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https://projecteuclid.org/journals/abstract-and-applied-analysis/volume-2014/issue-none/The-Generalized-Projective-Riccati-Equations-Method-for-Solving-Nonlinear-Evolution/10.1155/2014/259190.full
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math
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We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
E. M. E. Zayed. K. A. E. Alurrfi. "The Generalized Projective Riccati Equations Method for Solving Nonlinear Evolution Equations in Mathematical Physics." Abstr. Appl. Anal. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/259190
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224645595.10/warc/CC-MAIN-20230530095645-20230530125645-00299.warc.gz
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CC-MAIN-2023-23
| 662 | 2 |
https://www.transentis.com/page/stock-and-flow-diagrams
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math
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The last section on Causal Loop Diagrams
showed that to go beyond simply analyzing and visualizing the feedback structure of a system, a more powerful technique is needed:
a technique that visually distinguishes between the parts of the system and what causes them to change
a technique that allows for the precise – quantitative – specification of all the system’s parts and their interrelation
a technique that can provide a basis for simulating the behavior of the system over time
In short: we need a technique that enables us to create a business prototype of the system that will allow us to explore its behavior and to test the effect of changes to the system’s structure and the policies governing its behavior. Stock and flow diagrams, along with the mathematical expressions that specify each construct, provide such a technique.
What Exactly Are Stock And Flow Diagrams?
Stock and flow diagrams provide a richer visual language than causal loop diagrams, we distinguish between six main kinds of elements: stocks, flows, converters, connectors, sources and sinks. These elements are explained below and visualized in the following diagram:
Stocks. A stock represents a part of a system whose value at any given instant in time depends on the system's past behavior. The value of the stocks at a particular instant in time cannot simply be determined by measuring the value of the other parts of the system at that instant in time – the only way you can calculate it is by measuring how it changes at every instant and adding up all these changes.
This sounds more complicated than it is, so let us look at a simple example: driving a car along the motorway. Say you start driving at 8:00 AM and you want to know how far you have driven at 10:00 AM. We know that the only factor that determines this is the speed you were driving at. But it is not enough to just know your current speed at 10:00 AM, you actually need to know exactly how fast you were driving at every instant in time between 8:00 AM and 10:00 AM to calculate this. In this example, the distance you have driven is a stock – if you look at the dashboard in your car, you will most likely find a representation of this stock on your car’s dashboard: the mileage counter (odometer). On diagrams, stocks are represented by rectangles.
Flows. Flows represent the rate at which the stock is changing at any given instant, they either flow into a stock (causing it to increase) or flow out of a stock (causing it to decrease).
To continue our example above, the car’s velocity at any particular instant is a flow that flows into the mileage counter stock. It is important to note here that the distinction between stock and flow is not absolute – from the point of view of the mileage counter the velocity is a flow. But the velocity itself most likely also changes and depends on the acceleration and deceleration. So, even though we can determine the current velocity almost instantaneously (this is done by the speedometer), we again cannot explain why the velocity is at its current level without knowing the system's past behavior. On diagrams, flows are represented by small valves attached to flow pipes that lead into or out of stocks.
Converters. Converters either represent parts at the boundary of the system (i.e. parts whose value is not determined by the behavior of the system itself) or they represent parts of a system whose value can be derived from other parts of the system at any time through some computational procedure.
To continue our motorway example, we could assume that acceleration and deceleration are determined by outside circumstances (e.g. such as the positions of the accelerator and brake). In this case, we would model both the accelerator and brake positions as converters. On diagrams, converters are represented by small circles.
Connectors. Much like in causal loop diagrams the connectors of a system show how the parts of a system influence each other. Stocks can only be influenced by flows (i.e. there can be no connector that connects into a stock), flows can be influenced by stocks, other flows, and by converters. Converters either are not influenced at all (i.e. they are at the systems' boundary) or are influenced by stocks, flows and other converters.
Source/Sink. Sources and sinks are stocks that lie outside of the model's boundary – they are used to show that a stock is flowing from a source or into a sink that lies outside of the model's boundary. On diagrams, sources and sinks are represented by small clouds.
The notation used in stock and flow diagrams was originated by Jay Forrester in his book “Industrial Dynamics”. It was based on a hydraulic metaphor: the flow of water into and out of reservoirs. Hence the names of these elements and their visualization.
The key feature of a stock and flow diagram is that each construct can be precisely specified using a mathematical formalism – viewed from a mathematical perspective, such fully specified stock and flow models are just a way of visualizing a corresponding set of integral equations.
In most cases these integral equations cannot be solved analytically, but due to the computing power available today even on portable laptops, it is possible to solve these equations numerically using computer simulation techniques.
To make these definitions even more tangible, let us continue the simple project management example we started in the section on causal loop diagrams – to make reference easier, the diagram is repeated here:
Let us try and sort the parts in this diagram according to the categories we identified above:
We can make our thinking explicit in the following stock and flow diagram (note that we have added a new stock to represent the closed tasks):
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510528.86/warc/CC-MAIN-20230929190403-20230929220403-00870.warc.gz
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CC-MAIN-2023-40
| 5,788 | 22 |
https://forum.solidworks.com/thread/26464
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math
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I have two gears, worm gear and worm wheel. And I want to simulate them so that one can rotate. Distance between axis is 65.5. Can you help me to simulate? Thanks
Thanks Mr. Deepak Gupta, I find that what you mean after I install my version of SolidWorks from 2007 to 2009.
There's one thing I want to ask you, that is how to work with the "cam" for the application in the chain that connects between 2 sprockets. Where I want to transfer the transmission of gear box from gear motor sprocket to follower sproket. Assume the ratio of gear sprockets between motor and follower is 1:3.
Also how the application for the 3D model if all chains are connected. Thanks
Check this post and look at the video. Are you looking for something of this kind.
Retrieving data ...
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178370239.72/warc/CC-MAIN-20210305060756-20210305090756-00497.warc.gz
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CC-MAIN-2021-10
| 764 | 6 |
http://jayrenkwan.blogspot.com/2011/
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math
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Let's see , i still remember in the first day of 2011 , i wrote a blog post which are 11 thing i want to achieved in 2011 at here . Shall see how many i really achieved in 2011 .
#1 I want to study hard and play hard . ( Achieved )
I did study hard and play hard in this year ny attending a lot of event and gathering with friend.
#2 I want to work for many part time job ! I need money ! ( Half achieved )
I do work for a few part time job , but not many , but i still earn some money this year.
#3 I want to find a girlfriend ( Half Achieved )
I do found a girlfriend this year , but for some reason , we broke up for good .
#4 I want everyone to be happy , healthy , and safe ( Half Achieved )
Well , there are not everyone is happy , but thankfully they are healthy and safe.
#5 I want to know more new friend . ( Achieved )
This one definitely achieved , i get to know a lot of new friend , and is really good to have them as my friend.
#6 I want to blog more. ( Achieved )
I blog a lot this year .
#7 I want to join more movie screening / Event . ( Achieved )
I definitely join and attend more movie screening / event and i loving it.
#8 I want to change to a wifi phone ( If got money ) ( not achieved )
For now , i dont think i need a wifi phone as i got my laptop.
#9 I want to do more good deed , especially participate in charity event . ( Half Achieved)
I do participate in some charity event and do good deed , and i will continue do more good deed .
#10 I want to be a happy person with positive mind . ( Half Achieved )
I do try to be a happy person with postive mind but sometime i still emo and being negative minded.
#11 I want to be more independent . ( Not achieved )
I still think that i not independent enough.
And here's the 11 thing i gained in 2011 as of today .
#1. I joined my first marathon and get a finisher medal and certificate .
#2. I fell in love and fall out of love .
#3. I met some famous celebrity and took photo with them.
#4. I worked for my first ever sampling job .
#5 I enjoy meeting new friend and i had widen my social network .
#6 I am not that shy and start to talk more and be more sociable .
#7 I finally get to have a new and good camera .
#8 I gained weight .
#9 I completed my year 2 degree course.
#10 I tweet more.
#11 I officially a Diploma holder .
So there you go , farewell 2011 ! Let's welcome 2012 , the year of dragon , my year . Hope 2012 will be a better year for all of us.
Till then , bye.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948604248.93/warc/CC-MAIN-20171218025050-20171218051050-00004.warc.gz
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CC-MAIN-2017-51
| 2,454 | 37 |
http://behscraftfair.com/anytime-fitness-dtivly/how-to-measure-an-angle-with-a-ruler-df61b7
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math
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how to measure an angle with a ruler
Given an acute angle (the technique can be modified for obtuse angles), measure off a distance on each ray. To measure an angle and create an angled guide line, follow these steps: Select the Protractor tool (). We can measure lines using a tool called a ruler. Save yourself hours of frustration trying to get elements to line up by just measuring. How to Measure Angles with a Ruler. Click on the midpoint of a created ruler to convert it to a protractor. Be as accurate as possible with the measurements, as this will ensure that the result is as accurate as measuring the angle with a protractor. This button will tell you the angle that produced that particular sine. The points inside the angle lie in the interior region of the angle, and the points outside the angle lie in the exterior region of the angle. Both the ends and the corner of the measure tool can be snapped to a Try to measure the angles A, B and C inside the triangle. To retrieve the measurements from the blueprint, you need to use a specialty ruler referred to as a "scale or architects rule." create their own “angle ruler” (or “protractor,” if you want to use the formal term). No matter how well you try to be prepared, sometimes the unexpected occurs and you do not have the right tools at hand to do a job. if , then the approximation is. The center point is fixed to the cursor. By clicking and dragging the mouse button, you can determine the angle and number of pixels between the point of click and where the mouse pointer is located. All measurements except the angle are calculated in the unit of measure currently set in the Units & Rulers preference dialog box. This line will be referred to as the leg. create their own “angle ruler” (or “protractor,” if you want to use the formal term). In this tutorial, you will learn how to use the Ruler tool to measure and position an object in Photoshop. Once you measure the angle, write the reading between the two lines (as shown in the illustration). Provide students with various cut-out angles that they can measure with this angle ruler. if , then the approximation is. What is the difference between a theorem, a lemma, and a corollary? A ruler uses units called inches or centimeters to measure how long things are. Either of the other angles (the angles that are less than 90-degrees) can be used to define certain functions, called "trigonometric functions." He has written advertisements, book and video game reviews, technical articles and thesis papers. Now move the cross slider so a pair of pins line up with the angle you are measuring. The Measure Tool is used to gain knowledge about pixel distances in your working image. The architects rule, shaped like a triangle, has six sides. The cursor changes to a protractor. Holding down Ctrl enables snap to edges and vertices. The AR measure app has nine measurement modes; ruler, magnetometer, trajectory, face mesh, marker pin, angles, height, square, and level. Measuring an Object using the Ruler Tool Step 1: To operate this tool, all you require is to select it from the toolbar … This is in order to amend a - 7168033 He started working with Mechanical Turk and then started contracting with individuals and companies directly via the Web. Look at the protractor in the picture below to see how this works! This unique template tool is … You can easily measure the angle of any object around you by taking a picture and uploading it, then simply dragging the midpoint of the protractor over the vertex of the angle. This Interactive Ruler PowerPoint demonstrates a step-by-step process of measuring length. This brilliant, illustrated PowerPoint shows children how to correctly measure length to the nearest centimetre and millimetre. Ideal for maths lessons on measurement, children can follow along by measuring objects with their own ruler. This presentation can equally be … Extend the tape measure between the marks. Find the measure of each angle. A selected ruler can be deleted with Delete or X. You know what they say: Measure Twice. Step 3. (Use either a compass or a ruler to do so.) To measure an angle, hold the sky ruler up to your eye with the end touching your cheekbone. Now, add the acquired angle to 180°. How to Draw Angles Exceeding 180° Using a Semicircular Protractor Although drawing angles more than 180° using a regular semicircular protractor may seem like a tough job, it isn’t so. Each side will have two sets of dimensions, one starting from the left-hand side of the … * Draw a straight line with the ruler, and mark a point on it. Universal Desktop Ruler allows for measuring any angle on screen To measure an on-screen angle, choose the "Angle" menu item. The measure of two adjacent angles of a quadrilateral are 110° and 50°and the other two acute angles are equal. Professional Template Tool Practical Multi-Angle Ruler Layout Tool. The result of this calculation is the measurement of the angle you wanted measured. Divide the leg's length by the length of the hypotenuse using the calculator. Press the "inverse sine" button. To do this we are going to use one of the most commonly used tools in the … A good way to start thinking about the […] Measure the length of both the hypotenuse and the leg with the ruler. This article presents a neat way to approximate the measure of an angle using a ruler and discusses the accuracy of various versions of the method. Drag the protractor and rotate it using arrow keys. The rest of the article is devoted to looking at whether 60 is the best constant to be used in this approximation formula. It has a degrees setting so that you can set it at a precise angle, if necessary. The set square with integrated protractor is almost transparent, so you can have it on the screen, while you are working with the applications below. How to Use Ruler Tool in Photoshop? OK, so I figured out that if this is your question the below is exactly how to do that. Draw a vertical line connecting the 2 rays of the angle. Make a Sugihara Circle/Square Optical Illusion Out of Paper, Playing the probabilities in Settlers of Catan, E-Z Pass, speeding tickets, and the mean value theorem. Post was not sent - check your email addresses! It will usually be marked with the abbreviation "sin" with a negative 1 written above it and to the right. It’s the adorable angle. Actually, it’s just a pinch. Be careful which angle … The angle between the fence lines is now exactly 90 degrees. First, we should start with a 60 degree angle. Constructing an angle or triangle using a Protractor, Ruler and Pencil. Without changing its distance from the post, adjust the position of the second mark until it is exactly 5 feet distant from the first. This line will be called the base. Also, if you intend to have an angle measured precisely, all you need to do is a couple a ruler with a compass to measure the angle and draw a similar one. And learn how to measure objects and people more easily using the LiDAR Scanner on iPad Pro 12.9-inch (4th generation), iPad Pro 11-inch (2nd generation), iPhone 12 Pro, and iPhone 12 Pro Max. The FULL CIRCLE is 360° (360 degrees). Hook the speed square lip over the edge. Types of angles. A speed square is essentially a triangle-shaped ruler used for calculating angles or as a straight edge. Measuring angles is pretty simple: the size of an angle is based on how wide the angle is open. You should use a special device for measuring angles - a protractor. obviously, if , then the approximation is . A speed square has a lip on one of its sides that allows you to place it up against the edge of a board or other piece of material for accurate measurements. The ruler pivots to any position you want: horizontal, vertical, or any angle in between. Jason Thompson has been self-employed as a freelance writer since 2007. * Measure two units along the line and make a … These unique features make Virtual Nerd a viable alternative to private tutoring. In this DIY project guide you will learn how to accurately calculate an angle using a selection of different tools including protractors and angled bevels and then precisely mark the angle onto a given object ready for cutting. Multi Angle Measuring Ruler, Angle Template Tool, Aweohtle Six-sided Aluminum Alloy Metal Angle Finder Tool，Layout Tools Woodworking Ruler，Carpenter Ruler Universal Opening Locator for Construction 4.5 out of 5 stars 1,452. ... Another approach to measure angles via smartphone is based on image and photo analysis. Measuring an angle Measure an angle when you want to duplicate that angle elsewhere in your model or create plans, such as for a woodworking project. All measurements except the angle are calculated in the unit of measure currently set in the Units & Rulers preference dialog box. A protractor uses units called degrees to measure angles. You know what they The angle between those two rays is what will be measured. Save yourself hours of frustration trying to get elements to line up by just measuring. Ball State University: Basic Trigonometry, Calculator with inverse trigonometric functions. A straight angle. MB-Ruler helps you to measure distances and angles on the screen and distances on a map. A speed square is essentially a triangle-shaped ruler used for calculating angles or as a straight edge. In this non-linear system, users are free to take whatever path through the material best serves their needs. This gives you the sine of the angle you want to determine. Easy. This is used to measure angles and circles, the conveyors are transparent, circular or semicircular ruler. Many students have difficulty using a protractor to measure angles. If your document has an existing measuring line, selecting the Ruler tool causes it to be displayed. The symbol for degrees is a little circle °. Step 2. He claims that is approximately degrees. He attributes the discovery to a student of his, Tor Bertin. Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (. Method 1of 3:Acute 1. We measure angles using a tool called a protractor. Digital ruler-based angle meter. A ruler and compass construction refers to constructions using an unmarked ruler and a compass. The straight edge is where the pivot point begins and where you will compute and determine angles. Using trigonometry, it is easy to see that . To determine the number of degrees in an acute angle,... 2. Is or an inclusive or or an exclusive or? Constructing an angle or triangle using a protractor 1. Please note that AR Ruler app works only on ARCore-supported devices. Measure … Assuming sine takes angles in radians, but that is measured in degrees, this becomes . 3. Step 1. Along the outside of the protractor are 2 arcs of numbers. A sine is a trigonometric function. Use the outer arc if the angle you're measuring opens to the left. He illustrated this technique using . On Windows touch devices, you can use the Ruler on the Draw tab of the Ribbon to draw straight lines or to measure distance. Make sure that you have your calculator set to degrees, radians or gradients depending on which unit in which you want your angle measured. If you want to measure something smaller, just compare the angle on the screen with the protractor; If that thing is bigger, you can take a photo and upload it, then compare it with this transparent protractor; Acute angle. Find the degrees in the angle using the correct scale. A protractor is half of a circle. A half circle or a straight angle is 180°. Use the inner arc if the angle you're measuring opens to the right. If your document has an existing measuring line, selecting the Ruler tool causes it to be displayed. It measures from 0 to 180 degrees. Online angle meter Sometimes you need to measure angles, but you don't have a protractor at hand. How to measure an angle with a speed square: Place the speed square along the top edge of the object you are measuring. if then the approximation is. Also, because this tool has a ruler edge as well, you can trim off the appropriate length from a board while getting the correct angle for your edge in a single step, rather than two. Degree: The basic unit of measure for angles is the degree.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154053.17/warc/CC-MAIN-20210731043043-20210731073043-00289.warc.gz
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CC-MAIN-2021-31
| 12,296 | 2 |
https://webwork-ptx.aimath.org/webwork2/html2xml?courseID=anonymous&userID=anonymous&password=anonymous&course_password=anonymous&answersSubmitted=0&displayMode=MathJax&outputformat=simple&problemSeed=200&sourceFilePath=Library/Rochester/setDiffEQ5ModelingWith1stOrder/ns7_4_31c.pg
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math
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A tank contains
(a) What is the concentration of our solution in the tank initially?
(b) Find the amount of salt in the tank after 4 hours.
(c) Find the concentration of salt in the solution in the tank as time approaches infinity.
WeBWorK © 2000-2021 | host: https://webwork-ptx.aimath.org | course: anonymous | format: simple | theme: math4
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572408.31/warc/CC-MAIN-20220816151008-20220816181008-00553.warc.gz
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CC-MAIN-2022-33
| 343 | 5 |
http://dynamicscience.com.au/tester/solutions1/flight/velocitytimesgraphs.html
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math
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Displacement, velocity and acceleration of a falling ball.
Consider the video on the left. It shows a ball, at rest, being dropped from a height.
By pausing the video it is possible to see the time and displacement of the ball as it falls.
1. Using the graph paper provided roduce a:
- displacement vs time graph
- velocity vs time graph
2. Calculate the acceleration of the ball due to Earth's gravitational field.
We have captured four reference points along the ball's path at the following times.
3.12 seconds. Click to see the image
3.15 seconds. Click to see the image
3.28 seconds. Click to see the image
3.30 seconds. Click to see the image
Create a properly formatted table of data.
Use the graph paper on the following pages to construct the graphs.
Click to download a Word doc
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712297295329.99/warc/CC-MAIN-20240425130216-20240425160216-00232.warc.gz
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CC-MAIN-2024-18
| 788 | 15 |
http://www.mk-songbenqing.com/info/1077/12241.htm
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math
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讲座题目：Phase transition of eigenvalues in deformed Ginibre ensembles
讲座地点： 腾讯会议, 3428925924, 密码: 123456
报告摘要：Consider a random matrix of size N as an additive deformation of the complex Ginibre ensemble under a deterministic matrix X0 with a finite rank, independent of N. When some eigenvalues of X0 separate from the unit disk, outlier eigenvalues may appear asymptotically in the same locations, and their fluctuations exhibit surprising phenomena that highly depend on the Jordan canonical form of X0. These findings are largely due to Benaych-Georges and Rochet, Bordenave and Capitaine, and Tao. When all eigenvalues of X0 lie inside the unit disk, we prove that local eigenvalue statistics at the spectral edge form a new class of determinantal point processes, for which correlation kernels are characterized in terms of the repeated erfc integrals. This thus completes a non-Hermitian analogue of the BBP phase transition in Random Matrix Theory. Similar results hold for the deformed quaternion Ginibre ensemble.
报告人简介：Lu Zhang, School of Mathematical Sciences, student of University of Science and Technology of China, Hefei 230026, P.R. China.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334992.20/warc/CC-MAIN-20220927064738-20220927094738-00182.warc.gz
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CC-MAIN-2022-40
| 1,207 | 4 |
https://b28mathstutor.weebly.com/blog/a-bit-of-magic-with-maths
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math
|
Think of a number, multiply it by 2 and take away 6.
Now halve your answer and add 3. You should end up back at the number you first thought of.
Can you use algebra to explain why this happens?
Hint: start by using a letter for the number that you first thought of.
Try it before you read on...
Okay, so let's call the number that you started with "n".
We're going to start by "dressing it up" to make an algebraic expression.
"Think of a number, multiply it by 2 and take away 6."
If you multiply n by 2 then you get 2n.
Now take away 6 and you have 2n - 6.
Now we're going to "undress" it again to get the n on its own... but by a slightly different route!
"Now halve your answer and add 3."
How can we halve it? Well, 2n - 6 is the same as 2 lots of n and one lot of -6...
... and -6 is the same as 2 lots of -3
... so if you halve 2n - 6 then you get half of 2n and half of -6, giving n - 3.
The last step is easy: we now have n - 3, i.e. 3 less than n. If we add 3 to that then the -3 and the +3 cancel out
and we're left with just n, the number we started with!
How about this one?
Think of a number, add 4 and treble it (i.e. multiply it by 3). Take away 12. Tell me what you got and I'll tell you what number you started with. How do I do it?
Think it through and see if you can work it out yourself first.
Of course, I could do the whole calculation backwards (add 12, divide the answer by 3 and then take away 4) but the numbers are carefully chosen to make it much easier than that. In fact, all I have to do is to divide by 3. It's a bit like going through a labyrinth of side streets and eventually finding yourself just a few steps away from where you started!
Here's why: If you start with n and add 4 then you have n + 4. Treble it then you get 3 lots of n + 4, i.e. 3(n + 4).
This is the same as 3 lots of n and 3 lots of 4, which we can write as 3n + 12 (this is called multiplying out the bracket).
When you take away the 12 you're left with just 3n...
... so to get back to n I just have to divide by 3.
What we're doing here - in a mathematical sense - is building up equations and then solving them.
In the first example, you found the value of 2n - 6 and then "undressed the n" to get back to its original value.
In the second one you found the value of 3(n + 4), multiplied out the bracket and again "undressed the n" to find its value.
Here's a slightly harder one for you to mull over:
Think of a number. Double it, add 2 and multiply your answer by 3. Take away 6 from your answer. Now take away the number you first thought of.
If you were to tell me the number you'd ended up with, how could I work out the number you started with?
Can you make up some more of your own?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824115.18/warc/CC-MAIN-20181212181507-20181212203007-00442.warc.gz
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CC-MAIN-2018-51
| 2,699 | 32 |
https://www.maxvalue.com/pgloss.htm
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math
|
"A good science and engineering decision is a good business decision."
|Decision Precision training and consulting
This brief glossary will help you become familiar with key words that will be used in the course. It will be especially helpful for persons whose first language is not English and also for others less familiar with economic evaluation and probability concepts.
You will not be expected to memorize a lot of definitions. However, it is important to be able to recognize important terms. When you to understand a concept well, you will be able give someone a satisfactory definition or explanation.
The post-course reference handbook, Decision Analysis for Petroleum Exploration, contains an extensive glossary.
a repeated or systematic distortion of a value or statistic, imbalanced about its mean.
an up-front payment to obtain lease acreage a concession; also called lease bonus and signature bonus.
the amount of money or equivalents invested in a business. Capital projects, compared to expenses, are those investments that are capitalized (i.e., expensed across time through depreciation, depletion or amortization).
cashflow (or cash flow)
money entering or leaving the company treasury. Net cashflow is receipts net of cash expenses (including taxes paid) and capital expenditures.
an experiment, process or measurement whose outcome is not known beforehand. Represented in decision models as (synonymous) random variable, stochastic variable, or chance node.
complementary outcomes (events)
two distinct and different outcomes which together represent all the possible outcomes of a chance event.
determining a future value by multiplying periodic interest factors; interest is earned on the interest. The inverse of PV discounting.
the probability that an event will occur given that another event has already occurred.
a chance event having an infinite number of possible outcomes along a continuum.
relationship between variables such that changes in one (or more) variables is generally associated with changes in another. Synonymous with association. Correlation is caused by one or more dependency relationships.
cost of capital (CoC)
a price, expressed as an effective interest rate, that a company must pay for its funds.
cumulative distribution function (CDF)
the integration of a PDF, left-to-right, showing the probability (0-1, y-axis) of being ≦ the x-axis value. Has an S shape.
a graphical representation of a decision problem and the expected value calculations, consisting of decision, chance and terminal nodes connected by branches.
dependence or dependency
when the outcome of one chance event influences, or is influenced by, the outcome of another chance event. Dependent relationships are often represented by formula relationships or with correlation coefficients. Opposite of independence. Partial or shared dependency is the cause of correlation.
said of a model where all parameters are fixed or "determinate." Single-point solution. The antonym is stochastic (see).
discounted cash flow analysis (e.g., as in DCF analysis)
projecting a future cashflow stream and determining its present value.
discrete event or distribution
a chance event that as a finite number of outcomes, e.g., the number of "heads" from flipping 10 coins. Compare continuous event.
a price or cost increase with time, as a result of the combined effects of real price growth and inflation. Any of these can be positive or negative.
general term for any type of analysis used for asset appraisal, feasibility study, engineering evaluation, project assessment, and all other types of analyses related to decisions.
expected monetary value (EMV)
expected value of the NPV outcome. EMV = E(NPV) = EV NPV.
expected value (EV)
the probability-weighted average outcome. This is the same as the mean statistic. The "expected" word comes from "mathematical expectation" and EV not the outcome to expect.
an agreement to release a portion of ownership in a lease or license to another party in return for assumption of certain obligations.
a judged or predicted view of the event sequence or future state of the world. Usually calculation or estimation is involved.
frequency distribution (FD)
a graph or other characterization of the observed values in a sample data set. Commonly graphed as a frequency histogram (bar chart).
a graph showing frequency of observations counted in segments of the value range, usually presented as a bar chart with vertical bars.
the characteristic where one event does not affect the occurrence of another, and vice versa.
a rising general level of prices and wages in an economy, expressed as an annual percentage rate.
1. amount paid for the use of funds, e.g., interest earned by savings in a bank account.
2. ownership in a project, asset or entity.
the believed capacity for guessing accurately. Judgments based upon feelings and not logical thinking.
chance event comprised of two or more event outcomes occurring together.
a contract that temporarily transfers certain rights to an asset, e.g., mineral rights underlying land surface. Concession licenses are similar.
incremental difference, said of cashflows, cost of capital, profit, etc. A marginal project is one that is borderline economic, where the incremental value is negligible.
the arithmetic average of equally-likely outcomes or a set of observations. The probability-weighted average. Synonymous with expected value (EV) when referring to a probability distribution.
the most central value of a population or sample set. Point where it is equally likely to be above as below or that crossover point.
the particular outcome that is most likely. This is the highest point on a probability density function.
