN-20170822221214-20170823001214-00309.warc.gz"} |
http://www.gradesaver.com/lord-of-the-flies/q-and-a/whats-th-most-important-quote-for-th-following-and-where-ca-i-find-em-88979 | # whats th most important quote for th following and where ca i find em?
glasses
fire
lord of the flie
mask
beastie
flies
island
darkness
mountain
forest
beach
dead pilot
castle rock
scar
##### Answers 1
Sorry this is too much for this forum. Pick one or two and I can help. | 2017-04-26 04:16:43 | {"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": 0.9038770198822021, "perplexity": 3573.3082393177747}, "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-2017-17/segments/1492917121153.91/warc/CC-MAIN-20170423031201-00485-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/283024/how-to-define-redeclarelargemathoperator | # How to define ReDeclareLargeMathOperator
I want alter an existing math operator by applying a macro to it. In the MWE the \ReDeclareLargeMathOperator applies the \ProcessSymbol macro which in this example changes the color of the symbol as well make a hyperlink to a Wikipedia page.
However, my attempt to adapt the first reference listed below required a few a hack to get the smallest size to be correct for the \sum operator. But, this macro does work properly for the integral as the style is altered.
So, what is the best way to define \ReDeclareLargeMathOperator so that I can tweak the symbol yet have the same spacing as the default?
## Notes:
• The black text below is the default operator and the red text is the one that is the one defined with the \ReDeclareLargeMathOperator macro.
Sum: The horizontal spacing does not align with the default symbol. Even in inline mode there seems to be some additional horizontal spacing added prior to the symbol.
Integral: The spacing of the limits of integration are incorrect and the style of the integral symbol does not match.
## Code:
\documentclass{article}
\usepackage{xcolor}
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage[colorlinks=false, pdfborder={0 0 1}, allbordercolors=magenta]{hyperref}
\newcommand*{\ProcessSymbol}[2]{%
\color{red}\href{#2}{#1}%
}%
%% Adapted from https://tex.stackexchange.com/questions/23432/how-to-create-my-own-math-operator-with-limits
\newcommand*{\ReDeclareLargeMathOperator}[3]{%
% #1 = name of operator
% #2 = symbol
% #3 = web link
% ---------------------
\renewcommand#1{%
\vphantom{\OldSum}%
\mathop{\mathchoice%
{\vcenter{\hbox{\ProcessSymbol{\huge$#2$}{#3}}}}%
{\vcenter{\hbox{\ProcessSymbol{\Large$#2$}{#3}}}}%
{\vcenter{\hbox{\ProcessSymbol{$#2$}{#3}}}}%
{\vcenter{\hbox{\ProcessSymbol{$\scriptstyle#2$}{#3}}}}%
}\displaylimits%
}%
}%
%% So that we can test things and also ensure that limit placement matches
%% the height of where the original definition of \sum placed things.
\let\OldSum\sum
\let\OldInt\int
\ReDeclareLargeMathOperator{\sum}{\Sigma}{https://en.wikipedia.org/wiki/Summation}
\ReDeclareLargeMathOperator{\int}{\intop}{https://en.wikipedia.org/wiki/Integral}
\newcommand{\dx}{\mathrm{d}x}%
\begin{document}
\section{Sum}
In inline math $\OldSum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
&\displaystyle\OldSum_{i=0}^n i
\textstyle\OldSum_{i=0}^n i
\scriptstyle\OldSum_{i=0}^n i
\scriptscriptstyle\OldSum_{i=0}^n i
\quad%% so that we can view vertical spacing.
\displaystyle\sum_{i=0}^n i
\textstyle\sum_{i=0}^n i
\scriptstyle\sum_{i=0}^n i
\scriptscriptstyle\sum_{i=0}^n i &
\end{flalign*}
\noindent
In inline math $\sum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
&\displaystyle\sum_{i=0}^n i
\textstyle\sum_{i=0}^n i
\scriptstyle\sum_{i=0}^n i
\scriptscriptstyle\sum_{i=0}^n i
&
\end{flalign*}
% ----------------------------------------------------------------
\section{Integral}
In inline math $\OldInt_a^b y\dx$, and in display math it is:
\begin{flalign*}
&\displaystyle\OldInt_a^b y\dx
\textstyle\OldInt_a^b y\dx
\scriptstyle\OldInt_a^b y\dx
\scriptscriptstyle\OldInt_a^b y\dx
\quad%% so that we can view vertical spacing.
\displaystyle\int_a^b y\dx
\textstyle\int_a^b y\dx
\scriptstyle\int_a^b y\dx
\scriptscriptstyle\int_a^b y\dx &
&
\end{flalign*}
\noindent
In inline math $\int_a^b y\dx$, and in display math it is:
\begin{flalign*}
&\displaystyle\int_a^b y\dx
\textstyle\int_a^b y\dx
\scriptstyle\int_a^b y\dx
\scriptscriptstyle\int_a^b y\dx
&
\end{flalign*}
\end{document}
• \DeclareMathOperator has a precise semantic, so the name you're choosing is bad. But it's not the real important thing. You surely don't want to apply \huge and Large. – egreg Dec 14 '15 at 14:36
• With operators such as \sum and \bigcup there's no problem; there is with \int, because you won't get the kerning. – egreg Dec 14 '15 at 14:49
Why changing the symbol for \sum into \Sigma? It's surely wrong.
Operators such as \sum or \bigcup can be dealt with in a simpler way; for the integral some more work is needed, if you want to preserve the kerning. Thus the new \int command must absorb the possible \limits token and then the (optional) limits. Then a red integral is typeset as part of \href, with the limits added in the current color.
\documentclass{article}
\usepackage{xcolor}
\usepackage{amsmath}
\usepackage{etoolbox}
\usepackage[colorlinks=false, pdfborder={0 0 1}, allbordercolors=magenta]{hyperref}
%% Adapted from http://tex.stackexchange.com/questions/23432/how-to-create-my-own-math-operator-with-limits
\newcommand*{\ReDeclareLargeMathOperator}[2]{%
% #1 = name of operator
% #2 = web link
% ---------------------
\cslet{\string#1}#1%
\renewcommand#1{%
\mathop{%
\mathpalette{\ProcessSymbol}{{\csuse{\string#1}}{#2}}%
}\displaylimits
}%
}
\newcommand*{\ProcessSymbol}[2]{\doProcessSymbol{#1}#2}
\newcommand*{\doProcessSymbol}[3]{%
\vcenter{\hbox{\color{red}\href{#3}{$#1#2$}}}%
}
%% for integrals the above can't work
\makeatletter
}
}
}
}
}
}
\vcenter{\hbox{\color{red}%
\href{#2}{$#1% \linkedint@int\linkedint@limits _{\textcolor{linkedint@color}{\linkedint@lower}}% ^{\textcolor{linkedint@color}{\linkedint@upper}}%$}%
}}%
}
\makeatother
%% So that we can test things and also ensure that limit placement matches
%% the height of where the original definition of \sum placed things.
\let\OldSum\sum
\let\OldIntop\intop
\def\OldInt{\OldIntop\nolimits}
\ReDeclareLargeMathOperator{\sum}{https://en.wikipedia.org/wiki/Summation}
%\ReDeclareLargeMathOperator{\intop}{https://en.wikipedia.org/wiki/Integral}
\newcommand{\dx}{\mathrm{d}x}%
\begin{document}
\section{Sum}
In inline math $\OldSum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
&\displaystyle\OldSum_{i=0}^n i
\textstyle\OldSum_{i=0}^n i
\scriptstyle\OldSum_{i=0}^n i
\scriptscriptstyle\OldSum_{i=0}^n i
\quad%% so that we can view vertical spacing.
\displaystyle\sum_{i=0}^n i
\textstyle\sum_{i=0}^n i
\scriptstyle\sum_{i=0}^n i
\scriptscriptstyle\sum_{i=0}^n i &
\end{flalign*}
\noindent
In inline math $\sum_{i=0}^n i$, and in display math it is:
\begin{flalign*}
&\displaystyle\sum_{i=0}^n i
\textstyle\sum_{i=0}^n i
\scriptstyle\sum_{i=0}^n i
\scriptscriptstyle\sum_{i=0}^n i
&
\end{flalign*}
% ----------------------------------------------------------------
\section{Integral}
In inline math $\OldInt_a^b y\dx$, and in display math it is:
\begin{flalign*}
&\displaystyle\OldInt_a^b y\dx
\textstyle\OldInt_a^b y\dx
\scriptstyle\OldInt_a^b y\dx
\scriptscriptstyle\OldInt_a^b y\dx
\quad%% so that we can view vertical spacing.
\displaystyle\int_a^b y\dx
\textstyle\int_a^b y\dx
\scriptstyle\int_a^b y\dx
\scriptscriptstyle\int_a^b y\dx &
&
\end{flalign*}
\noindent
In inline math $\int_a^b y\dx$, and in display math it is:
\begin{flalign*}
&\displaystyle\int^b_a y\dx
\textstyle\int_a^b y\dx
\scriptstyle\int_a^b y\dx
\scriptscriptstyle\int_a^b y\dx
&
\end{flalign*}
\end{document}
• There is a slight problem with using int^b_a (as in the last red display mode integral in the image above). But, not an issue for me as I always use int_a^b, – Peter Grill Dec 14 '15 at 21:19
• So, what would be a better macro name to use here ? I don't know how the large operators are defined. Or was your comment related to the fact that I have changed the number of operators (which I agree is sufficient to warrant a different name). Also, is \int the only large operator that is the exception or are the other obvious ones that will need to be tweaked? – Peter Grill Dec 14 '15 at 21:21
• Does using \cslet{\string#1}#1 and {\csuse{\string#1}} do some magic? Seems to me that later could be replaced with just {#1}? Oh, I am guessing it has to do with \doProcessSymbol[3] which only provided with what appears to be just 2 parameters at invocation. I have seen this sort of magic before, but do not grok it. – Peter Grill Dec 14 '15 at 21:29
• @PeterGrill They define the macro \\sum (the second backslash is part of the name), the same trick as for commands with optional argument. – egreg Dec 14 '15 at 21:35 | 2019-10-15 08:34:53 | {"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": 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": 0.9663969874382019, "perplexity": 2843.5835538803535}, "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/1570986657949.34/warc/CC-MAIN-20191015082202-20191015105702-00061.warc.gz"} |
https://tex.stackexchange.com/questions/293935/mixing-hebrew-and-english-bibliographies | # Mixing Hebrew and English bibliographies?
