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https://socratic.org/questions/5705b1f011ef6b7d97c665a1
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math
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What is wrong with the statement #1 = sqrt(1) = sqrt((-1)*(-1)) = sqrt(-1) * sqrt(-1) = -1# ?
Why is this so?
Every number (Real or Complex) apart from
In order to tell them apart, we call one of them the principal square root and denote it by
Which one is principal?
If that sounds a little arbitrary, it is.
When you think about the square root of Complex numbers you start to see the problem better:
Imagine a point moving slowly anticlockwise around the unit circle in the Complex plane, starting from the point
Its principal square root also starts to move around the unit circle anticlockwise, but at half the speed.
When the original point has completed one full revolution, where is the point tracking the principal square root?
If we had just let it proceed smoothly on its journey then it would have only completed half a revolution, so would be at
In order that the principal square root be well defined, we need to choose somewhere to put a discontinuity - called a branch cut.
Most people put it just below the negative part of the Real axis. Some people prefer to put it just below the positive part of the Real axis.
Once we do this, the point representing the principal square root abruptly jumps from one side of the unit circle to the opposite side as the point representing the original number crosses the cut.
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CC-MAIN-2021-25
| 1,329 | 14 |
https://www.stat.math.ethz.ch/pipermail/r-devel/2001-June/022681.html
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math
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[Rd] Additional output in cancor
Mon, 11 Jun 2001 09:21:37 +0100
Can I suggest an additional output component in cancor, from package
mva? It would be useful to have the number of canonical correlation
vectors, equivalently the rank of the covariance between x and y (label
"rank"). This would usually be min(dx, dy), where dx and dy have
already been computed for the svd function, but there might be
situations where it was less than this, so I guess the safe option would
be to include
rank = qr(t(x) %*% y)$rank
among the outputs. Then the last four lines of the help might be
rk <- cxy$rank
all.equal(cor(x %*% cxy$xcoef[, 1:rk, drop=FALSE],
y %*% cxy$ycoef[, 1:rk, drop=FALSE]), diag(cxy$cor))
all.equal(cor(x %*% cxy$xcoef[, 1:rk, drop=FALSE]), diag(1, rk))
all.equal(cor(y %*% cxy$ycoef[, 1:rk, drop=FALSE]), diag(1, rk))
which I think is more intuitive.
More radically, the xcoef and ycoef components of cancor might
themselves be restricted to the appropriate columns (1:rank). This
might affect some existing code, although any code that uses the
non-informative columns has got to be broken, hasn't it?!
Can I also suggest an extra reference for the help page:
Mardia, K. V., J. T. Kent and J. M. Bibby (1979). Multivariate
Analysis, London, Academic Press Ltd, ch. 10.
Jonathan Rougier Science Laboratories
Department of Mathematical Sciences South Road
University of Durham Durham DH1 3LE
tel: +44 (0)191 374 2361, fax: +44 (0)191 374 7388
r-devel mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !) To: [email protected]
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CC-MAIN-2023-14
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https://socratic.org/questions/how-do-you-use-the-fundamental-theorem-of-calculus-to-find-the-derivative-of-int-5#492535
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math
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How do you use the Fundamental Theorem of Calculus to find the derivative of #int (cos(t^4) + t) dt# from -4 to sinx?
Use the Chain Rule along with the Fundamental Theorem of Calculus to get the answer
For a function
By the Chain Rule,
(In general, the Chain Rule says that, under appropriate assumptions about differentiability,
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CC-MAIN-2022-33
| 329 | 5 |
http://aspiritlikethewind.blogspot.com/2009/10/like-this-but-not-really.html
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math
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The calculus I'm supposed to be studying right now reminds me of how small the human mind really is. There seems to be a repeated theme through my textbook of 'It's like this, but not exactly.' I shouldn't be able to subtract infinity from infinity because it just doesn't make sense. I still end up doing it indirectly. This confuses me.
Because I am confused, I end up wondering how I can be studying infinity anyway. I struggle to grasp twenty years or ten thousand Rand properly. Numbers like a billion or a trillion are really sort of beyond me, but here I am trying to grasp infinity. That's probably why I keep on facing half-answers. There are analogies that explain it if you don't stretch them too far and explanations that make sense if you aren't too rigourous. At the end of the day, though, I think there are some things that are beyond human understanding.
Those things are not only studied in Philosophy and Theology degrees. Anything that is part of God's creation - our entire universe - fits into something bigger than we can understand. So the Maths books say 'Like this, but not really' and 'Infinity isn't a number, but if we treat it like one here it works out'. I guess I just have to accept that God has given some people the insight to find those things and to counter my confusion with a wonder at what He's created.
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CC-MAIN-2018-22
| 1,343 | 3 |
http://www.ck12.org/book/CK-12-Middle-School-Math-Concepts-Grade-8/r9/section/3.13/
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math
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The students at Floyd Middle School have been working hard fundraising. They sold popcorn, had a bake sale and a car wash. Finally with the time for purchasing band uniforms rapidly approaching, Mrs. Kline gathered the whole band together one afternoon to discuss their profit.
“We did very well,” she started. “We raised a total of $12,000 and we had $1,000 in our account, so we have $13,000 to spend on our uniforms. I know that may seem like a lot of money, but uniforms are expensive. We are only going to be able to purchase new jackets for everyone. If we have any money left over, we’ll buy new fingerless gloves because some of the ones we’re using look awful.”
“Mrs. Kline, did you already pick the design of the jacket?” Kayla asked from the second row.
“Yes. It was one of the ones we voted on last year,” she said holding up a picture of the shiny, new navy jacket. “Now I need a few people to figure out the cost and if we have enough for the gloves too.”
Kayla and Juan volunteered to work on the arithmetic. Here is the information Mrs. Kline gave them.
The jackets each cost $99.95.
The total budget is $13,000.
There are 144 students in the band.
“We will need to spend $11,512.80 on the jackets,” Kayla said to Juan.
“Wow, that’s a lot of money. How much can we spend on the gloves?”
That is a great question. It is one that can be answered by writing an inequality. The students need their total to be equal to or less than $13,000. In this Concept, you will learn how to work with inequalities that have addition and/or subtraction in them. Then you will use what you have learned to help Kayla and Juan with the band uniforms.
Sometimes, you will have an inequality that is not as straightforward as x>4. With this example, we know that the variable will be equal to any number that is greater than four. This is quite easy to work with and we can write a set of numbers to make this inequality a true statement.
What if it isn’t that simple?
Sometimes, you will see an inequality like this one.
Here we need to figure out the set of numbers that will make this a true statement. We are looking for a number that when added to three is greater than seven.
To figure this out, we will need to solve this inequality.
Solving an inequality is similar to solving an equation. Here are some number properties that can help you solve inequalities.
The addition property of inequality states that if the same number is added to each side of an inequality, the sense of the inequality stays the same. In other words, the inequality symbol does not change.
If a>b, then a+c>b+c. If a≥b, then a+c≥b+c.
If a<b, then a+c<b+c. If a≤b, then a+c≤b+c.
What about subtraction? Remember, subtracting a number, c, is the same as adding its opposite, −c. So, the addition property of inequality applies to subtraction as well. We can also state this as it’s own property.
The subtraction property of inequality states that if the same number is subtracted from each side of an inequality, the sense of the inequality stays the same. In other words, the inequality symbol does not change.
If a>b, then a−c>b−c. If a≥b, then a−c≥b−c.
If a<b, then a−c<b−c. If a≤b, then a−c≤b−c.