Monte Carlo simulation (simulation)
a process for modeling the behavior of a stochastic (probabilistic) system. A sampling technique is used to obtain trial values for key uncertain model input variables. By repeating the process for many trials, a frequency distribution is built up which approximates the true probability distribution for the system's output.
mutually exclusive outcomes
the situation where each outcome is distinct from all others.
meaning that only one alternative or project can be done, to the exclusion of others.
net cash flow (NCF)
cash flow from operations, net of capital expenditures, overhead, and taxes.
the frequently-encountered, bell-shaped distribution. Also called Gaussian distribution.
1. (noun) the purpose of an organization. Often, less correctly, used to mean a goal.
2a. (adjective) unbiased.
2b. (adjective) from comprehensive understanding or abundant data.
one that is free from bias, requiring bias-free assessment inputs, objective value measure, and calculation integrity that doesn't introduce bias.
adjective meaning the best, in the context of the decision situation. The optimum (a noun) on a value curve or surface determines the optimal values of decision variables.
a particular result or sample of a chance event
a family of prospects that share a common geologic history of source deposition, hydrocarbon generation, migration, reservoir development, etc.
a company's or individual's holdings of assets, projects, investments, or opportunities.
present value (PV or NPV)
the value of a future cashflow stream or amount as of today or earlier date. The sum of discounted cash flow (DCF) values. The discount rate represents policy or attitude toward time preference of money.
the likelihood of an event occurring, expressed as a number from 0 to 1 (or equivalent percentages). Synonyms: chance, likelihood. The sum of the probabilities of all possible outcomes equals 1.
probability density function (PDF)
a mathematical or graphical representation that represents the likelihood of different outcomes from a chance event. The integral of a PDF over its entire range equals 1.
a view of the sequence of events or future state of the world under an assumed set of assumptions. Compare forecast.
a defined local area in which a company hopes to discover valuable minerals.
a number usually obtained from sampling a 0-1 uniform distribution and used for event sampling in Monte Carlo simulation.
estimated volumes of remaining economically-recoverable mineral resources with current technology. Usually, this means proved reserves. Less certain categories are classified as probable and possible.
income recorded on the company's books. Realized in cashflow as cash receipts.
the quality of a system that relates to the possibility of different outcomes. There are unknowns about conditions of nature and about how systems operate. Risk is approximately synonymous with uncertainty for most people.
dislike of risk; conservative risk attitude.
obtaining examples from a parent population (PDF) or from measurement or experiment.
a possible sequence of events and a future state of the world.
a number that describes some attribute (location or shape) of a population or sample observations. The most common statistics are mean, median, mode, standard deviation, and variance.
stochastic (pronounced stow-KAStic)
an adjective meaning probabilistic, statistical, chaotic or random. The antonym is deterministic (see).
probability assessment or judgment that is, at least in part, based on opinion, hunches, feelings, and/or intuition. uncertainty often used synonymously with risk.
a value or symbol in a model that has a value or can be evaluated. Synonyms: parameter, input value.
working interest (W.I.)
the fraction of the cost burden borne by a working interest party (part-owner); participation or ownership fraction. Working interest times the wellhead production equals company gross production.
Copyright © 1996-2015 by John R. Schuyler. All Rights Reserved
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| 9,744 | 89 |
http://www.houserepairtalk.com/showthread.php?t=8439
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math
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Handy man, you are correct. I planned on adding 2x8 rafter ties. So I could NOT add the ties above that 4 ft. line? The door will come into the space near the point where the vaulted ceiling will flatten out.
The problem is that if I put in a regular (6'8") door, when you open it, you could be staring at 3-4 inches of ceiling. If I raise the ties, I get outside of that 1/3 rule.
My option are to shorten the door (not sure inspector would approve of that)
Lower the ties so they are exactly at 80", keeping most of the tie in the lower 1/3 but also having a portion in the upper 2/3 (if that makes sense). Also, not sure if inspector would like that option either. Any idea of that would still suffice?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190753.92/warc/CC-MAIN-20170322212950-00580-ip-10-233-31-227.ec2.internal.warc.gz
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| 705 | 4 |
http://duyendangviet.vn/epub/discrete-and-continuous-nonlinear-schroedinger-systems
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math
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By M. J. Ablowitz, B. Prinari, A. D. Trubatch
During the last thirty years major development has been made within the research of nonlinear waves--including "soliton equations", a category of nonlinear wave equations that come up usually in such components as nonlinear optics, fluid dynamics, and statistical physics. The vast curiosity during this box could be traced to realizing "solitons" and the linked improvement of a mode of answer termed the inverse scattering remodel (IST). The IST strategy applies to non-stop and discrete nonlinear Schrödinger (NLS) equations of scalar and vector sort. This paintings provides an in depth mathematical examine of the scattering thought, bargains soliton suggestions, and analyzes either scalar and vector soliton interactions. The authors offer complex scholars and researchers with an intensive and self-contained presentation of the IST as utilized to nonlinear Schrödinger platforms.
Read Online or Download Discrete and continuous nonlinear Schroedinger systems PDF
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Additional resources for Discrete and continuous nonlinear Schroedinger systems
37) This symmetry in the potential induces a symmetry between the Jost functions analytic in the upper k-plane and the Jost functions analytic in the lower k-plane. 2 The inverse scattering transform for NLS 29 In turn, this symmetry of the Jost functions induces a symmetry in the scattering data. 3). 38a) ∗ . 39b) and consequently ρ(k) ¯ = ∓ρ ∗ (k) Im k = 0. 39a) it follows that k j is a zero of a(k) in the upper k-plane iff k ∗j is ¯ a zero for a(k) in the lower k-plane. 36), J = J¯ and k¯ j = k ∗j , c¯ j = ∓c∗j j = 1, .
54a) −2ikx ¯ (1) N (x, k)dk. 54b) Case of poles ¯ Suppose now that the potential is such that a(k) and a(k) have a finite number of simple zeros in the regions Im k > 0 and Im k < 0, respectively, which we J J¯ denote as k j , Im k j > 0 j=1 and k¯ j , Im k¯ j < 0 j=1 . We shall also assume ¯ ) = 0 for any ξ ∈ R. 31b). 56) with denoting the derivative with respect to the spectral parameter k. Note that the equations defining the inverse problem for N (x, k) and N¯ (x, k) now depend J¯ J on the extra terms N j (x) j=1 and N¯ l (x) l=1 .
1 that if q, r ∈ L 1 (R), the Neumann series of the integral equations for M and N converge absolutely and uniformly (in x and k) in the upper k-plane, while the Neumann series of the integral equations for M¯ and N¯ converge absolutely and uniformly (in x and k) in the lower k-plane. These facts immediately imply that the Jost functions M(x, k) and N (x, k) are analytic func¯ tions of k for Im k > 0 and continuous for Im k ≥ 0, while M(x, k), and N¯ (x, k) are analytic functions of k for Im k < 0 and continuous for Im k ≤ 0.
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http://www.coolissues.com/mathematics/Riemann/riemann.htm
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math
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PROOF OF RIEMANN'S HYPOTHESIS
Riemann's hypothesis is proved using Riemann's functional equation
This page is now subject to the author's counterexample at http://www.coolissues.com/mathematics/Riemann/disproof.htm
The famous conjecture known as Riemann' s hypothesis1 is to classical analysis what Fermat's last theorem is to arithmetic. Euler (1737) noted that the formula
. . . . . . . . . . . . . . . . . . . . . . .x>1 . . . . . . . . . . . . . . . . . (1)
the sum extending to all positive integers n, and the product to all positive primes p. The necessary conditions of convergence hold for complex values of s with real part >1. Considering as a function of the complex variable s, Riemann (1859) proved that satisfies a functional equation
. . . . . . . . . . . . . . . .. . . . (2)
which led Riemann to the theorem that all the zeros of , except those at s=-2,-4,-6, . . . , lie in the strip of the s-plane for which where x is the real part of s. Riemann conjectured that all the zeros in the strip should lie on the line x= ½. Attempts to prove or disprove this conjecture have generated a vast and intricate department of analysis, especially since Hardy (1914) proved that has an infinity of zeros on x= ½ .2 The question is still open in 2008. A prize is available to prove or disprove Riemann's hypothesis.3
Finding Zeros Using Riemann's Zeta Function
When extended to values in the critical strip Riemann's zeta function is written as
. . . . . . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . (3)
It has already been shown that all zeros are in the critical strip and that they are symmetric about the critical line x= ½.4 I will now show that all zeros are on the critical line x= ½ and that functional equation (2) presents a problem.
Riemann's functional equation can be restated as in which at all points in the critical strip. Since functions and are single valued at each point in the critical strip they can be written in terms of their real and imaginary partsand in which
. . . . . .
. . . . . . . . . . . k=lnn (4)
in which k=lnn is the natural logarithm of n. Note that k is an irrational number.
On the critical line x= ½ and in which s~ is the conjugate of s. Thus, if =0 on the critical line then, since u=u'=0 and v=v'=0, =0 and Riemann's functional equation is satisfied. At all other points in the critical strip and . Thus, if =0 in the critical strip where then, since and , 0 and Riemann's functional equation cannot be satisfied. Riemann's functional equation, therefore, precludes zeroes at points where in the critical strip. All zeroes in the critical strip are on the critical line x= ½.
When , m=0,1,2, . . . equations (4) reduce to
. . . . . . . . . . k=lnn . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .(5)
in which u=u'=0 when x=1/2, since infinite series are conditionally converging series which can be made to converge to zero by a suitable rearrangement of terms. Accordingly, on the critical line x=1/2 when , m=0,1,2, . . . Note that since k is an irrational number y is a rational number. See ADDENDUM for another way of finding zeroes of .
Zeroes of the Riemann zeta function-The Functional Equation Problem
The Riemann zeta function has zeroes at the negative even integers. These are called the trivial zeroes. They are trivial in the sense that their existence is relatively easy to prove, for example, from sin(os/2)being 0 in the functional equation. The non-trivial zeroes have captured far more attention because their distribution not only is far less understood but, more importantly, their study yields impressive results concerning prime numbers and related objects in number theory. It is known that any non-trivial zero lies in the open strip , which is called the critical strip. The Riemann hypothesis, considered to be one of the greatest unsolved problems in mathematics, asserts that any non-trivial zero s has x = 1/2. In the theory of the Riemann zeta function, the set when x = 1/2 is called the critical line.
The location of the Riemann zeta function's zeroes is of great importance in the theory of numbers. From the fact that all non-trivial zeroes lie in the critical strip one can deduce the prime number theorem. It is known that there are infinitely many zeroes on the critical line. And, directly from the functional equation (2), one sees that the non-trivial zeroes are symmetric about the axis x=1/2. Furthermore, the fact that for all complex (~ indicating complex conjugation) implies (emphasis intended) that the zeroes of the Riemann zeta function are symmetric about the real axis.
Such reliance on functional equation (2) is not warranted. Essentially, functional equation (2) says that values of the zeta function at s can be computed from its values at 1-s, i.e., for each non trivial zero at 1-s, the value of s is also a zero of . I find zeroes by using equations (4) and (5). Not withstanding functional equation (2), is a necessary but not sufficient condition for finding the value of . The reason is simple. As expressed in (4) and (5), (3) is a conditionally converging series which can be made to converge to any number value by a suitable selection of terms. Knowing , therefore, does not necessarily establish .
Unless x=1/2, series u and u' are different series. Depending from the way terms are selected. each series has many possible values, including zero. It follows that at each point x,y in the critical strip, and on the critical line, the value of is unknown. There is no symmetry about the critical line. However, there is symmetry when x=1/2. We can say for sure that on the critical line the value, including zero, of which appears at +y is the same value at -y.
The sufficiency, therefore, of functional equation (2) is obtained when u=u' in equation (5), i.e., when x=1/2. All zeroes are located on the critical line x=1/2 when
. . . . . m=0,1,2, . . . k=lnn . . . . . . . . (6)
from which I conclude ny is a rational number. This can occur only if y is an integer or, if y=p/q is a rational non integer when n=kq, where p,q,k are integers. In either case, y is a rational number. Thus,
. . . . . . . . . . (7)
which says zeroes of exist on the critical line at rational number locations y=p/q when n=kq.
Connecting Critical Line Zeroes and Prime Numbers
The Prime Number Theorem (PNT) states that the yth prime py is of the order (~) of ylogy or that the number of primes ~ y/logy. A consequence of the PNT is that which says that we can find knowing py, or find py knowing , within some order of magnitude. The PNT was proved by Hadamard and de la Vallee Pousson (independently) using Riemann's Hypothesis, after showing that the zeroes of Riemann's zeta function cannot lie too far off the critical line. It is now known that Riemann's Hypothesis produces the result =Li(y)+O(ylny) where Li(y)=is Gauss's integral and the O term is the order of the error.5 It is well known, therefore, that the PNT is an approximate predictor of the number of primes in any interval y.
In the present proof, Riemann's zeta function on the critical line when k=lnn, m=0,1,2, . . . Since y is a single dimensional number, n=n(m) and
m=0,1,2, . . . . . . . . . . . . . . . . . . (8)which gives the number of zeroes of in the interval m located on the critical line. If each side of equation (8) is multiplied by
There are several ways of finding zeroes of . In the foregoing, I use infinite series (3) which can be made zero in two ways, first, by finding the limits of the entire series and, second, by finding each term is zero. In doing the latter, I find equations (5) represent and when , m=0,1,2, . . .
Since is an analytic function at a point so, another way of finding its zeroes is by expanding it into a Taylor's series and finding that all its derivatives are zero
. . . . . . . . . . . .. . . . . . (11)
in which is the n'th derivative of . Again, (11) can be made zero in one of two ways. Here, I find that all derivatives are zero in the same manner was previously equal to zero. When so is a zero of , and the sum in (11) are zero. Accordingly, since
. . . . . . . . . . . . . . . m=0,1,2, . . . , n'=1,2, . . . . . . . . . .(12)
1 Chris Caldwell The Riemann Hypothesis (University of Tennessee atMartin) at http://www.utm.edu/research/primes/notes/rh.html
2 E.T. Bell, The Development of Mathematics, Dover Publications, New York 1972. page 315.
3 Enrice Bombieri's The Riemann Hypothesis (Clay Mathematics Institute) at h ttp://www.claymath.org/prize_problems/riemann.htm
4 Caldwell note 1 above
5 Chris Caldwell "How Many Primes Are There" pages 5-7 at http://www.utm.edu/research/primes/howmany/shtml
Copyright © 2003, 2008 by James Constant
By same author: http://www.coolissues.com/mathematics/sameauthor.htm
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| 8,772 | 46 |
https://studylib.net/doc/15162575/2004-exam-i
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math
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EnvEcon 1 / Econ 3 Quiz 1 P. Berck Fall 2004 Answer all four of the following questions in your blue book. Each of the four questions is worth five points for a total of 20 points. 1. Define a. Complements b. Elasticity c. Indifference Curves d. Name and in one sentence each explain two agricultural policies that are not price support policies (i.e., not loan rate or target price – deficiency payment) 2. Use the diagram to answer the following questions. Assume PW = 1. a. What is income on budget constraint II? b. What is the price of bread on each of the three budget constraints? c. What are two points on the demand curve for bread? d. What happens to the demand curve for bread as income increases – why? Wine 6 5 II I 2.5 III 5 6 Bread 3. Draw a diagram and use it to explain the “loan rate” agricultural price support program. Be sure to show quantities produced and consumed and government purchases. A set aside program takes land out of production. What does it do to the supply curve? To the amount of money government pays to support the price? 4. Draw a picture showing how a tax results in a decreased quantity supplied. Label amount paid by consumers, amount received by producers, and the before and after-tax quantity. How can a tax be used to reduce pollution? Compare the use of a tax and a quantity restriction (quota) that have the same effect on output. Which does a firm prefer?
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CC-MAIN-2024-10
| 1,414 | 1 |
https://newscholarshub.com/college-acceptance-rate-2022/
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math
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college acceptance rate 2022
college acceptance rate 2022
College Acceptance Rates
The acceptance rate is the percentage of applicants who are accepted to a college. For example, a 50% acceptance rate means that 1 out of 2 applicants were accepted into that school. College application acceptance rates can be reported in different ways. A regular way to report the acceptance rate is to include all applicants (that includes first-time students as well as transfers) and only include those who have been accepted into the school for full-time enrollment.
On top of this, there are different factors that go into calculating an acceptance rate — here’s a general breakdown:
- Total number of applications received by the university (first-year and transfer)
- Total number of students admitted (first-year and transfer)
- Total number of first time freshmen admitted
It tells us about how hard it is for you to get into a particular college or university. The higher the number, it’s more likely you will be accepted because there are fewer applicants than there are available seats in your class.
Acceptance Rate Definition
What is the acceptance rate?
The acceptance rate of a university is the percentage of students who received an acceptance letter from that school and decided to enroll. The acceptance rate is also called the enrollment rate. A college with a high enrollment rate and a low acceptance rate will typically be more selective than one with high acceptance rates and low enrollment rates. For example, Stanford University has an 8% admission rate, while the University of California-Berkeley has an 18% admission rate. Even though both schools are highly ranked, Stanford is more selective than Berkeley because it admits fewer students into its programs each year.
How to Calculate Acceptance Rates
In order to calculate the acceptance rate, you need to know how many students applied and how many were accepted. The number of applicants can be found in a school’s statistics, but unfortunately, it is not always easy to locate this information. If you’re having trouble finding the number of applicants, try looking at the total enrollment of students instead. While this number will vary depending on if you’re looking at an undergraduate or graduate program, it can give you an idea of how competitive your dream school’s program is.
For example, let’s say that your dream college receives 20,000 applications per year and accepts 10% of them. This means that 2,000 people are admitted out of those 20,000 applicants—and only 1% are actually enrolled each year. In this scenario, where only 1% of applicants are accepted each year from such a large pool (20-30k), the university is considered “highly selective” or “ultra-exclusive” by admissions experts and professionals around world because less than 5% (in fact not even half!) get into their first choice college; meaning: 99% go elsewhere!
How to Calculate Entry Selectivity
- Calculate your acceptance rate. As mentioned, this is the number of students that applied and were accepted to your school (as a percentage). For example, if 60 students apply to your school, and 30 are accepted, you divide 30 by 60 to get an acceptance rate of 50%.
- Divide the results. If you want to calculate an entry selectivity score for the academic year 2021-22 based on the numbers from the 2020-21 academic year, divide 1 by 0.5, or use whatever other numbers you come up with in your own calculations. These results will be able to help you not only compare yourself to other schools but also understand how much more work you have yet to do in order
There are many different ways to measure college acceptance rates.
There are many different ways to measure college acceptance rates. You might see the overall acceptance rate, which can be defined as the number of students who were accepted to a college divided by the total number of students who applied. The formula for this looks like:
- Overall Acceptance Rate=Accepted/Applied
You might also come across an article that talks about what is known as the “selectivity rating,” which takes into account not only the number of applicants but also how likely those applicants are to attend that particular college or university if admitted. It goes up with every student who accepts an offer of admission and tends to be higher than the overall acceptance rate. This formula is usually expressed as:
- Selectivity Rating=Accepted/(Accepted+Offered Wait List)
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CC-MAIN-2023-23
| 4,510 | 23 |
http://www.maths.manchester.ac.uk/raag/index.php?preprint=0344
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math
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Real Algebraic and Analytic Geometry
Submission: 2012, July 25.
Let $f:\R^2\longrightarrow\R^2$ be a generic polynomial mapping. There are constructed quadratic forms whose signatures determine the number of positive and negative cusps of $f$.
Mathematics Subject Classification (2000): 14P99, 58K05.
Keywords and Phrases: Singularities, cusps.
Full text, 13p.: dvi 63k, pdf 278k.
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CC-MAIN-2019-18
| 380 | 6 |
https://cpep.org/physics/1834365-light-enters-water-from-air-at-an-angle-of-25-with-the-normal-1-if-wat.html
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math
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Find an answer to your question 👍 “Light enters water from air at an angle of 25° with the normal, Θ1. If water has an index of refraction of 1.33, determine Θ2. A) 18.5° B) ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510730.6/warc/CC-MAIN-20230930213821-20231001003821-00827.warc.gz
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CC-MAIN-2023-40
| 349 | 2 |
https://scite.ai/authors/k-k-d-adjai-ygEGRM
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math
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<abstract><p>In the attractive research field of nonlinear differential equations, there are a few studies devoted to finding exact and explicit harmonic and isochronous periodic solutions and limit cycles. In this contribution, we present some classes of polynomial mixed Lienard-type differential equations that can generate many equations with exact solutions. These classes of equations constitute counterexamples of the classical existence theorems.</p></abstract>
In this paper we study a Lienard equation without restoring force. Although this equation does not satisfy the classical existence theorems, we show, for the first time, that such an equation can exhibit harmonic periodic solutions. As such the usual existence theorems are not entirely adequate and satisfactory to predict the existence of periodic solutions.
In this paper, we present an exceptional Lienard equation consisting of a modified Van der Pol-Helmholtz oscillator equation. The equation, a frequency-dependent damping oscillator, does not satisfy the classical existence theorems but, nevertheless, has an isochronous centre at the origin. We exhibit the exact and explicit general harmonic and isochronous solutions by using the first integral approach. The numerical results match very well analytical solutions.Mathematics Subject Classi cation (2010). 34A05, 34A12, 34A34, 34C25, 34C60.
This paper is devoted to investigating the existence of exact harmonic solutions and limit cycles of certain modified Emden-type equations. The exact and general solutions obtained are in opposition to the predictions of classic existence theorems.
Although Jacobi elliptic functions have been known for almost two centuries, they are still the subject of intensive investigation. In this paper, contrary to the usual definition, we prove that the Jacobi elliptic functions can be defined by using nonconservative equations with limit cycles through existence theorems involving first integrals. This allows extending their validity domains, that is, their range of applications.
Real-world systems, such as physical and living systems, are generally subject to vibrations that can affect their long-term integrity and safety. Thus, the determination of the law that governs the evolution of the oscillatory quantity has become a major topic in modern engineering design. The process often leads to solving nonlinear differential equations. However, one can admit that the main objective of the theory of differential equations to obtain explicit solutions is far from being carried out. If we know how to solve linear systems, the case of systems of nonlinear differential equations is not in general solved. Isochronous nonlinear systems have therefore received particular attention. This chapter is devoted to presenting some recent developments and advances in the theory of isochronous oscillations of nonlinear systems. The harmonic oscillator as a prototype of isochronous systems is investigated to state some useful definitions (section 2), and the existence of second-order isochronous nonlinear systems having explicit elementary first integrals with an exact sinusoidal solution and higher-order autonomous nonlinear systems that reproduce the dynamics of the harmonic oscillator is proven (section 3). Finally, higher-order nonautonomous nonlinear systems that can exhibit isochronous oscillations are shown (section 4), and a conclusion for the chapter is presented.
In this paper we present a general class of differential equations of Ermakov-Pinney type which may serve as truly nonlinear oscillators. We show the existence of periodic solutions by exact integration after the phase plane analysis. The related quadratic Lienard type equations are examined to show for the first time that the Jacobi elliptic functions may be solution of second-order autonomous non-polynomial differential equations.
In this paper, we show the existence of damped Mathieu and periodic Lienard-type equations that can be solved in an explicit way or by quadrature. We prove for the first time an isochronous periodic solution for a Lienard-type equation with periodic coefficients, which does not exhibit parametric resonance.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100912.91/warc/CC-MAIN-20231209134916-20231209164916-00108.warc.gz
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CC-MAIN-2023-50
| 4,666 | 9 |
https://www.hackmath.net/en/math-problem/2708
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math
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We burned two unequally thick and long candles. Longer burnt for three and a half hours and shorter for five hours. After two hours of burning it was identical. How many times was longer candle longer then shorter?
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CC-MAIN-2020-29
| 3,094 | 34 |
https://www.ecmweb.com/design/making-short-circuit-calculations-easy
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math
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In this day of high fault currents, it's more important than ever to protect electrical equipment from extremely high current levels. Otherwise, the equipment will explode as it attempts to interrupt the fault. But fault current calculations have always been difficult to get a handle on, until now.
The new "Easy Way" kVA approach is taking the place of the abstract "Per Unit" method of short-circuit calculations from the past. With the kVA method, you can easily visualize what currents will flow where. And you can calculate them using an inexpensive handheld calculator in moments, regardless of the complexity of the electrical power system.
This method is simple because there are no awkward "base" changes to make, since kVAs are the same on both the primary and secondary sides of every transformer. Perhaps best of all, you only need one calculation to determine the short-circuit values at every point within the entire electrical power system. With the old Per Unit method, you needed a separate calculation for each point in the system.
You can obtain short-circuit kVA values from the electrical utility company, but short circuit power is also protected by generators and motors. The kVA produced by motors equals the motor starting inrush current, and the kVA produced by generators equals the kVA nameplate rating divided by its nameplate subtransient reactance rating "Xd."
For example, a 1000kVA generator with a subtransient rating of 0.15 instantaneously produces 1000/0.15, or 6666kVA. A 100hp motor instantaneously produces 100,000/.17kVA, or 588kVA. If this motor and generator connect to the same bus, then the short-circuit power available at that bus is the sum (6666 + 588), or 7254kVA. If the electrical utility is rated to deliver 100kVA to this same bus, then the total short-circuit power available at that bus is 107,254kVA.
Using the kVA method also greatly simplifies the short-circuit power attenuation (or holdback) provided by reactors, transformers, and conductors. For example, a 2000kVA 7% impedance transformer will pass through its windings a maximum of 2000/.07, or 28571kVA of power, if infinite power flows to one side of its windings. If instead of an infinite current source, the above bus connects to this transformer, then the amount of power that will be "let through" the transformer is the reciprocal of the sum of the reciprocals of the two, or 1/(1/107254 + 1/28571), or 22561kVA. You can determine transformer impedance, reactor impedance, or cable size with the kVA method quickly enough to make "what if" calculations.
Comparisons over several years have found results of the kVA method to be accurate within 3% of computer calculations using expensive software, so you can even use the kVA method as a "check" on the input and output of a computer calculation. This is an excellent benefit because standard engineering procedure requires you to check calculations using a different method from the one originally used.
Editors Note: EC&M's book, "Short-Circuit Calculations The Easy Way," explains the entire "Easy Way" kVA method in a step-by-step format. Available from EC&M Books, call (800) 543-7771 to order.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590199.42/warc/CC-MAIN-20180718135047-20180718155047-00111.warc.gz
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CC-MAIN-2018-30
| 3,173 | 8 |
https://www.pillartech.com/surface-treatment/resources/service-info/watt-density
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math
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What Is The Formula To Calculate Watt Density?
Watt Density is a measurement of the amount of energy being applied to the web. It is measured in Watts/Foot2/minute. Watt density takes into account the amount of power being applied (watts), the time it is being applied (minute) and the amount of material it is being applied to (Foot2).
Once the watt density is known to get a particular material to a certain dyne level, it can be used to predict the results if any of the parameters change such as line speed.
The formula to calculate watt density is as follows:
Example: A line is running at 100 feet per minutes (fpm), the power supply output is 1kW and 45 dyne is being achieved. you can expect the exact same results at 200 fpm at 2kW 300 fpm at 3kW, etc.