I have a .bib bibliography that has some entries completely in English and some completely in Hebrew.
I'd like to display the bibliography items so that the Hebrew items are justified right-to-left and the English items left-to-right. The bibliography should all be under one title ("Bibliography" or "References"), then all the Hebrew items, then all the English items.
I've tried many things but could not get anything to work. I am using LyX, so I prefer a solution using pdflatex and bibtex, but biber with biblatex might also be okay.
# MWE
In this MWE both files (.tex and .bib) are CP1255-encoded; the same result occurs with UTF8-encoding, but with UTF8, I need to \DeclareUnicodeCharacter all the Hebrew characters or it won't compile...
### mwe.bib
@article{EnglishExample,
title={Example},
author={John McAuthor},
year={2016},
journal={American Journal of Examples}
}
@article{HebrewExample,
title={דוגמה},
author={מחבר},
year={2016},
journal={כתב העת הישראלי לדוגמאות}
}
### mwe.tex
\documentclass[oneside,hebrew,english]{book}
\usepackage[T1]{fontenc}
\usepackage[cp1255,latin9]{inputenc}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
\makeatletter
\usepackage{apacite}
\makeatother
\usepackage{babel}
\begin{document}
\inputencoding{cp1255}%
\inputencoding{latin9}test \inputencoding{cp1255}\R{בדיקה}
\inputencoding{latin9}\bibliographystyle{apacite}
\nocite{*}
\bibliography{mwe}
\end{document}
In this example, the "test" in the document itself renders fine:
However, the bibliography looks like this:
I want it to look like this (excuse the inconsistent styling - I made this with MS Word...):
• Which things? Your question is unanswerable by anybody who cannot write or find some Hebrew. (I've answered questions on RTL typesetting, but only when they've contained an MWE. I'm probably not alone in this.) My guess is that BibTeX is hopeless for this. Or very, very painful. Biblatex can be used with BibTeX, but you want Biber here. You also want XeLaTeX and polyglossia for anything like a smooth experience. Mind you, I'm thinking unicode. Maybe you have Hebrew entries transliterated? In that case, scotch everything I said. – cfr Feb 15 '16 at 2:47
• Note that bidirectional typesetting really is much easier with XeTeX. How are you typesetting Hebrew now? cumulus? If that's the best LyX can do, I'd ditch LyX. Life will be easier by far. – cfr Feb 15 '16 at 2:51
• Thanks for the reply. I'll edit with a MWE soon, but basically, I have actual Hebrew, not transliterated. regarding Unicode, sure, I don't mind the encoding though - easiest would be UTF-8 but I don't mind cp1255 or ISO-8859-8 either. Clearly, if I switch to xetex with polyglossia, which LyX seems to kinda support, Unicode will be more native, but I still haven't figured out how to make it work... Right now I'm using culmus. – Yoni Rozenshein Feb 15 '16 at 6:53
• Edited with a MWE. – Yoni Rozenshein Feb 15 '16 at 7:56
• As cfr said, your life will be easier without LyX in this case. – Johannes_B Feb 15 '16 at 8:19
An approach using XeLaTeX with polyglossia and biblatex.
%\RequirePackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{EnglishExample,
title={Example},
author={John McAuthor},
year={2016},
journal={American Journal of Examples},
language={engllish},
keywords={english}
}
@article{HebrewExample,
title={דוגמה},
author={מחבר},
year={2016},
journal={כתב העת הישראלי לדוגמאות},
language={hebrew},
keywords={hebrew}
}
\end{filecontents}
\documentclass{article}
\usepackage{blindtext}
\usepackage{fontspec}
\setmainfont{Linux Libertine O}
\usepackage{polyglossia}
\setmainlanguage{english}
\setotherlanguage{hebrew}
\usepackage[style=apa]{biblatex}
\DeclareLanguageMapping{english}{english-apa}
\defbibenvironment{hebbib}{\begin{otherlanguage}{hebrew}
\list
{}
{\setlength{\leftmargin}{\bibhang}%
\setlength{\itemindent}{-\leftmargin}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}}
{\endlist\end{otherlanguage}}{\item}
\begin{document}
\blindtext
\begin{otherlanguage}{hebrew}בדיקה
(נהגה לַטֶךְ) היא שפת סימון ועריכת מסמכים. לרוב מסומנת
בלוגו \LaTeX. הרעיון העומד מאחורי שפה זו הוא לחסוך את
הטרחה שבעיצוב מכותב המסמך, ולהטיל מלאכה זו על
\end{otherlanguage}
\nocite{*} | 2019-10-21 07:11:25 | {"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": 0.9071556329727173, "perplexity": 9220.082283777367}, "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/1570987763641.74/warc/CC-MAIN-20191021070341-20191021093841-00320.warc.gz"} |
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# For a certain positive integer N, N^3 has exactly 13 unique factors. H
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For a certain positive integer N, N^3 has exactly 13 unique factors. H [#permalink]
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18 Feb 2017, 01:49
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### HideShow timer Statistics
For a certain positive integer N, N^3 has exactly 13 unique factors. How many unique factors does N have?
A. 1
B. 2
C. 3
D. 4
E. 5
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Joined: 11 Sep 2015
Posts: 3355
Re: For a certain positive integer N, N^3 has exactly 13 unique factors. H [#permalink]
### Show Tags
18 Feb 2017, 07:19
1
Top Contributor
5
Bunuel wrote:
For a certain positive integer N, N³ has exactly 13 unique factors. How many unique factors does N have?
A. 1
B. 2
C. 3
D. 4
E. 5
IMPORTANT:
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
-------now onto the question------------------------------------------------
In the above rule, notice that total number of divisors is a PRODUCT [e.g., (4+1)(3+1)(1+1) =(5)(4)(2) = 40]
In this question, we're told that there are 13 divisors.
There's only ONE WAY that the number 13 can be written as a product: 1 x 13
So, a number with 13 positive divisors must have a prime factorization that looks like this: prime^12
So, if N³ is equivalent to prime^12, then N must equal prime^4, since (prime^4)^3 = prime^12
For example, if N = 2^4, then N = 16
Notice that, if N = 2^4, then N³ = (2^4)^3 = 2^12
And, from the above rule, if N³ = 2^12, then the number of positive divisors of N³ = (12+1) = 13
How many unique factors does N have?
If N = 16 (or any other prime^4), then the factors of 16 = {1, 2, 4, 8, 16}
There are 5 factors.
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##### General Discussion
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Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: For a certain positive integer N, N^3 has exactly 13 unique factors. H [#permalink]
### Show Tags
18 Feb 2017, 02:10
3
Bunuel wrote:
For a certain positive integer N, N^3 has exactly 13 unique factors. How many unique factors does N have?
A. 1
B. 2
C. 3
D. 4
E. 5
13 - prime, hence we have only one possible option - $$p^{12}$$
$$p^{12} = (p^4)^3$$
$$N = p^4$$, where $$p$$ is prime.
$$N$$ has 5 distinct factors.
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Location: Malaysia
For a certain positive integer N, N^3 has exactly 13 unique factors. H [#permalink]
### Show Tags
20 Mar 2017, 00:30
1
Bunuel wrote:
For a certain positive integer N, $$N^3$$ has exactly 13 unique factors. How many unique factors does N have?
A. 1
B. 2
C. 3
D. 4
E. 5
OFFICIAL SOLUTION
The shortest way to solve this problem is by applying the Unique Factors Trick. That trick is a tool that enables the direct calculation of the total number of factors of any number based on that number’s prime factor list. Specifically, to count the total factors of any number, prime factor the number, discard the bases, add one to the exponents, and then multiply the values obtained. The result is the total factor count.
In the case at hand, we’re told that $$N^3$$ has exactly 13 factors. When we consider the Unique Factors Trick, we can see that 13 must be the result of multiplying a set of positive integers. However, 13 is prime; its only factors are 1 and 13. So our original exponents, before adding one to each, can only have been zeroes and a single 12. In other words, $$N^3$$ must be the 12th power of a prime number:
$$N^3=p^{12}$$
From there, we can take the cube root and find that N is the 4th power of the same prime:
$$N=p^4$$
Using the Unique Factors Trick once more, we discard the base and add one to the exponent to determine that N has 4+1=5 total factors. The correct answer is E.
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Re: For a certain positive integer N, N^3 has exactly 13 unique factors. H [#permalink]
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20 Mar 2017, 03:24
Bunuel wrote:
For a certain positive integer N, N^3 has exactly 13 unique factors. How many unique factors does N have?
A. 1
B. 2
C. 3
D. 4
E. 5
since 13 is a prime number therefore 12 will be the power of a prime number and that will be N^3
therefore n will be a prime number raised to the power 4
total factor will be 4 +1 =5
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Re: For a certain positive integer N, N^3 has exactly 13 unique factors. H [#permalink]
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25 Mar 2018, 14:32
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Re: For a certain positive integer N, N^3 has exactly 13 unique factors. H &nbs [#permalink] 25 Mar 2018, 14:32
Display posts from previous: Sort by | 2019-01-22 06:47:40 | {"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": 0.578924298286438, "perplexity": 2687.8552003015975}, "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-2019-04/segments/1547583829665.84/warc/CC-MAIN-20190122054634-20190122080634-00277.warc.gz"} |
https://itectec.com/ubuntu/ubuntu-how-to-bring-up-a-network-interface-only-if-it-is-physically-present-in-ubuntu-14-04/ | # Ubuntu – How to bring up a network interface only if it is physically present in Ubuntu 14.04
12.0414.04bootnetworkingwireless
This is a follow-up on my old question:
What would be the best way to make kernel bring a network interface up
only if it is physically plugged in? So, if it doesn't exist, just
move on with initializing other interfaces (if any) and continue to
the login screen, without "waiting for network configuration" delay.