Applying these properties makes our work quite simple. You can think of solving inequalities in the same way that you thought of solving equations. The big difference is that your answer will be a set of numbers and not a single number. Just like with equations, you need to be sure that your answer makes the mathematical statement true. If it doesn’t, then you need to rethink your answer.
Now let’s look at solving inequalities.
Solve this inequality and graph its solution: n−3<5.
Solve the inequality as you would solve an equation, by using inverse operations. Since the 3 is subtracted from n, add 3 to both sides of the inequality to solve it. Since you are adding the same number to both sides of the inequality, the addition property of inequality applies. According to that property, we know that the inequality symbol should stay the same when we add the same number, 3, to both sides of the inequality.
Think back! To solve inequalities, you may need to remember how to add and subtract integers. Pay attention to the sign when you work with these values.
Now, graph the solution. The inequality n<8 is read as “n is less than 8.” So, the solution set for this inequality includes all numbers that are less than 8, but it does not include 8.
Draw a number line from 0 to 10. Add an open circle at 8 to show that 7 is not a solution for this inequality. Then draw an arrow showing all numbers less than 8.
Solve this inequality and graph its solution: −2≤x+4
Use inverse operations to isolate the variable. Since the 4 is added to x, subtract 4 from both sides of the inequality to solve it. Since you are subtracting the same number from both sides of the inequality, the subtraction property of inequality applies. According to that property, the inequality symbol should stay the same when we subtract the same number, 4, from both sides of the inequality.
Now, we should graph the solution. However, before we can do that, we need to rewrite the inequality so the variable is listed first. The inequality −6≤x is read as “-6 is less than or equal to x.” If we list the x first, we must reverse the inequality symbol. That means changing the “less than or equal to” symbol (≤) to a “less than or equal to symbol” (≥).
So, −6≤x equivalent to x≥−6.
This makes sense. If -6 is less than or equal to x, then x must be greater than or equal to -6.
The inequality x≥−6 is read as “x is greater than or equal to -6.” So, the solutions of this inequality include -6 and all numbers that are greater than -6.
Draw a number line from -10 to 0. Add a closed circle at -6 to show that -6 is a solution for this inequality. Then draw an arrow showing all numbers greater than -6.
Now let's go back to the dilemma at the beginning of the Concept.
First, we write an inequality to represent the uniform cost, unknown cost of gloves, and the total budget for everything. The total of the uniforms and gloves must be less than or equal to the total budget.
$11,512=cost of uniforms
x=budget for gloves
Here is the inequality.
We solve the inequality by using inverse operations.
The students will have a maximum budget of $1487.20 to spend on the gloves.
a mathematical statement using an equals sign where the quantity on one side of the equals is the same as the quantity on the other side.
a mathematical statement where the value on one side of an inequality symbol can be less than, greater than and sometimes also equal to the quantity on the other side. The key is that the quantities are not necessarily equal.
Addition Property of Inequality
You can add a quantity to both sides of an inequality and it does not change the sense of the inequality.
Subtraction Property of Inequality
You can subtract a quantity from both sides of an inequality and it does not change the sense of the inequality.
Here is one for you to try on your own.
At the store, Talia bought one item—a $4.99 bottle of shampoo. Let d represent the amount in dollars that she handed the clerk. She received more than $5 in change.
a. Write an inequality to represent d, the number of dollars Talia handed the clerk to pay for the shampoo.
b. List three possible values of d.
Consider part a first.
Use a number, an operation sign, a variable, or an inequality symbol to represent each part of the problem. The fact that this problem involves “change” may help you see that you should write a subtraction expression to represent the first part of this problem. To represent how much change Talia received, you will need to subtract the cost of the shampoo from the amount she handed the clerk. The key words “more than”, in this case, indicate that you should use a > symbol. Use this information to write an inequality for this problem.
(dollars handed to the clerk)−(cost of $4.99 bottle of shampoo)>($5 in change)↓↓↓↓↓d−4.99> 5
So, this problem can be represented by the inequality d−4.99>5.
Next, consider part b.
Solve the inequality to help you find three possible values for d. To solve this inequality, add 4.99 to both sides. Do not change the inequality symbol.
According to the inequality above, the amount Talia handed the clerk was more than $9.99.
So, three possible values of d are $10.00, $10.99, and $20.00. These are only 3 possible answers. You could choose any amount that is greater than $9.99.
Khan Academy Inequalities Using Addition and Subtraction
Directions: Solve the following inequalities.
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| 8,720 | 65 |
https://quizack.com/programming-languages/alligation/mcq
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math
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10. A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to it. From this resultant solution 30 L is withdrawn and then replaced with water. The resultant ratio of milk water in the final solution is 3:7. Find the original volume of the solution.
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CC-MAIN-2023-23
| 307 | 1 |
https://www.physicsforums.com/threads/momentum-kleppner-classical-mechanics-freight-car-and-hopper.951043/
|
math
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Member has been reminded to provide typed text instead of barely readable pictures.
Freight car and hopper*
An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track.
Find the speed when a mass of sand m has been transferred.
The Attempt at a Solution
The solution answer has an extra b*t in the denominator and + answer. Where is the flaw in my method? Now I understand this can be done shorter using impulse and exact values but I prefer the more general approach and deduce specific cases at the end. Thanks
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| 631 | 6 |
https://dogwater-fountain.com/snafu-season-3.html
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math
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The My Teen Romantic Comedy SNAFU Season 3 release date was originally scheduled for the spring 2020 anime season, but the third season, My Teen Romantic Comedy …###
Jul 14, 2020 · My Teen Romantic Comedy SNAFU Climax is now currently running as part of the Summer 2020 season, and this final season of the series …###
Apr 07, 2020 · My Teen Romantic Comedy SNAFU happens to be one of them, and fans are curious when its slated season will make its debut. Originally, the third season …###
My Teen Romantic Comedy SNAFU Season 3: This anime has proved that it is bold enough to stand out from its peers. So lets check out the details.###
Stream “Ahiru no Sora” Season 3 on HIDIVE. March 25, 2020, 5:00 PM. Halftime’s over, and it’s time for the 3rd quarter of Ahiru no Sora. Join us on Wednesday, April 1, 2020 at 9:55... MORE .###
Jul 13, 2020 · With SNAFU’s Season 3 premiere having just aired, today I’d like to sift through all that we’ve recently learned, and perhaps extrapolate where we’re going from here.
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CC-MAIN-2020-50
| 1,038 | 6 |
https://ir.canterbury.ac.nz/handle/10092/8214
|
math
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Infinite sets of polynomial conserved densities for nonlinear evolution equations
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The infinite sets of polynomial conserved densities which have been found for the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the Sine-Gordon equation, and the classical nonlinear shallow-water equations, are investigated using Noether's theorem. These sets are identified as energy or momentum densities of sets of higher-order integro-differential equations. These higher-order equations are obtained by operating n times on the evolution equation under consideration, with a nonlinear integro-differential operator, and hence their solution sets contain that of the evolution equation under consideration. The technique has possibilities for predicting the existence of infinite sets of polynomial conserved densities for other nonlinear evolution equations.