If the example above were a 48 inch treat width, one side treat – a watt density of 2.5 watts/ Ft2/minute is required obtain 45 dyne.(Electrode width = 4feet)
The Same Formula Can Be Used To Determine:
1. Required Power at a certain line speed.
Using the same example, lets say you would like to increase your line speed to 500 FPM and still get 45 dyne on the same material, the formula can be used as follows:
500 fpm x 4ft x one side x 2.5 Watts/Ft2/Min. = 5000 watts
5Kw is required to get 45 dyne at 500fpm.
2. Maximum speed capacity:
Using the same example lets say you have a 3.5Kw power supply and you would like to know the fastest line speed you can achieve and still get 45 dyne. The formula can be used as follows:
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CC-MAIN-2023-23
| 1,490 | 13 |
https://sg.answers.yahoo.com/question/index?qid=20120417215452AAj9FQI
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math
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How do I solve: lim n-->inf (2n+1)!/(2n+3)!?
originally, it was the sum of the series (from 0-inf) of (-1)^n/(2n+1)!
I need to find if it's converging absolutely or conditionally so I proved it converged using the alternating series test and I thought of using the ratio test to prove that it either diverges or converges and got stuck at the part above. Any advice?
- Tex-sLv 58 years ago
not explicit but as n increases, say to 100....
21! / 23! or 1 / (202 * 203) ---> 0
- Anonymous8 years ago
(2n+1)! will cancel.
That goes to 0, woo. But there's no need to prove it in multiple ways.
And technically it should be negative since (-1)^(n+1)/(-1)^(n)= -1
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739048.46/warc/CC-MAIN-20200813161908-20200813191908-00219.warc.gz
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CC-MAIN-2020-34
| 656 | 10 |
http://perplexus.info/show.php?pid=77&cid=3623
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math
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A crime has occured in Carborough, involving a taxi. The police interviewed an eyewitness, who stated that the taxi involved was blue.
The police know that 85% of taxis in Carborough are blue, the other 15% being green. They also know that statistically witnesses in these situations tend to be correct 80% of the time - which means they report things wrong the other 20% of the time.
What is the probability that the taxi involved in the crime was actually blue?
The more paradoxical version of this puzzle results if the witness stated that the taxi involved was green. This is the way that works out:
As before, let's say the city has a total of 100 taxis (this way we can have a one to one relationship between taxis and percent).
Of these 100, 85 are blue, and 15 are green.
Again, let's look at both cases:
85/100 blue taxi is involved. Since the witness will be wrong 20% of the time, they will say they saw a blue taxi 68 times, and claim that the taxi was green the other 17 times.
15/100 green taxi is involved. 12 witnesses would correctly identify a green taxi, but 3 would wrongly claim to have seen a blue one.
This time we know that the witness said they saw a green taxi. There is a total of 17+12 = 39 percent chance for that to happen. Of those 39%, 12% of the time the taxi will in truth be green. Thus the probability of the taxi being green is 12/39 = approximately 30.8%.
Thus it is only about 31% likely that the color of the cab agrees with the witness's description.
Posted by Charlie
on 2003-03-26 14:09:57
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202635.43/warc/CC-MAIN-20190322054710-20190322080710-00443.warc.gz
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CC-MAIN-2019-13
| 1,532 | 13 |
http://mathematics.csust.xk.hnlat.com/index.php?m=content&c=index&a=show&catid=2200&id=55413&siteid=23
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math
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MathWorld is the web's most extensive mathematical resource, provided as a free service to the world's mathematics and internet communities as part of a commitment to education and educational outreach by Wolfram Research, makers of Mathematica.
MathWorld has been assembled over more than a decade by Eric W. Weisstein with assistance from thousands of contributors. Since its contents first appeared online in 1995, MathWorld has emerged as a nexus of mathematical information in both the mathematics and educational communities. It not only reaches millions of readers from all continents of the globe, but also serves as a clearinghouse for new mathematical discoveries that are routinely contributed by researchers. Its entries are extensively referenced in journals and books spanning all educational levels, including those read by researchers, elementary school students and teachers, engineers, and hobbyists.
MathWorld continues to grow and evolve with the assistance of thousands of contributors. Careful oversight of all aspects of its content and interface by creator Eric Weisstein, and more recently with able assistance from MathWorld associate Ed Pegg, Jr., provides an exacting level of quality, accuracy, and consistency. As a result, MathWorld is considered not only the clearest and most readable online resource for mathematics, but also one of the most reliable.
MathWorld is actively developed and maintained. The site is updated daily, thus achieving extremely rapid communication of new and extended results--many of which are provided by outside contributors--while at the same time maintaining a degree of editorial oversight and consistency across (and among) the site's nearly 13,000 entries that is simply not possible for other sites.
MathWorld currently features a number of innovative interactive elements that enhance its usability for a variety of different readers. These features include:
The MathWorld Classroom, which provides a set of pop-up"capsule summaries"for more than 300 mathematical terms.
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Several types of interactive entries, including LiveGraphics3D applets for interactive three-dimensional geometry.
A powerful full-text search engine with both basic and advanced searching capabilities.
Dublin Core and Mathematics Subject Classification metadata in the HTML headers of each page.
Special information for Mathematica users.
The technology behind MathWorld is heavily based on Mathematica. In addition to being indispensable in the derivation, validation, and visualization of MathWorld's content, Mathematica is used to build the website itself, taking advantage of its advanced mathematical typesetting and data-processing capabilities.
The MathWorld team welcomes your feedback. Please visit the extensive set of Q&A pages where you can find answers to many common queries. If you have comments, please use the comment form to send a message to the MathWorld team. Contributions of new entries are especially appreciated and, after editorial review, appear on MathWorld with grateful attribution to their authors. Please also note that there are a number of things you can do to help support MathWorld as a free public resource. Finally, feel free to add links to MathWorld entries to your own pages.
On behalf of the MathWorld team and Wolfram Research, thanks for using MathWorld. We hope that you find it helpful in your mathematical journeys, and we look forward to continuing building--with your help--what has become one of the world's great internet encyclopedias.
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CC-MAIN-2019-30
| 3,665 | 15 |
https://fr.slideserve.com/chakra/modeling-and-performance-evaluation-of-computer-systems
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math
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Chapter 3Quantifying Performance Models Performance by Design: Computer Capacity Planning by Example Daniel A. Menascé, Virgilio A.F. Almeida, Lawrence W. Dowdy Prentice Hall, 2004
Outline • Introduction • Stochastic Modeling vs. Operational Analysis • Basic Performance Results • Utilization Law • Service Demand Law • The Forced Flow Law • Little's Law • Interactive Response Time Law • Bounds on Performance • Using QN Models • Concluding Remarks • Exercises • Bibliography
Introduction (1) • Chapter 2 introduced the basic framework that will be used throughout the book to think about performance issues in computer systems: • queuing networks. • That chapter concentrated on the • qualitative aspects of these models and • looked at how a computer system can be mapped into a network of queues. • This chapter focuses on the quantitative aspects of these models and
Introduction (2) • Introduce the input parameters and performance metrics that can be obtained from the QN models. The notions of • service times, • arrival rates, • service demands, • utilization, • response time, • queue lengths, • throughput, and • waiting time are discussed here in more precise terms.
Stochastic Modeling vs. Operational Analysis • SM • Ergodic stationary Markov process in equilibrium. • Coxian distributions of service times. • independence in service times and routing. • OA • finite time interval • measurable quantities • testable assumptions OA made analytic modeling accessible to capacity planners in large computing environments.
Application and Analysis of QN • Applications • System Sizing; Capacity Planning; Tuning • Analysis Techniques • Global Balance Solution • Massive sets of Simultaneous Linear Equations • Bounds Analysis • Asymptotic Bounds (ABA), Balanced System Bounds (BSB) • Solutions of “Separable” Models • Exact (Convolution, eMVA) • Approximate (aMVA) • Generalizations beyond “Separable” Models • aMVA with extended equations
Basic Performance Results (1) • This section presents the approach known as operational analysis , used to establish relationships among quantities based • on measured or • known data about computer systems. • To see how the operational approach might be applied, consider the following motivating problem.
Motivating Problem • Motivating problem:Suppose that during an observation period of 1 minute, • a single resource (e.g., the CPU) is observed to be busy for 36 sec. • A total of 1800 transactions are observed to arrive to the system. • The total number of observed completions is 1800 transactions (i.e., as many completions as arrivals occurred in the observation period). • What is the performance of the system (e.g., • the mean service time per transaction, • the utilization of the resource, • the system throughput)?
Measured Quantities Operational Variables • The following is a partial list of such measured quantities: • T: length of time in the observation period • K: number of resources in the system • Bi: total busy time of resourcei in the observation period T • Ai: total number of service requests (i.e., arrivals) to resource i in the observation period T • A0: total number of requests submitted to the system in the observation period T • Ci: total number of service completions from resource i in the observation period T • C0: total number of requests completed by the system in the observation period T
Derived Variables • From these known measurable quantities, called operational variables, a set of derived quantities can be obtained. A partial list includes the following: • Si: mean service time per completion at resource i; Si = Bi /Ci • Ui: utilization of resource i; Ui = Bi /T • Xi: throughput (i.e., completions per unit time) of resource i; Xi = Ci /T • i: arrival rate (i.e., arrivals per unit time) at resourcei; i= Ai /T • X0: system throughput; X0 = C0 /T • Vi: average number of visits (i.e., the visit count) per request to resource i; Vi = Ci /C0
Operational Analysis of motivating problem (1) • Using the notation above, the motivating problem can be formally stated and solved in a straightforward manner using operational analysis. • The measured quantities are:
Operational Analysis motivating problem (2) • Thus, the derived quantities are :
Multiple Class • The notation presented above can be easily extended to the multiple class case by considering that R is the number of classes and by adding the class number r (r = 1, ···, R) to the subscript. • For example, • Ui,r is the utilization of resource i due to requests of class r and • X0,r is the throughput of class r requests.
Operational Law • The subsections that follow discuss several useful relationships called: operational laws between operational variables. • Utilization Law, • Service Demand Law, • The Forced Flow Law, • Little's Law, • Interactive Response Time Law,
Utilization Law • As seen above, the utilization of a resource is defined as Ui = Bi /T • Dividing the numerator and denominator of this ratio by the number of completions from resource i, Ci, during the observation interval, yields (3.2.1 )
Utilization Law and Throughput • The ratio Bi/Ciis simply the average time that the resource was busy for each completion from resource i, i.e., the average service time Siper visit to the resource. • The ratio T/Ci is just the inverse of the resource throughput Xi. • Thus, the relation known as the Utilization Law can be written as: (3.2.2)
Utilization Law (3) • If the number of completions from resource i during the observation interval T is equal to the number of arrivals in that interval, i.e., if Ci = Ai, then Xi = i and the relationship given by the Utilization Law becomes Ui = Sixi. • If resource i has m servers, as in a multiprocessor, • the Utilization Law becomes Ui = (Six Xi)/m. • The multiclass version of the Utilization Law is Ui,r = Si,rx Xi,r .
Example 3.1. (1) • The bandwidth of a communication link is 56,000 bps and it is used to transmit 1500-byte packets that flow through the link at a rate of 3 packets/second. • What is the utilization of the link? • Start by identifying the operational variables provided or that can be obtained from the measured data. • The link is the resource (K = 1) for which the utilization is to be computed. • The throughputof that resource,X1, is 3 packets/second. • What is the average service time per packet?
Example 3.1. (2) • In other words, what is the average transmission time? • Each packet has 1,500 bytes/packet x 8 bits/byte = 12,000 bits/packet. • Thus, it takes 12,000 bits/56,000 bits/sec = 0.214 sec to transmit a packet over this link. • Therefore, S1 = 0.214 sec/packet. • Using the Utilization Law, we compute the utilization of the link as S1 x X1= 0.214 x 3 = 0.642 = 64.2%.
Example 3.2. (1) • Consider a computer system with one CPU and three disks used to support a database server. • Assume that all database transactions have similar resource demands and that the database server is under a constant load of transactions. • Thus, the system is modelled using a single-class closed QN, as indicated in Fig. 3.1. • The CPU is resource 1 and the disks are numbered from 2 to 4. • Measurements taken during one hour provide the number of transactions executed (13,680), • the number of reads and writes per second on each disk and their utilization, as indicated in Table 3.1.
Example 3.2. (2) • What is the average service time per request on each disk? • What is the database server's throughput? Figure 3.1. Closed QN model of a database server.
Example 3.2. (3) • The throughput of each disk, denoted by Xi (i = 2, 3, 4), is the total number of I/Os per second, i.e., the sum of the number of reads and writes per second. • This value is indicated in the fourth column of the table. • Using the Utilization Law, the average service time is computed as Si as Ui/Xi. • Thus, S2 = U2/X2 = 0.30/32 = 0.0094 sec, • S3 = U3/X3 = 0.41/36 = 0.0114 sec, and • S4 = U4/X4 = 0.54/50 = 0.0108 sec. • The throughput, X0, of the database server is given by X0 = C0/T = 13,680 transactions/3,600 seconds = 3.8 tps.
Service Demand Law (1) • The service demand, denoted as Di, is defined as the total average time spent by a typical request of a given type obtaining service from resource i. • Throughout its existence, a request may visit several devices, possibly multiple times. • However, for any given request, its service demand is the sum of all service times during all visits to a given resource. • Note that, by definition, service demand does not include queuing time since it is the sum of service times. • If different requests have very different service times, using a multiclass model is more appropriate.
Service Demand Law (2) • In this case, define Di,r, as the service demand of requests of class r at resource i. • To illustrate the concept of service demand, consider that six transactions perform three I/Os on a disk. • The service time, in msec, for each I/O and each transaction is given in Table 3.2. • The last line shows the sum of the service times over all I/Os for each transaction. • The average of these sums is 36.2 msec. • This is the service demand on this disk due to the workload generated by the six transactions.
Table 3.2. Service times in msec for six requests. Each transactions performs three I/Os on a disk. Service demand on this disk due to the workload generated by the six transactions. (33+41+36+32+36+39)/6=36.2 msec.
Service Demand Law (3) • By multiplying the utilization Ui of a resource by the measurement interval T one obtains the total time the resource was busy. • If this time is divided by the total number of completed requests, C0, the average amount of time that the resource was busy serving each request is derived. • This is precisely the service demand. So, • This relationship is called the Service Demand Law, which can also be written as Di = Vix Si . (3.2.3)
Service Demand Law (4) • By definition of the service demand (and since Di = Ui /X0 = (Bi /T)/(C0 /T) = Bi /C0 = (Cix Si )/C0 = (Ci /C0) x Si = Vix Si). • In many cases, Eq. (3.2.3) indicates that the service demand can be computed directly from the device utilization and system throughput. • The multiclass version of the Service Demand Law is Di,r = Ui,r /X0,r = Vi,rx Si,r.
Example 3.3. (1) • A Web server is monitored for 10 minutes and its CPU is observed to be busy 90% of the monitoring period. • The Web server log reveals that 30,000 requests are processed in that interval. • What is the CPU service demand of requests to the Web server? • The observation period T is 600 (= 10 x 60) seconds.
Example 3.3. (2) • The Web server throughput, X0, is equal to the number of completed requests C0 divided by the observation interval; • X0 = 30,000/600 = 50 requests/sec. • The CPU utilization is UCPU = 0.9. • Thus, the service demand at the CPU is • DCPU = UCPU/X0 = 0.9/50 = 0.018 seconds/request.
Example 3.4. • What are the service demands at the CPU and the three disks for the database server of Example 3.2 • assuming that the CPU utilization is 35% measured during the same one-hour interval? • Remember that the database server's throughput was computed to be 3.8 tps. • Using the Service Demand Law and the utilization values for the three disks shown in Table 3.1, yields: • DCPU = 0.35/3.8 = 0.092 sec/transaction, • Ddisk1 = 0.30/3.8 = 0.079 sec/transaction, • Ddisk2 = 0.41/3.8 = 0.108 sec/transaction, and • Ddisk3 = 0.54/3.8 = 0.142 sec/transaction.
The Forced Flow Law (1) • There is an easy way to relate the • throughput of resource i, Xi, • to the system throughput, X0. • Assume for the moment that every transaction that completes from the database server of Example 3.2 performs an average of two I/Os on disk 1. • That is, suppose that for every one visit that the transaction makes to the database server, it visits disk 1 an average of two times. • What is the throughput of that disk in I/Os per second?
The Forced Flow Law (2) • Since 3.8 transactions complete per second (i.e., the system throughput, X0) and each one performs two I/Os on average on disk 1, • the throughput of disk 1 is 7.6 (= 2.0 x 3.8) I/Os per second. • In other words, the throughput of a resource (Xi) is equal to the average number of visits (Vi) made by a request to that resource multiplied by the system throughput (X0). • This relation is called the Forced Flow Law: • The multiclass version of the Forced Flow Law is: Xi,r = Vi,rx X0,r. (3.2.4)
Example 3.5. • What is the average number of I/Os on each disk in Example 3.2? • The value of Vi for each disk i, according to the Forced Flow Law, can be obtained as Xi/X0. • The database server throughput is 3.8 tps and the throughput of each disk in I/Os per second is given in the fourth column of Table 3.1. • Thus, V1 = X1/X0 = 32/3.8 = 8.4 visits to disk 1 per database transaction. • Similarly, V2 = X2 /X0 = 36/3.8 = 9.5 and • V3 = X3/X0 = 50/3.8 = 13.2.
Little's Law (1) • Little's result states that the average number of folks in the pub (i.e., the queue length) is equal to the departure rate of customers from the pub times the average time each customer stays in the pub (see Fig. 3.2).
Little's Law (2) • This result applies across a wide range of assumptions. • For instance, consider a deterministic situation where a new customer walks into the pub every hour on the hour. • Upon entering the pub, suppose that there are three other customers in the pub. • Suppose that the bartender regularly kicks out the customer who has been there the longest, every hour at the half hour. • Thus, a new customer will enter at 9:00, 10:00, 11:00, ..., and • the oldest remaining customer will be booted out at 9:30, 10:30, 11:30, ....
Little's Law (3) • It is clear that the average number of persons in the pub will be , • since 4 customers will be in the pub for the first half hour of every hour and • only 3 customers will be in the pub for the second half hour of every hour. • The departure rate of customers at the pub is one customer per hour. • The time spent in the pub by any customer is hours. Thus, via Little's Law:
Little's Law (4) • Also, it does not matter which customer the bartender kicks out. • For instance, suppose that the bartender chooses a customer at random to kick out. • We leave it as an exercise to show that the average time spent in the pub in this case would also be hours. • [Hint: the average time a customer spends in the pub is one half hour with probability 0.25, one and a half hours with probability (0.75)(0.25) = 0.1875 (i.e., the customer avoided the bartender the first time around, but was chosen the second), two and a half hours with probability (0.75)(0.75)(0.25), and so on.]
Little's Law (5) • Little's Law applies to any "black box", which may contain an arbitrary set of components. • If the box contains a single resource (e.g., a single CPU, a single pub) or if the box contains a complex system (e.g., the Internet, a city full of pubs and shops), Little's Law holds. • Thus, Little's Law can be restated as (3.2.5 )
Little's Law (6) • For example, consider the single server queue of Fig. 3.3. • Let the designated box be the server only, excluding the queue. • Applying Little's Law, the average number of customers in the box is interpreted as the average number of customers in the server. • The server will either have a single customer who is utilizing the server, or the server will have no customer present. • The probability that a single customer is utilizing the server is equal to the server utilization. • The probability that no customer is present is equal to the probability that the server is idle.
Little's Law (7) • Thus, the average number of customers in the server equals: • This simply equals the server's utilization. • Therefore, the average number of customers in the server, N s, equals the server's utilization. • Thus, with this interpretation of Little's Law, • This result is simply the Utilization Law! • Now consider that the box includes both the waiting queue and the server. (3.2.6 )
Little's Law (8) • The average number of customers in the box (waiting queue + server), denoted by Ni, is equal, according to Little's Law, to the average time spent in the box, which is the response time Ri, times the throughput Xi. • Thus, Ni = Rix Xi. • Little's Law indicates that • ,where is the average number of customers in the queue and • Withe average waitingtime in the queue prior to receiving service.
Example 3.6. (1) • Consider the database server of Example 3.2 and assume that during the same measurement interval the average number of database transactions in execution was 16. • What was the response time of database transactions during that measurement interval? • The throughput of the database server was already determined as being 3.8 tps. • Apply Little's Law and consider the entire database server as the box.
Example 3.6. (2) • The average number in the box is the average number N of concurrent database transactions in execution (i.e., 16). • The average time in the box is the average response time R desired. • Thus, R = N/X0 = 16/3.8 = 4.2 sec.
Interactive Response Time Law (1) • Consider an interactive system composed of • M clients, • average think time is denoted by Z and • average response time is R. • See Fig. 3.4. • The think time is defined as the time elapsed since a customer receives a reply to a request until a subsequent request is submitted. • The response time is the time elapsed between successive think times by a client.
Interactive Response Time Law (2) • Let and be the average number of clients thinking and waiting for a response, respectively. • By viewing clients as moving between workstations and the database server, depending upon whether or not they are in the think state, and represent the average number of clients at the workstations and at the database server, respectively. • Clearly, since a client is either in the think state or waiting for a reply to a submitted request. • By applying Little's Law to the box containing just the workstations, • Since the average number of requests submitted per unit time (throughput of the set of clients) must equal the number of completed requests per unit time (system throughput X0). (3.2.7)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154302.46/warc/CC-MAIN-20210802012641-20210802042641-00585.warc.gz
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CC-MAIN-2021-31
| 18,708 | 45 |
http://www.docstoc.com/docs/30988455/Accounting-for-corporations---percentage-of-sales-method
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math
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Sub: Accounts Topic: Accounting for Corporations
Calculation of additional finance needed using percentage of sales method.
ClassOf1 provides expert guidance to College, Graduate, and High school students on homework and assignment problems in
Math, Sciences, Finance, Marketing, Statistics, Economics, Engineering, and many other subjects.
BPC anticipates reaching a sales level of $6 million in one year. The company expects a net
income during the next year to equal $400,000. Over the past several years, the company has
been paying 50k in dividends to its stockholders. The company expects to continue this policy
for at least the next year. The actual balance sheet and income statement for BPC are as
Balance sheet as of December 31, 2005
Cash 200,000 Accounts Payable 600,000
Accounts receivable 400,000 Notes Payable 500,000
Current liabilities 1,100,000
Current assets 1,800,000 Long-term debt 200,000
Net fixed assets 500,000 Stockholder’s equity 1,000,000
Total assets 2,300,000 Total Liabilities and equity 2,300,000
Using the percentage of sales method, calculate the additional financing needed over the next
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00501-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 1,125 | 16 |
https://supremeacademicpapers.com/homework-help-solved-4938-2/
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math
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Looking back at the data examples you have provided in the previous discussion questions on this issue, how might adding confidence intervals help managers accept the results better? Why?Ask a manager in your organization if they would prefer a single point estimate or a range for important measures, and why? Please share what they say.
Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you?
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818067.32/warc/CC-MAIN-20240421225303-20240422015303-00544.warc.gz
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CC-MAIN-2024-18
| 577 | 2 |
https://srstudentlets.co.uk/properties.asp?action=more&id=8
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math
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SPACIOUS FIVE BEDROOM HOUSE conveniently situated a short walk from Chrischurch University. The property comprises one ground floor and four first floor bedrooms, all with double beds and tv aerial sockets in all bedrooms, modern bedroom furniture, ground floor bathroom and first foor WC, a modern fitted kitchen, and great lounge with comfy sofas. landlord maintained garden
Off road parking.
HMO APPROVED WITH CANTERBURY CITY COUNCIL
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HALF RENT FOR FIRST MONTH
Excellent position for town centre, near to local shops.
Rent to include electric, gas, water, sewerage.
VIEWING: By prior appointment, call: 01227 368262, or email [email protected]
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487598213.5/warc/CC-MAIN-20210613012009-20210613042009-00027.warc.gz
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CC-MAIN-2021-25
| 687 | 8 |
https://byjus.com/question-answer/question-15-a-building-is-in-the-form-of-a-cylinder-surmounted-by-a-hemispherical/
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math
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A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 411921m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?
Open in App
Let total height of the building = internal diameter of the dome = 2 r m
∴Radius of building ( or dome) = 2r2=rm
Height of cylinder = 2r – r = r m ∴ Volume of the hemispherical dome cylinder = 23πr3m3 ∴Total volume of the building = Volume of the cylinder + Volume of hemispherical dome =(πr3+23πr3)m3=53πr3m3
According to the question, Volume of the building = volume of the air ⇒53πr3=411921⇒53πr3=88021⇒r3=880×7×321×22×5=40×2121×5=8m3 ⇒r=2m ∴ Height of the building = 2r=2×2=4m
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817790.98/warc/CC-MAIN-20240421163736-20240421193736-00295.warc.gz
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CC-MAIN-2024-18
| 748 | 6 |
http://www.slideshare.net/karniksingh/triangles-25476418
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math
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On Basis of Length of Sides, there are 3 types of Triangles
• Equilateral Triangle
• Isosceles Triangle
• Scalene Triangle
On Basis of Angles, there are 3 types of triangles
• Acute Angled Triangle
• Obtuse Angled Triangle
• Right Angled Triangle
TYPES OF TRIANGLES
• Angle sum property-
Angle sum Property of a Triangle is that the sum of all interior angles of
a Triangle is equal to 180˚.
• Exterior angle property-
Exterior angle Property of a Triangle is that An exterior angle of the
Triangle is equal to sum of two opposite interior angles of the Triangle
• Pythagorus theoram-
Pythagoras Theorem is a theorem given by Pythagoras. The theorem is
that In a Right Angled Triangle the square of the hypotenuse is equal to
the sum of squares of the rest of the two sides.
Properties of an isosceles triangle
• Angle opposite to the equal sides of an
isosceles triangle are equal.
• The sides opposite to the equal angles of
a triangle are equal.
1. The Line Segment joining the midpoint of the base of the Triangle is
called Median of the Triangle.
2. A Line Segment which connects a vertex of a Triangle to the
midpoint of the opposite side is called Median of the Triangle.
Altitudes of a triangle
The Line Segment drawn from a Vertex of a
Triangle perpendicular to its opposite side is
called an Altitude or Height of a Triangle.
A line that passes through midpoint of the
or the line which bisects the third side of the
triangle and is perpendicular to it is called the
Perpendicular Bisector of that Triangle.
A line segment that bisects an angle of a triangle
Is called Angle Bisector of the triangle.
•Two figures are congruent, if they are
of the same shape and of the same
•Two circles of the same radii are
•Two squares of the same sides are
SSS criteria of congruency
If the three sides of one Triangle
are equal to the three sides of
another Triangle. Then the
triangles are congruent by the
SSS criteria is called Side-
Side-Side criteria of congruency.
SAS criteria of congruency
If two sides and the angle included
between them is equal to the
corresponding two sides and the
angle between them of another
triangle. Then the both triangles are
congruent by SAS criteria i.e. Side-
Angle-Side Criteria of Congruency.
ASA criteria of congruency
If two angles and a side of a Triangle is
equal to the corresponding two angles
and a side of the another triangle then
the triangles are congruent by the ASA
Criteria i.e. Angle Side-Angle Criteria of
AAS criteria of congruency
If two angles and one side of one
triangle are equal to angles to two
angles and the corresponding side of
the other triangle then the two triangles
RHS criteria of congruency
If the hypotenuse, and a leg of one right
angled triangle is equal to corresponding
hypotenuse and the leg of another right
angled triangle then the both triangles are
congruent by the RHS criteria i.e. Right
Angle-Hypotenuse-Side Criteria of
• In a triangle ,angle opposite to the longer
side is larger.