The solution then came up with then was the following in etc/network/interfaces, it used to work in 12.04:
auto wlan9
iface wlan9 inet manual
wpa-ssid MYSSD
wpa-psk MYKEY
wpa-proto RSN
wpa-pairwise CCMP
wpa-group CCMP
wireless-power off
pre-up if [ -f /sys/class/net/wlan9/operstate ]; then ifconfig wlan9 up; fi
up if [ -f /sys/class/net/wlan9/operstate ]; then dhclient wlan9; fi
Unfortunately, it stopped working once I upgraded to 14.04 Trusty Tahr. If the interface is physically absent (i.e. the USB WiFi card unplugged), I again experience the 2 minutes "waiting for network configuration" delay.
How can I get the same logic working in 14.04?
start on net-device-added INTERFACE=wlan9 | 2021-06-24 03:57:30 | {"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": 0.18668709695339203, "perplexity": 11599.941400070142}, "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/1623488550571.96/warc/CC-MAIN-20210624015641-20210624045641-00552.warc.gz"} |
https://math.stackexchange.com/questions/3130477/what-is-the-probability-of-getting-equal-numbers-of-heads-and-tails | # What is the probability of getting equal numbers of heads and tails?
I'm doing my hw, there is a question that I am not sure if I'm correct.
Here is the question
A fair coin is thrown repeatedly.
What is the probability that on the $$n$$ th throw, the numbers of heads and tails to date are equal?
$$\mathrm{The\ required\ situation\ holds\ only\ when} \ n\ \mathrm{is\ even.}\\ \mathrm{Let}\ n=2k,\ \mathrm{then\ the\ required\ probability} = {2k \choose k} \left( \frac{1}{2} \right)^{k} \left( \frac{1}{2} \right)^{k} = {2k \choose k} \left( \frac{1}{2} \right)^{2k} \\ \mathrm{And\ I \ searched\ this\ question\ online\ and\ found\ that\ someone\ said\ that\ the \ probability\ is} \left( \frac{n}{2} \right)\left( \frac{1}{2} \right)^{n}$$ Here is the link: https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.779221.html
I also tried to expand $${2k \choose k}$$ but failed to get the expression $$\left( \frac{n}{2} \right)$$
May I know whether I am correct or where did I do it wrongly, thanks.
• Your answer is correct. The other answer should read $\binom{n}{\frac{n}{2}}\left(\frac{1}{2}\right)^n$, where $n$ is even. – N. F. Taussig Feb 28 at 17:30
The linked answer is wrong even for $$n=2$$. For $$n=2$$ we have $$HT$$ and $$TH$$ as the only possible winning paths, so the answer is $$\frac 12$$. But $$\frac 22\times \left( \frac 12\right)^2=\frac 14$$.
Worth noting that the answer you provide correctly gives $$\binom 21\times \left( \frac 12\right)^2=\frac 12$$
Indeed, your answer is correct for all (even) $$n$$.
Firstly, I think you should also give the (trivial) solution for the case when $$n$$ is odd. For the case where $$n$$ is even your result is correct and the linked answer is incorrect. Presumably what that person meant to say was $${2k \choose k} = {n \choose n/2}$$, because the assertion that $${2k \choose k} = \tfrac{n}{2}$$ is not generally true. | 2019-05-22 01:00:34 | {"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": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8830657005310059, "perplexity": 100.8324855688509}, "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/1558232256600.32/warc/CC-MAIN-20190522002845-20190522024845-00267.warc.gz"} |
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Text Solution
Solution : Light mass (beta particle) than the particle a (He nucleus)
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Transcript
hello friends to our question is radiation out from the source One Direction perpendicular to the show the parts of radiation AP and answer the following questions in terms of A B and C why does the radiation track than that cup article that are rejected as a radiation are alpha beta and gamma particle charge charge on alpha beta and gamma particle particle is equal to the mass of proton and the mass of Beta particle is equals to mass of electron and mass of Gamma particle
zero now friends you can clearly see that you buy and ratio cube I am ratio for an Alpha particle for Alpha particle it is to buy more time MP that is equal to 2 x of MP and forget it comes out to be equal to buy any also we know that is so we can say that you buy and ratio 2 ratio of an article is much greater than that of Alpha particle
beta particle beta particle which one is the beta particle particle is moving closer to the direction of electric field hence we can say that faculty would be having a negative charge to beta particle is the particle and Alpha particle that is particle is moving in the direction of electric field to Alpha particle particle and collected from the conclusion we can say that particles
deflect reflect more than particle particle ke it has more charge by mass wishing wish thank you friend | 2022-08-09 22:45:53 | {"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": 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": 0.4455764889717102, "perplexity": 646.905390997544}, "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-2022-33/segments/1659882571090.80/warc/CC-MAIN-20220809215803-20220810005803-00466.warc.gz"} |
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https://math.stackexchange.com/questions/2142258/weak-convergence-and-hahn-banach-theorm | # Weak Convergence and Hahn-Banach Theorm
Kreyzig proves the following lemma:
Let $(x_n)$ be a weakly convergent sequence in a normed space $X$, then the weak limit $x$ of $(x_n)$ is unique.
He begins by supposing $(x_n)$ converges weakly to two limits, say $x$ and $y$. By supposition, this means $f(x_n) \rightarrow f(x)$ and $f(x_n) \rightarrow f(y)$. $f$ is linear. So $$f(x) - f(y) = f(x-y) = 0$$
Then Kreyzig uses Hahn-Banach theorem to assert this implies $x-y = 0$. I don't understand why this doesn't just follow from $f$ being linear, don't linear maps between normed spaces need to preserve 0 as they do for inner product spaces?
• Yes, linear maps preserve $0$, but the crux is the other direction. Not every $z$ that is mapped to $0$ must itself be $0$. But by Hahn-Banach, every $z$ that is mapped to $0$ by all continuous linear functionals must itself be $0$. – Daniel Fischer Feb 13 '17 at 11:36
• @DanielFischer thanks! – yoshi Feb 13 '17 at 16:23
If $x-y$ is not zero, you can define on $vect(x-y)$ a linear function $g$ such that $g(x-y)=1$. Hahn Banach implies that you can extend $g$ to a bounded function $f$ defined on $X$.You have $f(x-y)=g(x-y)=1$. Contradiction.
• What do you mean by $vect()$? – mavavilj Apr 9 '18 at 8:01 | 2019-08-23 02:19:44 | {"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": 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": 0.9713716506958008, "perplexity": 214.45207693779406}, "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-2019-35/segments/1566027317817.76/warc/CC-MAIN-20190823020039-20190823042039-00312.warc.gz"} |
https://www.electro-tech-online.com/threads/lathe-tachometer-with-pic16f886.94232/ | # Lathe Tachometer with PIC16F886
Status
Not open for further replies.
#### tgrandahl
##### New Member
Hello,
I am working on replacement tachometer for a 30Yr old lathe that im helping rebuild. I am planning on using a hall sensor pickup and a 4x7-seg display readout. The system needs to read from 10Rpm to 5000Rpm, the hall pickup is from a 30 tooth gear.
I have had experience writing assembly for mega128 mC's although its been a few years. This will be my first venture into PIC land.
From reading around it looks like a PicKit 2 is a well regarded programmer / debugger?
I am also considering a PIC16F886 as I would like a chip with an internal oscillator, as well as comparator and 16-bit timer.
The main function would increment a count variable everytime a comparator interrupt occurs from the hall sensor.
I would like to update the display every .5 sec, so i have been planning on using a timer that would interrupt after this long. At the timer interrupt the current count value will be fed into a LUT function using "case" statements that will output the binary to drive the 7-seg's from the current count.
The 7-segs will then be updated and the 7-segs cleared.
Does this sounds like an efficient way of accomplishing my goal with using this chip?
Also, I would like a resolution of 5rpm, this would result with almost 1000 values in that LUT, I am concerned that this will not fit within this device, as the binary values for the display alone will be almost 16kb. How can i translate this into program memory requirements to size my device?
#### Pommie
##### Well-Known Member
You could use the comparator interrupt to count pulses but with a multiplex interrupt as well it could get messy. I would suggest feeding the comparator output into the Timer1 input and use timer1 to count the pulses. Use timer2 to generate a 1mS interrupt to multiplex the display and use this interrupt to work out when the 0.5 seconds is up. With a range of 10RPM (5 pulses per second) to 5000RPM (2500pps), timer1 will contain 2.5 (yuk) to 1250 and so your table will contain over 1000 entries. This is not a problem as you have 8K of 14 bit memory and so each location can contain 1 entry in BCD format (assuming 3 relevant digits). Using 2 locations per timer1 value will still only use 1/3 of the memory.
The Pickit2 or a clone (Junebug) is an excellent choice.
Mike.
#### Mr RB
##### Well-Known Member
I just think that's a poor way to do it; the effort to generate the table and the poor resolution and accuracy of the final system.
I would measure the elapsed period of 4, 16 or 32 pulses (depending what speed range the lathe is in) using the PIC timer you can get an elapsed time accurate to fractions of a microsecond, even more accurate if you average the period over a number of input pulses.
Then use a math function to calculate "frequency" in RPM which will give you full accuracy, using all 4 digits, so for low ranges it could say 12.72 RPM as an example.
No look up table needed, and much better accuracy and finer resolution.
#### Pommie
##### Well-Known Member
I just think that's a poor way to do it; the effort to generate the table and the poor resolution and accuracy of the final system.
I would measure the elapsed period of 4, 16 or 32 pulses (depending what speed range the lathe is in) using the PIC timer you can get an elapsed time accurate to fractions of a microsecond, even more accurate if you average the period over a number of input pulses.
Then use a math function to calculate "frequency" in RPM which will give you full accuracy, using all 4 digits, so for low ranges it could say 12.72 RPM as an example.
No look up table needed, and much better accuracy and finer resolution.
