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# Moved. See https://slott56.github.io. All new content goes to the new site. This is a legacy, and will likely be dropped five years after the last post in Jan 2023.
## Thursday, February 17, 2011
### TDD -- From SME Spreadsheet to TestCase to Code
In "Unit Test Case, Subject Matter Experts and Requirements" I suggested that it's often pretty easy to get a spreadsheet of full-worked out examples from subject-matter experts. Indeed, if your following TDD, that spreadsheet of examples is solid gold.
Let's consider something relatively simple. Let's say we're working on some fancy calculations. Our users explain until they're blue in the face. We take careful notes. We think we understand. To confirm, we ask for a simple spreadsheet with inputs and outputs.
We get something like the following. The latitudes and longitudes are inputs. The ranges and bearings are outputs. [The math can be seen at "Calculate distance, bearing and more between Latitude/Longitude points".]
Latitude 1Longitude 1Latitude 2Longitude 2rangebearing
50 21 50N004 09 25W42 21 04N071 02 27W2805 nm260 07 38
Only it has a a few more rows with different examples. Equator Crossing. Prime Meridian Crossing. All the usual suspects.
TDD Means Making Test Cases
Step one, then, is to parse the spreadsheet full of examples and create some domain-specific examples. Since it's far, far easier to work with .CSV files, we'll presume that we can save the carefully-crafted spreadsheet as a simple .CSV with the columns shown above.
Step two will be to create working Python code from the domain-specific examples.
The creation of test cases is a matter of building some intermediate representation out of the spreadsheet. This is where plenty of parsing and obscure special-case data handling may be necessary.
`from __future__ import divisionimport csvfrom collections import namedtupleimport relatlon_pat= re.compile("(\d+)\s+(\d+)\s+(\d+)([NSWE])")def latlon( txt ): match= latlon_pat.match( txt ) d, m, s, h = match.groups() return float(d)+float(m)/60+float(s)/3600, hangle_pat= re.compile("(\d+)\s+(\d+)\s+(\d+)")def angle( txt ): match= angle_pat.match( txt ) d, m, s = match.groups() return float(d)+float(m)/60+float(s)/3600range_pat= re.compile("(\d+)\s*(\D+)")def range( txt ): match= range_pat.match( txt ) d, units = match.groups() return float(d), unitsRangeBearing= namedtuple("RangeBearing","lat1,lon1,lat2,lon2,rng,brg")def test_iter( filename="sample_data.csv" ): with open(filename,"r") as source: rdr= csv.DictReader( source ) for row in rdr: print row tc= RangeBearing( latlon(row['Latitude 1']), latlon(row['Longitude 1']), latlon(row['Latitude 2']), latlon(row['Longitude 2']), range(row['range']), angle(row['bearing']) ) yield tc for tc in test_iter(): print tc`
This is long, but, it handles a lot of the formatting vagaries that users are prone to.
From Abstract to TestCase
Once we have a generator to build test cases as abstraction examples, generating code for Java or Python or anything else is just a little template-fu.
` from string import Templatetestcase= Template("""class Test_\${name}( unittest.TestCase ): def setUp( self ): self.p1= LatLon( lat=GlobeAngle(*\$lat1), lon=GlobeAngle(*\$lon1) ) self.p2= LatLon( lat=GlobeAngle(*\$lat2), lon=GlobeAngle(*\$lon2) ) def test_should_compute( self ): d, brg = range_bearing( p1, p2, R=\$units ) self.assertEquals( \$dist, int(d) ) self.assertEquals( \$brg, map(int,map(round,brg.deg)))""")for name, tc in enumerate( test_iter() ): units= tc.rng[1].upper() dist= tc.rng[0] code= testcase.substitute( name=name, dist=dist, units=units, **tc._asdict() ) print code`
This shows a simple template with values filled in. Often, we have to generate a hair more than this. A few imports, a "unittest.main()" is usually sufficient to transform a spreadsheet into unit tests that we can confidently use for test-driven development.
## Tuesday, February 8, 2011
### Unit Test Case, Subject Matter Experts and Requirements
Here's a typical "I don't like TDD" question: the topic is "Does TDD really work for complex projects?"
Part of the question focused on the difficulty of preparing test cases that cover the requirements. In particular, there was some hand-wringing over conflicting and contradictory requirements.
Here's what's worked for me.
Preparation. The users provide the test cases as a spreadsheet showing the business rules. The columns are attributes of some business document or case. The rows are specific test cases. Users can (and often will) do this at the drop of a hat. Often complex, narrative requirements written by business analysts are based on such a spreadsheet.
This is remarkably easy for must users to produce. It's just a spreadsheet (or multiple spreadsheets) with concrete examples. It's often easier for users to make concrete examples than it is for them to write more general business rules.
Automated Test Case Construction
Here's what can easily happen next.
Write a Python script to parse the spreadsheet and extract the cases. There will be some ad-hoc rules, inconsistent test cases, small technical problems. The spreadsheets will be formatted poorly or inconsistently.
Once the cases are parsed, it's easy to then create a Unittest.TestCase template of some kind. Use Jinja2 or even Python's string.Template class to rough out the template for the test case. The specifics get filled into the unit test template.
The outline of test case construction is something like this. Details vary with target language, test case design, and overall test case packaging approach.
`t = SomeTemplate()for case_dict in testCaseParser( "some.xls" ): code= t.render( **case_dict ) with open(testcaseName(**case_dict ),'w') as result: result.write( code )`
You now have a fully-populated tree of unit test classes, modules and packages built from the end-user source documents.
You have your tests. You can start doing TDD.
Scenarios
One of the earliest problems you'll have is test case spreadsheets that are broken. Wrong column titles, wrong formatting, something wrong. Go meet with the user or expert that built the spreadsheet and get the thing straightened out.
Perhaps there's some business subtlety to this. Or perhaps they're just careless. What's important is that the spreadsheets have to be parsed by simple scripts to create simple unit tests. If you can't arrive at a workable solution, you have Big Issues and it's better to resolve it now than try to press on to implementation with a user or SME that's uncooperative.
Another problem you'll have is that tests will be inconsistent. This will be confusing at first because you've got code that passed one test, and fails another test and you can't tell what the differences between the tests are. You have to go meet with the users or SME's and resolve what the issue is. Why are the tests inconsistent? Often, attributes are missing from the spreadsheet -- attributes they each assumed -- and attributes you didn't have explicitly written down anywhere. Other times there's confusion that needs to be resolved before any programming should begin.
The Big Payoff
When the tests all pass, you're ready for performance and final acceptance testing. Here's where TDD (and having the users own the test cases) pays out well.
Let's say we're running the final acceptance test cases and the users balk at some result. "Can't be right" they say.
What do we do?
Actually, almost nothing. Get the correct answer into a spreadsheet somewhere. The test cases were incomplete. This always happens. Outside TDD, it's called "requirements problem" or "scope creep" or something else. Inside TDD, it's called "test coverage" and some more test cases are required. Either way, test cases are always incomplete.
It may be that they're actually changing an earlier test case. Users get examples wrong, too. Either way (omission or error) we're just fixing the spreadsheets, regenerating the test cases, and starting up the TDD process with the revised suite of test cases.
Bug Fixing
Interestingly, a bug fix after production roll-out is no different from an acceptance test problem. Indeed it's no different from anything that's happened so far.
A user spots a bug. They report it. We ask for the concrete example that exemplifies the correct answer.
We regenerate the test cases from the spreadsheets and start doing development. 80% of the time, the new example is actually a change to an existing example. And since the users built the example spreadsheets with the test data, they can maintain those spreadsheets to clarify the bugs. 20% of the time it's a new requirement. Either way, the test cases are as complete and consistent as the users are capable of producing.
## Wednesday, February 2, 2011
### Escaping the Relational Schema Trap
We're struggling with our Relational Schema. We're not alone, of course, everyone struggles with the relational model. The technology imposes difficult limitations and we work around them.
There's kind of a 4-step process through which the relational schema erodes into irrelevance. The concept of a schema is not irrelevant. It's the rigid relational schema that's a problem.
Many DBA's will say that the relational model is the ultimate in flexibility. They're right, but they're missing the point. The relational database clearly separates the physical storage from the logical model as seen in tables and columns. It's flexible, but the presence of a rigid relational schema limits the pace of business change.
"Clearly," the DBA says, "you don't know how to use ALTER." I beg to differ. I can use ALTER; however, it doesn't permit the broad, sweeping scope of change that the business demands.
In order to attempt to match the pace of business change, we're using an ORM layer. This allows us to fabricate methods and properties left, right and center. We can tackle some pretty big problems with simple code changes. This, however, is no longer helping.
Straws and Camels
When designing a database, we have to be cognizant of the nature and tempo of change. In highly-regulated, very settled business applications (back-office accounting, for example) the data model is well known. Changes are mostly distinctive reporting changes and the tempo is pretty lethargic. It's the back office. Sorry, but innovation rarely happens there.
Each change is just a another hand-full of straw thrown on the camel's back. It happens fairly slowly. And there aren't many surprises. Hacks, workarounds and technical debt accumulates slowly.
In innovative, novel, experimental businesses, however, the nature and tempo are very different. The changes are disruptive, "what are you saying?" kinds of changes. They are "throw out the bathwater, the babies, the cribs and fire the nursemaid" kinds of changes. The tempo is semi-annual reinvent everything. Hacks, workarounds and technical debt get out of control suddenly.
Important Lesson Learned. When the customer misunderstands the offering and asks for something completely senseless, it's good to listen and try to build that -- even if it wasn't what you were offering. In some cases, the original offering was too complex or contrived. In other cases, the offering didn't create enough value. But when you offer [X] and the customer asks how much it will cost for [Y], you have disruptive, sudden, and surprising database changes.
This is bales of hay through onto an unprepared camel. Backs can get broken.
Coping
One common coping strategy is SQL ALTER statements to fiddle with the logical model. This has to be coupled with CREATE TABLE AS SELECT scripts to do open-heart surgery on the logical model. Married with modified ORM definitions. This requires some careful "schema versioning" techniques.
Another coping strategy is lots of "Expansion" columns in the tables. These can be renamed and repurposed without physical storage changes. The rows haven't physically changed, but the column name morphed from "EXPANSION_INT_01" to "Some_Real_Attribute". This doesn't prevent the CREATE TABLE AS SELECT scripts to do open-heart surgery. It still requires some careful "schema versioning" techniques to be sure that the ORM layer matches the logical schema.
A third -- and perhaps most popular -- coping strategy is manpower. Just having dedicated DBA's and maintenance programmers is a common way to handle this. Some folks object, saying that a large staff isn't a way to "cope with change" but is a basic "cost of doing business".
It's false, by the way, to claim that dedicated DBA's are essential. A solo developer can design and implement a database and application software with no help at all. Indeed, in most organizations, developers design and build databases, then turn them over to DBA's for operational support. If the nature of change is minor and tempo of change is slow, a solo developer can deal perfectly well with the database. A dedicated DBA is someone we add when the developer gets swamped by too much change.
(Some DBA's like to claim that the developers never get normalization or indexing correct. I counter with the observation that some DBA's don't get this right, either. DBA's aren't essential. They're a popular way to cope with the nature and tempo of change.)
In the ORM world, there are schema migration toolkits. Projects like Storm, this list for Django, Embarcadero Change Manager for Oracle, and numerous others attempt to support the schema evolution and change management problem. All of this is a clever way to cope with a problem inherent in our choice of technology.
Chaos Theory
Rather than invent clever coping mechanisms, let's take a step back. If we're inventing technology to work around the fixed relational schema, it might be time to rethink the relational schema.
"Oh noes," DBA's cry, "we must have a fixed logical model otherwise chaos ensues."
Really? How come we're always altering that schema? How come we're always adding tables and restructuring the tables?
"Oh that? That's 'controlled change'," the DBA responds.
No, that's slow chaos.
Here's how it plays out. We have a disruptive change. We negotiate with the DBA's to restructure the database. And the test database. And the QA database. We do the development database without any help from the DBA's. We fix the ORM layers. We unit test the changes.
Then we plan and coordinate the production rollout of this change with the DBA's. Note. We already made the change in development. We're not allowed to make the change in production. The DBA's then suggest design alternatives. Normalization isn't "right". Or there are physical changes that need to be declared in the table definitions. We redo the development database. And the ORM layer. And rerun the unit tests.
Because the production database couldn't be touched -- and we had paying customers -- we copied production data into a development database and started doing "production" in development. Now that we're about to make the official production change, we have two databases. The official database content is out-of-date. The development database is a mixture of live production and test data. Sigh.
Rethinking Schema
If the schema is a problem, perhaps we can live without it. Enter NoSQL databases.
Here's how you start down the slippery slope.
Phase I. You need a fairly radical database change. Rather than wait weeks for the DBA's, you ask for a single "BLOB" column. You take the extra data elements for the radical change, JSON encode them, and store the JSON representation in the BLOB field. Now you have a "subschema" buried inside a single BLOB column.
Since this is a simple ALTER, the DBA's will do it without a lot of negotiation or delay. You have a hybrid database with a mixture of schema and noSQL.
Phase II. You need an even more radical change. Rather than wait weeks for the DBA's, you ask for a few tables that have just a primary key and a BLOB column. You've basically invented a document-structured database inside SQL, bypassing the SQL schema entirely.
Phase III. While waiting for the Phase II changes to be implemented, you convert the customer data from their obscure, stupid format into a simple sequential file of JSON documents and write your own simple map-reduce algorithms in Python. Sure, performance is poor, but you're up and running without any database overheads.
Phase IV. Start looking for alternatives.
This MongoDB looks really nice. PyMongo offers lots of hints and guidance.
At least one person is looking at mango, a MongoDB database adapter for Django. For us, this isn't the best idea. We use OpenAM for identity management, so our Users and Sessions are simply cloned from OpenAM by an authentication backend that gets the user from OpenAM. SQLite works fine for this.
We think we can use Django's ORM and a relational database for User and Session. For everything else, we need to look closely and MongoDB.
Wins and Losses
The big win is the ability to handle disruptive change a little bit more gracefully.
The big loss in switching away from the Django ORM is we lose the built-in admin pages. We have to build admin Forms and view functions. While this is a bit of a burden, we've already customized every model form heavily. Switching from ModelForm to Form and adding the missing fields isn't much additional work.
The biggest issue with document-oriented data models is assuring that the documents comply with some essential or core schema. Schemas are inescapable. The question is more a matter of how the schema limits change. Having a Django Form to validate JSON documents for the "essential" features is far more flexible than having a Django Model class and a mapping to a relational database.
Schema migration becomes a non-issue until we have to expand the essential schema, which changes the validation rules, and may render old documents retroactively invalid. This is not a new problem -- Relational folks cope with this, also -- but if it's the only problem, then we may have streamlined the process of making disruptive business changes.
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You are on page 1of 6
# TUTORIAL 5 CPE614
## MULTIPLE UTILITIES & COGENERATION
1.
2.
3.
4. The pulp and paper industry companies comprises of used wood as raw material and
produce pulp, paper, paperboard and other cellulose-based products. In integration process, the
extract of stream data of a heat recovery in pulp and paper industry has been represented in
Table 1.
No Type (MW.K-1)
2 Hot 70 20 2.0
## 5 Cold 50 100 2.4
By assuming Tmin = 10C
a) Design a problem table analysis (PTA) and grand composite curve (GCC) with data given.
Thus, in pulp and paper industry it is operated at power consumption of 11 MW. The alternative
cogeneration schemes of steam turbine and gas turbine have been used be compared
economically.
b) An exhaust saturated steam turbine is been used for process heating at 190C. At same
conditions, superheated steam is generated in boiler house of 45 bars with a temperature
of 325C. With the isentropic efficiency of 87%, a superheated steam is expanded in a
single-stage turbine. Determine the maximum of power of these possible exhaust steams.
c) Measure the power generation if a gas turbine has been applied in this industry with a
flowrate of air of 70 kg.s-1 (Given: Cp air = 1.00 kJ/kg.C). Moreover, the gas turbine has
an efficiency of 50% with an exhaust temperature of 450C. While, the ambient
temperature in this system was 20C.
d) Calculate the most cost effective between steam turbine and gas turbine. Given of
information: Cost of fuel from gas turbine is \$6.5 GW -1, cost imported electricity is \$17 GW -
1
, cost exported electricity is \$11 GW -1, cost of fuel for steam generation is \$4 GW -1, and
overall efficiency of steam turbine is 80%.
5. Cogeneration or combine heat and power concept has been embraced by many process plants
to improve energy efficiency.
a) Define the concept of cogeneration and explain the significance of having such approach
to improve the utility system.
## b) State two common types of cogeneration heat engine.
A group of process engineers conducted a study on energy efficiency for a section of the preheat
train in hydroskimmer refinery to achieve minimum operating cost. The problem table cascade for
the process is shown in Table 1. Given that the ∆Tmin of 20C.
Table 1 The Problem Table Cascade
525 789
515 1080
435 850
415 384
350 550
205 567
185 90
135 0
125 250
115 475
95 460
70 260
## a) Construct the grand composite curve (GCC) on a graph paper.
b) Perform an appropriate placement of the utilities against the GCC to achieve minimum
utility cost using the available utilities in Table 2. Clearly indicate the utilities and the duties
on the GCC. Justify your selection by providing the total utility cost.
## Stream Temperatures, (C) Cost (currency unit/kW)
VHP steam 550 10.5
HP steam 350 6.0
MP Steam 250 3.5
Cooling water 20-25 0.2
## c) Comment on the possibility of generating saturated LP steam at 120C (shifted
temperature) from the process. Demonstrate this possibility on the GCC (as drawn in part
(i) with indicate red line) and quantify the amount of steam generated in kg/hr. (Given C p
and heat vaporization of steam at 120C are 5.6012 kJ/kg.C and 2202.1 kJ/kg,
respectively).
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## Arizona COVID-19 Update – 6/27/20
The chart above is the one I’ve been thinking about putting together for quite a while now. It’s really busy, but it has a ton of information in it. Here’s how to read it.
1. Normalizing Case Counts by Population: I’m comparing both Pima and Maricopa counties (the two largest in the state by far) on a cases per 1000 basis. Why do I do this? If I compare them on raw numbers of cases, it looks like Pima County is doing SO much better than Maricopa because they have 1/4 the cases. However, Pima also has 1/4 the population. This is one way the news media exaggerates stories, probably because it looks stark and dramatic when you don’t compare appropriately. When I do this the right way, you can see that Pima and Maricopa had the same exact slope (more or less) up until Memorial Day. This is the purple arrow. After memorial day, we see case growth accelerate in both counties but a good deal faster in Maricopa County. This is the source of much of the overall case growth in Arizona.
2. Polynomial Trend Lines: The fat, light blue and pink lines are the trend lines for Maricopa and Pima respectfully. These are both modeled with 3rd Order Polynomials, which essentially means that the formula to create the trend line is something like Ax^3 + Bx^2 + Cx + D. This essentially shows that the case growth is accelerating (curving upward). Almost every state’s case growth right now can be modeled with this same kind of function. The trend line allows us to do simple predictions for the next few days on what the case growth might be. It is not a good predictor for much more than a few days out because the situation is too complex for that.
3. Testing Numbers and Results: The yellow dashed line represents the numbers of tests on each day. I had to pull these numbers from the state’s online Dashboard manually because they won’t let us download it. So the data may be off by 5-10 tests per day. Note that the Test Numbers are represented on the secondary Y-axis (the one on the right). This can be confusing, but it allows me to provide more valuable visualizations. I also tried to capture the weekly percent positive for the tests. As you can see the percent of tests that are positive is growing. I’ll try to offer some possible explanations for that in my conclusion.
4. Data Lags: Note that I extend the blue “Stay at Home” rectangle about 10 days past the 5/17 expiration date. I do this to demonstrate that most of the data we see every day has the potential for being as much as 10 days old. Data collection isn’t very clean and efficient when dealing with health-related issues. Any time you look at COVID-19 data, whether it is the CDC or the WHO or the AZ DHS, you need to remember that it’s likely reporting the state from a week or so beforehand. I’ve seen some embarrassing data analyses during this outbreak by professional media that did not account for the fact that recent data is likely to be underreported due to this lag. The testing numbers above are a good result. I have no reason to believe that AZ has slowed testing in the last week. We just don’t have the accurate numbers in yet.
5. Events/Triggers: I’ve labeled various events and triggers on the chart. The stay at home order and its expiration are interesting, as is Memorial Day. Face Masks became mandatory in AZ on about 6/20. You can be sure that will be added as an important event as the time goes on and more data comes in. My expectation is that we’ll see some sort of change in the trends in late June or early July (to account for the data lag but also the 14 day hospitalization cycle time).
6. Hospitalization: I’m not including hospitalization stats in this chart, largely because first, the chart is already too busy, but second, I have a hard time trusting/believing the states and counties hospitalization data, which all seem to contradict one another. Suffice it to be said that right now hospitals in the state are jam packed with COVID cases and there’s not much margin (at least in the traditional sense).
Analysis of the Chart
1. Comparison of Pima and Maricopa Cases per 1000: As mentioned above, it’s very interesting to me that the case growth up until Memorial Day in both counties is essentially linear and basically the same slope. Ending the stay at home order doesn’t seem to have dramatically impacted this case growth rate (even considering the data lag). Two events seem to have occurred simultaneously that may be causal for the dramatic case growth lately. First is Memorial Day. We see the exponential case growth start a few days after Memorial Day. It may well be that a number of people contracted the virus during Memorial Day activities (we’ll probably never know if the protests/riots contributed due to bad data on those events). Maybe there were super-spreader events during the holiday too that we haven’t identified. The second major event that certainly contributes is the doubling of testing that also started about this same time. The state was conducting an average of about 8K tests per day up until about June 4th when it doubled this to an average of about 16K tests per day. During the stay at home period there was an extreme bias in the tests toward sick patients because one could barely get tested unless they exhibited symptoms. Even then, only about 5% of tests were positive. The spreading that may have occurred around Memorial day combined with the doubling of testing have resulted in not just doubling the number of cases, but exponential growth, because now the percent positive rates are approaching 20%.
2. Why are the Tests’ positivity rates so high? This is interesting to think about but here are a few possible reasons. First: There is a lot more virus out there now since Memorial Day and people are catching it. One telling stat is what I have shown a few times (which still holds) that shows that the growth rate of infections in the 65+ community is still the same now as it was during the stay at home order. In short, this demographic is still travelling down the same purple arrow! All other groups are reflecting the exponential growth trend. It is likely that the 65+ community is being just as careful now as they did during stay at home orders (and maybe group homes have also become more careful) and they’re avoiding the bloom in the virus. Everyone else is exposed to a larger population of the virus. This is speculation, but it makes sens. Second: It may well be that there is emerging another kind of testing bias and now people who are more likely to be infected are more likely to get tested. For instance, since I can’t see WHERE the tests are being conducted, there’s a chance that a higher percentage of tests are coming from regions that are already having major outbreaks (border counties, native communities). This is possible, especially given that there appears to be clear indications that the virus is more prevalent in some areas than others. The only way to really prevent this bias is to do what some European countries did and randomize testing. Otherwise we have no real idea of what’s happening. Third point: I’m convinced that we’re not seeing issues with false positives on the PCR tests (but I still believe there are high false positives on the antibody tests that make them somewhat less informational right now).
3. Why are the Rates different for Pima and Maricopa County? First, one thing we’re seeing is that the rates can be very different in different regions. Not just across the world or across US states, but even by AZ Zip codes. After about 3 weeks of tracking this I’m still seeing the less wealthy zip codes have the highest overall numbers of cases per 1000 people AND the highest growth rates over time. This is interesting to analyze because it makes one curious about why this is happening. There are a number of hypotheses for this. It’s possible that people who are overall less healthy (maybe they don’t have good health care) may be more likely to get infected and then need to seek medical care. However, it does appear that this isn’t a very solid hypothesis when one looks at the demographics where the largest number of cases by far is in the younger, healthier age groups. Culture is one hypotheses I hear, for this, where the cultures in less wealthy regions have evolved to rely on others much more than the cultures in wealthy regions require. There are also ethnic cultures and traditions that may have some causality. Also, based on this evidence, some of the activities that are more commonly engaged in the wealthier zip codes (dining out, going to the gym, etc.) may actually be less causal of infections than we thought. From my observation, also, the culture of mask wearing in Arizona is stronger in the wealthier zip codes than in less wealthy or rural zip codes. It’s possible that this has an impact, but time will tell how significant of one. Regardless, there’s still much to learn about this.
4. Case Severity: With this virus, just like with the flu, there is a very wide range of severity. Measuring cases is interesting from a numbers standpoint, but it is not a good representation for the severity of an outbreak. A very large majority of the new cases we’ve been measuring (and in some cases, stressing about) are asymptomatic (or low-symptomatic) cases that aren’t requiring medical attention. The better measure of severity is deaths, of course, but also hospital cycle times and capacity measures (because they’re leading indicators for deaths). The hospital measures are extremely hard for a number of reasons mentioned in an earlier article on this site… Hospitals and their staffs are clearly being stressed with the growth in severe cases (even thought this growth is very small compared to the asymptomatic cases). Some of this is because this disease forces a 2-plus week cycle time on cases, something that appears to be extremely unusual for viral infections.
The Effect of Wealth on Cases in a Region
Above is the latest comparison of COVID-19 cases per 1000 population compared to median income. Note that the lowest median income zip codes is on the left and the highest is on the right. The average number of cases per 1000 for the poorest 25 zip codes is 9. The average for the wealthiest 25 zip codes is 2.6. You can see the yellow trend line shows a decrease in cases from the left to the right (case counts are on a logarithmic scale on the right y-axis). The red line are actual cases per 1K for the zip codes. Note that you may not see your zip code labeled on the chart (only about every 10th zip are labeled because otherwise the chart would extend around the room!).
Case growth follows this exact same trend. This means that the regions with the highest rate of change in their case counts (hot spots) tend to be on the left of this chart. This indicates that the overall trend of more cases in less weathy areas is not changing.
The Effect of Population Density
One explanation for the “wealth effect” is population density. This makes sense in light of the now-ubiquitous 6 Feet of Separation. Many of the lower income areas with high outbreaks are in zip codes that are known to have large numbers of people living in dense environments (apartment complexes, for instance). However, some of the regions with the highest outbreaks are rural and agricultural regions that have very low population density.
Overall, however, the chart above does show that the cases per 1K tends to go up as population density increases. The trend line is fit with an exponential function that has a decent (but not ideal) fit. Most likely, density is one component of the problem, but is likely not one of the larger components.
The Effect of Median Age
Another interesting characteristic of some zip codes that may be driving higher case counts is median age. This makes sense, especially since we already know that most of the cases in the current outbreak are asymptomatic cases among younger people. Therefore, this chart tells a very clear story. Outbreaks are much higher in regions with lower median ages.
## COVID-19 Update: The latest on Cases by Latitude
I’ve been fascinated throughout this outbreak at how it breaks across latitude ranges. Here’s the latest info on Latitude.
The above chart shows cumulative numbers normalized by the population for each region. This shows the upper North latitudes continue to lead in total cumulative cases and deaths per 1000 persons but a couple of the South latitude ranges are starting to catch up (Brazil, Ecuador, Chile, Argentina, South Africa).
Notably, the middle latitude ranges are still far less affected cumulatively.
Now above we see the instantaneous rates of change across the latitude bands. This chart shows us where today’s hot spots are. Note that the US latitudes are very low because overall, US cases are low compared to population. Most of the US cases right now are happening in the 30-40 N Latitude range (Arizona, Texas, California), but the rates in these locations are not large enough to show a significant spike in instantaneous rates (which are spiking for Africa and South America across the board right now). Note that 20-30 N. Latitude are starting to show increased slope in cases and deaths. This is largely due to a growing number of cases in India and Bangladesh.
## COVID-19 Update: The Troubles with Hospitalization Data
Hospitalization data right now seems to be one of the most critical signals that a COVID-19 outbreak in a region is getting serious. However, hospitalization data is really hard to analyze for a number of reasons:
1. Hospitals don’t like to share data. In many cases in the United States (including Arizona) there was no hospitalization data during the first part of COVID-19. This was not the case with European countries. I can make a number of guesses about this including Health Information Privacy (HIPAA), inconsistent data collection, and even a sense of unwillingness by private and public hospitals alike to reveal too much about their business. However, with COVID-19 there seems to be a renewed sense that hospitals are a public good and need to be more transparent. Arizona has a new executive order (23-2020) governing the reporting of COVID-19 data.
2. There doesn’t seem to be a strong central governance around hospitalization data. Before COVID-19 this was always what I assumed that CDC did, but now I think it’s just a function of the state’s Health Department. I think that if CDC created guidelines and reporting rules, we would have much richer and much more predictive data sets around the health of people in the US. Until then, however, it requires someone to clean data, hand-build datasets, etc., to extract useful information.
3. Hospital data tends towards the anecdotal side. I have had many forwards from people on LinkedIn or Facebook that came from the cousin of their sister-in-law, who is a surgeon in New York explaining how overwhelmed the ICU is there in whatever town they serve. Then an hour later I get another forward from some connection in the very next county in New York explaining why their hospital has no COVID cases. This is very, very common. I think some of this is due to the above lack of transparency in hospitals, where data is even hidden from employees. I’ve had more than one person who works in a hospital in Arizona tell me at some point during the COVID-19 outbreak that there is only around XX people in the COVID ward right now — “But don’t tell anyone”. I don’t understand the perceived secrecy of this data, but due to the secrecy and poor data reporting, the ancecdote tends to carry the day. Until the next day when the opposite story comes out.
4. Hospitalizations classified as COVID-19 may not have initially sought treatment for COVID. Florida is starting to run into a new kind of COVID-asymptomatic hospital patient who seeks care for an unrelated issue (broken leg, etc.) and then is tested and found to have COVID-19. This is challenging. Does the patient need to go to the COVID ward? Initially, it seems that yes, they were, but now the state is starting to handle these patients differently (and save the COVID ward for those with COVID symptoms). This is unlikely to be affecting ICU bed numbers, of course, but is possibly affecting inpatient bed counts (which are already reaching maximums as well).
5. The hospital business and processes are not well understood by the layman, even by the hospital employee at times. This results in lack of understanding of the real meaning behind a data visualization.
Overview of Arizona ICU Bed Management during COVID-19
One thing that is very interesting to me is ICU bed management. Obviously hospitals want to leverage their invested ICU bed capital to make money. This would seem to require limited excess capacity in the ICU — i.e., most beds full most of the time. During COVID-19 one of the earlier stories was how COVID would overrun the ICU’s at most hospitals. I believe this did happen to an extent in New York, but it hasn’t happened yet in Arizona. COVID-19 patients are still less than 40% of all the ICU beds occupied in Arizona, but the number has been growing. See the chart below which compares the percentage of all occupied ICU beds that have a COVID-19 patient in them.
Thoughts:
1. It seems like the COVID patients peaked as a percentage of the total ICU bed population in mid-April and then gradually tapered off until the lockdown easing was fairly much complete. We then see acceleration in cases drive up the percentage of COVID-19 patients to near 40%. Note there is still 15+% unoccupied ICU beds (though I’m not sure if they’re in the right places). But clearly, whoever the non-COVID patients in the ICU are, they’re decreasing. There may be an element of elective surgeries in the non-COVID ICU population, but I don’t think they’re as many as usual.
2. I can’t fully get my arms around what this chart is telling me, other than perhaps it shows that hospitals know how to manage their ICU bed resources. The total percentage of ICU beds filled in the state has gone from 74% around 5/21 to about 85% today (total about 130 beds). They have done this while COVID-19 cases in the ICU have increased by about 230 people (hence, the now-higher percentage of COVID patients in ICU beds). I don’t know how they made up those extra 100 people, but they did it somehow. They have some margin to work with, I suppose, because even today, 60+% of all inhabitants of the ICU are non-COVID.
3. This management is why the increase in hospital bed numbers has been linear while the COVID-19 case growth has been exponential. Here’s a view of hospitalization just compared with the numbers of 65+ COVID-19 cases. Note that the 65+ group which looks pretty linear when compared to the 20-44 age group cases still looks exponential when compared to the hospitalization (especially the ICU) rates.
## COVID-19 Arizona Update – Where are the Cases Happening?
The state AZHS Dashboard provides a download and a map of COVID-19 Cases by Zip code. I was playing with the data and noticed that most of the regions with higher cases per 1000 were areas that were known to have lower median incomes. This intrigued me, because we really don’t know much about who is involved in this current wave of COVID-19 infections (other than the age demographics that I presented in previous articles).
COVID-19 Outbreak Info by the richest and poorest zip codes in Arizona
First caveat… due to tribal regulations, I have zero data for tribal regions, many of which would qualify as areas with very low median incomes. This is too bad and if anyone from these regions is interested in having their data analyzed securely, please contact me.
My thoughts on this chart:
1. It is pretty clear that COVID-19 outbreaks are much higher in Zip Codes with lower median incomes. The yellow trend line on the chart shows a R2 score of just under 0.5, which indicates that the trend is a pretty solid fit considering this is real-world data. The average number of cases per 1000 in the poorest 20 zip codes is over 9 and the average of cases per 1000 for the richest 20 zip codes is 1.9. Even if you subtract the Yuma and Nogales zip codes that have some of the highest case rates in the country, the average for the 20 poorest zip codes is 6.5. I posted this chart on Facebook looking for theories on why the situation is this pronounced. There was a lot of good discussion about this, and it is clear that whatever is causal for this disparity, it is comprised of multiple cultural and economic variables.
2. Lots of businesses that were shut down during the state’s COVID-19 lockdown (gyms, restaurants, and even churches) probably have a much higher representation in the wealthier zip codes, where very large gyms, restaurants, and churches thrive. This would be an interesting study. It does seem like the current outbreak probably has much less to do with these kinds of businesses than we would have guessed.
3. Some of these regions that have much higher cases per 1000 people are agricultural areas. Most of these particular regions also have a very low death rate. Perhaps there’s something they’re doing that makes them more likely to get infected but less likely to be badly affected.
4. I also suspect that one influential variable is mask usage. My observation in Tucson is that the Foothills region has been much more diligent around face coverings than other parts of Tucson (and certainly rural Arizona). This may be one reason the Tucson Foothills zip code COVID-19 cases per 1000 are extremely low. This may also apply to regions in Phoenix that are similar to the Tucson Foothills.
5. Now that Pima and Maricopa county are mandating face coverings in public, we have a great opportunity for a natural experiment on the value of Face Coverings. My guess would be that we’ll see the case count flatten out in about two weeks. The question is whether this would have happened anyway. Hopefully we can compare mask vs. no mask regions afterwards.
Zip Codes with the largest Percent Increases in COVID-19 Cases
Arizona had a few really big case numbers in the days since I posted my first chart comparing cases with median income. Below are the zip codes that had the highest percent increase in the last 2 days. As you can see, these areas of fastest increase are generally in lower-income areas.
COVID-19 Cases by Zip Codes Sorted by Median Age
Unsurprisingly, the zip codes that trend younger are also showing a higher case count in general. This aligns with data where we see the 20-44 age group far outpacing the others in new cases. Interesting trivia: Based off the data from usa.com (came from the American Community Survey of 2010-1014), Colorado City’s median age is 15.
COVID-19 Cases Plotted Against Population Density
Following a similar approach, I also put together a scatter plot showing COVID-19 Cases per 1K people plotted against the Population Density of a Zip Code. The trend is one of the strongest yet (the R2 Coefficient is .29 which is usually pretty decent with non-laboratory data). Not a real surprise, but I imagine that density might be a good proxy for large apartment complexes. I’m thinking about ventilation, etc., when I wonder if people in apartment complexes (perhaps less expensive ones have poorer filtration?) have a higher risk of becoming infected with COVID-19.
## COVID-19 Arizona Update – 6/16/20
I continue to focus a bit on my home state, Arizona, due to the attention the large increase in post-easing cases has brought nationally. Over the last week most of the trends have continued.
Summary:
1. Cases continue growing, but it looks like the rate over the last week might be linear. I’ll show data from the two largest counties, Maricopa (Phoenix) and Pima (Tucson).
2. Border cases continue to grow. Santa Cruz county now has a case rate of over 20 cases per 1000 people. This is larger than the case rate for the state of New York. Yuma County’s case rate is 14 per 1000 people.
3. Arizona’s case rate as a whole is under 5 per 1000 people. There have been misleading stories that appear to indicate that Arizona has passed New York in normalized cases. This is only true when one considers the number of cases per person over the last week. Cumulatively, New York’s 19 cases per 1000 people is nearly 4x that of Arizona. Arizona’s case rate puts it at #23 in the nation, whereas New York’s is #1.
4. Arizona’s death rate as a whole is 0.166 deaths per 1000 people. For comparison, New York’s is 1.57 deaths per 1000. Arizona’s death rate is also 23rd in the nation (strange). Our counties range from 0.78 in both Navajo and Apache Counties down to 0.03 in both Graham and Yavapai Counties. Maricopa and Pima are 0.12 and 0.21 respectively.
5. Hospitalization has increased across the board in the state. It’s hard to pin down where exactly the hospitals are filling and where they aren’t due to the way the state shares data. Statewide, ICU bed usage is at 82%, which represents 1,347 ICU beds in use. This is up from 1,192 last week, a difference of 155 patients. Of these, 74, or about 1/2 are COVID-19 (or suspected) patients. When I add up all the hospital bed increases (not necessarily due to COVID patients) over the last month I get a 69% increase. The increase in hospitalization due just to COVID-19 patients was 72%. This sounded very high to me, so I went to the CDC Influenza Tracker site for comparison. The flu season in 2020 saw a one-month 34% increase in all hospital beds across the country (only due to flu). I then looked at what I knew was a bad flu year (2017-2018) and saw a 186% increase in hospitalization due to flu alone that year. One caveat is that one can’t determine what KIND of hospital beds were occupied during this flu season, so hard to compare perfectly to our situation. However, our 72% over the last month is about double the worst flu month this year and less than half of the worst month during a bad flu year. I’ll keep watching the numbers and hopefully it doesn’t keep increasing.
Normalized Cases by Age Group
What I’ve done below is figure out the populations of each Arizona age group below and then normalize the numbers of cases per age group by their population. This allows me to see for a given age group the number of cases per 1000 members of that group. I do the same for Deaths and Hospitalizations.
Interesting things to note:
1. Other than the <20 group, the number of cases per 1000 is pretty close for all other groups. This seems to confirm that the <20 group is much less likely to get infected by COVID. This group has been less tested than the other groups, but the number of tests seems to be a reasonable sample to give a decent estimate for the population.
2. The other metrics (deaths, hospitalizations) differ widely across the different age groups, as one might expect.
3. What this shows is that even at this stage, this disease is still pretty rare (at least per the formal counts). Other than the <20 group, somewhere under 1% of the population has been recorded to be infected. For the Arizona 20-44 age population that is driving most of the new cases, only .04% (of the whole group) has been hospitalized and .003% has died. 4.85% of the confirmed cases in this group has required hospitalization and 0.35% of the confirmed cases has died. Hopefully that explanation helps you read the table. Clearly, getting COVID-19 if you’re over 65 is really concerning (even though only .83% of that population has gotten it yet) due to the 28% hospitalization rate and 16% death rate for people who actually get the virus.
Update on Cases by Demographic
Note that age demographic case trends have continued at pretty much the same rates over the last week. Pima shows a one-day slowdown, but I don’t read much into that yet because it is most likely to be a data collection issue if it doesn’t continue for 3-4 days.
Hospitalizations Compared to Cases
The hospitalization rate (though I showed that it was increasing up above) still looks flat when compared to the case growth. Even though we know that hospitals have limited number of beds, I take this as good because the increase in hospitalization is much, much lower than the increase in cases. In Maricopa we saw about 200 new hospitalizations (only about 40 were ICU beds) to about 6000 new cases over the last week, about 3% of all cases. And looking at the chart, it appears that if trends continue, we’ll be seeing even lower percentages of all cases in the future. Again, this points to a boom in recording less serious cases. It is most likely that this is largely due to the greatly increased number of tests the state has been conducting. These asymptomatic cases may have been around all along but only now are we measuring them. This is why I think looking at hospitalization rates is the best metric now.