• In a triangle, side opposite to the
larger(greater) angle is longer.
• Sum of any two sides of a triangle is
greater than the third side.
• Difference of any two sides of a triangle
is smaller than the third side.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982297973.29/warc/CC-MAIN-20160823195817-00279-ip-10-153-172-175.ec2.internal.warc.gz
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CC-MAIN-2016-36
| 3,223 | 83 |
http://tohomeworkdxol.blogdasilvana.info/pie-chart-transport-mode-of-students.html
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math
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In math worksheet on pie chart students can practice different types of questions on pie graphs from the given data we need to calculate the central angle of the components to construct the questions given in worksheet on pie chart. Tell students that pie charts (or circle graphs) are used to represent data as portions (or segments) of a whole explain that just as they would see a pizza pie cut up into pieces, a pie chart is divided into different pieces of data. 2) interpreting a pie chart: after the discussion about pie charts and time use, show the students the pie chart in the “analyzing a pie chart” section and ask them the questions about it 3) creating a pie chart: both print and microsoft excel versions of the activity are available. The charts below show the percentage of students joining north west university the charts below give information about the electricity generation in two countries in 2009 the pie charts below show the spending of a school in the uk from 1981 to 2001. The table compares modes of transport used in four countries: canada, belgium, germany and the netherlands percentage of journeys made by car, bicycle, public transport and on foot are given the bar chart shows the results of a survey into reasons people in the canada travel to work by car.
Each slice of the pie may be opened to produce a list of concepts on which the student can choose to work learning mode by clicking on any of the items suggested in the pie chart, the student makes an immediate transition into the learning mode. 'interpreting pie charts' is the starter activity - allowing for discussion between students and for the teacher to encourage students to deepen their understanding 'pie chart questions'- answers have been provided and would work well printed onto tracing paper for easy checking of the drawings. The pie chart provides information about the nations of students coming to england from abroad to study in 2001 bar chart is the breakdown of far eastern region and gives detailed information about the number of students coming from far eastern countries, prc, india, japan, korea, malaysia and singapore.
A lesson on describing ielts pie charts and shows you the range of vocabulary you need to get a band 90 score top tips for ielts ielts pie charts – transport test yourself a little more the means of transport – i could also use “mode of transport”, but that is in the question. Constructing circle graphs or pie charts a pie chart (also called a pie graph or circle graph) makes use of sectors in a circle the angle of a sector is proportional to the frequency of the data total number of students = 750 + 420 + 630 = 1,800 draw the circle, measure in each sector label each sector and the pie chart. The bar chart illustrates the frequency with which americans ate in fast food establishments from 2003 to 2013 it is clear that the majority of americans ate in fast food restaurants between once a week and once a month in all three years.
Why data interpretation pie charts in this section you can learn and practice data interpretation questions based on pie charts and improve your skills in order to face the interview, competitive examination and various entrance test (cat, gate, gre, mat, bank exam, railway exam etc) with full confidence. Mathematics (linear) – 1ma0 pie charts materials required for examination items included with question papers ruler graduated in centimetres and nil millimetres, protractor, compasses, noreen carries out a survey of some students the pie chart shows some information about their favourite holiday. This pie chart is missing some data give your little one a fun activity with this blank pie chart, a great way to introduce her to fractions and the idea of graphing information try filling the graph with some data, be it different quarters of pizza toppings or the different ingredients that go into a recipe. Learners practice using pie charts, charts, and graphs that are used to keep track and display information the lesson is needed for them to increase skills necessary to take portions of the ged exam. On this worksheet students must create a pie chart based on tabular data includes a partially complete calculation table as a prompt.
Bar graph basics like pie charts, bar graphs are appropriate for both nominal (demographic) and ordinal (ranked) data they display data at relative sizes, except the visual is a bar rather than a pie slice. A resource for free-standing mathematics qualifications pie charts the nuffield foundation 1 photo-copiable a pie chart shows how something is divided into parts - it is a good way of showing the proportion (or fraction) of the data that is in each category work through this example. A model pie chart report – step by step this lesson gives you a step-by-step approach to dealing with pie charts in task 1 i talk you through how to identify the main points, select the supporting details and then structure your report. Eg 200 students might be asked to indicate their favourite subject at school out of maths, english and science a pie chart is a way of illustrating inform ation by using a circle as the whole and sections of the circle to represent parts of the whole ÿ the mode of the predicted.
Reading pie charts - examples with solutions the pie chart below shows the percentages of types of transportation used by 800 students to come to school a) how many students, in the school, come to school by bicycle africa, north america, south america, europe and australia is 134 million square kilometers the pie chart below shows. Stats quiz 1 study play true a population is a collection of all individuals, objects, or measurements of interest a pie chart can be used to summarize the data a group of 100 students were surveyed about their interest in a new economics major interest was measured in terms of high, medium, or low. 21122 - minitab express: pie charts the following data set (from college board) contain the mean sat scores for each of the 50 states and washington, dc, as well the participation rates and geographic region of each state.
The remainder of the pie is corresponds to the students with hazel eyes the resulting pie chart is pictured above note that number of students in each category is written on each pie piece. B eye color of students in statistics class c speed of travel of a jet d your weight a a pie chart b a histogram c a bivariate table b mode c mean d none of the above ____ 25 it is possible for a variable to have a one mode b many modes c no mode. Pie-of-pie and bar-of-pie charts make it easier to see small slices of a pie chart these chart types separate the smaller slices from the main pie chart and display them in a secondary pie—or stacked bar chart. 84 creating bar graphs and pie charts 647 84 objectives 1 use a table to create a bar graph 2 this pie chart represents the results of a survey that asked students how they get to school most often (a) transportation 12 clothing 13 entertainment 30% food 10% other 5% entertainment 10% clothing 20% transportation 5.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039748901.87/warc/CC-MAIN-20181121133036-20181121155036-00394.warc.gz
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CC-MAIN-2018-47
| 7,087 | 7 |
https://www.physicsforums.com/threads/whats-the-different-between-a-converge-and-diverge-integral.140569/
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math
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What's the different between a 'converge' and 'diverge' integral?
Do you mean what is the difference between a convergent integral and a divergent integral?
yea, the different between a convergent integral and a divergent integral
One converges and one diverges..? One has a finite limit, the other has an infinite limit..? One evaluates to a number and the other does not( it has an infinite limit approaching one of the bounds).
Separate names with a comma.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823705.4/warc/CC-MAIN-20181211215732-20181212001232-00168.warc.gz
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CC-MAIN-2018-51
| 459 | 5 |
http://www.chegg.com/homework-help/questions-and-answers/system-consists-two-atoms-masses-m-mrespectively-m-q439237
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math
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A system consists of two atoms, with masses m and Mrespectively and m<<M. Hence we can assume that the heavieratom is at rest and the lighter atom is moving under theinteractionforce between the two atoms. The potential energy of theinteraction is given by: .Here r is the distance between thetwo atoms and c,d are positive constants of approximateunits.
<Question> : The total mechanical energy of the systemis E. Describe the motion of the lighter atom if E is larger thanzero. What is the range of r the atom could move? What are theanswers if E is less than zero? Express the range in terms ofc,d,m,E.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660887.60/warc/CC-MAIN-20160924173740-00287-ip-10-143-35-109.ec2.internal.warc.gz
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CC-MAIN-2016-40
| 605 | 2 |
http://www.palmflying.com/air-density-calculator-1-0.html
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math
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This software entitled as AirDensity 1.0, is a Palm-OS application and helps you calculate both Air Density and Density Altitude. It works as a flying air dens
ity calculator that can calculate air density and density altitude based on input of three variables: temperature in Fahrenheit, relative humidity as a % satura tion, and barometric pressure.
If you are a pilot, you can then use the density altitude calculation to determine the length of runway that you need for lift-of
f given the weight of your plane, fuel, passengers and cargo.
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704645477/warc/CC-MAIN-20130516114405-00065-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 543 | 4 |
https://cinderzelda.com/musictutor/inter.htm
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math
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|To determine the numeric aspect of an interval, count the lines and spaces. We don't even need to know the clef to do this. We do have to remember when counting intervals the first note is 1. When counting steps the first note is 0 (zero).
The interval of 1, that is notes with the same letter name, is called a unison. An interval of 2 is called a "second", 3 - "third", 4 - "fourth", 5 -"fifth", 6 - "sixth", 7 - "seventh" and 8 - "octave". Intervals of a ninth to a thirteenth are often named but intervals over two octaves (fifteenth) are referred to by the number of octaves plus the remainder (the piano keyboard has a range of seven-octaves and a minor-third).
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570913.16/warc/CC-MAIN-20220809064307-20220809094307-00552.warc.gz
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CC-MAIN-2022-33
| 668 | 2 |
https://www.fishpond.co.nz/Books/Policy-Analysis-David-L-Weimer-Aidan-R-Vining/9780205781300
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math
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Preface Acknowledgments List of Figures List of Tables Part 1: Introduction to Public Policy Analysis 1. Preview: The Canadian Salmon Fishery 2. What is Policy Analysis? 3. Toward Professional Ethics Part 2: Conceptual Foundations for Problem Analysis 4. Efficiency and the Idealized Competitive Model 5. Rationales for Public Policy: Market Failures 6. Rationales for Public Policy: Other Limitations of the Competitive Framework 7. Rationales for Public Policy: Distributional and Other Goals 8. Limits to Public Intervention: Government Failures 9. Policy Problems as Market and Government Failure Part 3: Conceptual Foundations for Solution Analysis 10. Correcting Market and Government Failures: Generic Policy Instruments 11. Adoption 12. Landing on Your Feet: Organizing Your Policy Analysis 13. Implementation Part 4: Doing Policy Analysis 14. Government Supply: Drawing Organizational Boundaries 15. Gathering Information for Policy Analysis 16: Goals/Alternatives Matrices: Some Examples from CBO Studies 17: Benefit-Cost Analysis 18: When Statistics Count: Revising the Lead Standard for Gasoline Part 5: Conclusion 19: Doing Well and Doing Good
David Weimer is a Professor at University of Wisconsin-Madison, USA. Aidan R. Vining is a Professor at Simon Fraser University, Canada.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210408.15/warc/CC-MAIN-20180816015316-20180816035316-00649.warc.gz
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CC-MAIN-2018-34
| 1,292 | 2 |
http://xphomeworkjhzz.modelbook.us/calculus-problem.html
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math
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Calculus problem solver can solve differentiation of any arbitrary equation and output the result it can provide detailed step-by-step solutions to given. Exercises and problems in calculus john m erdman portland state university version august 1 largely irrelevant to the solution of the problem ix. The clep calculus exam covers skills and concepts that are usually taught in a one-semester college course in calculus. Calculus is part of the acclaimed art of problem solving curriculum designed to challenge high-performing middle and high school students calculus covers all topics.
Read reviews, compare customer ratings, see screenshots, and learn more about fx calculus problem solver download fx calculus problem solver and enjoy it. An example calculus word problem could be helpful here, since i feel like there are many types of word problems that fall into this category. Chapters: 1: introduction to calculus, 2: derivatives, 3: applications of the derivative, 4: the chain rule, 5: integrals, 6: exponentials and logarithms, 7. Need help in college calculus our time-saving video lessons cover everything with clear explanations and tons of step-by-step examples. Learn problem solving methods that you can apply across real-world ap calculus ab is roughly equivalent to a first semester college calculus course devoted to.
Math 1110 (lecture 002) august 30, 2013 pre-calculus review problems | solutions 1 algebra and geometry problem 1 give equations for the following lines in both. Category archives: calculus solved problems in calculus solving quadratic equations ii: problem 2-9: differentiating polynomial and. Hey i have a course project where i have to find/develop 15 slightly difficult calculus problems and solve them any suggestions (i'm not asking for.
How is calculus used in the real world update cancel make up a calculus problem and solve it how is calculus used in the modern world. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields join them it only takes a minute.
Calculus science anatomy & physiology astronomy astrophysics biology chemistry earth science environmental science organic chemistry calculus 1 problem.
Math 113 – calculus iii exam 3 practice problems fall 2005 1 suppose the motion of a particle is given by x = 4cost, y = sint (a) describe the motion of the. Applications of integral calculus arise whenever the problem is to compute a number that is in principle (approximately) equal to the sum of the solutions of many. Calculus ii [practice problems] to fix this problem you will need to put your browser in compatibly mode calculus i (practice problems.
First year calculus calculus instructors, high school as well as college, who have been looking for a textbook with some of the elements offered here. - this is a sample clip from the calculus i course on coolmathguycom you may view this entire section for free at coolmathguycom. Fx calculus solver helps your math problem solving in algebra and calculus.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589573.27/warc/CC-MAIN-20180717051134-20180717071121-00031.warc.gz
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CC-MAIN-2018-30
| 3,052 | 7 |
http://www.uta.edu/paleomap/geol1435/latitude.htm
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math
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The latitude-longitude system is the system most commonly used to locate features on topographic and other maps. Lines of latitude form the top and bottom margins of the map and lines of longitude from the left and right margins. Latitude is the angular distance measured with respect to a central point along a plane passed through the earth at the position of the earth's largest circumference. This plane is designated as a line of zero degrees ( 0° ) and is referred to as the equator of the earth (see Figure 7.1). Latitude then varies between 0° and 90° north and south of the equator.
Longitude is the angular distance measured east or west from a plane that passes through the north and south poles at the position of Greenwich, England. This line of longitude is referred to as the prime meridian and is assigned a value of 0° longitude. The position of the prime meridian was chosen arbitrarily. Because the earth is essentially a sphere, lines of longitude range from 0° to 180° east and west of the prime meridian with 0° east and west longitude beginning at the prime meridian and 180° east and west longitude being at a point on the other side of the earth directly opposite the prime meridian. The line defining the 180° east and west longitude is referred to as the International Date Line. International time is measured with respect to the prime meridian, while the International Date Line serves to mark the change in days. The plane defined by the prime meridian and the International Date Line serves to divide the earth into eastern and western hemispheres.
Latitude and longitude provide a very accurate method for locating points on the surface of the earth or for defining a specific area such as the area covered by a topographic map. This accuracy is the result of the way in which latitude and longitude are measured where 1° of latitude or longitude is divided into 60 equal interval or 60 minutes ( 60' ), and each minute is subdivided into 60 equal intervals or 60 seconds ( 60" ). The apostrophe symbol ( ' ) is used to denote the minutes of a degree ( ° ), and the quotation symbol ( " ) denotes the seconds of one minute. Thus 1° = 60' = 3600".
Topographic maps developed by the United States Geological Survey (U.S.G.S.) are commonly available in three sizes: 30', 15' and 7½' (7' 30") quadrangles. A 30' quadrangle is 30' (½ of a degree of latitude or longitude) on a side and represents one-quarter of the area defined by 1° of latitude or longitude [8063 to 11,547 sq. km (3,150 to 4,510 sq. miles)](see Figure 7.2). A 15' quadrangle is one-quarter of the area of a 30' quadrangle and a 7½' quadrangle is one-quarter of a 15' quadrangle (Figure 7.2). The range in area that quadrangles represent is controlled by the convergence of line of longitude as they approach the north and south poles.
Because of the difference in areas covered by these topographic maps, a 7½' quadrangle would be chosen if great detail was desired for a small area, a 15' quadrangle for medium detail of a larger area, and a 30' quadrangle for general detail of a rather large area. Topographic maps which cover even larger areas are also available, but because they cover one or more degrees of latitude and longitude the convention is to refer to these maps by thier scale such as "one to two hundred and fifty thousand (1:250,000)", "one to five hundred thousand (1:500,000)", and "one to one million (1:1,000,000)." The largest of these, 1:1,000,000, covers an area of 188,760 to 263,063 sq. km (73,734 to 102,758 sq. mi).
Back to lab 7 intro
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| 3,578 | 6 |
http://e-booksdirectory.com/details.php?ebook=10176
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math
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Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory
by R. Fenn, D.P. Ilyutko, L.H. Kauffman, V.O. Manturov
Publisher: arXiv 2014
Number of pages: 66
The purpose of this paper is to give an introduction to virtual knot theory and to record a collection of research problems that the authors have found fascinating. The second section of the paper introduces the theory and discusses some problems in that context.
Home page url
Download or read it online for free here:
by S. Hong, J. Kalliongis, D. McCullough, J. H. Rubinstein - arXiv
The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature. For any elliptic 3-manifold M, the inclusion from the isometry group of M to the diffeomorphism group of M is a homotopy equivalence.
by M. Boittin, E. Callahan, D. Goldberg, J. Remes - Ohio State University
This is an innovative project by a group of Yale undergraduates: A Multi-Disciplinary Exploration of Non-Orientable Surfaces. The course is designed to be included as a short segment in a late middle school or early high school math course.
by Andrew Ranicki, Norman Levitt, Frank Quinn - Springer
The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.
by J. P. May - Springer
The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory.
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CC-MAIN-2018-30
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http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=10426&option_lang=eng
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math
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This article is cited in 2 scientific papers (total in 2 papers)
Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations
V. V. Grushina, S. Yu. Dobrokhotovbc
a National Research University "Higher School of Economics"
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow
c Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moskovskaya obl.
The system of equations of gravity surface waves is considered in the case where the basin's bottom is given by a rapidly oscillating function against a background of slow variations of the bottom. Under the assumption that the lengths of the waves under study are greater than the characteristic length of the basin bottom's oscillations but can be much less than the characteristic dimensions of the domain where these waves propagate, the adiabatic approximation is used to pass to a reduced homogenized equation of wave equation type or to the linearized Boussinesq equation with dispersion that is “anomalous” in the theory of surface waves (equations of wave equation type with added fourth derivatives). The rapidly varying solutions of the reduced equation can be found (and they were also found in the authors' works) by asymptotic methods, for example, by the WKB method, and in the case of focal points, by the Maslov canonical operator and its generalizations.
surface waves, homogenization, asymptotic methods, small parameter, adiabatic approximation, rapidly oscillating function.
PDF file (608 kB)
Mathematical Notes, 2014, 95:3, 324–337
V. V. Grushin, S. Yu. Dobrokhotov, “Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations”, Mat. Zametki, 95:3 (2014), 359–375; Math. Notes, 95:3 (2014), 324–337
Citation in format AMSBIB
\by V.~V.~Grushin, S.~Yu.~Dobrokhotov
\paper Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations
\jour Mat. Zametki
\jour Math. Notes
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Dobrokhotov S.Yu. Grushin V.V. Sergeev S.A. Tirozzi B., “Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections”, Russ. J. Math. Phys., 23:4 (2016), 455–474
Karaeva D.A. Karaev A.D. Nazaikinskii V.E., “Homogenization Method in the Problem of Long Wave Propagation From a Localized Source in a Basin Over An Uneven Bottom”, Differ. Equ., 54:8 (2018), 1057–1072
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https://forums.aat.org.uk/Forum/discussion/448075/aat-practice-assessment-2-task-8-1-8-b-ii-required-sales-volume-units
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math
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AAT Practice Assessment 2, Task 8 (1.8) b)ii/ Required Sales Volume units
I get how to work this out (Total Fixed costs / Target Fixed Cost per unit, so 145,000/5.75) but as I get an answer of 25217.391 it doesn't make sense to me to round it down to 25,217 (which is the answer they give). 25,217 units sold would only give £144,997.75 which does not (quite) cover the required Fixed Costs (£145,000). So surely you need to make one more: 25,218?
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http://wmatem.eis.uva.es/~marsan/publications/preprints/sansatur/node2.html
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math
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Next: Non-integrability of the J22-problem Up: Non-integrable cases in satellite Previous: Introduction
Let us begin by recalling a non-integrability criterion for 2-degrees of freedom Hamiltonian systems, with homogeneous potential of integer degree, obtained by Yoshida in 1987 . Such a result is expressed as follows:
Theorem 1: Let
be a homogeneous potential function of degree
and compute the quantity (integrability coefficient)
where is the Hessian matrix of and is a solution of the algebraic equation .
If is in the so-called non-integrability regions Sk, then the 2-degrees of freedom Hamitonian system is non-integrable, i.e. there cannot exist an additional integral which is complex analytic in .
For our purposes, it suffices to consider
and the Sk given by
Now, let us consider the Hamiltonian of the truncated zonal satellite
in Cartesian canonical variables
is the disturbing potential, Pk(x) is the Legendre polynomial of order k, and are coefficients which can be considered as small parameters.
If we carry out a change to cylindrical variables the
Hamiltonian (3) is transformed into
where and the vertical component of the angular momentum, is a first integral since the coordinate is ignorable.
The Hamiltonian (5) has the integrals H= const. and const., which are independent and are in involution (i.e. the Poisson bracket ). Let us suppose that there exists a third first integral F, independent of the other two and in involution with them, that is, verifying since always holds provided F is a first integral.
it is obvious that F does not depend on .
If we perform the reduction of order of the Hamiltonian (5),
by considering as
a parameter, it is clear that if (5) is completely
integrable with integrals H,
and F, the reduction will also be so with integrals
Likewise, if the integrals of (5) are meromorphic,
so are those of the reduction. Moreover, we can assume that F is
since otherwise it suffices to multiply F by a suitable power of
is a first integral
and F are so. In consequence, if (3)
is Liouville integrable, so is
which is obtained by making in the reduction of (5) to two degrees of freedom.
Notice that, as the potential of this 2-degrees of freedom Hamiltonian
consists of a finite number of homogeneous terms, whose degrees vary from
-1 (corresponding to the Keplerian term) to -n-1, we are in conditions
to apply the Yoshida theorem (, theorem
4.1), which allows us to establish the non-existence of an additional meromorphic
integral if the integrability coeficient
of either the lowest or highest order part is in their corresponding non-integrability
regions. To this end, proceeding as Yoshida ,
by performing a suitable change of scale, the Hamiltonian (6)
which is taken as Hamiltonian of an auxiliary problem (see for details).
As the potential Vn is homogeneous of order m=-n-1,
according to Theorem 1, the non-existence of any other meromorphic
integral simply depends on finding a solution
of the algebraic equation
and on the value of the integrability coefficient
It is easily checked that the system (8)
admits a solution of the form ,
where z0 is a solution to the equation
On the other hand, by using well known properties of Legengre polynomials,
straightforward calculations allow us to compute the trace
to find that the integrability coefficient
As the non integrability regions S-n-1 defined in (2) contain the interval , we conclude that the auxiliary Hamiltonian (7) is non-integrable.
Now, coming back to the Hamiltonian (6), according to Yoshida (, theorem 4.1), in our case, it holds for the lowest order -n-1 and hence (6) is non-integrable. In consequence, as explained before, the original problem (5) is not Liouville integrable through meromorphic integrals.
Let us remark that the choice of the solution to (8) carried out here has allowed us to prove the non-integrability of any truncation of the zonal satellite problem irrespective of whether it ends in even or in odd harmonics, while the solution chosen by Irigoyen and Simó to set up the non-integrability of the J2-problem (whose truncation ends in J2) would only be useful to prove the non-integrability of truncations ending in even harmonics.
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https://goopennc.oercommons.org/courseware/lesson/3378/overview
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math
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T4T Problem Solving - Part 2 (OA.1 & NBT.5)
This resource is from Tools4NCTeachers.
This file contains a set of 26 tasks (including scoring rubric, recording sheet, printable materials, and student work samples). The tasks may be used for instruction or assessment.This is Part 2 of 2. Part 1 also contains tasks related to probelm solving.
Here is a sample of this resource. Click the attachments to download the fully-formatted collection of assessments and support materials.
John’s Baseball Cards
Operations and Algebraic Thinking
Number and Operations in Base Ten
Represent and solve problems involving addition & subtraction.
Use place value understanding and properties of operations to add and subtract.
NC.2.OA.1 Represent and solve addition an subtraction word problems, within 100, with unknowns in all positions, by using representations and equations with a symbol for the unknown number to represent the problem, when solving:
NC.2.NBT.5 Demonstrate fluency with addition and subtraction, within 100, by:
SF, Pencil, Paper, counters and base ten materials available
Provide materials to the student. Read the problem to the student: John collected 67 baseball cards. His friend gave him 28 more baseball cards. How many cards does John have now? Write an equation that represents this problem. Use a symbol for the unknown number.
Once an equation is written, say: Solve the problem and use words, numbers or pictures to explain your reasoning.
Continuum of Understanding
Not Yet Proficient
Standards for Mathematical Practice
1. Makes sense and perseveres in solving problems.
2. Reasons abstractly and quantitatively.
3. Constructs viable arguments and critiques the reasoning of others.
4. Models with mathematics.
5. Uses appropriate tools strategically.
6. Attends to precision.
7. Looks for and makes use of structure.
8. Looks for and expresses regularity in repeated reasoning.
John collected 67 baseball cards. His friend gave him 28 more baseball cards. How many cards does John have now?
Write an equation that represents this problem. Use a symbol for the unknown number.
Solve the problem.
Use words, numbers or pictures to explain your reasoning.
__________________ baseball cards
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https://mellaly.com/exploring-the-psychological-impact-of-47-xyy-syndrome-on-individuals-and-families/
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math
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# The Psychological Impact of 47 XYY Syndrome on Individuals and Families
– Definition of 47 XYY syndrome
– Prevalence and incidence
## Physical Impact of 47 XYY Syndrome
– Physical characteristics
– Health risks and complications
## Psychological Impact on Individuals with 47 XYY Syndrome
– Behavioral issues and developmental delays
– Learning difficulties and cognitive impairments
– Relationship difficulties and social isolation
## Psychological Impact on Families of Individuals with 47 XYY Syndrome
– Impact on family dynamics
– Emotional struggles and stress
– Support and resources available
## Treatment and Support
– Behavioral therapies and interventions
– Educational support and accommodations
– Mental health support
## Stigma and Misconceptions
– Myths and misconceptions surrounding 47 XYY syndrome
– Addressing stigmatization and raising awareness
– Summary of key points
– Future directions for research and support
1. Is 47 XYY syndrome hereditary?
– There is a rare chance of passing the extra Y chromosome from father to son. However, most cases occur as a random genetic error during the formation of sperm or eggs.
2. Can individuals with 47 XYY syndrome live a normal life?
– Yes, with appropriate support and interventions, individuals with 47 XYY syndrome can lead happy and fulfilling lives.
3. Can 47 XYY syndrome be cured?
– No, there is no cure for 47 XYY syndrome, but symptoms can be managed with appropriate treatment and support.
4. Can individuals with 47 XYY syndrome have children?
– Yes, most men with 47 XYY syndrome are able to father children.
5. Is 47 XYY syndrome a form of mental illness?
– No, 47 XYY syndrome is a genetic condition that can lead to developmental and behavioral challenges, but it is not a mental illness.
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http://www.coloradocountydemocrats.com/amortization-schedule-with-balloon-payment-and-extra-payments/
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math
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Once you have filled out all your information click on the calculate button to see the side-by-side results for your old loan and the loan with extra payments made. At the bottom of the calculator there is also an option to turn on displaying a monthly amortization schedule with your results.
Free Excel Amortization Schedule Templates Smartsheet – A balloon payment is when you schedule payments so that your loan will be paid off in one large chunk at the end, after a series of smaller payments are made to reduce the principal. This loan amortization template will calculate both your monthly payments and the balloon payment amount and schedule.
Balloon Loan Calculator. This tool figures a loan’s monthly and balloon payments, based on the amount borrowed, the loan term and the annual interest rate. Then, once you have calculated the monthly payment, click on the "Create Amortization Schedule" button to create a report you can print out.