Agree completely, that is the best way to do it, however most people shy away from maths in asm. Lookup tables are just easier.
Mike.
#### Mike - K8LH
##### Well-Known Member
Does that "30 tooth gear" mean you'll get 30 pulses per revolution from the Hall sensor?
#### Chippie
##### Member
IIRC, a Hall sensor requires a magnet in order to generate a pulse...
However in answer to the question, 30 pulses would be generated by a suitable sensor...
As it happens I'm working on a similar project, I'm using a slotted opto and a wheel( which is directly mounted on the spindle) with 20 slots in it...PIC is a 16F628A and displaying on a 2*16 line display......
#### Mike - K8LH
##### Well-Known Member
Chippie,
So you could potentially count pulses at quarter second intervals on your 20 ppr opto-sensor and collect 50 pulses for 10 RPM and 25,000 pulses for 5000 RPM, correct? That's 0.2 RPM resolution, isn't it? If so, that's pretty neat.
Mike
#### Chippie
##### Member
Ermm...I'm suffering brain fade at the moment so my maths is a bit rusty...
I'm trying to limit the upper speed to around 3000 rpm as I have a 3phase motor and VFD ( yeah despite the grey matter acting up atm I managed to do a 1ph to 3ph conversion using a Teco FM50 ) and the speed can go up a lot higher if I increase the motor frequency to 100Hz...but I dont really want to do that.
#### tgrandahl
##### New Member
May I ask what effect the "30 tooth gear" will have on the number of pulses generated per revolution. I apologize for not being able to deduce that info' from your original post.
If you're going to count pulses, would there be any advantage generating multiple pulses per revolution, especially for the lower speeds?
The hall sensor will output 30 pulses per revolution of the spindle, the sensor outputs about 2.2V while low and about 4.7V while high. I think having a larger number of pulses per revolution will certainly help with lower speeds, I am however considering the 30 pulses / rev fixed for this project.
I agree with the guys. Using simple math is a good alternative to a large table. If as Pommie suggested you were getting 2 to 1250 pulses in 1/2 second which correspond to 8 to 5000 RPMs then you could shift this 16 bit number two places to the left to get a number in the range of 8 to 5000 (4 RPM resolution). Run this number through a bin2dec or bin2asc routine to extract your 4 digit LED display data.
I like this idea a lot, although having a finer resolution would be nice its simple and still eliminates the need for the table.
I would measure the elapsed period of 4, 16 or 32 pulses (depending what speed range the lathe is in) using the PIC timer you can get an elapsed time accurate to fractions of a microsecond, even more accurate if you average the period over a number of input pulses.
Then use a math function to calculate "frequency" in RPM which will give you full accuracy, using all 4 digits, so for low ranges it could say 12.72 RPM as an example.
I would love the increase in resolution, although I am still thinking through how the math works here.
I have not used any asm math functions before although they look straight forward enough. From looking at the available functions here I am not sure how to approach the situation. I am considering using this 24bit by 16bit division.
(6,000,000 / time for 30 pulse count in mS) = RPM in hundredths.
Then use a bin2dec function and shift the digits as the reading grows over 100's and 1000's.
#### Chippie
##### Member
Rather than invent the wheel here chaps, what I did was take an existing pic application( it was used to measure the speed of a boat prop..) and modify the code accordingly...There was a lot of other functionality in the code which I took out...I took me about 3 attempts to get it to compile without errors....Besides I'm too old and lazy to write code....
The maths routines were part of the code and I retained them in order for it to work...They were written by Pete Hemsley...if needed I can email them to those interested...
Last edited:
#### tgrandahl
##### New Member
is anyone here familiar with the PIC16F886? I am using HI-Tech C and c-wizard to make init files and for some reason there is no comparator option provided for configuring peripherals when I select this chip. However it is listed as a feature on Maxim's website and in the user manual. Is this just a bug in c-wiz or did i miss some fine print?
Additionally I am looking at using
this binary to ASCII converter for breaking out the digits, although i am still not quite sure how to implement it. I fell like sometimes its easier to write your own code than understand someone else's.
this SPI interface
for outputting to my 7-seg driver
Last edited:
#### Mr RB
##### Well-Known Member
...
So you could potentially count pulses at quarter second intervals on your 20 ppr opto-sensor and collect 50 pulses for 10 RPM and 25,000 pulses for 5000 RPM, correct? That's 0.2 RPM resolution, isn't it? If so, that's pretty neat.
...
Actually that's the problem Mike it's not 10 rev per second but RPM, so 10 RPM is only 0.167 rotations a second, even with a 30 pulse encoder thats only 5 pulses per second with a +/- 1 pulse count error. So 4-6 pulses per second which is lousy resolution for the lookup table.
I don't see that the math part is gonna be much harder really than the lookup table system. It might even be easier.
Lets say you can easily use the timer to measure pulse period and get a period (in uS) for one spindle revolution;
RPM = (60 mil / period uS)
Or if you just get a period for one pulse count (which is 1/30th spindle rev);
RPM = (2 mil / period uS)
Which is now much more manageable. Just do the 1/period conversion as a successive addition, so keep adding period to Y until Y reaches 2000000. The math was discussed recently in the chronograph thread? This is plenty fast enough to do one calc every 1/2 sec or 1/4 sec.
#### Mike - K8LH
##### Well-Known Member
Thanks Roman. Makes perfect sense. My goof by thinking revs/second instead of revs/minute.
Take care. Mike
#### tgrandahl
##### New Member
Actually that's the problem Mike it's not 10 rev per second but RPM, so 10 RPM is only 0.167 rotations a second, even with a 30 pulse encoder thats only 5 pulses per second with a +/- 1 pulse count error. So 4-6 pulses per second which is lousy resolution for the lookup table.
I don't see that the math part is gonna be much harder really than the lookup table system. It might even be easier.
Lets say you can easily use the timer to measure pulse period and get a period (in uS) for one spindle revolution;
RPM = (60 mil / period uS)
Or if you just get a period for one pulse count (which is 1/30th spindle rev);
RPM = (2 mil / period uS)
Which is now much more manageable. Just do the 1/period conversion as a successive addition, so keep adding period to Y until Y reaches 2000000. The math was discussed recently in the chronograph thread? This is plenty fast enough to do one calc every 1/2 sec or 1/4 sec.
Yes, this exactly what I was thinking, Im a little confused as to exactly how to implement it though.
This is the first Pic C I have written and I don't remember much C.
Regarding the math, I am assuming I need to use a 32bit unsigned int32 to hold the denominator values for time count as well as numerator constants.
Do I need to use a division function such as the one here?:
PIC Microcontoller Math Method 48 by 24 bit division by Andy Lee
Or can i simply use "div_constant / t_count = rpm" and the HI_TECH C compiler will figure it out.
In that case do i even need to declare the numerator as a constant or can i just type it into the code?
What happens to the remainder in this case, does it just round down?
Im also assuming here that I can work with variables longer than 8bits in the PIC16F886 even though its an 8bit micro. Is the data just broken up into different registers?
Sorry for the newb questions but im not finding any answers that make sense to me elsewhere.
#### Pommie
##### Well-Known Member
It's early in the morning and so maybe my brain is not awake yet but, don't you just multiply the pulses per second by a fixed value to get RPM. If you use 1 second as the time base then it is simply multiply by 2.
To smooth out your reading you may want to consider doing a very simple moving average. Simply keeping the last 4 values and averaging them will provide a much steadier reading.
I haven't used HiTech C but every compiler I have used has handled the maths with no problem.
Mike.
#### Mr RB
##### Well-Known Member
Yeah if you are doing it in C it gets pretty easy, for one reason C will handle the long variables and division for you and for the other reason that there are a ton of code samples and C projects out there you can call on.
Rather than completely reinvent the wheel you could look up some "microcontroller C code" for "tacho" "frequency meter" "speedo" etc they all do the same basic method of; averaging the input pulses, inversion to turn a period into a frequency, scale to appropriate display units and drive a display in digits.
Even if you want to code it from scratch for fun and experience I would suggest looking at a couple of existing projects first.
#### tgrandahl
##### New Member
soo, im making progress
So I have spent about 4 days familiarizing and playing with mplab and hitech c now. Ultimately I have had issues getting consistent readings for the pulses period. So I stripped the code down to just the pulse counting part.
I have port b set to input and interrupt on change enabled.
When an interrupt occurs it increments hall_count.
The main function checks to see if three pulses have been recorded before it records the time.
I am running the code in debug mode with a pickit2 and having issues getting consistent time readings.
using a 555 to generate a input steady input signal, the period of the input signal fluctuated < 1uS looking at it with my scope.
My time_count is always coming up around 400 counts low and can fluctuate greatly. What can I do to get more repeatable readings?