## COVID-19 Update: What’s Going On in Arizona – Part 2
After posting part one of this overview, I had an idea of how to gather data on the thing that I was most curious about, the age groupings of the new cases. I was fortunate that Fox10 in Phoenix had been taking screenshots of the daily cases and breakdowns from Maricopa county, so I went through their blog and pulled the numbers out by hand. It turns out that this was a very valuable activity, so I scrounged around on the internet until I found a similar situation for Pima County. Combined, these account for most of the population of the state, so their numbers should be representative of what’s happening.
Case Breakdown by Age Groups
These two plots tell a very interesting story since they contain data from the state lockdown (started easing on 5/1) as well as data from the post-lockdown. There are some obvious things to see:
1. Exponential case growth starts around 5/28 in all but one age demographic. Case acceleration is largest in both counties by far in the 20-44 year group. There is slight acceleration in the other groups (note that the Pima chart separates the 45-54 and 55-64 brackets whereas Maricopa does not).
2. The one exception to the above is the 65+ bracket, which seems to have had the same case slope since 4/9. This is interesting, because it makes the case that the accelerating case growth in the state since 5/28 has not impacted the most vulnerable population (~80% of deaths and ~70% of hospitalizations).
3. The lockdown seems to have succeeded in maintaining linear growth in cases for all age groups. The lockdown started gradually easing in about 1 week increments on 5/1. The exponential growth started about 3 weeks after easing started. Hard to take much away from this other than the first steps of easing (opening up some restaurants, etc.) appears to not be responsible for the exponential growth by themselves.
Conclusion from this data
The main conclusion I take away is that the factors driving 65+ case growth do not seem to have been affected by the state lockdown. Why do I make this conclusion? The 65+ group is the ONLY age group with linear growth in cases at a constant slope on this graph. The lockdown did not affect the slope and the easing has not affected the slope. This needs to be studied more, but it makes the case that the state lockdown in AZ was not effective in achieving the goal of protecting the most vulnerable age group. Since this group drives the hospitalization numbers (which we are all concerned about, of course), it would seem that whatever approaches we take to COVID-19 should be targeted at decreasing their COVID-19 infection slope.
To the above point, evidence continues to grow that superspreading events are responsible for most of the case growth. See this preprint for the latest research on this effect. According to this research from Hong Kong, 20% of the cases were responsible for 80% of the COVID-19 transmission and 70% of infected people never transmit the disease at all. They also claimed that social events were more responsible for transmission than family or work (unless you work in a meat packing plant, I guess…). This does seem to give some weight to the notion that better managing the events that might be associated with superspreading (including the oversight of workers in group homes, etc.) would have more effect on the hospitalization and death rate than economic lockdowns, which appear to have little to no effect on over 65 case growth rates.
Hospitalization Data
I was fortunate that Maricopa county is also collecting data on hospitalization by day and was able to build a time series plot there as well. This data is presented for the current date in the state’s Tableau Dashboard, but I haven’t found anyone yet that has captured that data every day so that trends could be analyzed. So all I have is Maricopa County, but what it shows is interesting.
What do we see here? First, we note that as the number of cases started going exponential (accelerating) on 5/28, hospitalization just took a small tick up and then stayed flat. There may be a few reasons for this:
1. At some point during the lockdown, hospitals stopped doing elective surgeries. Sometimes these surgeries end up populating the ICU. This is bad for the hospitals because elective surgeries are fairly lucrative economically for the hospital. Therefore, as soon as it made sense after easing started hospitals went back to elective surgeries. My guess is that they’re quite good at managing their hospital bed usage (ICU or otherwise) due to the economic effects of being good at doing so. This might explain how flat the hospitalization growth is in the chart. It would seem that once COVID-19 cases started growing again on 5/28 the hospitals saw a bump up in their numbers as COVID patients started flowing again into ICU’s which had been collecting patients from elective surgeries, etc., during the easing. Once absorbed, the rates have flattened off again (at a higher number, but perhaps that’s for the time being). I’m curious about the unusually high hospitalization cycle time for COVID (I hear 14 days…) and how that impacts the hospitals’ abilities to manage flow through their ICU beds.
2. Since hospitalization rates aren’t really growing (and certainly not at an exponential rate, which is what everyone has feared), the chart above makes the case that all the concern about AZ case growth rates is misplaced (though I suppose it makes for a good story on a slow news day) as nearly all of the cases each day appear to be either asymptomatic or at least low enough symptoms to not require hospital admission. This is good and probably is exactly what the case and hospitalization data would look like in flu season if we were to track it this closely.
3. We know that ~70% of COVID-19 hospitalizations are in the 65+ group, so I think this strengthens the case that most of the new cases in the younger demographics are not overly symptomatic. Add this to the testing results I discovered in part 1 of this series and it seems clear that probably close to all of the new cases that are contributing to the growth were discovered during the huge testing blitzes that have been happening and are not reasons for concern.
Conclusion
The media has been excessively focused on case growth in Arizona, but I believe the data indicates clearly that there is no emergency happening.
• Most of the new cases are in younger demographics, are not requiring hospitalization, and were uncovered through testing. This is good and is part of the reality of having a novel virus in the environment.
• Hospitalization growth is not a concern and reflects something that hospitals manage every year during outbreaks of flu or other pathogens. They are very good at managing their case loads (but I’ve heard they need to manage their beds at somewhere near 80% capacity to make money anyway). Once hospital bed occupancy hit 75% the growth slowed to a crawl and now seems to be flat.
• Case growth in the most susceptible age group does not seem to have been affected by the economic shutdown. Additionally, the growth of mask wearing in Pima County that started in May also appears to have had no impact on the 65+ growth rate. This makes me wonder if other approaches may be more effective at ultimately limiting deaths and hospitalizations that overwhelmingly come from this group. This is an area that obviously bears more study.
Questions I have
After writing this I still have some questions that are interesting to me. I will use this space to capture a few:
I note above that the lockdown seem to have had no effect on growth of cases in the 65 plus group. My evidence for this is that post-easing, we’re seeing exponential growth in all other groups but not 65+. I have a few questions that I can’t answer about this:
1. Does the incredible growth in testing invalidate the assertion that case growth is higher after easing than before? I.e., are we catching cases now due to testing that we would not have caught before testing started? If true, perhaps there is no case acceleration, we just changed the way we measure in mid-stream. Also, if true, there may be less indication that case growth in the other demographics doesn’t affect case growth in over 65.
2. Is the shallow, linear slope of 65+ case growth due to their increased likelihood at wearing face coverings? I have no data on this, but it would stand to reason that the group who’s lives and health is most threatened by this virus may take greater precautions. I suspect that testing in this group hasn’t increased nearly as much as it has in other groups because I’m pretty confident that most tests conducted prior to the testing blitz were only given to people who had a strong prior for being infected. That would mean that most tests would have been given to people with symptoms (and a very high percentage of the other age groups are asymptomatic)
I also have questions about the efficacy of face coverings on asymptomatic people as source control. I understand the logic that it is easier to mandate that everyone do something that appears to have benefits, but I’m not sure if the evidence indicates that there is a compelling reason to deprive liberty in this way. I keep evaluating this…
1. Evidence continues to mount that wearing face coverings is more effective than extreme social distancing. A very recent paper published in the proceedings of the National Academy of Sciences (LINK) makes the case that it is airborne transmission via aerosols that is the dominant route for transmission of COVID and that a facemask as source control on an infected person is the most effective mechanism to prevent atomization of the virus-containing droplets. If the virus is atomized, six feet of distance is no longer protective, and indeed, some evidence indicates that cloth masks on passers-by do not filter out these aerosols. My question, however, is whether this kind of atomization can occur in a pre-symptomatic person who is not coughing? Also, can atomization be caused by a pre-symptomatic person talking loud? I have seen evidence of atomization of flu and other viruses occurring through coughing, but that is not pre-symptomatic behavior.
## COVID-19 Update: What’s Going on in Arizona?
Arizona is about three weeks after reopening and there has been a lot of increase in case growth. Headlines like this are catching attention with the leader:
PHOENIX – Experts around the country and in Arizona are raising alarms about the state’s COVID-19 situation because cases and hospitalizations have increased for the past two weeks. The increase in cases can’t solely be attributed to increased testing in Arizona, experts say.
Lets look at the data and see if it doesn’t give us some clues. There’s a good chance the “experts” haven’t done this…
Here is data on all the counties in Arizona from 6/10/2020. I have sorted these by the case growth rate, which as you might remember is the slope of the tangent to the curve (involves calculus, just trust me, this is how you find the change rate of a curve).
What do we see here?
• The highest two counties by instantaneous rate of change (IROC_confirmed) are Santa Cruz and Yuma. Both of these happen to have highly traveled border crossings. The Nogales port of entry in Santa Cruz County sees around 10M people cross this border legally per year. The crossing near Yuma sees about 7M people cross. The Calexico crossing in California an hour or so west of Yuma sees about 12M people cross per year (and yes, Imperial County, CA, is seeing similar numbers to Yuma and Santa Cruz counties. So I have to assume that there is some contagion between Mexico’s cases and these two port of entry counties. Depending on how the state’s case growth is being counted, the numbers from these two counties could be significant. The high acceleration in case growth in these counties (dIROC_confirmed) indicates that they are seeing exponential growth. This is concerning and there’s a possibility cases may spread northward in Arizona from these counties. Both are fairly isolated, however, so perhaps that will minimize it.
• Maricopa county continues to see the majority of the actual cases in the state. This isn’t surprising due to their large population (about 4x larger than Pima county). We are clearly seeing exponential growth in cases — but not deaths. See time series charts later in this post. I’d guess that in this large, wealthy county most of the case growth is due to increased testing and social distancing lapses. There’s no data to indicate that protests are causing any of these cases. Note however that the acceleration of case growth is very small still, so most likely we’re not seeing a major exponential growth situation like we saw in New York City.
• Apache, Navajo, and Coconino counties all have Native American reservation outbreaks. It does seem like these are slowing down (see time series charts).
• Deaths per 1000 persons in the state is still very small compared to most other states.
Testing
As you can see in the chart above, AZ started a testing blitz a bit before they took the first phase of opening the economy. They report that they’ve conducted 416K tests so far. It does appear that the lions share of these testa have occurred after May 1. Assuming an average of 9K tests per day and over around 25 days (maybe some days they took off), we get at least 225,000 tests since May 1. The state’s advertised average positive test rate is 6.4%. Multiplying these, we get 14,400 positive tests that came from the increased testing. This accounts for nearly all the cases shown on the AZ Case curve above. Since it is widely reported that 50% of people with COVID-19 never know that they have it, lets assume only 7K of these new cases are symptomatic. Compare this to the 8-9K of cases before May 1, which one might assume are nearly all symptomatic (because testing was only given to symptomatic people), then you may see that symptomatic cases are flattening out. Not sure if this is true, but it seems likely that the graph now is showing at least 7K cases which would not have appeared before May 1.
Arizona’s Rank in the US per COVID-19 Cases
There’s a misleading chart that NPR has put out (it’s an experimental graph that Johns Hopkins is showing) in this article that makes a comparison between Arizona and New York. Both axes are logarithmic, largely because the New York data is so much greater than any other state, but the X axis is measuring total cases since January. The y-axis is averaging the last seven days’ worth of cases. The intent is to highlight case growth late in the outbreak cycle. In theory, states who had their outbreaks early will look as if their cases are dropping and states who did not have early outbreaks will show increases as large spikes. I think the whole format is not informative and is very misleading when comparing two states. Also, the cases aren’t normalized (which would allow them to not use logarithmic axes). Anyway, very bad plot which tells us nothing. It certainly doesn’t tell us that AZ is in crisis. See below for more measured data that tells us to be cautious, but not that we’re in difficult straits. First, I show a chart of the top states ranked by the Rate of Change of Confirmed Cases per 1000 persons.
Note that Arizona has moved up to 4th on the list. This (IROC_confirmed) is a volatile metric as the case growth curves are not a cumulative measure and can change to represent recent trends. But it is far more accurate and informative than a 7 day case average! To demonstrate the volatility, Arizona was 10-15 places further down the list earlier in the week. Here we see a bit of a resurgence in Louisiana along with some spillover cases from DC (which had a very steep bloom in cases a few weeks back). I was told by a friend in Virginia that the bars in DC are far more accessible right now than those in VA or MD due to more extreme social distancing in those states. So this might explain the VA and MD cases. Things to note:
• Note that there is a really legitimate difference between Deaths per 1000 and Cases per 1000 between Arizona (and Alabama) and the other states at the top of this list.
• Also, note that the COVID-19 deaths that occurred on this day in these states (Delta_Deaths) is fairly low. This has been the trend ever since probably mid-May. For an idea of the magnitude of these deaths, see below:
I put this table together using CDC US-wide stats and assuming uniform distribution of these deaths across all states (may not be a perfect assumption, but I imagine it’s good enough for demonstration). The table shows the COVID-19 deaths on 6/9 compared to the expected deaths per day of the top causes of death in the US (2017 numbers — the CDC always seems to be behind). As you can see COVID-19 deaths, even in a period of lower death rates ARE STILL A MAJOR CAUSE OF DEATH. However, they are not the leading cause of death in a majority of these states (and in California, they are well below the top 2). The point is that numbers like this, while troubling, do not pose a threat to our existence. Hopefully that is helpful. Keep this table handy as the numbers change. If deaths go up or down, this will remain a handy reference to risks that we are already capable of understanding and accepting.
Hospitals
This is a different issue, as there’s not clear data on the hospital situation. Headlines like this from Tucson’s newspaper are very concerning. The assertion is that ICU space is running out in Maricopa and Pima counties. Arizona doesn’t collect data very well (although they have improved quite a bit since the crisis started) and therefore we’re lacking good access to hospitalization data and recovery data. We know from the above table that there were 595 new active cases in the state yesterday. How many of those will eventually wind up in a hospital? This is hard to predict, as it depends on who is getting infected. If 300 of the 595 are younger people who have lapsed in social distancing then the number could be small. We don’t know this, because the state doesn’t break down new cases by demographics (see AZDHS data dashboard). All the state tells us is the number of hospitalizations per day (and it appears there’s about a 1 week lag on this data) and some data on the numbers of different kinds of hospital beds in use. In the chart below, we see that the percentage of ICU beds that are in use right now has gone up from about 62% of capacity (the chart tells me this equals 741 beds) in early March (before COVID hit AZ) to 79% (1302 beds) yesterday. This seems very significant, but I wonder how many of these 1302 beds are in use due to COVID-19? Fortunately, we have that data from the state (assuming it is correct and there’s no lag) and I have pasted it below. It does seem like there’s some average number of beds that were in use during the early COVID-19 period from looking at the first couple of months and averaging… (ignore the first day, that looks like bad data collection). So it would seem that before our recent surge in cases there were around 300 beds in use on average due to COVID. So our number today (413) minus 300 would seem to be the growth in ICU usage due to the recent surge in cases. From the top chart, I infer that there must be around 1650 ICU beds in the state. Therefore, since the lockdown was ended, Arizona has seen COVID-19 cases consume 25% of its total ICU bed capacity (413/1650), compared to 18% (300/1650) during the lockdown period.
Ventilators
From the chart below, it would seem like ventilator capacity is still fairly significant. From a different chart that the state puts out (again, assuming all this data is accurate), it would appear like ventilator usage is up about 70 from the lockdown period. What we don’t know is if these ventilators are in the right places or not… There are other charts on the AZDHS data dashboard that show details about different kinds of hospital beds, etc. It would be very useful if they could show cumulative hospital admissions and recoveries over time, because if that data was available, it would be easier to understand the cycle time of this disease on the hospital system.
Time Series Plots by Arizona County
This is for the Data Nerds. Here are a few of today’s time series plots of cases by county (and deaths for a couple of counties). Note that most of these counties are seeing acceleration of case growth (i.e., exponential growth) but the two largest are showing potential deceleration in their death rates.
Conclusion
Essentially, yes, cases are growing but deaths are decreasing. We don’t know enough to understand how much concern to have. I continue keeping in mind that most people are going to get this virus. I read that it binds 10x better to the ACE2 receptor than SARS, so while SARS may not have been a threat to most of us, COVID-19 will likely hit us all… Probably no reason to be panicked, but certainly reason to take caution.
## COVID-19 Update: Post-Lockdown Outbreaks
We’re seeing Case Growth in various regions and this is being noticed by news media, etc. It isn’t clear yet what is causing the new case growth, but states exiting lockdowns are probably a part of the reason at least. Here are some visualizations about one week apart to give kind of a time-lapse effect on case growth. Note that these diagrams are straight counts of cases and deaths (not normalized by population). This may give the effect that a region with a large population is being hard hit when they may not be… Also, these snapshots show one day’s numbers, not cumulative counts.
The Color represents the number of new cases, the diameter of the bubble represents the number of new deaths.
Data from 6/3/2020
Data from 5/27/2020
Data from 5/20/2020
Data from 5/13/2020
Data from 5/6/2020
Conclusion
Take a look at the images above. We have seen lots of different phases of this disease in the last month and clearly things change fast. A few things to take away:
1. Deaths are significantly down. It seems like this is the case across the country, especially in the Northeast region.
2. Cases are up in certain regions. California and Illinois are seeing new cases and both are seeing deaths. However, there are numerous regions with cases and zero deaths that don’t show up because the diameter of the bubble (deaths) is so small. Perhaps this is good and is a picture of where we are re: treating this virus. Or maybe the deaths will start increasing in these regions in the next few days.
3. Overall, Cases are down. Note that the legend on the colorbar tops out at ~3500 on 5/6 but on the most recent chart it’s about ~1000. This is because case counts were higher overall a month ago.
4. Most regions are still relatively untouched by COVID-19.
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# Thread: Prove lim(sin(1/x)) as x tends to 0 does not exist
1. ## Prove lim(sin(1/x)) as x tends to 0 does not exist
assume there is a limit, L. So we have that for all ${\epsilon}>0$ there exists a ${\sigma}>0$ such that $|x-0|=|x|<{\sigma} ->|sin(1/x)-L|<{\epsilon}$
Consider when x>_0 and let ${\epsilon}$=1/2.
Then |x|=x -> $0 |sin(1/x)-L|<1/2$
Thanks
2. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
Do you need to use an $\displaystyle \epsilon - \delta$ proof? Couldn't you just say that since the function oscillates, it is impossible to say that $\displaystyle \sin{X}$ approaches a particular value as $\displaystyle X \to \infty$?
3. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
no I need to use epsilon delta
4. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
We need an $\displaystyle L$ such that $\displaystyle \forall \epsilon > 0, \exists \delta$ such that $\displaystyle \left|\sin{\left(\frac{1}{x}\right)} - L \right| < \epsilon$ if $\displaystyle |x - 0| = |x| < \delta$.
On any interval $\displaystyle (-\epsilon + \bar{x}, \bar{x} + \epsilon)$ we have $\displaystyle x \in (-\delta, \delta)$ such that $\displaystyle f(x) = \pm 1$. Consequently for $\displaystyle \epsilon < 2$ we can't have $\displaystyle \left|\sin{\left(\frac{1}{x}\right)} - L\right| < \epsilon$ for any $\displaystyle L$ and any $\displaystyle \delta > 0$. Thus we can not satisfy the definition no matter what we choose for $\displaystyle L$.
5. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
Sorry, I don't quite understand. what x bar? Do you mean L. Then I don't know why f(x) must take the values + or - 1 in any (-delta,delta). Lastly you seem to imply L must be eith + or -1 meaning the distance between sin(1/x) and L will be 2 at some point. Why is this the case?
6. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
$\displaystyle \bar{x}$ is some $\displaystyle x$ close to $\displaystyle 0$.
The proof basically states that for values infinitessimally close to $\displaystyle x = 0$, it can be said that $\displaystyle f(x)$ is equal to both $\displaystyle 1$ and $\displaystyle -1$, which is enough to show that you can not "zoom in" on an $\displaystyle L$ as you make $\displaystyle \epsilon$ and $\displaystyle \delta$ smaller.
7. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
Consider the sequence $x_n = \frac 2 {n\pi}$, for $n = 1, 2, ...$.
8. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
In fact, consider the two sequences $x_n= \frac{1}{2n\pi}$ and $x_m= \frac{1}{n\pi}$. You need to know that f(x) goes to L as x goes to a if and only if f(xn) goes to L for every sequence {xn} that goes to L.
9. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
You need to know that f(x) goes to L as x goes to a if and only if f(xn) goes to L for every sequence {xn} that goes to L. Is that a general theorem?
Don't know how you know 1/2npi goes to L but I will roll with it for now
sin(2npi)=0 so need delta such that if 0<|1/(2npi)|<delta then |-L|=|L|< e. But we can make e arbitarily small so it can be made less than |L| which is a contradiction. So f((1/2npi))has no limit so f(x) has no limit. Am I correct?
10. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
I've done more working
11. ## Re: Prove lim(sin(1/x)) as x tends to 0 does not exist
Given any $\delta> 0$, there exist an integer n such that $\frac{2}{n\pi}< \delta$. That means that every number from $-\frac{2}{n\pi}$ to $+\frac{2}{n\pi}$ are less than $\delta$. For those values of x, sin(1/x) becomes $-sin(n\pi/2)= -1$ and $sin(n\pi/2)= 1$. That is, no matter how small $\delta$ is, there will exist values of x less than $\delta$ such that sin(1/x) takes on values of 1 and -1. You can't guarentee any $\epsilon$ less than 2.
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### show that function f(x)=sin1/x for x does not equal to 0 has no limit as x tenda to 0
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http://en.wikipedia.org/wiki/Laplace%e2%80%93Carson_transform
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# Laplace–Carson transform
In mathematics, the Laplace–Carson transform, named after Pierre Simon Laplace and John Renshaw Carson, is an integral transform with significant applications in the field of physics and engineering, particularly in the field of railway engineering.
## Definition
Let $V(j,t)$ be a function and $p$ a complex variable. The Laplace–Carson transform is defined as:[1]
$V^\ast(j,p) = p\int^{\infty}_0 V(j,t) e^{-pt} \, dt$
The inverse Laplace–Carson transform is:
$V(j,t) = \frac{1}{2\pi i} \int^{a_0+i\infty}_{a_0-i\infty} e^{tp} \frac{V^\ast(j,p)}{p} \, dp$
where $a_0$ is a real-valued constant, $i\infty$ refers to the imaginary axis, which indicates the integral is carried out along a straight line parallel to the imaginary axis lying to the right of all the singularities of the following expression:
$e^{tp}\frac{V(j,t)}{p}$
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An army camp has food enough for 240 people for 28 days. If only 112 soldiers are there in the camp, how many day
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### Question Asked by a Student from EXXAMM.com Team
Q 2226745671. An army camp has food enough for 240 people for 28 days. If
only 112 soldiers are there in the camp, how many days will
the food last?
IBPS-CLERK 2017 Mock Prelims
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56
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120
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60
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90
E
None of these
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# Ascending chain condition on subnormal subgroups is normal subgroup-closed
This article gives the statement, and possibly proof, of a group property (i.e., group satisfying ascending chain condition on subnormal subgroups) satisfying a group metaproperty (i.e., normal subgroup-closed group property)
View all group metaproperty satisfactions | View all group metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for group properties
Get more facts about group satisfying ascending chain condition on subnormal subgroups |Get facts that use property satisfaction of group satisfying ascending chain condition on subnormal subgroups | Get facts that use property satisfaction of group satisfying ascending chain condition on subnormal subgroups|Get more facts about normal subgroup-closed group property
## Statement
### Property-theoretic statement
The property of being a group satisfying ascending chain condition on subnormal subgroups is a normal subgroup-closed group property.
### Statement with symbols
Suppose $G$ is a group satisfying ascending chain condition on subnormal subgroups and $N$ is a normal subgroup of $G$. Then, $N$ is also a group satisfying ascending chain condition on subnormal subgroups.
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# Boolean logic
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Boolean logic is a complete system for logical operations, used in many systems. It was named after George Boole, who first defined an algebraic system of logic in the mid 19th century. Boolean logic has many applications in electronics, computer hardware and software, and is the basis of all modern digital electronics. In 1938, Claude Shannon showed how electric circuits with relays were a model for Boolean logic. This fact soon proved enormously consequential with the emergence of the electronic computer.
Using the algebra of sets, this article contains a basic introduction to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications. The Boolean algebra article discusses a type of algebraic structure that satisfies the axioms of Boolean logic. The binary arithmetic article discusses the use of binary numbers in computer systems.
## Set logic vs. Boolean logicEdit
Sets can contain any elements. We will first start out by discussing general set logic, then restrict ourselves to Boolean logic, where elements (or "bits") each contain only two possible values, called various names, such as "true" and "false", "yes" and "no", "on" and "off", or "1" and "0".
## TermsEdit
Let X be a set:
• An element is one member of a set. This is denoted by $\in$. If it's not an element of the set, this is denoted by $\notin$.
• The universe is the set X, sometimes denoted by 1. Note that this use of the word universe means "all elements being considered", which are not necessarily the same as "all elements there are".
• The empty set or null set is the set of no elements, denoted by $\varnothing$ and sometimes 0.
• A unary operator applies to a single set. There is one unary operator, called logical NOT. It works by taking the complement with respect to the universe, i.e. the set of all elements under consideration.
• A binary operator applies to two sets. The basic binary operators are logical OR and logical AND. They perform the union and intersection of sets. There are also other derived binary operators, such as XOR (exclusive OR).
• A subset is denoted by $A \subseteq B$ and means every element in set A is also in set B.
• A superset is denoted by $A \supseteq B$ and means every element in set B is also in set A.
• The identity or equivalence of two sets is denoted by $A \equiv B$ and means that every element in set A is also in set B and every element in set B is also in set A.
• A proper subset is denoted by $A \subset B$ and means every element in set A is also in set B and the two sets are not identical.
• A proper superset is denoted by $A \supset B$ and means every element in set B is also in set A and the two sets are not identical.
## ExampleEdit
Imagine that set A contains all even numbers (multiples of two) in "the universe" (defined in the example below as all integers between 0 and 30 inclusive) and set B contains all multiples of three in "the universe". Then the intersection of the two sets (all elements in sets A AND B) would be all multiples of six in "the universe". The complement of set A (all elements NOT in set A) would be all odd numbers in "the universe".
### Chaining operations togetherEdit
While at most two sets are joined in any Boolean operation, the new set formed by that operation can then be joined with other sets utilizing additional Boolean operations. Using the previous example, we can define a new set C as the set of all multiples of five in "the universe". Thus "sets A AND B AND C" would be all multiples of 30 in "the universe". If more convenient, we may consider set AB to be the intersection of sets A and B, or the set of all multiples of six in "the universe". Then we can say "sets AB AND C" are the set of all multiples of 30 in "the universe". We could then take it a step further, and call this result set ABC.
### Use of parenthesesEdit
While any number of logical ANDs (or any number of logical ORs) may be chained together without ambiguity, the combination of ANDs and ORs and NOTs can lead to ambiguous cases. In such cases, parentheses may be used to clarify the order of operations. As always, the operations within the innermost pair is performed first, followed by the next pair out, etc., until all operations within parentheses have been completed. Then any operations outside the parentheses are performed.
### Application to binary valuesEdit
In this example we have used natural numbers, while in Boolean logic binary numbers are used. The universe, for example, could contain just two elements, "0" and "1" (or "true" and "false", "yes" and "no", "on" or "off", etc.). We could also combine binary values together to get binary words, such as, in the case of two digits, "00", "01", "10", and "11". Applying set logic to those values, we could have a set of all values where the first digit is "0" ("00" and "01") and the set of all values where the first and second digits are different ("01" and "10"). The intersection of the two sets would then be the single element, "01". This could be shown by the following Boolean expression, where "1st" is the first digit and "2nd" is the second digit:
(NOT 1st) AND (1st XOR 2nd)
## PropertiesEdit
We define symbols for the two primary binary operations as $\land / \cap$ (logical AND/set intersection) and $\lor / \cup$ (logical OR/set union), and for the single unary operation $\lnot$ / ~ (logical NOT/set complement). We will also use the values 0 (logical FALSE/the empty set) and 1 (logical TRUE/the universe). The following properties apply to both Boolean logic and set logic (although only the notation for Boolean logic is displayed here):
$a \lor (b \lor c) = (a \lor b) \lor c$ $a \land (b \land c) = (a \land b) \land c$ associativity $a \lor b = b \lor a$ $a \land b = b \land a$ commutativity $a \lor (a \land b) = a$ $a \land (a \lor b) = a$ absorption $a \lor (b \land c) = (a \lor b) \land (a \lor c)$ $a \land (b \lor c) = (a \land b) \lor (a \land c)$ distributivity $a \lor \lnot a = 1$ $a \land \lnot a = 0$ complements $a \lor a = a$ $a \land a = a$ idempotency $a \lor 0 = a$ $a \land 1 = a$ boundedness $a \lor 1 = 1$ $a \land 0 = 0$ $\lnot 0 = 1$ $\lnot 1 = 0$ 0 and 1 are complements $\lnot (a \lor b) = \lnot a \land \lnot b$ $\lnot (a \land b) = \lnot a \lor \lnot b$ de Morgan's laws $\lnot \lnot a = a$ involution
The first three properties define a lattice; the first five define a Boolean algebra. The remaining five are a consequence of the first five.
## Other notationsEdit
Mathematicians and engineers often use plus (+) for OR and a product sign ($\cdot$) for AND. OR and AND are somewhat analogous to addition and multiplication in other algebraic structures, and this notation makes it very easy to get sum of products form for normal algebra. NOT may be represented by a line drawn above the expression being negated ($\overline{x}$). It also commonly leads to giving $\cdot$ a higher precedence than +, removing the need for parenthesis in some cases.
Programmers will often use a pipe symbol (|) for OR, an ampersand (&) for AND, and a tilde (~) for NOT. In many programming languages, these symbols stand for bitwise operations. "||", "&&", and "!" are used for variants of these operations.
Another notation uses "meet" for AND and "join" for OR. However, this can lead to confusion, as the term "join" is also commonly used for any Boolean operation which combines sets together, which includes both AND and OR.
## Basic mathematics use of Boolean termsEdit
• In the case of simultaneous equations, they are connected with an implied logical AND:
x + y = 2
AND
x - y = 2
• The same applies to simultaneous inequalities:
x + y < 2
AND
x - y < 2
• The greater than or equals sign ($\ge$) and less than or equals sign ($\le$) may be assumed to contain a logical OR:
X < 2
OR
X = 2
• The plus/minus sign ($\pm$), as in the case of the solution to a square root problem, may be taken as logical OR:
WIDTH = 3
OR
WIDTH = -3
## English language use of Boolean termsEdit
Care should be taken when converting an English sentence into a formal boolean statement. Many English sentences have imprecise meanings. E.g., "All that glitters is not gold,"[1] could mean nothing that glitters is gold, or some things that glitter are not gold.
In certain cases, AND and OR can be used interchangeably in English:
• I always carry an umbrella for when it rains and snows.
• I always carry an umbrella for when it rains or snows.
• I never walk in the rain or snow.
Sometimes the English words "and" and "or" have a meaning that is apparently opposite of its meaning in boolean logic:
• "Give me all the red and blue berries," usually means, "Give me all berries that are red or blue". (The former might have been interpreted has a request for berries that are each both red and blue.) An alternative phrasing for this request would be, "Give me all berries that are red and all berries that are blue."
Depending on the context, the word "or" may correspond with either logical OR or logical XOR:
• The waitress asked, "Would you like cream or sugar with your coffee?" (Logical OR.)
Logical XOR can be translated as "one, or the other, but not both". In most cases, this concept is most effectively communicated in English using "either/or".
The word combination "and/or" is sometimes used in English to specify a logical OR, when just using the word "or" alone might have been mistaken as meaning logical XOR:
• "I'm having chicken and/or beef for dinner." (Logical OR.) An alternative phrasing for standard written English would be, "For dinner, I'm having chicken or beef (or both)."
This can be a significant challenge when providing precise specifications for a computer program or electronic circuit in English. The description of such functionality may be ambiguous. Take for example the statement, "The program should verify that the applicant has checked the male or female box." This should be interpreted as an XOR and a verification performed to ensure that one, and only one, box is selected. In other cases the proper interpretation of English may be less obvious; the author of the specification should be consulted to determine the original intent.
## ApplicationsEdit
### Digital electronic circuit designEdit
Boolean logic is also used for circuit design in electrical engineering; here 0 and 1 may represent the two different states of one bit in a digital circuit, typically high and low voltage. Circuits are described by expressions containing variables, and two such expressions are equal for all values of the variables if, and only if, the corresponding circuits have the same input-output behavior. Furthermore, every possible input-output behavior can be modeled by a suitable Boolean expression.
Basic logic gates such as AND, OR, and NOT gates may be used alone, or in conjunction with NAND, NOR, and XOR gates, to control digital electronics and circuitry. Whether these gates are wired in series or parallel controls the precedence of the operations.
### Database applicationsEdit
Relational databases use SQL, or other database-specific languages, to perform queries, which may contain Boolean logic. For this application, each record in a table may be considered to be an "element" of a "set". For example, in SQL, these SELECT statements are used to retrieve data from tables in the database:
SELECT * FROM employees WHERE last_name = 'Dean' AND first_name = 'James' ;
SELECT * FROM employees WHERE last_name = 'Dean' OR first_name = 'James' ;
SELECT * FROM employees WHERE NOT last_name = 'Dean' ;
Parentheses may be used to explicitly specify the order in which Boolean operations occur, when multiple operations are present:
SELECT * FROM employees WHERE (NOT last_name = 'Smith') AND (first_name = 'John' OR first_name = 'Mary') ;
Multiple sets of nested parentheses may also be used, where needed.
Any Boolean operation (or operations) which combines two (or more) tables together is referred to as a join, in relational database terminology.
In the field of Electronic Medical Records, some software applications use Boolean logic to query their patient databases, in what has been named Concept Processing technology.
### Search engine queriesEdit
Search engine queries also employ Boolean logic. For this application, each web page on the Internet may be considered to be an "element" of a "set". The following examples use a syntax supported by Google.[3]
• Doublequotes are used to combine whitespace-separated words into a single search term.[4]
• Whitespace is used to specify logical AND, as it is the default operator for joining search terms:
"Search term 1" "Search term 2"
• The OR keyword is used for logical OR:
"Search term 1" OR "Search term 2"
• The minus sign is used for logical NOT (AND NOT):
"Search term 1" -"Search term 2"
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# Monotonicity of function $f(x)=(1+1/x)^x$ [duplicate]
Possible Duplicate:
How to prove $(1+1/x)^x$ is increasing when $x&gt;0$?
$$f(x)=(1+1/x)^x$$ Where $x>0$
I am in search to find a proof that the function $f(x)$ is always increasing in its any real number domain. As the above function always increasing a slight variation in the form of function will change the outcome in opposite way.That is when we change the exponent $x$ by ($1+x$) of the above function and letting all the expression on the right hand side intact, this new function will always be decreasing for real domain $x>0$.
• Did you compute it's derivative?
– tst
Nov 25, 2012 at 2:34
• $x$^$X$ can be decided,then only if slight changes can be made with$(X+1)$^$x$ things begin to be look complicated,so i thought there is something intriguing to play with it. Nov 25, 2012 at 2:51
• for $x$<0 answer is obvious.it is always increasing.when the exponent is $(x+1)$ this problem i found on net when could not solve the first one,but could not understand their proofs so posted here. Nov 25, 2012 at 3:10
• This function is not defined for $x\in[-1,0]$, since you cannot neatly raise negative numbers to noninteger powers. So your domain is $(-\infty,-1)\cup(0,\infty)$. Nov 25, 2012 at 3:45
– user856
Nov 25, 2012 at 6:27
Here is an idea, it is based on the fact that the composition of two increasing functions is an increasing function. Let
$$f(x) = \left(1+\frac{1}{x}\right)^x \,.$$
Now, consider the function
$$g(x) = x\ln\left(1+\frac{1}{x}\right)$$
and prove that it is an increasing function. Then note that, $f(x) = e^{g(x)}$ is a composition of two increasing functions ( since $e^x$ is an increasing function ).
• then the computed answer is that f($x$) is an increasing function but if i replace exponent of f($x$) ,$x$ by ($1+x$),then the function will be a decreasing function but it should be increasing too as our discussion ,i found this on net as i was inquiring on internet for f($x$) with exponent $x$. Nov 25, 2012 at 16:46
• @AbhinavAnand: In this case $g(x)=(1+x)\ln(1+1/x)$ which is a decreasing function. Nov 25, 2012 at 18:54
Compute the derivative. Are you familiar with first derivative test? The derivative will tell you the slope of the function at any given point, you can use this information to tell you about how the function behaves.
For example, positive slope means an increasing function.
• This is probably circular reasoning. To know the derivative of $e^x$, you first need to deduce some properties of the number $e$ itself. Nov 25, 2012 at 2:38
• Fair enough, but its not clear what tools are available for approaching this problem. I'm just suggesting a possible approach. Nov 25, 2012 at 2:41
• i have computed the first derivative trough taking log of the function but the derivative is even more complicated to decide whether the derivative function is always positive or whatever. Nov 25, 2012 at 2:42
• If you compute the derivative you will see that is is zero when $\log(1+\frac 1x)=\frac{1}{1+x}$. Now you have to think when this does happen.
– tst
Nov 25, 2012 at 4:35
• What would zero derivative do help in solving the problem? Nov 25, 2012 at 4:51
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# Search:
Tag: next
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# How do i make number round to .1 (one number after dot)
You can write your topic however you want, but you need to answer these questions:
1. What do you want to achieve? Keep it simple and clear!
so basically when i collect an model i get a new multi which formula is multi*multi or multi^2 and i use 1.025x as multi in a few models i get smth like 1.34567831235…
2. What is the issue? Include screenshots / videos if possible!
1th question
3. What solutions have you tried so far? Did you look for solutions on the Developer Hub?
I know about math round, but i need it to round to format .1 not to integer
My code:
``````local RCMultiE = game.Workspace.RemoteEvents.RCMultiE
local MoneyMulti = 1.025
local ClicksMulti = 1.1
RCMultiE.OnServerEvent:Connect(function(player)
local RCMultiMoney = player.Stats.RCMultiMoney
local RCMultiClicks = player.Stats.RCMultiClicks
RCMultiMoney.Value *= math.round(MoneyMulti)
RCMultiClicks.Value *= ClicksMulti
end)
``````
With math round i can go to only integer numbers, i don’t know any thing which could make number round to .1
`math.round(x*n)/n`
Where `x` is your number, and `n` is the place.
For example: to round `1.4567` to the tenths place, `math.round(1.4567*10)/10` = `1.5`
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## Calculating Stirling Numbers using C#
A “Stirling number of the second kind” is the number of ways to group/partition n items into k subsets. For example, the number of ways to group n=4 items into k=2 subsets is 7. Suppose the 4 items are a, b, c, d. Then S(4,2) = 7 and the seven groupings are: (a | bcd), (b | acd), (c | abd), (d | abc), (ab |cd), (ac | bd), and (ad | bc).
The value of S(n,k) gets astronomically large, very quickly. For example, S(100, 3) =
85,896,253,455,335,221,205,584,888,180,155,511,368,666,317,646
How did I compute this? I wrote a C# function. First, I got one of many math definitions for S(n,k) from Wikipedia:
To code a function that computes S(n,k) because the answers can be so big, I needed to use the C# BigInteger data type which is not visible by default to a C# program. The type lives in namespace System.Numerics. If you examine the equation above you can see you need a Factorial function (outside the summation), an integer Power function (used in two places), and a Choose function. The Choose(n,k) function returns the number of ways to choose k items from n items, where order does not matter. For example, Choose(4,2) = 6 because there are six ways to select 2 items from 4 items. Suppose the four items are q, r, s, t. Then the six ways are (q r), (q s), (q t), (r s), (r t), and (s t).