How To Calculate A Balloon Payment Balloon Auto Loan Calculator How To Calculate Balloon Payment – Lake Water Real Estate – First, the balloon payment will always be equal to the loan amount. Therefore, it isn’t possible to solve for the balloon payment. Or looked at in a different way, the user cannot provide a periodic payment amount. The calculator will always calculate the regular payment amount since it is the interest due.
land contract with balloon payment and extra payments. – The contract is based on 30 year amortization schedule with 5% APR calculated monthly based on remaining principal. I am approaching the end of the contract when a balloon payment of the remaining principle is due. I have been making payments in excess of the minimum monthly payments every month since the beginning of the contract.
Balloon Auto Loan Calculator Definition Balloon Payment How To Calculate A balloon payment bank rate Com Mortgage Calculator Refinance Calculator – Should You Refinance? | Zillow – Try our easy-to-use refinance calculator and see if you could save by refinancing. Estimate your new monthly mortgage payment, savings and breakeven point.How to calculate balloon equity mortgage payoff. – How to Calculate Balloon Equity Mortgage Payoff. For example, if the annual rate is 4.92 percent, or 0.0492, divide 0.0492 by 12 to get 0.0041. Add 1 to the monthly rate. In this example, add 1 to 0.0041 to get 1.0041. Raise the result to the number of payments you make before the balloon payment is due.Bank Rate Com Mortgage Calculator Mortgage Calculator – Interest – Use our mortgage loan calculator to determine the monthly payments for any fixed-rate loan. Just enter the amount and terms, and our mortgage calculator does the rest. Click on "Show Amortization" Table to see how much interest you’ll pay each month and over the lifetime of the loan.Balloon payment definition and meaning | Collins English. – A balloon payment is a large final payment of a loan. At the end of the five years, the loan will be due and payable and the investor will have a balloon payment to make. One form of deferring principals is to make a balloon payment at the end of the term.Bank Rate Com Mortgage Calculator Balloon Auto Loan Calculator Mortgage Refinance Calculator from Bank of America – Mortgage Refinance Calculator from Bank of America Use this refinance calculator to see if refinancing your mortgage is right for you. Calculate estimated monthly payments and rate options for a variety of loan terms to see if you can reduce your monthly mortgage payments. refinance calculator, mortgage refinance calculator, refinancing mortgage calculator, refinance mortgage calculator
Loan calculator with extra payments – templates.office.com – Loan calculator with extra payments. This loan calculator template generates a loan amortization schedule based on the details you specify. Enter the interest rate, loan amount, and loan period, and see what your monthly principal and interest payments will be.
28 Tables to Calculate Loan Amortization Schedule (Excel) – Scheduling Extra Payments in Amortization Schedule. When you have extra payments in hand, you either choose to schedule extra payments in a lump sum or at regular intervals in the loan schedule. The advantage of making extra payments can help you in saving money in compounding interest and reduce the length of your loan too.
Balloon Loan Calculator | Single or Multiple Extra Payments – However, this amortization schedule will create a balloon payment schedule and you can set both the loan date and first payment date. To use for a balloon schedule, enter all 4 values (loan amount, number of payments [payment number balloon is due], interest rate and normal payment amount) and calculator will show final balloon payment.
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| 4,784 | 9 |
https://econpapers.repec.org/paper/mprmprres/fd33fca139d04cb0945ba22f0eb2a6e5.htm
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math
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US Life Expectancy: The Authors Reply
Arline T. Geronimus,
Javier M. Rodriguez and
Timothy A. Waidmann
Mathematica Policy Research Reports from Mathematica Policy Research
Keywords: US; Life; Expectancy (search for similar items in EconPapers)
JEL-codes: I (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-hea
References: Add references at CitEc
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Export reference: BibTeX
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Persistent link: https://EconPapers.repec.org/RePEc:mpr:mprres:fd33fca139d04cb0945ba22f0eb2a6e5
Access Statistics for this paper
More papers in Mathematica Policy Research Reports from Mathematica Policy Research Mathematica Policy Research P.O. Box 2393 Princeton, NJ 08543-2393 Attn: Communications. Contact information at EDIRC.
Bibliographic data for series maintained by Joanne Pfleiderer ().
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https://constructivist.info/authors/jonas-l%C3%B6wgren
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math
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Author: Jonas Löwgren
Bio Note: Jonas Löwgren is professor of interaction and information design at Linköping University, Sweden. He specializes in collaborative media design, interactive visualization and the design theory of digital materials. More information is at http://jonas.lowgren.info/
Affiliation: Linköping University, Sweden
Publications in Constructivist Foundations
Reader Impact Factor: 0.22 The RIF of an author expresses how many times more often the texts of this author have been downloaded than the average text, i.e., RIF = dn/D, with d = number of downloads of all texts of this author, D = number of all downloads of all texts, n = number of all texts published.
Löwgren J. (2015) The rtd community and the big picture. Constructivist Foundations 11(1): 28–30. http://constructivist.info/11/1/028
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| 827 | 6 |
https://research.cs.wisc.edu/techreports/viewreport.php?report=100
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math
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Minimum Error Bounds for Multidimensional Spline Approximation
Approximation of a smooth function f on a rectangular domain 9 c E' , by a tensor product of splines of degree m is considered. A basis for the product spline is formed using a single one-dimensional spline function. The approximation is computed, using linear programming, so as to minimize the maximum error on a discrete grid Q i 0, with grid size h. Realistic a posteriori bounds on the error in the uniform norm are given. Convergence of the approximation to a best approximation as h -+ 0 is shown. The extension to linear boundary value problems is also discussed.
Download this report (PDF)
Return to tech report index
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| 689 | 4 |
http://www.kgbanswers.com/which-equivalent-fraction-would-you-have-to-use-in-order-to-add-35-to-2125/4733510
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math
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Which equivalent fraction would you have to use in order to add 3/5 to 21\\25
In order to add fractions, the denominators (the bottom numbers) must be the same. We can convert the first fraction of 3/5 to 15/25 by multiplying both the numerator (the top number) and the denominator by 5. Then we have 15/25 + 21/25. To add these fractions, we simply add the numerators together and keep the denominator, which results in 36/25. This reduces to 1 11/25, or 1/44.
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| 461 | 2 |
https://graduateway.com/measurement-of-the-speed-of-sound-in-air/
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math
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Measurement of the Speed of Sound in Air
Physics 1 Experiment #4: “Measurement of the Speed of Sound in Air” Measurement of the Speed of Sound in Air Write-up The data on the hand drawn graph, previously shown, fits that of a straight line; this means that there is a linear relationship between the dependent (position) and independent (time) variables. The value of the slope of the line determined by hand is the same as the value obtained from the linear regression done with the calculator because the points chosen were as precise as the graph obtained from excel.
The experimental velocity obtained from calculating the slope of the graph of position vs. time measured in lab was found to be: Vexp=34. 526 cm/ms The distance(cm) a sound pulse will travel in a time period of 0. 50 ms is calculated by doing the following: d=d0+V0t+12at2 d=0+V0t+0 d=34. 526cmms*0. 50 ms = 17. 263 cm A light pulse with the speed of 3. 00*10^8 will travel in 0. 50 ms a distance of : 3. 00*108ms*0. 0006214 miles1 m=x miles0. 50 ms*1000 ms1 s=93. 21 miles An experimental measurement with little or no systematic error is said to be of high accuracy.
More Essay Examples on Measurement Rubric
An experimental measurement with little or no random error is said to be of high precision. The Vaccepted = 346. 98 m/sec does not fall within the interval determined by the limits of the precision, as the following is not true for this experiment: ±? V=VexpSDMX ±? V=34. 526cmms0. 063cm61. 362cm=0. 035cmms Vacc-Vexp ? ?Vexp 1. 72ms? 0. 35ms In the above formula the error in time can be ignored as the error is associated with consistently centering the sharp peak of the voltage trace on the oscilloscope’s 0.
50 ms vertical grid lines. Furthermore, the reason Vaccepted did not fall within the interval determined by the limits of our experimental error determined before, is due to systematic error, which can be a consequence of not accounting for a temperature variable in the tube. In fact if there was a temperature dependence in the tube , the temperature that would be responsible for the lack of precision would be as follows: Vexp=332. 1171+TC273. 15=345. 26 TC=22. 05 ?
One can state that as a consequence of this experiment that the accepted speed of sound can be measured , with high precision , when taking into account all factors including temperature for the limitations in my claims are due to the systematic error in the system, otherwise the experimental value would be more precise when compared to the accepted value. Finally as compared to the accepted value of 346. 975 m/s , the experimental value found was 345. 3±0. 4 ms
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| 2,641 | 7 |
https://www.justanswer.co.uk/immigration-law/8r20u-hi-there-i-met-girlfriend-who-chinese-national.html
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math
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Ask an Immigration Solicitor. Get an Answer ASAP.
She has a student visa, I dont know any of the details apart from it expires January 25th.
Her current salary is £18,500 per annum.
I currently don't have an annual salary as I'm looking for work.
Thankyou very much for the information you have provided so far. I personally have savings in excess of £16,000. How does this effect the situation?
I have savings of £20,000.
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| 425 | 6 |
https://onepetro.org/PETSOCATM/proceedings-abstract/90ATM/All-90ATM/PETSOC-90-01/5650
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math
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An algorithm to compute pressure distributions in commingled reservoirs that are produced via complex completion systems is described. We show that single layer solutions for systems of interest can be readily combined to obtain pressure distributions in commingled reservoirs for combinations of rock type. Completion schemes and outer boundary conditions for each layer may be different. Theoretical claims are substantiated by considering example applications.
This communication presents a stable and robust algorithm to compute responses at wells that produce commingled reservoirs. We take advantage of the unique feature of commingled reservoir production for the constant terminal pressure solution and present an algorithm to determine the well response for constant or variable rate production. Expressions to compute sand-face layer rates are also presented. The advantages of the algorithm we present are:
any combinations of wellbore and outer boundary conditions can be incorporated and the combinations can be different in each layer,
characteristics of each layer including rock type can be different.
existing codes for single layer systems can be used with minor modifications to compute commingled reservoir responses, and
approximate solutions for various situations of interest can be derived. Our intent is similar to that in Refs. 1–3, in that this algorithm will enable analysts to obtain commingled reservoir responses for interactive analysis and history matching purposes.
The efficacy of the algorithm has been tested by comparing responses with standard solutions. 4–7 In general solutions are in agreement to at least three digits.
We consider the flow of a slightly compressible fluid of constant viscosity in a commingled reservoir. Each layer is assumed to be a uniform porous medium. However, the properties, rock type, completion conditions, location of boundaries and the boundary condition (closed, constant pressure) in each layer are entirely arbitrary. The initial pressure in each layer is assumed to be different.
Solutions discussed in this work will be presented for convenience in dimensionless form. The Van Everdingen-Hurst8 definitions will be used in this work. For describing properties of the entire reservoir system we use thickness averaged permeability. kh and thickness averaged porosity compressibility product oct i.e.:
Equation (1) (Available in full paper) and Equation (2) (Available in full paper)
Here J is the layer index and n is the total number of layers.
To outline the algorithm, we will for simplicity assume that the initial pressure in each layer is identical> It is well-known that if a commingled reservoir is produced at a constant pressure, then the layers are effectively decoupled and production from each layer is independent of the other layer.9 Thus, if qD(tD) is the total production rate from the commingled reservoir based on kh and qD is the flow rate from layers J based on kJhJ then
Equation (3) (Available in full paper)
The algorithm takes advantage of Eq. 3 and Dubamel's theorem which is given by
Equation (4) (Available in full paper)
Equation (5) (Available in full paper)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988802.93/warc/CC-MAIN-20210507181103-20210507211103-00038.warc.gz
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CC-MAIN-2021-21
| 3,168 | 16 |
https://math.answers.com/Q/James_has_33_coins_in_his_pocket_all_of_them_nickels_and_quarters_If_he_has_a_total_of_2.65_how_many_quarters_does_he_have
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math
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This problem can be solved by solving the system of equation. Total worth of coins: $2.65 Total number of coins: 33 n= number of nickels q= number of quarters since we know that there are 33 coins total, we can set the equation like this: number of nickels + number of quarters = total number of coins => n+q=33 We also know that the worth of these coins is $2.65. each nickel is worth of $0.05 each quarter is worth of $0.25 therefore we can set the equation: 0.05 x number of nickels + 0.25 x number of quarters = total worth of coins. 0.05n+0.25q=2.65 However, for convienience, we should multiply the equation above by 100 to get rid of decimals. Thus it is 5n+25q=265 you will now have a following set of 2 equations: n+q=33 5n+25q=265 Use the SUBSTITUTION METHOD to solve either n or q for solving n: (replace q with n if you're willing to solve q instead) n+q=33 => n=33-q (since n is equal to 33-q, we can -q -q substitue n in the other equation.) 5(33-q)+25q=265 => 165-5q+25q=265 => 20q=100 => q=5 -165 -165 /20 /20 There are 5 quareters as a result.(or 28 nickels) since you know that q=5 you can substitute q in the first equation. n+(5)=33 => n=28 - 5 -5 therefore, there are 5 quarters and 28 nickels. ELIMINATION METHOD: n x -5 + q x -5 = 33 x -5 => -5n-5q=-165 5n+25q=265 + 5n+25q=265 ------------- 20q=100 => q=5 /20 /20 Or simply we can say: if we have x quarters, we have .25x value of them. So the value of nickels will be 2.65 - .25x. Since we have 33 coins, and x quarters, then the number of nickels will be 33 - x. So the value of all nickels would be also .05(33 - x). Thus, we have:
2.65 - .25x = .05(33 - x)
2.65 - .25x = 1.65 - .05x
2.65 - 1.65 - .25x + .25x = 1.65 - 1.65 - .05x + .25x
1 = .20x
1/.20 = .20x/.20
x = 5 the number of quarters 33 - x
= 33 - 5
= 28 the number of nickels. Thus, we have 5 quarters and 28 nickels.
4 nickels and 5 quarters
47 Quarters 83 Nickels
7 quarters and 11 nickles
7 nickels, 4 dimes, and 3 quarters.
10 quarters and 5 nickels
7 quarters = 1.7511 nickels = 0.551.75 + 0.55 = 2.30
7 nickels, 3 quarters
8 of them.
She has 11 nickels.
Helen has twice as many dimes as nickels and five more quarters than nickels the value of her coins is 4.75 how many dimes does she have?
3 quarters and 10 nickels.
10 quarters and 50 pennies
In the US, we use pennies, nickels, dimes and quarters.
4 quarters and 3 nickels
Ten (10) nickels and Three (3) quarters.
8 quarters and 12 nickels
3 quarters & 2 nickels
The coins in the store's cash register total $12.50. The cash register contains only nickels, dimes, and quarters. There are twice as many dimes as nickels. There are also twice as many quarters as dimes. How many quarters are in the cash register?
you have 3 quarters 31 dimes and 65 pennies
The question suggests that there are 24 coins. 13 of them are pennies, 14 are nickels, and 16 are dimes and the rest are quarters. To answer this question, One would add the number of pennies, nickels, and dimes and subtract the sum of those coins from 24. The difference of the two numbers would be the amount of quarters. However, 13+14+16=43. 24-43= -19 There can't be -19 quarters.
4 quarters. 100 pennies. 10 dimes. 20 nickels
10 nickels and 2 quarters
Two quarters, a dime, two nickels, and a penny
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588246.79/warc/CC-MAIN-20211028003812-20211028033812-00595.warc.gz
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CC-MAIN-2021-43
| 3,257 | 32 |
https://www.morewords.com/word/factorials
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math
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Definition of factorials
The word factorials uses 10 letters: a, a, c, f, i, l, o, r, s, t
factorials is playable in:
Meanings of factorials
plural of factorial
Direct anagrams of factorials
Words with the same length and used letters. Useful for word puzzles.
Other words with the same letter pairs
Find words containing the letter combinations found in factorials.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710534.53/warc/CC-MAIN-20221128171516-20221128201516-00596.warc.gz
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CC-MAIN-2022-49
| 366 | 9 |
https://www.sugardaddyforme.com/sugar-daddies/mi/melvindale
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math
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I value my time dearly$$$$!!
I'm 27 with no kids and single I love to have lots of fun,and travel take trips if im not in school. I'm a very concervative, respectful, caring, kind,gentle, organized, mannerabe person to be around. Im in school part time ...read more
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402118004.92/warc/CC-MAIN-20200930044533-20200930074533-00604.warc.gz
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CC-MAIN-2020-40
| 265 | 2 |
http://dmoz-odp.org/Science/Math/Combinatorics/Research_Groups/
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math
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Academic research groups in Combinatorics.
Related categories 2
(Australia) The University of Queensland
Centre for Discrete Mathematics and Computing.
(Europe) Combinatorics, Geometry and Computation
A European graduate programme.
Algorithms Project. Interests in design and analysis of algorithms, computer algebra, combinatorial analysis and asymptotics.
(France) Laboratoire d'informatique de l'IGM
Research into the relations between algebra and combinatorics.
(Italy) Catania University
Catania Combinatorial Group. History, people, activities, visitors.
Japanese Center for Combinatorics and its Applications. A virtual research centre. Links, lists.
(New Zealand) University of Auckland
Centre for Discrete Mathematics and Theoretical Computer Science.
Combinatorics group at Chalmers University of Technology and Gothenburg University.
(UK) Queen Mary College, London
Design Research Group. Courses, lecture notes, members, design resources.
(USA) Texas A+M
Algebra and Combinatorics. Members, conferences, resources.
British Combinatorial Committee
Conference listings, bulletin and links maintained by Peter Cameron.
Last update:September 23, 2016 at 9:45:08 UTC
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267163146.90/warc/CC-MAIN-20180926022052-20180926042452-00527.warc.gz
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CC-MAIN-2018-39
| 1,173 | 22 |
https://able2know.org/topic/257920-1
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math
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Sun 26 Oct, 2014 12:03 am
Hello,buddies.l am seeking your help to solve this physics.
A charge 4uC placed 60cm away from the charge -4uC.What's the electric field:1.a point P midway between the charges? 2.At a point Q 4ocm from P and equidistant from the two charges.
Thank you all in advance
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323583423.96/warc/CC-MAIN-20211016043926-20211016073926-00365.warc.gz
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CC-MAIN-2021-43
| 292 | 4 |
http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-1-1
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math
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It is known that there is a comeagre set of mutually conjugate measure preserving homeomorphisms of Cantor space equipped with the coinflipping probability measure, i.e., Haar measure. We show that the generic measure preserving homeomorphism is moreover conjugate to all of its powers. It follows that the generic measure preserving homeomorphism extends to an action of (ℚ, +) by measure preserving homeomorphisms, and, in fact, to an action of the locally compact ring 𝔄 of finite adèles.
Similarly, S. Solecki has proved that there is a comeagre set of mutually conjugate isometries of the rational Urysohn metric space. We prove that these are all conjugate with their powers and therefore also embed into ℚ-actions. In fact, we extend these actions to actions of 𝔄 as in the case of measure preserving homeomorphisms.
We also consider a notion of topological similarity in Polish groups and use this to give simplified proofs of the meagreness of conjugacy classes in the automorphism group of the standard probability space and in the isometry group of the Urysohn metric space.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510368.33/warc/CC-MAIN-20230928063033-20230928093033-00192.warc.gz
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CC-MAIN-2023-40
| 1,096 | 3 |
https://www.jiskha.com/display.cgi?id=1359312755
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math
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posted by Darrin .
Write the equation for the reaction associated with the Ka2 of sulfuric acid, H2SO4.
Write the equation for the reaction associated with the Kb2 of carbonate, CO32–.
1 H2SO4 ==> H^+ + HSO4^-
2 HSO4^ ==> H^+ + SO4^2-
1 is 100 ionized; therefore, there is no k1.
k2 = (H^+)(SO4^2-)/HSO4^-)
Do the same kind of thing with the hydrolysis of CO3^2-
1 CO3^2- + HOH ==> HCO3^- + OH^-
k1 = ....
2 HCO3^- + HOH ==> H2CO3 + OH^-
k2 = (H2CO3)(OH^-)/(HCO3^-) = ?
bob you are literally always wrong
DrBob222 is 100% correct. The acid will lose hydronium ions in water, whereas a base will gain hydronium ions in water; remember that the arrows must be pointing in both directions when writing these chemical equations due to equilibrium (strong acids and bases completely dissociate in water). It's actually not all that simple but best way to put it for those having difficulty understanding.
Bob's biggest fans
We Love you Bob, let the haters hate, they don't know what they're talking about
My Sapling grade is suffering, thanks Bob
I think Bob just put the equation in a different format than Sapling is asking for. I got
HSO4^- <--> SO4^2-(aq) + H^+(aq)
HCO3^-(aq) + H2O(l) <--> H2CO3(aq) + OH-(aq)
soooo he is kinda wrong?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891750.87/warc/CC-MAIN-20180123052242-20180123072242-00384.warc.gz
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CC-MAIN-2018-05
| 1,236 | 21 |
http://mathschoolinternational.com/Math-Books/Books-FUNCTIONAL-ANALYSIS/01-Math-Books-FUNCTIONAL-ANALYSIS.aspx
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math
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Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc
Here we provide thousands of Question and their ANSWERS. Our question is helpful in ECAT, UPSC(IAS/IPS/IFS), ESE, EES, NTS FSc, BSc and all kinds of MATH/IQ TESTS.
MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of
Functional Analysis eBooks . We hope mathematician or person who’s interested in mathematics like these books.
Normed Spaces. Banach Spaces
Inner Product Spaces. Hilbert Spaces
Fundamental Theorems for Normed and Banach Spaces
Further Applications: Banach Fixed Point Theorem
Further Applications: Approximation Theory
Spectral Theory of Linear Operators in Normed, Spaces
Compact Linear Operators on Normed Spaces and Their Spectrum.
Spectral Theory of Bounded Self-Adjoint Linear Operators
Unbounded Linear Operators in Hilbert Space
Unbounded Linear Operators in Quantum Mechanics
Appendix 1. Some Material for Review and Reference
Appendix 2. Answers to Odd-Numbered Problems.
Appendix 3. References.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743521.59/warc/CC-MAIN-20181117123417-20181117145417-00505.warc.gz
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CC-MAIN-2018-47
| 1,093 | 17 |
https://www.abrakid.com/the-number-soothsayer/
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math
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This one is a favorite of mine. Two spectators each hold out any number of fingers on one of their hands. (E.g. one might put out 3 fingers and the other, 2.) A third spectator tells the magician, who is looking the other way, the total (in this example, 5). The magician immediately announces that spectator #1 is holding out 2 fingers, and #2 is holding out 3. Just lucky? No, because you play 2 more rounds and the magician is correct each time! How can she possibly know this? One of the spectators is a confederate. He holds out 3 fingers in round #1, and in subsequent rounds, however many fingers spectator #2 held out the last round. So, e.g., in our above example, spectator #1 is the confederate. When you hear “5”, you know that #1 has 3, so #2 must have 2. In round 2, suppose the total is 6. You know that spectator #1 has 2 (same as #2 had the previous round), so #2 must have 4!
I like that this trick needs no props, and it hones subtracting in your head quickly. For a little more challenge, let the 2 people each use 2 hands. Good luck!
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100942.92/warc/CC-MAIN-20231209170619-20231209200619-00771.warc.gz
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CC-MAIN-2023-50
| 1,058 | 2 |
https://www.hackmath.net/en/math-problem/1861
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math
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What is 7+8-(5×2)+5-4+(6×(5-3)+6)-(8+10)-7+6?
Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):
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At the bus stop 8 people take out and 10 people take into bus. Next stop 6 take out and 5 take in. On the third stop 6 take out and 3 take in. The bus traveled further with 39 people. How many passengers were originally at the bus?
400 employees cast their votes in a board member election that has only 2 candidates. 120 people vote for candidate A, while half of the remaining voters abstain. How many votes does candidate B receive?
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Add up the number writtens in Roman numerals. Write the results as a roman numbers.
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Add up the number writtens in Roman numerals. Write the results as a decimal number.
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Flood waters in some US village meant that the homes had to evacuate 364 people. 50 of them stayed at elementary schools, 59 them slept with their friends and others went to relatives. How many people have gone to relatives?
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Added together and write as decimal number: LXVII + MLXIV
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665726.39/warc/CC-MAIN-20191112175604-20191112203604-00177.warc.gz
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CC-MAIN-2019-47
| 2,511 | 35 |
http://www.hillviewprep.com/problem-of-the-day/category/kinematics
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math
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The stratosphere is the layer of the Earth’s atmosphere that is more than 10 kilometers (km) and less than 50 km above the Earth’s surface. Which of the following inequalities describes all possible heights x, in km, above the Earth’s surface that are in the stratosphere?
A) |x + 10| < 50
B) |x − 10| < 50
C) |x + 30| < 20
D) |x − 30| < 20
A car traveling at 22.4 m/s skids to a stop in 2.55 s. Determine the skidding distance of the car (assume uniform acceleration).
If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)?
Write something about yourself. No need to be fancy, just an overview.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670770.21/warc/CC-MAIN-20191121101711-20191121125711-00121.warc.gz
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CC-MAIN-2019-47
| 720 | 8 |
https://community.oracle.com/customerconnect/discussion/39742/can-you-report-on-answers-to-ace-questions
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math
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Can you report on answers to ACE questions?
I apologize if this question has been answered already. I did some searching and my results didn't produce much so I thought it would be safe to post.
When it comes to answers to ACE questions, is there a way to report on this in Taleo OBI? For example, we have a standard ACE question regarding salary, would it be possible to report on candidates for a requisition and add what each candidate answered to this question?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511406.34/warc/CC-MAIN-20231004184208-20231004214208-00584.warc.gz
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CC-MAIN-2023-40
| 465 | 3 |
https://digitalcommons.mtu.edu/michigantech-p/5544/
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math
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Large deflections of cantilever beams of nonlinear materials
This paper deals with the large deflections (finite) of thin cantilever beams of nonlinear materials, subjected to a concentrated load at the free end. The stress-strain relationships of the materials are represented by the Ludwick relation. Because of the large deflections, geometrical nonlinearity arises and, therefore, the analysis is formulated according to the nonlinear bending theory. Consequently, the exact expression of the curvature is used in the moment-curvature relationship. The resulting second-order nonlinear differential equation is solved numerically using fourth-order Runge-Kutta method. For comparison purposes, the differential equation is solved for linear material and the results are compared to the exact solution which uses elliptic integrals. Deflections and rotations along the central axis of beams of nonlinear materials are obtained. The numerical algorithm was performed on the UNIVAC 1110. © 1981.
Computers and Structures
Large deflections of cantilever beams of nonlinear materials.