Code:
// Tyler Grandahl
// 16F867A Tachometer
//
#include <htc.h>
#define _XTAL_FREQ 20000000 // define the clock freq
/* Program device configuration word
* Oscillator = HS
* Watchdog Timer = Off
* Power Up Timer = Off
* Brown Out Detect = On
* Low Voltage Program = Enabled
* Flash Program Write = Write Protection Off
* Background Debug = Disabled
* Data EE Read Protect = Off
* Code Protect = Off
*/
__CONFIG(HS & WDTDIS & PWRTDIS & BOREN & LVPEN & WRTEN & DEBUGDIS & DUNPROT & UNPROTECT);
// Global Variables
volatile char hall_count;
volatile char time_count;
volatile long time;
volatile short freq;
// Peripheral initialization function
void init(void)
{
/***** Common Code ****
// port b interrupts enabled
* Global interrupt disabled during initialization
*/
INTCON = 0b00001000;
/* Port directions: 1=input, 0=output
*/
TRISB = 0b11111111;
//Timer 1:enabled
//1:1 prescaller
//
T1CON = 0b00000001;
ei(); // Global interrupts enabled
}
/***************************************/
/*************** Main Function *********/
/***************************************/
void main()
{
hall_count = 0; // clear the counter just incase its not zero
time_count = 0; // clear the timer counter just incase
init(); // function call to initilization function to get things started
while(1)
{
if(hall_count == 3)
{
// the time calculation
time = 0;
time = (TMR1L+(256*TMR1H)); // calculate the elapsed time in uS and write to time register
time = (time + (64000*time_count));
freq = (5000000/(time/3));
T1CON = 0b00000000; //disable timer 1 to record the elapsed time
time_count = 0; // reset counter values
TMR1H = 0;
TMR1L = 0;
hall_count = 0;
T1CON = 0b00000001; // re enable timer 1 for another count
}
// timer overflow counter, polls value of TMR1H, when high the timer is stopped, zeroed, and time_count is increminted.
if (TMR1H >= 250)
{
T1CON = 0b00000000; //disable timer 1 to record the elapsed time
time_count ++;
TMR1H = 0;
T1CON = 0b00000001; // re enable timer 1 for another count
}
}
}
/*****************************/
/********* INTERRUPTS ********/
/*****************************/
void interrupt my_isr(void)
{
if((RB4 == 1))
{
//__delay_us(200);
//CLRWDT();
//if((RB4 == 1))
// {
hall_count ++;
if (hall_count == 3)
{
T1CON = 0b00000000; //disable timer 1 to record the elapsed time
//INTCON = 0b01000000;
}
// }
}
RBIF = 0;
}
#### Mr RB
##### Well-Known Member
That's a rather sloppy procedure. You are stopping TMR1 which can cause issues and you are reading TMR1L and TMR1H in the middle of a C expression which can really cause issues...
I would try a totally different approach. Leave TMR1 free running, ie never stop it or write to it. First thing when you get in your interrupt grab the TMR1 value using assembler, starting with TMR1L, like this;
Code:
// read TMR1 in asm for speed
asm MOVF TMR1L,W // 16bit timer capture occurs this instruction
asm MOVWF t1_low
asm MOVF TMR1H,W
asm MOVWF t1_high
// now correct TMR1H if TMR1L rolled between reads;
if(t1_low >= 254) t1_high--;
I've used that code for years in many 16bit timer speed control applications, it will give a perfect instantaneous read of the 16bit timer but requires that TMR1 be set at 1:1 prescaler (which is best anyway since you need precision).
Some of the new PICs can read a 16bit timer accurately in 1 hit, but not the 16F876 you are using.
Once you grab that 16bit value in every interrupt, you can subtract the previous 16bit value from the new 16bit value giving an elapsed time that will self correct every cycle and give 100% average accuracy in measuring the period between events. It's also best to store the last few values in a circular buffer and average them to reduce display jitter.
Then you have an accurate period, you can do the calc to turn it into a freq display (RPM etc).
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872 | 2021-09-24 05:11:18 | {"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": 0.3491849899291992, "perplexity": 2929.7436147465555}, "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/1631780057504.60/warc/CC-MAIN-20210924050055-20210924080055-00639.warc.gz"} |
https://socratic.org/questions/alicia-draws-an-equilateral-triangle-and-then-rotates-it-about-its-center-throug | # Alicia draws an equilateral triangle and then rotates it about its center. Through which angle measures can she rotate the equilateral triangle to map it onto itself?
Sep 16, 2016
(360°)/3 = 120° which is the size of each exterior angle.
#### Explanation:
An equilateral triangle has 3 lines of symmetry, but of more importance in this case, it has rotational symmetry of order 3. This means that in a rotation of 360° the same image appears 3 times.
(360°)/3 = 120° which is the size of each exterior angle.
The triangle rotates through the exterior angle so that the next vertex can be in the same position as the previous one.
IN the same way, a square will rotate through 360/4 = 90°
A pentagon will rotate through 360/5 = 72° for the figure to map onto itself. | 2021-12-04 05:48:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "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": 0.7439510226249695, "perplexity": 557.7150126142584}, "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/1637964362930.53/warc/CC-MAIN-20211204033320-20211204063320-00089.warc.gz"} |
https://www.proofwiki.org/wiki/Definition:Indexed_Product | # Definition:Product Notation (Algebra)/Index
(Redirected from Definition:Indexed Product)
## Definition
Let $\struct {S, \times}$ be an algebraic structure where the operation $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.
Let $\tuple {a_1, a_2, \ldots, a_n} \in S^n$ be an ordered $n$-tuple in $S$.
The composite is called the product of $\tuple {a_1, a_2, \ldots, a_n}$, and is written:
$\ds \prod_{j \mathop = 1}^n a_j = \paren {a_1 \times a_2 \times \cdots \times a_n}$
## Multiplicand
The set of elements $\set {a_j \in S: 1 \le j \le n, \map R j}$ is called the multiplicand.
## Notation
The sign $\ds \prod$ is called the product sign and is derived from the capital Greek letter $\Pi$, which is $\mathrm P$, the first letter of product.
## Also see
• Results about products can be found here.
## Historical Note
The originally investigation into the theory of infinite products was carried out by Leonhard Paul Euler. | 2022-05-24 10:06:53 | {"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": 0.8694840669631958, "perplexity": 714.1140947548711}, "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/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00077.warc.gz"} |
https://toph.co/p/and-yet-another-and-problem | # Practice on Toph
Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.
# And... Yet Another AND Problem
By YouKnowWho · Limits 1s, 512 MB
YouKn0wWho has an integer $n$. He wants to find an integer sequence $a$ of size exactly $2n$ such that $0 \le a_i \lt 2^n$ for each valid $i$ and for each integer $k$ from $0$ to $2^n - 1$, there exists at least one non-empty subsequence of $a$ such that the bitwise AND of the elements of that subsequence is $k$.
Help YouKn0wWho find such a sequence. If there are multiple such sequences, output any. It can be shown that such a sequence always exists under the given constraints.
A sequence $b$ is a subsequence of a sequence $c$ if $b$ can be obtained from $c$ by deletion of several (possibly, zero or all) elements.
## Input
The first and only line of the input will contain single integer $n \, (1 \le n \le 18)$.
## Output
Output $2n$ integers $a_1, a_2, \ldots a_{2n}(0 \le a_i \lt 2^n)$ such that it satisfies the conditions mentioned in the statement. If there are multiple such sequences, output any.
## Samples
InputOutput
1
1 0
InputOutput
2
3 1 0 2
InputOutput
3
4 3 5 6 7 1
In the third test case, you can achieve each integer from $0$ to $2^3-1=7$ as bitwise AND of the elements of some non-empty subsequence of $a$:
• $a_1 \mathbin{\&} a_3 \mathbin{\&} a_6 = 4 \mathbin{\&} 5 \mathbin{\&} 1 = 0$
• $a_6=1$
• $a_2 \mathbin{\&} a_4 \mathbin{\&} a_5 = 3 \mathbin{\&} 6 \mathbin{\&} 7 = 2$
• $a_2 = 3$
• $a_1 = 4$
• $a_3=5$
• $a_4 \mathbin{\&} a_5 = 6 \mathbin{\&} 7 = 6$
• $a_5 = 7$
Here, $\&$ is the bitwise AND operator.
### Statistics
71% Solution Ratio
Noshin_1703086Earliest, 1w ago
Hotash_MeyeFastest, 0.0s
Noshin_1703086Lightest, 131 kB
FrdhsnShortest, 356B | 2021-11-28 23:54:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 29, "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": 0.5974392890930176, "perplexity": 704.8685275664606}, "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/1637964358673.74/warc/CC-MAIN-20211128224316-20211129014316-00525.warc.gz"} |
https://socratic.org/questions/if-32-l-of-a-gas-at-room-temperature-exerts-a-pressure-of-6-kpa-on-its-container-1 | # If 32 L of a gas at room temperature exerts a pressure of 6 kPa on its container, what pressure will the gas exert if the container's volume changes to 2 L?
Feb 28, 2016
96kPa will be the pressure exerted by gas in container, if its volume changes to 2L.
#### Explanation:
Assume that temperature at two volumes (i.e. 32L and 2L) remains unchanged.
Case i :
${V}_{1} = 32 L$
${P}_{1} = 6000 P a$
case ii:
${V}_{2} = 2 L$
P_2=?
we know that
${V}_{1} \propto \frac{1}{{P}_{1}}$$- - - - - - \left(1\right)$
${V}_{2} \propto \frac{1}{{P}_{2}}$$- - - - - - \left(2\right)$
doing $\left(1\right) / \left(2\right)$
$\frac{{V}_{1}}{{V}_{2}} = \frac{{P}_{2}}{{P}_{1}}$
substitute given data above equation
$\frac{32}{2} = \frac{{P}_{2}}{6000}$
${P}_{2} = 16 \times 6000$
${P}_{2} = 96000 P a$ | 2019-09-22 03:46:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "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": 0.5992822647094727, "perplexity": 3619.63119058367}, "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/1568514575076.30/warc/CC-MAIN-20190922032904-20190922054904-00269.warc.gz"} |
https://socratic.org/questions/59542d68b72cff0a2218ad0c | # Question 8ad0c
Jun 28, 2017
Here's how you can do that.
#### Explanation:
As you know, density represents mass per unit of volume.
In your case, an unknown substance is said to have a density of ${\text{0.384 g cm}}^{- 3}$, which means that every ${\text{1 cm}}^{3}$ of this substance has a mass of $\text{0.384 g}$.
${\text{density" = "0.384 g"/"1 cm}}^{3}$
Now, your goal here is to convert the mass from grams to pounds and the unit of volume from cubic centimeters to cubic feet.