So, here’s Factorial:
```static BigInteger Factorial(int n)
{
if (n == 0) return 1;
BigInteger ans = 1;
for (int i = 1; i <= n; ++i)
ans *= i;
return ans;
}
```
Here’s a Power:
```static BigInteger Power(int m, int p)
{
// m raised to the pth power
BigInteger result = 1;
for (int i = 0; i < p; ++i)
result = result * m;
return result;
}
```
And here’s a Choose:
```static BigInteger Choose(int n, int k)
{
if (n < 0 || k < 0)
throw new Exception("Negative argument in Choose");
if (n < k) return 0; // special
if (n == k) return 1; // short-circuit
int delta, iMax;
if (k < n - k) // ex: Choose(100,3)
{
delta = n - k;
iMax = k;
}
else // ex: Choose(100,97)
{
delta = k;
iMax = n - k;
}
BigInteger ans = delta + 1;
for (int i = 2; i <= iMax; ++i)
ans = (ans * (delta + i)) / i;
return ans;
}
```
The Choose function is not at all obvious, but that’s another topic. Putting it all together, here’s a C# method that computes S(n,k):
```static BigInteger Stirling(int n, int k)
{
BigInteger sum = 0;
for (int j = 0; j <= k; ++j)
{
BigInteger a = Power(-1, k - j);
BigInteger b = Choose(k, j);
BigInteger c = Power(j, n);
sum += a * b * c;
}
return sum / Factorial(k);
}
```
I called the function as
```int n = 100;
in k = 3;
Console.WriteLine(Stirling(n, k));
```
All in all, an interesting function.
This entry was posted in Machine Learning. Bookmark the permalink.
### 2 Responses to Calculating Stirling Numbers using C#
1. mvaneerde says:
Another common way to calculate Stirling numbers of the second kind is to build a table using the recurrence relation S(n, k) = k S(n – 1, k) + S(n – 1, k – 1).
The motivation for the recurrence relation can be understood as follows:
Suppose you are one of n people and you collectively need to form k groups.
You could be antisocial and form a group by yourself. Then the other (n – 1) people can form (k – 1) groups in S(n – 1, k – 1) ways.
Or you could decide to be social and be part of a group with other people. Let the other (n – 1) people form k groups; they can do this in S(n – 1, k) ways. You then have k choices for which group to join, so there are k S(n – 1, k) ways to do this.
Total: S(n, k) = k S(n – 1, k) + S(n – 1, k – 1).
• (author reply to Matthew) Very nicely explained. It’s be interesting to code up a recursive Stirling number method based on the recurrence relationship and then investigate its performance versus the iterative definition. JM
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# SOC SCI 10A Chapter Notes - Chapter 11: Point Estimation, Statistical Inference, Interval Estimation
22 views2 pages
5 Dec 2016
School
Department
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## Document Summary
Assume that we compute the statistic p for a sample of size n from a populations with proportion equal to p. The sampling distribution of p can be describes as: Its mean i called the expected value of p. Its standard deviation is called the standard error of pits shape is binomial (the same as the shape of b(n,p) ) 11. 2 the normal approximation to the sampling distribution of p: when n is 30 or more, the sampling distribution of p, the sample proportion, is approximately normal. 11. 3 con dence interval estimates for p, the population proportion. Inferential statistics is the branch of statistics which describes techniques for drawing conclusions about an entire population based on data obtained from a random sample. The two common types of inferences about populations are. Point estimates of population parameters: con dence interval estimates of population parameters.
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Home / Arithmetic Aptitude / Time and Work :: Discussion
### Discussion :: Time and Work
1. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
2. A. 15 days B. 20 days C. 25 days D. 30 days
Answer : Option C
Explanation :
(A + B)'s 1 day's work =$$\frac { 1 } {10 }$$
C's 1 day's work =$$\frac { 1 } {50 }$$
(A + B + C)'s 1 day's work =[$$\frac { 1 } {10 }$$+$$\frac { 1 } {50 }$$]=$$\frac { 6 } {50 }$$=$$\frac { 3 } {25}$$.... (i)
A's 1 day's work = (B + C)'s 1 day's work .... (ii)
From (i) and (ii), we get: 2 x (A's 1 day's work) =$$\frac { 3 } {25}$$
A's 1 day's work =$$\frac { 3 } {50}$$
B's 1 day's work[$$\frac { 1 } {10 }$$-$$\frac { 3 } {50 }$$]=$$\frac { 2 } {50}$$=$$\frac { 1 } {25 }$$
So, B alone could do the work in 25 days.
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Mathematics
vybez:
Simplify to create an equivalent expression. 5(10k+1)+2(2+8k) A. 66k + 9 B. 64k + 9 C. 66k + 54 D. 64k - 9
snowflake0531:
The distributive property \[a(b+c) = ab+ac\] So using the distributive property, get rid of the parenthesis of 5(10k+1) + 2(2+8k),
vybez:
ok
snowflake0531:
So what do you get
vybez:
66k + 9?
snowflake0531:
yep
vybez:
snowflake0531:
Well, it's A
vybez:
ok ty for the help :)
snowflake0531:
yw~
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## Measure the speed of light with a hot dog (sausage) and your microwave
As a science geek, I couldn’t help but be delighted by this bit of tomfoolery (via Reddit). In a nutshell, the idea is to place a hot dog on the floor of your microwave (so it doesn’t rotate), then cook the hot dog until it starts to bubble. Use a ruler to measure the length of the burn marks, throw some math at it, and voilà, you have an approximation for the speed of light.
To get a better understanding of why this works, take a look at the video below (HT to Peter Hosey).
Because Science!
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A Physical Game for Factoring and Primes: Groups! (Plus: Math for Love grows)
I’ve been out of touch on the old web-log lately, but after a three week hiatus, I’m back!
If you glance at the rest of the site, you might notice that there’s another person working with me. I haven’t officially announced it here yet, so I will now: the exceptional Katherine Cook has joined Math for Love. She’s going to be co-teaching, tutoring, consulting, and blogging here soon. (I’m a huge fan of her previous blogging.) I’m thrilled to have her working with me.
I’ve also got a great game to share. Katherine and I had a one day math circle in December, and came up with a really cool group activity for kids: a kind of factoring-based musical chairs. It’s called:
Groups
Rules: You need space to move around. The kids all stand up, and you call out different numbers (Three!). The kids, then, have to get into groups of that size. If there’s an odd person or two out, well, they lose that round, but the winning and losing doesn’t matter–just move on to a different number. You can hit numbers you’ve called before.
Now here’s what makes it interesting: we played with 12 kids, and virtually every number we called out–2, 3, 4, 6, 1, 12 (one big group!)–no one was cut out. When we called five, though, that ended–two people were left out when the groups formed. But then one of us joined in, making the whole group equal to 13, and suddenly there was practically no number we called that didn’t leave someone out!
A fun game, with a mystery underneath. We played with K-2nd graders (plus some parents), and we’re going to be continuing with an 8 week circle which will delve into this mystery. Why do some numbers break up nicely, and others always leave someone groupless? How can you tell which numbers will do what?
For every age, there’s an appropriate mystery. Prime numbers and division are appropriate for virtually every age.
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# The Percent Proportion – Two Breakout Activities!
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The Percent Proportion – Two Breakout Activities!
What is a Google Breakout video.
This activity includes two different breakout activities designed to meet the needs of all of your students.
This activity includes two different breakout activities designed to meet the needs of all of your students.
Activity Details:
Students are first required to solve ten percent problems using the percent proportion.
The first breakout (level 1) consists of fairly easy problems while the second breakout (level 2) contains more advanced problems. Once the solutions have been calculated students use the answers as codes to break out! The Google breakout forms are included with this purchase.
Your kids will love this activity especially if there is a prize involved for successfully breaking out!
This activity also includes an interactive video lesson and notes about the percent proportion that may be incorporated into your lesson.
This purchase includes a calculations worksheet for each breakout for your students to show their work. I use this activity as part of my 7th-grade percent unit.
Enjoy!
"The mission of Wrestle with Math is to create engaging, highly effective resources for the math classroom"
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2014-03-11T21:31:46-04:00
This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Combine like terms so
2x + 8x + 6x
& 15 + 30
16x + 45
• Brainly User
2014-03-11T22:27:44-04:00
This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
2x+8x+6x+15+30
=
2x + 8x + 6x=16x
15 + 30= 45
Final answer is 16x + 45
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# Transposition method
Updated On: 17-04-2022
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Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Very Important Questions
FAQs on Linear Equation In One Variable
Introduction
Equation: a statement of equality which contains one or more unknown quality or variable ( literals) is called an equation
Linear Equation: an equation involving only linear polynomials is called a linear equation
Solution: a value of the variable which when substituted for the variable in on equation makes
is said to satisfy the equation and is called a solution or a root of the equation .
Solving an equation: solving an equation means determining its roots
Solving equations having variable terms on one side and number(s) on the other side
Transposition method
Solve :
Solve :
Cross-multiplication method for solving equations of the form
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#### Calculate the percentage composition in terms of mass of a solution obtained by mixing 400 g of a 25% solution and 300 g of 30% solution. Option 1) 25.42 Option 2) 28.92 Option 3) 27.14 Option 4) 26.53
As we learnt
Mass percent of solution -
Mass percent = ((mass of solute)/(mass of solution) ) X 100
- wherein
it is mass of solute present in 100 gram solution.
mass of solute in 1st solution = 0.25 x 400 = 100g
mass of solute in 2nd solution = 0.3 x 300 = 90g
mass of solute in total mixtue = 190g
Total mass of the mixture = 700g
Mass % of mixtur
Option 1)
25.42
Option 2)
28.92
Option 3)
27.14
Option 4)
26.53
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# INTRODUCTION TO PROBABILITY ROUSSAS PDF
Purchase Introduction to Probability – 2nd Edition. Probability Theory and Stochastic Processes; Introduction to Probability Authors: George Roussas. Purchase An Introduction to Probability and Statistical Inference – 2nd Edition. Roussas, this book introduces readers with no prior knowledge in probability or. Roussas introduces readers with no prior knowledge in probability or statistics, to a thinking process to guide them toward the best solution to a posed question.
Author: Mashakar Yodal Country: Namibia Language: English (Spanish) Genre: Finance Published (Last): 18 May 2008 Pages: 242 PDF File Size: 2.32 Mb ePub File Size: 7.58 Mb ISBN: 562-7-64730-635-2 Downloads: 38873 Price: Free* [*Free Regsitration Required] Uploader: Tanos
Roussas earned a B. Conditional Probability and Independence 5. Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Readers should be comfortable with multiple integrals and, in spots, a little linear algebra. I would be happy to adopt this book.
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### Introduction to Probability : George G. Roussas :
The first eight chapters are a perfect fit. There are a lot more examples and I like that the exercises are not too technologically dependent. Roussas is the author of five books, the author or co-author of five special volumes, and the author or co-author of dozens of research articles published in leading journals and special volumes. Answers to even-numbered exercises are given and detailed answers to all exercises are available to instructors on the book companion site. After introducing fundamental probability concepts, the book proceeds to topics including conditional probability and independence; numerical characteristics of a random variable; probabilith distributions; joint probability density function of two random variables and related quantities; joint moment generating function, covariance and correlation coefficient of two random variables; transformation of random variables; the Weak Intfoduction of Large Numbers; the Central Limit Theorem; and statistical inference.
EL ANTIEDIPO CAPITALISMO Y ESQUIZOFRENIA PDF
Roussas has been honored with a Festschrift, and he has given featured interviews for the Statistical Science and the Statistical Periscope.
Table of contents Preface 1. Description Introduction to Probability, Second Edition, discusses probability theory in a mathematically rigorous, yet accessible way. Each section provides relevant proofs, followed by exercises and useful hints.
This book will be of interest to upper level undergraduate students and graduate level students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, probabilitty some of the social sciences.
Home Contact Us Help Free delivery worldwide. Some Motivating Examples 2. They support concepts well, and they are of high quality. He rouszas a Fellow of the following professional societies: The examples and exercises are carefully selected and are even better than many texts currently available in the market Transformation of Random Variables The Best Books of Independence of Random Variables and Some Applications Check out the top books of the year on our page Best Books of The Concept of Probability and Basic Intrkduction 4.
Some Special Distributions 7. Numerical Characteristics of a Random Variable 6.
Dispatched from the UK in 1 business day When will my order arrive? I would definitely adopt this for my Intro Probability course.
BIONICLE BOTAR INSTRUCTIONS PDF
## Introduction to Probability
The writing is clear and concise. This one-semester basic probability textbook explains important concepts of probability while providing useful exercises and examples of real world applications for students to consider. By using our website you agree to our use of cookies. Numerous solved examples and exercises are provided in each chapter. Throughout his career, Roussas served as Dean, Vice President for Academic Affairs, and Chancellor at two universities; also, he served as an Associate Dean at UC-Davis, helping to transform that institution’s statistical unit into one of national and international renown.
I am satisfied with the topics covered in each chapter and the order in which they are presented. This edition demonstrates the applicability of probability to many human activities with examples and illustrations.
Some Fundamental Concepts 3.
Roussas was an associate editor of four journals since their inception, and is now a member of the Editorial Board of the journal Statistical Inference for Stochastic Processes. Product details Format Hardback pages Dimensions x x
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Find the pH when 150 ml 1 M \$\ce{NaOH}\$ has been added to 100 ml 1 M \$\ce{H3PO4}\$. What I know: \$\$\ce{H3PO4 + NaOH -> NaH2PO4 + H2O}\$\$ \$\$\ce{NaH2PO4 + NaOH -> Na2HPO4 + H2O}\$\$ Finally 50 millimoles \$\ce{Na2HPO4}\$ and 50 millimoles \$\ce{NaH2PO4}\$ remains. Hence it will be =3×1+31+4×16=98 Add / Edited: 03.07.2015 / Evaluation of information: 5.0 out of 5 / number of votes: 1. 3NaOH + H3PO4 --> Na3PO4 + 3H2O b. The Questions and Answers of the total number of different kinds of buffers obtained during the titration of H3PO3 with NaOH are are solved by group of students and teacher of Class 11, which is also the largest student community of Class 11. Every 3 moles of NaOH … So for every 3 moles of NaOH, there needs to be 1 mole of H3PO4. The product of neutralisation of H3PO3 and 2NaOH will be :-H3PO3 + 2 NaOH -----> Na2H2PO3 + H2O. In this reaction 1g equivalent NaOH reacts with one mole H3PO4. When Phosphorous acid reacts with Sodium Hydroxide gives Sodium hypophosphite and Water. Should I apply acid buffer equation? pH, hydrogen ion concentration Calculator. But if it's what I think it is, here is the what I have: a. Please register to post comments. Become a Patron! I'm stuck with this question. pH calculation formula: pH = -log(1/H +) Where: H +: Hydrogen ion concentration in the solution H + concentration of acid is depended on its pKa, for strong acid like HCl, its pKa=1, thus H + concentration of 1 M HCl is also 1 M; for weak acid such as acetic acid, its pKa=0.0000175, thus H + concentration of 1 M acetic acid is: 1 * 0.0000175 = 0.0000175 M So molar mass of the acid is its equivalent mass. Сoding to search: H3PO3 + NaOH = NaH2PO3 + H2O. NaOH is monoacidic base. ChemiDay you always could choose go nuts or keep calm with us or without. 22.4g of Sodium Hydroxide Work: The balanced equation is the ratio of moles to each element. So its molar mass is same as equivalent mass. As we know that H3PO3 is a dibasic acid.
## h3po3 + naoh
Sudoku Pdf Hard, Worx Landroid Wire Connector, World Of Illumination, Boss Ds-1 Pedal, Book Title Generator Romance, Raw Chana During Pregnancy, Small Tabletop Fountain, Sudoku Pdf Hard,
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//--------------------------------------------------------------------------------- // The AliKFVertex class // . // @author S.Gorbunov, I.Kisel // @version 1.0 // @since 13.05.07 // // Class to reconstruct and store primary and secondary vertices. // The method is described in CBM-SOFT note 2007-003, // ``Reconstruction of decayed particles based on the Kalman filter'', // http://www.gsi.de/documents/DOC-2007-May-14-1.pdf // // This class is ALICE interface to general mathematics in AliKFParticleBase // // -= Copyright © ALICE HLT Group =- //_________________________________________________________________________________ #ifndef ALIKFVERTEX_H #define ALIKFVERTEX_H #include "AliKFParticle.h" #include "AliVVertex.h" class AliKFVertex : public AliKFParticle { public: //* //* INITIALIZATION //* //* Constructor (empty) AliKFVertex():AliKFParticle(),fIsConstrained(0){ } //* Destructor (empty) ~AliKFVertex(){} //* Initialisation from VVertex AliKFVertex( const AliVVertex &vertex ); //* //* ACCESSORS //* //* Number of tracks composing the vertex Int_t GetNContributors() const { return (fNDF+3)/2; } //* //* CONSTRUCTION OF THE VERTEX BY ITS DAUGHTERS //* USING THE KALMAN FILTER METHOD //* //* Simple way to construct vertices ex. D0 = Pion + Kaon; void operator +=( const AliKFParticle &Daughter ); //* Subtract particle from vertex AliKFVertex operator -( const AliKFParticle &Daughter ) const; void operator -=( const AliKFParticle &Daughter ); //* Set beam constraint to the primary vertex void SetBeamConstraint( Double_t X, Double_t Y, Double_t Z, Double_t ErrX, Double_t ErrY, Double_t ErrZ ); //* Set beam constraint off void SetBeamConstraintOff(); //* Construct vertex with selection of tracks (primary vertex) void ConstructPrimaryVertex( const AliKFParticle *vDaughters[], int NDaughters, Bool_t vtxFlag[], Double_t ChiCut=3.5 ); protected: Bool_t fIsConstrained; // Is the beam constraint set ClassDef( AliKFVertex, 1 ); }; //--------------------------------------------------------------------- // // Inline implementation of the AliKFVertex methods // //--------------------------------------------------------------------- inline void AliKFVertex::operator +=( const AliKFParticle &Daughter ) { AliKFParticle::operator +=( Daughter ); } inline void AliKFVertex::operator -=( const AliKFParticle &Daughter ) { Daughter.SubtractFromVertex( *this ); } inline AliKFVertex AliKFVertex::operator -( const AliKFParticle &Daughter ) const { AliKFVertex tmp = *this; Daughter.SubtractFromVertex( tmp ); return tmp; } #endif
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# T.i.P.S.
• Student must use the various forms of positive and negative rational numbers to add, subtract, multiply, and divide in problem solving situations that may include multiple various forms of numbers within a problem situation. Students should recall how to convert numbers between decimals, fractions, and percents.
# Example
• During a recent shopping trip, Erin bought six shirts that cost \$15.95 each. How much change did Erin receive if she paid with a \$100 bill?
Hint
Possible Solutions
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https://socratic.org/questions/how-do-you-evaluate-sec-2-arcsin-1-3
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# How do you evaluate sec(2 arcsin(-1/3))?
Jul 19, 2016
$\frac{9}{7}$
#### Explanation:
Let $a = a r c \sin \left(- \frac{1}{3}\right)$. Then,
$\sin a = \left(- \frac{1}{3}\right)$.
So, $\cos 2 a = 1 - 2 {\sin}^{2} a = 1 - 2 \left(\frac{1}{9}\right) = \frac{7}{9}$
The given expression is $\sec 2 a = \frac{1}{\cos 2 a} = \frac{9}{7}$..
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http://www.dropzone.com/cgi-bin/forum/gforum.cgi?post=748145;sb=post_username;so=DESC;forum_view=forum_view_collapsed;guest=104705338
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Forums: Skydiving: Safety and Training:
How Long ...?
Zoter
Nov 8, 2003, 10:02 AM
Post #1 of 10 (888 views)
Shortcut
How Long ...? Can't Post
If I exit at 13K and pull at 4K.......assuming I fall on my belly at approx 120mph...how long is my freefall...and is there a nice simple calculation to work this out that incorparates exit altitude and pull altitude?
I aint no mathematics teacher
Nov 8, 2003, 10:11 AM
Post #2 of 10 (864 views)
Shortcut
Re: [Zoter] How Long ...? [In reply to] Can't Post
look in the front of your log book, there is probably a scale.
Clouds are my enemy
Nov 8, 2003, 10:14 AM
Post #3 of 10 (862 views)
Shortcut
Re: [Zoter] How Long ...? [In reply to] Can't Post
At 4K you're about 24 seconds from certain death, at 3K it's about 18, and about 12 at 2K. Does that help?
-
Jim
Casch
Nov 8, 2003, 10:14 AM
Post #4 of 10 (862 views)
Shortcut
Re: [Zoter] How Long ...? [In reply to] Can't Post
120mph = 176ft/s
The first 1K ft takes approximately 10-12 seconds, then every 1K ft after that takes approximately 5.5 seconds.
T = Freefall Time
E = Exit Altitude (i.e. 3 or 10 or 13 etc.)
P = Pull Altitude (i.e. 3 or 10 or 13 etc.)
T = ((E - P) - 1) * 5.5 + 10
Zoter
Nov 8, 2003, 10:35 AM
Post #5 of 10 (852 views)
Shortcut
Re: [Casch] How Long ...? [In reply to] Can't Post
Thanks...thats the ticket !
and damn....Jimbo... I was thinking about the time I just had...rather than the time I had left !!!! but thanks for the clarity anyways
(This post was edited by Zoter on Nov 8, 2003, 10:43 AM)
Nov 8, 2003, 11:37 AM
Post #6 of 10 (824 views)
Shortcut
Re: [Zoter] How Long ...? [In reply to] Can't Post
Think of it this way, what's behind you isn't likely to hurt, what's in front of you though could kill you. (I suppose that wouldn't hurt for too long though. )
-
Jim
(This post was edited by Jimbo on Nov 8, 2003, 11:38 AM)
Blahr
Nov 8, 2003, 12:22 PM
Post #7 of 10 (807 views)
Shortcut
Re: [Zoter] How Long ...? [In reply to] Can't Post
55 seconds freefall from 13k to 4k at 120 mph
Zoter
Nov 9, 2003, 3:03 AM
Post #8 of 10 (704 views)
Shortcut
Re: [Jimbo] How Long ...? [In reply to] Can't Post
Yeah jimbo there its important to know that side of the equation as well......although....I wont need to be so accurate that I can enter it in my logbook afterwards
Tonto (D 515)
Moderator
Nov 10, 2003, 4:44 AM
Post #9 of 10 (585 views)
Shortcut
Re: [Jimbo] How Long ...? [In reply to] Can't Post
(I suppose that wouldn't hurt for too long though. )
Yeah - but it would be VERY sore...
t
lazyfrog
Nov 10, 2003, 11:36 AM
Post #10 of 10 (525 views)
Shortcut
Re: [Zoter] How Long ...? [In reply to] Can't Post
do in meters... 50m per second...
Forums : Skydiving : Safety and Training
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January 14, 2017
## Introduction
Here we will know about “how to perform k-means clustering in R” and “how to find best value of k in k-means clustering”
### Importing library
##### Let’s open RStudio and follow along !!
Let’s import the ggplot2 library which is needed for ggplot visualization
``````library(ggplot2)
``````
Let’s import the data set named “iris” into the data frame named “DataFrame”
``````DataFrame<-iris
``````
### Looking at data structure
Let’s check the str of the data set
``````str(DataFrame)
``````
``````## 'data.frame': 150 obs. of 5 variables:
## \$ Sepal.Length: num 5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
## \$ Sepal.Width : num 3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
## \$ Petal.Length: num 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
## \$ Petal.Width : num 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
## \$ Species : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...
``````
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Machine Learning and Data Science best online courses
### 2D plot before k-means clustering
Let’s have a look on 2D plot of Petal.Length and Petal.Width.We can easily from the plot that data points are clustered and data points can be divided into three clusters or groups.
``````ggplot(DataFrame) + geom_point(aes(x=Petal.Length,
y=Petal.Width,
color = Species,
size=2))+
scale_x_continuous(name = "Length of Petal")+
scale_y_continuous(name="Width of Petal")+
theme_bw()
``````
### Performing k-means Clustering
We already know that there are three clusters or groups in this data set
based on the Species variable.They are setosa,versicolor and virginica
So let’s fit the kmeans algorithm using k-means function and see what k-means tells.centers=3 inside the k-means function means that “we are trying to look for 3 clusters or groups in the data “.
``````set.seed(12345)
kmeansClust <- kmeans(DataFrame[, 1:4],centers=3)
``````
### Summary of k-means model
The output of this kmeans algorithm is as follows.
``````kmeansClust
``````
``````## K-means clustering with 3 clusters of sizes 62, 38, 50
##
## Cluster means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1 5.901613 2.748387 4.393548 1.433871
## 2 6.850000 3.073684 5.742105 2.071053
## 3 5.006000 3.428000 1.462000 0.246000
##
## Clustering vector:
## [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [36] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [71] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2
## [106] 2 1 2 2 2 2 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 1 2
## [141] 2 2 1 2 2 2 1 2 2 1
##
## Within cluster sum of squares by cluster:
## [1] 39.82097 23.87947 15.15100
## (between_SS / total_SS = 88.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"
``````
### Variance before Clustering
The total variance in the data before clustering is
``````wss <- (nrow(DataFrame)-1)*sum(apply(DataFrame[,1:4],2,var))
wss
``````
``````## [1] 681.3706
``````
### Finding best value of k
Let’s pretend that we don’t know the Species variable and so we also don’t know about the number of clusters in the data.So we need to fit the algorithm with different values of “number of clusters” or “k”, say from 2 to 15.
We should expect the elbow point to be around 3 which is equal to the number of clusters in the data.
``````for (i in 2:15) wss[i] <- sum(kmeans(DataFrame[,1:4],
centers=i)\$withinss)
``````
### SSE(Sum of squared error) vs k
Look for a bend or elbow in the sum of squared error (SSE) scree plot.The location of the elbow in the resulting plot suggests a suitable number of clusters for this kmeans algorithm is 3:
``````plot(1:15, wss, type="b", xlab="Number of Clusters",
ylab="Within groups sum of squares")
``````
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https://www.chess.com/forum/view/chess960-chess-variants/why-is-chess960-is-called-chess960-is-it-because-it-have-960-different-start
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Forums
# Why is Chess960 is called Chess960? Is it because it have 960 different starting potisions?
Sort:
Yes.
Repilied THIS fast?
But I'm still not sure.
Maybe because something else.
It is the reason.
BTW, the starting position you've shown is *not* a legal 960 starting position.
The rooks are on one side of the king, which is illegal.
um......
then another question: why it is not called "postision960"?
^That is a legal position. It's not the same as the one in post #1.
And I have no clue. Chess960 sounds better to me, and English is my first language, or pretty close to it at least.
……
Then I will wait for others.
?
Morphysrevenges wrote:
no, it's because there are 960 different dumb questions about why it's called chess 960.
Lol
Yes.
• 4 white squares for 1 bishop, 4 black squares for the other bishop
• Then there are 6 available fields for the lady
• Then there are 5 available fields for the 2 Knights (10 posibilities)
• Then the remaining King and Rooks can only be placed in 1 way
4*4*6*10*1 = 960
Morphysrevenges wrote:
no, it's because there are 960 different dumb questions about why it's called chess 960.
Now it's 961
but @Serphiot, how can we know that all those positions (960 of them) will be such that the rooks are not on the same side of the King... does not seem obvious...
stephanebordas wrote:
but @Serphiot, how can we know that all those positions (960 of them) will be such that the rooks are not on the same side of the King... does not seem obvious...
He puts the king and rooks on last.
If there are 3 slots available, exactly one permutation will have the king between both rooks.
There's not 960 starting positions because the conventional chess position is rejected. I don't know if the mirror image is rejected: probably not, since castling would be different, so it wouldn't be a true mirror image. So there's 959 positions.
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# Vulturing Ultimate X Bonus Streak
## Introduction
This article presumes the reader already understands the rules for Ultimate X Bonus Streak. Briefly, this is a video poker variant where a winning hand not only pays immediately, but in many cases awards multipliers on up to the next five hands. If the previous player left a game with enough multipliers on future hands, then it is positive play for the vulture* to play off those multipliers and leave.
*: A "vulture" is a player who plays "variable state" or "accumulator" games left in a state with over a 100% return to player by the previous player. The vulture trolls around the casino, looking for such games. When he finds one, he plays it a short time, leaving it in a negative state. This is much like a vulture swooping down on a dead carcass with some meat on it, quickly eating it, and flying off.
It is obvious that Ultimate X Bonus Streak is such a game, but I have never seen anything published on when to play it. So, I stepped in to provide such numbers (shut up, Wiz!).
## Double Double Bonus
In all my advice, remember that a hand with no indicated multiplier still has a multiplier of 1x.
### 3 Play
For 3-play Double Double Bonus, I assumed the 6/5 pay table, with streaks of 2-4, 2-4-8, and 2-4-8-10-12. The base game, with no feature, has an RTP of 94.66%. With the feature, the RTP is 95.05%. You should play if any of the following are true:
• Total multiplier on the next hand equal 7 or more.
• Total multiplier on the next two hands equal 10 or more.
### 5 Play
For 5-play Double Double Bonus, I assumed the 6/5 pay table, with streaks of 2-4, 2-4-8, and 2-4-8-10-12. The base game, with no feature, has an RTP of 94.66%. With the feature, the RTP is 94.95%. You should play if any of the following are true:
• Total multiplier on the next hand equal 11 or more.
• Total multiplier on the next two hands equal 18 or more.
• Total multiplier on the next three hands equal 26 or more.
### 10 Play
For 10-play Double Double Bonus, I assumed the 8/5 pay table, with streaks of 2-3-4 and 2-4-8-10-12. The base game, with no feature, has an RTP of 96.79%. With the feature, the RTP is 97.24%. You should play if any of the following are true:
• Total multiplier on the next hand equal 21 or more.
• Total multiplier on the next two hands equal 34 or more.
• Total multiplier on the next three hands equal 43 or more.
## Deuces Wild
In all my advice, remember that a hand with no indicated multiplier still has a multiplier of 1x.
### 3 Play
For 3-play Deuces Wild, I assumed the 25-15-10-4-3-2-2 pay table, with streaks of 2-2-4 and 2-2-3-4-10-15-25. The base game, with no feature, has an RTP of 94.82%. With the feature, the RTP is 95.08%. You should play if any of the following are true:
• Total multiplier on the next hand equal 7 or more.
• Total multiplier on the next two hands equal 10 or more.
### 5 Play
For 3-play Deuces Wild, I assumed the 25-15-10-4-3-2-2 pay table, with streaks of 2-2-4 and 2-2-3-4-10-15-25. The base game, with no feature, has an RTP of 94.82%. With the feature, the RTP is 94.93%. You should play if any of the following are true:
• Total multiplier on the next hand equal 11 or more.
• Total multiplier on the next two hands equal 15 or more.
• Total multiplier on the next three hands equal 25 or more.
### 10 Play
For 3-play Deuces Wild, I assumed the 25-16-13-4-3-2-2 pay table, with streaks of 2-2-4 and 2-2-3-4-10-15-25. The base game, with no feature, has an RTP of 96.77%. With the feature, the RTP is 96.99%. You should play if any of the following are true:
• Total multiplier on the next hand equal 21 or more.
• Total multiplier on the next two hands equal 32 or more.
• Total multiplier on the next three hands equal 44 or more.
## Other Games and Pay Tables
I know that there are many other games and pay table tables available for this game. Find the play points above was very time consuming and tedious, so please forgive me that I ran through only two games. I think it is safe to use the Double Double Bonus strategy on any game with no wild cards. Likewise, I think it is safe to use the deuces wild strategy on Bonus Deuces .
## Methodology
The analysis in this page was done by random simulation and assuming the player uses optimal strategy for the base game with no feature. It was a very difficult and time-consuming project. I consider it one of my proudest works, which, as usual, will mean nobody will ever read it.
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# slide rule
slide rule, instrument for making numerical computations and readings, the results of which may be read easily and quickly after performing simple mechanical manipulations. Multiplication and division, finding of powers and roots, and other more complicated calculations may be performed with a slide rule. Based on John Napier's principle of the logarithm, it came into use after Edmund Gunter created a logarithmic scale in 1620. Gunter's rule consisted of a straight line on which numbers were spaced at intervals proportional to their common logarithms. Using this scale, William Oughtred and Edmund Wingate developed independently (c.1630) the first slide rules. Amédée Mannheim, a French army officer, in 1850 established the form that it maintained thereafter. This had three parts, the stock, the slide, and the cursor (indicator). The stock consisted of two fixed parallel rules, each with a scale on its inner edge. The slide was a single rule, moving between them. It had two scales on its outer edge, each scale corresponding to the fixed scale to which it was adjacent. The cursor, a transparent square with a hairline, could be moved the length of the rule to aid in reading it. In its many varieties it had additional scales for such calculation as logarithms, trigonometric functions, and square roots. By the late 1980s they had been supplanted by the electronic calculators, which were easier to use and more accurate.
#### See more Encyclopedia articles on: Mathematics
Related content from HighBeam Research on: slide rule
# 24 X 7
## Private Tutor
24 x 7 Tutor Availability Unlimited Online Tutoring 1-on-1 Tutoring
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# Cartesian and vector equation of a plane
A plane can be completely illustrated by denoting two intersecting lines which can be translated into a fixed point A and two nonparallel direction vectors. The position vector of any general point P on the plane passing through point A and having direction vectors and is given by the equation
## Vector equation of a plane
Parametric equation of a plane: λ , μ are called a parameters λ,μ
If N is considered to be normal to a given plane, then all other normals to that plane are considered parallel to which are resultantly scalar multiples of N., In particular,we can say that there are two normals of length 1:
Normal/Scalar product form of vector equation of a plane
Consider a vector n passing through a point A. Only one plane through A can be is perpendicular to the vector. Now consider R being any point on the plane other than A as shown above. Then we can say that
Cartesian equation of a plane
=
Therefore, the Cartesian form is
where n1, n2 and n3 are the components of n and where is called the normal vector.
Example: Find the equation of the plane passing through the three points P1(1,-1,4), P2(2,7,-1), and P3(5,0,-1).
Hence, consider one point on the plane:
In vector form:
Any non-zero scalar multiples of is also a normal vector of the plane. Therefore, Multiply by -1.
Example: Find the equation of the plane with normal vector containing the point (-2, 3, 4).
Example:Find the distance of the plane = 8 from the origin, and the unit vector perpendicular to the plane.
Example: Find the Cartesian equation of the plane through the point A (1, 1, 1) perpendicular to the vector
Solution:
Example: Show that the following vector is perpendicular to the plane containing the points A(1, 0, 2), B(2, 3, -1) and C(2, 2, -1 ).
Solution:
In conclusion, n is a vector that is perpendicular to 2 vectors in the plane so is perpendicular to the plane.
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# PUPM calculation
Register Blogs Members List Search Today's Posts Mark Forums Read
April 13, 2009, 06:56 PUMP calculation #1 New Member Zvonko Kostovski Join Date: Apr 2009 Location: Skopje, Macedonia Posts: 13 Rep Power: 10 I'm having a problem calculating a pump (spiral pump inlet-impeller-pump spiral (outlet)) I'm using only frosen rotor (someone thold me that this is OK for calculating pump Q-H curve and efficiency) the problem is that I allvays get efficincy to be 3-6 %% less that is should be (in optimal point) an the q-h curve is not as expected in lower q than otimal it has lower H and for greater Q i get higher H than the expected curve this is what i do after starting CFX pre import meshes (gtm) (inlet-impeller-pump) for inlet I have mass flow (for example 300 kg/s) and for outlet preasure (0 Pa), what is the reference preasure ? (also 0 Pa or atmosphere preasure) and after the solver in CXF post, when I go to MAcro Calculator - > Liquid Pump Performance , what Reference Radius and Reference High mean (diameter of impeller / 2 and hight difference between inlet and outlet) Please someone help, I was traying to find tutorial for similar problem but only found one tutorial for axial turbine and that is very different I'm willing to give the files to someone who wants to help me solve this kind of problem Last edited by zona; April 13, 2009 at 12:38.
April 14, 2009, 03:06 #2 Member SanS Join Date: Mar 2009 Posts: 41 Rep Power: 10 Hi, Rather than using the macro, you would be better off to calculate the way you would do in a test rig. Determine the pressure head, velocity head, torque from POST and then calculate efficiency. Also read thru the ANSYS CFX Best Practices mentioned in the manual.
April 14, 2009, 08:53 #3 New Member Zvonko Kostovski Join Date: Apr 2009 Location: Skopje, Macedonia Posts: 13 Rep Power: 10 thanks, I'll tray it what is reference radius and hight I can't find definition in manuals
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# Thread: Compute without Limit - support for fractions and 2G Digits!
1. ## Compute without Limit - support for fractions and 2G Digits!
I made a *.so Libary for Linux.
(This libary is called rol or Rechnen ohne Limit. Translated to english this would mean Compute without Limit.)
With this Libary, you can compute with numbers that can have up to 2 147 483 647 Digits!
These numbers can also have +/- (be positive/negative - how do you say this in english?).
Of course it supports numbers with a '.' in it (eg: 3.14).
It also supports fraction like one third. they are written like this: 1|3 .
Features:
-Can compute with numbers up to 2 147 483 647 digits.
-Can do*,/,+,-
-Can do <,>,==
-Supports .
-You can tell the Division how precise it should be.
-You can use it as .so libary
-You can migrate older Projects from normal to with Rechnen ohne Limit (-->english: Compute without Limit)
-It supports +/- (positive/negative)
-Fractions!
Look here for the anouncement of Version 1.4 : http://forum.etlamsoft.de/viewtopic.php?f=31&t=26
I would be glad if you could look at it and tell me what I could make better.
etlam
2. Couple of remarks. First, the header file cannot be included without first doing:
Code:
```#include <string>
using namespace std;```
Your header file should #include <string> itself. However, it should not do a using namespace std; - use std::string.
Your program, while it seems to work with "rols"/numbers (haven't tested this well yet), seems to break std::string. Consider this example:
Code:
```#include <string>
#include <iostream>
using namespace std;
#include "rol.h"
int main()
{
rol r;
std::string s1, s2;
r = "123";
s1 = "abc";
s2 = "def";
s1 = s1 + s2;
r = r + s2;
std::cout << s1 << std::endl;
std::cout << r << std::endl;
return 0;
}```
Which gives:
Code:
```+0
+123```
When the first line ought to read "abcdef". If you really want to use std::string to hold your numerical data, derive a class from it, name it rol, and get rid of the typedef.
You library appears to write temporary files. (And not clean them up?) Doesn't seem friendly to me, and a library such as rol really shouldn't need file I/O, should it?
Divison by zero locks up in what appears to be an infinite loop.
One of my nitpicks towards libraries of this nature: a*b may be faster than b*a, depending on how I ordered the operands. (In my test, 40 bytes of "123412341..." times "2000" took 1.353s or 0.335s. If it's faster to have one operand on one side, have the function do a length test, and swap operands if needed.
Speed: Finding 100! (factorial) is taking some time...
Finally, aside from your function names being in German(?):
Code:
`extern void multiplikation(string,string,string);`
I'm going to assume this does multiplication. If so, how does it return an answer? There is no return value, no pointers, no references. (And three arguments?)
My preference is to leave argument names in the header files. This clarifies at a glace what the argument to the functions are.
Otherwise, so far it is getting the correct answers. Well done.
I'll try to answer every point.
Originally Posted by Cactus_Hugger
Couple of remarks. First, the header file cannot be included without first doing:
Code:
```#include <string>
using namespace std;```
Your header file should #include <string> itself. However, it should not do a using namespace std; - use std::string.
Yes, I did forget to do that.
Will be fixed for next version.
Originally Posted by Cactus_Hugger
Your program, while it seems to work with "rols"/numbers (haven't tested this well yet), seems to break std::string. Consider this example:
[example]
Which gives:
Code:
```+0
+123```
When the first line ought to read "abcdef". If you really want to use std::string to hold your numerical data, derive a class from it, name it rol, and get rid of the typedef.
Huh? Strange. I'll have a look at this.
But you shouldn't add strings and rols.
Originally Posted by Cactus_Hugger
You library appears to write temporary files. (And not clean them up?) Doesn't seem friendly to me, and a library such as rol really shouldn't need file I/O, should it?