Computers and Structures,
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5544
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178378872.82/warc/CC-MAIN-20210307200746-20210307230746-00204.warc.gz
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CC-MAIN-2021-10
| 1,177 | 6 |
https://www.sparrho.com/item/chain-reduction-preserves-the-unrooted-subtree-prune-and-regraft-distance/a001bf/
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math
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Indexed on: 07 Nov '16Published on: 07 Nov '16Published in: arXiv - Computer Science - Discrete Mathematics
The subtree prune-and-regraft (SPR) distance metric is a fundamental way of comparing evolutionary trees. It has wide-ranging applications, such as to study lateral genetic transfer, viral recombination, and Markov chain Monte Carlo phylogenetic inference. Although the rooted version of SPR distance can be com puted relatively efficiently between rooted trees using fixed-parameter-tractable algorithms, in the unrooted case previous algorithms are unable to compute distances larger than 7. One important tool for efficient computation in the rooted case is called chain reduction, which replaces an arbitrary chain of subtrees identical in both trees with a chain of three leaves. Whether chain reduction preserves SPR distance in the unrooted case has remained an open question since it was conjectured in 2001 by Allen and Steel, and was presented as a challenge question at the 2007 Isaac Newton Institute for Mathematical Sciences program on phylogenetics. In this paper we prove that chain reduction preserves the unrooted SPR distance. We do so by introducing a structure called a socket agreement forest that restricts edge modification to predetermined socket vertices, permitting detailed analysis and modification of SPR move sequences. This new chain reduction theorem reduces the unrooted distance problem to a linear size problem kernel, substantially improving on the previous best quadratic size kernel.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00428.warc.gz
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CC-MAIN-2020-50
| 1,530 | 2 |
http://www.broadcastingcable.com/video/B_C_Hall_Of_Fame/3327-Tony_Vinciquerra_B_C_Hall_of_Famer.php
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math
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Sign up to get online access to the latest magazine content and more »
Lady Gaga will headline the Super Bowl 51 halftime show, the singer confirmed Thursday on Twitter.
Beginning later this year, VR entertainment app company NextVR and concert company Live Nation will
Complete Coverage: On Demand Summit
The Times Center, New York, NY
Waldorf Astoria, New York City, New York
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s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662159.54/warc/CC-MAIN-20160924173742-00254-ip-10-143-35-109.ec2.internal.warc.gz
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CC-MAIN-2016-40
| 382 | 6 |
https://mmsanotherstage2019.com/during-a-party-everyone-shook-hands-with-everybody-else/
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math
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Brian was a geometry teacher through the Teach because that America program and started the geometry routine at his school
The formula because that the number of handshakes possible at a party through n human being is# handshakes = n*(n - 1)/2.
This is since each of the n civilization can shake hands through n - 1 people (they would not shake their own hand), and also the handshake in between two civilization is not counted twice.
You are watching: During a party everyone shook hands with everybody else
This formula have the right to be provided for any variety of people. For example, v a party that 10 people, find the number of handshakes possible.
# handshakes = 10*(10 - 1)/2.
# handshakes = 10*(9)/2.
# handshakes = 90/2.
# handshakes = 45
So, there room 45 handshakes that have the right to be made between 10 people.
See more: Are There Any Symbols In A Sound Of Thunder The Butterfly Symbolizes
Let’s speak you invited 10 civilization over because that a party, just how many feasible handshakes would there be? and also again i’m going to counting a handshake as if you have actually two world meeting each various other that would certainly be one handshake. What we’re walking to execute is we’re going to use mathematical modelling which method you’re kind of utilizing a snapshot to define a problem.So stop say you had two people, a mathematically version of that would simply be a heat segment and you’d say the the variety of handshakes feasible here is one.Okay therefore our goal is ultimately to number out because that n number of people how many handshakes, so stop look at a couple of more examples. Let’s say you had three people, the mathematical model there would certainly be 1, 2, 3 people and also there would be three handshakes, for this reason three human being three handshakes. You have actually four world you’re going to have 4 dots which represent for human being at the party and you’re going to have 4 handshakes yet you’re likewise going to have actually two more.So we’ve acquired one, three a full of six. So ns noticing that us don’t have a linear role here, we’ll execute one critical one. If you have actually five people at a party, you going come have five people and also then you’re going to have five more handshakes because that a full of 10.So a couple of ways that you can do this, you could say oh well these space the triangular numbers so I know the formula or you might say fine looking at my version how can I come up with the variety of handshakes. Fine the number of people we’re going to say is n and also if I have one person. How numerous times could I shake hands. Right here I might shake hands one time, i beg your pardon is one much less than two. Here I could shake two times which is one much less than three. Right here I might shake one, two, 3 times. So i’m seeing the the number of handshakes is one less than the total variety of people since I have the right to shake hands v everyone there other than for myself.Just favor with the diagonal problem we’re walk to count every single one of these handshakes. So ns going have to have divide that entirety term through 2. For this reason the number of handshakes in ~ a party is the variety of people times the number of people minus 1, due to the fact that you’re taking yourself out of the equation and also you’re walking to divide it by 2 since you don’t want to twin count every person, excuse me friend don’t want to double count every handshake.So it is our formula because that the number of handshakes with n variety of people.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662515501.4/warc/CC-MAIN-20220517031843-20220517061843-00186.warc.gz
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CC-MAIN-2022-21
| 3,607 | 12 |
http://vinar.vin.bg.ac.rs/handle/123456789/3393
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math
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Chain length probability distribution - equivalence of ASYNNNI and 1d Ising model
АуториMilić, Mirjana M.
Чланак у часопису
МетаподациПриказ свих података о документу
An expression for the chain length probability distribution p(l) of a one dimensional Ising chain was derived using the cluster variation method formalism, the p(l) being expressed through the pair cluster probabilities. It was shown numerically that the same expression also applies in the case of one dimensional chains formed along one of the next-nearest neighbor interactions included in the two dimensional ASYNNNI (Asymmetric Next-Nearest Neighbor Ising) model, widely used to describe the statistics of oxygen ordering in the basal CuO (x) planes of the YBa(2)Cu(3)O(6+x) type high-T (c) superconducting materials. Equivalency between ASYNNNI and 1d Ising model is discussed.
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http://www.ask.com/web?qsrc=60&o=41647999&oo=41647999&l=dir&gc=1&q=Determining+Concentration+of+Solution
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math
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Concentrations of Solutions. There are a number of ways to express the relative
amounts of solute and solvent in a solution. This page describes calculations for
How to Calculate the Concentration of a Solution. In Chemistry, a solution is a
homogeneous mixture of two things - a solute and the solvent that it's dissolved in
See how to calculate the concentration of a chemical solution in percent
composition by mass, volume percent, molarity, molality, and normality.
An aqueous solution consists of at least two components, the solvent (water) ...
One could do by keeping track of the concentration by determining the mass of ...
Calculating the concentration of solutions in moles per litre (molarity), a tutorial
suitable for chemistry students.
www.ask.com/youtube?q=Determining Concentration of Solution&v=XIv3Nr0upc8
Nov 14, 2011 ... How to calculate the concentration of a solution if you're given the number of
moles of solute and the volume you are mixing it into. C = n/V Ask ...
www.ask.com/youtube?q=Determining Concentration of Solution&v=UMPyExRPsuw
Sep 11, 2012 ... Chemistry Tips. Looking for college credit for Chemistry? ... Concentration of
Solutions Introduction: Mass/Volume % (m/v)% - Duration: 7:26.
Aug 2, 2013 ... Such concentration calculations are needed when starting with the solid form of a
chemical and a solution needs to be prepared with the ...
California State Standard: Students know how to calculate the concentration of a
solute in terms of grams per liter, molarity, parts per million, and percent ...
The concentration of a solution is generally measured in molarity. To determine
the molarity of a solution, divide the number of moles of solute by the volume of ...
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https://www.johndcook.com/blog/2020/04/20/truncated-cauchy-distribution/
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math
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The Cauchy distribution is the probability distribution on the real line with density proportional to 1/(1 + x²). It comes up often as an example of a fat-tailed distribution, one that can wreak havoc on intuition and on applications. It has no mean and no variance.
The truncated Cauchy distribution has the same density, with a different proportionality constant, over a finite interval [a, b]. It’s a well-behaved distribution, with a mean, variance, and any other moment you might care about.
Here’s a sort of paradox. The Cauchy distribution is pathological, but the truncated Cauchy distribution is perfectly well behaved. But if a is a big negative number and b is a big positive number, surely the Cauchy distribution on [a, b] is sorta like the full Cauchy distribution.
I will argue here that in some sense the truncated Cauchy distribution isn’t so well behaved after all, and that a Cauchy distribution truncated to a large interval is indeed like a Cauchy distribution.
You can show that the variance of the truncated Cauchy distribution over a large interval is approximately equal to the length of the interval. So if you want to get around the problems of a Cauchy distribution by truncating it to live on a large interval, you’ve got a problem: it matters very much how you truncate it. For example, you might think “It doesn’t matter, make it [-100, 100]. Or why not [-1000, 1000] just to be sure it’s big enough.” But the variances of the two truncations differ by a factor of 10.
Textbooks usually say that the Cauchy distribution has no variance. It’s more instructive to say that it has infinite variance. And as the length of the interval you truncate the Cauchy to approaches infinity, so does its variance.
The mean of the Cauchy distribution does not exist. It fails to exist in a different way than the variance. The integral defining the variance of a Cauchy distribution diverges to +∞. But the integral defining the mean of the Cauchy simply does not exist. You can get different values of the integral depending on how you let the end points go off to infinity. In fact, you could get any value you want by specifying a particular way for truncation interval to grow to the real line.
So once again you can’t simply say “Just truncate it to a big interval” because the mean depends on how you choose your interval.
If we were working with a thin-tailed distribution, like a normal, and truncating it to a big interval, the choice of interval would make little difference. If you truncate a normal distribution to [-10, 5], or [-33, 42], or [-2000, 1000] makes almost no difference to the mean or the variance. But for the Cauchy distribution, it makes a substantial difference.
I’ve experimented with something new in this post: it’s deliberately short on details. Lots of words, no equations. Everything in this post can be made precise, and you may consider it an exercise to make everything precise if you’re so inclined.
By leaving out the details, I hope to focus attention on the philosophical points of the post. I expect this will go over well with people who don’t want to see the details, and with people who can easily supply the details, but maybe not with people in between.
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http://zhclg.com/advances-in-engineering-structures-mechanics-amp-construction/stresses-in-plastic-zone.htm
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math
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Stresses in Plastic Zone
In view of the fact that in plane stress, ац = 0, а22 = aY at the blunted crack tip and ац + а22 must be harmonic, choose
ац + а22 = ау (sin p(z — X0) + sin p(Z — X0)). where p is a constant and z = x + iy. Rewrite the above equation in the form
ац + а22 = 2ау sin p(x — X0) cosh py. (6)
On x-axis, y = 0 and ац + а22 = 2ау sin p(x — x0). For a Mises solid therefore,
a22 = ау I sin/? (x – xo)H—-= cos/?(x – xo)l,
ац = ay 1 sin/?(х — xq)——— — cosp(x — xq)
To satisfy ац = 0 at the crack tip x = xt, choose p such that p(xt — x0) = n/6. Note that on the extended crack-line in the plastic zone, ац = а22 except at the point where p(x — x0) = n/2.
To reconcile the chosen plastic field with LEFM field in the elastic domain, choose а11 = а22 = ау at the yield point (x = xY = rY, y = 0). This is possible provided p(xY — x) = n/2, or xY = 3xt — 2×0. Therefore, the plastic zone is lp = xY — xt = 2(xt — x0) = n/3p. To find its value, evaluate P = a22ds and equate it with P = 2aYrY obtained from LEFM. The result is
p = 1 /(хул/3) and the plastic zone size is
lp = ~i=rY = —— I — la
with p, lp and xY known, it is easy to evaluate x0 = xY — n/2p and xt = xY — lp.
To find the crack opening in the plastic observe that on the crack surface x = xc, y = yc, ац = а22 = aY and hence the equation of the deformed crack is
sin p(xc — x0) cosh pyc = 0.5.
Since the value of p is already known, the above equation can be used to find the deformed crack surface in the plastic domain. The surface in the elastic domain is obtained from the solution of Singh et al. and for S ^ E, it can be expressed in the form
xe = a cos p, ye = — sin p.
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http://travel-tours.travelerinc.com/two-cars-travel-in-the-same-direction-along-a-straight-highway-one-at-a-constant-speed-of-55-mihr.html
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math
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Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/hr ?
Related Questions and Answers
- What is the answer to this problem? please put the answer in plain site if possible?
- Finding the speed and direction of a plane?
- If time slows down as acceleration increases, how can you measure the speed of light?
Tags: Car Travel, Lead, Travel Direction
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https://bbludata.wordpress.com/1-6/
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math
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|The big bang theory in light of a quiet expansion of 201+ notations.
Three questions open up a more simple mathematical model of the universe:
1. Can this model, a Quiet Expansion (QE), actually defuse the big bang? The math within the QE model could redefine the first four “epochs”(and most-key elements) of the big bang theory (bbt). If it is defused and becomes an historic statement, From Lemaître to Hawking, science can move on within somewhat-prescribed boundary conditions and known parameters. The first four epochs of the big bang theory can readily be subjected to redefinition. These “epochs” amount to less than a trillionth-of-a-trillionth a second.
2. Are ethics and values built into the fabric of the universe? The QE model establishes a simple continuity equation from the first moment in time through the Age of the Universe (this day and this moment). These simple mathematical constructions quickly evolve as geometrical constructions and symmetry groups. Mathematically the constructions become quite dynamic and some harmonic. Continuity, symmetry and harmony are the foundations for a natural value equation deep-seated within the universe. Most every flavor of ethics, morals, and values can be appreciated for what they do and don’t do, and for why they are.
3. How can we more fully understand the finite-infinite relation? This finite-infinite relation is perhaps best described as a study of perfection and moments of perfection and that the geometries and mathematics of imperfection are also better defined and understood as a result and known today as quantum mechanics.Consider the four epochs in question:Planck Epoch or a Planck Moment: The finite-infinite relation most intimately defines the first notation and is necessarily within all notations building from the first. An infinitesimal duration, it is the beginning that creates space and time and then extends within space and time much like the birthing process. As of today, the Planck base units are our simplest-deepest-best description of this moment.Grand Unification and the Electroweak Epochs or Processes: Based on the fact that entities and things require a necessary amount of space that only becomes available from the 67th notation and above, the first 60 to 66 notations are foundational to all notations. Using the analogy of the birthing process, all the forms-and-functions, then processes-and-procedures, and then relations-and-systems prior to the actual birthing event, are the first 60 or so notations. Here that finite-infinite relation creates the foundational order, the most basic relations, and many dynamical systems prior to the uniqueness of every reasonable analogue to the birthing event.
The Grand Unification processes continue beyond the 67th notation as specific Unification processes. The electroweak processes now begin to manifest and the measurements given by the big bang theorists can be tweaked and integrated within the Quiet Expansion model.
Inflationary Epoch or Processes: Just as there are still many many questions about cellular division, there are even more open questions within this model. However, the force, the infinitesimal amount of energy, available to this process are working ratios of the Planck base units whereby order, relations, and dynamics evolve with a perfect continuity, perfect symmetry, and a deep harmony within every sphere and basic structure. This concept was initially put forth as a philosophical orientation to life, and then it was explored in a post about numbers called,
On Constructing the Universe From Scratch (see pages 5 and 6).
Background Introduction: This is page 1 of 37. Here, side-by-side, all 37 pages can be horizontally-scrolled as a single page. It is the entire model of the universe called, Big Board – little universe. The vertically-scrolled chart was completed in February 2015. The first chart was done in December 2011. Here we continue the process of encapsulating everything, everywhere in the universe, throughout all time. Though this chart suggests that space-time-mass-energy-temperature are necessarily and inextricably related, the challenge of this model is to demonstrate how this is so. This work is quite at odds with the big bang theory (bbt), yet we believe every formula and relation defined throughout the bbt history can also be found within our emerging model and view of the universe. To broaden its perspective, we will also attempt to examine as many transitions as possible between the finite-infinite, especially the role of pi, projective geometries, bifurcation theory, the dimensionless constants, and number theory.
Key concept: Planck Temperature has been moved to the top of the chart. One of the working assumptions of the project is that everything starts most simply and complexity comes later, and that space-and-time are finite, discrete, derivative and quantized. Of course, this logic will be further discussed.
Key questions: What mathematics are at work? The simple answer is, “All mathematics are at work here. No formula is exempt. And, eventually every formula will be in some way tied back to this model.” Notwithstanding, here is our first, introductory post about numbers.
Speed of Light: A simple calculation is to divide the Planck Length by Planck Time. Using just the units displayed above, the result is 299,777,406.78 m/sec. Using 3.23239/1.078212 the result is 2.99791692172 or 299,791,692.172 m/sec. These simple results, first posted on May 3, 2016, will be tweaked. Of course, the result of experimental measurement is 299,792,458 meters/second in a vacuum. Within notation 3, it is 1.29295 divided by 4.312848 which equals 299,790,300.98. There is much more to come!
Entitive Manifestations: Though not an active row until July 4, 2016, the nature of thingness has been part of our mindscape for many, many years going back to Martin Heidegger’s key question, What is a thing? Our first charts of the Big Board-little universe all focused on things determined by the multiple of the Planck Length. All the data from those earlier charts will now be integrated within our horizontally-scrolled chart.
Help wanted: For every notation, we would like to have an expert and a team. Within this group of notations, we especially seek help from people who can help us re-enact Max Planck’s thinking and the veracity of each formulation of the Planck base units.
Can you help us?
Key words, primary concepts, and links to references for these ten notations:
1. Geometries: Projective, Euclidean, differential (Riemannian, Lie groups, etc), discrete and combinatorial, algebraic and transformational…
2. The Pre-Measureable Structure of Matter: Might we conclude that this Small-Scale Universe is the structure that holds things together? Is it a re-definition of the ether? Is it MIT Frank Wilczek’s grid?
3. Renormalization(Scale Invariance https://en.wikipedia.org/wiki/Scale_invariance), Universality, isotropy, homogeneity: Is it possible that everything-everywhere in the universe shares the first 67 notations, and uniquely evolves with those characteristics given within the 67th to 134th notations, and then begins to manifest in each of the large-scale notations, unfolding uniquely in the 201st as “the given within the current moment”?
Editor’s note: Can you help upgrade that last sentence? I’ll be profoundly grateful. -BEC
Finite-Infinite: Studied throughout the history of humanity, this model provides a basis for a thorough reexamination of the concepts, mathematics and principles that operate between the two. Already there are several posts that open these reflections: (1) What is finite? And, what is truly infinite? and (2) Finite-Infinite reflections.
1. The areas above and below the numbers and discussions could also be used for graphics that are related to these notations. Perhaps a color background could reflect its temperature in its part of the universe.
2. Perhaps the area above the “Big Board-little universe” title (underlined) can be used for related graphics and color.
3. This “one page” board ideally would be a wiki page where schools and universities and the public could collaborate, update and add data.
4. Base-2 notation from the five Planck Base Units to their maximums is still early-stage work. We’ll be adding dimensionless constants. Could this table be a spreadsheet? April 27, 2016: More updating to come.
Process: Examples of Horizontal Scrolling Horizontal Scrolling Example #1, #2, #3 and #4 (pop up windows).
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| 8,553 | 26 |
http://fullhomework.com/downloads/expert-solutions-22/
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math
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1. Two spheres, each of mass M=2.33 g, are attached to pieces of string of length L=45 cm to a common point. The strings initially hang straight down, with the spheres just touching one another. An equal amount of charge, q , is placed on each sphere. The resulting forces on the spheres cause each string to hang at an angle of Ɵ=10 ͦ from the vertical. Determine q, the amount of charge on each sphere.
2. A 2-kW heater element from a dryer has a length of 80 cm. If a 10 cm section is removed, what power is used by the now shortened element at 120 V?
3. A conducting solid sphere of radius 20 cm is located with its center at the origin of a three-dimensional coordinate system. A charge of 0.271 nC is placed on the sphere.
(a) What is the magnitude of the electric field at point (x, y, z)=(23.1 cm, 1.1 cm, 0 cm)?
(b) What is the angle of this electric field with the x-axis at this point?
(c) What is the magnitude of the electric field at point (x, y, z)=(4.1 cm, 1.1 cm, 0 cm) ?
4. Two parallel plates are held at potentials of +200 V and -100 V. The plates are separated by 1 cm.
(a) Find the electric field between the plates.
(b) An electron is initially placed midway between the plates. Find its kinetic energy when it hits the positive plate.
5. A point charge of +2 μC is located at (2.5 m, 3.2 m). A second point charge of -3.1 μC is located at (-2.1 m, 1 m).
(a) What is the combined electrostatic potential of this two charges at x=20.1 cm, also on the x-axis?
(b) At which point(s) on the x-axis does this potential have minimum?
6. A 5-nF capacitor charged to 60 V and a 7-nF capacitor charged to 40 V are connected with the negative plate of each connected with the negative plate of the other. What is the final charge on the 7-nF capacitor?
7. A current density of 6×10-13 A/m2 exists in the atmosphere at a location where the electric field is 100 V/m. Calculate the electric conductivity of the Earth’s atmosphere in this region
8. When a 40-V emf device is placed across two resistors in series, a current of 10 A is flowing in each of the resistors. When the same emf device is placed across the same two resistors in parallel, the current through the emf device is 50 A. What is the magnitude of the larger of the two resistors?
9. A parallel-plate capacitor is charged and then disconnected from a battery. By what factor does the stored energy change ( increase or decrease) when the plate separation is doubled ?
10. A small but measurable current of 1.2×10-10 A exists in a copper wire whose diameter is 2.5 mm. The number of charge carriers per unit volume is 8.49 x1028 m-3. Assuming the current is uniform, calculate (a) the current density and (b) electron drift speed.
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CC-MAIN-2020-40
| 2,715 | 17 |
http://www.gullybaba.com/ignou/mba-assignments-questions/ignou-mba-MS51-assignment-questions.htm
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math
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MS-51 Operations Research
Note: Please attempt all the questions and send it to the Coordinator of the study
center you are attached with
Find out the optimal solution of the following LP problem through SIMPLEX method.
Maximise Z = 20 x 1 + 6 x 2 + 8 x 3
8 x 1 + 2 x 2 + 3 x 3 ≤ 200
4 x 1 + 3 x 2 ≤ 150
2 x 1 + x 3 ≤ 50
x 1 , x 2 and x 3 > 0
Write dual of the problem given in Q.1. Explain the significance of dual variable in any LP problem.
- a) Explain the difference between pure strategy and mixed strategy.
b) How the concept of dominance is used in simplifying the solution of a
a) Discuss the parameters of Queing problem.
b) Telephone department will install a second booth when convinced that an
arrival would expect to waiting for at least 3 minutes to get his chance. By how
much should be the flow of arrivals in order to justify a second booth. Length
of phone call average is 3 min. Assume arrival and servicing rate as Poisson.
Write short notes on the following
- Integer Programming
- Dynamic Programming
- Monte Carlo Simulation
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| 1,054 | 21 |
https://phukhoathaiha.org/qa/question-how-much-math-is-needed-for-phd-in-economics.html
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math
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- What kind of math is used in macroeconomics?
- Is economics hard to study?
- Is micro harder than macro?
- What is the highest paying job in economics?
- Is it hard to get a PhD in mathematics?
- Is it better to take micro or macro first?
- Does Google hire math PhDs?
- Do economists make good money?
- Is economics an easy degree?
- Can I study economics without maths?
- How do I get into a good PhD in economics?
- How difficult is math in economics?
- Is a masters in economics hard?
- Do economists use calculus?
- How long does a PhD in math take?
- Which country is best to study economics?
- Do you need to be good at math to be an economist?
- How hard is a PhD in economics?
- How long does a PhD in economics take?
- Is a PhD program Hard?
- Is economics harder than finance?
What kind of math is used in macroeconomics?
The types of math used in economics are primarily algebra, calculus and statistics.
Algebra is used to make computations such as total cost and total revenue.
Calculus is used to find the derivatives of utility curves, profit maximization curves and growth models..
Is economics hard to study?
Even though economics is a social science, it can be as difficult and demanding as any of the more challenging academic subjects, including math, chemistry, etc. To do well in economics requires time, dedication, and good study habits.
Is micro harder than macro?
At the entry-level, microeconomics is more difficult than macroeconomics because it requires at least some minimal understanding of calculus-level mathematical concepts. … Calculus is introduced at the macroeconomic level, but not nearly in as great a depth as it is in microeconomics.
What is the highest paying job in economics?
Best economics degree jobsCredit analyst. National Average Salary: $57,327 per year. … Personal finance advisor. National Average Salary: $65,526 per year. … Policy analyst. National Average Salary: $66,462 per year. … Supply chain analyst. … Economic consultant. … Business reporter. … Loan officer. … Portfolio manager.More items…•
Is it hard to get a PhD in mathematics?
It does just become objectively difficult, even for the people who are naturally good at it, the ones that have excelled at maths their whole lives. The level of abstraction would be too much for most people I think. with some work it is doable. it also vastly depends on the program you apply to.
Is it better to take micro or macro first?
Taking into account all of the above, most economics students are better off studying microeconomics first, and then progressing on to macroeconomics. That way, the principles of economics can be learned on an individual level, before being applied to the wider society and world.
Does Google hire math PhDs?
Google hires mathematicians i.e. those who have PhDs in math, and the answer to that question is yes — there not be many openings, but there certainly are some openings).
Do economists make good money?
An entry-level Economist with less than 1 year experience can expect to earn an average total compensation (includes tips, bonus, and overtime pay) of ₹510,643 based on 36 salaries. … An experienced Economist with 10-19 years of experience earns an average total compensation of ₹2,000,000 based on 14 salaries.
Is economics an easy degree?
Economics is not a particularly hard major at the undergraduate level. Most colleges do not require you to take a lot of mathematics classes. … Economics is an easy major if all you aim to do is to memorize old theories and regurgitate them as if they were truth.
Can I study economics without maths?
No, you strictly can’t pursue Economics hons without maths. … In such scenario Maths become compulsory for this course. For Economics, they teach you the basic things, which are required in further years, so even if u haven’t studied Eco in 12th, you will be able to sail through it, provided you do some hardwork.
How do I get into a good PhD in economics?
Here is the not-very-surprising list of things that will help you get into a good econ PhD program:good grades, especially in whatever math and economics classes you take,a good score on the math GRE,some math classes and a statistics class on your transcript,More items…•
How difficult is math in economics?
No . economics maths is not tough,Economics is not a particularly hard major at the undergraduate level. … The most prepared of economics majors, however, will choose to take mathematics classes on a level almost equivalent to a mathematics major, many would even double major.
Is a masters in economics hard?
Macro courses are more varied, but they mostly involve optimization problems (solving endless amounts of Lagrangians). If you are not comfortable with mathematics, higher-level economics will be very off-putting. So yes, masters economics is definitely much harder than undergrad.
Do economists use calculus?
Calculus is the mathematical study of change. Economists use calculus in order to study economic change whether it involves the world or human behavior. In economics, calculus is used to study and record complex information – commonly on graphs and curves.
How long does a PhD in math take?
between 3 and 5 yearsGenerally, PhD Mathematics programs take between 3 and 5 years to complete and although requirements differ depending on the academic institution and specific program, candidates must have the appropriate educational background, training, and experience in mathematics.
Which country is best to study economics?
Read on for our top picks for international students interested in studying Economics:The United States.The United Kingdom.The Netherlands.Australia.Switzerland.China.Italy.
Do you need to be good at math to be an economist?
The application and understanding of Economics happens when you study Math and apply your knowledge of Mathematics to understand Economics. Topics like Calculus & Linear Algebra are extremely important. … However, if you plan to pursue Economics further like Post Graduate level, you will need Maths, for sure.
How hard is a PhD in economics?
A PhD in any field not just economics is difficult, not so much because of the content or requirements, but because it is a research training exercise. You are learning and applying skills and abilities that you likely never had before or at least developing those that you had that weren’t very well developed.
How long does a PhD in economics take?
5-7 yearsIn this profile we focus on doing an Economics PhD in the US, which usually takes 5-7 years. In the first two years you take classes and the remaining time is spent on writing a dissertation. You usually have to teach during your PhD.
Is a PhD program Hard?