A well-known conversion factor that you can use to convert the mass of ${\text{1 cm}}^{3}$ of this substance is
$\text{1 kg = 2.20462 lbs}$
Now, you should already know that
$\text{1 kg} = {10}^{3}$ $\text{g}$
so you can say that you have
0.384 color(red)(cancel(color(black)("g"))) * (1 color(red)(cancel(color(black)("kg"))))/(10^3color(red)(cancel(color(black)("g")))) * "2.20462 lbs"/(1color(red)(cancel(color(black)("kg")))) = 8.467 * 10^(-4) $\text{lbs}$
At this point, you can rewrite the density as
"density" = (8.467 * 10^(-4)color(white)(.)"lbs")/"1 cm"^3 color(white)(color(blue)( larr " equal to 0.384 g")/a
Finally, to convert the volume, use the conversion factor
$\text{1 ft = 0.3048 m}$
A more useful form will be
$\text{1 ft"^3 = "0.3048 m" * "0.3048 m" * "0.3048 m}$
$= {\text{0.028317 m}}^{3}$
As you know, you have
$\text{1 m} = {10}^{2}$ $\text{cm}$
This means that ${\text{1 cm}}^{3}$ will be equivalent to
$\text{1 cm"^3 = "1 cm" * "1 cm" * "1 cm}$
= 1 color(red)(cancel(color(black)("cm"))) * "1 m"/(10^2color(red)(cancel(color(black)("cm")))) * 1 color(red)(cancel(color(black)("cm"))) * "1 m"/(10^2color(red)(cancel(color(black)("cm")))) * 1 color(red)(cancel(color(black)("cm"))) * "1 m"/(10^2color(red)(cancel(color(black)("cm"))))
$= \text{1 m" * "1 m" * "1 m} \cdot {10}^{- 6}$
$= {10}^{- 6}$ ${\text{m}}^{3}$
You can thus say that you have
10^(-6) color(red)(cancel(color(black)("m"^3))) * "1 ft"^3/(0.028317color(red)(cancel(color(black)("m"^3)))) = 3.5314 * 10^(-5) ${\text{ft}}^{3}$
At this point, the density of the substance is equal to
"density" = (8.467 * 10^(-4)color(white)(.)"lbs")/(3.5314 * 10^(-5)color(white)(.)"ft"^3) color(white)(color(blue)( larr " equal to 0.384 g")/color(blue)(larr " equal to 1 cm"^3)
To find the mass of one unit of volume, i.e. of ${\text{1 ft}}^{3}$, simply divide the numerator and the denominator
"density" = color(darkgreen)(ul(color(black)(24.0 color(white)(.)"lbs ft"^(-3))))#
The answer must be rounded to three sig figs, the number of sig figs you have for the density of the substance. | 2020-08-04 16:57:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 27, "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": 0.7319040298461914, "perplexity": 1893.7396616418782}, "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/1596439735881.90/warc/CC-MAIN-20200804161521-20200804191521-00590.warc.gz"} |
http://physics.stackexchange.com/questions/30814/relativity-at-the-bus-stop | # Relativity at the bus stop [closed]
This happened to me last week. So I was at my university waiting for the bus. Now there are two buses I can take, let's just call them Bus A and Bus B.
Let's assume the number line is the path of the bus and the university is at $x = 0$ (and $x\geq0$).
My destination is $x = 2$ and Bus A takes me straight to there. Bus A on the other hand only takes me to $x = 1$ and to get to $x = 2$, I have to wait at $x = 1$ until a Bus B comes and takes me to $x = 2$.
Assume that the traffic level is the same and both buses have the same speed/acceleration.
What happened me to last week was that I waited for Bus B to come, but it didn't so I decided to take Bus A which took me to $x = 1$ and as soon as I got out of Bus A, I see a Bus B speeding up from behind and I got onto Bus B immediately.
How could this have had happened?
-
Assume facts that are false (i.e. that bases in the real world have some idealized behavior) and your experience will differ from you expectation. That's just life, not physics. – dmckee Jun 26 '12 at 21:33
## closed as off topic by Colin K, dmckee♦Jun 26 '12 at 21:32
Questions on Physics Stack Exchange are expected to relate to physics within the scope defined in the FAQ. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about closed questions here. | 2013-05-23 21:32:10 | {"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": 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": 0.45548608899116516, "perplexity": 649.1552284964794}, "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-2013-20/segments/1368703830643/warc/CC-MAIN-20130516113030-00085-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://luc.lino-framework.org/blog/2015/0223.html | # Monday, February 23, 2015¶
I continued to research and document about GFK fields in /dev/gfks and /tutorials/gfks/index.
I understood that the allow_stale_generic_foreignkey attribute can be replaced by a nullable ForeignKey, so I removed this feature and adapted the only place where it was used (lino.modlib.changes).
I added a column “Action” to the BrokenGFKs table. See get_broken_generic_related.
TODO: a management command to cleanup broken GFK fields. This would execute the suggested actions (delete and clear) without any further user interaction.
## RefundConfirmation has no doctor_type¶
This error message occured in Eupen in yesterday’s version. The reason was that create_doctor_choice may not do:
if not self.doctor_type:
but must do:
if not self.doctor_type_id:
This is because doctor_type is not nullable, and because Django behaves oddly in that case. I told them already 5 years ago that this behaviour is odd, but they don’t listen to me. Oh (wow!) I just noticed that 3 months ago they even started to consider that I might be right. Thanks, simon29.
I also wrote a docstring for ForeignKeyStoreField.parse_form_value.
I added a section “Creating a doctor” in The Social Aids module to test this.
I changed the language distribution of lino_welfare.projects.eupen from “de fr nl” to “de fr en”. Which –as expected– caused some changes in the test suite. But I think that it is necessary so that Mahmoud an optential other future team members can follow. | 2018-10-15 22:23:43 | {"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": 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": 0.26760050654411316, "perplexity": 5736.990748473846}, "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-2018-43/segments/1539583509845.17/warc/CC-MAIN-20181015205152-20181015230652-00001.warc.gz"} |
https://gitee.com/openharmony/developtools_hdc_standard/blob/master/hdc.gni | The current repo belongs to Closed status, and some functions are restricted. For details, please refer to the description of repo status
## OpenHarmony / developtools_hdc_standardClosed .gitee-modal { width: 500px !important; }
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hdc.gni 1.25 KB
Faith authored 2022-02-15 15:14 . update build
# Copyright (C) 2021 Huawei Device Co., Ltd.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
declare_args() {
# build with --gn-args "hdc_debug=true, which is used to debug"
hdc_debug = false
hdc_host_hide_debug_win = true
hdc_support_uart = true
if (is_mac) {
hdc_support_uart = false
}
hdc_test_coverage = false
hdc_jdwp_test = false
js_jdwp_connect = true
}
code_check_flag = [
"-Wformat",
"-Wall",
"-Wmissing-field-initializers",
"-Wuninitialized",
"-Wnull-pointer-arithmetic",
"-Wunused-lambda-capture",
"-Wuser-defined-warnings",
"-Wenum-compare-switch",
"-Wunneeded-internal-declaration",
"-Wundefined-var-template",
"-Wnonportable-include-path",
"-Wformat-extra-args",
"-Wformat",
"-Wsign-compare",
"-Woverloaded-virtual",
]
1
https://gitee.com/openharmony/developtools_hdc_standard.git
git@gitee.com:openharmony/developtools_hdc_standard.git
openharmony
developtools_hdc_standard
developtools_hdc_standard
master | 2023-03-29 19:11:04 | {"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": 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": 0.1747095137834549, "perplexity": 13807.8732366965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2023-14/segments/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00410.warc.gz"} |
https://docs.vespa.ai/en/reference/config-files.html | # Custom Configuration File Reference
This is the reference for config file definitions. It is useful for developing applications that has configurable components for the Vespa Container, where configuration for individual components may be provided by defining <config> elements within the component's scope in services.xml.
## Config definition files
Config definition files are part of the source code of your application and have a .def suffix. Each file defines and documents the content and semantics of one configuration type. Vespa's builtin .def files are found in \$VESPA_HOME/share/vespa/configdefinitions/.
### Package
Package is a mandatory statement that is used to define the package for the java class generated to represent the file. For container component developers, it is recommended to use a separate package for each bundle that needs to export config classes, to avoid conflicts between bundles that contain configurable components. Package must be the first non-comment line, and can only contain lower-case characters and dots:
package=com.mydomain.mypackage
### Parameter names
Config definition files contain lines on the form:
parameterName type [default=value] [range=[min,max]]
camelCase in parameter names is recommended for readability.
### Parameter types
Supported types for variables in the .def file:
int 32 bit signed integer value 64 bit signed integer value 64 bit IEEE float value Enumerated types. A set of strings representing the valid values for the parameter, e.g: foo enum {BAR, BAZ, QUUX} default=BAR A boolean (true/false) value A String value. Default values must be enclosed in quotation marks (" "), and any internal quotation marks must be escaped by backslash. Likewise, newlines must be escaped to \n A path to a physical file in the application package. This makes it possible to access files from the application package in container components. Path parameters cannot have default values, so the path must be given in services.xml. The path to the file is relative to the root of the application package. The content will be available as a java.nio.file.Path instance when the component accessing this config is constructed. Similar to path, an arbitrary URL of a file that should be downloaded and made available to container components. The file content will be available as a java.io.File instance when the component accessing this config is constructed. Note that if the file takes a long time to download, it will also take a long time for the container to come up with the configuration referencing it. A config-id to another configuration (only for internal vespa usage)
### Structs
Structs are used to group a number of parameters that naturally belong together. A struct is declared by adding a '.' between the struct name and each member's name:
basicStruct.foo string
basicStruct.bar int
### Arrays
Arrays are declared by appending square brackets to the parameter name. Arrays can either contain simple values, or have children. Children can be simple parameters and/or structs and/or other arrays. Arbitrarily complex structures can be built to any depth. Examples:
intArr[] int # Integer value array
row[].column[] int # Array of integer value arrays
complexArr[].foo string # Complex array that contains
complexArr[].bar double # … two simple parameters
complexArr[].coord.x int # … and a struct called 'coord'
complexArr[].coord.y int
complexArr[].coord.depths[] double # … that contains a double array
Note that arrays cannot have default values, even for simple value arrays. An array that has children cannot contain simple values, and vice versa. In the example above, intArr and row.column could not have children, while row and complexArr are not allowed to contain values.