Yes, these files are there, because first I used functions like
division(string a, string b, string c);
Where these function took the two numbers stored in a and b (those strings are file names) and wrote the result in a file named c.
But eg. division uses temporary files from the addition, so I can't delete them there.
Those function are still used inside rol addition.
For next version, I'll try to delete those files, or store them in a extra folder.
Originally Posted by Cactus_Hugger
Divison by zero locks up in what appears to be an infinite loop.
Mhh...
I will test at the beginning if its divisded by zero, but what should then the result be?
I have to think about that.
Originally Posted by Cactus_Hugger
One of my nitpicks towards libraries of this nature: a*b may be faster than b*a, depending on how I ordered the operands. (In my test, 40 bytes of "123412341..." times "2000" took 1.353s or 0.335s. If it's faster to have one operand on one side, have the function do a length test, and swap operands if needed.
I havent understanded that good.
Do you mean a big number * a small number is faster?
Or a small number * a big number is faster?
I'll have a look at this.
But maybe, instead of doing the test, I could look at why this happens, and make it equal-fast.
I think this happens because of something in the main loop, and a few times the main loop by a lot times the small loop is faster than a lot times the main loop by a few times the small loop.
Originally Posted by Cactus_Hugger
Speed: Finding 100! (factorial) is taking some time...
Yes, for next Version I'll make support for root and power and the things you wrote here.
And than, for the Version after that I'll look at the speed.
Originally Posted by Cactus_Hugger
Finally, aside from your function names being in German(?):
Code:
`extern void multiplikation(string,string,string);`
I'm going to assume this does multiplication. If so, how does it return an answer? There is no return value, no pointers, no references. (And three arguments?)
These functions are old!
Look to the up (How do you say that in english?)
Originally Posted by Cactus_Hugger
My preference is to leave argument names in the header files. This clarifies at a glace what the argument to the functions are.
I havent understanded this.
Could you please repeat this in easier english?
Originally Posted by Cactus_Hugger
Otherwise, so far it is getting the correct answers. Well done.
Thanks!
etlam
4. My preference is to leave argument names in the header files. This clarifies at a glace what the argument to the functions are.
I havent understanded this.
Could you please repeat this in easier english?
Leaving argument names in makes function prototypes easier to read. Which makes more sense? This?
Code:
`string fullname(string, string);`
Or this?
Code:
`string fullname(string firstname, string lastname);`
Hint: the second one.
5. Yes, O.K.,
I'll do this!
etlam
6. ## RoL Version 1.5.0
Now Version 1.5.0 of RoL was realeased, coming with a lot of new features!
See here for the worklog
This is a tutorial explaining how to use RoL.
Whats new in this Version:
- I overloaded +,-,*,/,!,==,>,< for the class rol.
- rol can be used nearly as easy as for example int.
- Much faster now
- No use of temporany files anymore
- new mathematical functions: to the power,root, exp, ln, abs , min, max
- trigonometric Functions: sinx, sina, cosx,cosa,tanx,tana,cotx,secx,cscx, sinh, cosh, tanh, coth, sech, csch (sinx means as radient and sina means as °)
If you find bugs or want to ask something you can also write it to the forum related to Rol.
I would be glad if you could look at it and tell me what I could make better.
etlam
7. Originally Posted by etlam
-Can compute with numbers up to 2 147 483 647 digits.
Then it's not really "without limits," is it?
8. @brewbuck: Not really - but I think 2G digits has a touch of unlimited.
The biggest known prime number has a bit under 10M digits, and they needed more than a month to compute it.
And its not very likely that someone would need more than 2G digits...
etlam
9. Have you considered extending that to a 64-bit size for 64-bit architecture machines - it should add very little extra execution time, and whilst the number of digits is sufficient for large integer calculations, should you wish to calculate something like pi to many digits precision, you may find that 2G digits isn't quite sufficient.
--
Mats
10. Yes, with that you dont need more than 2G I meant the normal things, but Pi is one thing where this isnt enough.
I already thought about this for 64 Bit machines, but the problem is that I dont have a 64 Bit machine, where I could test this.
I could also use multidimensional arrays, but this would slow down everything, and I thought that it wouldnt be worth if for the part of the users, which dont need more than 2G its lets say 20% more time.
etlam
11. The other problem with 32-bit machines is of course that you are limited to about 3GB of user-space memory, so even if you have huge amount of memory, if you have many parts in the calculation, you won't even get close to 2G digits in a number when you are limited by the size of the user-space memory. Again, 64-bit machines should solve that.
A 64-bit processor + motherboard + memory shouldn't set you back very much - about 300 euros should get you a decent system with a reasonable amount of memory - you do want something with more than 4GB if you REALLY want to show that it can do more than 2G digits tho', so you may need to get into either more expensive motherboard and/or memory sticks for that - but for the initial implementation you don't need anythign more than a simple Athlon64 or late-ish Intel Pentium 4/Core 2 processor.
--
Mats
12. This is what i reckon would be the best translation, my german is limited though, so there might be room for improvement...
Code:
`nachkommastellenkuerzen(rol x,3);`
Basically what this does is to remove digits after the comma (nach komma), in english this is called Rounding, so perhaps something like this:
Code:
```round()
roundoff()
loseprecision()```
On the forum you linked to, you wrote that:
rol hoch(rol a, rol b);
this does a^b
By a^b i presume you mean a to the power of b? And not a XOR b? If so then this function basically does the same as the pow() function in the math.h header(link), so i guess one of these names would suffice?
Code:
```pow()
exp()```
Perhaps it's best to avoid pow() since it's already in math.h, best not confuse everyone
rol wurzel(rol x, rol n);
this is the opposite of ^ (called radical?)
it does the nth radical(???) of x.
I'm not quite sure i understand this one. The inverse function of exp() is the natural logarithm, but you already have that function named as ln(), so what is this one then? Could it be Nth root?
Code:
```root()
nroot()```
abs(rol x);
This changes the +/- to +.
This is called the absolute value, so i don't think you really need to change this one Alternatively you could call it:
Code:
`absvalue()`
ln(rol x);
The naturally logarithm of x.
No need to change this either
If you have any other functions you need translated, or variables, just let me know, be happy to help...
Edit: Looks like i mixed up THE exponential function and exponentiation in general. With this in mind i don't think you should name your function exp(), but rather pow()
13. Thank you, that will relly helped me.
For the next Version I will name the functions in your translations.
Originally Posted by Neo1
Code:
```round()
roundoff()
loseprecision()```
I will use loseprecision here, because this is what the function was first for.
Originally Posted by Neo1
By a^b i presume you mean a to the power of b?
Yes, its the a to the power of b.
Originally Posted by Neo1
Perhaps it's best to avoid pow() since it's already in math.h, best not confuse everyone
I think I will use something like rpow (r for rol)...
Originally Posted by Neo1
I'm not quite sure i understand this one. The inverse function of exp() is the natural logarithm, but you already have that function named as ln(), so what is this one then? Could it be Nth root?
In RoL, exp means e to the power of something, and ln is the reverse one.
With wurzel I mean the nth root. I will call it root.
Originally Posted by Neo1
If you have any other functions you need translated, or variables, just let me know, be happy to help...
Maybe you could help translate the variables, which control the accuracy.
You find them here
etlam
14. long division_nachkommastellen;
The direct translation of this would be division_placesaftercomma, but perhaps you should go with division_digitsaftercomma or division_precision? Up to you
long ln_nachkommastellen_genauigkeit;
Same as above, genauigkeit translates to accuracy or precision. ln_digitsaftercomma_accuracy ? Perhaps you should change this one if you plan on translating it
long wurzelgenauigkeit;
Something along the lines of nroot_accuracy.
long wurzelgenauigkeitnks;
This one is abit strange as well. Maybe nroot_accuracy_dac? Where dac == nks...
long hochnks;
rolpow_dac
long expgenauigkeit;
long expnachkommastellen;
long singenauigkeit;
long sinnks = 10;
exp_accuracy
exp_dac
sin_accuracy
sin_dac
But those 4 are very confusing/interchangeable, i think you should comment your code very well if you chose those names...
15. Thank you!
For the next version these names will be in english.
etlam
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• AAMT Top Drawer Teachers
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This activity helps students develop an understanding of graphical representations, interpret and analyze line plots, and determine the best way to display data.
Subject:
Mathematics
Material Type:
Interactive
Provider:
AAMT Top Drawer Teachers
Author:
Jane Watson
04/04/2013
Educational Use
Rating
0.0 stars
This activity is designed to help students overcome the confusion that can arise when they learn that a square is also a rectangle—and a rhombus and a parallelogram. Students create a flowchart to visualize the properties of quadrilaterals. In the finished flowchart, the quadrilateral is at the top and the square is at the bottom, because the square has the greatest number of properties.
Subject:
Mathematics
Material Type:
Interactive
Provider:
Top Drawer Teachers AAMT
Author:
Top Drawer Teachers AAMT
04/04/2013
Unrestricted Use
CC BY
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This activity gives students the opportunity to use concrete and dynamic representations of the shapes. At the completion of this activity, students will have a discovered a list of properties for each of the six special quadrilaterals. The final page of the quiz enables students to summarize all their findings in a table that can be retained for future use.
Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
AAMT Top Drawer Teachers
Author:
AAMT — TOP DRAWER TEACHERS
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https://calculator.services/ziwipeak-feeding-calculator/
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# The Ziwipeak Feeding Calculator for Your Pet
Rate this post
Published on: June 28, 2023
Created by RAKIBUL MANNAN / Fact-checked by Monjurul Kader
Ziwipeak Feeding Calculator
# Ziwipeak Feeding Calculator
The Ziwipeak Feeding Calculator is designed to help pet owners determine the appropriate daily feeding amount of Ziwipeak pet food for their pets. The calculation formula used in the calculator is based on the pet's weight and their activity level.
The formula for calculating the daily feeding amount is:
Daily Feeding (grams) = Weight (kg) × Activity Level × 0.03
Weight (kg) is the pet's weight in kilograms, which the user inputs. Activity Level is a multiplier that varies based on the pet's level of daily activity, with three options: Low (1), Moderate (1.5), and High (2). The constant 0.03 is an estimation of the daily food intake required per kilogram of body weight.
Using this formula, the calculator provides a recommended daily feeding amount in grams of Ziwipeak pet food to maintain a healthy weight and support the pet's energy needs.
As pet owners, we always strive to provide the best nutrition for our furry companions. One highly regarded option is Ziwipeak pet food, known for its high-quality ingredients and commitment to pet health. Ensuring that your pet receives the proper amount of food is crucial, and that's where the Ziwipeak Feeding Calculator comes in. Here, we'll explore the importance of proper nutrition and guide you through using the Ziwipeak Feeding Calculator to determine the perfect daily feeding amount for your pet.
## Understanding Your Pet's Nutritional Needs
Several factors influence a pet's nutritional requirements, such as age, weight, activity level, and health conditions. Younger pets, for example, have different nutritional needs than senior pets. Additionally, a highly active pet will require more calories and nutrients to maintain its energy levels. It's essential to understand your pet's unique needs to provide them with optimal nutrition. Ziwipeak pet food is formulated to meet these varying requirements, helping your pet maintain a healthy weight and thrive.
## How to Use the Ziwipeak Feeding Calculator
The Ziwipeak Feeding Calculator is a user-friendly tool that considers your pet's weight and activity level to determine the appropriate daily feeding amount. Here's a step-by-step guide:
• Enter your pet's weight (in kilograms) in the designated input field.
• Choose your pet's activity level from the drop-down menu (Low, Moderate, or High).
• Click the "Calculate" button to generate the recommended daily feeding amount (in grams).
Interpreting the results:
While the calculator provides a good starting point, it's important to keep in mind that each pet is unique. You may need to adjust the feeding amount based on your pet's specific needs and consult your veterinarian if you have any concerns. Additionally, as your pet's weight and activity level change over time, it's a good idea to periodically reevaluate their feeding amount using the calculator.
#### How Much Should I Tip My Dog Groomer?
When it comes to showing appreciation for your dog groomer, many factors play a role in determining how much to tip. To calculate grooming tips easily, consider factors like the service provided, the groomer's experience, and the overall satisfaction you and your furry friend feel after the grooming session. Taking these things into account will help ensure a fair and considerate tip for your dog groomer's exceptional work.
#### Can the calculator be used for pets of all ages and sizes?
Yes, the calculator is designed to accommodate pets of various ages, breeds, and sizes. However, if your pet has special dietary needs or health conditions, it's best to consult your veterinarian for personalized advice.
#### How often should I update my pet's feeding amount using the calculator?
It's a good idea to reassess your pet's feeding amount every few months or whenever you notice significant changes in their weight or activity level. Regular check-ups with your veterinarian can also help ensure that your pet is on track with their nutrition.
## Tips for a Successful Transition to Ziwipeak Pet Food
When introducing Ziwipeak pet food to your pet's diet, it's important to make the transition gradually. Start by mixing a small amount of Ziwipeak with your pet's current food, gradually increasing the proportion of Ziwipeak over a week or two. Keep an eye on your pet's health and weight during the transition, and don't hesitate to seek advice from your veterinarian if you encounter any issues.
## Wrapping Up a Conclusion
The Ziwipeak Feeding Calculator is a valuable tool for pet owners looking to provide their pets with optimal nutrition. By considering your pet's weight and activity level, you can determine the perfect daily feeding amount to help your pet maintain a healthy weight and thrive. Remember to monitor your pet's health and consult your veterinarian for personalized advice as needed. By prioritizing your pet's nutrition and making informed choices, you can ensure a happy and healthy life for your furry friend.
We encourage you to try the Ziwipeak Feeding Calculator and share your experiences with fellow pet owners. Your pet's well-being is worth the effort, and the Ziwipeak Feeding Calculator can help you make the right choices for their dietary needs.
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https://casadimenotti.com/line-plot-4th-grade/line-plot-worksheet-second-grade-refrence-stem-and-leaf-plot/
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Math Worksheets Line Plot Fourth Grade With Fractions 4th Worksheet Games Activities
By Claudette Lesperance at December 25 2018 15:56:38
Mathematics, or more colloquially, "math", is one of the most important subjects that students learn in school. Not only do good mathematical skills form a necessary for understanding of other subjects, especially the sciences, but also, math is an important life skill. Learning math usually of course begins at young age, sometimes even at home, with learning numbers and counting. At kindergarten and then school, students then progress through arithmetic (addition, subtraction, multiplication, and division), and eventually to more advanced topics such as algebra, geometry, graphs and charts, and statistics.
What do you mean by that? How will you know if you've arrived? A better goal statement is "I am going to lose 10 pounds, be able to do 50 push-ups without a break, and run 3 miles in under 25 minutes by my next birthday." No wiggle room there! You will know if you've succeeded or failed. And, assuming the targets are also appropriately challenging or significant, you will have a strong goal statement. Why do I want to achieve this goal? What are the benefits I'm seeking. This could be a very long list. Referring back to the fitness goal, you may want to look better at the beach, beat a friend in a race, improve your heart health or any number of other possibilities. The purpose of this step is to identify your deepest motivations, get them on paper, and refer to them as you progress towards your goal.
Gallery of Line Plot 4th Grade
It is widely understood that math has a global use and acceptance. People are also aware of the rate at which math is advancing today at various fields of research and study. Many mathematicians will talk about the pattern and structure of math worksheets which are helpful for people in working fields. Math has helped science and technology reach a higher level of advancement. Letter Books: These are books that frequently use the same phonemes over and over so students can understand them (the link between a letter and the sound it makes). For instance, "Baby bear bounced balls". These books are really good, especially if you have the book as a colouring book that you can fill out together. Here's a good activity: say the sound like "b says...buh buh, ball" and then students race to colour in their balls in their workbook. You can hang these up after and everyone will have fun.
What are the three primary steps I need to take to reach this goal? At this point you simply synthesize all the points from the previous step into the three logical big steps that will get you to your destination. For instance, back to the fitness scenario, the steps might be to establish a better eating-out routine, to join a fitness club, and to work out three times a week. Which habits (daily, weekly, monthly) do I need to establish to reach my goal? Don't miss the power of this step! Every big goal requires new habits if we are to get there, a new routine in some small or great way, usually on the daily and weekly level. Our lives really are simply the sum total of our habits. We change our lives primarily by changing our habits.
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http://www.sporcle.com/games/bigalsirkp/simeqns
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# Science / Simultaneous Equations
Random Science Quiz
## Can you name the correct solutions?
#### by bigalsirkp Quiz not verified by Sporcle
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3x - 4y = -6 and 2y + x = 8
7x - 2y = 15 and 3y - x = 6
4y + 6x = 32 and y - 3x = 17
2(x + y) = 9 and 8x - y = 0
3x - 2y = 14 and y + 3x = -16
3x - y = 11 and 2y + 9x = -7
x + y = 17 and 3y - 2x = 101
4y + 2x = 0 and 9x - y = 2.375
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https://www.centerforcorporatesustainability.org/average-annual-percentage-rate/
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# Average Annual Percentage Rate
### Contents
The fdic began posting the National Rate and Rate Cap on May 18, 2009. Data is not available prior to May 18, 2009. This historical data can be accessed at Previous Rates.. 1 National rates are calculated based on a simple average of rates paid (uses annual percentage yield) by all insured depository institutions and branches for which data are available.
The effective APR, annual percentage rate, or the mathematically correct annual percentage rate here is 25.7%. You might say, "Hey, Sal, that’s still not too far off "from the reported APR, where they just take "this number and multiply by 365, instead of taking "this number and taking it to the 365 power."
Powell’s remarks triggered a stock market rally, with the dow jones industrial average up nearly 100 points in late. said.
Average Credit Card purchase interest rate (APR): By Card Type. The average credit card interest rate varies significantly depending on the type of card you’re looking at. rewards credit cards will generally have a higher average APR as a group to make up for the additional benefits that these cards provide.
Best Site For Mortgage Rates Internet-based mortgage companies often offer the best mortgage rates, but who are you really working with? We show you how to find the best online mortgage lenders and discuss when it’s worth getting your mortgage online versus working with a local bank or broker.
An annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment. APR is expressed as a percentage that represents the actual yearly cost of funds over the.
The average annual percentage rate on a personal loan will range from 10% to 28% in 2019. Actual rates will vary based on how creditworthy you are, the length of the loan, the loan amount, and the lender.
Other loan rates, including auto loans, tend to increase as the benchmark interest rate increases. Edmunds said the average annual percentage rate on new financed vehicles averaged 5.8% in September,
How to Calculate Growth Rate or Percent Change. In the example, multiplying 0.11 times 100 gives you an average annual growth rate of 11 percent. Tips. Some financial investments, such as savings accounts or bonds, compound periodically instead of continuously.
Current Us Prime Rate Prime Rate Canada | Prime Rate Explained, Prime Rate. – Prime Rate. The prime rate in Canada is currently 3.95%. The prime rate, also known as the prime lending rate, is the annual interest rate Canada’s major banks and financial institutions use to set interest rates for variable loans and lines of credit, including variable-rate mortgages.
Annualized rate of return measures the compound annual growth rate of an investment and can be tricky to calculate by hand. Users can calculate the annualized rate of return in Excel using the "XIRR" formula. To perform the calculation, you must have the Analysis ToolPak add-in installed.
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http://www.helpmykidlearn.ie/activities/10-12/detail/how-computers-work
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Activity
# How computers work
### What to do with this activity?
Does your child know that everything we see and hear on computers or mobile phones (which are mini computers) - all the letters, words, numbers, videos, pictures and sound - is translated by the computer into just two numbers - 1 and 0. Each number is called a "bit" and corresponds to being either switched off (a zero) or switched on (number 1). It's called binary code. There are no numbers 2, 3, 4, 5, 6, 7, 8 or 9 in a binary system, but of course those numbers and every number can be expressed just using ones and zeros!
Here's a TedX video that shows you how sounds, pictures and everything else are expressed with just ones and zeros. Don't try to figure out every single thing - it's enough to understand it in general terms.
If you have a child who enjoys mathematics, see if you can translate numbers from 2 upwards into binary code. Maths is Fun shows you how here
• #### Why am I doing this?
Maths makes sense to children when they use it in everyday life - like measuring things, working out distances, estimating food for dinner or money for groceries. The more opportunities you give your child to use the maths they learn at school through everyday activities the more they will understand and enjoy working with numbers.
• #### How can I do more?
Discuss maths that you see around you. For example, talk about sales in shops – half price, 25% off, what is good value? Or how much will the item cost after the discount?
##### Rate this activity
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How would you rate it?
1 = Poor, 5 = Great.
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http://www.mathworks.com/matlabcentral/fileexchange/2170-mastering-mechanics-1-using-matlab-5/content/hull/mech1/displace.m
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Code covered by the BSD License
# Mastering Mechanics 1: Using MATLAB 5
### Doug Hull (view profile)
20 Aug 2002 (Updated )
Companion Software
[D, Slope]=displace(x,Moment,type,placement,E,I)
```function [D, Slope]=displace(x,Moment,type,placement,E,I)
%DISPLACE Displacement of a beam.
% [DISPLACEMENT,SLOPE]=DISPLACE(X,MOMENT,TYPE,PLACEMENT,E,I) will find the
% DISPLACEMENT and SLOPE of a beam that is being acted upon by the MOMENT
% given to it. The MOMENT data should be developed with the DIAGRAM and
% DIAGRAMINTEGRAL routines.
%
% TYPE describes the type of supports used, the options are:
% ['place' 'place'] for a pin supported beam.
% ['slope' 'place'] and ['place' 'slope'] for a beam that has a
% restriction on it's slope at one point and its placement at that or
% another point. Often the place and slope restraints will be at the
% same point for a fixed support like the wall in a cantilevered beam.
% PLACEMENT is a two entry vector describing the place along the beam that
% the corresponding support is acting.
% E is the Young's modulus of the beam.
% I is the area moment of inertia of the beams cross section.
%
% Details are to be found in Mastering Mechanics I, Douglas W. Hull,
% Prentice Hall, 1998
% Douglas W. Hull, 1998
% Copyright (c) 1998-99 by Prentice Hall
% Version 1.00
type=lower(type);
if nargin<5 E=1; end
if nargin<6 I=1; end
%type is either 'place' or 'slope', will be in a vector with two words
%placement is the distance along the x that the restraint is placed
first=type(1:5);
second=type(6:10);
if ~(strcmp(first,'place') | strcmp(first,'slope'))
disp('Invalid restraint type, use ''slope'' or ''place''');
return
end
if ~(strcmp(second,'place') | strcmp(second,'slope'))
disp('Invalid restraint type, use ''slope'' or ''place''');
return
end
if strcmp(second,'slope') & strcmp(first,'slope')
disp('Can not deal with ''slope'' ''slope'' restraint.')
disp('Try a redundancy routine.')
return
end
Slope=diagramintegral(x,Moment);
if strcmp(first,'slope')
Slope=Slope-interpolate(x,Slope,placement(1));
D=diagramintegral(x,Slope);
D=D-interpolate(x,D,placement(2));
elseif strcmp(second,'slope')
Slope=Slope-interpolate(x,Slope,placement(2));
D=diagramintegral(x,Slope);
D=D-interpolate(x,D,placement(1));
else
D=diagramintegral(x,Slope);
ErrorMatrix=[-interpolate(x,D,placement(1)); -interpolate(x,D,placement(2))];
PlaceMatrix=[placement' [1 1]'];
Coefs=inv(PlaceMatrix)*ErrorMatrix;
Slope=Slope+Coefs(1);
D=(D+Coefs(1)*x+Coefs(2));
end
Slope=Slope/(E*I);
D=D/(E*I);
```
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https://www.wtfprofessor.com/
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## Work Done By Friction (Physics 1 Problem Solution)
Having a hard time calculating the work done by friction? Turns out all it takes is a few FBDs, a little trig, and understanding the work equation. In this post and video, we go through a solution to a work done by friction (and work done by gravity) physics problem involving a man, an incline… Continue Reading
## How To Do Homework FAST: 2 Steps to Speed (Without Anxiety)
I think we can all safely agree: Homework (especially those ridiculously long WebAssign problem sets) can be a royal pain in the ass. It takes forever to finish. It leaves you feeling tired, frustrated, and wondering whether you've actually learned anything at all, despite all that time you spent in class. It was created by… Continue Reading
## How To Conquer Finals Week: My Secret 4-Step Formula
We all know finals week (in all it's stress inducing glory) is the most crucial time of year. But does it have to be so insane? I say no, and here's why. Finals is the time of year that you need to focus the most. The large majority of your grade is about to be… Continue Reading
## Gravitational Potential Energy Examples (Physics 1 Breakdown)
Does reading through gravitational potential energy examples in your textbook make your brain want to explode? In this video I break down a Physics 1 exam problem that covers gravitational potential energy, orbits, escape velocity, and all the relationships between them that you'll need to know. A space station of mass 400,000 kg, orbits the… Continue Reading
## How To Focus On Studying: Boost Your Willpower (In 4 Steps)
All of us want to know how to focus on studying consistently, but often it's almost impossible to do. Want to know how to do it, and why willpower is the key to staying focused while studying? We'll cover that in this video. Click here to download the free "Stay Focused While Studying" PDF Quick… Continue Reading
## Good Places to Study (Does Your Environment Matter?)
What are some good places to study? Does study environment matter? The research is in, and what it says is quite interesting... So in today's video I answer a question about whether there's actually such a thing as a "best" study location, or whether you're just as well off on the couch. Then, I'll offer… Continue Reading
## Change In Momentum Problems (Physics 1 Solution Breakdown)
Change in momentum problems usually involve figure skaters, bullets, and other ridiculous scenarios. But don't be fooled by the flash and dance - there's a method to the madness. And in this video I go through an example of a conceptual change in momentum problem from a Physics 1 exam, step-by-step. Download the full Change… Continue Reading
## Physics 2: How To Decode Electricity And Magnetism
Physics 2 (electricity and magnetism) can be a cruel bitch of a course. Download a free PDF copy of this post to take with you If you've ever come across a circuit with a resistor, capacitor, and inductor in series with some sort of complex switching mechanism in between them, and then are asked to… Continue Reading
## How to Pay Attention in Class: 4 Tips for Boring Lecture
Most of us want figure out how to pay attention in class more often, but it's tough, especially during that horrible, boring lecture you've got coming up next. So let me know if this sounds familiar... You're sitting there, and the professor is scribbling non-stop on the board. Symbols, diagrams, equations; you really have no… Continue Reading
## Molarity Problems (Chemistry 1 Exam Solution Breakdown)
In this video I go through how to break down molarity problems (pulled from an actual general chemistry 1 exam), and understand the relationship between molarity, moles and molecular mass. On the surface it seems like a very straightforward problem. There's not a lot of work involved here. But if you're not solid on it… Continue Reading
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In an earlier post “OS.walk in Python“, I described how to use os.walk and showed some examples on how to use it in scripts. First, let’s talk about bubble charts in Python. Find all mp3 files with os.walk and fnmatch. Python Program for Bubble Sort using For Loop. Since 2001, Processing has promoted software literacy within the visual arts and visual literacy within technology. To analyze the bubble sort, we should note that regardless of how the items are arranged in the initial list, $$n-1$$ passes will be made to sort a list of size n. Table 1 shows the number of comparisons for each pass. Let’s take a tour of the top 6 sorting algorithms and see how we can implement them in Python!
Python Examples Python Examples Python Compiler Python Exercises Python Quiz Python Certificate. Next, we are using For Loop to insert elements into the List. 3. After that, we are sorting the list items using the Python bubble sort algorithm. Scatterplot with varying point sizes and hues¶. TIP: Please visit Python Tutorial to learn Python Programming with practical examples. Project: Unique-Python Author: DipanshKhandelwal File: turtle_triangle.py MIT License : Example 1. Recall that the sum of the first n integers is $$\frac{1}{2}n^{2} + \frac{1}{2}n$$. In this article, We will understand bubble sort in python with its working. Let’s build a Python bubble … Return the number of times the value "cherry" appears int the fruits list: fruits = ['apple', 'banana', 'cherry'] x = fruits.count("cherry") Python Bubble Charts. We will also see python code for bubble … You can vote up the examples you like or vote down the ones you don't like. Example. $python test_grader.py --image images/test_03.png This time the reader did a little better, scoring a 60%: Figure 12: Building a bubble sheet scanner and test grader using Python and OpenCV. This Python program allows the user to enter the List Size. The examples are categorized based on the topics including List, strings, dictionary, tuple, sets, and many more. The total number of comparisons is the sum of the first $$n-1$$ integers. Processing is a flexible software sketchbook and a language for learning how to code within the context of the visual arts. Do you know about Python Modules vs Packages. Following Python section contains a wide collection of Python programming examples. In this particular example, the reader simply marked all answers along a diagonal:$ python test_grader.py --image images/test_04.png Let's look at an example and sort the array 8, 5, 3, 1, 4, 7, 9: Such a chart is a scatter plot with an extra dimension, which makes it apparently 3-dimensional. This means larger bubbles denotes higher values. The idea behind Bubble Sort is very simple, we look at pairs of adjacent elements in an array, one pair at a time, and swap their positions if the first element is larger than the second, or simply move on if it isn't. TIP: Please refer to List article to understand everything about Python … Python List count() Method List Methods.
Bubble Sort. They are from open source Python projects. Python source code: [download source: scatter_bubbles.py] This page contains the list of Python programming examples which covers the concepts including basic and simple python programs, number programs, string programs, List Programs, series programs etc. The following are code examples for showing how to use turtle.Turtle(). Bubble Sort. In this article, I will show how to use the os.walk() module function to walk a directory tree, and the fnmatch module for matching file names. This algorithm is called bubble sort, because with each iteration the largest data item in the list bubbles up towards the last place in the list, just like a water bubble rises up to the water surface.
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# math
posted by .
a water tank measures 12o feet in diameter and is 50 feet high .how many cubic feet of water can it hold ,to the nearest cubic foot ?
• math -
V = pi * r^2 * h
V = 3.14 * 6^2 * 50
V = 3.14 * 36 * 50
V = ?
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## Wednesday, February 3, 2010
### Another Post Just To Prove I Still Post
The latest post on Scat strategy has been half-finished for over a week, as I have been working on presentations of old and new research. Also, I'm still trying to find a new trivia night; I may give up soon and just start posting my own stuff. For now, here's a fun definition:
Let Ak be the set {1, 2, ..., k}. A graph G has an optimal t-tone coloring if each vertex can be assigned a t-element subset of Ak in such a way that if vertices u and v are distance d apart (in other words, the shortest path in G connecting these vertices contains d edges), then their subsets have at most d-1 elements in common.
For example, vertices adjacent to each other can have no shared elements in their subsets, while if the distance between two vertices is greater than t, they may be assigned identical subsets.
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School Fair Necklaces
Stage: 1 and 2 Challenge Level:
Rob and Jennie were making necklaces to sell at the school fair.
They decided to make them very mathematical.
Each necklace was to have eight beads, four of one colour and four of another.
And each had to be symmetrical, like this.
How many different necklaces could they make?
Can you find them all?
How do you know there aren't any others?
What if they had 9 beads, five of one colour and four of another?
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Statistics is a section of mathematics that manages the collection, interpretation, analysis and presentation of different numerical data. In other words, Statistics is a collection of quantitative data. Academic task offering 2000+ Statistics MCQs for the preparation of different schools, colleges, and universities examinations to get good marks. Solved statistics question and answer cover multiple topics such as basic statistics mcqs, sampling mcqs, probability mcqs, Probability distributions, correlation and regression analysis, sampling distributions Techniques, statistical inference, time-series analysis, data presentation mcqs, statistical software mcqs, index numbers mcqs, design of experiments mcqs, statistical quality control, random variables mcqs, Non-Parametric statistics mcqs – and much more. These statistic multiple choice questions are also helpful for the preparation of various interviews, entrance examinations, other competitive examinations, and jobs like PPSC Statistics Lecturer’s jobs, Statistical Officers, Data Entry Operator, etc. for all Experienced, Freshers and Students. Also, check MCQs on Agriculture here.
Statistics is a section of mathematics that manages the collection, interpretation, analysis and presentation of different numerical data. In other words, Statistics is a collection of quantitative data. Academic task offering 2000+ Statistics MCQs for the preparation of different schools, colleges, and universities examinations to get good marks. Solved statistics question and answer cover multiple topics such as basic statistics mcqs, sampling mcqs, probability mcqs, Probability distributions, correlation and regression analysis, sampling distributions Techniques, statistical inference, time-series analysis, data presentation mcqs, statistical software mcqs, index numbers mcqs, design of experiments mcqs, statistical quality control, random variables mcqs, Non-Parametric statistics mcqs – and much more. These statistic multiple choice questions are also helpful for the preparation of various interviews, entrance examinations, other competitive examinations, and jobs like PPSC Statistics Lecturer’s jobs, Statistical Officers, Data Entry Operator, etc. for all Experienced, Freshers and Students. Also, check MCQs on Agriculture here.
11. Statistics has handicap dealing with_____________?
A. Constant
B. Variable
C. Quantitative data
D. Qualitative data
12. Major area of statistics today is concerned with drawing of conclusions from__________?
A. Samples
B. Primary
C. Two
D. Complete study
13. The Number of road accidents is the example of____________?
A. variable
B. Constant
C. Discrete variable
D. Continuous variable
14. In Statistics, a population consists of:_____________?
A. All People living in a country
B. All People living in the are under study
C. All subjects or objects whose characteristics are being studied
D. None of the above
15. The sum of squares of deviation is least if measure from__________?
A. Mean
B. Mode
C. Median
D. Variance
16. Variance is always calculated from___________?
A. Mean
B. Variance
C. Geometric Mean
D. Median
E. Mode
17. The sum of values divided by their number is called___________?
A. Median
B. Harmonic Mean
C. Mean
D. Mode
E. None of these
18. Arithmetic Mean is___________affected by extreme values?
A. Not
B. Highly
C. Less
D. None of these
19. The data collected by NADRA to issue National Identity cards are______________?
A. Official data
B. un-official data
C. Primary data
D. Secondary data
20. Village Patwari collecting the data about cotton crops is the example of_____________?
A. variable
B. Constant
C. Primary data
D. Secondary data
NOTE
IF YOU THINK ANY OF THE MCQ ABOVE IS WRONG.
PLEASE COMMENT WITH CORRECT ANSWER AND ITS DETAIL EXPLANATION IN COMMENT BOX.
THANK YOU
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# How to get Taylor polynomial for functions?
3 vues (au cours des 30 derniers jours)
Carter Wunch le 19 Avr 2021
I'm looking to write a program where i can input a function, like exp(x) or sin(x), and have the program return the Taylor polynomials for the function.
This is what I have so far. I am fairly new to Matlab and am still getting used to the software.
str=input('Function? ','s');
T=taylor(s);
sympref('PolynomialDisplayStyle','ascend');
disp T
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### Réponse acceptée
Rafael Hernandez-Walls le 19 Avr 2021
You can use a function that is in the MAThWORKS fileexchange (I put the link):
str=input('Function? ','s'); %tray with: cos(x)
% https://la.mathworks.com/matlabcentral/fileexchange/67519-str2syms-symstr
z = str2syms(str)
T=taylor(z)
%
T =
x^4/24 - x^2/2 + 1
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ch 1-Introduction to Probability
# ch 1-Introduction to Probability - STAT 230 Introduction to...
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STAT 230: Introduction to Probability and Random Variables Summer 2009 1 Probability 1.1 Sample space and Events Definition 1. Random Experiment A random experiment is an experiment for which the outcomes cannot be deter- mined ahead of time. Definition 2. Sample Space The sample space Ω is the collection of all possible outcomes. Elements ω in Ω are called simple outcomes. Definition 3. Event An event is a subset of the sample space. We say that an event occurs if and only if the outcome of the random experiment is an element of the event. Example 1. For example, consider the experiment where you draw a random card from a standard deck. The sample space consists of the 52 cards and one event is A = { card drawn is red } . Example 2. Suppose the experiment consists of tossing a coin twice. The sample space is Ω = { ( H, H ) , ( H, T ) , ( T, H ) , ( T, T ) } . The outcomes in the event A = { first toss is Head } are { (H,H),(H,T) } . Example 3. Consider the experiment where a pair of 6-sided die are rolled. The sample space is Ω = ( i, j ); i = 1 .. 6 , j = 1 .. 6 . The outcomes in A = { the second roll is 3 } are { (i,3);i=1..6 } . Example 4. Suppose we roll a 6-sided die and toss a coin. For the events A = { the die is even } and B = { the coin is Head } , then: A = { (2,H),(2,T),(4,H),(4,T),(6,H),(6,T) } . B = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H) } . A’ = { (1,H),(1,T),(3,H),(3,T),(5,H),(5,T) } . B’ = { (1,T),(2,T),(3,T),(4,T),(5,T),(6,T) } . A B = { (2,H),(4,H),(6,H) } . 1
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A B 0 = { (2,T),(4,T),(6,T) } . Definition 4. Mutually Exclusive Events A 1 , A 2 , ..., A n are mutually exclusive events if they cannot occur at the same time i.e A 1 , A 2 , .., A n are disjoint sets: A i A j = for all i 6 = j. In the case n=2, two events A and B are said to be mutually exclusive if A and B are disjoint: A B = Definition 5. Exhaustive events A 1 , A 2 , ..., A n are exhaustive events if A 1 A 2 ... A n = Ω . Definition 6. Partition A 1 , A 2 , ..., A n form a partition of the sample space Ω if they are mutually exclu- sive and exhaustive events. Example 5. A partition for the experiment where a 6-sided die is rolled and a coin is tossed is: A 1 = { the coin is Head } = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H) } and A 2 = { the coin is Tail } = { (1,T),(2,T),(3,T),(4,T),(5,T),(6,T) } . proof: A 1 A 2 = and A 1 A 2 = Ω . 1.2 Probability Definition 7. Probability (Kolmogorov’s axioms) Let Ω be the sample space for a random experiment. A function P defined on the events of Ω is called a probability (or probability measure) if it satisfies the following three conditions: (a)- P ( A ) 0 for each event A. (b)- P (Ω) = 1 . (c)- IfA 1 , .., A n are mutually exclusive events then P ( A 1 A 2 ... A n ) = P ( A 1 ) + P ( A 2 ) + ... + P ( A n ) for all n. Theorem 1. (a)- Complementation Rule : for any event A, with complement A’; P ( A 0 ) = 1 - P ( A ) . (b)- Addition Rule : for any two events A and B; P ( A B ) = P ( A ) + P ( B ) - P ( A B ) . (c)- Inclusion-Exclusion Rule : for any three events A, B and C; P ( A B C ) = P ( A )+ P ( B )+ P ( C ) - P ( A B ) - P ( A C ) - P ( B C )+ P ( A B C ) . 2
(d)- Law of Partitions : If A 1 , A 2 , ..., A n form a partition of the sample space Ω , then for any event B; P ( B ) = P ( B A 1 ) + P ( B A 2 ) + ... + P ( B A n ) .
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Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > eqtrdi GIF version
Theorem eqtrdi 2190
Description: An equality transitivity deduction. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqtrdi.1 (𝜑𝐴 = 𝐵)
eqtrdi.2 𝐵 = 𝐶
Assertion
Ref Expression
eqtrdi (𝜑𝐴 = 𝐶)
Proof of Theorem eqtrdi
StepHypRef Expression
1 eqtrdi.1 . 2 (𝜑𝐴 = 𝐵)
2 eqtrdi.2 . . 3 𝐵 = 𝐶
32a1i 9 . 2 (𝜑𝐵 = 𝐶)
41, 3eqtrd 2174 1 (𝜑𝐴 = 𝐶)
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compute angle/local command¶
Syntax¶
```compute ID group-ID angle/local value1 value2 ... keyword args ...