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| 939 | 4 |
https://www.vde-verlag.de/proceedings-de/453152804.html
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math
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On the Degrees of Freedom in the Interaction between Sets of Elementary Scatterers
Konferenz: EuCAP 2009 - 3rd European Conference on Antennas and Propagation
23.03.2009 - 27.03.2009 in Berlin, Germany
Tagungsband: EuCAP 2009
Seiten: 4Sprache: EnglischTyp: PDFPersönliche VDE-Mitglieder erhalten auf diesen Artikel 10% Rabatt
Heldring, A.; Tamayo, J. M.; Rius, J. M. (Dept. of Signal Theory & Comm, Polytechnic University of Catalonia, c/ J.Girona 1, 08034, Barcelona, Spain)
A series of numerical experiments has been executed to investigate the number of degrees of freedom in the interaction between large scattering bodies. The relation between degrees of freedom and operating frequency establishes the computational complexity for integral equation methods fast solvers based on matrix block compression. In 2D the theoretical asymptotic relation for large frequency soon becomes clear. On the other hand, in 3D even a tendency towards the asymptotic value fails to appear for bodies of hundreds of wavelengths in diameter.
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CC-MAIN-2023-14
| 1,030 | 7 |
http://www.math-problems-solved.com/q50338_7x6_does_7x4817
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math
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how do you resolve this : n+(n)2=42
n + n^2 = 42
(i'm presuming that you want to find the possible values of n?)
So, subtract 42 from both sides of the equation:
n + n^2 - 42 = 0
So now you want to factorise this equation, this means you think of the possible numbers that you could multiply together to get 42.
There are many different options for this. You could chose: 42x1, 21x2, 14x3, 7x6.
But we need a value that is going to give us our equation and in this example only 7x6 will work (don't forget that the 42 is negative, and therefore one of the numbers that you place in the brackets has to be negative too):
So, n + n^2 - 42 = (n + 7)(n - 6) = 0
(n+ 7)(n - 6) = 0 at two values of n, when n=-7 and when n=6. Read More: ...
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CC-MAIN-2018-05
| 734 | 10 |
https://hellothinkster.com/blog/geometry-help-teach-proofs-like-math-tutor/
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math
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Last Updated on August 3, 2023 by user
Geometry is the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids and higher dimensional analogs. For many students, this proves to be a barrier to math success, and they will often turn to you, the parent, for geometry help.
But this can create its own problems. Even if you excelled at geometry and math as a student, it’s likely been a while since you have practiced it, and you may not be able to explain it in the way your student was taught in school.
Don’t worry if you don’t have directed tutoring experience or even remember anything from your math class- that’s why we have put together this guide for you so that you can teach geometry proofs to your student as a private math tutor or teacher would. It will also help improve your child’s study skills in terms of how to layout proofs according to what the teacher deems necessary.
Taking your student to a specialized math center for a session with a private tutor may not be convenient or available in your area. That’s when you have to take matters into your own hands despite not having any direct tutoring experience.
For some students, their problem with understanding geometry could be inherent in their nature. There is some evidence to suggest
that people tend to either relate to math in a more numbers-driven, arithmetical way or a visual/geometric way.
For those in the first group, reasoning spatially is not as easy as it is for the second group, which makes it harder to learn geometric concepts. But don’t give up; math skills can quickly be learned and developed over time!
One of the most common of all geometry problems is the two-column proof.
Two-column proofs are dreaded by many students as they require them to not only give factual statements to answer the proof but also require students to provide a reason for every statement that is given.
This added step takes extra time and can be frustrating for many students.
These five steps are based on this video by Rick Scarfi.
In the video, Scarfi breaks down what is needed to complete and master two-column proofs. With these tips, you’ll be able to provide a great tutoring session and geometry help to your student whether it’s with homework or test prep.
The postulates, theorems, definitions, and properties of geometry are very important for solving two-column proofs. This is where the statements and reasons come from, and your student needs to have a solid knowledge of these – or know where they can find them – to solve geometry problems if they don’t have access to online math tutoring.
These should all be available in your student’s geometry textbook they will be toting with them for homework. It can also be useful to create a reference sheet to use when working on these types of problems. The more of these that your student has mastered, the quicker they can solve proofs without having to review their reference sheet.
Geometry problems are typically visual, and going the extra step to label the drawing that has been provided is key to solving them. If you do not have a drawing, it is recommended that your student draw a picture of what is given for a visual example to review while working through the proof.
Your student will use the given statement to label the pieces of the drawing that are being considered. For example, if the statement indicates that two lines are parallel, your student may want to draw over them or highlight them to get a better visual representation of the problem they are solving. You may also suggest that they mark the midpoint of a line inside the drawing with an “m” or another indicator, so the center is visually clear as well. This is just one of the tips that an experienced tutor employs.
“The picture is a visual to help you to think through the proof,” Scarfi says. It’s all a part of learning.
Your student can continue labeling as he/she works through the various steps of each proof. Remember: labeling should not be limited to just the beginning of the problem.
In this example below, you can see that Scarfi labeled the parallel lines AS and TB, congruent angles 5 and 2 and then 6 and 1, the midpoint at O and congruent sides AO and OB.
When completed, proofs will often look messy – and this is a good thing! Sometimes, labeling in the later steps can lead your student to the full answer, as they can literally see where the statements are leading them.
Geometry proofs are interesting as they tell your student what they need to prove. Your student just has to figure out how it is proven.
It may seem obvious, but knowing what is it that you are trying to prove is the key to solving any proof problem. For example, what the problem is asking your student to prove might not have any of the same numbers as having been given in the visual elements of the problem.
You can see this in the following example, as angle 7 is not stated in the given.
This tells your child that, at some point, while he or she is attempting to provide a solution, they will have to provide a statement – and corresponding reason – that lets them use this number.
Another teaching tip, Scarfi suggests writing out what you are proving (again) underneath the columns to give your student clear direction as they take on the geometry problem. Knowing what they are trying to prove can help your student narrow down postulates, theorems, definitions, and properties to the ones that will be most helpful in solving the problem.
After getting them narrowed to a few of the most appropriate ones, your student has fewer variables to work with, and then they can focus on determining which answer is the right one.
It’s important to fill out the given information first when solving proofs. Sometimes an obvious step is overlooked as a given, so be sure to go over all of these first.
If your student is at the level of creating their own statements (rather than having them provided by the teacher), they’ll typically want to put the “given statements” in the first step.
It’s also important to remember that the “given statements” are provided on purpose to help your student decide the best way to prove what has already been established. The “given statement” is there to tip you off to the other theorems, postulates, properties, and definitions that are true for this problem so that you can use these to solve the proof.
Sometimes, what you are trying to prove in a geometry proof falls outside of the knowledge you can gather from the statements that have been given. By knowing the theorems, postulates, properties, and definitions, your student can introduce their own additional givens based on what they already know.
For example, the “given statement” below does not mention angle 7, which your student is trying to prove.
But, if the “given statement” helps your student figure out that the triangle is an isosceles triangle, your student can then use what they know about the definition of an isosceles triangle and its angles to figure out the third angle (See step 4 in the example below) and move to the next step.
This is a great example of using a strong math foundation to solve new problems – a skill we often encourage here at Thinkster!
Sometimes a mathematics course teacher or the teaching assistant wants to make sure that the statements within the proof solution are symmetrical.
In the example below, the “given statement” shown in step 1 has SA (from triangle SOA) on the left and TB (from triangle TOB) on the right, but what is being proven has them reversed. If your teacher is very technical, they may want your student to use a symmetric property to switch them around to match what is being proven – shown in step 5.
It’s also important to write out the reasons in the way that your student’s teacher prefers. The teacher may want everything written out in the long form or he or she may want your child to use specific symbols and abbreviations.
In this same vein, you don’t want to end your proof too early.