### Maps
Maps are declared by appending curly brackets to the parameter name. Arbitrarily complex structures are supported also here. Examples:
myMap{} int
complexMap{}.nestedMap{}.id int
complexMap{}.nestedMap{}.name string
## Generic configuration in services.xml
services.xmlhas four types of elements:
individual service elements (e.g. searcher, handler, searchnode) - creates a service, but has no child elements that create services (e.g. content, container, document-processing - creates a group of services and can have all types of child elements (e.g. accesslog) - configures a service or a group of services and can only have other dedicated config elements as children always named config
Generic config elements can be added to most elements that lead to one or more services being created - i.e. service group elements and individual service elements. The config is then applied to all services created by that element and all descendant elements.
For example, by adding config for container, the config will be applied to all container components in that cluster. Config at a deeper level has priority, so this config can be overridden for individual components by setting the same config values in e.g. handler or server elements.
Given the following config definition, let's say its name is example.def:
package=com.mydomain.example
stringVal string
myArray[].name string
myArray[].type enum {T1, T2, T3} default=T1
myArray[].intArr[] int
myMap{} string
basicStruct.foo string
basicStruct.bar int default=0 range=[-100,100]
boolVal bool
myFile path
myUrl url
To set all the values for this config in services.xml, add the following xml at the desired element:
<config name="com.mydomain.example">
<stringVal>val</stringVal>
<myArray>
<item>
<name>elem_0</name>
<type>T2</type>
<intArr>
<item>0</item>
<item>1</item>
</intArr>
</item>
<item>
<name>elem_1</name>
<type>T3</type>
<intArr>
<item>0</item>
<item>1</item>
</intArr>
</item>
</myArray>
<myMap>
<item key="key1">val1</item>
<item key="key2">val2</item>
</myMap>
<basicStruct>
<foo>str</foo>
<bar>3</bar>
</basicStruct>
<boolVal>true</boolVal>
<myFile>components/file1.txt</myFile>
<myUrl>https://docs.vespa.ai/en/reference/query-api-reference.html</myUrl>
</config>
Note that each '.' in the parameter's definition corresponds to a child element in the xml. It is not necessary to set values that already have a default in the .def file, if you want to keep the default value. Hence, in the example above, basicStruct.bar and myArray[].type could have been ommited in the xml without generating any errors when deploying the application.
### Configuring arrays
Assigning values to arrays is done by using the <item> element. This ensures that the given config values do not overwrite any existing array elements from higher-level xml elements in services, or from Vespa itself. | 2021-10-26 15:37:14 | {"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": 0.21356907486915588, "perplexity": 3464.1083817570475}, "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-2021-43/segments/1634323587908.20/warc/CC-MAIN-20211026134839-20211026164839-00174.warc.gz"} |
https://www.physicsforums.com/threads/c-method-question.968646/page-2 | # C/++/# C# method question
#### jedishrfu
Mentor
I was thinking of this song when I wrote forever and a day
#### rcgldr
Homework Helper
Historical trivia - although early versions of Fortran did not support recursion, the somewhat unusual mathematical language APL, which dates back to the 1960's, did.
#### phinds
Gold Member
Historical trivia - although early versions of Fortran did not support recursion, the somewhat unusual mathematical language APL, which dates back to the 1960's, did.
Fortran's development was, apparently, a bit scattershot and not academically rigorous. It was supported by IBM computers.
At the same time (more or less) ALGOL was developed as an academically rigorous language and it was supported by Burroughs computers. It allowed recursion. ALGOL was at that time the only acceptable language for submitting sample code / algorithms to the Association for Computing Machinery
#### .Scott
Homework Helper
@Chestermiller
As many have already replied, this is an example of recursion. You will also get recursion when funcA calls funcB and funcB calls funcA - hopefully with some check that prevents the process from continuing ad infinitum. As @rcgldr explained, each time a function is called, it allocates a block of memory on the stack for the local variables.
Most computer languages support recursion. If you write a program with functions that are recursive and without a check to keep the recursion finite, the compiler might catch it and give you a warning. More typically, it will make it to runtime where a "stack overflow" will be generated and reported.
The concept of separating the compiled program (code) from the data has become the norm - so much so that some of the terminology related to this is rarely used anymore. For example, a "pure code" block is a section of memory that contains only code and no data - once execution begins, it is in essence read-only. But nowadays, programmers seldom refer to a code block as "pure" because the alternative is considered absurd.
There was a day when every byte of memory was precious and parameters were always passed to a function by writing them to memory that was within the code block. Or, worse yet (by today's standards) instructions within a function would be modified before the function was called. The HP2100 series minicomputers stored the return address (from the calling routine) at the word before the function. This made their code blocks inherently impure.
There is a related term: reentrancy - whether a function can be called again before it has completed. Recursion requires reentrancy. But any routine that is shared among separate concurrent execution threads must also be reentrant.
#### harborsparrow
Gold Member
Many good responses so far.
A classic programming exercise is to have students solve a problem using recursion (which extends the "stack" automatically), and then also solve the same program without recursion, which requires the student arduously to store the state of the calculation after each step by manual coding in arrays.
Once you understand how to do that, then it is time to learn about tail recursion, a clever trick that prevents stack overflow absolutely. This following example is for Scala (an extension of Java). The example contains an excellent description of tail recursion:
https://www.scala-exercises.org/scala_tutorial/tail_recursion
#### FactChecker
Gold Member
2018 Award
The factorial is a simple example of a problem that recursion can be used to solve, but not the best because it is so easy to do in a loop. A better example is the Tower of Hanoi puzzle. Trying to do that in a loop would require a lot of effort to keep track of each step so that the information of the different steps does not get mixed up. The recursion approach allows the computer to keep track of it all with little effort on the programmer's part.
#### stevendaryl
Staff Emeritus
I never studied compiler theory, so I don't actually know how recursion is implemented, at the machine level. I can understand it at the level of "rewrite rules". If you have a definition of $f(x)$ such as:
f(x) = if (x=0) then 1 else x * f(x-1)
then you could eventually turn, say, f(17) into an answer by continually doing one of two things:
1. Evaluate the "if-then-else" to replace it by the "then" or the "else" branch.
2. Replace expressions involving f by its definition
So for example, an evaluation sequence might be
f(17)
if (17 = 0) then 1 else 17 * f(17-1)
17*f(17-1)
17*f(16)
17*(if (16 = 0) then 1 else 16*f(16-1))
etc.
How it's actually done is something involving stacks
#### Paul Colby
Gold Member
I first ran across recursion in programming in the 80's using c. It was like a religious experience. Newer flavors of FORTRAN support recursion (and much much more)
#### rbelli1
Gold Member
a clever trick that prevents stack overflow absolutely
This trick only fixes the stack issue if your optimizer knows the trick.
BoB
#### sysprog
This trick only fixes the stack issue if your optimizer knows the trick.
BoB
Presumably, @harborsparrow was well aware of that when citing Scala as an example. Scala compiles to JVM byte codes, and was designed with tail recursion in mind. From the wikipedia Scala article:
Tail recursion
Functional programming languages commonly provide tail call optimization to allow for extensive use of recursion without stack overflow problems. Limitations in Java bytecode complicate tail call optimization on the JVM. In general, a function that calls itself with a tail call can be optimized, but mutually recursive functions cannot. Trampolines have been suggested as a workaround.[32] Trampoline support has been provided by the Scala library with the object scala.util.control.TailCalls since Scala 2.8.0 (released 14 July 2010). A function may optionally be annotated with @tailrec, in which case it will not compile unless it is tail recursive.[33]
#### Paul Colby
Gold Member
Since the mean topic of this thread is recursion I would mention Lisp or it's simpler more modern dialect, Scheme. Lisp is an ancient language appearing at or before FORTRAN. Tail recursion is explicitly called out in the Scheme spec. One free implementation I would recommend is Chicken Scheme which has the option of compiling into c or running interactively.
Like lisp, scheme has a very minimal syntax. The factorial function is coded
(define (factorial N)
(if (< N 1) 1 (* N (factorial (- N 1)))))
I just now computed (factorial 3000) with no issues. Chicken Scheme implements unlimited integer and rational arithmetic. Rational numbers like 1/2 are 1/2 not 0.49999999.. Which is nice when needed.
Of course I recommend Scheme for recreational programming purposes only.
Haskell is another more modern functional language which embraces both recursion and lazy function evaluation. It is without equal at being the most annoying computer language ever devised IMO. It makes programming like talking to dolphins or space aliens. Even so, many interesting programming concepts are exposed.
#### sysprog
It is without equal at being the most annoying computer language ever devised IMO.
You haven't encountered Intercal, Maleboge, or Befunge? You can find those, and other languages, that make Haskell, by comparison, seem straightforward, clean, tidy, perspicuous, and even soothing, at https://esolangs.org/wiki/Language_list
#### stevendaryl
Staff Emeritus
Haskell is another more modern functional language which embraces both recursion and lazy function evaluation. It is without equal at being the most annoying computer language ever devised IMO. It makes programming like talking to dolphins or space aliens. Even so, many interesting programming concepts are exposed.
Why do you find Haskell annoying? It's certainly a very different way of thinking about programming.
The problem with slick programming languages with recursion is that it is very easy to write a program that will take the lifetime of the universe to complete. Of course, you can do that in any language, but if you don't use recursion, it's a little more obvious that you've done something suspicious.
#### Paul Colby
Gold Member
Why do you find Haskell annoying? It's certainly a very different way of thinking about programming.
Well, programming is a means to an end for a major segment of the population. Anything that keeps one from that end is annoying. Haskell is more of an obstruction than a solution for the types of problems I typically encounter. Hence, it's annoying.
#### stevendaryl
Staff Emeritus
Well, programming is a means to an end for a major segment of the population. Anything that keeps one from that end is annoying. Haskell is more of an obstruction than a solution for the types of problems I typically encounter. Hence, it's annoying.
I guess I was asking why do you feel it is more of an obstruction than a solution.
#### Paul Colby
Gold Member
You haven't encountered Intercal, Maleboge, or Befunge?
I was restricting, excluding parody languages.
#### Paul Colby
Gold Member
I guess I was asking why do you feel it is more of an obstruction than a solution.
How many device drivers have you written in Haskell?
#### stevendaryl
Staff Emeritus
How many device drivers have you written in Haskell?