```
• ID, group-ID are documented in compute command
• angle/local = style name of this compute command
• one or more values may be appended
• value = theta or eng or v_name
```theta = tabulate angles
eng = tabulate angle energies
v_name = equal-style variable with name (see below)```
• zero or more keyword/args pairs may be appended
• keyword = set
```set args = theta name
theta = only currently allowed arg
name = name of variable to set with theta```
Examples¶
```compute 1 all angle/local theta
compute 1 all angle/local eng theta
compute 1 all angle/local theta v_cos set theta t
```
Description¶
Define a computation that calculates properties of individual angle interactions. The number of datums generated, aggregated across all processors, equals the number of angles in the system, modified by the group parameter as explained below.
The value theta is the angle for the 3 atoms in the interaction.
The value eng is the interaction energy for the angle.
The value v_name can be used together with the set keyword to compute a user-specified function of the angle theta. The name specified for the v_name value is the name of an equal-style variable which should evaluate a formula based on a variable which will store the angle theta. This other variable must be an internal-style variable defined in the input script; its initial numeric value can be anything. It must be an internal-style variable, because this command resets its value directly. The set keyword is used to identify the name of this other variable associated with theta.
Note that the value of theta for each angle which stored in the internal variable is in radians, not degrees.
As an example, these commands can be added to the bench/in.rhodo script to compute the cosine and cosine^2 of every angle in the system and output the statistics in various ways:
```variable t internal 0.0
variable cos equal cos(v_t)
variable cossq equal cos(v_t)*cos(v_t)
compute 1 all property/local aatom1 aatom2 aatom3 atype
compute 2 all angle/local eng theta v_cos v_cossq set theta t
dump 1 all local 100 tmp.dump c_1[*] c_2[*]
compute 3 all reduce ave c_2[*]
thermo_style custom step temp press c_3[*]
fix 10 all ave/histo 10 10 100 -1 1 20 c_2[3] mode vector file tmp.histo
```
The dump local command will output the energy, angle, cosine(angle), cosine^2(angle) for every angle in the system. The thermo_style command will print the average of those quantities via the compute reduce command with thermo output. And the fix ave/histo command will histogram the cosine(angle) values and write them to a file.
The local data stored by this command is generated by looping over all the atoms owned on a processor and their angles. An angle will only be included if all 3 atoms in the angle are in the specified compute group. Any angles that have been broken (see the angle_style command) by setting their angle type to 0 are not included. Angles that have been turned off (see the fix shake or delete_bonds commands) by setting their angle type negative are written into the file, but their energy will be 0.0.
Note that as atoms migrate from processor to processor, there will be no consistent ordering of the entries within the local vector or array from one timestep to the next. The only consistency that is guaranteed is that the ordering on a particular timestep will be the same for local vectors or arrays generated by other compute commands. For example, angle output from the compute property/local command can be combined with data from this command and output by the dump local command in a consistent way.
Here is an example of how to do this:
```compute 1 all property/local atype aatom1 aatom2 aatom3
compute 2 all angle/local theta eng
dump 1 all local 1000 tmp.dump index c_1[1] c_1[2] c_1[3] c_1[4] c_2[1] c_2[2]
```
Output info¶
This compute calculates a local vector or local array depending on the number of values. The length of the vector or number of rows in the array is the number of angles. If a single value is specified, a local vector is produced. If two or more values are specified, a local array is produced where the number of columns = the number of values. The vector or array can be accessed by any command that uses local values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.
The output for theta will be in degrees. The output for eng will be in energy units.
none
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CompoundFactor - Maple Help
Finance
CompoundFactor
return a compound factor for the specified date or time
Calling Sequence CompoundFactor(rate, time, opts) CompoundFactor(rate, date, opts)
Parameters
rate - real constant, list(realcons), Vector or a yield term structure; given interest rate time - non-negative real number, list(non-negative), or Vector; time in years date - a string containing a date specification in a format recognized by ParseDate or a Date data structure; date opts - equations of the form option = value where option is one of referencedate, compounding, or daycounter; specify options for the CompoundFactor command
Options
• compounding = Simple, Continuous, Annual, Semiannual, EveryFourthMonth, Quarterly, Bimonthly, Monthly, SimpleThenAnnual, SimpleThenSemiannual, SimpleThenEveryFourthMonth, SimpleThenQuarterly, SimpleThenBimonthly, SimpleThenMonthly -- This option specifies the compounding type for the given interest rate.
• daycounter = Actual360, Actual365Fixed, AFB, Bond, Euro, Historical, ISDA, ISMA, OneDay, Simple, Thirty360BondBasis, Thirty360EuroBondBasis, Thirty360European, Thirty360Italian, Thirty360USA, or a day counter data structure created using the DayCounter constructor -- This option provides a day counter which will be used to convert the period between two dates to a fraction of the year. The default day count convention can be set using the Settings command.
• referencedate = a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies the reference date, that is, the date when the compound factor is equal to 1.
Description
• The CompoundFactor(rate, time, opts) calling sequence computes the compound factor at the specified time corresponding to the given interest rate. The interest rate and time can be given as lists in which case the array or their combinations are returned.
• The CompoundFactor(rate, date, opts) calling sequence computes the compound factor on the specified date corresponding to the given interest rate. The value of the daycounter option is used to compute the distance between date and the reference date (which is set to the global evaluation date by default).
Examples
> $\mathrm{with}\left(\mathrm{Finance}\right):$
> $\mathrm{rate1}≔0.06:$
> $\mathrm{compound1}≔\mathrm{CompoundFactor}\left(\mathrm{rate1},1.0,\mathrm{compounding}=\mathrm{Monthly}\right)$
${\mathrm{compound1}}{≔}{1.061677812}$ (1)
> $\mathrm{rate2}≔\mathrm{ImpliedRate}\left(\mathrm{compound1},1.0,\mathrm{Monthly}\right)$
${\mathrm{rate2}}{≔}{0.06000000013}$ (2)
> $\mathrm{cmpdlist}≔\left[1.2,1.05,1.8\right]:$
> $\mathrm{timelist}≔\left[0.2,2.5,3.2\right]:$
> $\mathrm{cflist}≔\mathrm{CompoundFactor}\left(\mathrm{cmpdlist},\mathrm{timelist},\mathrm{compounding}=\mathrm{Monthly}\right)$
${\mathrm{cflist}}{≔}\left[\begin{array}{ccc}{1.25702074308744}& {17.4494022688864}& {38.8578806542540}\\ {1.22301064607623}& {12.3844854941888}& {25.0543880753591}\\ {1.39853975717975}& {66.2117719567858}& {214.188953817854}\end{array}\right]$ (3)
> $\mathrm{CompoundFactor}\left(\mathrm{rate1},"January 02, 2006",\mathrm{compounding}=\mathrm{Monthly},\mathrm{daycounter}=\mathrm{Actual365Fixed},\mathrm{referencedate}="January 02, 2005"\right)$
${1.061677812}$ (4)
> $\mathrm{rate3}≔\mathrm{ZeroCurve}\left(0.05,\mathrm{referencedate}="January 02, 2005"\right)$
${\mathrm{rate3}}{≔}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (5)
> $\mathrm{compound3}≔\mathrm{CompoundFactor}\left(\mathrm{rate3},"January 02, 2006"\right)$
${\mathrm{compound3}}{≔}{1.051271096}$ (6)
> $\mathrm{ImpliedRate}\left(\mathrm{compound3},"January 02, 2005","January 02, 2006",\mathrm{Continuous}\right)$
${0.04999999964}$ (7)
> $\mathrm{ImpliedRate}\left(\mathrm{compound3},"January 02, 2005","January 02, 2006",\mathrm{Monthly}\right)$
${0.05010431113}$ (8)
Compatibility
• The Finance[CompoundFactor] command was introduced in Maple 15.
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# UNIT TEST ON PROPORTIONAL REASONING
## Presentation on theme: "UNIT TEST ON PROPORTIONAL REASONING"— Presentation transcript:
UNIT TEST ON PROPORTIONAL REASONING
VOCABULARY LIST UNIT TEST ON PROPORTIONAL REASONING
RATIO A COMPARISON OF 2 NUMBERS OFTEN WRITTEN IN FRACTION FORM
WHAT IS THE RATIO OF GIRLS TO BOYS IN THE CLASSROOM?
RATE A COMPARISON OF 2 DIFFERENT KINDS OF UNITS (MILES PER HOUR)
WRITE THE TIME PER CLASS PERIOD AS A RATE
RATE OF CHANGE DESCRIBES HOW ONE QUANTITY CHANGES IN RELATION TO ANOTHER CAN EASILY BE SEEN BY THE CHANGES ON A GRAPH
SLOPE RATE OF CHANGE BETWEEN 2 POINTS ON A LINE (CHANGE IN Y / CHANGE IN X)
PROPORTION AN EQUATION THAT SHOWS 2 EQUIVALENT RATIOS
IF THERE WERE 50 BOYS IN THIS CLASS, HOW MANY GIRLS WOULD THERE BE? (USE THE RATIO FROM THE FIRST SLIDE)
DIRECTLY PROPORTIONAL
HAVING A CONSTANT RATIO PIZZA HUT IS OFFERING PIZZAS FOR \$ 10 EACH (ANY SIZE, TOPPING, CRUST). IF YOU ORDER 4 PIZZAS, HOW MUCH WILL IT COST? IS THE RELATIONSHIP BETWEEN NUMBER OF PIZZAS AND TOTAL PRICE DIRECTLY PROPORTIONAL?
NONPROPORTIONAL NO CONSTANT RATIO BETWEEN QUANTITIES
NUMBER OF ITEMS ORDERED AT AN ONLINE STORE TOTAL AMOUNT PAID 10 \$49.95 7 \$14.87 4 \$24.95 15 \$ 0.89
INVERSELY PROPORTIONAL
As one quantity becomes smaller, the other becomes larger. An example is the relationship between the speed and time it takes to travel a fixed distance. If you drive 60 mph, you can drive 60 miles in 1 hour. If you drive 30 mph, it will take you 2 hours to drive the same 60 miles. Speed in mph Time in hours /3 1 Inversely proportional relationships have a constant of proportionality. It can be found from a combination of the speed and time that works for all pairs of speed and time. What is the constant of proportionality for the above relationship? How does this relate to the graph of the data? How long will it take you to drive 60 miles if you drive at 2 mph? 25 mph? 65 mph? How fast must you drive to cover the 60 miles in 5 hours? 3 hours?
SCALE FACTOR RATIO OF THE LENGTHS OF 2 CORRESPONDING SIDES OF 2 SIMILAR POLYGONS 6.25 5 8 10
RATIO OF AREAS = SCALE FACTOR SQUARED (TIMES ITSELF)
RATIO OF VOLUMES = SCALE FACTOR CUBED (TIMES ITSELF TWICE) SCALE FACTOR = 4 RATIO OF AREAS = SCALE FACTOR = 3/4 RATIO OF VOLUMES =
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# 445213
## 445,213 is an odd composite number composed of two prime numbers multiplied together.
What does the number 445213 look like?
This visualization shows the relationship between its 2 prime factors (large circles) and 4 divisors.
445213 is an odd composite number. It is composed of two distinct prime numbers multiplied together. It has a total of four divisors.
## Prime factorization of 445213:
### 17 × 26189
See below for interesting mathematical facts about the number 445213 from the Numbermatics database.
### Names of 445213
• Cardinal: 445213 can be written as Four hundred forty-five thousand, two hundred thirteen.
### Scientific notation
• Scientific notation: 4.45213 × 105
### Factors of 445213
• Number of distinct prime factors ω(n): 2
• Total number of prime factors Ω(n): 2
• Sum of prime factors: 26206
### Divisors of 445213
• Number of divisors d(n): 4
• Complete list of divisors:
• Sum of all divisors σ(n): 471420
• Sum of proper divisors (its aliquot sum) s(n): 26207
• 445213 is a deficient number, because the sum of its proper divisors (26207) is less than itself. Its deficiency is 419006
### Bases of 445213
• Binary: 11011001011000111012
• Base-36: 9JJ1
### Squares and roots of 445213
• 445213 squared (4452132) is 198214615369
• 445213 cubed (4452133) is 88247723552278597
• The square root of 445213 is 667.2428343565
• The cube root of 445213 is 76.3582463299
### Scales and comparisons
How big is 445213?
• 445,213 seconds is equal to 5 days, 3 hours, 40 minutes, 13 seconds.
• To count from 1 to 445,213 would take you about five days.
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)
• A cube with a volume of 445213 cubic inches would be around 6.4 feet tall.
### Recreational maths with 445213
• 445213 backwards is 312544
• The number of decimal digits it has is: 6
• The sum of 445213's digits is 19
• More coming soon!
HTML: To link to this page, just copy and paste the link below into your blog, web page or email.
BBCODE: To link to this page in a forum post or comment box, just copy and paste the link code below:
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# INR22.93 Total Cost of Fuel from Hyderabad to Pune, Connected by Kalaburagi
Your trip to Pune will consume a total of 9.17 gallons of fuel.
Trip start from Hyderabad and continues through Kalaburagi. Trip ends at Pune.
• 366.8 Miles (Trip Total)
• Route 1 (131.8 mi) Hyderabad » Kalaburagi
Fuel Cost INR8.24
Fuel Consumption 3.30 gallons
• Route 2 (235 mi) Kalaburagi » Pune
Fuel Cost INR14.69
Fuel Consumption 5.88 gallons
The map above shows you the route which was used to calculate fuel cost and consumption.
### Fuel Calculations Summary
Fuel calculations start from Hyderabad, Telangana, India and end at Pune, Maharashtra, India.
Route goes through Kalaburagi, Karnataka, India.
Fuel is costing you INR2.50 per gallon and your vehicle is consuming 40 MPG. The formula can be changed here.
The driving distance from Hyderabad to Kalaburagi to Pune plays a major role in the cost of your trip due to the amount of fuel that is being consumed. If you need to analyze the details of the distance for this trip, you may do so by viewing the distance from Hyderabad to Kalaburagi to Pune.
Or maybe you'd like to see why certain roads were chosen for the route. You can do so by zooming in on the map and choosing different views. Take a look now by viewing the road map from Hyderabad to Kalaburagi to Pune.
Of course, what good is it knowing the cost of the trip and seeing how to get there if you don't have exact directions? Well it is possible to get exact driving directions from Hyderabad to Kalaburagi to Pune.
Did you also know that how elevated the land is can have an impact on fuel consumption and cost? Well, if areas on the way to Pune are highly elevated, your vehicle may have to consume more gas because the engine would need to work harder to make it up there. In some cases, certain vehicles may not even be able to climb up the land. To find out, see route elevation from Hyderabad to Kalaburagi to Pune.
Travel time is of the essence when it comes to traveling which is why calculating the travel time is of the utmost importance. See the travel time from Hyderabad to Kalaburagi to Pune.
Speaking of travel time, a flight to Pune takes up a lot less. How much less? Flight time from Hyderabad to Kalaburagi to Pune.
Cost is of course why we are here... so is it worth flying? Well this depends on how far your trip is. Planes get to where they need to go faster due to the speed and shorter distance that they travel. They travel shorter distances due to their ability to fly straight to their destination rather than having to worry about roads and obstacles that are in a motor vehicle's way. You can see for yourself the flight route on a map by viewing the flight distance from Hyderabad to Kalaburagi to Pune.
*The cost above should be taken as an ESTIMATE due to factors which affect fuel consumption and cost of fuel.
Recent Fuel Calculations for Hyderabad IN:
Fuel Cost from Hyderabad to Hanamkonda
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HW7E_SaraPoet_PSYCH354B01
# HW7E_SaraPoet_PSYCH354B01 - PSYC 354 HOMEWORK 7 Confidence...
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PSYC 354 H OMEWORK 7 Confidence Intervals, Effect Size, and Statistical Power When submitting this file, be sure the filename includes your full name, course and section. Example: HW7_JohnDoe_354B01 Be sure you have reviewed this module/week’s lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Part I: Concepts Questions 1–8: Answer the questions in the spaces provided. Part I: Questions 1a–1e Fill in the highlighted blanks with the best word or words. 1-a) The confidence interval is centered around the __mean___ of the sample. 1-b) Cohen‘s d measures the difference between means in terms of __standard deviation, not standard error__ . 1-c) According to Cohen‘s conventions, a d value of __appropriate measure of effect size for a z statistic___ indicates a large effect. 1-d) A study that calculates the mean effect size from the individual effect sizes of many studies is called a(n) _meta-analysis___ . 1-e) Statistical power refers to the probability of successfully rejecting the _null hypothesis. Part I: Questions 2–5 End-of-chapter problems: Complete the following problems. If applicable, remember to show work in your homework document to receive partial Page 1 of 8
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PSYC 354 credit. 2) List five factors that affect statistical power. For each, indicate how a researcher can leverage/manipulate that factor to increase power in a study.
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# 2.3 Estimations, equations and variables (algebraic equations)
Page 1 / 1
## Memorandum
14. (a) 100
(b) 12
(c) 124
(d) 8
15. (a) 10 99 75 5
(c)
______ 8 ______ 21 39 ______ 74 ______
16.2 (a) 5 х + 7 = 22
(b) 8 х - 10 = 46
(c) 5 + 9 х = 59
(d) х - 13 = 6
16.3 (a) 21
(b) 17
(c) 34
18 (a) 72 (j) 30
(b) 12 (k) 5
(c) 7 (l) 57
(d) 141 000 (m) 9
1. 900 (n) 9 987
2. 47 (o) 125
(g) 135
(h) 336
(i) 7
20. (a) х >10
(b) y <2 000
(c) ( c +8)>6
(d) y <50
(e) k – ( k ÷ 2)<20
## Activity: estimations, equations and variables (algebraic equations) [lo 1.7.2, lo 1.9.1, lo 1.10, lo 2.5]
14. Now replace the letters with the correct numbers in the following flow diagram:
15. Puzzles!
a) Can you solve the following?
I am thinking of a particular number. When I multiply this number by 7, then subtract 6 and divide the answer by 8, the quotient is 8. What is the number that I have in mind?________________________________________________________
I am starting with 9. When I multiply this by 12, than add 2 and subtract 11, the answer is_____________________________________________________________
b) We can compile a table that will help us with problems like these.
Number 9 7 5 Number × 12 + 2 – 11 99 75 51
c) We could replace the word "number" with any letter of the alphabet. Can you fill in the missing numbers in the following table?
k 6 ________ 13 _________ (k × 5) + 9 49 114
16.1 Did you know?
The statement (k x 5) + 9 = 49 is referred to as an algebraic equation. “Algebra” is the “study of number sentences”.
16.2 Write the algebraic equation for the following:
a) A particular number x 5 + 7 = 22
____________________________________________________________________
b) 8 x a number – 10 = 46 ______________________________________
c) 5 + (9 x a number) = 59 _______________________________________
d) When 13 is subtracted from a bigger number the difference is 6.
_____________________________________________________________________
16.3 Solve the following equations: (You may use your pocket calculator).
a) 49 x a – 29 = 1 000
_____________________________________________________________________
b) (b + 15) x 6 = 192
_____________________________________________________________________
c) 16 x c – 15 = 529
_____________________________________________________________________
17. Did you know?
The letters that are used in place of numbers are called variables.
18. Let's first see how you do in your next mental arithmetic test.
a) 9 x 8 = ___________________________
b) ___________________________ x 4 = 48
c) 4 x ___________________________ = 28
d) 6 x 235 x 100 = ______________________
e) 25 x 9 x 4 = _________________________
f) 16 + 17 + 14 = ______________________
g) 104 + 15 + 16 = _____________________
h) Triple: 112: = _________________________
i) 42 ÷ 6 = ___________________________
j) ___________________________ ÷ 6 = 5
k) 35 ÷ ___________________________ = 7
l) (7 x 3) + (4 x 9) =_______________________
m) 4 x 9 + ___________________________ = 45
n) 10 000 – 13 = ___________________________
o) 5 to the power of 3 = _______________________
15
19. Did you know?
When we use>and<-signs in numbers sentences, e.g. when we
want to say that a number divided by 4 is smaller than 5, we write
it like this:
y ÷ 4<5
If we, for example, wished to say that a number multiplied by 5 is greater than 16, we would write it like this:
b x 5>16
Number sentences like these, which do not have the = sign, are called
inequalities.
20. Write the following word sentences as inequalities:
a) The number of sweets that I have is more than 10.
_____________________________________________________________________
b) The number of learners in our school is greater than 2 000.
_____________________________________________________________________
c) A number increased by 8, is greater than 6.
_____________________________________________________________________
d) There are less than 50 learners in our class.
_____________________________________________________________________
e) If I give away half of my marbles, I shall have fewer than 20.
_____________________________________________________________________
## Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:
1.7.2: multiple operations with integers;
1.7.7: exponents;
1.10: uses a range of strategies to check solutions and judges the reasonableness of solutions.
Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Assessment Standard 2.1: We know this when the learner solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x - 8 = 4).
Assessment Standard 2.1: We know this when the learner investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns;
Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:
2.3.2: flow diagrams;
2.3.3: tables;
Assessment Standard 2.5: We know this when the learner solves or completes number sentences by inspection or by trial-and-improvement, checking the solutions by substitution (e.g. 2 x - 8 = 4).
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
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Berger describes sociologists as concerned with
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https://www.physicsforums.com/threads/symmetrisation-of-wave-function-for-fermions.912818/
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# A Symmetrisation of wave function for fermions
1. Apr 27, 2017
### djelovin
The wave function for fermions has to be anti-symmetric with respect to exchange of positions of electrons, but what if it depends on wave vector as well. Does they have to be exchanged as well, in other words, for two-electron system what is correct
Ψ(r1,k1,r2,k2) = - Ψ(r2,k1,r1,k2)
or
Ψ(r1,k1,r2,k2) = - Ψ(r2,k2,r1,k1)
2. Apr 27, 2017
### Orodruin
Staff Emeritus
The wave vector and the position are just different representations of the same Hilbert space. You can use either to represent your state but not both at the same time.
That being said, it is the overall state that should be antisymmetric under the exchange of the electrons. If you have an additional degree of freedom that the state depends on (spin comes to mind) then you need to make the full state antisymmetric. If the state in the additional degree of freedom is already antisymmetric your spatial wavefunction will be symmetric. Positronium in the spin-0 state comes to mind.
3. Apr 27, 2017
### djelovin
Thanx for quick replay,
That somewhat clarifies my problem.
However I have particles in continuum, in the presence of some potential, that are described by Coulomb (Coulomb-like to be more precise) wave function that does depend on both, wave vector and position at the same time.
https://en.wikipedia.org/wiki/Coulomb_wave_function
The system is in singlet state, so spin related part can be taken out.
Last edited: Apr 27, 2017
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# Area 1/2=Absinc
### Area 1/2=Absinc
Area 1/2=absinC * (Obtuse Acute) Area formula: Where b = base length and h = height. When you have two sides and their included angle, the law of sine can be used in finding the area of the oblique triangle. For the base, we use one of the sides – lets say we have base c For the height draw an perpendicular line from C to the base line c. * For the acute case an extended base line can be made to show this altitude, as h will touch the base outside the triangle.
In the obtuse triangle do we now have two right triangles and find h by taking the sine: Sin = opp/hyp | | | | Both is now sat equal to h and can be substituted in for the height in the originally triangle formula. Eq. b sinA = h Base: c Area = (base)(height) Area = (base)(b SinA) Area= (c)(b SinA) As it has no influence in which order the base and the opposite value comes, they will be arranged alphabetically. | | | | * Area = bc SinA * When the base = c and the height = (a sin B): When the base = c and the height = (b sin A): If eq. were used as a base, the height would equal (a sin C): + Example + label ABC A= 65 degrees b= 5 a= 7 c = 8 Area= . 5 (b)(h) To find the height take the Sin (opposite/hypp) then we’ll have h/b b= 5 Sin (A) = (h/b) = = bSin(A) = h Sin(65) = (h/5) == 5Sin(65) = h In order not to handle too many numbers we can substitute this into the area equation * * Area = ? (b)(h) * Area = ? (c)(bSinA) – Usually arranged alphabetically (bcSinA) * * Then substitute the values into this new equation * * Area = 1/2 (8)(5Sin(65)) * Area = 16. 53657358980207 * ? 16. 54 cm2 * * *
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https://www.airmilescalculator.com/distance/phl-to-czm/
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# How far is Cozumel from Philadelphia, PA?
The distance between Philadelphia (Philadelphia International Airport) and Cozumel (Cozumel International Airport) is 1502 miles / 2417 kilometers / 1305 nautical miles.
The driving distance from Philadelphia (PHL) to Cozumel (CZM) is 3293 miles / 5299 kilometers, and travel time by car is about 68 hours 14 minutes.
1502
Miles
2417
Kilometers
1305
Nautical miles
3 h 20 min
180 kg
## Distance from Philadelphia to Cozumel
There are several ways to calculate the distance from Philadelphia to Cozumel. Here are two standard methods:
Vincenty's formula (applied above)
• 1501.860 miles
• 2417.009 kilometers
• 1305.081 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet.
Haversine formula
• 1504.801 miles
• 2421.743 kilometers
• 1307.637 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## How long does it take to fly from Philadelphia to Cozumel?
The estimated flight time from Philadelphia International Airport to Cozumel International Airport is 3 hours and 20 minutes.
## Flight carbon footprint between Philadelphia International Airport (PHL) and Cozumel International Airport (CZM)
On average, flying from Philadelphia to Cozumel generates about 180 kg of CO2 per passenger, and 180 kilograms equals 396 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Philadelphia to Cozumel
See the map of the shortest flight path between Philadelphia International Airport (PHL) and Cozumel International Airport (CZM).
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http://www.reddit.com/r/askscience/comments/2b00hz/why_does_temperature_of_air_not_increase_when/
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[–]Quark/Gluon Jets | Hadronic Calorimeters 7 points8 points (4 children)
sorry, this has been archived and can no longer be voted on
It does, but the temperature increase depends on how you increase the pressure. Also you're missing one key component, the ideal gas law is as follows:
PV = nRT
n = moles of gas (Not Constant!)
When your pumping your bike tire up you're increasing the moles or amount of air in the tire. That's where the pressure is coming from, you could get the same pressure out without adding more air, but you'd have to heat the system, or reduce the volume.
[–][S] 2 points3 points (1 child)
sorry, this has been archived and can no longer be voted on
thank you
[–]Nuclear Magnetic Resonance 0 points1 point (0 children)
sorry, this has been archived and can no longer be voted on
You might also be interested in the Wikipedia article on adiabatic processes.
[–] 2 points3 points (0 children)
sorry, this has been archived and can no longer be voted on
I'm not sure if this is covered in some of the previous answers (and apologies if it is), but if you are holding your finger over the pump outlet nozzle, the other possibility is that you are compensating for the increase in pressure by a reduction in volume. As you push down the plunger, the volume inside gets reduced by roughly the ratio of the pressure increase. Thus the temperature increase is probably minimal.
pV = nRT; if P increases by 4x, you are achieving this by reducing V by ~ 4x. So the impact on T is minimal.
[–] 1 point2 points (0 children)
sorry, this has been archived and can no longer be voted on
A third potential answer is that the air might have gained a fair amount of thermal energy but isn't doing a good job of conducting it to you. Air is known to be a fantastically good insulator to prevent heat transfer.
By touching the metal you can only get the heat from the nearest bits of the air in the tube, just the parts touching that metal. To get the rest to conduct out would take a long time.
So that's a third good reason it doesn't work like you expect.
[–]Physical Organic Chemistry | Reactive Intermediates 0 points1 point (0 children)
sorry, this has been archived and can no longer be voted on
it does, a practical application is a diesel engine, the air is compressed in the cylinder to generate enough heat to ignite the diesel fuel once the fuel is introduced, no spark needed
[–] 0 points1 point (4 children)
sorry, this has been archived and can no longer be voted on
The air isn't obligated to remain hot after you compress it. In the case of your finger and the bike pump, only a very small area of air and skin were in contact. There's a lot of metal and/or plastic in the nozzle of your pump that acts as a heat sink for the tiny volume of air it holds. The rest of your finger, and active heat transfer by your circulatory system, take heat away from the small patch of skin. You're not going from atmospheric to 60 psi in a single quick pump either. The hot air is losing heat the whole time you're pumping.
/u/AsAChemicalEngineer makes a good point about n changing during the pumping process - even after the pump has fully cooled, it will still be at a higher pressure than it started if you haven't let any air out. However, its final pressure will be lower than when it had that much air in it and was also hot. The difference between the maximum and final pressures would depend on how fast you pumped, and how quickly the pump lost heat to its surroundings.
[–]Quark/Gluon Jets | Hadronic Calorimeters -1 points0 points (3 children)
sorry, this has been archived and can no longer be voted on
A bike pump is a pretty complicated tool. Each individual pump occurs though a valve/spring which is only open when you "pump" down. Otherwise it remains closed, otherwise air floods back into your bike pump. If you draw the PV diagram for it, it's a very interesting sawtooth pattern going up.
When the valve is open and the volume is reduced, there is an increase in temperature like you said, but the temperature change isn't all that much. Most of the pressure comes from the amount of gas and not the volume compression. Now an automatic pump will significantly heat the air, your final pump pressure might very well be 5%-10% lower when you come back later.
I'm also completely ignoring heating from friction, but it's actually pretty mind blowing how complicated pump thermo is.
[–] 0 points1 point (2 children)
sorry, this has been archived and can no longer be voted on
It's not trivially the case that hand pumps don't get hot - I have used some that get hot to the touch, and others that don't. It's not helpful to just assume temperature change is negligible when the point of the question is to figure out why the change might be small.
How hot the air gets depends not just on the total volume change and friction involved, but the rates at which energy enters and leaves the system as work and heat. It's possible to pump so slowly that it is an effectively isothermal process, but it's also possible to pump fast enough that the pump becomes hot.
[–]Quark/Gluon Jets | Hadronic Calorimeters 0 points1 point (1 child)
sorry, this has been archived and can no longer be voted on
I think I'm explaining myself poorly. The point I'm trying to make is that the majority of the pressure you read on the meter of a well designed pump comes from mass transfer and not compressive heating.
[–] 0 points1 point (0 children)
sorry, this has been archived and can no longer be voted on
Oh, I agree with that.
[–]Chemical Engineering 0 points1 point (0 children)
sorry, this has been archived and can no longer be voted on
The joule-thompson (http://en.m.wikipedia.org/wiki/Joule%E2%80%93Thomson_effect) effect will play a role in the outlet temperature of the gas. Gases are generally cooled by the effect.
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# Quantization by cohomology
Ok, so I have heard some cool stuff here and there about how to Quantize Yang-Mills via cohomology, can anyone refer any texts in the literature that have shed some light on this, I mean I have some knowledge as to the basic heuristics. I know this is a really trivial question, but again I am a not very experienced yet, can someone sketch the basic technique,. ..
-
(The following is likely not the answer you are looking for, but it is an answer to what you actually ask.)
The case can be made that all of quantization is via cohomology, namely that quantization is fundamentally pull-push in some generalized cohomology theory, hence is index theory.
For geometric quantization in mechanics this insight is usually attributed to Bott: geometric quantization is really push-forward of the pre-quantum data in complex K-theory, see here on the nLab for how this works and see at
for more references. The basics of this insight are old, but still not very widely appreciated.
One can further conceptualize this and observe that the mechanical system encoded by some Poisson manifold is the boundary field theory of the corresponding non-perturbative 2d Poisson-Chern-Simons theory (this is discussed here) and that it is the natural "holographic" quantization of the boundary of that 2d QFT which is given by push-forward in K-theory. This is spelled out fairly comprehensively in
One can then ask how to quantize not just mechanics (1-dimensional field theory) but also higher dimension field theory cohomologically. Some comments on how to quantize 2-dimensional field theory by pull-push in eliptic cohomology/tmf are at the end of the above thesis, but much less is known here.
The basic mechanism of the cohomological quantization discussed by Nuiten is remarkably "fundamental". In a note I am writing
it is observed that at the heart of it cohomological quantization is a fundamental operation in Grothendieck's "yoga of six functors". This is, as discussed there, essentially the cohomological integration mechanism that also appears in section 4.1 of the recent
To feel one's way as to the cohomological quantization of higher dimensional field theories, there is for instance the article
• Daniel S. Freed, Michael J. Hopkins, Constantin Teleman, Consistent Orientation of Moduli Spaces (arXiv:0711.1909)
which discusses quantization of something like a simplified version of Chern-Simons theory via pull-push in complex K-theory. By the close relation of Chern-Simons theory to Yang-Mills theory, you may imagine this getting a tad closer to the remote goal of quantization of Yang-Mills theory via pull-push in generalized cohomology.
-
John Baez's introductory lectures can be found at http://math.ucr.edu/home/baez/qg-fall2006/qg-fall2006.html
-
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Definition and General Form of Linear Equation
The general form of linear equation is
ax + by + c = 0
Write 2x + 3y = 20 in general form
2x + 3y = 20
2x + 3y − 20 = 0
Comparing with ax + by + c = 0
a = 2, b = 3, c = −20
Write 2x = y as an equation in two variable
Get live Maths 1-on-1 Classs - Class 6 to 12
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# X/3=Y/2 ; 2X/3-Y/2=2
1
by Papa123
2016-02-02T20:22:00+05:30
X/3=y/2
x=3y/2---(1)
2x/3-y/2 = 2
2(3y/2)/3-y/2 = 2
3y/3-y/2 = 2
(6y-3y)/6 = 2
3y=12
y = 4-----(2)
Substituting (2) in (1) ,
x = 3(4)/2 = 6.
Therefore,x=6,y=4
Ok
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## Narrow Search
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Now showing results 1-10 of 74
# Bringing Ocean Sciences & Engineering Practices to the Classroom
Emphasizing the synergies between science and engineering, these video clips highlight the research of professional ocean scientists and engineers in various disciplines. The clips are accompanied by additional relevant content including images,... (View More)
# How to Calculate Sea Ice Changes
This set of three videos illustrates how math is used in satellite data analysis. NASA climate scientist Claire Parkinson explains how the Arctic and Antarctic sea ice covers are measured from satellite data and how math is used to determine trends... (View More)
Audience: Middle school, High school, Higher education
Materials Cost: Free
# Cloud Droplets and Rain Drops
In these math problems, students will examine the characteristics of water droplets in clouds.
Keywords: Clouds; Raindrops
Audience: Middle school
Materials Cost: Free
# Building for Hurricanes: Engineering Design Challenge
This activity is a short engineering design challenge to be completed by individual students or small teams. A real-world problem is presented, designing buildings for hurricane-prone areas, but in a simulated way that works in a classroom, after... (View More)
# Working with Rainfall Rates and Water Volume
In this problem set, students learn about rainfall rates and how to convert them into the volume of water that falls.
Audience: High school
Materials Cost: Free
# Exploring the Lunar Surface
The lessons in this book focus on scale and proportion as mathematical topics, using the 5E instructional cycle. Students explore lunar images, and a number of hands-on activities are also provided to allow students to create and explore... (View More)
Keywords: Lunar images; Craters
Audience: Elementary school
# Estimating Planar Areas Using Analogue Methods
This math problem determines the areas of simple and complex planar figures using measurement of mass and proportional constructs. Materials are inexpensive or easily found (poster board, scissors, ruler, sharp pencil, right angle), but also... (View More)
# Remote Sensing Math
This collection of 103 individual sets of math problems derives from images and data generated by NASA remote sensing technology. Whether used as a challenge activity, enrichment activity and/or a formative assessment, the problems allow students to... (View More)
Audience: Middle school, High school
Materials Cost: Free
# Carbon Production in the US 2002-39
In this problem set, learners will analyze an image of carbon dioxide emissions in the continental US in a given year to answer a series of questions. Answer key is provided. This is part of Earth Math: A Brief Mathematical Guide to Earth Science... (View More)
Audience: Middle school
Materials Cost: Free
# Studying Ocean Plankton from Space
In this problem set, learners will use an image of satellite-acquired ocean color data to answer a series of questions about the concentration of phytoplankton in certain areas. Answer key is provided. this is part of Earth Math: A Brief... (View More)
Audience: Middle school
Materials Cost: Free
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Daniel Schaeffler
President
Tensile Testing—Part 2: Terminology
June 1, 2020
All materials possess physical and mechanical properties. Measurement of physical properties occurs without changing the material itself, and includes density, mass, melting and boiling points, and electrical and thermal conductivity. These remain constant under the same composition, temperature and pressure.
Mechanical properties characterize how a material responds under an applied load, and include strength, ductility, hardness, wear resistance, impact resistance and fatigue. Mechanical properties quantify a material’s functionality limits, helping to determine the expected performance or service life of a manufactured component.
The type of test used to evaluate mechanical properties depends on the loading conditions we are attempting to replicate. A tensile test assesses how a material reacts under tensile loads, and can determine many of the parameters important for characterizing a material’s formability.
Most tests prescribe use of a standard sample shape, and for tensile testing we use a test piece shaped like a dogbone. Last month, we described dogbone test samples (www.metalformingmagazine.com/article/?/quality-control/material-testing/tensile-testing-part-1-3a-equipment-2c-samples-and-procedure), and the equipment and procedures used for tensile testing. Here we’ll provide some standard terms and definitions related to tensile testing.
Force and Extension
A tensile test involves gripping the dogbone sample at each end and pulling it apart. We then record the pulling force and associated extension of the sample in this destructive test at regular time increments, until the sample fractures.
In English units, force is measured in lb., and the sample’s cross-section–determined by multiplying the actual sheet thickness by the dogbone sample width–in sq. in. Therefore, the English unit for strength is lb./in.2, abbreviated as psi. Most engineered metals have tensile-strength levels in excess of 10,000 psi, leading to a further abbreviation: 1000 psi = 1 ksi. So, 50,000 psi = 50 ksi.
However, most of the world uses the International System of Units (SI), with force measured in N, mass in kg, length in m, and strength in Pa. The tensile strength of most metal alloys exceeds 1 million Pa (or 1 MPa); 1 ksi equals approximately 7 MPa, so 50 ksi = 350 MPa.
Extension represents the increase in length that occurs in a predefined section of the dogbone, known as gauge length. Calculate elongation as the percent increase represented by the extension relative to gauge length. For example, if gauge length before testing is 2 in., and the tensile test results in the distance between the gauge marks increasing to 2.3 in., the 0.3-in. measured extension results in a calculated elongation of 15 percent.
Stress and Strain and Everything Else
We use force and extension to measure stress and strain, displayed graphically on a stress-strain curve (see the accompanying image). Stress changes as a function of the applied strain.
Application of force leads to deflection of the test sample, and of the sheet metal in a stamping press. Permanent deformation must occur in order for an engineered part to take shape, but no permanent deformation occurs upon removal of a sufficiently low applied force. This is known as elastic deformation; the slope of the stress-strain curve in this linear region represents the modulus of elasticity (or Young’s modulus or the elastic modulus). As the modulus increases, so does a material’s rigidity. Alloys with a higher modulus also exhibit less-severe springback at a given strength.
After applying a critical load, the stress-strain response no longer remains linear. And, after load removal and relief of the elastic strains, some permanent deformation remains. At this point, the material has yielded, with this critical load known as yield strength. High-yield-strength products are more difficult to form in a stamping press, as well as deform in an automobile crash.
Increasing the applied load, either during a tensile test or as the press ram approaches bottom dead center, leads to the sheet metal gaining strength, through a process called strain hardening or work hardening. We use the slope of the stress-strain curve in this region to calculate the strain-hardening exponent (n-value). High-n-value metal grades distribute strains more uniformly in the early stages of load application, delaying strain localization and early failure.
As the dogbone sample elongates during the tensile test, its width and thickness decrease. We use the changes in width and thickness to calculate the plastic strain ratio (r-value), also called the Lankford coefficient or plastic-anisotropy ratio. Higher-r-value alloys possess increased resistance to thinning, critical when deep-drawing cups and cylinders.
If the dogbone sample were able to maintain its original cross-sectional area, then work hardening would require ever-increasing loads to pull the sample apart. In reality, the shrinking width and thickness decrease the cross-section as the test progresses. Since strength is load divided by cross-sectional area, at the beginning of the test the increase in work hardening is more significant than the cross-section decrease, which leads to a positive slope in the stress-strain curve. After a critical amount of deformation, the impact of the cross-section decrease takes over, and the calculated strength appears to decrease, resulting in a negative slope in the stress-strain curve.