The drop-out rate for PhDs is high. In the United States, only 57% of PhD students obtained their PhD 10 years after enrollment. … Contrary to popular belief, a PhD is not intellectually difficult but it calls for discipline and stamina.
Is economics harder than finance?
Economics varies more though. There are very easy courses you can take, as well as extremely challenging ones—especially at the graduate level. If you’re just talking about a basic bachelors degree though, then finance is probably a little harder but not by much. … Is a major in finance better than a major in economics?
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| 7,337 | 65 |
https://www.sneakerboy.com/shop-sneakers/asics-mens-ubs-3-gel-nimbus-9-1650519963-ss22asic12.html
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math
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Asics Mens UB3-S GEL-NIMBUS 9. Created by the Kiko Kostadinov Studio. Inspired by the concept of outdoor exploration. The team repurposed the heritage trainer with influences found in nature.vvElements from scenic landscapes and encounters with the sea are translated onto the uppers colour palettes. Utility features like the elongated tongue loops add to the shoes rugged aesthetic. The segmented midsoles GEL technology inserts in the heel and forefoot are designed to increase shock absorption. This makes the shoe more adaptable for different surroundings.
Free Shipping for orders over $400 AUD.
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| 609 | 2 |
http://www.fredmiranda.com/forum/viewedits.php?mid=11098201&page=4
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math
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Upload & Sell: Off
| Re: silly inverse square law question. |
curious80 wrote: So when we go back we do not get any more light rays because everything outside the original area is black.
We get the same number of light rays reflecting off the black (unless the black is a black hole that will not allow any light to escape/reflect).
We get the same number of light rays, but the additional amount of energy being absorbed by the black cloth, renders less energy being reflected. The magnitude of the energy is reduced, but the direction remains iaw AI=AR. Thus the amount of energy reaching the sensor is now less and and cannot be converted into as strong of a signal (or is insufficient energy to effect a change to the negative), and that area of the scene is then recorded as black. The original area still yields a same exposure value, because it is the same reflection of energy with or without a black cloth on surrounding areas.
AI=AR (absorption & refraction).
Conservation of energy requires that the total amount of energy remain constant and is divided among that which is absorbed (color), refracted (transmitted through translucent/transparent material) and reflected. As the refractive index, angle of incidence and color absorption characteristics change, so does the amount of energy remaining available for reflection.
Sure, to be completely pedantic we have to say that the black part does reflect rays which are very low energy and these form the very dark image on the sensor (though it doesn\'t effect the end result). So to summarize with this assumption: Initially we set the camera such that we capture just the original uncovered part of the box as I drew above. Now we move the lens+sensor back. We loose some rays from the original part of the box, but as you said we gain some more \"low energy rays\" from the black part of the image. However these extra low energy rays are just used to form the dark image of the black cloth. As far as the image of the original box is concerned, it only depends on the rays from come from that original part of the box. And we have lost some of those rays. So the total energy that is not reaching from original part of the box to the image of that original part on the sensor has gone down. Are we in agreement now?
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http://onlinelibrary.wiley.com/doi/10.1029/EO066i018p00233/abstract
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math
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Five years after Voyager 1 and 2 encountered Jupiter's intriguing satellite Io, many geologic questions remain open. What is the composition of Io? How large a part does sulfur play in the formation of landforms? Are the flows seen on Io sulfur or silicate, and how are they emplaced? What methods can we use to find out? Finally, what can the upcoming Galileo mission to Jupiter tell us that will help answer these questions?
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https://communities.sas.com/t5/SAS-Statistical-Procedures/how-to-get-Adjusted-survival-curve/td-p/302131?nobounce
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math
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10-03-2016 03:50 PM
Assuming SAS/STAT 14.1 (SAS 9.4)
Add the PLOTS=Survival statement to your PROC PHREG statement to get a survival curve. Note that the survival curve will be for a specified age value, usually the average. You can choose to have a different value used if required, usually to make it easier to interpret or explain.
10-13-2016 03:59 PM
Uh...you can't take an average of a categorical variable? Possibly an ordinal, but it wouldn't make logistical sense.
Use the Reference Category or a category of interest in this case. See what the documentation states as well.
Need further help from the community? Please ask a new question.
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https://electrowiring.herokuapp.com/post/block-diagram-of-general-measurement-system
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math
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BLOCK DIAGRAM OF GENERAL MEASUREMENT SYSTEM
Draw block diagram for generalized measurement system and
1. Primary sensing element, which senses the quantity under measurement. 2. Variable conversion element, which modifies suitably the output of the primary sensing element, and. 3. Data presentation element that renders the indication on a calibrated scale. The block diagram is shown below. Detailed descriptions of each block are as follows.
Block Diagram of Basic Measurement System and Explanation
Nov 29, 2012Block Diagram of Basic Measurement System and Explanation (Working) of Its Each Block. The Basic Measurement system is a set of different blocks which can be used to measure any quantity or to specify anything which can be measured. The block diagram of a simple measurement system is given above.
Generalized Measurement System « Mechteacher
It helps to understand how a measurement system works. Block diagram of generalized measurement system: Components of Generalized Measurement System: A generalized measurement system consists of the following components: Primary Sensing Element; Variable Conversion Element; Variable Manipulation Element; Data Processing Element; Data Transmission
Block diagram of instrumentation system - Polytechnic Hub
The block diagram shown above is of basic instrumentation system. It consist of primary sensing element, variable manipulation element, data transmission element and data presentation element. Primary sensing element. The primary sensing element is also known as sensor. Basically transducers are used as a primary sensing element.
DE-13: Lesson 2. ELEMENTS OF GENERALIZED MEASUREMENT
Fig. 2.1 Block diagram of functional elements of a measurement system / instrument. 2.3 Functional Elements of a Bourdon Pressure Gauge. As an example of a measurement system, consider the simple Bourdon tube pressure gauge as shown in Fig. 2.2. This gauge offers a good example of a measurement system.
Telemetry Systems | Electricalvoice
Apr 16, 2018Fig.1 Block diagram of a telemetry system. Q. Why it is necessary to use telemetry in an instrumentation system? In modern measurement systems, the various components comprising the system are usually located at a distance from each other.
Block diagram - Wikipedia
A block diagram is a diagram of a system in which the principal parts or functions are represented by blocks connected by lines that show the relationships of the blocks. They are heavily used in engineering in hardware design, electronic design, software design, and process flow diagrams.[PDF]
A GENERALIZED MEASUREMENT SYSTEM
A GENERALIZED MEASUREMENT SYSTEM MEASUREMENTS: The measurement of a given quantity is essentially an act or the result of comparison between the quantity (whose magnitude is unknown) & a predefined Standard. Since two quantities are compared, the result is expressed in numerical values. BASIC REQUIREMENTS OF MEASUREMENT:
Block Diagrams of Control System | Electrical4U
Mar 23, 2019The block diagram is to represent a control system in diagram form. In other words, practical representation of a control system is its block diagram. It is not always convenient to derive the entire transfer function of a complex control system in a single function.
Instrumentation Systems - Digital and Analog Instrumentation
Jul 13, 2011The correct combination of these blocks in a measurement system helps in converting a process condition into a suitable indication. These blocks are also called as functional units and are present in all instrumentation systems. All together, instrumentation systems can be classified into two. They are. 1. Analog Instrumentation System
Related searches for block diagram of general measurement sys
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| 3,954 | 23 |
https://rational-equations.com/in-rational-equations/y-intercept/linear-programming-worded.html
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math
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Hello there I have almost taken the decision to look fora algebra tutor , because I've been having a lot of problems with algebra homework this year. Every day when I come home from school I waste all the afternoon with my math homework, and after all the time spent I still seem to be getting the incorrect answers. However I'm also not certain whether a algebra private teacher is worth it, since it's not cheap , and who knows, maybe it's not even that good . Does anyone know anything about linear programming worded problems that can help me? Or maybe some explanations regarding radicals,rational equations or function range? Any ideas will be much appreciated .
Aaah May God save us students from the evil of linear programming worded problems. I used to face same problems that you do when I was there. I always used to be confused in Algebra 1, Remedial Algebra and Algebra 1. I was worst in linear programming worded problems till I came to know of Algebrator. It is really useful and I would truly recommend it. The best part of the software is that it will also help you learn algebra and not just give your answers. I found Algebrator effective and am sure it will help you too. Let me know.
Hello there. Algebrator is really amazing ! It’s been months since I used this software and it worked like magic! Algebra problems that I used to spend answering for hours just take me 4-5 minutes to answer now. Just enter the problem in the program and it will take care of the solving and the best thing is that it shows the whole solution so you don’t have to figure out how did it come to that answer.
I remember having often faced difficulties with exponent rules, algebraic signs and radicals. A truly great piece of math program is Algebrator software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Algebra 2, Pre Algebra and Basic Math. I greatly recommend the program.
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http://www.tes.co.uk/teaching-resource/times-table-test-grids-6035157/
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math
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times table test grids
Last updated 31 October 2010, created 05 February 2010, viewed 4,664
3 times table test girds I made, A, B, C each one goes up to the 9.5 x table (past 2, 3, 4, 6, 7, 8, 9, 10, 11, 12 and then decimals for extension pupils!)
Each one is in a different random order and also has 3 random deciaml questions and answers for each times table.
I use them for the weekly t More…imes table test, to ask them the questions and then they swap books and use these sheets to mark them themselves, or TA uses them and marks with them.
Hope you find them useful, let me know if you like them too!
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http://www.dummies.com/how-to/content/asvab-practice-mathematics-knowledge-sample-questi.html
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math
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ASVAB Practice: Mathematics Knowledge Sample Questions
One of the subtests on the ASVAB is the Mathematics Knowledge test. Take a look at the following sample questions to see what kind of knowledge you will need for test day.
Time: 24 minutes for 25 questions
Directions: Mathematics Knowledge is the fifth subtest on the ASVAB. The questions are designed to test your ability to solve general mathematical problems. Each question is followed by four possible answers. Decide which answer is correct, and then mark the corresponding space on your answer sheet. Use your scratch paper for any figuring you want to do. You may not use a calculator.
Simplify: 2 + 2y + 4 + y
(A)3y + 6
(B)3y + 8
(D)2y2 + 6
What is the value of x?Credit: Illustration by Thomson Digital
(5 – 2)! =
How many factors does the number 51 have?
The number 0.405 is what percent of 0.9?
The measure of angle P is m°. What is the measure of the complement of angle P?
(A)(180 – m) °
(B)(90 – m) °
(C)(m – 90) °
(D)(m – 180) °
What is the length b in the right triangle?Credit: Illustration by Thomson Digital
Translate the following sentence into an equation: x decreased by 11 is twice x.
(A)11 – x = 2x
(B)x – 11 = 2
(C)11 – x = 2
(D)x – 11 = 2x
The mean of 5, 7, 8, 10, 4, and x is 7.5. What is the value of x?
Answers and explanations
A. 3y+ 6
This expression has two pairs of like terms. First, 2 and 4 are like terms and have a sum of 6. The terms 2y and y are also like terms and have a sum of 3y (remember that y is the same as 1y).
The sum of the angles of a triangle is always equal to 180°. To find the value of x, subtract 34° and 108° from 180°: 180° – 34° – 108° = 38°.
Using the order of operations, simplify inside the parentheses first: (5 – 2)! = 3!. The expression 3! is the product of all whole numbers from 3 down to 1: 3! = 3(2)(1) = 6.
The factors of a number are all the numbers, including the number and 1, that divide into the number without a remainder. The number 51 has four factors: 1, 3, 17, and 51.
B. 45 percent
Write this sentence as an equation, using x to represent the percent you’re trying to find: 0.405 = 0.9x. Divide both sides by 0.9 to get x alone on one side of the equal sign.
You convert the decimal 0.45 to a percent by multiplying 0.45 by 100: 0.45(100) = 45 percent.
B. (90 –m)°
If two angles are complementary, the sum of their measures is 90°. Because the measure of angle P is m°, you find the complement of angle P by subtracting its measure from 90°.
D. 7 cm
Because the triangle is a right triangle, you need the Pythagorean theorem: a2 + b2 = c2. You know the lengths of side a and the hypotenuse (c), so plug those values into the theorem and solve for b:
Use the positive answer because a length is never negative.
D. x– 11 = 2x
When you decrease something, you’re subtracting from it. In this instance, you’re taking 11 away from x; that means you have x – 11. Is means equals in mathematical terms (and you know that every equation must have an equal sign). Twice x means 2x. Your equation will look like this: x – 11 = 2x.
The mean is the sum of all values divided by the number of values, or the average. First, find the sum of the values: 5 + 7 + 8 + 10 + 4 + x = 34 + x. Because there are six values, you’ll set this side of the equation up as a fraction:
You already know the answer to the equation is 7.5, so your equation will look like this:
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https://www.knowpia.com/knowpedia/Doyle_spiral
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math
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In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane, each tangent to six others. The sequences of circles linked to each other through opposite points of tangency lie on logarithmic spirals (or, in degenerate cases, circles or lines) having, in general, three different shapes of spirals.
These patterns are named after mathematician Peter G. Doyle, who made an important contribution to their mathematical construction in the late 1980s or early 1990s. However, their study in phyllotaxis (the mathematics of plant growth) dates back to the early 20th century.
Based on these properties, it follows that one can find positive real numbers , , and , so that each circle of radius is surrounded by circles whose radii are (in cyclic order) , , , , , and . Only certain triples of numbers , , and defined in this way work; others lead to systems of circles that, when continued ad infinitum, eventually overlap each other.
The sequences of tangent circles with opposite points of tangency and radii have centers that (in most cases) lie on finitely many logarithmic spirals, all meeting at a central point. Similarly one obtains a different set of logarithmic spirals for the sequences of circles with radii and . In certain cases, one of , , or can equal 1, in which case these sequences of tangent circles return to their start after finitely many steps, and the centers of the circles in the sequence lie on one of infinitely many concentric circles (instead of finitely many logarithmic spirals) all centered on the central point. A third possibility is that, for one of , , or , the sequences of circles have centers that lie on finitely many rays, all meeting at the same central point. In all cases, there exists a system of symmetries of the plane, combining scaling and rotation around the central point, that take any circle of the packing to any other circle.
The precise shape of any Doyle spiral can be parameterized by a pair of natural numbers describing the number of spiral arms for each of the three ways of grouping circles by their opposite points of tangency. If the numbers of arms of two of the three types of spiral arm are and , with and with fewer than arms of the third type, then the number of arms of the third type is necessarily . As special cases of this formula, when the arms of the third type degenerate to circles, and there are infinitely many of them. And when the two types of arms with the smaller number of copies are mirror reflections of each other and the arms with copies degenerate to straight lines. For example, in the illustration shown, there are eight spiral arms with the same shape as the shaded arm, another eight spiral arms with the mirror reflected shape, and sixteen radial lines of circles, so this spiral can be parameterized as , .
Alternatively, the Doyle spiral can be parameterized by a pair of real numbers and describing the relative sizes of the circles. Peter Doyle observed that, when a unit circle is surrounded by of six other circles with radii , , , , , and , then these six surrounding circles close up to form a ring of mutually tangent circles, all tangent to the central unit circle. The Doyle spiral can then be constructed by using the same relative radii for rings of six circles surrounding each previously-constructed circle. The resulting system of circles closes up on itself to form a non-crossing Doyle spiral of circles in the plane only for certain special pairs of numbers and , which can be found from the integer parameters and by a numerical search. When is not one of these special pairs, the resulting system of circles still consists of spiral arms all wrapping around a central point, but with a rotation angle around that central point that is not an integer fraction of , causing them to overlap non-locally. The two real parameters can also be combined into a single complex number, interpreting the plane in which the circles are drawn as the complex plane. The parameters associated with a Doyle spiral must be algebraic numbers.
Coxeter's loxodromic sequence of tangent circles is a Doyle spiral with parameters and or with and , where denotes the golden ratio. Within the single spiral arm of tightest curvature, the circles form a sequence whose radii are powers of , in which each four consecutive circles in the sequence are tangent.
The standard hexagonal packing of the plane by unit circles can also be interpreted as a degenerate special case of the Doyle spiral, the case obtained by using the parameters . Unlike other Doyle spirals, it has no central limit point.
Spirals of tangent circles, often with Fibonacci numbers of arms, have been used to model phyllotaxis, the spiral growth patterns characteristic of certain plant species, beginning with the work of Gerrit van Iterson in 1907. In this application, a single spiral of circles may be called a parastichy and the parameters and of the Doyle spiral may be called parastichy numbers. The difference is also a parastichy number (if nonzero), the number of parastichies of the third type. When the two parastichy numbers and are either consecutive Fibonacci numbers, or Fibonacci numbers that are one step apart from each other in the sequence of Fibonacci numbers, then the third parastichy number will also be a Fibonacci number. For modeling plant growth in this way, spiral packings of tangent circles on surfaces other than the plane, including cylinders and cones, may also be used.
The Doyle spirals (and the hexagonal packing of the plane) are the only possible "coherent hexagonal circle packings" in the plane, where "coherent" means that no two circles overlap and "hexagonal" means that each circle is tangent to six others that surround it by a ring of tangent circles. Applying a Möbius transformation to a Doyle spiral can produce a related pattern of non-crossing tangent circles, each tangent to six others, with a double-spiral pattern in which the connected sequences of circles spiral out of one center point and into another; however, some circles in this pattern will not be surrounded by their six neighboring circles.
Additional patterns are possible with six circles surrounding each interior circle but only covering a partial subset of the plane and with circles on the boundary of that region not completely surrounded by other circles. It is also possible to form spiral patterns of tangent circles whose local structure resembles a square grid rather than a hexagonal grid, or to continuously transform these patterns into Doyle packings or vice versa. However, the space of realizations of locally-square spiral packings is infinite-dimensional, unlike the Doyle spirals which can be determined only by a constant number of parameters.
It is also possible to describe spiraling systems of overlapping circles that cover the plane, rather than non-crossing circles that pack the plane, with each point of the plane covered by at most two circles except for points where three circles meet at angles, and with each circle surrounded by six others. These have many properties in common with the Doyle spirals.
The Doyle spiral, in which the circle centers lie on logarithmic spirals and their radii increase geometrically in proportion to their distance from the central limit point, should be distinguished from a different spiral pattern of disjoint but non-tangent unit circles, also resembling certain forms of plant growth such as the seed heads of sunflowers. This different pattern can be obtained by placing the centers of unit circles on an appropriately scaled Fermat's spiral, at angular offsets of from each other relative to the center of the spiral, where again is the golden ratio. For more, see Fermat's spiral § The golden ratio and the golden angle.
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https://byjus.com/question-answer/the-velocity-time-graph-for-two-uniformly-accelerated-bodies-a-and-b-make-angles-30deg/
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math
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The velocity time graph for two uniformly accelerated bodies a and b make angles 30° and 60° with the time axis.which body has less acceleration ?
Acceleration = Slope of velocity time graph with time at x-axis
Slope = Tanx
Ratio of their acceleration = Tan30 : Tan60 = 1/sqrt(3) : sqrt(3) = 1 : 3
theb body a has less accleration
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964360881.12/warc/CC-MAIN-20211201173718-20211201203718-00519.warc.gz
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https://vlab.amrita.edu/?sub=1&brch=75&sim=328&cnt=5
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math
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1. A circuit containing a resistor of 20 ohms in series with a 100 µF capacitor connected to a 220 V, 50 Hz supply. Determine the current and its phase w.r.to the E.M.F.
2. Construct a series RC circuit with 25 Ω resistor, 1µF capacitor and AC power source of 50 Volt. Vary the frequency of the power source, observe the variation of current through the circuit and plot graph between frequency Vs current.
3. In a RC circuit , 12 Vrm is measured across the resistance, 15 Vrms measured across the capacitor. What is the value of RMS source voltage?
4. A resistance and capacitor are in a series across 20V AC source. Calculate the circuit impedance, Vrms, total current, phase angle, voltage across each component.
5. A 25 Ω resistor and capacitor with a capacitive reactance of 120 Ω are in series across the an AC source. What will be the circuit impedance ?
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https://istopdeath.com/find-the-derivative-d-dx-cube-root-of-x/
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math
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Use to rewrite as .
Differentiate using the Power Rule which states that is where .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Rewrite the expression using the negative exponent rule .
Multiply and .
Find the Derivative – d/dx cube root of x
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| 428 | 12 |
https://www.teachme2.co.za/additional-mathematics-tutors-soweto
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math
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Highest Quality Additional Mathematics Tutors in Soweto. Get Additional Mathematics Lessons in your home with Teach Me 2
I am a graduate who is able to explain Mathematical concepts in a very simplified manner. I have a great knowledge of Mathematics and am passionate about teaching others. I obtained distinctions for maths throughout my studies.
I managed to pass all my modules (Statistics, Applied Maths, Calculus and Computer Science) with distinctions (with an average of 85%).
I believe Maths is a language of it's own and it is found in every aspect of life. As an Engineering student I continuously use it in my studies and practicals
I am a BCom General Business Management graduate, who is currently pursuing his BCom Honours in Economics. I excelled in Advanced Level Mathematics and can easily transfer this knowledge onto others.
I did Additional Mathematics until grade 10 and I possess the required skills to teach high-schoolers. Moreover, I excelled in Maths in high school which has made it easier to tutor Additional Maths.
Mathematics requires constant practice. Ideally, having a passion for this subject is beneficial.
I've found that maths can be very enjoyable when you understand how to do it, and practice is the best way to understand. When helping others with Maths, I try to focus on the joy you can get out of it, as this helped me to achieve better marks.
University: Additional Mathematics I(79%) & II(85%). Skilled in functions & limits, trigonometry, differentiation, integration, drawing functions, real & complex roots, exponents & logarithms, absolute value, induction, financial & recursive models.
I am excellent when it comes to Mathematics, and have experience in various fields of Mathematics.
Since l liked Mathematics, l challenged myself to do more, so l chose Additional Maths. I have helped some of my friends with their exam preparations.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823009.19/warc/CC-MAIN-20181209185547-20181209211547-00448.warc.gz
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| 1,888 | 11 |
https://teenskepchick.org/2013/06/24/the-physics-philes-lesson-54-axis-in-motion/
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math
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The Physics Philes, lesson 54: Axis in Motion
So far in my studies of rotational motion, I’ve focused on rotating rigid bodies where the axis of rotation is stationary. But what about when the axis of rotation is actually moving? What then? Well all your questions will be answered in the coming weeks.
I should probably first establish what I’m talking about when I say the axis rotation is moving. Picture a baton twirler. Or, if you’d rather, this mace twirler I found on YouTube:
The baton (or mace) is rotating around its center of mass. But it’s also flying through the air from one hand to the other. What we have is what physicists call combined translation and rotation. Translational motion is when the center of mass moves from one position to another. Most motion we see is some combination of translation and rotational motion. In fact, every possible motion of a rigid body can be represented as a combination of translational motion of the center of mass and rotation about an axis through the center of mass.
The kinetic energy of a rigid body has both translational and rotational motions. Don’t believe me? I’ll prove it!
For a bit of illustration – and no post would be complete without one – I drew you a diagram.
This is supposed to be a diagram of a rigid rotating body, with a typical particle denoted by m_i.. The velocity of the particle is the vector sum of the velocity of the center of mass and the velocity of the particle relative to the center of mass.
Now let’s dig back into our brain baggage and remember that kinetic energy can be expressed with the equation 1/2mv^2, which can also be expressed like this:
If we substitute that vector sum equation into this we eventually get:
The total kinetic energy is the sum of all the particles making up the body. If we express the three terms in this equation as separate sums, we get:
We can rearrange some stuff…
Okokok. Let’s see what we have. See the m in the first term? That is the total mass M of the rigid body. The second term is zero because it’s equal to the total mass times the velocity of the center of mass at the center of mass. The last term is the kinetic energy of the rotation around the center of mass. We can replace the final term with the equation for the kinetic energy of a rotating body and we get
The first term is associated with the motion of the center of mass and the second term is associated with the rotation about an axis through the center of mass. Voila! We have a relationship!
This is just an introduction. Next week we’ll dig a little bit deeper into this concept and hopefully it will start to make a little bit more real world sense.
Featured image credit: Flickr
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https://news.ycombinator.com/item?id=18044603
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math
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Anyhow I think a song gets more complex as it more commonly breaks the patterns the human mind finds in them.
To put it differently: here, Knuth heard a popular song that seems to be just “That's the way uh huh uh huh I like it uh huh uh huh” repeated endlessly, found it funny, and wrote an elaborate joke culminating in that observation, hewing to the style of CS publications. Why does that make you sad? It's not as if someone's bit of humour has prevented others from saying “real things”.
• It is known that almost all songs of length n require
a text of length ~ n — here the reference is not a reference to the musical literature as one might expect, but a reference to Chaitin! This is similar to Kolmogorov complexity, “almost all real numbers are uncomputable / undefinable”, etc. :-)
• By the Distributive Law and the Commutative Law , we have — a reference to Chrystal, the standard algebra textbook of the 19th century. (See also Underwood Dudley's “What is Mathematics For?”)
• possible to generalize this lemma [...] provided that the sequence <V_k> satisfies a certain smoothness condition. Details will appear in a future paper — typical papers (and of course even the author knows there will no future paper) :-) Cf. Polya's “cheap” generalization.
• The coefficient of √n was further improved by a Scottish farmer named O. MacDonald — even when making a joke, he has a serious reference to Kennedy's book on folk songs, giving the page number where other farmyard songs are discussed. In fact the entire list of references is rather scholarly.
• R₁ = ‘Ee-igh, ’² ‘oh! ’ — the ² here is not a footnote, but “square”, i.e. the string repeated two times
• The whole proof of Lemma 2 is a wonderful (and educational) formalization of the song
• Therefore if MacDonald's farm animals ultimately have long names they should make slightly shorter noises.
• A fundamental improvement was claimed in England in 1824, when the true love of U. Jack gave to him a total of 12 ladies dancing, 22 lords a-leaping, 30 drummers drumming, [...] during the twelve days of Christmas — the reference is a reference to a MoMA artwork, see https://www.worthpoint.com/worthopedia/ben-shahn-titled-book...
• (see ) — the here is a faux reference; it reads ”U. Jack, "Logarithmic growth of verses," Acta Perdix 15 (1826), 1-65535” and apart from “U. Jack” and the number of pages, note that “Perdix” = partridge
• J. W. Blatz of Milwaukee, Wisconsin who first discovered a class of songs known as "m Bottles of Beer on the Wall"; her elegant construction... — Knuth is from Milwaukee, Wisconsin, and J. W. Blatz is https://en.wikipedia.org/wiki/Valentin_Blatz_Brewing_Company
• the song "I'll drink m if you'll drink m + 1." However, the English start at m = 1 and get no higher than m = 9, possibly because they actually drink the beer instead of allowing the bottles to fall.
• all practical requirements for song generation with limited memory space. In fact, 99 bottles of beer usually seemed to be more than sufficient in most cases.
• However, the advent of modern drugs has led to demands for still less memory, and the ultimate improvement of Theorem 1 has consequently just been announced
• [Well you should just read it]
• Acknowledgment. I wish to thank J. M. Knuth and J. S. Knuth for suggesting the topic of this paper. — finally giving away the reason for the existence of this article: these are his children; they were probably 12 and 10 at the time.
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http://slideplayer.com/slide/785130/
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math
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Presentation on theme: "Problem Solving Starter - Presents"— Presentation transcript:
1 Problem Solving Starter - Presents Gurmit paid £21 for five presentsFor A and B he paid a total of £6.For B and C he paid a total of £10.For c and D he paid a total of £7.For D and E he paid a total of £9.How much did Gurmit pay for each present?