You may have been able to prove the first or second aspects of the proof, but many teachers will want their students to show all of the statements and reasons they can use to complete the proof.
For example, to prove that two triangles are congruent, your student may have already been able to show that two of the angles within each triangle are congruent and two sides are equal in length. These are shown in steps 2 and 3 below.
It may be important to take this one step further and actually write out that the sides being equal length also make them congruent, which you can see in step 4:
Keep a Proof Reasons List
The postulates, theorems, properties, and definitions are likely all in your student’s textbook, but it can be easier to create a list or reference guide with your own notes to help you remember when to use them. Flashcards can also be helpful in learning these, according to this blog by Mrs. E.
If your student is still new to geometry and struggling to memorize all of these concepts, it can be useful to have them write out the concepts they are using in their reasoning when explaining a statement. This is another teaching tip and will help them, and you, see that they know what these postulates, theorems, properties, and definitions say, and – more importantly – that they know what they mean.
We know geometry can be some of the most difficult lessons to handle.
If your child needs extra geometry help and you don’t have the spare time, or the education, to help them master their geometry concepts, Thinkster will pair your child with an online math tutor who is an expert at geometry processes and is dedicated to making sure your child learns them properly.
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CC-MAIN-2023-50
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https://entrepreneursnews.net/all-you-truly-need-to-know-about-algebra/
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math
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Variable-based math is one of the general areas of number shuffling. When in doubt, is the assessment of numerical pictures and the guidelines for controlling these photos in conditions; It is a unified recipe of fundamentally all math. All you truly need to know about Algebra
Straightforward variable-based numerical arrangements with the control of components. Like they were numbers (see picture), and is in this manner urgent in all purposes of science. Sensible is the name given in polynomial numerical mentoring. To the assessment of arithmetical plans like social events, rings, and fields. Direct polynomial math, which administers straight conditions and straight mappings. Is utilized for present-day portrayals of calculation and has different utilitarian applications (for instance. In weather conditions measuring).
There are different areas of number shuffling that are related to polynomial math, some have “variable based math” to name. For example, commutative polynomial math and some don’t, like the Galois hypothesis. All you truly need to know about Algebra
The term variable-based math is utilized not exclusively to name a field of calculating and some subfields; It is utilized for naming express kinds of mathematical plans. Like polynomial math over a field, generally, suggested as polynomial math. From time to time, a similar enunciation is utilized for the subfield and its truly mathematical plans; For instance, Boolean polynomial math and Boolean variable-based math. A mathematician tended to a huge master’s in polynomial math is called an algebraist. To scrutinize more educational articles visit whatisss.
Word – medium
The word variable-based mathematical comes from Arabic:, Romanized: al-jabr, lit. The Restoration of the Broken Parts, by the Persian mathematician. And stargazer al-Khwarizmi, mid-tenth century book quiet al-Jaber wa el-Muqabala named “The Science of Restoring and Balancing”. In his work, the term al-jabr suggests the activity of moving a term beginning. With one side of a situation and afterward onto the following. Short for fundamentally polynomial math or polynomial math in Latin.
The word, finally, entered the English language during. The fifteenth quite a while from Spanish, Italian, or Medieval Latin. It for the most part proposes the operation to supplant broken or secluded bones. Numerical importance was first kept (in English) in the sixteenth 100 years. All you truly need to know about Algebra
Variable based math as a piece of science
Variable-based math started with calculations like computing, in which letters tended to be numbers. This permitted confirmations of properties that are authentic despite the numbers in question. Generally speaking, and in current education, the assessment of variable-based mathematical beginnings. With tending to conditions, for example, the quadratic condition above. Before the sixteenth 100 years, science was isolated into just two subfields, ascertaining and calculation. Notwithstanding the way that two or three strategies, which were grown a ton sooner.
Can today be viewed as logarithmic, the improvement of variable-based math and, before the long. Little examination as subfields of science returns just to the sixteenth or seventeenth 100 years. From the late nineteenth 100 years, different new areas of science arose, an immense piece of which utilized both math and calculation. And in every practical sense, totally utilized variable-based math. And you should be comfortable with Radius vs Diameter.
Early History of Algebra
The fundamental preparations of polynomial math can be followed back to the old Babylonians, who developed a critical degree of computing structure with which they had the decision to perform evaluations in an algorithmic style. The Babylonians made arrangements to figure manage genuine results with respect to issues reliably settled today utilizing straight conditions, quadratic conditions, and wearisome direct conditions. All you truly need to know about Algebra
Inquisitively, most Egyptians of this period, as well as Greek and Chinese number shuffling in the fundamental thousand years BC, overall, took care of such conditions by mathematical strategies, as depicted in the Rhind Mathematical Papyrus, Euclid’s Elements, and Nine Chapters on Mathematical Huh. Craftsmanship.
Science didn’t make in Islam.
Whenever Plato, Greek math had changed unquestionably. Diophantus (third century AD) was an Alexandrian Greek mathematician and writer of development of books called Arithmetica. These unions sort out some way to address arithmetical conditions, and in number hypothesis, have incited the undeniable level thought of the Diophantine condition.
The previous practices examined above impacted the Persian mathematician Muhammad ibn Musa al-Khwarizmi (c. 780-850). He later shaped the organized book on Computation by Completeness and Balance, which spread out polynomial math as a numerical discipline freed from assessment and working out.
Greek mathematicians like Hero and Diophantus of Alexandria, as well as Indian mathematicians like Brahmagupta, went on with the Egyptian and Babylonian practices, notwithstanding the way that Diophantus’ Arithmetica and Brahmagupta’s Brahmasphussiddhanta are at a more raised level. For instance, the fundamental complete computing strategy is s. instead of written in words
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CC-MAIN-2023-14
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https://studydaddy.com/question/statistics---lab-week-2-name-_______________________-math221-statistical-concept
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math
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Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
Statistics - Lab Week 2 Name:_______________________ Math221 Statistical Concepts:
Statistics – Lab Week 2Name:_______________________Math221Statistical Concepts:•Using MINITAB•Graphics•Shapes of Distributions•Descriptive Statistics•Empirical RuleData in MINITABMINITAB is a powerful, yet user-friendly, data analysis software package. You can launch MINITAB by finding the icon and double clicking on it. After a moment you will see two windows, the Session Window in the top half of the screen and the Worksheet or Data Window in the bottom half.Data have already been formatted and entered into a MINITAB worksheet. Go to the eCollege Doc sharing site to download this data file. The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the MINITAB Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. Included with this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions.Complete the answers below and paste the answers from MiniTab below each question. Type your answers to the questions where noted. Therefore, your response to the lab will be this ONE document submitted to the dropbox.Code SheetVariable NameQuestionDriveQuestion 1 – How long does it take you to drive to the school on average (to the nearest minute)?StateQuestion 2 – What state/country were you born?TempQuestion 3 – What is the temperature outside right now?RankQuestion 4 – Rank all of the courses you are currently taking. The class you look most forward to taking will be ranked one, next two, and so on. What is the rank assigned to this class?HeightQuestion 5 – What is your height to the nearest inch?ShoeQuestion 6 – What is your shoe size?SleepQuestion 7 – How many hours did you sleep last night?GenderQuestion 8 – What is your gender?RaceQuestion 9 – What is your race?CarQuestion 10 – What color of car do you drive?TVQuestion 11 – How long (on average) do you spend a day watching TV?MoneyQuestion 12 – How much money do you have with you right now?CoinQuestion 13 – Flip a coin 10 times. How many times did you get tails?Die1Question 14 – Roll a six-sided die 10 times and record the results.Die2Die3Die4Die5Die6Die7Die8Die9Die10Creating Graphs1.Create a Pie Chart for the variable Car – Pull up Graph > Pie Chart and click in the categories variables box so that the list of variables will show up on the left. Now double click on the variable name ‘Car” in the box at the left of the window. Include a title by clicking on the “Labels…” button and typing it in the correct text area (put your name in as the title) and click OK. Click OK again to create graph. Click on the graph and use Ctrl+C to copy and come back here, click below this question and use Ctrl+V to paste it in this Word document.2.Create a histogram for the variable Height – Pull up Graph > Histograms and choose “Simple”. Then set the graph variable to “height”. Include a title by clicking on the “Labels…” button and typing it in the correct text area (put your name in as the title) and click OK. Copy and paste the graph here.3.Create a stem and leaf chart for the variable Money – Pull up Graph > Stem-and Leaf and set Variables: to “Money”. Enter 10 for the Increment: and click OK. The leaves of the stem-leaf plot will be the one’s digits of the values in the “Money” variable. Note: the first column of the stem-leaf plot that you create is the count. The row with the count in parentheses includes the median. The counts below the median cumulate from the bottom of the plot.Copy and paste the graph here.Calculating Descriptive StatisticsClick OK. Type the mean and the standard deviation for both males and females in the space below this question.MeanStandard deviationFemalesMalesSelect File > Save Worksheet As to save the data set. You must either keep a copy of this data or download it again off the web site for future labs.Short Answer Writing AssignmentAll answers should be complete sentences. 5.What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.6.What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.7.What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer.8.Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers.9.Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.10.Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.11.Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.