Ultimate tensile strength (or tensile strength) is the stress at the apex of the stress-strain curve; the strain at this point is called uniform elongation. The name comes from the rectangular profile within the gauge region that exists from the beginning of the test until reaching uniform elongation. Characterization of the post-uniform elongation zone includes a rapidly shrinking cross-section evidenced by local thinning, called a neck. Strains localizing to form a neck indicate a high stress area and a loss of load-carrying ability. Uniform elongation indicates the beginning of necking, which occurs prior to fracture. A local neck prevents the forming of a deeper part profile and serves as a crack-initiation site. Additional loading, including fatigue loading during the life of the part, may cause a neck to progress to fracture.
Total elongation at fracture represents the strain associated with complete separation of the dogbone test sample. The certified material-properties document included with a coil shipment typically includes this value. Instead, stampers should consider evaluating uniform elongation to better characterize formability. And, taking on additional significance in understanding the failure behavior of advanced high-strength steels: the reduction of area measured at the broken faces after the test sample fractures.
Remember that generating tensile-test results occurs with a test coupon pulled lengthwise, which is free to contract in the perpendicular direction. In contrast, the product shape constrains material flow in engineered stampings. MF
Technologies: Materials, Quality Control
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## Search found 342 matches
Fri Jan 08, 2016 3:59 pm UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 10622
### Re: Blue Eyes with Superrationality
I want to expand on SirGabriel's point further. Flewk, what happens in the following scenarios (with superrational islanders etc)? Who leaves, and on what day? 1) There are 5 blue eyed islanders. 2) There are 4 blue eyed islanders and 1 brown eyed islander. 3) You are on an island and see 4 blue eye...
Wed Jan 06, 2016 2:06 pm UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 10622
### Re: Blue Eyes with Superrationality
They will leave the island after one night instead of waiting two nights like I would. If they waited until the second night, then I know for sure that I am blue because the people who see 3 blues would have left on the first night. Ok, given that statement, what would you need to see to leave on n...
Tue Jan 05, 2016 11:25 pm UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 10622
### Re: Blue Eyes with Superrationality
They will leave the island after one night instead of waiting two nights like I would. If they waited until the second night, then I know for sure that I am blue because the people who see 3 blues would have left on the first night. Ok, given that statement, what would you need to see to leave on n...
Fri Dec 11, 2015 5:03 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099
### Re: Describe an Inconsistent System.
Given a system that contains a contradiction; that system can prove anything (is inconsistent). The system of axiomatic mathematics contains contradictions. Therefore the system of axiomatic mathematics is inconsistent. This is where we have problems, as expertly outlined already. Your use of the w...
Mon Dec 07, 2015 1:30 am UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099
### Re: Describe an Inconsistent System.
Part 1. Any proof within an axiomatic system only applies to that axiomatic system. On that we are in agreement. Inconsistent systems tend to be discarded quickly because the ability to prove anything and its inverse isn't very constructive. However, this leaves the nature of inconsistency less exa...
Fri Dec 04, 2015 4:16 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099
### Re: Describe an Inconsistent System.
I get the impression that people think the Principle of Explosion is weaker than it actually is... using the Principle of Explosion on an inconsistent system we can prove anything/everything . Given an inconsistent system we can prove that every subset of that system is self inconsistent. Perhaps y...
Thu Dec 03, 2015 7:26 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099
### Re: Describe an Inconsistent System.
Given an inconsistent system, we know that we can prove that each statement within that system is both true and false (ref: the Principle of Explosion). As such, every statement within an inconsistent system is, itself, inconsistent. There are no degrees of inconsistency. There is no hierarchy of i...
Wed Dec 02, 2015 2:07 pm UTC
Forum: Mathematics
Topic: Describe an Inconsistent System.
Replies: 44
Views: 8099
### Re: Describe an Inconsistent System.
Let us take Cauchy's argument at face value. Cauchy has proven that a given system is consistent despite a superset being inconsistent. At the same time, it has been asserted by Treatid without proof that every subset of an inconsistent system is inconsistent. Fixed that for you. Please justify you...
Fri Nov 20, 2015 3:27 pm UTC
Forum: Movies and TV Shows
Topic: Tonight's South Park...(Merged Scott Tenorman)
Replies: 93
Views: 31834
### Re: South Park
I'm not aware of South Park ever doing a story arc for more than 3 episodes. So we aren't counting the time Kenny stayed dead for an entire season, and they needed to find a new fourth friend? Admittedly, this season's interconnections have been bigger, but I don't remember an episode that season w...
Tue Oct 27, 2015 3:02 pm UTC
Forum: Gaming
Topic: Saints Row IV - Greatest Superhero Game Ever
Replies: 18
Views: 6447
### Re: Saints Row IV - Greatest Superhero Game Ever
I also just started playing through this, after the recommendations from another thread, and it's been a blast so far. I'm concerned the game feels a little short, at least in terms of main story so far, but I'm having a great time running around and shooting things in increasingly ridiculous ways. ...
Sun Sep 27, 2015 3:14 pm UTC
Forum: Logic Puzzles
Topic: Kings on a Chessboard
Replies: 6
Views: 3411
### Re: Kings on a Chessboard
I agree with Jestingrabbit, but only if the kings only care about the spaces they're on. If we add the rules of chess, meaning kings can't move into check, that solution could fail- as soon as white moves into rows 4-5 in columns D-E, black can't legally follow but might have other asymmetric moves....
Fri Sep 18, 2015 2:38 pm UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 26333
### Re: Anti-Gambler's Fallacy
No, I accept that there's more likely explanations after witnessing the events, what I'm saying is that it's irrational to think about them on the universe where it happened by chance. That is, either it happened by chance with probability 1, or it didn't. Suppose I have 5 cards of different colors...
Tue Sep 08, 2015 5:03 am UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 26333
### Re: Anti-Gambler's Fallacy
Vytron, you said it really well, except in the example given you use incorrect probabilities - using photos of hands including 0-10 fingers would leave us with a probability space of 11 outcomes, not 10. Dropping the option of 0 fingers fixes it... For me, whether I continue has little to do with th...
Thu Aug 27, 2015 1:21 am UTC
Forum: Logic Puzzles
Topic: Saving the islanders
Replies: 7
Views: 2481
### Re: Saving the islanders
Questions 1-2: If the second guru on day k points out at least k blue eyed islanders, that does cut off the chain of logic and keeps anyone else from dying. Cradarc is right that information can't "go away", but one can collapse the possibility spaces in a more desirable fashion. A 4-p...
Fri Jul 31, 2015 5:25 am UTC
Forum: Mathematics
Topic: Prove that 25+8*(n!)) is not square
Replies: 10
Views: 3394
### Re: Prove that 25+8*(n!)) is not square
if n>=25 then 25+8*(n!) is always divisible by 25. So if it is a perfect square it has to be the square of a number divisible by 5. (For n<25 we already know there are no squares by previous poster) That's actually true for n>=10. Since 10! Is divisible by 25. More specifically an odd multiple of 5...
Tue Jul 21, 2015 8:37 pm UTC
Forum: Logic Puzzles
Topic: Rethinking Blue Eyes - A Logic Puzzle
Replies: 97
Views: 14973
### Re: Rethinking Blue Eyes - A Logic Puzzle
And that is giving up, since it has been shown no magic voice can exist that would help the prisoners. Oh well. On the contrary, it only shows that there is a risk that they fail with any magic voice. However, if we take the entire text of the original puzzle as additional givens, we know they do n...
Thu Jul 02, 2015 2:00 am UTC
Forum: Mathematics
Topic: How many integers between 100 and 999 with repeated digits
Replies: 5
Views: 4359
### Re: How many integers between 100 and 999 with repeated digi
many thanks! So, while not really another way, you could also just kind of collapse your cases II-IV into one case... New Case 2: How many integers have two repeated digits? 9 · 9 · 1 · 3 C 2 = 243 Even if it's trivial, can you explain me better this passage? There are 9 ways to choose the first di...
Tue Jun 16, 2015 8:42 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853
### Re: My write-up of the "Blue Eyes" solution (SPOILER A
There are no real people who think there could be someone who didn't already know that the guru can see blue eyes, but there are 24 second-level virtual people who do (A's model of B's model of C, etc) - precisely the virtual people who think someone might leave on the first night. For me, the prob...
Mon Jun 15, 2015 9:26 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853
### Re: My write-up of the "Blue Eyes" solution (SPOILER A
Arklarp, in case you missed the link in the OP, http://forums.xkcd.com/viewtopic.php?f=3&t=80149. Please look carefully at the first couple, and possibly #5 if you still aren't happy. If after reading these you still have concerns, see if you can reframe your objections to explain why they aren'...
Fri Jun 12, 2015 7:20 pm UTC
Forum: Gaming
Topic: Too Many Games - the backlog thread
Replies: 12
Views: 3175
### Re: Too Many Games - the backlog thread
A dangerous suggestion. It's difficult to mix in even light games with the monster that is PoE. If you get a little bit distracted because SR4 is so awesome and you don't feel like thinking too hard for a few days, details start to slip. You forget some of the several hundreds of spells and abiliti...
Wed Jun 10, 2015 3:40 am UTC
Forum: Gaming
Topic: Too Many Games - the backlog thread
Replies: 12
Views: 3175
### Re: Too Many Games - the backlog thread
I plan to. Pillars of Eternity still has all of my free time locked down until I finish that.
Tue Jun 09, 2015 2:11 pm UTC
Forum: Gaming
Topic: Too Many Games - the backlog thread
Replies: 12
Views: 3175
### Re: Too Many Games - the backlog thread
Hundreds of games, literally. The most recent additions are Saints Row 4, Sunless Sea, and all of the Total War franchise except for the first Medieval and Shogun games.
And just in case you didn't have this problem yet, the Steam Summer Sale starts in 48 hours or so...
Fri Jun 05, 2015 2:08 am UTC
Forum: Mathematics
Topic: Stubborn bettor
Replies: 99
Views: 12205
### Re: Stubborn bettor
Goahead, it is possible that your theoretical two bettors can both be winners. This can only happen if one of them "wins" and quits, then the other goes on a hot streak afterward. An example of such a sequence would be BBBB (first player quits with 16, second has -4) RRRR (second player ge...
Thu Jun 04, 2015 8:27 pm UTC
Forum: Mathematics
Topic: Stubborn bettor
Replies: 99
Views: 12205
### Re: Stubborn bettor
Using the stubborn method will guaranty you in 98% of the cases to reach 10 dollars with a capital of 490 dollars. You loose only in 2% of the cases. But you lose a lot more when you lose. 98% of the time you win \$10, 2% of the time you lose \$490. The expected value of this game is 0. Actually the ...
Mon May 25, 2015 5:25 am UTC
Topic: 1529: "Bracket"
Replies: 191
Views: 50036
### Re: 1529: "Bracket"
title="I'm staring at the "doctor" section, and I can't help but feel like I've forgotten someone."
I always feel weird getting Dr Zhivago and Dr Moreau backward...
Wed May 13, 2015 5:32 pm UTC
Topic: 1524: "Dimensions"
Replies: 79
Views: 14570
### Re: 1524: "Dimensions"
mattcoz wrote:
Envelope Generator wrote:May I ask you if you've considered all the possibilities that "down" might offer you?
What is "down" in terms of dimensions?
Toward the enemy's gate, of course.
Tue May 05, 2015 9:33 pm UTC
Forum: Mathematics
Topic: A maths joke I don't get
Replies: 8
Views: 9254
### Re: A maths joke I don't get
It's a really lame joke, but I think the answer is probably
Spoiler:
d/dy, as ce^x is not a varying function of y and therefore the partial derivative is 0. The "joke" coming from the fact that d(e^x)/dx is e^x, so e^x is "invincible" to differential operators.
Sun Apr 19, 2015 6:45 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853
### Re: My write-up of the "Blue Eyes" solution (SPOILER A
To prove that it can't be done in less than 100 days, consider it from the other direction. If the blue-eyed people leave on day X, why would they do so? The possibility of 99 blue-eyed people must have been eliminated within the past 24 hours. The guru's statement obviously doesn't do that in that...
Sun Apr 19, 2015 2:28 am UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853
### Re: My write-up of the "Blue Eyes" solution (SPOILER A
Steve - Interesting take, though I think you missed the point when I tried to restate your proposed strategy - if you're allowed to create a strategy that says "go here if A, go there if B", why not take it further? On day one, if you see two islanders with the same eye color, grab their h...
Sat Apr 18, 2015 7:50 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853
### Re: My write-up of the "Blue Eyes" solution (SPOILER A
I would agree with gmal, in that your "go to the dock" is an illegal communication - the islanders don't go to the dock already knowing their eye color, they go because they want to discover it (and depending on the circumstance, they may not). In the case of having a single islander with ...
Tue Mar 03, 2015 7:46 pm UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1036
Views: 404243
### Re: Harry Potter and the Methods of Rationality
post 114/115 speculation: Does Harry have enough time turner mojo left to make the bad things that happened on the way to the graveyard only seemingly bad? The obvious technique would be to relay a message back to Dumbledore, making the mirror "trap" a fake somehow. Another thing that cou...
Tue Feb 10, 2015 7:30 am UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 10706
### Re: How do axioms specify a new system vs continuing an old
Neither A nor B assert that x and !x are true simultaneously (for any statement x). This is where I disagree. I don't think A and B are distinct. Your argument is that A and B are distinct systems. As such, a statement in B has no impact on A. However, we are using A to specify how the axioms of B ...
Tue Feb 10, 2015 2:10 am UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 10706
### Re: How do axioms specify a new system vs continuing an old
We have a number of true and false statements with respect to system 'A'. If we assert that a false statement is true (or vice versa), then that newly true statement is a contradiction of what we have already established. We have created an inconsistency with respect to system 'A'. Now, we take tha...
Sun Feb 08, 2015 3:42 pm UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 10706
### Re: How do axioms specify a new system vs continuing an old
You suggested we could mix true and false statements from A to form a set of axioms. Given that A is the context for interpreting those axioms - mixing true and false statements will lead to a contradiction. This isn't a question of whether the individual statements are true or false. In the contex...
Sat Jan 31, 2015 8:30 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 13903
### Re: Circularity in Formal Languages?
1. Any contradiction in an axiomatic system means that every statement of that system can be contradicted. Such a system is null. 2. A statement only has meaning with respect to a (defined) set of axioms. 3. Axioms are, themselves, statements. 4. Informal languages (and the elements thereof) are no...
Tue Jan 27, 2015 4:41 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 13903
### Re: Circularity in Formal Languages?
Treatid, I'm not sure I understand your entire response there, but I'll take one part that stands out, namely your response to FG saying that ZFC is inconsistent. If you choose to define the empty set in the way that you did, namely as being a set that contains itself, then that axiomatic system whi...
Fri Dec 19, 2014 12:18 am UTC
Forum: Movies and TV Shows
Topic: Primquel Sub Titles
Replies: 10
Views: 3563
### Re: Primquel Sub Titles
The Matrix Rewatchable?
This really is harder than it sounds
Fri Nov 28, 2014 8:43 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853
### Re: My write-up of the "Blue Eyes" solution (SPOILER A
Let's consider the two-person case further, as you state that two people with blue eyes can not deduce their own eye color. Given that this is true, imagine you (a brown-eyed person) standing with those two people. Can they deduce their eye color now? Since you don't know your own eye color, you kno...
Sat Nov 22, 2014 2:18 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 418853
### Re: My write-up of the "Blue Eyes" solution (SPOILER A
Potatoberg - You keep asserting that the desired solution requires unjustifiable, unreasonable, or otherwise "wrong" assumptions. You've previously stated that a perfect logician should not make any assumptions at all, a statement that invalidates many of the popular puzzles on this forum....
Thu Nov 13, 2014 2:13 am UTC
Forum: Movies and TV Shows
Topic: Star Wars: Episode 7: Electric Boogaleven
Replies: 479
Views: 115012
### Re: Star Wars: Episode 7: Electric Boogaleven
It's the only title so far that doesn't refer to a character or a group of them (presumably). A New Hope? Luke is the new hope, surely. Anakin was their only hope, but he turned evil and now they've got a new one. Fixed for you. And I don't have a problem with the new title, mostly because I still ...
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Q. 1 C5.0( 4 Votes )
# Write number like this:Instead of a square of four numbers, take a square of nine numbers and mark only the numbers at the four corners.What is the difference of diagonal products? Explain using algebra.
Consider the green square and consider the four corner elements ( red circles)
Diagonal products: 1× 13 = 13
3× 11 = 33
Difference between diagonal products = 33 - 13 = 20
Now, consider this green square and consider the corner elements (red circles)
Diagonal products: 8× 20 = 160
18× 10 = 180
Difference between diagonal products = 180 – 160 = 20
So, we observe that the difference between diagonal products in the above cases is also coming out to be same and is equal to 20.
Explanation using Algebra,
Let the first number in the square be x, the others can be filled in as below,
Diagonal products: x (x+12) = x2 + 12x
(x+10)(x+2) = x(x+2) + 10(x+2) = (x2 + 2x) + (10x+ 20)
= x2 + 12x + 20
Clearly, we can observe that the difference between diagonal products is always equal to 20.
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# Java Population Projection Calculator
The program below is the answer to Liang's Introduction to Java Programming (9th Edition) Chapter 1 Exercise 1.11.
```/**
*
* @Author: Aghatise Osazuwa
* Website: www.cscprogrammingtutorials.com
*
* Exercise 1.11 - Population Projection
*
*/
import java.util.Scanner;
public class PopulationProjection {
public static void main(String[] args) {
int birth = 7;
int death = 13;
int immigrant = 45;
int currentPopulation = 312032486;
int year = 365;
int yearlyBirths = (((60 * 60 * 24 * year) / birth));
int yearlyDeaths = (((60 * 60 * 24 * year) / death));
int yearlyImmigrants = (((60 * 60 * 24 * year) / immigrant));
int yearlyPopulation = (yearlyBirths + yearlyImmigrants - yearlyDeaths);
System.out.println("Current Year Population = " + currentPopulation);
System.out.println("Next Year's Population = "
+ (currentPopulation + yearlyPopulation));
System.out.println("Next Two Year's Population = "
+ (currentPopulation + (yearlyPopulation * 2)));
System.out.println("Next Three Year's Population = "
+ (currentPopulation + (yearlyPopulation * 3)));
System.out.println("Next Four Year's Population = "
+ (currentPopulation + (yearlyPopulation * 4)));
System.out.println("Next Five Year'ss Population = "
+ (currentPopulation + (yearlyPopulation * 5)));
}
}
```
Click here to see other solutions to Introduction to Java Programming.
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https://dgtal-team.github.io/doc-nightly/geometry_2meshes_2digpoly-curvature-measures-cnc-3d_8cpp-example.html
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DGtal 1.3.beta
geometry/meshes/digpoly-curvature-measures-cnc-3d.cpp
Computation of mean and Gaussian curvatures on a mesh defined by a an implicit shape discretized as a digital surface, using constant or interpolated corrected curvature measures (based on the theory of corrected normal currents). It uses a digital normal vector estimator to improve curvature estimations. Errors with respect to true expected curvatures are also computed.
This first example uses constant per face corrected normal vector field to compute curvatures.
# "Al" vol file
./examples/geometry/meshes/digpoly-curvature-measures-cnc-3d torus 10 0.5 1.0 Const
outputs
Using face-*Constant* Corrected Normal Current
- surface has 2584 surfels.
[SurfaceMesh (OK) #V=2584 #VN=0 #E=5168 #F=2584 #FN=0 E[IF]=4 E[IV]=4 E[IFE]=2]
- CTrivial normal t-ring=3 (discrete)
Expected mean curvatures: min=0.125 max=0.3125
Computed mean curvatures: min=0.118944 max=0.365712
Expected Gaussian curvatures: min=-0.125 max=0.0625
Computed Gaussian curvatures: min=-0.214727 max=0.09246
|H-H_CNC|_oo = 0.0798986
|H-H_CNC|_2 = 0.0274956
|G-G_CNC|_oo = 0.0897268
|G-G_CNC|_2 = 0.0176866
This second example uses vertex-interpolated corrected normal vector field to compute curvatures.
./examples/geometry/meshes/digpoly-curvature-measures-cnc-3d torus 10 0.5 1.0 Interp
outputs
Using vertex-*Interpolated* Corrected Normal Current
- surface has 2584 surfels.
[SurfaceMesh (OK) #V=2584 #VN=0 #E=5168 #F=2584 #FN=0 E[IF]=4 E[IV]=4 E[IFE]=2]
- CTrivial normal t-ring=3 (discrete)
Expected mean curvatures: min=0.125 max=0.3125
Computed mean curvatures: min=0.146652 max=0.33483
Expected Gaussian curvatures: min=-0.125 max=0.0625
Computed Gaussian curvatures: min=-0.1556 max=0.0751507
|H-H_CNC|_oo = 0.0576324
|H-H_CNC|_2 = 0.0201468
|G-G_CNC|_oo = 0.0320427
|G-G_CNC|_2 = 0.00918083
It also produces several OBJ files to display curvature estimation results, example-cnc-H.obj and example-cnc-G.obj as well as the associated MTL file.
Face-constant corrected mean curvature measure, r=1 Face-constant corrected Gaussian curvature measure, r=1 Vertex-interpolated corrected mean curvature measure, r=1 Vertex-interpolated corrected Gaussian curvature measure, r=1
Curvature measures on meshes and digital surfaces
Note
In opposition with Normal Cycle curvature measures, constant or interpolated corrected curvature measures can take into account an external normal vector field to estimate curvatures with better accuracy.
#include <iostream>
#include <fstream>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/geometry/meshes/CorrectedNormalCurrentComputer.h"
#include "DGtal/helpers/Shortcuts.h"
#include "DGtal/helpers/ShortcutsGeometry.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/io/colormaps/QuantifiedColorMap.h"
makeColorMap( double min_value, double max_value )
{
}
void usage( int argc, char* argv[] )
{
using namespace DGtal;
using namespace DGtal::Z3i;
typedef Shortcuts< KSpace > SH;
std::cout << "Usage: " << std::endl
<< "\t" << argv[ 0 ] << " <P> <B> <h> <R> <mode>" << std::endl
<< std::endl
<< "Computation of mean and Gaussian curvatures on an " << std::endl
<< "digitized implicit shape using constant or " << std::endl
<< "interpolated corrected curvature measures (based " << std::endl
<< "on the theory of corrected normal currents)." << std::endl
<< "- builds the surface mesh from polynomial <P>" << std::endl
<< "- <B> defines the digitization space size [-B,B]^3" << std::endl
<< "- <h> is the gridstep digitization" << std::endl
<< "- <R> is the radius of the measuring balls" << std::endl
<< "- <mode> is either Const for constant corrected normal" << std::endl
<< " vector field or Interp for interpolated corrected" << std::endl
<< " normal vector field." << std::endl
<< "It produces several OBJ files to display mean and" << std::endl
<< "Gaussian curvature estimation results: example-cnc-H.obj" << std::endl
<< "and example-cnc-G.obj as well as the associated MTL file." << std::endl;
std::cout << "You may either write your own polynomial as 3*x^2*y-z^2*x*y+1" << std::endl
<<"or use a predefined polynomial in the following list:" << std::endl;
auto L = SH::getPolynomialList();
for ( const auto& p : L )
std::cout << p.first << " : " << p.second << std::endl;
}
int main( int argc, char* argv[] )
{
if ( argc <= 1 )
{
usage( argc, argv );
return 0;
}
using namespace DGtal;
using namespace DGtal::Z3i;
typedef Shortcuts< KSpace > SH;
std::string poly = argv[ 1 ]; // polynomial
const double B = argc > 2 ? atof( argv[ 2 ] ) : 1.0; // max ||_oo bbox
const double h = argc > 3 ? atof( argv[ 3 ] ) : 1.0; // gridstep
const double R = argc > 4 ? atof( argv[ 4 ] ) : 2.0; // radius of measuring ball
std::string mode = argc > 5 ? argv[ 5 ] : "Const"; // either Const or Interp
bool interpolated = mode == "Interp";
if ( interpolated )
std::cout << "Using vertex-*Interpolated* Corrected Normal Current" << std::endl;
else
std::cout << "Using face-*Constant* Corrected Normal Current" << std::endl;
// Read polynomial and build digital surface
auto params = SH::defaultParameters() | SHG::defaultParameters();
params( "t-ring", 3 )( "surfaceTraversal", "Default" );
params( "polynomial", poly )( "gridstep", h );
params( "minAABB", -B )( "maxAABB", B );
params( "offset", 3.0 );
auto shape = SH::makeImplicitShape3D( params );
auto K = SH::getKSpace( params );
auto dshape = SH::makeDigitizedImplicitShape3D( shape, params );
auto bimage = SH::makeBinaryImage( dshape, params );
if ( bimage == nullptr )
{
trace.error() << "Unable to read polynomial <"
<< poly.c_str() << ">" << std::endl;
return 1;
}
auto sembedder = SH::getSCellEmbedder( K );
auto embedder = SH::getCellEmbedder( K );
auto surface = SH::makeDigitalSurface( bimage, K, params );
auto surfels = SH::getSurfelRange( surface, params );
trace.info() << "- surface has " << surfels.size()<< " surfels." << std::endl;
SM smesh;
std::vector< SM::Vertices > faces;
SH::Cell2Index c2i;
auto pointels = SH::getPointelRange( c2i, surface );
auto vertices = SH::RealPoints( pointels.size() );
std::transform( pointels.cbegin(), pointels.cend(), vertices.begin(),
[&] (const SH::Cell& c) { return h * embedder( c ); } );
for ( auto&& surfel : *surface )
{
const auto primal_surfel_vtcs = SH::getPointelRange( K, surfel );
SM::Vertices face;
for ( auto&& primal_vtx : primal_surfel_vtcs )
face.push_back( c2i[ primal_vtx ] );
faces.push_back( face );
}
smesh.init( vertices.cbegin(), vertices.cend(),
faces.cbegin(), faces.cend() );
trace.info() << smesh << std::endl;
auto exp_H = SHG::getMeanCurvatures( shape, K, surfels, params );
auto exp_G = SHG::getGaussianCurvatures( shape, K, surfels, params );
// Builds a CorrectedNormalCurrentComputer object onto the SurfaceMesh object
CNC cnc( smesh );
// Estimates normal vectors using Convolved Trivial Normal estimator
auto face_normals = SHG::getCTrivialNormalVectors( surface, surfels, params );
// Set corrected face normals => Corrected Normal Current with
// constant per face corrected vector field.
smesh.setFaceNormals( face_normals.cbegin(), face_normals.cend() ); // CCNC
// Set corrected vertex normals => Corrected Normal Current with
// smooth linearly interpolated per face corrected vector field.
if ( interpolated ) smesh.computeVertexNormalsFromFaceNormals(); // ICNC
// computes area, mean and Gaussian curvature measures
auto mu0 = cnc.computeMu0();
auto mu1 = cnc.computeMu1();
auto mu2 = cnc.computeMu2();
// estimates mean (H) and Gaussian (G) curvatures by measure normalization.
std::vector< double > H( smesh.nbFaces() );
std::vector< double > G( smesh.nbFaces() );
for ( auto f = 0; f < smesh.nbFaces(); ++f )
{
const auto b = smesh.faceCentroid( f );
const auto area = mu0.measure( b, R, f );
H[ f ] = cnc.meanCurvature ( area, mu1.measure( b, R, f ) );
G[ f ] = cnc.GaussianCurvature( area, mu2.measure( b, R, f ) );
}
auto H_min_max = std::minmax_element( H.cbegin(), H.cend() );
auto G_min_max = std::minmax_element( G.cbegin(), G.cend() );
auto exp_H_min_max = std::minmax_element( exp_H.cbegin(), exp_H.cend() );
auto exp_G_min_max = std::minmax_element( exp_G.cbegin(), exp_G.cend() );
std::cout << "Expected mean curvatures:"
<< " min=" << *exp_H_min_max.first << " max=" << *exp_H_min_max.second
<< std::endl;
std::cout << "Computed mean curvatures:"
<< " min=" << *H_min_max.first << " max=" << *H_min_max.second
<< std::endl;
std::cout << "Expected Gaussian curvatures:"
<< " min=" << *exp_G_min_max.first << " max=" << *exp_G_min_max.second
<< std::endl;
std::cout << "Computed Gaussian curvatures:"
<< " min=" << *G_min_max.first << " max=" << *G_min_max.second
<< std::endl;
const auto error_H = SHG::getScalarsAbsoluteDifference( H, exp_H );
const auto stat_error_H = SHG::getStatistic( error_H );
const auto error_H_l2 = SHG::getScalarsNormL2( H, exp_H );
trace.info() << "|H-H_CNC|_oo = " << stat_error_H.max() << std::endl;
trace.info() << "|H-H_CNC|_2 = " << error_H_l2 << std::endl;
const auto error_G = SHG::getScalarsAbsoluteDifference( G, exp_G );
const auto stat_error_G = SHG::getStatistic( error_G );
const auto error_G_l2 = SHG::getScalarsNormL2( G, exp_G );
trace.info() << "|G-G_CNC|_oo = " << stat_error_G.max() << std::endl;
trace.info() << "|G-G_CNC|_2 = " << error_G_l2 << std::endl;
// Remove normals for better blocky display.
smesh.vertexNormals() = SH::RealVectors();
smesh.faceNormals() = SH::RealVectors();
const double Hmax = std::max( fabs( *exp_H_min_max.first ),
fabs( *exp_H_min_max.second ) );
const double Gmax = std::max( fabs( *exp_G_min_max.first ),
fabs( *exp_G_min_max.second ) );
const auto colormapH = makeQuantifiedColorMap( makeColorMap( -Hmax, Hmax ) );
const auto colormapG = makeQuantifiedColorMap( makeColorMap( -Gmax, Gmax ) );
auto colorsH = SMW::Colors( smesh.nbFaces() );
auto colorsG = SMW::Colors( smesh.nbFaces() );
for ( auto i = 0; i < smesh.nbFaces(); i++ )
{
colorsH[ i ] = colormapH( H[ i ] );
colorsG[ i ] = colormapG( G[ i ] );
}
SMW::writeOBJ( "example-cnc-H", smesh, colorsH );
SMW::writeOBJ( "example-cnc-G", smesh, colorsG );
return 0;
}
max
int max(int a, int b)
Definition: testArithmeticalDSS.cpp:1108
DGtal::Trace::error
std::ostream & error()
DGtal::Color
Structure representing an RGB triple with alpha component.
Definition: Color.h:67
DGtal::trace
Trace trace
Definition: Common.h:154
K
KSpace K
Definition: testCubicalComplex.cpp:62
DGtal::SurfaceMesh
Aim: Represents an embedded mesh as faces and a list of vertices. Vertices may be shared among faces ...
Definition: SurfaceMesh.h:91
DGtal::SurfaceMeshWriter
Aim: An helper class for writing mesh file formats (Waverfront OBJ at this point) and creating a Surf...
Definition: SurfaceMeshWriter.h:64
makeColorMap
DGtal::GradientColorMap< double > makeColorMap(double min_value, double max_value)
[curvature-comparator-Includes]
Definition: curvature-comparator-ii-cnc-3d.cpp:89
DGtal::Shortcuts
Aim: This class is used to simplify shape and surface creation. With it, you can create new shapes an...
Definition: Shortcuts.h:104
DGtal::CorrectedNormalCurrentComputer
Aim: Utility class to compute curvature measures induced by (1) a corrected normal current defined by...
Definition: CorrectedNormalCurrentComputer.h:69
boost::vertices
std::pair< typename graph_traits< DGtal::DigitalSurface< TDigitalSurfaceContainer > >::vertex_iterator, typename graph_traits< DGtal::DigitalSurface< TDigitalSurfaceContainer > >::vertex_iterator > vertices(const DGtal::DigitalSurface< TDigitalSurfaceContainer > &digSurf)
DGtal::Trace::info
std::ostream & info()
Vertices
SMesh::Vertices Vertices
Definition: fullConvexitySphereGeodesics.cpp:118
DGtal
DGtal is the top-level namespace which contains all DGtal functions and types.
DGtal::Z3i
Z3i this namespace gathers the standard of types for 3D imagery.
DGtal::ShortcutsGeometry
Aim: This class is used to simplify shape and surface creation. With it, you can create new shapes an...
Definition: ShortcutsGeometry.h:76
main
int main(int argc, char **argv)
Definition: testArithmeticDSS-benchmark.cpp:147
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Post Go back to editing
Category: Hardware
how to measure power factor when i read the value shows 18218(decimal) the reference meter shows powerfactor of .64 . i get a constant constant by dividing 18218/640 =28 and when i check with .94 pf load it shows .2 error why is this happening
[edited by: emassa at 1:48 PM (GMT -5) on 23 Feb 2023]
Parents
• Did you phase calibrate? Verify phase calibration by reading energy at pf1 and pf 0.5 the energy register should read half the value at pf.5. You can use any pf just scale the expected value in the energy register.
Dave
• i am reading 0x10A register for PF . how is the pf reading is converted into actual reading is there any equation or any other way.
• pf 1 = 0x7FFF= 32767
pf/lsb = 1/32,767= 3.051850947599719e-5 = 2^-15
pf 0x10A = 266 * 3.051850947599719e-5 = 0.0081179235206153 or pf 0
Dave
• thanks for me to helping me
as per above calculation
PF=24891 * 3.0518509475997192297128208258309e-5 = 0.75963621936704
which are the other registers affect the PF(0x10A) readings.
• Phase compensation register PHCALA and PHCALB and WATT and VA gain
Pf uses Active and apparent power so calibrate phase first. Then active power gain and apparent power gain.
Dave
• PF VALUE COMES WITH LARGE VARIATION WHAT IS THE REASON BEHIND THIS ENEGY ACCUMATION ALSO VERY HIGH WHAT WILL BE REASON
• Can you show me some numbers from the ADE7953?
in register codes and your converted numbers
Watt
VA
VAR
PF
And what you expect.
Dave
WATT = 0x11689 [ watt conversion= (0x11689*100)/898] conversion is done for making as integer I doesn't use float value
VA =0xB01A
AVAR =0xB00F
PF =0x7FFF68 [ pf conversion = 0x7FFF68*306/10000 ]
In PF some times I get 1 after conversion sometimes it will be .997
Write_ADE7953(PGAI_REG, 0x03, 1); //0x008 3 gain 8
these are my initialization VRMS IRMS AND WATT ARE correct.
WATT = 0x11689 [ watt conversion= (0x11689*100)/898] conversion is done for making as integer I doesn't use float value
VA =0xB01A
AVAR =0xB00F
PF =0x7FFF68 [ pf conversion = 0x7FFF68*306/10000 ]
In PF some times I get 1 after conversion sometimes it will be .997
Write_ADE7953(PGAI_REG, 0x03, 1); //0x008 3 gain 8
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# The Imperial Cereal Machine – Rude Goldberg Project
Our task for this project was to plan out and create a Rube Goldberg machine. A Rube Goldberg machine is a machine that is designed to perform a simple task in an indirect or super complicated way. Linked in a somewhat domino effect, these machines have many simple devices all triggering each other. A Drawing […]
# Week 17 – Arithmetic Series
What is an Arithmetic series? While building onto last week’s topic I did, arithmetic is in the same field of ideas when it comes to sequences. A sequence that ends on a certain number (not infinite) is an arithmetic series. We use arithmetic series to find the sum of all of the numbers in […]
# Week 16 – Sequences
What are sequences? It is usually a list of numbers but can also be a list of other things. Each of the objects or numbers in the list are called terms, elements, member meaning all the same thing. If the sequence is to go on forever then it is called an infinite sequence. For sequences […]
# Week 15 – Solving Systems
What is a system? In math, a system is a two or more linear equations involving the same set of variables. Meaning each system must have x and y in the equation or what other variables you are using for the equation. One example of a system is this: How to solve a system? There […]
# Wonder Project – Information Fluency Reflection
Information Fluency Reflection What questions did you need to research in order to research your topic? At the start of my project, I tried to think of small questions that I would need to answer before I could get to a conclusion for my topic. First, I thought of what are the differences in conditions […]
# Astronomy Wonder Project
If we were to live on Mars, how would the different conditions affect the human body over time, and would one-day humans be considered a different species? I have always had an interest in the side of astronomy that includes humans and us being able to explore other planets. Which lead me to wonder, how […]
# Week 11 – Finding Distances on a Coordinate Plane
Before we start to find the distances of lines, there are three different types of lines that you can find. The first one is a horizontal line, a horizontal line is a line that is a straight line that goes from left to right. And on a coordinate plane, a horizontal line runs parallel to […]
# Week 10 – Function Notation
What is a function again? It is a special group that is a part of relations. This group only has one output for every input. This means that all functions are relations but not all relations are functions. An example of a function is how each person only has one biological father. So what is […]
# Self Reflection for Science 10 – Biotechnology Project
This is the video our group created:
# Week 9 – Relations and Functions
What is a relation? A “relation” is just a relationship between sets of information. For example; think of all the people in one of your classes, and think of their heights. The pairing of names and heights is a relation. The set of all the starting points (input) is called “the domain” and the set of […]
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This lesson focuses on calculating the areas of rectangles. It is designed to enable adult students to successfully master basic geometry knowledge in order to achieve their High School Equivalency (HSE). Areas to be covered include types of polygons, quadrilaterals, rectangles; calculating areas of rectangle and calculating costs. Students will apply this knowledge to practical areas of their lives such as calculating the costs of purchasing carpets or painting of walls
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Mathematics
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Winston Lawrence
05/05/2016
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In this 25-day module, students work with two- and three-dimensional figures. Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms. The second half of the module turns to extending students understanding of two-dimensional figures. Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths. They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifying the shapes by reasoning about their attributes. This module fills a gap between Grade 4s work with two-dimensional figures and Grade 6s work with volume and area.
Subject:
Geometry
Material Type:
Module
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New York State Education Department
Provider Set:
EngageNY
01/17/2014
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Subject:
Geometry
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Activity/Lab
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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
08/06/2015
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In this activity, learners walk the sides and interior angles of various polygons drawn on the playground. As they do so, learners practice rotating clockwise 180 and 360 degrees. Learners discover there is a pattern to the sum of the interior angles of any polygon.
Subject:
Geometry
Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Exploratorium
Gordon and Betty Moore Foundation
National Science Foundation
The Exploratorium
12/07/2010
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Skills are refined through making pen and ink drawings, watercolor paintings, and sculptures focusing on proportion, value, and scale. Translating words into pictures and pictures into words is investigated through depicting setting, combining shapes for meaning, using color for mood and responding to art. Students also create prints and then explain the printmaking procedure in writing.
\The K-6 lesson handbooks were originally produced for the Lake Washington School District with grants from 4culture and ArtsWA. Encourage your colleagues, other schools, and organizations to use these materials for non-commercial, educational purposes at no cost by downloading their own copy at: http://artsedwashington.org/portfolio-items/alic-2
Subject:
Visual Arts
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Lesson
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Washington ArtsEd
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# Merge two 1D array's into a new 1D array. Trouble appending last index
• August 30th, 2012, 09:46 AM
norske_lab
Merge two 1D array's into a new 1D array. Trouble appending last index
Hello, i am having trouble appending the rest of my original array to my new array.
I am suppose to shuffle two arrays and put the output into a new array.
For instance.
int [] A = {2,3,4,5};
int [] B = {1,5,6,9,123};
A and B are my two arrays that i need to shuffle into array C
So C's output is:
int [] C = {2,1,3,5,4,6,5,9,123}
The problem i encounter is that it doesn't want to append the longer array so my output right now is
int [] C = {2,1,3,5,4,6,5,9,0}
my code is
Code :
``` int [] A = {2,3,4,5}; int [] B = {1,5,6,9,123}; int Lengthmin = (A.length<B.length? A.length:B.length); int[] C= new int [A.length+B.length]; for(int i =0;i<Lengthmin;i++) { C[2*i]=A[i]; C[2*i+1]=B[i]; } //didnt include printing the array```
Thanks in advanced for any help!