2 Gurmit paid £2, £4, £6, £1, and £8 for the five presents. Solution – PresentsGurmit paid £2, £4, £6, £1, and £8 for the five presents.
3 Problem Solving Starter – Three Digits Don’t forget youcan onlyhave up to 9beads on eachstick!Imagine you have 25 beads.You have to make a three-digit number on an abacus.You must use all 25 beds for each number you make.How many different three-digit numbers can you make?Write them in order.
4 You can make six different numbers. Solution – Three digitsYou can make six different numbers.In order, the numbers are: 799, 889, 898, 979, 988, 997.
5 Problem Solving Starter – Make Five Numbers Take 10 cards numbered 0 to 9.Each time use all ten cards.Arrange the cards to make:Five numbers that are multiples of 3Five numbers that are multiples of 7Five prime numbersMake up more problems to use all ten cards to make five special numbers.
6 Solution – Make Five Numbers 12, 39, 45, 60, 787, 42, 63, 98, 1055, 23, 67, 89, 401There are other solutions.
7 Problem Solving Starter – Maze Start with zero.Find a route from ‘start’ to ‘end’ that totals 100Which route has the highest total?Which has the lowest total?Now try some different starting numbers.Start+ 6X 9÷ 2+ 9X 7÷ 3X 5X 5- 6X 3- 5÷ 3X 7- 8End
8 Solution – MazeThere are two routes that total 100 exactly:+6 x7 -6 x3 -8 =100+9 x7 ÷3 x5 -5 =100The route giving the highest total is:+9 x7 -6 x7 -8 =391The route giving the lowest total is:+6 x7 ÷3 x3 -8 =34
9 Problem Solving Starter – Eggs Mrs Choy spent exactly £10 on 100 eggs for her shop.Large eggs cost her 50p each.Medium eggs cost her 10p each.Small eggs cost her 5p each.For two of the sizes, she bought the same number of eggs.How many of each size did she buy?
10 Solution – EggsMrs Choy bought:10 large eggs at 50p each10 medium eggs at 10p each80 small eggs at 5p each.
11 Problem Solving Starter – Flash Harry In April Flash Harry bought a saddle for £100.In May he sold it for £200.In June he was sorry he had sold it.So he bought it back for £300.In July he got tired of it.So he sold it for £400.Overall, did Flash Harry make or lose money?How much did he make or lose?
12 Solution – Flash HarryFlash Harry’s bank balance looked like this:April - £100May + £100June - £200July + £200So Harry made £200 overall.
13 Problem Solving Starter – Age old Problems My age this year is a multiple of 8.Next year it will be a multiple of 7.How old am I?2. Last year my age was a square number.Next year it will be a cube number.How long must I wait until my age is both a square number and a cube?My mum was 27 when I was born. * years ago she was twice as old as I shall be in 5 years’ time.How old am I now?
14 Solution – Age old Problems I am 48 years old (or possibly 104)2. I am now 26 years old. In 38 years’ time, when I am 64, my age will be both a square number and a cube.I am 9 years old now.
15 Problem Solving Starter – Zids and Zods Zids have 4 spots.Zods have 9 spots.Altogether some Zids and Zods have 48 spots.How many Zids are there?How many Zods?What if Zids have 5 spots, Zods have 7 spots, and there are 140 spots together?Find as many solutions as you can.
16 Problem Solving Solution – Zids and Zods There are 3 Zids with 4 spots and 4 Zods with 9 spots.If Zids have 5 spots and Zods have 7 spots, the possible ways of making 140 are:28 Zids;21 Zids and 5 Zods;14 Zids and 10 Zods;1 Zids and 15 Zods;20 Zods.
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http://waset.org/author/kittipong-tripetch
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math
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This paper proposes a study of input impedance of 2 types of CMOS active inductors. It derives 2 input impedance formulas. The first formula is the input impedance of the grounded active inductor. The second formula is the input impedance of the floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of the fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption.
Two types of floating active resistors based on a complementary regulated cascode topology with cross-coupled regulated transistors are presented in this paper. The first topology is a high swing complementary regulated cascode active resistor. The second topology is a complementary common gate with a regulated cross coupled transistor. The small-signal input resistances of the floating resistors are derived. Three graphs of the input current versus the input voltage for different aspect ratios are designed and plotted using the Cadence Spectre 0.18-µm Rohm Semiconductor process. The total harmonic distortion graphs are plotted for three different aspect ratios with different input-voltage amplitudes and different input frequencies. From the simulation results, it is observed that a resistance of approximately 8.52 MΩ can be obtained from supply voltage at ±0.9 V.
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CC-MAIN-2019-18
| 1,512 | 2 |
https://www.pdfchm.net/publisher/birkhauser/
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math
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Data Modeling for Metrology and Testing in Measurement Science This book and companion DVD provide a comprehensive set of modeling methods for data and uncertainty analysis, taking readers beyond mainstream methods described in standard texts. The emphasis throughout is on techniques having a broad range of real-world applications in measurement science. Mainstream methods of data modeling and analysis... An Introduction to Tensors and Group Theory for Physicists
The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects...
Finite Frames: Theory and Applications (Applied and Numerical Harmonic Analysis)
Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad...
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http://www.prenhall.com/books/ect_013891995X.html
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math
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Basic Technical College Mathematics, 2/e
Published August, 1993 by Prentice Hall Career & Technology
Copyright 1994, 322 pp.
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mailings on this subject.
See other books about:
Trades/Technical Math-Tech Math/Tech Physics
This book has been fully revised and is suited for technical
schools, community colleges and proprietary schools. It is intended to
provide readers with the math skills essential to a wide variety of
industrial, technical and trade areas and can be used a mathematics
supplement in content courses in areas like Drafting, Machine
Technology, and Automotive Technology. The coverage in this edition now
includes a review of arithmetic, algebra, geometry and trigonometry.
each mathematical skill is developed by a simple, easy-to-
follow, step-by-step process.
all of the material is fresh and original, offering new and
innovative methods in line with current trends of teaching mathematics.
presents authentic, real-world applications
improves coverage of scientific notation, powers and roots.
provides substantial number of practice problems.
PART I. ARITHMETIC.
1. Fundamental Operations of Arithmetic.
2. Common Fractions.
5. Powers and Roots.
PART II. BASIC ALGEBRA.
6. Definitions and Basic Operations of Algebra.
PART III. APPLIED GEOMETRY.
7. Simple Equations and Formulas.
8. Formula Evaluation.
9. Formula Transposition.
10. Ratio and Proportion.
11. Basic Definitions and Properties of Geometry.
12. Perimeters and Areas of Plane Geometric Figures.
13. Surface Areas and Volumes of Geometric Figures.
14. Construction of Simple Geometric Figures.
15. Fundamentals of Trigonometry.
16. Solution of Right Triangles.
17. Solution of Oblique Triangles.
18. Fundamentals and Applications of the Metric System.
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https://scienceandtechblog.com/mathematicians-report-possible-development-on-showing-the-riemann-hypothesis/
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math
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Scientists have actually made what may be brand-new headway towards an evidence of the Riemann hypothesis, among the most impenetrable issues in mathematics. The hypothesis, proposed 160 years back, might assist unwind the secrets of prime numbers.
Mathematicians made the advance by taking on an associated concern about a group of expressions called Jensen polynomials, they report Might 21 in Procedures of the National Academy of Sciences However the guesswork is so challenging to confirm that even this development is not always an indication that a service is near ( SN Online: 9/25/18).
At the heart of the Riemann hypothesis is an enigmatic mathematical entity called the Riemann zeta function. It’s totally linked to prime numbers– entire numbers that can’t be formed by increasing 2 smaller sized numbers– and how they are dispersed along the number line. The Riemann hypothesis recommends that the function’s worth equates to absolutely no just at points that fall on a single line when the function is graphed, with the exception of particular apparent points. However, as the function has considerably a lot of these “nos,” this is hard to validate. The puzzle is thought about so crucial therefore challenging that there is a $ 1 million reward for a service, provided by the Clay Mathematics Institute.
However Jensen polynomials may be a crucial to opening the Riemann hypothesis. Mathematicians have actually formerly revealed that the Riemann hypothesis holds true if all the Jensen polynomials related to the Riemann zeta function have just nos that are genuine, suggesting the worths for which the polynomial equates to absolutely no are not fictional numbers– they do not include the square root of unfavorable 1. However there are considerably a lot of these Jensen polynomials.
Studying Jensen polynomials is among a range of methods for assaulting the Riemann hypothesis. The concept is more than 90 years of ages, and previous research studies have actually shown that a little subset of the Jensen polynomials have genuine roots. However development was sluggish, and efforts had actually stalled.
Now, mathematician Ken Ono and associates have actually revealed that a lot of these polynomials certainly have genuine roots, pleasing a big portion of what’s required to show the Riemann hypothesis.
” Any development in any instructions associated to the Riemann hypothesis is remarkable,” states mathematician Dimitar Dimitrov of the State University of São Paulo. Dimitrov believed “it would be difficult that anybody will make any development in this instructions,” he states, “however they did.”
It’s tough to state whether this development might ultimately result in an evidence. “I am extremely hesitant to forecast anything,” states mathematician George Andrews of Penn State, who was not included with the research study. Numerous strides have actually been made on the Riemann hypothesis in the past, however each advance has actually failed. Nevertheless, with other significant mathematical issues that were fixed in current years, such as Fermat’s last theorem( SN: 11/ 5/94, p. 295), it wasn’t clear that the option loomed till it remained in hand. “You never ever understand when something is going to break.”
The outcome supports the dominating perspective amongst mathematicians that the Riemann hypothesis is right. “We have actually made a great deal of development that uses brand-new proof that the Riemann hypothesis ought to hold true,” states Ono, of Emory University in Atlanta.
If the Riemann hypothesis is eventually shown right, it would not just light up the prime numbers, however would likewise right away validate lots of mathematical concepts that have actually been revealed to be right presuming the Riemann hypothesis holds true.
In addition to its Riemann hypothesis ramifications, the brand-new outcome likewise reveals some information of what’s called the partition function, which counts the variety of possible methods to produce a number from the amount of favorable entire numbers ( SN: 6/17/00, p. 396). For instance, the number 4 can be made in 5 various methods: 3 +1, 2 +2, 2 +1 +1, 1 +1 +1 +1, or simply the number 4 itself.
The outcome verifies an earlier proposal about the information of how that partition function grows with bigger numbers. “That was an open concern … for a long period of time,” Andrews states. The genuine reward would be showing the Riemann hypothesis, he keeps in mind. That will need to wait.
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https://mezopotamyaajansi31.com/tum-haberler/content/saveZip/144556
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math
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How to solve maths question
This can be a great way to check your work or to see How to solve maths question. Our website will give you answers to homework.
How can we solve maths question
In this blog post, we will provide you with a step-by-step guide on How to solve maths question. A radical is a square root or any other root. The number underneath the radical sign is called the radicand. In order to solve a radical, you must find the number that when multiplied by itself produces the radicand. This is called the principal square root and it is always positive. For example, the square root of 16 is 4 because 4 times 4 equals 16. The symbol for square root is . To find other roots, you use division. For example, the third root of 64 is 4 because 4 times 4 times 4 equals 64. The symbol for the third root is . Sometimes, you will see radicals that cannot be simplified further. These are called irrational numbers and they cannot be expressed as a whole number or a fraction. An example of an irrational number is . Although radicals can seem daunting at first, with a little practice, they can be easily solved!
Solving natural log equations can be tricky, but there are a few simple steps you can follow to make the process a little easier. First, identify the base of the equation. This is usually denoted by the letter "e", but it could also be another number. Next, take the log of both sides of the equation. This will give you an equation that is in the form "log b x = c". Now, all you need to do is solve for x. You can do this by exponentiating both sides of the equation and taking the inverse log of both sides. Once you have done this, you should be left with an equation that is in the form "x = b^c". Solving this type of equation is a relatively simple matter of plugging in the values for b and c and solving for x. following these steps should help you to Solving natural log equations with ease.
First, it is important to read the problem carefully and identify the key information. Second, students should consider what type of operation they need to use to solve the problem. Third, they should work through the problem step-by-step, using each piece of information only once. By following these steps, students will be better prepared to tackle even the most challenging math problems.
Math questions and answers can be a great resource when you're stuck on a tough math problem. Sometimes all you need is a little bit of help to get over the hump, and there's no shame in that. Math questions and answers can be found all over the internet, in books, and even in magazines. Just do a quick search and you'll find tons of resources to help you out. And if you really get stuck, don't forget to ask your teacher or tutor for help. They'll be more than happy to walk you through the problem until you understand it.
In this case, we are looking for the distance travelled by the second train when it overtakes the first. We can rearrange the formula to solve for T: T = D/R. We know that the second train is travelling at 70 mph, so R = 70. We also know that the distance between the two trains when they meet will be the same as the distance travelled by the first train in one hour, which we can calculate by multiplying 60 by 1 hour (60 x 1 = 60). So, plugging these values into our equation gives us: T = 60/70. This simplifies to 0.857 hours, or 51.4 minutes. So, after 51 minutes of travel, the second train will overtake the first.
We cover all types of math problems
this app can replace a scientific calculator pretty much and it’s the only app that can do so it can be a bit frustrating from time to time and the scanning feature does not work for long complex equations but the graphs are really good (even if it lacks the ability to add multiple equations) and the app has everything you could possibly need!
Just a perfect app for math problems and amazing smart calculator which is super easy to use and all other features are also amazing, but with the camera scanning I'll love to see the crop and scan feature also. And once it is added no other math solving app, we'll be able to come near it.
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https://books.google.com/books?id=--O6AAAAIAAJ&q=comparative+statics&dq=related:STANFORD36105001915565&source=gbs_word_cloud_r&hl=en
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math
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The structure of economics: a mathematical analysis
This text combines mathematical economics with microeconomic theory and can be required or recommended as part of a course in graduate microeconomic theory, advanced undergraduate or graduate-level mathematical economics, or any advanced topics course. It also has reference value for international, library, professional and reference markets. This revision addresses significant new topics--the theory of contracts and markets with imperfect information--that have recently become prominent in the microeconomics literature.
89 pages matching comparative statics in this book
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analysis assert behavior budget capital chain rule choice functions column comparative statics concave Consider constraint consumer consumption convex cost function cost-minimization decision variables defined demand curves demand functions determinant differential economics elasticity envelope theorem equal Euler's theorem example f(xu x2 factor prices factor-demand curves firm first-order conditions held constant Hence homogeneous functions homogeneous of degree homothetic hypothesis identical implied increase indifference curves input integral isoquants labor Lagrange multiplier lagrangian level curves marginal cost marginal product marginal utility mathematical matrix maximize maximum minimum money income negative objective function output price parameter partial derivatives postulate price changes principal minors problem production function profit-maximizing profits refutable represents respect revealed preference second partials second-order conditions slope Slutsky equation solution solved substitution sufficient second-order conditions Suppose tangency theory tion unit utility function vector yields
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https://cs.nyu.edu/pipermail/fom/2000-June/004141.html
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math
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FOM: the Urbana meeting
friedman at math.ohio-state.edu
Tue Jun 27 04:33:46 EDT 2000
Reply to Martin Davis 6/20/00 1:35PM:
>I was on the Program Committee for the Urbana ASL meeting, and the
>committee was enthusiastic about the proposed panel on the need for
>"new axioms". Some time ago in a telephone conversation, Harvey told
>me that I am an "extreme Platonist". Being a great fan of Harvey's
>work on the necessary use of large cardinals, I took his comment
>quite seriously and began to wonder. Is that really me?
Yes, because I under the impression that you think that any
intelligible set theoretic question, quantifying even over all sets -
regardless of where they lie in the cumulative hierarchy - is a well
defined mathematical problem in the same sense as, say, the Riemann
hypothesis or the twin prime conjecture. That there is an absolute
right and an absolute wrong answer. And that it is part of normal
mathematical activity to work on such questions just as it is
to work on RH or TP, at least in the sense that there is no
special difference in kind between the two activities that justifies
calling one "normal mathematical activity" and the other "not normal
>Harvey said .. the bad news is that set theory in particular and
>foundational studies in general are on hard times and that
>unchecked, things would only get worse. The good news is that
>Harvey's new Boolean Relation Theory will save the day: Because it
>is a single appealing theme, whose necessary methods range from what
>mathematicians are used to, all the way through Mahlo cardinals, and
>eventually all the way up the large cardinal hierarchy,
>mathematicians will be led to accept these methods because they will
>see that they are needed to solve problems that interest them.
This is more or less accurate, but I said it slightly differently,
and let me say it here even slightly differently than I said it in
Mathematical logic is in very bad shape sociologically and
politically, and that part of the difficulties come from the focus of
Virtually all major scientific areas are born with the discovery and
development of striking new models of some phenomenon that exists
independently of that new scientific area. In most cases, the subject
really attracts attraction and attains an identity through striking
findings that are based on the striking new models.
Mathematical logic fits very much into this framework. We all know
the great models of the phenomenon known as logical reasoning (through
mathematical reasoning (through set theory), and algorithmic
procedures, and others. And we all know the striking findings in the
early part of the 20th century that really gave the subject its
In order to maximize the impact of a subject on the wider
intellectual community, one must periodically - better yet,
continuously - strive for the renewal and fresh perspective one gains
by revisiting its origins in order to reflect more subtle features of
the seminal phenomena. This is normal and standard.
E.g., in partial differential equations, one continually strives to
get more subtle information about more equations that model more
closely more subtle physical phenomena. The same is true of
mathematical economics, etcetera.
However, it is extremely important not to try to force the pace of
this natural evolution beyond what can be productively accommodated
at any given stage in the development of the subject. This merely
leads to a counterproductive negativity that is unwarranted. Every
subject, including the most successful and revered areas of pure
mathematics, look like dismal failures when looked at with such
unrealistic expectations. There is a natural evolution of subjects.
Nevertheless, I have insisted that the commonly referred to four main
areas of mathematical logic, set theory, model theory, recursion
theory, proof theory, are in dire need of such renewal. Actually,
some appropriate renewal is already taking place in some parts of some of
the areas, but not in others. I like to think that I am always striving to
point the way towards renewal.
>He also implied that the traditional set theory community is on the
>wrong track. I certainly applaud Harvey's program, but I assume that
>since Harvey is devoting himself to this program, he believes that
>the results he gets are TRUE. What I don't understand is what he'll
>tell mathematicians who want to know why they should believe this.
Yes, of course I believe that the results that I get are TRUE, but what
results? The results that it is necessary and sufficient to use large
cardinals to get such and such, or such and such can only be done with
large cardinals, or such and such is outright equivalent to the
1-consistency or consistency of large cardinals, etcetera.
That is where my role as f.o.m. expert ends, and where, if I wish to
continue, my role as ph.o.m. begins.
Namely, my f.o.m. expert role is to show that basic natural elementary
universally accessible concrete mathematics - part of the unremoveable
furniture of mathematics as we know it - is inexorably tied up with large
cardinals, through their 1-consistency or consistency.
This is in a context in which it is conventional wisdom among
mathematicians that basic natural elementary universally accessible
concrete mathematics - part of the unremoveable furniture of mathematics as
we know it - is in no way tied up with large cardinals, or their
1-consistency or consistency.
More explicitly, this is in a context in which set theory is not viewed as
part of mathematics, but rather as a scheme for establishing rigor in
mathematics. Set theory is regarded as a framework for interpreting
mathematics, and not a part of mathematics itself. This is the modern view,
hardened by the brief and fleeting experience with experimenting with set
theoretic questions taken literally. Nowadays, set theoretic formulations
are used only when they simplify the underlying mathematics. When they
create their own peculiar problems - arising out of pathological cases
which have nothing to do with the underlying mathematics - then they
discard them as utterly irrelevant and useless.
I think that I have some singular contributions to make to this situation
as an f.o.m. expert, but I am less sure that I have, at this time, some
singular contributions to make to this situation as a ph.o.m. expert. (Of
course, there is the question of just who does have singular contributions
to make to such issues as ph.o.m. experts).
>... I think the question
>of to what extent this faculty can be effective in exploring the
>infinite is an empirical question that can only be decided by trying
>and analyzing the results. Do we obtain a coherent picture? Or does
>it all dissolve in vagueness and contradictions?
I will take your use of the word "infinite" to mean "the absolutely
unrestricted infinite" - not just the natural numbers, or even sets of
natural numbers. I.e., full blown set theory.
It is obvious that we get a coherent picture that does not appear to
dissolve into contradictions. But does it dissolve into vagueness if we
push it too hard? I certainly think that the experience with the continuum
hypothesis and related questions definitely makes it at least *appear* that
it all dissolves into vagueness when things are pushed too literally.
I know that some set theorists are hopeful that the continuum hypothesis
and related questions will not continue to make it appear that it all
dissolves into vagueness when pushed literally. However, at this point, the
set theorists have pretty much abandoned the idea that there will be a fix
(i.e., resolution of such problems as the continuum hypothesis) that can be
readily understood and accepted by people who are not experts in set
theory. I.e., in the same sense that the usual axioms of ZFC can be readily
understood and accepted, even with such additional axioms as strongly
inaccessible cardinals, or even such additional axioms as the existence of
a probability measure on all subsets of [0,1].
I am doubtful that the *appearance* that it all dissolves into vagueness
when pushed literally will be erased by any esoteric "fix" understandable
only by experts in set theory.
Undoubtedly there will be a great effort ultimately made to reduce any such
esoteric "fix" to commonly understandable - and commonly convincing -
Equally surely, there will be a great effort ultimately made to show that
there is no "simple" fix that is as "simple" as the usual axioms of set
theory. I have a plan for this.
Of the prospects for the last two paragraphs - I'll put my money on the
>From this point of view, the work of set-theorists has been crucial
>in suggesting that it is the former that is the case.
And the work of set-theorists has been crucial in suggesting that this is
not the case, because the set theorists have shown that so many set
theoretic problems like the continuum hypothesis are independent of ZFC
together with so many additional axioms.
>The use of PD
>in providing an elegant theory of the projective hierarchy and the
>discovery that PD is implied by large cardinal axioms encourages the
>view that one is dealing with a situation where there is an
>objective fact-of-the-matter with respect to the propositions being
The fact that other axioms solve the same problems differently cuts in the
other direction. A perfectly legitimate conclusion from all this is that
there is no "objective fact-of-the-matter" since it is not an "objective
fact-of-the-matter" whether V = L is true or whether large cardinals are
true. It is just that both of these hypotheses are sufficient to settle
these particular questions.
As I have said in the Urbana meeting, the set theorist wants to accept
large cardinals because of the extra delicate and interesting set theoretic
structure that entails, and is missing under V = L. But the mathematician
doesn't welcome such extra set theoretic structure - as it is irrelevant
and sharply different in flavor to underlying mathematical issues. So if
forced to make a choice, mathematicians would greatly prefer V = L.
>The more recent work showing that consistency strength
>alone of certain of these axioms suffices to determine the truth
>values of sentences of given complexity, further enhances this
This sentence is mathematically false on its face. An accurate statement is
far more technical, making any "perception" less convincing.
> I am at a loss to understand why Harvey thinks that this
>work and his are at cross-purposes; it is clear to me that each
>needs the other: Harvey to show concretely that the higher
>infinities have specific interesting consequences way down, the
>set-theorists to map out the infinite terrain and provide a
>convincing case for a coherent robust state of affairs.
Cross-purposes is not the way I would put it. It's more like this. There is
a poker game going on in a barn. The players are in a long and heated
dispute as to whether or not it is legal for one of them to raise the pot
for the third time. This argument is going on unabated while the barn is
being consumed in a devastating fire.
I'm sitting here working my god damn xxx off to put out the fire while set
theorists are arguing about their rules of poker, calmly sitting in the
middle of that fire.
To put out the fire, one needs only to use some cardinal that is at least
beyond ZFC. To the general mathematical community, anything that large is
already grotesquely large - it takes experts in set theory to discern one
from the other.
The cardinals involved in what I am doing to put the fire out were already
set up in the years 1911-1913.
And while the fire is raging, nobody cares about some esoteric explanation
of just how "coherently robust the state of affairs is" to experts in set
theory. After all, these experts in set theory talking about "coherent
robust states of affairs" are starting to be being consumed in the fire!!
>Sol maintains that CH is inherently vague and for that reason it is
>pointless to expect that the question will ever be resolved. ... he does
>that the concept of the continuum (or equivalently, the power set of
>omega) is well-defined.
The equivalence between the continuum and the power set of omega is not
generally accepted by some leading core mathematicians because the
correspondence is not a natural mathematical object. In fact, many do not
believe that our usual model of the continuum in terms of Dedekind cuts and
the like fairly represents the continuum.
This is in consonance with my earlier statement about set theory being an
interpretation of mathematics rather than a part of mathematics.
>...for someone with Sol's beliefs, CH can have no
>determinate truth value. ...has been
>held by such great mathematicians as Brouwer and Weyl... what bothers me
>is how his
>conclusion will be received by readers of his MONTHLY article with
>little training in foundations.
I am uncomfortable with other aspects of Sol's article, also. I plan to
write something for the Monthly in due course about BRT. Why don't you
write something for the Monthly about your extreme Platonism?
>...mathematicians presume that the Goedel-Cohen independence results
>have settled the matter about CH, imagining that it is quite like
>the situation with the parallel postulate, and there is nothing more
>to be said.
There is a lot to be said for this preumption, given what has actually been
accomplished. However, what they don't generally realize is
i) how demonstrably irrelevant the CH is for any questions they really care
about, even if they suspect it;
ii) that there is an axiom of restriction, V = L, that dispenses with the
CH and all related questions.
>Such folk hearing Sol's conclusion about CH will likely
>nod their heads. But typically, they work with the continuum every
>day, and by no means are likely to share Sol's belief that it is a
>questionable concept, the belief on which his conclusion is based.
But the way they work with the continuum is not as a set theoretic object.
So the relationship between what mathematicians are doing and what Sol's
views are is, to my mind, quite unclear. Perhaps you ought to ask Sol about
what he thinks of this.
> I chose to talk about Goedel's Legacy. ... the question remains: are any
>problems of genuine
>mathematical interest likely to be examples of the incompleteness
>phenomenon, even such problems of central importance as the Riemann
>Hypothesis (as Goedel ventured to suggest). ...I suggested
>that ... interested people could be divided into three
>classes: optimists (people who think that such interesting
>undecidable propositions will be found - or even, are already being
>found), skeptics (people who think that Gödel incompleteness will
>not affect propositions of real interest to mathematicians), and
>pessimists(thinks that even if there are such propositions, it will
>be hopeless to prove them). In replying to a question from Dana
>Scott, I admitted that I am an optimist.
My own view is this:
i) it is likely that every non set theoretic statement in the normal
mathematical literature is decided by ZFC; (this can be made very precise,
but that's for another time and place).
ii) BRT will be accepted as having results "of genuine mathematical
interest", and is chock full of incompleteness phenomena. The most
immediately convincing ones will be in terms of classifications and
specific theorems about classifications.
iii) additional classification problems throughout mathematics - even more
mathematically friendly than BRT - will surface following the lead of BRT,
and the incompleteness phenomena will also routinely appear there. E.g.,
instead of looking at Boolean relations, one looks at solutions to
iv) the hallmark of these new kinds of classification problems is that
there are always just a finite number of cases. The number of cases is
generally quite large, like 2^512. The idea is that large cardinals are
supposed to settle all of the instances, but some instances cannot be
settled without large cardinals. Also, there are general features of the
classification that are stated as single theorems which can only be proved
using large cardinals.
More information about the FOM
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CC-MAIN-2018-05
| 16,169 | 256 |
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