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https://forum.knittinghelp.com/t/how-to-wind-unwind/67573
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math
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I was watching the Knitting Daily Show on PBS and I wondered (as a non-spinner) if there’s a right and a wrong way to unwind a ball. It seems to me if it’s done the wrong way the plys might be weakend?
Is there a wrong side to wind/unwind from? And can you tell if you’re pulling from the “right” end? Of course it depends on how you wound it (to pull from inside or not).
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CC-MAIN-2022-33
| 382 | 2 |
http://www.biology.arizona.edu/biomath/tutorials/linear/Basics_LinearFunctions.html
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math
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To understand linear relationships in biology, we must first learn about linear functions and how they differ from nonlinear functions.
Definition: Linear and Nonlinear Functions
The key feature of linear functions is that the dependent variable (y) changes
at a constant rate with the independent variable (x). In other words, for some
fixed change in x there is a corresponding fixed change in y. As the name implies, linear functions are graphically represented by lines.
Definition: A linear function is a function that has a constant rate of change and can be represented by the equation y = mx + b, where m and b are constants. That is, for a fixed change in the independent variable there is a corresponding fixed change in the dependent variable.
If we take the change in x to be a one unit increase (e.g., from x to x + 1), then a linear function will have a corresponding constant change in the variable y. This idea will be explored more in the next section when slope is discussed.
Nonlinear functions, on the other hand,
have different changes in y for a fixed change
Definition: A nonlinear function is a function that is not linear. That is, for a fixed change in the independent variable, there is NOT a corresponding fixed change in the dependent variable.
The following graph depicts a nonlinear function with a non constant rate of change,
In this example, there is both a 5 unit increase in y and a 11 unit decrease in y corresponding to a one unit increase in x. A nonlinear function does not exhibit a constant rate of change, and therefore is not graphically represented by a line. In fact, you probably think of nonlinear functions as being curves. The following table summarizes some of the general differences between linear and nonlinear functions:
Domain and range is all real numbers.
Graphically represented by a straight line.
Domain and range can vary.
Often graphically represented by a curve.
Representing linear functions
Linear functions can be written in slope-intercept form as,
y(x) = mx + b.
We can use
the slope-intercept form of a line to demonstrate that a linear function has a
constant rate of change. To see this, consider a one unit increase in x (i.e. from
x to x + 1). According to our linear equation, a one unit increase in x results in,
y (x + 1) = m(x + 1) + b = mx + m + b.
Examining the difference in the y values for a one unit increase in x gives,
y (x + 1) − y (x) = mx + m + b − (mx + b) = m.
That is, a one unit increase in x corresponds to an m unit increase or decrease
in y, depending on whether m is positive or negative.
In the next
section we will explore the concept of slope.
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CC-MAIN-2023-06
| 2,647 | 30 |
http://www.jstor.org/stable/2102541
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math
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You are not currently logged in.
Access JSTOR through your library or other institution:
An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems
D. A. Edwards and D. S. Cohen
SIAM Journal on Applied Mathematics
Vol. 55, No. 3 (Jun., 1995), pp. 662-676
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2102541
Page Count: 15
You can always find the topics here!Topics: Polymers, Mathematical problems, Boundary conditions, Glass, Mathematical constants, Mathematics, Materials, Materials science, Diffusion coefficient, Mathematical independent variables
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Select the topics that are inaccurate.
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In the context of analyzing a new model for nonlinear diffusion in polymers, an unusual condition appears at the moving interface between the glassy and rubbery phases of the polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our equations, has received very little attention in the mathematical literature. Due to the unusual form of the moving-boundary condition, further study is needed as to the existence and uniqueness of solutions satisfying such a condition. The moving boundary condition which results is not solvable by similarity solutions, but can be solved by integral equation techniques. A solution process is outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic of a dissolving polymer.
SIAM Journal on Applied Mathematics © 1995 Society for Industrial and Applied Mathematics
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https://www.lotterypost.com/thread/136612
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math
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|Posted: June 17, 2006, 2:09 pm - IP Logged|
Introducing ZEN's Doubles Magic...
If this program can't make you money, then I just don't know what to say...
It generates 100 doubles to play in the pick 4 for a box win of $187.50
Type in all ten digits, 0 thru 9 in any order.
If the winning draw contains any double and you have placed your digits right, you win - guaranteed!
In order for the digits to be placed correctly, the double digit must either be one of the first 5 digits you type in or one of the last 5 digits you type in, DAH!!! Of course it will be, but here's the kicker...
The other two digits cannot be within the same group of five digits WITH the double digit.
If you type in the numbers like this... 5810346972 then any double that comes up in the draw will win IF the double number is 5, 8, 1, 0, or 3 and the remaining two digits of the draw are 4, 6, 9, 7 or 2. OR, if the double number is 4, 6, 9, 7, or 2 and the remaining digits of the draw are 5, 8, 1, 0, or 3. You will still win that drawing for $187.50
If, using the same example above, the double number is 5, but one of the other digits is 8, 1, 0, or 3 you will not win, even if the fourth digit is a 4, 6, 9, 7, or 2.
The double number within the group of five digits cannot be part of any other numbers in the draw. The other two numbers must be in the last set of 5 digits you type in, or vica versa.
Good luck! I'll see you at the bank!!!
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https://vyconvert.com/posts/Three-Methods-for-Converting-Inches-to-Feet.html
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math
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Three Methods for Converting Inches to Feet
Once you know the basics, converting between inches and feet is a breeze. Since there are 12 inches in a foot, simply divide the number of inches you have by 12 to get the corresponding number of feet.
Measure your current height in inches. Whether you're using a calculator or not, jot down or punch in this sum. Don't forget to put the word "inches" next to the number if you recorded it. "
- OK, here's a problem to follow along with. In order to convert a girl's height of 70 inches to feet, we must first write down 70 inches.