• August 30th, 2012, 12:57 PM
Zaphod_b
Re: Merge two 1D array's into a new 1D array. Trouble appending last index
Quote:
Originally Posted by norske_lab
...it doesn't want to ...
It does exactly what you told it to, right? It interleaves elements from the two source arrays into the target array until it gets to the end of the shorter of the source arrays, right?
So...
To use your program as a starting point, you can make a new loop to execute after the first loop. The counter for this new loop can start at the next index of C and will be incremented each time through the loop until all elements of C have been written. Each time it goes through the loop it gets another value from the longer of the source arrays and stores it in the target:
Code :
```Begin Loop If A is shorter, get the value of the next element of B and store in C If B is shorter, get the value of the next element of A and store in C End Loop```
Heck; I'll kick it off:
Code java:
``` for (int i = ???; i < C.length; i++) { C[i] = ??? // Either A[something] or B[something] }```
The only questions are:
1. What is the "next index of C" that this loops starts at?
2. What is the the source array (is it A or is it B?) and what is the index of the source array value that is copied into C[i] each time through the loop?
If you can't figure the answers in your head, or even with pencil and paper (gasp), then put print statements inside your first loop to see what it has done by the time it gets ready for the second loop.
Cheers!
Z
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# NCERT Solutions for Class 9 Maths Chapter 11 Constructions
NCERT solutions for class 9 maths chapter 11 Constructions: The chapter deals with the construction of certain angles and also triangles in certain conditions. In the previous chapters, you learnt to draw an approximate figure while writing the solutions. In this chapter, the scenario is different because the main purpose to introduce this chapter in the curriculum is to develop an approach to create an accurate geometric figure using some hints. CBSE NCERT solutions for class 9 maths chapter 11 Constructions has designed to provide you help in creating those accurate figures. Let's understand the kinds of questions which appear in this particular chapter. For example, you are asked to give a sketch of a roof of a triangular shape with a given perimeter and two base angles. The concepts learnt in this particular chapter can be used in the designing such cases.
CBSE NCERT solutions for class 9 maths chapter 11 Constructions has point by point solutions to every constructional problem. When there is any constructional project to start, then the first step to initiate that project is the planning and drawing. Geometrical constructions have their own line of study. If you want to pursue your career in this domain then the higher study related to this can be civil engineering and architecture. In this chapter, there are 2 exercises having total of 14 questions. Solutions of NCERT for class 9 maths chapter 11 Constructions have an in-depth solution to each and every question present in the practice exercises. For 360 degree help in your school examination preparation, you can use NCERT solutions for other chapters, classes, and subjects.
## Q1 Construct an angle of 90o at the initial point of a given ray and justify the construction.
The steps of construction to follow:
Step 1: Draw a ray OP.
Then, take O as the centre and any radius draw an arc cutting OP at Q.
Step 2: Now, taking Q as the centre and with the same radius as before draw an arc cutting the previous arc at R. Repeat the process with R to cut the previous arc at S.
Step 3: Take R and S as centre draw the arc of radius more than the half of RS and draw two arcs intersecting at A. Then, join OA.
Hence, $\angle POA = 90^{\circ }$.
Justification:
We need to justify, $\angle POA = 90^{\circ }$
So, join OR and OS and RQ. we obtain
By construction OQ = OS = QR.
So, $\triangle ROQ$ is an equilateral triangle. Similarly $\triangle SOR$ is an equilateral triangle.
So, $\angle SOR = 60^{\circ}$
Now, $\angle ROQ = 60^{\circ}$ that means $\angle ROP = 60^{\circ}$.
Then, join AS and AR:
Now, in triangles OSA and ORA:
$SR = SR$ (common)
$AS = AR$ (Radii of same arcs)
$OS = OR$ (radii of the same arcs)
So, $\angle SOA = \angle ROA = \frac{1}{2}\angle SOR$
Therefore, $\angle ROA = 30^{\circ}$
and $\angle POA = \angle ROA+\angle POR = 30^{\circ} +60^{\circ} =90^{\circ}$
Hence, justified.
The steps of construction to follow:
Step 1: Draw a ray OY.
Then, take O as the centre and any radius, mark a point A on the arc ABC.
Step 2: Now, taking A as the centre and the same radius, mark a point B on the arc ABC.
Step 3: Take B as a centre and the same radius, mark a point C on the arc ABC.
Step 4: Now, taking C and B as centre one by one, draw an arc from each centre intersecting each other at a point X.
Step 5: X and O are joined and a ray making an angle $90^{\circ}$ with OY is formed.
Let the arc AC touches OX at E
Step 6: With A and E as centres, 2 arcs are marked intersecting each other at D and the bisector of angle XOY is drawn.
Justification:
By construction we have,
$\angle XOY = 90^{\circ}$
We constructed the bisector of $\angle XOY$ as $\angle DOY$
Thus,
$\angle DOY = \frac{1}{2}\angle XOY = \frac{1}{2}\times90^{\circ} = 45^{\circ}$
Steps to construction to follow:
Step 1: Draw a ray OY.
Step 2: Now, take A as a center and take any radius, then draw an arc AB cutting OY at A.
Step 3: Take A and B as centres, draw 2 arcs are marked intersecting each other at X and hence, the bisector of $30^{\circ}$ is constructed.
Thus, $\angle XOY$ is the required angle.
Steps to construction to follow:
Step 1: Draw a ray OY.
Step 2: Now, take A as a centre and take any radius, then mark a point B on the arc
Step 3: Take B as a centre with the same radius, mark a point C on the arc ABC.
Step 4: Now, taking B and C as centres simultaneously, then draw an arc from each centre intersecting each other at a point X. Then join X and O and a ray making an angle with OY is formed.
Let the arc AC touches OX at E
Step 5: Now, with A and E as centres, mark 2 arcs which intersect each other at D and we obtain the bisector of the angle $XOY$.
Steps to construction to follow:
Step 1: Draw a ray OY.
Step 2: Now, take A as a centre and take any radius, draw an arc AB which cuts OY at A.
Step 3: Take A and B as a centre, then mark 2 arcs which intersect each other at X and Hence, the bisector is constructed of $30^{\circ}$.
Step 4: Now, with A and E as centres, mark 2 arcs which intersect each other at D and we obtain the bisector of the angle $XOY$.
Thus, the angle of $15^{\circ}$ is obtained which is $\angle EOY.$
Steps to construction to follow:
Step 1: Draw a ray OY.
Step 2: Now, taking O as the centre draw an arc ABC.
Step 3: On taking A as a centre, draw two arcs B and C on the arc ABC.
Step 4: Now, taking B and C as centres, arcs are made to intersect at point E and the $\angle EOY = 90^{\circ}$ is constructed.
Step 5: Taking A and C as centres, arcs are made to intersect at D.
Step 6: Now, join OD and hence, $\angle DOY = 75^{\circ}$ is constructed.
Hence, $\angle DOY$ is the required angle.
The steps of construction to be followed:
Step 1: Draw a ray OY.
Step 2: Then, taking O as a centre, draw an arc ABC.
Step 3: Now, with A as a centre, draw two arcs B and C which are made on the arc ABC.
Step 4: Taking B and C as centres simultaneously, arcs are made to intersect at E and $\angle EOY =90^{\circ}$ is constructed.
Step 5: With B and C as centres, arcs are made to intersect at X.
Step 6: Join the OX and we get $\angle XOY =105^{\circ}$ is constructed.
Thus, the angle $XOY$ is $105^{\circ}.$
The steps of construction to be followed:
Step 1: Draw a ray DY.
Step 2: Draw an arc ACD with O as a center.
Step 3: Now, with A as a centre, draw two arcs B and C on the arc ACD.
Step 4: Taking B and C as centres, arcs are made to intersect at E and the angle formed is $\angle EOY = 90^{\circ}$.
Step 5: Take F and D as centres, draw arcs to intersect at point X or the bisector of angle EOD is made.
Step 6: Join OX and the $\angle XOY = 135^{\circ}$ is made.
Hence, the angle required $\angle XOY$ is $135^{\circ}$.
The following steps to make an equilateral triangle:
Step 1: Draw a line segment AB = 4 cm.
Step 2: With A and B as centres, make two arcs in the line segment AB. Mark it as D and E respectively.
Step 3: Now, with D and E as centres, make the two arcs cutting the previous arcs respectively, and forming an angle of $60^{\circ }$ each.
Step 4: Extend the lines of A and B until they intersect each other at point C.
Hence, triangle constructed is ABC which is equilateral.
Now, Justification;
Since the angles constructed are of $60^{\circ }$ each, so the third angle will also be $60^{\circ }$.
$\left [ \because The\ sum\ of\ all\ angles\ of\ triangle = 180^{\circ} \right ]$
## NCERT solutions for class 9 maths chapter 11 Constructions Excercise: 11.2
The steps of construction are as follows:
Step 1: Draw a line segment BC of 7cm length. Taking the help of protractor make an $\angle XBC = 75^{\circ}$.
Step 2: Now, cut a line segment BD having 13 cm on BX which is $(AB+AC).$
Step 3: Now, join CD.
Step 4: Draw a perpendicular bisector of CD to intersect BD at a point A. Join AC. Then ABC is the required triangle
Hence, the required triangle is ABC.
The steps of construction to be followed:
Step 1: Draw a line segment BC = 8cm and make an angle of $45^{\circ}$ at point B i.e., $\angle XBC.$
Step 2: Now, cut the line segment BD = 3.5 cm on ray BX. i.e.$(AB-AC)$.
Step 3: Join CD and draw a perpendicular bisector of CD i.e., PQ.
Step 4: Let the perpendicular bisector of CD intersects BX at point A. Then,
Step 5: Join AC, to get the required triangle $\triangle ABC.$
The steps of construction to be followed:
Step 1: Draw a ray QX and cut off a line segment QR which is equal to 6 cm in length.
Step 2: With an angle of $60^{\circ}$ with QR, construct a ray QY and extend it to form a line YQY'.
Step 3: Now, cut off a line segment QS equal to 2 cm from QY' and join RS.
Y
Y'
Step 4: Draw a perpendicular bisector of RS which intersects QY at a point P.
Step 5: Join PR to get the required triangle $\triangle PQR.$
The steps of construction to be followed:
Step 1: For given $XY+YZ+ZX = 11 cm$, a line segment $PQ =11 cm$ is drawn.
Step 2: At points, P and Q angles of $\angle RPQ = 30^{\circ}$ and $\angle SQP =90^{\circ}$ are constructed respectively.
Step 3: Now, bisects the angle RPQ and SQP. The bisectors of these angles intersect each other at a point X.
Step 4: Construct the perpendicular bisector of PX and QX, name them as TU and WV respectively.
Step 5: Let the bisector TU intersect PQ at Y and bisector WV intersect PQ at Z. Then XY and ZY are joined.
Therefore, $\triangle XYZ$ is the required triangle.
The steps of construction to follow:
Step 1: Draw a ray BX and Cut off a line segment $BC=12cm$ from the ray.
Step 2: Now, construct an angle $\angle XBY = 90^{\circ}$.
Step 3: Cut off a line segment BD of length 18 cm on BY. Then join the CD.
Step 4: Now, construct a perpendicular bisector of CD which intersects BD at A and AC is joined.
Thus, the constructed triangle is ABC.
## NCERT solutions for class 9 maths chapter wise
Chapter No. Chapter Name Chapter 1 NCERT solutions for class 9 maths chapter 1 Number Systems Chapter 2 CBSE NCERT solutions for class 9 maths chapter 2 Polynomials Chapter 3 Solutions of NCERT class 9 maths chapter 3 Coordinate Geometry Chapter 4 NCERT solutions for class 9 maths chapter 4 Linear Equations In Two Variables Chapter 5 CBSE NCERT solutions for class 9 maths chapter 5 Introduction to Euclid's Geometry Chapter 6 Solutions of NCERT class 9 maths chapter 6 Lines And Angles Chapter 7 NCERT solutions for class 9 maths chapter 7 Triangles Chapter 8 CBSE NCERT solutions for class 9 maths chapter 8 Quadrilaterals Chapter 9 Solutions of NCERT class 9 maths chapter 9 Areas of Parallelograms and Triangles Chapter 10 NCERT solutions for class 9 maths chapter 10 Circles Chapter 11 CBSE NCERT solutions for class 9 maths chapter 11 Constructions Chapter 12 Solutions of NCERT class 9 maths chapter 12 Heron’s Formula Chapter 13 NCERT solutions for class 9 maths chapter 13 Surface Area and Volumes Chapter 14 CBSE NCERT solutions for class 9 maths chapter 14 Statistics Chapter 15 Solutions of NCERT class 9 maths chapter 15 Probability
## How to use NCERT solutions for class 9 maths chapter 11 Constructions
• Understand the basic construction of angles using the previous class book.
• Learn the constructional process of triangles and rectangles.
• Go through some solved examples to understand the solutions pattern.
• Apply the concepts learned in the practice exercises.
• If you feel trouble in solving any problem then take the assistance of NCERT solutions for class 9 maths chapter 11 Constructions.
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Question Text A block is being pushed against a wall by a force as shown in the figure. The coefficient of friction is 0.25 . The magnitude of acceleration of the block is : (Take ) Updated On Apr 9, 2023 Topic Laws of motion Subject Physics Class Class 11 Answer Type Text solution:1 Video solution: 3 Upvotes 327 Avg. Video Duration 10 min
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http://www.cyclelicio.us/2009/tuesday-transit-quiz-caltrain-express-limited-and-local-runs/
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# Tuesday Transit Quiz: Caltrain express, limited, and local runs
I think I’ll try to start a “Tuesday Transit Quiz” series here. They’re designed in part to test your knowledge of transit systems — both specifics and in general — and provide some tips that can be helpful to you.
This initial transit quiz should be fairly easy for any regular user of Caltrain. Here’s the scenario:
You’re running late at San Jose Diridon Station and missed Caltrain #323 at 7:45 AM. You need to be at San Francisco 4th & King by 9 AM to make your meeting this morning. You glance at the platform assignment sign as you run down the ramp and see these departure times and trains:
* 7:50 AM # 225
* 7:55 AM # 227
* 8:03 AM # 329
You don’t have the train schedule memorized so you don’t know the San Francisco arrival times for these trains. You’re not familiar with Diridon Station so you don’t know where the train schedules are posted. When you get to the platform you have about 15 seconds to decide if you should jump on the 7:50 train. Which train do you hop on and why?
I’ll post the answer later today as an update to this post. There are two possible good answers, in my opinion. Which train would you pick?
## 4 Comments
1. BikeBoy says:
OK, here's my warped answer, as an infrequent and generally inept CalTrain user:
I'd pick the #329, because my original #323 might have been an express (San Jose to 4th & King in 1:15) and the numbers are the most similar, possibly implying that #329 might also be an express and therefore my best choice. But, this being CalTrain, my perfectly logical answer is almost guaranteed to be wrong 😉
2. BikeBoy says:
OK, here's my warped answer, as an infrequent and generally inept CalTrain user:I'd pick the #329, because my original #323 might have been an express (San Jose to 4th & King in 1:15) and the numbers are the most similar, possibly implying that #329 might also be an express and therefore my best choice. But, this being CalTrain, my perfectly logical answer is almost guaranteed to be wrong 😉
3. Yokota Fritz says:
Bike Boy, you're absolutely correct. #2xx trains are "limited" trains, while all #3xx trains are express trains with only 5 stops between San Jose and 4th & King. The #2xx trains take about 1 hr 20 minutes between SJ and SF, while the Express runs can take less than 60 minutes.
It turns out in this example that you'd arrive in SF 5 minutes sooner on #225 than on the Express, but if it was me I would also have jumped on the Express if I didn't have time to look at schedules.
4. Yokota Fritz says:
Bike Boy, you're absolutely correct. #2xx trains are "limited" trains, while all #3xx trains are express trains with only 5 stops between San Jose and 4th & King. The #2xx trains take about 1 hr 20 minutes between SJ and SF, while the Express runs can take less than 60 minutes.It turns out in this example that you'd arrive in SF 5 minutes sooner on #225 than on the Express, but if it was me I would also have jumped on the Express if I didn't have time to look at schedules.
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https://tbc-python.fossee.in/convert-notebook/Electronic_Communication_by_D._Roddy/Chapter4_Noise_1.ipynb
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Chapter 4 Noise¶
Example 4.2.1,Pg.no 120¶
In [1]:
from math import sqrt
T=290.0
BW=1*10**6 #Noise bandwidth in hertz
k=1.38*10**-23 #Boltzman constant in J/K
R=50.0 #Determination of thermal noise power Pn
Pn=k*T*BW
#Pn=round(Pn,1)
print 'The value of thermal noise power is',Pn,'W'
#Determination of RMS noise voltage
En=sqrt(4*R*k*T*BW)
En=En*(10**6)
En=round(En,2)
print 'The value of RMS noise voltage is',En,'uV'
The value of thermal noise power is 4.002e-15 W
The value of RMS noise voltage is 0.89 uV
Example 4.2.2,Pg.no.122¶
In [2]:
from math import sqrt
R1=20000.0
R2=50000.0
k=1.38*10**-23 #Boltzman constant in J/K
T=290.0
BW=100*10**3 #Determination of thermal noise voltage for 20Kohm resistor
En1=sqrt(4*R1*k*T*BW)
En1=En1*(10**6)
En1=round(En1,2)
print 'a) i )The value of RMS noise voltage is',En1,'uV'
#Determination of thermal noise voltage for 50 kohm resistor
En2=En1*sqrt(R2/R1)
En2=En2*10**6
print ' ii)The value of RMS noise voltage is',En2,'uV'
#Determination of thermal noise voltage for 20K & 50k resistor in series
Rser=R1+R2 #Series combination of R1 & R2
En3=En1*sqrt(Rser/R1)
En3=En3*10**6
En3=round(En3,2)
print 'b)The value of RMS noise voltage is',En3,'uV'
#Determination of thermal noise voltage for 20K & 50k resistor in parellel
Rpar=(R1*R2)/(R1+R2) #parallel combination of R1 & R2
En4=En1*sqrt(Rpar/R1)
En4=En4*10**6
En4=round(En4,2)
print 'c)The value of RMS noise voltage is',En4,'uV'
a) i )The value of RMS noise voltage is 5.66 uV
ii)The value of RMS noise voltage is 8949245.77828 uV
b)The value of RMS noise voltage is 10588890.4 uV
c)The value of RMS noise voltage is 4783573.08 uV
Example 4.2.3,Pg.no.128¶
In [3]:
from math import sqrt,pi
f=120*10**6
c=25*10**-12 #capacitance of 12 pF
Q=30.0 #Q−factor of the ckt is 30
BW=10*10**3 #channel BW of the receiver is 10 KHz
k=1.38*10**-23 #Boltzman constant in J/K
T=290.0 #Room temp
#Determination of effective noise voltage Rd appearing at i /p at room temp
Rd=Q/(2*pi*f*c)
Rd=Rd/1000
Rd=round(Rd,2)
print 'The value of Rd is',Rd,'kohm'
Vn=sqrt(4*Rd*k*T*BW)
Vn=Vn*10**6
Vn=round(Vn,2)
print 'The value of effective noise voltage is',Vn,'uV'
The value of Rd is 1.59 kohm
The value of effective noise voltage is 0.02 uV
Example 4.3.1,Pg.no.131¶
In [4]:
from math import sqrt
Idc=10**-3
Bn=10**6 #Effective noise BW=1 MHz
q=1.6*10**-19 #Charge on electron in coulombs
#Determination of noise component current In in DC current of Idc=1 mA
In=sqrt(2*Idc*q*Bn)
In=In*10**9
In=round(In,2)
print 'The value of noise current In is',In,'nA'
The value of noise current In is 17.89 nA
Example 4.11.1,Pg.no.135¶
In [5]:
import math
from math import pi,sqrt
#An amplifier is given
Rn=300.0 #Equivalent noise resistance
Ieq=5*10**-6 #Equivalent noise current is 5 uA
Rs=150.0 #Amplifier fed from 150 ohm,10 uV rms sinusoidal source
Vs=10*10**-6
Bn=10*10**6 #Noise BW is 10 MHz
#Assume the following
kT=4*10**-21 #k is Boltzman constant in J/K & T is room temp
q=1.6*10**-19 #Charge on electron in coloumbs
#Determination of shot noise current
Ina=sqrt(2*q*Ieq*Bn)
Ina=Ina*(10**9)
print 'The value of shot noise current Ina is',Ina,'nA'
#Noise voltage developed by this across source resistance is
V=Ina*Rs
V=V*(10**6)
V=round(V,2)
print 'The value of noise voltage across Rs is',V,'uV'
#Noise voltage developed across Rn resistance is
Vna=sqrt(4*Rn*kT*Bn)*10**6
Vna=round(Vna,2)
print 'The value of noise voltage across Rn is',Vna,'uV'
#Determination of thermal noise voltage from source
Vns=sqrt(4*Rs*kT*Bn)*10**6
Vns=round(Vns,2)
print 'The value of thermal noise voltage at Rs is',Vns,'uV'
#Determination of total noise voltage at input
Vn=(((V)**2)+((Vna)**2)+((Vns)**2))**(1/2)
Vn=Vn*(10**6)
print 'The value of total noise voltage Vn is',Vn,'uV'
#Determination of signal to noise ratio in dB
SNR=20*(math.log10(Vs/Vn))
print 'The value of signal to noise ratio is',SNR,'dB'
The value of shot noise current Ina is 4.0 nA
The value of noise voltage across Rs is 600000000.0 uV
The value of noise voltage across Rn is 6.93 uV
The value of thermal noise voltage at Rs is 4.9 uV
The value of total noise voltage Vn is 1000000.0 uV
The value of signal to noise ratio is -220.0 dB
Example 4.12.1,Pg.no.136¶
In [6]:
import math
SNR1=60.0
l=3.0 #Determination of output signal to noise ratio
SNR=(SNR1) -10*math.log10(l)
SNR=round(SNR,2)
print 'The value of output signal to noise ratio is',SNR,'dB'
The value of output signal to noise ratio is 55.23 dB
Example 4.12.2,Pg.no.137¶
In [14]:
import math
SNRdB1=60.0 #SNR is 60 dB for Ist link
SNRdB2=60.0 #SNR is 60 dB for IInd link
SNRdB3=40.0 #SNR is 40 dB for IIIrd link
#Determination of power in watt
snr1=10**(-SNRdB1/10)
snr2=10**(-SNRdB2/10)
snr3=10**(-SNRdB3/10)
#Determination of overall SNR
SNR=snr3
#Determination of total SNR in dB
SNRdB=10*(-math.log10(SNR))
print 'The value of output signal to noise ratio is',SNRdB,'dB'
The value of output signal to noise ratio is 40.0 dB
Example 4.13.1,Pg.no.139¶
In [15]:
import math
SNRin=35.0 #SNR at i /p of amplifier
F=7.0 #Noise figure of an amplifier
#Determination of output SNR
SNRout=SNRin-F
print 'The value of output signal to noise ratio is',SNRout,'dB'
The value of output signal to noise ratio is 28.0 dB
Example 4.14.1,Pg.no.140¶
In [16]:
import math
f=13.0 #Noise figure of an amplifier
Bn=1*10**6
kT=4*10**-21 #k is Boltzman constant in J/K & T is room temp
F=10**(f/10)
#Determination of equivalent amplifier input noise
Pna=(F-1)*kT*Bn*10**12
Pna=round(Pna,2)
print 'The value of input noise is',Pna,'pW'
The value of input noise is 0.08 pW
Example 4.15.1,Pg.no.141¶
In [17]:
import math
f1=9.0 #Noise fig for amplifier
f2=20.0 #Noise fig for mixer
g=15.0 #power gain
#Converting dB in power ratio
F1=10**(f1/10)
F2=10**(f2/10)
G=10**(g/10)
#Determination of overall noise fig . reffered at i / p
F=F1+(F2-1)/G #converting in dB
FdB=10*math.log10(F)
FdB=round(FdB,2)
print 'The overall noise fig is',FdB,'dB'
The overall noise fig is 10.44 dB
Example 4.17.1,Pg.no.143¶
In [18]:
import math
F=6.0 #Noise fig .=6 dB
#Determination of noise factor
Fn=10**(6/10)
print 'The value of noise factor is',Fn
The value of noise factor is 1
Example 4.18.1,Pg.no.144¶
In [19]:
import math
f=12.0
Tm=290.0 #Room temp value
T=90.0
g=50.0 #calculating power ratio
F=10**(f/10)
G=10**(g/10)
#Determination of equivalent noise at room temp
Tem=(F-1)*Tm
Tem=round(Tem,2)
print 'The value of equivalent noise at room temp is',Tem,'k'
#Determination of equivalent noise at 90 k temp
Te=T+(Tem/G)
Te=round(Te,2)
print 'The value of equivalent noise at noise temp=90 is',Te,'K'
The value of equivalent noise at room temp is 4306.19 k
The value of equivalent noise at noise temp=90 is 90.04 K
Example 4.19.1,Pg.no.146¶
In [20]:
import math
enr=14.0
To=290.0 #Room temp in K
y=9.0 #Y−factor is 9 dB
#converting dB in power ratio
ENR=10**(enr/10)
Y=10**(y/10) #From def of ENR the hot temp is
Th=To*(ENR+1)
Th=round(Th,2)
print 'The value of hot temp Th is',Th,'k'
#Determination of equivalent noise temp
Te=(Th-(Y*To))/(Y-1)
Te=round(Te,2)
print 'The value of equivalent noise temp Te is',Te,'K'
The value of hot temp Th is 7574.47 k
The value of equivalent noise temp Te is 759.14 K
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https://carlo-hamalainen.net/blog/2009/8/22/honesty-in-science
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# Honesty in science
### 2009-08-22
In my day job I work on mathematics (discrete mathematics, mainly to do with latin squares). My research output is modest. It is by no means ground-breaking stuff. I doubt that I'll ever win the Clay maths prize for solving the Riemann hypothesis, nor will I ever win the Fields medal.
I can, however, take credit that I have always focussed on the mathematics itself. I've stated my claims as clearly as possible, provided source code to support computational claims, and made as much of my work freely available on reliable sites (mainly on the arXiv). What you see is what you get. On a daily basis I throw away a lot of what I do. That's the nature of mathematics and science.
It then saddens me to read things like this: Dembski does it again. The paper in question is pushing another agenda through an otherwise normal scientific journal. This is an offence to the journal and the other people who have published there.
The paper itself is surreal. On p. 1054:
The simple idea of importance sampling is to query more frequently near to the target. As shown in Fig. 1, active information is introduced by variation of the distribution of the search space to one where more probability mass is concentrated about the target.
Our use of importance sampling is not conventional. The procedure is typically used to determine expected values using Monte Carlo simulation using fewer randomly generated queries by focusing attention on queries closer to the target. We are interested, rather, in locating a single point in T.
The term "importance sampling" is very well known in the statistics community. It has a very clear and agreed-upon meaning. To change that is silly at best, and dishonest at worst. In fact, misusing well known terms is a good sign that you're a crank.
One standard application of importance sampling is to estimate an integral numerically. For a simple example, you might want to estimate the area under the curve in this picture:
The main benefit of importance sampling is that your estimates will be "close together" (mathematically, their standard deviation will be smaller than a uniform sampling Monte Carlo approach). The red dots in the following plot are the absolute errors from a uniform sampling estimator of the value of the integral, while the green dots are the absolute errors from an importance sampling estimator:
More precisely, the standard deviation of the errors of the uniform and importance sampling estimates is 0.0193 and 0.0001, respectively. The code is available as a Sage worksheet: Importance_sampling.sws.
For some reason, Dembski says that "We are interested, rather, in locating a single point in T". In our picture, the only sensible thing that his statement could mean is that he wants to find the peak of the curve. Right? But we have algorithms specifically formulated for doing that sort of thing. Back in undergrad I remember learning about Newton's method and other search/optimisation algorithms.
If you're searching for a point in some space, then just say that.
For a thorough rebuke of the information theory rubbish in Dembski's paper, see Mark C. Chu-Carroll's post.
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https://zbook.org/read/14f3ba_st-jude-math-a-thon-sample-funbook-fy21.html
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# St. Jude Math-A-Thon Sample Funbook FY21
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LEVEL K-8SAMPLE FUNBOOKstjude.org/mathSt. Jude patients and friendsJaxon and Clayton
LEVEL KFUNBOOKJungle Hide and SeekThis jungle is filled with wild animals! Count each animal. Write down how many you see.1.2.4.3.5.6.Goodcounting!7. Which animal do you see the most?8. Which animal do you see the least?
LEVEL 1FUNBOOKLine UpRobots took a bite out of these number lines!Write the missing numbers in the shapes below.1.2.3.4.5.
LEVEL 3FUNBOOKNumber PuzzlerUse the clues below to complete the puzzle.ACROSSDOWNA. Three thousand, four hundred ninety-eightA. 3,000 500 8C. 1 thousand, 2 hundreds, 6 tens, 7 onesB. Nine thousand, three hundred fourteenF. 10 more than 125D. 2 thousands, 4 tens, 9 onesH. 400 50 6E. 2 hundred less than 916J. Eight thousand, two hundred forty-oneG. 3 thousands, 1 hundred, 2 tens, 3 onesK. 90 more than 804I. Five thousand, four hundred thirtyL. 200 50 2K. 100 less than 182N. 30 more than 2M. 5,000 700 30 4P. 4,000 200 30 7O. 2 thousands, 5 hundreds, 9 tensR. 3 hundreds, 5 onesP. 400 9S. 100 less than 1,003Q. Twenty-threeR. 300 90 1
LEVEL 4FUNBOOKThis Land Is Your LandRead the information about each state below.Then write the standard form (numerals) for the area of each state.1. California is home to the2. Illinois has an area of 50,000Golden Gate Bridge. Its area 6,000 300 40 3 squarein square miles is 100,000 miles. It is home to Abraham50,000 8,000 600 40 8.Lincoln and Barack Obama.3. Check out the Great Lakes inMichigan. The state’s area isfifty-eight thousand, fivehundred thirteen square miles.Area:Area:Area:4. With an area of two hundredsixty-six thousand, eighthundred seventy-four squaremiles, Texas is second in sizeonly to Alaska.5. Tennessee is home toSt. Jude Children’s ResearchHospital. Its area is forty-twothousand, one hundredforty-six square miles.6. At 8,000 200 60 2square miles, Massachusettsis home to the sites of theBoston Tea Party andPaul Revere’s midnight ride.Area:Area:Area:7. Take a field trip across this great land! Connect the dots starting from the state you labeledwith the smallest area and working your way to the state you labeled with the greatest area.
LEVEL 5FUNBOOKThe Solar System andthe Sun: Far Out!The Numerators are flying into space to measure each planet’s distance from the sun (in miles)!Read each number name below. Write the standard form of the number on each blank line. Then look atthe chart to see how “far out” each planet is, and write each planet’s name next to the correct answer.1.2. Eight hundred eighty-six million, seven hundred thousand miles2.3. Ninety-two million, nine hundred sixty thousand miles3.4. Two billion, seven hundred ninety-four million miles4.5. Four hundred eighty-three million, six hundred thousand miles5.6. Sixty-seven million, two hundred thousand miles6.7. One billion, seven hundred eighty-three million miles7.8. One hundred forty-one million, six hundred thousand miles8.0,00arth9200 E141,6,9 V60en,0us006 M7,20er0,cu00ry035,900,0000,00603,48 Mars88n Jupiter6,700,000,00 Satur1,783,00,00 Uranus2,794eptune N000,00001. Thirty-five million, nine hundred thousand miles
LEVEL 6FUNBOOKReboot the RobotA giant robot has attacked the Numerators! But a secret code phrase will deactivate it. While the Numeratorsbattle the ’bot, they need you to find the secret phrase. Solve each fraction division problem and write youranswers in simplest form. After you solve all the problems, you’ll find some of your answers beneath the blanksbelow. Write the letter that is next to each answer in the blank above the correct fraction.
LEVEL 7FUNBOOKBeware the Dis-Count!If you shop at the Dis-Count’s Discount Cape Emporium, prepare to have extra money taken fromyou—unless you can calculate the discounted prices or the sales tax. Help the Numerators keep theDis-Count from biting into his customers’ wallets! If necessary, round to the nearest cent.
LEVEL 8FUNBOOK“Tri,” “Tri” Again, Ninjas!The Numerators are under attack by the Math Ninjas! While they fight them off,you find the missing angle in each of their triangular weapons shown!1. x 2. x 3. x 4. x 5. x 6. x 7. x 8. x Whew! Thanks forhelping us take care ofthose nasty ninjas!
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http://azfoo.net/gdt/babs/bars/mesa/202/westbound/87/
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BARS::Approaching AZ Hwy-87 on Loop 202 in Mesa, Arizona
This road sign is on westbound Loop 202 (Red Mountain Freeway) in Mesa, Arizona.
``` +-----------------------------------+
| Val Vista Dr 1/2 |
| McDowell Rd 2 1/2 |
| AZ Hwy-87 Country Club Dr 6 |
+-----------------------------------+
```
``` the numbers are: (1/2) (2 1/2) 87 6
the math is: sqrt(sqrt(87 - 6)) - (1/2) = 2 1/2
observe...
87 - 6 = 81
sqrt(81) = 9
sqrt(9) = 3
3 - 1/2 = 2 1/2
```
Creator: Gerald Thurman [gthurman@gmail.com]
Created: 18 November 2008
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http://www.braingle.com/brainteasers/teaser.php?op=2&id=29700&comm=0
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Browse Teasers
Search Teasers
## Triples 4
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.
Puzzle ID: #29700 Fun: (2.7) Difficulty: (2.12) Category: Series Submitted By: bigSWAFF_69_
A Triple is a Series with 6 sets, each with 3 numbers apiece. The relationship between the first two numbers are the same throughout all of the sets, and the relationship between the last two numbers is also the same, however, it is different than the first relationship.Try and find the missing numbers:
2 16 8
3 36 12
4 64 16
5 ___ __
_ 144 __
_ ___ 28
2 16 8
3 36 12
4 64 16
5 100 20
6 144 24
7 196 28
Relationship for first two numbers: double it, square the double (2 doubled=4, 4 squared=16)
Relationship for last two numbers: divide by first number (16 divided by 2= 8)
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## What Next?
See another brain teaser just like this one...
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which ones you have seen, and even make your own.
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https://topic.alibabacloud.com/a/data-structure-and-algorithm-analysis-2-stack-implementation_8_8_31813504.html
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# Data Structure and algorithm analysis (2) stack implementation
Source: Internet
Author: User
`/*stack.h*/`
` typedef int ElementType;/* START: fig3_45.txt */ #ifndef _Stack_h #define _Stack_h struct StackRecord; typedef struct StackRecord *Stack; int IsEmpty( Stack S ); int IsFull( Stack S ); Stack CreateStack( int MaxElements ); void DisposeStack( Stack S ); void MakeEmpty( Stack S ); void Push( ElementType X, Stack S ); ElementType Top( Stack S ); void Pop( Stack S ); ElementType TopAndPop( Stack S ); #endif /* _Stack_h *//* END */`
`/×stack.c*/ #include "stackar.h" #include "fatal.h" #include <stdlib.h> #define EmptyTOS ( -1 ) #define MinStackSize ( 5 ) struct StackRecord { int Capacity; int TopOfStack; ElementType *Array; };/* START: fig3_48.txt */ int IsEmpty( Stack S ) { return S->TopOfStack == EmptyTOS; }/* END */ int IsFull( Stack S ) { return S->TopOfStack == S->Capacity - 1; }/* START: fig3_46.txt */ Stack CreateStack( int MaxElements ) { Stack S;/* 1*/ if( MaxElements < MinStackSize )/* 2*/ Error( "Stack size is too small" );/* 3*/ S = malloc( sizeof( struct StackRecord ) );/* 4*/ if( S == NULL )/* 5*/ FatalError( "Out of space!!!" );/* 6*/ S->Array = malloc( sizeof( ElementType ) * MaxElements );/* 7*/ if( S->Array == NULL )/* 8*/ FatalError( "Out of space!!!" );/* 9*/ S->Capacity = MaxElements;/*10*/ MakeEmpty( S );/*11*/ return S; }/* END *//* START: fig3_49.txt */ void MakeEmpty( Stack S ) { S->TopOfStack = EmptyTOS; }/* END *//* START: fig3_47.txt */ void DisposeStack( Stack S ) { if( S != NULL ) { free( S->Array ); free( S ); } }/* END *//* START: fig3_50.txt */ void Push( ElementType X, Stack S ) { if( IsFull( S ) ) Error( "Full stack" ); else S->Array[ ++S->TopOfStack ] = X; }/* END *//* START: fig3_51.txt */ ElementType Top( Stack S ) { if( !IsEmpty( S ) ) return S->Array[ S->TopOfStack ]; Error( "Empty stack" ); return 0; /* Return value used to avoid warning */ }/* END *//* START: fig3_52.txt */ void Pop( Stack S ) { if( IsEmpty( S ) ) Error( "Empty stack" ); else S->TopOfStack--; }/* END *//* START: fig3_53.txt */ ElementType TopAndPop( Stack S ) { if( !IsEmpty( S ) ) return S->Array[ S->TopOfStack-- ]; Error( "Empty stack" ); return 0; /* Return value used to avoid warning */ }/* END */`
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## Geometry Marathon : Season 3
For discussing Olympiad level Geometry Problems
nahin munkar
Posts: 55
Joined: Mon Aug 17, 2015 6:51 pm
Location: banasree,dhaka
### Geometry Marathon : Season 3
$\Re$evived $\Re$ules :
Let's revive geo marathon (after 6 yrs only ) . The rules will be almost same as before, just enhance solving time duration for 2 days . The difficulty level should be around G1-G5 compared with ISL(IMO Shortlist). Solver will post his own solution of the former problem within 2 days from the time of posting that one & also add a new problem. (Otherwise, if the problem is remained unsolved for 2 days, the proposer will provide that's solution & jump to next ). Thus, this marathon will move forward.
N.B.
1. Don't forget to type the problem number.
2. Try to use LaTeX code
3. Be sure about your provided problem.
Let's make a trip to the world of geometry Here we go....................
Problem 1
$\triangle ABC,$ ,a right triangle with $\angle A = 90^0$, is inscribed in circle $\Gamma.$ Point $E$ lies on the interior of arc ${BC}$ (not containing $A$) with $EA>EC.$ Point $F$ lies on ray $EC$ with $\angle EAC = \angle CAF.$ Segment $BF$ meets $\Gamma$ again at $D$ (other than $B$). Let $O$ denote the circumcenter of triangle $DEF.$ Prove that $A,C,O$ are collinear
Last edited by nahin munkar on Fri Jan 06, 2017 1:03 pm, edited 14 times in total.
# Mathematicians stand on each other's shoulders. ~ Carl Friedrich Gauss
Raiyan Jamil
Posts: 138
Joined: Fri Mar 29, 2013 3:49 pm
### Re: Geometry Marathon : Season 3
$\text {Solution of Problem 1:}$
Let $AB$ meet $CE$ at $X$. SInce $\angle A=90^o$ and $\angle EAC= \angle CAF$,$\Rightarrow$ $(X,C;E,F)=-1$. And $B(X,C;E,F) \Rightarrow ADCE$ is a harmonic quadrilateral. So, if the perpendicular bisector of $DE$ intersects $AC$ at $Y$, then $Y$ is also the intersection of $D$ and $E$ tangents.So,$DY=EY$.
Now it is enough to prove $EY=FY$. Here,
$\angle CYE=180^o-(\angle ECY+\angle CEY)$
$=180^o-(\angle ACF+\angle EAC)$
$=180^o-(\angle ACF+\angle CAF)$
$= \angle AFC$
$\Rightarrow AEYF$ is cyclic.
So, since $AY$ is the angle bisector of $\angle EAF$,$Y$ is the midpoint of arc $EF$ of circle $AEYF$ not containing $A \Rightarrow EY=FY$ as desired.
Last edited by Raiyan Jamil on Fri Jan 06, 2017 3:24 pm, edited 1 time in total.