Certainly Haskell isn't the right language for that.
#### sysprog
Paul Colby said:
I was restricting, excluding parody languages.
Mais, bien sûr, Monsieur [but of course, Sir]; c'était une blague [that was a joke].
#### sysprog
Certainly Haskell isn't the right language for that.
Might that qualify as an understatement?
#### sysprog
How many device drivers have you written in Haskell?
The same implicit criticism is applicable to any other languages that are not readily capable of low-level machine-specific operations. As functional languages go, I think Haskell is pretty good. Why single it out as the most annoying language?
#### Paul Colby
Gold Member
Why single it out as the most annoying language?
Here, I was joking....
Well, I hadn't yet touched on Haskells many typographical failings. These are a clear matter of personal preference. But then I find indentation in python egregious but quickly put that irritant aside for its many many strong points. Haskell hates side effects and for me a computer is a side effect.
#### sysprog
Paul Colby said:
Haskell hates side effects and for me a computer is a side effect.
You appear to be using the term 'side effect' in a manner other than to denote its functional-language-specific meaning whereby it refers to local functions modifying things that are global or otherwise outside their pre-designated scope.
#### Paul Colby
Gold Member
You appear to be using the term 'side effect' in a manner other than to denote its functional-language-specific meaning whereby it refers to local functions modifying things that are global or otherwise outside their pre-designated scope.
Cool, so the ADF435 frequency synthesizer chip has 6 hardware registers that are set by serial toggling various GPIO lines in the proper sequence. How is this done in Haskell?
"C# method question"
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• Solo and co-op problem solving | 2019-05-20 14:22:41 | {"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": 0.44614654779434204, "perplexity": 2921.2715117835296}, "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/1558232256040.41/warc/CC-MAIN-20190520142005-20190520164005-00368.warc.gz"} |
https://crypto.stackexchange.com/questions/80436/how-much-entropy-do-i-need-to-add-to-passwords-if-they-are-not-used-in-conjuncti | # How much entropy do I need to add to passwords if they are NOT used in conjunction with logins
I'm building a system to authenticate users to a website via a single use login token. This token can either be included in links OR typed in directly by the user as a code. Because of that second requirement I'm interested in the token being as short as possible in order to improve user experience.
There are plenty of guidelines regarding "regular" password strength, i.e. for a password to be used in conjunction with a login handle (email, username...). But in my case I believe the entropy needs to be higher since an attacker would essentially be targeting all users in the system at once when doing a brute force attack: if they guess any of the currently valid tokens they'll get into that random user's account.
So the solution needs to take into account how many valid tokens exist in the system.
So, if I can have up to $$v$$ valid tokens at any point in time in the system, how much more entropy do my tokens need to have? Do I just need to add $$log_2(v)$$ bits of entropy or is there something else to take into account? How can we prove that?
PS: I'm focusing here on the additional entropy required compared to "regular" password systems as a way to focus the discussion, as there are various measures that can be put in place to reduce required entropy (rate limiting, token expiration policies etc.) that could be applied, but this is not my question :)
• This is subjective and depends on your threat model and constraints. Is there any reason you can't use 128 bits (16 bytes)? – SAI Peregrinus May 3 at 22:29
• There's one use case where users will need to type these in, so if I can reduce the size without compromising security that's helpful. And I don't think it's subjective or depends on the threat model, I tried to make this clear in the PS: the question is really that in this case an attack is targeting multiple passwords/tokens at once and I'm not sure by how much I need to increase entropy to compensate for that. – Jules Olléon May 3 at 23:01
• how are you verifying tokens? direct lookup against an index? or, are the tokens hashed to obtain the identifier? if the latter, any hardness-factor to obtain the hash (ie. argon2?) – brynk May 4 at 4:12
Summarizing the question:
I can have up to $$v$$ valid tokens at any point in time in the system, how much more entropy do my tokens need to have compared to "regular" password systems?
In addition to regular password entropy, $$\log_2(v)$$ bit extra is enough if the number of online attempts $$a$$ that an attacker can make is unchanged. That amount of additional entropy is necessary if you want no increase in the probability $$\epsilon$$ that $$a$$ online attempts succeed to find a working token, compared to the probability of logging into any account assuming the list of accounts is large and known to the attacker¹. Less extra entropy may be needed to maintain the probability that an adversary logs into a particular account², but how much depends on the distribution of passwords assumed in calculating password entropy.
Caution: Except when the system (rather than users) assign uniformly random password values, password entropy has almost nothing to do with the base-2 logarithm of the number of possible passwords. It varies widely with the restrictions put by the system on the choice of password, and with how dearly users care for the security of the data protected by the password. Also, that a certain password entropy is used is no proof that it is enough! And, the hypothesis of constant $$a$$ might not apply³.
Therefore, you can and should compute directly (without reference to a password-based system) how much entropy is needed in a token: that's $$\log_2(v)+\log_2(1/\epsilon)+\log_2(a)$$ bit⁴. The simplest and best is that the token is this many bits chosen independently and uniformly at random. That's assuming no information leak beyond correct/incorrect token, like getting an answer faster when the beginning of a token is correct, as notoriously occurs for comparisons using memcmp.
One may choose $$\log_2(1/\epsilon)=20$$ (slightly less that one chance in a million) and $$a$$ the number of possible attempts in a day given countermeasures³ to limit this in the server, or the sheer server capacity or link bandwidth absent such countermeasure. The estimation of $$a$$ should account for the possibility of concurrent attacks ($$a$$ is independent of network lag).
¹ Making the best attack strategy to test all accounts for the most likely password (or the few most likely ones starting from the most likely).
² Making the best attack strategy to test the account targeted for passwords approximately in decreasing order of likelihood.
³ Countermeasures to lower $$a$$ are easier with passwords and small user lists (or user lists assumed not to leak), because we can limit the number of login attempts per day/hour/minute and per user, something that might be impossible in the token context. Limiting the total number of attempts per second for the whole server opens to Denial of Service attacks, and limiting per attacker based on IP address is both difficult and uncertain: attackers may use multiple IP addresses using botnets, generate IPv6 addresses on the fly, or maybe spoof IP addresses if acting deep enough in the network infrastructure.
⁴ Proof for that formula: there are $$k$$ possible tokens, and $$v$$ of them are assigned uniformly at random and independently (except for being distinct). Attackers make $$a$$ attempts to log in by submitting a token, different at each time which maximizes their chances. Each attempt has the same probability $$1/k$$ to hit a particular token irrespective of the index of the attempt (for the same reason that the order in picking straws is immaterial to the probability one has to pick the shortest straw). Since these $$a$$ events are exclusive, the probability to hit any particular token in $$a$$ attempts is $$a/k$$. By the union bound, the probability $$\epsilon$$ to hit at least one of the $$v$$ tokens is at most $$v$$ times larger, that is $$\epsilon\le v\,a/k$$, and close to that for the low $$\epsilon$$ that we want in practice. Thus we want $$k\ge v\,a/\epsilon$$, and that only errs slightly, always on the safe side. Taking the base-2 logarithm, that gives $$\log_2 k\ge\log_2(v)+\log_2(1/\epsilon)+\log_2(a)$$.
• Awesome, I realize the formula to derive entropy needed from $v$, $\epsilon$ and $a$ is exactly what I was looking for - I was referring to "regular password strength" because I hadn't figured how to express it in terms of $a$ and $\epsilon$ like you did, even though I was looking at the right variables. Very nice way to formulate it! Now is there a somewhat more formal proof for the $log_2(v)$ part? – Jules Olléon May 4 at 10:08
• Also yes on everything you said around it - token will be generated using a proper RNG etc. And I will likely implement a rate limit to set an upper bound on $a$, with the caveats you mentioned in mind - BTW I think you meant DOS attack, not DNS, right? – Jules Olléon May 4 at 10:13
• @JulesOlléon: I managed to make a proof, with some help. Independently: take note of the important condition that I added after the formula. – fgrieu May 4 at 16:39
• @JulesOlléon: I stand by exactly $a/k$ for the probability to hit at least once one particular token in $a$ attempts with the strategy of not making the same guess twice (which is best). $1-(1-1/k)^a$ would apply with the strategy of using an independent random try at each of $a$ attempts, and is a (slightly) lower probability for $a\ge2$. In both cases the probability is $1/k$ to hit that particular token at a given try, but the not-twice-the-same-guess strategy makes the hitting events exclusive, hence the different formula to compute the probability of hitting at least once. – fgrieu May 5 at 10:40
• Oooh gotcha, yes you're absolutely right, for some reason the sentence about the probability being "irrespective of the index of the attempt" confused me and my mind went to "independent" rather than "exclusive" events... but you're right, it's like picking $a$ cards out of a deck of $k$ cards, the probability that your hand includes a specific card is $a/k$. – Jules Olléon May 5 at 10:55
Entropy $$H$$ is not only defined from the domain/alphabet/encoding. It ultimately depends on the distribution of the words chosen over this alphabet. Roughly speaking, considering a discrete variable $$x_i \sim {X}$$, the Shannon Entropy is defined by
$$H(X) = - \sum P(x_i) log P(x_i)$$
That is the point: if you choose these codes in an (almost) uniform and independent way, the entropy can be easily calculated. You said "~27 bits", so if you have codes over a 27 bits space, you don't need to think about entropy, because it will demand an effort proportional to $$2^{27}$$. This is a easy math if your probability distribution is uniform over this domain.
Here is the problem: cryptographic protocols always suppose random keys, but truly randomness is not easy. This is when Min-Entropy ($$H_{min}$$) is a more suitable definition: because Entropy is an average measure ("conditional"). Min-Entropy considers that your distribution is not perfectly uniform and that the adversary can guess. Take a look in this Crypto.SE discussion here.
In conclusion, you must look at the source of your randomness, because its (Min-)Entropy will be the determinant of your bit code size. | 2020-07-05 09:40:34 | {"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": 33, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.665462851524353, "perplexity": 635.0944209158008}, "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/1593655887319.41/warc/CC-MAIN-20200705090648-20200705120648-00126.warc.gz"} |