Get the twelfths by dividing this sum. How many times can 12 be squeezed into your measurement in inches? A whole number will be the result if you insert it exactly that many times into your inches. There will be a decimal, fraction, or mixed number if it doesn't round off to exactly your number of inches.
- To illustrate, if we divide 70 inches by 12, we get 5 83 5 and 10/12 (5 and 5/6) or 5 remainder 10 are alternate notations. If you want to know more about remainders, keep reading!
Use feet for your answer. You've just been given the correct answer in terms of feet. Put the word "feet" in front of it. If this is for school, and you fail to include the label, you may receive fewer points.
- The final tally was 5. Instead of writing 83, we would use 5 83 feet A young lady of five years Weighing in at 83 feet in height
Multiply by 12 to convert back to inches. Simply multiply your feet measurement by 12 to get your inches. Since multiplying is equivalent to dividing backwards, the resultant number of inches will be the same as before.
- Here's how we solved a sample problem: Inches: 83 x 12 = 70 Our original measurement in inches was as follows:
5It's the same procedure for decimals and fractions. However, inches are not always written as whole numbers. Follow the same steps outlined above if your inch measurement is represented as a fraction or decimal. If you need assistance dividing decimals or fractions, check out the relevant articles on WikiHow.
- Let's apply this to a sample issue to demonstrate. 15 feet? We'll figure it out. Sizes of 4 inches and 15 and 2/5 inches are Number-wise, these are the same even if they are not written that way.
- 15 (decimal) 4 / 12 = 1 28 feet
- 15 plus 2/5 equals (75 plus 2)/5, which is 77 and a half fifths of an inch. 1 and 17/60 feet is equal to 77/5 inches (12 inches minus 5.5 inches).
Subtract 12 from the inches to get the correct answer. Mixes of feet and inches are commonly used in place of fractions or decimals when expressing lengths in feet. To give just one example, the expression "five feet, nine inches tall" is commonly used to describe a person's height. These "feet and inches" measurements are simple to obtain. The standard first step is to divide by 12.
- Let's convert feet and inches here: 28 inches equals So, let's begin by dividing 28 by 12. 28 / 12 = 2 33
Determine the remaining part If the numbers don't "fit" evenly when you divide them, you'll end up with a remainder. The term "remainder" is used to describe this amount. If you divide 16 by 5, for instance, you get three almost-perfect fits of 5. 1 is still "left over" Since 3 is a remainder, 1 is the answer to 16 / 5, etc. Now, check your division problem for the resulting fraction.
- Our example shows that 12 multiplied by 28 yields a remainder of 4. 12 × 2 = 24 Because 24 is 4 less than 28, the difference is 4. Here's where we could put in our answer: 2 33, as 2 R 4
To convert between feet and inches, round up to the nearest whole number. Knowing the whole number and the remainder of a calculation makes converting to "feet and inches" a breeze. How many feet do you have in total? The number of inches you're left with is your remainder. Use the format "x feet, y inches" for your response. "
- The solution to our example problem was found to be 2 R 4. Having two feet in our solution is a given given that 2 is a whole number. Since the answer to the division problem is 4, we know that there are four inches. Our final answer is 2 yards and 4 inches
Multiply the feet by 12, then add the inches to get back to feet and inches. When dealing with these types of measurements, converting back to inches can be a little more challenging than usual. Multiply the number of feet by 12 to get started. You can calculate the length in inches this way. Adding the other set of inches yields a solution expressed solely in inches.
- Here, we multiply 2' by 12' to get our answer. 2 x 12 = 24 inches This plus the additional 4 inches equals 28 inches. Those are the original inches we used.
How do I multiply 5' 8" by 7"?
To get the correct height in inches, you must first do the following conversion: 5 ft 8 in = (5 x 12) 8 = 68 in Finally, multiply 68 inches by 7 inches. In other words, that's an area of 476 square inches.
Get the feet and inches equivalent of (5110 mm)
5,110 mm ÷ 25 4 = 201 18 inches You get 16 feet, 9 inches if you divide 12 18 inches
A mixed number of 45 inches needs to be converted to feet.
To determine the number of feet, divide the total number of inches by 12, as there are 12 inches in a foot. Approximately 3 feet and 9 inches (3 3/4 feet) is the result of dividing 45 by 12.
Put Your Doubts to the Test
Since wikiHow is based on the same "wiki" model as sites like Wikipedia, many of our articles are co-written by several authors. In total, 19 people (some of whom remain anonymous) worked to edit and improve this article. As of today, this post has been viewed 309,363 times.
Updated: Thursday, August 29, 2022
Categories: Aids to Conversion
Inches to feet is a simple conversion. To convert inches to feet, simply divide the desired number by 12, as there are 12 inches in 1 foot. A height of 24 inches, for instance, can be converted to feet by dividing by 12, yielding a result of 2 feet. A fraction will be included in the result if the number of inches cannot be converted into a whole number of feet. Say, for illustration, you are gauging a length of 50 inches. If you take 12 and divide by 4, you get about 2. To the nearest hundredth of an inch, 17 feet For objects with a diameter of less than 12 inches, the result of the conversion is also a fraction of a foot. 7 inches divided by 12 equals roughly 0. Just over a foot and a half, or 58 feet Multiplying by 12 will get you back to inches from feet. If you get a result like 5, this can be useful as well. If you have a length measurement in feet and inches format, for example 5 feet, and you only need to convert the decimal portion back to inches, you can do that. Add up the 5 multiplied by 12 gives you 6 inches; rewrite this as 5 feet, 6 inches. Below you'll find information on what to do if the inches are given as a decimal.
- Write your favorite authors a letter.
Article Quick Read Time: 7 minutes To create DateTime objects from strings, you must first specify the format of the dates and times in the string. Timekeeping systems in various civilizations have different sequences for days, months, and years. There are a few different
PDFs are used for a wide variety of document purposes, but despite their adaptability and widespread acceptance, they are almost impossible to edit. Because of this, it is necessary to convert PDFs to another word format, just as most users always seek to convert PDFs to Excel if editing the
The formula for converting Fahrenheit to Celsius is C = (F - 32) 5/9. Simply plug in the Fahrenheit temperature and you'll get the corresponding Celsius temperature.
Percent to fraction conversion tables and simple formulas are provided, along with a few examples and explanations to help you grasp the concept.
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https://pwntestprep.com/tag/triangles/
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math
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Hi! Can you please explain number 1 on page 242 on the 4th edition of the PWN book?
Thomas is making a sign in the shape of a regular hexagon with 4-inch sides, which he will cut out from a rectangular sheet of metal. What is the sum of the areas of the four triangles that will be removed from the rectangle?
A triangle’s base was increased by 15%. If its area is increased by 38%, what percent was the height of the triangle increased by?
I’ll draw this as best I can: Look OK? Now let me draw a few more segments in blue… See what’s going on there? All of the small triangles in the figure are the same! (You can prove this with triangle similarity/congruence rules easily enough—I won’t spend the time doing so here, though.) We (more…)
Question from March SAT: Section 4 #33
Hello Mr. Mike. Can you please explain how to solve Similar triangle problems? I especially find confusing identifying equal sides and making proportions. I have an example problem, please see the link below.
How do you do Test 2 Section 3 Number 18?
Test 7 Section 3 #17
I don’t know how to navigate your site yet, so please forgive me if you have already answered this question. Regarding question number 8 in your book, will you further explain why y=180-x is the same angle degree as the unmarked angle? I know y=2x because of geometry, but I do not understand how y can also equal x?