A smile is the best way to get through a tough situation, even if it's a fake smile.
tanmoy
Posts: 281
Joined: Fri Oct 18, 2013 11:56 pm
### Re: Geometry Marathon : Season 3
nahin munkar wrote:Problem 1
$\triangle ABC,$ ,a right triangle with $\angle A = 90^0$, is inscribed in circle $\Gamma.$ Point $E$ lies on the interior of arc ${BC}$ (not containing $A$) with $EA>EC.$ Point $F$ lies on ray $EC$ with $\angle EAC = \angle CAF.$ Segment $BF$ meets $\Gamma$ again at $D$ (other than $B$). Let $O$ denote the circumcenter of triangle $DEF.$ Prove that $A,C,O$ are collinear
My Solution:
Our goal is to show that $A,F,O,E$ are concyclic. Because then as $OE=OF$, $O$ lies on the internal bisector of $\angle EAF$ i.e. on $AC$.
We will show that $\angle FAE+\angle EOF=180^{\circ}$.
Let $\angle EAF=2x$ $\Rightarrow$ $\angle EAC=x=\angle EBC=\angle EDC$. Also, $\angle FDC=90^{\circ}$(Since $BC$ is the diameter of $(ABC)$.)
Then $\angle EDF=90^{\circ}+x$
Now,$\angle EOF=360^{\circ}-2\angle EDF=360^{\circ}-2(90^{\circ}+x)=180^{\circ}-2x=180^{\circ}-\angle FAE$.
Done.
Last edited by tanmoy on Sat Jan 07, 2017 11:19 am, edited 1 time in total.
I like girls and mathematics; both are beautiful.
tanmoy
Posts: 281
Joined: Fri Oct 18, 2013 11:56 pm
### Re: Geometry Marathon : Season 3
Problem 2
In $\triangle ABC$, $\angle ABC=90^{\circ}$. Let $D$ be any point on side $AC$, $D \neq A,C$. The circumcircle of $\triangle BDC$ and the circle with center $C$ and radius $CD$ intersect at $D,E$. Let $F$ be a point on side $BC$ so that $AF \parallel DE$. $X$ is another point on $BC$(Different from $F$) so that $XB=BF$. The circumcircle of $\triangle BDC$ and the circumcircle of $\triangle AXC$ intersect at $C,Y$.
Prove that $Y,F,D$ are collinear.
I like girls and mathematics; both are beautiful.
Raiyan Jamil
Posts: 138
Joined: Fri Mar 29, 2013 3:49 pm
### Re: Geometry Marathon : Season 3
$\text{Solution of Problem 2:}$
Let $FD$ and $AB$ meet at $Y'$. Now, $\angle DBF=\angle DBC=\angle DEC=\angle EDC=\angle FAC=\angle FAD \Rightarrow BFDA$ is cyclic $\Rightarrow FDA=Y'DA=90^\circ$.
Now, $\angle BY'D=\angle AY'D=90^\circ-\angle BAD=\angle BCD \Rightarrow Y'$ lies on circle $BCD$.
Now, it's left to prove that $Y'$ lies on circle $AXC$ i.e. $Y'$ coincides with $Y.$
Here, $\angle XAY'=\angle XAB=\angle BAF=\angle BDF=\angle BDY'=\angle BCY'=\angle XCY' \Rightarrow XACY'$ is cyclic as desired.
**I'll post another problem within a while if none other posts here till then.**
A smile is the best way to get through a tough situation, even if it's a fake smile.
Raiyan Jamil
Posts: 138
Joined: Fri Mar 29, 2013 3:49 pm
### Re: Geometry Marathon : Season 3
$\text{Problem 3:}$
In Acute angled triangle $ABC$, let $D$ be the point where $A$ angle bisector meets $BC$. The perpendicular from $B$ to $AD$ meets the circumcircle of $ABD$ at $E$. If $O$ is the circumcentre of triangle $ABC$ then prove that $A,E$ and $O$ are collinear.
A smile is the best way to get through a tough situation, even if it's a fake smile.
nahin munkar
Posts: 55
Joined: Mon Aug 17, 2015 6:51 pm
Location: banasree,dhaka
### Re: Geometry Marathon : Season 3
tanmoy wrote:Problem 2
In $\triangle ABC$, $\angle ABC=90^{\circ}$. Let $D$ be any point on side $AC$, $D \neq A,C$. The circumcircle of $\triangle BDC$ and the circle with center $C$ and radius $CD$ intersect at $D,E$. Let $F$ be a point on side $BC$ so that $AF \parallel DE$. $X$ is another point on $BC$(Different from $F$) so that $XB=BF$. The circumcircle of $\triangle BDC$ and the circumcircle of $\triangle AXC$ intersect at $C,Y$.
Prove that $Y,F,D$ are collinear.
A very nice problem indeed.
Solution of problem 2:
We denote the center of $\odot BCD$ by $O$ & $CY \cap ED = L$.
$\spadesuit$ Claim 1 : $A,Y,B$ collinear
proof :
By property of radical axis of $\odot BCD$ & $\odot (C,CD)$, we can see $CY \perp ED$ & $EL=DL$. It's easy to see that, CY is a diameter of $\odot BCD$ . $B,E,C,D,Y$ are con-cyclic by statement. So, $\angle YBC = 90^0$.
Given, $\angle ABC = 90^0$.
So, from here,
$\angle ABC = 90^0$ = $\angle YBC = 90^0$.
we get , $A,Y,B$ collinear.$\spadesuit$
$\clubsuit$ Claim 2 : $CY \perp AF$
proof :
We extend $CY$ and $CY \cap AF = C'$ .
As, $DE||AF$ & $CC' \perp ED \Longrightarrow CC' \perp AF \Longrightarrow CY \perp AF$.$\clubsuit$
$\bigstar$ So,By claim $1$ & $2$, $Y$ is the orthocenter of $\triangle AFC$ .
As, $\angle YDC = 90^0$ & $Y$ is orthocenter of $\triangle AFC$ , $FYD$ must be a line.
So, $F ,Y, D$ are collinear . Done ! $\blacksquare$
Last edited by nahin munkar on Fri Jan 06, 2017 9:04 pm, edited 2 times in total.
# Mathematicians stand on each other's shoulders. ~ Carl Friedrich Gauss
nahin munkar
Posts: 55
Joined: Mon Aug 17, 2015 6:51 pm
Location: banasree,dhaka
### Re: Geometry Marathon : Season 3
Raiyan Jamil wrote:$\text{Problem 3:}$
In Acute angled triangle $ABC$, let $D$ be the point where $A$ angle bisector meets $BC$. The perpendicular from $B$ to $AD$ meets the circumcircle of $ABD$ at $E$. If $O$ is the circumcentre of triangle $ABC$ then prove that $A,E$ and $O$ are collinear.
Solution of problem 3 :
Let, $H$ be orthocenter of $\triangle ABC$.
So,We know, $O$ & $H$ are isogonal conjugates .
Let, $A'$ be the projection on $BC$ on $A$.
$\bigstar$ In $\triangle AA'E$,
$\angle AA'D =90^0$
$\angle ADA'= \theta$
$\bigstar$ In $\triangle ABE$,
$\angle AXE= 90^0$
& $\angle AEB = \theta$
So, $\triangle AA'E \sim \triangle ABE$
$\Longrightarrow$ $\angle A'AD= \angle EAD$
For this , $E$ & $H$ also isogonal conjugate. So, $A,O,E$ lie on a line . Thus, $A,O,E$ are collinear. $\blacksquare$
Last edited by nahin munkar on Fri Jan 06, 2017 9:01 pm, edited 1 time in total.
# Mathematicians stand on each other's shoulders. ~ Carl Friedrich Gauss
nahin munkar
Posts: 55
Joined: Mon Aug 17, 2015 6:51 pm
Location: banasree,dhaka
### Re: Geometry Marathon : Season 3
Problem 4:
Let $ABC$ be a triangle and $m$ a line which intersects the sides $AB$ and $AC$ at interior points $D$ and $F$, respectively, and intersects the line $BC$ at a point $E$ such that $C$ lies between $B$ and $E$. The parallel lines from the points $A$, $B$, $C$ to the line $m$ intersect the circumcircle of triangle $ABC$ at the points $A_1$, $B_1$ and $C_1$, respectively (apart from $A$, $B$, $C$). Prove that the lines $A_1E$ , $B_1F$ and $C_1D$ pass through the same point.
# Mathematicians stand on each other's shoulders. ~ Carl Friedrich Gauss
joydip
Posts: 47
Joined: Tue May 17, 2016 11:52 am
### Re: Geometry Marathon : Season 3
Solution of problem 4 :
Let $B_1F$ meet (ABC) again at $K$, $KC_1\cap AB = D_1$.Applying pascal's theorem on hexagon $BACC_1KB_1$ we get $CC_1 \| BB_1 \| FD_1$ . So , $D=D_1$. So $K,D,C_1$ are collinear. Similerly $K,E,A_1$ are collinear.
Last edited by joydip on Fri Jan 06, 2017 10:00 pm, edited 1 time in total.
The more I learn, the more I realize how much I don't know.
- Albert Einstein
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# If else problem
100+ P: 553 Basic if statement question: If ( .... ) { If (....) // If 1 *** If (....) // If 2 *** If (....) // If 3 *** } else if ( .... ) { if (something = something) { if (....) // *** This and the next 2 If statements are identical to those if (....) // in code above... how would you avoid duplicating the same if (....) // if statements.. here are only 3 but what if there are 10s? } } One solution to avoid duplicating the the same if statements is to use goto statement, but is there any othe rbetter and preferred way of doing it? Thanks Aug 4 '07 #1
10 Replies
P: 41 Basic if statement question: If ( .... ) { If (....) // If 1 *** If (....) // If 2 *** If (....) // If 3 *** } else if ( .... ) { if (something = something) { if (....) // *** This and the next 2 If statements are identical to those if (....) // in code above... how would you avoid duplicating the same if (....) // if statements.. here are only 3 but what if there are 10s? } } One solution to avoid duplicating the the same if statements is to use goto statement, but is there any othe rbetter and preferred way of doing it? Thanks you could use a function: Expand|Select|Wrap|Line Numbers bool ifFunction(bool state) { if(...) if(...) if(...) return true; return false; } and then use it like this Expand|Select|Wrap|Line Numbers If ( .... ) { if(ifFunction(...)) } else if ( .... ) { if (something = something) { if(ifFunction(...)) } } Aug 4 '07 #2
Expert Mod 5K+ P: 9,197 And you could make that function inline to avoid the overhead of a call. Aug 4 '07 #3
Expert 10K+ P: 11,448 you could use a function: Expand|Select|Wrap|Line Numbers bool ifFunction(bool state) { if(...) if(...) if(...) return true; return false; } and then use it like this Expand|Select|Wrap|Line Numbers If ( .... ) { if(ifFunction(...)) } else if ( .... ) { if (something = something) { if(ifFunction(...)) } } How about a little Boolean algebra? T => (A , B , C) !T => (D , B , C) rewriting the terms yields T => A !T => D B C this reduces easily to code like this: Expand|Select|Wrap|Line Numbers if (T) A; else D; B; C; kind regards, Jos Aug 4 '07 #4
Expert Mod 5K+ P: 9,197 How about a little Boolean algebra? Ah yes. DeMorgan's Theorem and Karnaugh Maps. Check out Introduction to Boolean Algebra and Logic Design by Gerhard Hoernes (McGraw-Hill 1964). Aug 4 '07 #5
Expert 10K+ P: 11,448 Ah yes. DeMorgan's Theorem and Karnaugh Maps. Check out Introduction to Boolean Algebra and Logic Design by Gerhard Hoernes (McGraw-Hill 1964). Yes, it's fun isn't it? Have a look at the Quine McCluskey (sp?) algorithm for a better, less human oriented, less visual approach at boolean logic formula minimization; those Karnaugh maps are a disaster in that respect. kind regards, Jos Aug 4 '07 #6
Expert Mod 5K+ P: 9,197 less visual approach at boolean logic formula minimization; those Karnaugh maps are a disaster in that respect. Not if you use Gray Code. Aug 4 '07 #7
Expert 10K+ P: 11,448 Not if you use Gray Code. Care to elaborate? because I don't understand how, e.g. a 3 variables Karaugh map (8 cells) would be organized such that a Gray code can come in handy. It might be just me because I've been lazy all day in my back garden ;-) kind regards, Jos (<-- no noticable brain activity to be found) Aug 4 '07 #8
Expert Mod 5K+ P: 9,197 In a Gray code only one bit can change state to advance to the next code in the sequence. There are various forms but here is one: 000 001 011 010 110 111 101 100 By using a Gray code on the toroidal Karanugh map and plotting your true states of your Boolean equation, should any two true states be adjacant then one of the variables is irrelevant. That's because it changed state and did not affect the outcome. Four adjacent true points mean two irrelevant variables. And, of course, the open sequares are the inverse. It's much easier for reduction than using a Vietsch diagram and measuring Aug 4 '07 #9
Expert 10K+ P: 11,448 In a Gray code only one bit can change state to advance to the next code in the sequence. There are various forms but here is one: 000 001 011 010 110 111 101 100 By using a Gray code on the toroidal Karanugh map and plotting your true states of your Boolean equation, should any two true states be adjacant then one of the variables is irrelevant. That's because it changed state and did not affect the outcome. Four adjacent true points mean two irrelevant variables. And, of course, the open sequares are the inverse. It's much easier for reduction than using a Vietsch diagram and measuring Yes I know what Gray codes are; but still, finding 'adjacent' areas is still a very visual process; the Q-McK algorithm simply produces tables of the terrms of disjunctive normal forms and produces a reduced table (if possible) etc. etc. until no further reduction is possible (it tries to find 'resolutions' just like those Gray code numbers). The Karnaugh maps make me dizzy above three (four?) variables; the Q-McK algorithm doesn't care about many variables are used. Doing that by hand is a boring and error prone process. I agree Karnaugh maps are more fun to work (play?) with for humans using just a few variables. kind regards, Jos Aug 4 '07 #10
P: 8 Getting back to the question You can use compound expression in if Expand|Select|Wrap|Line Numbers Ex.. if (age >= 0) if (age < 120) print age is valid to if (age >= 0) && (age < 120) print age is valid ========================= if (age < 0) || (age >= 120) print age is valid to if (age < 0) print age is valid else if (age >= 120) peint age is valid Aug 4 '07 #11
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# Distance between Boise, ID (BOI) and Seattle, WA (SEA)
Flight distance from Boise to Seattle (Boise Airport – Seattle–Tacoma International Airport) is 399 miles / 642 kilometers / 347 nautical miles. Estimated flight time is 1 hour 15 minutes.
Driving distance from Boise (BOI) to Seattle (SEA) is 501 miles / 806 kilometers and travel time by car is about 9 hours 20 minutes.
399
Miles
642
Kilometers
347
Nautical miles
1 h 15 min
## How far is Seattle from Boise?
There are several ways to calculate distances between Los Angeles and Chicago. Here are two common methods:
Vincenty's formula (applied above)
• 398.910 miles
• 641.984 kilometers
• 346.644 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth.
Haversine formula
• 398.382 miles
• 641.133 kilometers
• 346.184 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## Flight Duration
Estimated flight time from Boise Airport to Seattle–Tacoma International Airport is 1 hour 15 minutes.
## Time difference
The time difference between Boise and Seattle is 1 hour. Seattle is 1 hour behind Boise.
Boise time to Seattle time converter
## Carbon dioxide emissions
On average flying from Boise to Seattle generates about 84 kg of CO2 per passenger, 84 kilograms is equal to 185 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Boise to Seattle
Shortest flight path between Boise Airport (BOI) and Seattle–Tacoma International Airport (SEA).
## Airport information
Origin Boise Airport
City: Boise, ID
Country: United States
IATA Code: BOI
ICAO Code: KBOI
Coordinates: 43°33′51″N, 116°13′22″W
Destination Seattle–Tacoma International Airport
City: Seattle, WA
Country: United States
IATA Code: SEA
ICAO Code: KSEA
Coordinates: 47°26′56″N, 122°18′32″W
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# Aptitude | GATE CS 1998 | Question 17
The octal representation of an integer is (342)8. If this were to be treated as an eight bit integer in an 8085 based computer, its decimal equivalent is
(A) 226
(B) -98
(C) 76
(D) -30
Answer: (D)
Explanation: (342)8=(011100010)2=(11100010)2.
If we treat this as an 8-bit integer, the first bit becomes sign bit and since it is “1”, number is negative. 8085 uses 2’s complement representation for integers and hence the decimal equivalent will be
(00011110)2 = -30
So, option (D) is correct.
Quiz of this Question
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Example problem: Adaptive solution of the 2D advection diffusion equation with flux boundary conditions
In this problem we will discuss the 2D advection-diffusion problem with Neumann (flux) boundary conditions, using oomph-lib's mesh adaptation routines.
Two-dimensional advection-diffusion problem in a rectangular domain Solve in the rectangular domain . We split the domain boundary into two parts so that , where . On we apply the Dirichlet boundary conditions where the function is given. On we apply the Neumann conditions where the function is given.
As always, we validate the code by choosing the boundary data and the source functions such that
is the exact solution of the problem. The plot below shows the numerical solution for , a Peclet number of , and four different values of the "steepness parameter", and .
Animation of the adaptive solution for various values of the `steepness parameter'.
As in the example with Dirichlet boundary conditions, the unforced case is a lot more interesting. The plot below shows the result for a zero source function , Dirichlet boundary conditions determined from the "exact solution" of the forced problem for , and a prescribed flux of on .
Plot of the adaptive solution of the unforced problem.
Along , the value of is enforced by the Dirichlet boundary condition (2) and, as in the previous example, the "wind" either sweeps this value into the interior of the domain or creates a sharp boundary layer within which the solution that is "swept" along from the interior adjusts itself to the prescribed boundary value. Along , the flux boundary condition (3) imposes the normal derivative of the solution. This boundary condition is much "softer" than the Dirichlet condition and does not create boundary layers that are as sharp as the ones that develop on .
# The driver code
The driver code for this problem is so similar to the corresponding Poisson problem that we do not list it here. The modifications are the same as those discussed in the advection diffusion problem with Dirichlet boundary conditions: We have to specify the wind function and the Peclet number.
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# A frequency modulated signal with a carrier frequency of ′′f′′c is given by, s(t)=20cos[2πfct+12sin(2000πt)+5cos(2000πt)] The maximum phase deviation of the signal s(t) is equal to
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Solution
## The correct option is B 13 rad The phase of the given modulated signal is, ϕ(t)=12sin(2000πt)+5cos(2000πt) rad =√(12)2+(5)2[cos(2000πt−α)] rad =13cos(2000πt−α) rad Where, α=tan−1(125) Maximum phase deviation of the signal s(t) is, Δϕmax=|ϕ(t)|max=13 rad
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you are viewing a single comment's thread.
[–] 1 point2 points
sorry, this has been archived and can no longer be voted on
Ok, so, you can divide any unit in half right? What about doing it again? And again? Do that a dozen more times. Now a hundred. You can still divide it in half. There are an infinitely small number of fractions for any given measurement.
[–] 1 point2 points
sorry, this has been archived and can no longer be voted on
Right, and then you continue ad infinitum, except that, as I understand it, a Plank's length would be the theoretically smallest you could go. Additionally, there are philosophical arguments against the possibility of an ininite reduction in length, for instance, that if you reduced in length infinitely, you would have an infinite number of segments, which would mean that you would have an object of infinite length (like in Zeno's Paradox).
[–] 1 point2 points
sorry, this has been archived and can no longer be voted on
Well that's more of a question of mathematics vs. physics, and the whole idea was philosophical to begin with. It's basically semantics I suppose, ergo I don't see what's wrong with the joke. The Planck is the theoretical smallest unit because we currently cannot "measure nor detect" anything smaller. That's not to say at some point in the future we won't, but I guess that's currently irrelevant. A length having infinite divisions doesn't really equate to infinite length IMO, but more semantics. Bleh.
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# Stitch and sliding constraints
## Stitch constraints ¶
Stitch constraints are now able to stitch a point to the closest position on a primitive, not just to another point. This is extremely useful for stitching cloth together. For example, now you can stitch a pocket to a shirt anywhere on a triangle or quad, instead of being limited to only points. Stitching to the closest position also works with polylines. This ability is very useful to create smooth and realistic looking sliding.
Stitching to points.
Stitching to the closest position on a primitive.
Stitching to points.
Stitching to the closest position on a polyline.
## Sliding constraints ¶
Sliding constraints are stitch or attach constraints that can slide across the surface of target geometry. In order to create sliding constraints, you need to use Attach to Geometry or Stitch constraints, both of which have the ability to constrain points to the closest position on a primitive. To enable this, turn on the Use Closest Location on Primitive checkbox on the Vellum Constraints node. You also need to turn on Sliding Rate, which will allow the constraint to slide along the target geometry at this rate during the simulation. Set the Target Group Type to Primitives, and choose your target geometry as the Target Group.
The Sliding Rate controls how quickly the sliding will occur. A value of 1 matches the constrained point’s velocity. Decreasing this value will cause it to slide slower. It can also be scaled by attribute at simulation time.
### Sliding Methods ¶
There are two methods for sliding along target geometry: Closest Point and Traverse Polygons. The Sliding Method drop-down can be found on the Motion collapsible menu of Advanced tab of the Vellum Solver.
The Closest Point method is the easiest, quickest, and simplest as it just finds the next closest point. However, it can skip over gaps if there are concavities in your geometry or places where two pieces of geometry meet, for example where the arm meets the body of a character. This becomes a problem when the closest point is on non-connected target geometry.
The Traverse Polygons method walks outward from the current sliding position along the connected polygons, which can be slower but uses connectivity to avoid skipping over gaps. This is slower at high resolutions, so the general recommendation is to start with the Closest Point method (which is the default) and if you start seeing jumps between gaps that are problematic, switch to Traverse Polygons method.
This image shows constraints skipping over the gap in geometry to the lower level with the Closest Point method.
This image shows the constraints stopping at the lowest point and not skipping over the gap with the Traverse Polygons method.
### Tips and troubleshooting ¶
• You can optionally use a Sliding Attribute for finer control. This attribute scales the Sliding Rate as the points move along the geometry. In the video above, the constraints in the blue area slide faster than the constraints in the red area.
• Turning on Tangent Stiffness will slow down sliding, since the constraints are fighting with gravity to keep the points in place. You can work around this by increasing the Sliding Rate.
• If your constraints are improperly jumping across concavities in the target geometry, you can change the Sliding Method on the Advanced tab of the Vellum Solver from Closest Point to Traverse Polygons. This method starts from the current target primitive and successively walks outwards, finding the closest point on the surrounding primitives. This approach is more expensive, but handles concave target geometry better. In the video above, Traverse Polygons is turned on so that the constraints don’t jump from the top of the circle to the bottom as the object slides downward.
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# LRO Educator Resource Kit
Each lesson or activity in this toolkit is related to NASA's Lunar Reconnaissance Orbiter (LRO). The toolkit is designed so that each lesson can be done independently, or combined and taught in a sequence. The Teacher Implementation Guide provides... (View More)
# Design Challenge - Deploying the Satellites' Antennae
This is an activity about using models to solve a problem. Learners will use a previously constructed model of the MMS satellite to determine if the centrifugal force of the rotating MMS model is sufficient to push the satellite's antennae outward,... (View More)
Audience: Middle school
# MRC: Selecting Teams Rover Mission (Grades 6-8)
Learners will review what they have learned about scientific and engineering investigation, construct a valid scientific question that can be answered by data and/or modeling, and choose an appropriate mission for their rover that will answer their... (View More)
# Comparing Cosmic Cameras
Learners will take and then compare the images taken by a camera - to learn about focal length (and its effects on field of view), resolution, and ultimately how cameras take close-up pictures of far away objects. Finally, they will apply this... (View More)
# Design Challenge: How do You Keep Things from Getting Too Hot?
This is a lesson about designing and building an effective sunshade for a model MESSENGER craft. Learners will build a model of MESSENGER. They will use a scientific approach to solve problems and work as a cooperative team. They will discover their... (View More)
# Snow Goggles and Limiting Sunlight
This is a lesson about radiation and the use of the scientific method to solve problems of too much radiation. Learners will build snow goggles similar to those used by the Inuit (designed to block unwanted light, while increasing the viewer's... (View More)
# Design Challenge: How to Keep Gelatin from Melting?
This is a activity about applying the scientific method to a design challenge. Learners will design and build a platform that will be placed on a heat source. The platform is expected to serve as an insulator for a cube of gelatin. The goal is to... (View More)
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Algebra Tutorials!
Sunday 18th of March
Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
Ineq. #4:
Ineq. #5:
Ineq. #6:
Ineq. #7:
Ineq. #8:
Ineq. #9:
Solve for:
Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:
pie value math
Author Message
interTisd
Registered: 11.04.2002
From: esperanto.org.il
Posted: Thursday 28th of Dec 08:06 Hi guys ! Are there any online resources to learn about the basics of pie value math? I didn’t really get the chance to cover the entire syllabus as yet. This is probably why I encounter problems while solving equations .
Jahm Xjardx
Registered: 07.08.2005
From: Odense, Denmark, EU
CHS`
Registered: 04.07.2001
From: Victoria City, Hong Kong Island, Hong Kong
Posted: Saturday 30th of Dec 07:33 Hello, I am a mathematics teacher. I use this software whenever I get stuck at any equation . Algebrator is undoubtedly a very handy software.
IvElKiCsEs
Registered: 17.12.2002
From: UK
Posted: Sunday 31st of Dec 20:00 Wow. I did not know that there could be a solution for me. May be I should take this on. I am already comforted to know that the solution to my problems is at hand. I am raring to try this out. Can you tell me where I can access this program?
Dolknankey
Registered: 24.10.2003
From: Where the trout streams flow and the air is nice
Posted: Tuesday 02nd of Jan 16:38 The program can be found at http://www.gre-test-prep.com/order-of-operations-1.html.
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https://dsp.stackexchange.com/questions/30709/heterodyne-detection
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Heterodyne detection
Prove that with appropriate choices of the phase $\varphi$, one can recover the quadratures of $m(t).$
Attempt
The context of this question is weak optical signals combined with a strong local oscillator at a beamsplitter. And $m(t)$ refers to the complex modulating signal.
The signal field is given by: $f(t)=Re \Big[ m(t) \exp (j2 \pi \nu_c) \Big],$ with $m(t)=m_1 (t) + j m_2 (t).$
This is linearly combined with the stronger coherent local oscillator which has the form:
$$c(t) = Re \{ A \exp \Big[ j(2 \pi \nu_{het} t - \varphi) \Big] \},$$
where $\nu_{het} = \nu_c + \Delta,$ has been shifted from the carrier frequency by $\Delta.$ So the output field would be:
$$g_1 (t) = Re \{ R \ A \exp \Big[ j(2 \pi \nu_{het} t - \varphi) \Big] + T \ m(t) \exp (j 2 \pi \nu_c) \},$$
where $R$ and $T$ are reflection and transmission coefficients for the beamsplitter (I was told that for this problem we can assume for simplicity that $R$ is real and $T$ is imaginary).
I am unsure how to proceed with the proof so any explanation would be appreciated.
• I don't see a question here. Commented May 10, 2016 at 14:46
• Are you sure your transmitted signal $f(t)$ is supposed to be added to the signal from the local oscillator $c(t)$? That doesn't make sense to me. I do not have any knowledge of optical communications but in wireless communications the transmitted signal is multiplied with the signal from the local oscillator so the frequency of the message can either shift to baseband or to some intermediate frequency in the case of a heterodyne receiver. Commented May 11, 2016 at 13:36
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https://zh.coursera.org/learn/operations-research-algorithms/reviews?authMode=signup
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4.8
35 个评分
7 条评论
## 课程概述
Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Electrical Engineering, etc. The series of courses consists of three parts, we focus on deterministic optimization techniques, which is a major part of the field of OR. As the second part of the series, we study some efficient algorithms for solving linear programs, integer programs, and nonlinear programs. We also introduce the basic computer implementation of solving different programs, integer programs, and nonlinear programs and thus an example of algorithm application will be discussed....
## 1 - Operations Research (2): Optimization Algorithms 的 9 个评论（共 9 个）
Feb 22, 2021
Very boring. Forum is dead. Flaws in grading. I finished it, but never again. Bax experience.
Mar 10, 2021
Very clear explanations and great coverage from main points of view -- mathematical, technical and even business (which is quite rare combination). High-quality LaTeX slides evoke nostalgia, and real cases give good sense of how one can use these tools in the real world
Jun 28, 2021
It's a course that teaches you to solve the model you've built.
Apr 17, 2021
Mar 29, 2022
Extremelly good course!
May 30, 2022
good for beginners!!
Dec 10, 2021
The course is good, but homework assignments could be made clear. For example, the objective value for an optimal solution in LP/IP formulations is often confused in homework instructions. For heuristics algorithms hints, it is better to hint the type of algorithm (greedy, brute-force, dynamic, etc) and let the students find their solutions since this course is not focused on heuristics.
Sep 16, 2021
The Course was done earlier, hence, there was no one to answer the forums or questions, otherwise a very good course to learn about applying Python.
Mar 8, 2022
El curso es bastante interesante pero también me parece que está explicado de forma muy pobre.
Las diapositivas en si mismas no te permiten guiarte y entender todo de forma autónoma y la parte de programación está explicada realmente mal. También considero que faltan ejemplos de programación.
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https://brilliant.org/problems/you-take-one-side-ill-take-the-other/
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# You take one side, I'll take the other
Calculus Level 4
Suppose we have two concentric circles of radii $$3$$ and $$4$$, respectively. Let $$R$$ be the largest rectangle with two adjacent vertices on the radius $$3$$ circle and two adjacent vertices on the radius $$4$$ circle.
Let $$x$$ and $$y$$ be the dimensions of $$R$$, with $$x \gt y$$. Then if $$x - y = \dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers, find $$a + b$$.
×
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https://matthewdharris.com/2016/04/27/gaussian-process-in-feature-space/?like_comment=271&_wpnonce=5dd02b5f9b
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# Gaussian Process in Feature Space
[In the last post, I talked about showing various learning algorithms from the perspective of predictions within the “feature space”. Feature space being a perspective of the model that looks at the predictions relative to the variables used in the model, as opposed geographic distribution or individual performance metrics.
I am adding to that post the Gaussian Process (GP) model and a fun animation Or two.
#### So what’s a GP?
The explanation will differ depending on the domain of the person you ask but essentially a GP is a mathematical construction that uses a multivariate Gaussian distribution to represent an infinite number of functions the describe your data, priors, and covariance. Each data point gets Gaussian distribution and these are all jointly represented as the multivariate Gaussian. The choice of the Gaussian is key to this as it makes the problem tractable based on some very convenient properties of the multivariate Gaussian. When referring to a GP one may be talking about regression, classification, a fully Bayesian method, some form or arbitrary functions, or some other cool stuff I am too dense to understand. That is a broad and overly-simplistic explanation, but I am overly-simplistic and trying to figure it out myself. There is a lot of great material on the web and videos on youtube to learn about GP.
#### So why use it for archaeology?
GP’s allow for the the estimation of stationary nonlinear continuous functions across an arbitrary dimensional space; so it has that going for it… which is nice. But more to the point, it allows for the selection of a specific likelihood, priors, and a covariance structure (kernel) to create a highly tunable probabilisitic classifier. The examples below use the kernlab::gausspr() function to compute the GP using Laplace approximation with a Gaussian noise kernel. The $\sigma$ hyperparameter of this Gaussian kernel is what is being optimized in the models below. There are many kernels that can be used in modeling a GP. One of the ideal aspects of a GP for archaeological data is that the continuous domain of the GP can over geographic space taking into consideration natural correlation in out samples. This has strong connections to Kriging as a form of spatial regression in the geostatistical realm, as well as relation to the SVM kernel methods of the previous post.
#### On to the plots…
As in the previous post, the plot here has the intention to show how the prediction of site probability (yellow to purple raster backdrop) responds within a bivariate feature space. Further, how the training data (red dots) and test data (green dots) lay in relation to the predictions. Also as previously discussed, this method is more in tune with an exploratory analysis and not necessarily a presentation to convey an understanding; as this plot require a bit more un-communicated context [more on that in a later post]. What is to be taken from this is to see how the algorithm extrapolates prediction probability throughout the space of possible samples and then beyond into unknown regions. Then repeat this process over a range of hyperparameters to see how the sensitive the model is to changes. This allows the analyst to see a model fit and the balance between underfit vs. overfit without having to rely solely on a single metric; which may not embody the nuance of the actual fit. That, or maybe I just like pictures…
The above plot shows the predictions of a GP with a $\sigma$ = 1. The AUC of this model on test data is a respectable 0.809. Seeing the prediction in feature space offers a few interesting tidbits. Firstly, is the heightened probability at the upper right hand corner and around TPI = 1 and CD Conf = -1. The remainder of the probability mass is with the mass of data points around TPI = -1 and CD Conf = -1. My broad hypothesis is that sites are more likely at lower values of these two variables essentially closer to confluences on landforms that are more level. The former mentioned peaks in probability at higher TPI and high TPI + CD Conf immediately suggest three nonexclusive and non-exhaustive possibilities, 1) outliers that are specific to this data; 2) my hypothesis needs to be broadened to anticipate sites in other areas; and 3) the model is not generalizing well. another interesting aspect is that the prediction of low probability is where there are few if any site samples, but lots of background samples, but is at ~0.5 probability where there are no samples . Essentially without data, the prior probability of 0.5 [not sure either way] is not unaffected.
For nonexclusive and non-exhaustive possibility #1, we could run a number of analysis to better understand the nature of these outlying samples. Ideally, we would have a notion of this before getting to this stage. Depending on the outcome of that analysis we would be confronted with decisions regarding these being of a different population [in the data sense, not cultural, but maybe cultural…] or what we level of false-negatives we are willing to accept to focus our predictions on the areas that are not outliers. Possibility #2 follows right after the tradeoff of false-negatives and false-positives. If we broaden our hypothesis, then we need to accept that more of the landscape is sensitive and conversely that additional variables/models should be considered. This is not a bad thing at all, but where you go from there is entirely dependent on why you are making the model in the first place (management, research, etc…). Finally, possibility #3 is a more technical issue, but inherently related to the previous two issues. The models ability to generalize is relative to what you are using it for (in part, your assumptions), how representative your data is, and how your model incorporates these two things. In a general sense, the tuning of the model hyperparameter $\sigma$ allows us to balance our assumptions, intentions, and data to find the closest fit to our target. Note, I did not say the correct or even the best model because sometimes… well, sometimes stuff just doesn’t work out.
#### Hyperparameter search
Dealing with issues #1 and #2 are up to you and beyond the scope here, but we can take a look at #3. Using the same plot as above, we can see what happens as we alter the $\sigma^2$ hyperparameter. In an ideal world, all model hyperparameters would have great intuitive understanding and we would have a fare idea of what we expected it to be based on our domain knowledge. In the real world, this is not the case. Many hyperparameters have a fair range where we expect decent results, but some are pretty nebulous. Fortunately, sigma ($\sigma$) is well known in the world of Gaussians and simply controls the variance of the distribution; the larger the sigma, the wider the Gaussian. In this implementation, the hyperparameter sigma is the inverse kernel width, leading to the smaller the sigma, the wider the Gaussian. Some thought on that twist can be found here. Given that my hypothesis assumes that the data is very noisy and that sites will be found at a wider variety of areas that my data suggests, I would tend to believe that a smaller sigma (wider Gaussian = more variance) would be preferable; even at the expense of predictive accuracy on the know data.
#### What is the best sigma?
I don’t know, lets sweep some plausible parameters and see what the plots look like vis a vis the performance metric (AUC).
As the sigma in increased, the model piles more predictive mass onto the training point locations. This makes sense given that the sigma is the inverse kernel width and larger sigma equals a more narrow kernel; therefore spiked probabilities. Based on this, it is clear that the model appears to generalize better with smaller values of sigma. If we compare the gif to the the charted metrics below, we how the AUC corresponds to the increasing sigma for both training and test sets. This is a pretty standard view of the trade-off between model complexity (increasing sigma) and model generalization (increased test set AUC). The bottom line is that while training data continues to show improvement as sigma increases, the independent test set has the highest AUC at the lowest AUC; this is the most general model. The findings of the line graph below mirror the spatial arrangement of predictive mass in the gif above. Low sigma creates wide and sweeping predictions of large areas of feature space leading to predicting much of the data well, but misses some completely; generalizes well. Alternatively, the high sigma model zeros in on the training data, to the detriment of missing areas that very well may have observations in the test sets; generalizes poorly.
Okay, so lowest sigma, or thereabouts, gives us the best generalization, fits the anticipated response, and achieves a relatively high AUC by correctly classifying many of the test observations at a high probability. Do this over a k-folds CV and we check the error metric variance. Speaking of, as mentioned in this post, I have come up with better metrics for ultimately describing site prediction accuracy. However, in much of my testing, AUC has been the best metric to screen the hyperparameter space.
### IN 3D!!!!!!!!!
Ok, but what does it look like looped in 3D!?!? Tufte may be rolling in his grave (he is not dead), but I really like this as far an in intuition building animation. This is over and under fitting visualized. Perhaps a bit 1990’s, or something, but darn if it does not drive home the point of data fit and generalization across the hyperparameter range. I could use “small multiples” or distill the over/underfit into a single metric to graph, but it misses on the interactivity of seeing a response across a continuous space.
Or as the say…
## 2 thoughts on “Gaussian Process in Feature Space”
1. […] Gaussian Process in Feature Space […]
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# How To Calculate Profitability Index In Excel
Understanding the profitability index is essential for investors and business owners looking to evaluate the potential returns on their investments. Excel, with its powerful computational abilities, is commonly used for this financial analysis.
This guide will walk you through the step-by-step process of calculating the profitability index in Excel. However, we will also explore why Sourcetable offers a more streamlined and user-friendly alternative for performing these calculations.
## Calculate Profitability Index in Excel
### Understanding Profitability Index
The Profitability Index (PI), also known as the profit investment ratio, measures the relationship between the costs and benefits of a proposed project. It ranks projects based on the value they create per unit of investment, using the Present Value of Future Cash Flows and the Initial Investment for calculation.
### Calculating PI in Excel
To calculate the Profitability Index in Excel, divide the Present Value of Future Cash Flows by the Initial Investment. Projects with a PI greater than 1 are considered value-creating and preferable, while those with a PI less than 1 are not profitable and tend to destroy value.
### Step-by-Step PI Calculation
In Excel, input the Present Value of Future Cash Flows in one cell and the Initial Investment in another. Use the formula "=PV of Future Cash Flows / Initial Investment" to get the PI. Excel's built-in functions can assist in calculating the Present Value if needed. A PI above 1 indicates a potentially profitable project.
### Comparing Multiple Projects
The Profitability Index is advantageous for comparing multiple projects, especially when considering Net Present Value. It provides a more accurate comparison by accounting for the initial investment, making it similar to the benefit-cost ratio.
For users without Excel, WPS Spreadsheet is a free alternative that supports Excel file formats. It offers a range of functions and formulas for complex calculations, including the Profitability Index. Like Excel, it allows for data analysis, sorting, filtering, and cloud integration for collaboration.
## Common Use Cases
• Comparing the relative profitability of multiple investment projects
• Evaluating the cost-effectiveness of a proposed capital expenditure
• Assisting in the prioritization of projects under capital constraints
• Measuring the value created per unit of investment
• Conducting sensitivity analysis on the financial viability of potential investments
## Excel vs. Sourcetable: A Comparative Analysis
Discover the power of Sourcetable, an innovative spreadsheet solution designed to streamline data integration. Unlike Excel, Sourcetable excels in aggregating data from multiple sources into a single, cohesive interface.
Experience the future of data manipulation with Sourcetable's AI copilot. This advanced feature surpasses Excel's capabilities by assisting users in formula creation, offering templates, and more via an intuitive chat interface.
Embrace the simplicity of Sourcetable's spreadsheet-like environment, a user-friendly alternative to Excel's complex functionalities. Sourcetable is tailored to enhance productivity for those seeking a seamless data handling experience.
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