How do you do #18 in Test 6 Section 3 without a calculator?
Can you please do #20 from the no calculator section in test 5?
Can you please explain College Board Test 5 Section 4 #36?
I understand that angle A is half of x- the only part of the college board explanation I’m not understanding is why we do (360-x) while setting up the equation. Thanks!
Test 3 Section 3 #18
Triangles ABC and ABD share side AB.
Triangle ABC has area Q and triangle ABD has area R. If AD is longer than AC and BD is longer than BC, which of the following could be true?
III R < Q
I chose "I" only but the answer was E (all of them could be.) How can the second and third condition be true?
Thanks in advance!
question on Math Quiz 4 #9: I get the answer and the proposed solution (area of large triangle minus area of small triangle). But my daughter worked the problem differently and I think what she did was correct, but she got a slightly different answer and I can’t figure out exactly why.
Her solution: she used Pythag Theorem to get the hypot of small triangle: so 4^2 + 1^2 = c^2…. so c=Sqrt(17). This is base of large triangle. So A= 1/2 bXh, or 1/2 (sqrt 17)(8), she got 16.492.
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https://www.reference.com/web?q=how+many+pounds+in+a+kg&qo=contentPageRelatedSearch&o=600605&l=dir
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math
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1 pounds is equal to 0.45359237 kilogram. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between pounds and kilograms. Type in your own numbers in the form to convert the units! ›› Quick conversion chart of pounds to kg. 1 pounds to kg = 0.45359 kg. 5 pounds to kg = 2.26796 kg
Quick and easy pounds to kilograms conversion. If you're just trying to convert pounds to kilograms for cooking or to know your own weight, there's a handy rule of thumb you can use: To get kilograms, divide by 2 then take off 1/10th of your answer Eg 100 pounds… Divide by two = 50 Kg. Take off 1/10th = (50 – 5) = 45 Kg.
Kilograms to pounds conversion (kg to lbs) helps you to calculate how many pounds in a kilogram weight metric units, also list kg to lbs conversion table.
For example, to find out how many pounds (lbs) there are in a kilogram and a half, multiply 1.5 by 2.20462262, that makes 3.3 lbs in 1.5 kilograms. If you would like to convert from pounds to kilograms and also get more information please check lbs to kg page to find out how many kilos in "x" pounds.
Kg to Pounds How to convert Pounds to Kilograms. 1 pound (lb) is equal to 0.45359237 kilograms (kg). 1 lb = 0.45359237 kg. The mass m in kilograms (kg) is equal to the mass m in pounds (lb) times 0.45359237:. m (kg) = m (lb) × 0.45359237. Example. Convert 5 lb to kilograms:
To find out how many kilograms in "x" pounds, as a formula multiply the number of pounds "x" by 0.4536. For example, to find out how many kilograms there are in a pound and a half, multiply 1.5 by 0.45359, that makes 0.68 kilograms (680 grams) in 1.5 pounds.
Kilograms. The kg is defined as being equal to the mass of the International Prototype of the Kilogram (IPK), a block of platinum-iridium alloy manufactured in 1889 and stored at the International Bureau of Weights and Measures in Sèvres, France.
One kilogram equals 2.679 Troy (or apothecaries) pounds. One kilogram equals 2.204 avoirdupois pounds. Now to your answer. If you have 3.23 pounds of X divide it by either the 2.204 = 1.4655 kilos or 2.679 = 1.2056 kilos. I hadn’t have to make these calculations for a long time.
A pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms. A pound is defined as exactly 0.45359237 kilograms. Kilograms to Pounds Conversions
Kilograms to Pounds conversion. Enter the weight (mass) in kilograms and press the Convert button ... Calculation: Pounds to Kg How to convert Kilograms to Pounds. 1 kilogram (kg) is equal to 2.20462262185 pounds (lbs). 1 kg = 2.20462262185 lb. The mass m in pounds (lb) is equal to the mass m in kilograms (kg) divided by 0.45359237: m (lb) = m ...
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s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578577686.60/warc/CC-MAIN-20190422175312-20190422200445-00049.warc.gz
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CC-MAIN-2019-18
| 2,767 | 10 |
https://www.repository.cam.ac.uk/items/75deddf8-69bf-4a73-b4d0-2d5261193048
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math
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The Gregory--Laflamme Instability and Conservation Laws for Linearised Gravity
This thesis is concerned with the black hole stability problem in general relativity. In particular, it presents stability and instability results associated to the linearised vacuum Einstein equation on black hole backgrounds.
The first chapter of this thesis gives a direct rigorous mathematical proof of the Gregory--Laflamme instability for the 5-dimensional Schwarzschild black string. Under a choice of ansatz for the perturbation and a gauge choice, the linearised vacuum Einstein equation reduces to an ODE problem for a single function. In this work, the ODE is cast into a Schrödinger eigenvalue equation to which an energy functional is assigned. It is then shown by direct variational methods that the lowest eigenfunction gives rise to an exponentially growing mode solution which has admissible behaviour at the future event horizon and spacelike infinity. After the addition of a pure gauge solution, this gives rise to a regular exponentially growing mode solution of the linearised vacuum Einstein equation in harmonic/transverse-traceless gauge.
The remainder of this thesis is concerned with conservation laws associated to the linearised vacuum Einstein equation. For later application, chapter 2 of this thesis contains a review of the double null gauge for the vacuum Einstein equations. In chapter 3, the `canonical energy' conservation law of Hollands and Wald is studied. This canonical energy conservation law gives an appealing criterion for stability of black holes based upon a conserved current. The method is appealing in its simplicity as it requires one to 'simply’ check the sign of the canonical energy Ε with Ε>0 implying weak stability and Ε<0 implying instability. However, in practice establishing the sign of E proves difficult. Indeed, even for the 4-dimensional Schwarzschild black hole exterior the positivity was not previously established. In this thesis, a resolution to this issue for the Schwarzschild black hole is presented by connecting to another weak stability result of Holzegel which exploits the double null gauge. Further weak stability statements for the Schwarzschild black hole (including a proof of mode stability) arising from the canonical energy are also established.
In chapter 4, some preliminary results associated to a novel conserved current associated to the linearised vacuum Einstein equation are presented. This can be viewed as a modification/simplification of the conserved current associated to the canonical energy. In particular, applications of this current to other black hole spacetimes are discussed.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679511159.96/warc/CC-MAIN-20231211112008-20231211142008-00128.warc.gz
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CC-MAIN-2023-50
| 2,667 | 5 |
https://amaze1990.com/northwestern-technical-college-knot-activity-scatter-plot-questions/
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math
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Procedure: Get a small string that is anywhere from 13 to 15 centimeters in length.
Measure the length of your string and record the measurement in the table below.
Put one knot in the string, measure the length of the string, and record the length in
the table below. (Remember that the more precise you are with your measurements
the better this will work) You don’t need to stretch your string super tight but
stretch it straight.
Length of String (in
1. Graph the data by hand by placing x’s on the graph below. Make sure you
label and scale your x and y-axis.
2. What is the y intercept for the data?_____________ What does the y-intercept
represent in this case?
3. What type of mathematical model does the data appear to fit?
4. Draw a line through the y-intercept and through as many other points as
5. Find the slope of the line you drew by picking two points on the line.
6. Write a sentence interpreting the slope in this situation.
7. Use the slope and y intercept to write the equation of the line.
8. Post your equation in the discussion and compare yours to another
classmate. Are they the same? If so, why? If not, why not?
9. Now input your data into a spreadsheet and make a scatter-plot. Add a trend
line to the data(in statistics it is called a line of best fit or regression line).
10. What is the slope?____________________ What is the y-intercept?____________________
11. Write the equation of the line using the slope and y-intercept from #10.
12. How does your equation using the spreadsheet’s regression compare with
the equation you wrote when you drew the line by hand? Explain.
Use your equation you got from the spreadsheet to complete the following
13. Graphically, the y-intercept is where the graph intersects the y-axis. It can be
found by letting x=0. Use the equation to find the y-intercept.
14. Graphically, the x-intercept is where the graph crosses the x-axis. It can be
found by letting y=0. Use the equation to find the x-intercept.
15. Interpret the meaning of the x-intercept for the string problem.
Purchase answer to see full
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224649348.41/warc/CC-MAIN-20230603233121-20230604023121-00493.warc.gz
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CC-MAIN-2023-23
| 2,077 | 31 |
https://circuitglobe.com/applications-of-zener-diodes.html
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math
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Zener diodes find wide applications commercially and industrially. Some of the important applications of a Zener Diodes are as a Voltage Regulator or Stabilizer, as a Meter Protector and as a Wave-Shaper. They are discussed below in detail.
As a Voltage Stabilizer
The major application of a Zener diode in the electronic circuit is as a Voltage Regulator. It provides a constant voltage to the load from a source whose voltage may vary over a sufficient range.
The figure below shows the circuit arrangement of the Zener diode as a regulator.
In the above circuit, the Zener diode of Zener Voltage VZ is connected across the load RL in reverse condition. The constant voltage (V0 = VZ) is the desired voltage across the load. The output voltage fluctuation is absorbed by a series resistor R which is connected in series with the circuit. This maintains a constant voltage (V0) across the load.
Let a variable voltage Vin be applied across the load RL. When the value of Vin is less than Zener voltage VZ to the Zener diode no current flows through it and the same voltage appearing across the load. The Zener diodes conduct a large current when the input voltage Vin is more than the Zener Voltage Vz. As a result, a large amount of current flows through series resistor R which increases the voltage drop across it.
Thus, the input voltage, excess of Vz (i.e. Vin – VZ) is absorbed by the series resistor. Hence, a constant voltage V0 = Vz is maintained across the load RL. When a Zener diode of Zener voltage Vz is connected in the reverse direction parallel to the load, it maintains a constant voltage across the load equal to Vz and hence stabilizes the output voltage.
For Meter Protection
Zener diodes are generally employed in multimeters to protect the meter movement against the damage from the accidental overloads. The Zener diode is connected in parallel with the meter from the safety point of view.
The circuit diagram is shown below:
The Meter movement is protected from any damage as most of the current passes through the Zener diode, in case of any accidental overload. When the meter movement is required to be protected, regardless of the applied polarity (i.e when an alternating current is passed).
The circuit arrangement is modified as shown in the figure below:
Zener diodes are also used to convert sine wave into square waves. The circuit arrangement is shown below:
During the positive and negative half cycle, when the voltage across the diodes is below Zener value they offer a high resistance path. The input voltage appearing across the output terminals. However, when the input voltage increases beyond the Zener value, the Zener diode offers a low resistance path and conduct large current.
As a result, a heavy voltage drop appears across the series resistor R and hence the peaks of the input wave are clipped off when appearing at the output as shown in the above figure. The input sine wave is clipped off at the peaks and a square wave appears at the output.
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CC-MAIN-2024-18
| 3,002 | 15 |
http://lewistonchamber.org/northern-territory/lines-and-angles-class-7-pdf.php
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math
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RD Sharma Class 7 Maths Solutions Chapter 14 Lines and
Lines, Line Segments, Rays and Angles - Lines, Line Segments, Rays and Angles What is a Line? A line is a straight path that goes on forever in both directions. (There …... Lines and Angles RS Aggarwal Class 7 Maths Solutions . Lines and Angles RS Aggarwal Class 7 Maths Solutions
CBSE Class 07 - Mathematics - Data Handling - NCERT
Geometrical concepts and properties quiz questions and answers pdf on if two angles are said to be supplementary angles and one of angle is of 122 ° then other angle is of for grade 6 math tutor questions with answers.... Two pairs of interior alternate angles : Angles marked 1 and 2 form one pair of interior alternate angles, while angles marked 3 and 4 form another pair of interior alternate angles. 2. Two pairs of exterior alternate angles : Angles marked 5 and 8 form one pair, while angles marked 6 and 7 form the other pair of exterior alternate angles.
LINES AND ANGLES cbsemaths4u.com
Get here NCERT Solutions for Class 7 Maths Chapter 5. These NCERT Solutions for Class 7 of Maths subject includes detailed answers of all the questions in Chapter 5 –Lines and Angles provided in NCERT Book which is prescribed for class 7 in schools. baby led weaning cookbook pdf Class 7 Lines And Angles CBSE Questions & Answers This is Mathematics Class 7 Lines and Angles CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.
Lines and Angles NCERT Solutions Class 9 Maths - Vedantu
If the lines m and n are parallel to each other, then determine the angles ∠5 and ∠7. Solution : Determining one pair can make it possible to find all the other angles. hydraulic system design handbook pdf CBSE Class 9 - Lines and Angles (Worksheet-2) Lines and Angles (Worksheet-2) Question: Fill in the blanks 1. Three or more points said to be _____ if there is a line which contains all these points. 2. Two lines are called _____ lines, if they have common point. 3. Three or more lines intersecting at the same point are called as _____ lines. 4. An angle whose measure is less than 90° is
How long can it take?
IX Lines and Angles JSUNIL TUTORIAL CBSE MATHS & SCIENCE
- NCERT Solutions for Class 9 Maths Chapter 6 Lines and
- Class 7 Math- Chapter wise Extra Questions and Video Lessons
- Selina Concise Mathematics class 7 ICSE Solutions Lines
- Lines and Angles NCERT Solutions Class 9 Maths - Vedantu
Lines And Angles Class 7 Pdf
class Vll (iv) 1300 500 Chapter 5 - Lines and Angles Mathematics 1300 + = 180 Sum of the measures of these angles = These angles are supplementary angles.
- Let's study the properties of the angles formed when two lines intersect each other and also the properties of the angles formed when a line intersects two or more parallel lines at distinct points. Let's then use the knowledge of these properties to practice deductive reasoning.
- Interior Angles On The Same Side Of the transversal
Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles. Further, many a times, we simply use the words alternate angles for alternate interior angles.
- Class 7 Mathematics ncert Solutions in pdf for free Download are given in this website. Ncert Mathematics class 7 solutions PDF and Mathematics ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.
- Get here NCERT Solutions for Class 7 Maths Chapter 5. These NCERT Solutions for Class 7 of Maths subject includes detailed answers of all the questions in Chapter 5 –Lines and Angles provided in NCERT Book which is prescribed for class 7 in schools.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578596571.63/warc/CC-MAIN-20190423094921-20190423120921-00455.warc.gz
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CC-MAIN-2019-18
| 3,738 | 21 |
http://sayanzoo.ru/02-2016-71.php
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math
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Algebraic equations practice games
One Step Equation GameHave fun solving one-step equations by playing this interesting math basketball game.Equation GameIn this interactive concentration game, students will try to match each equation with the correct solution as fast as they can.AbsoluteValue EquationsDo you know how to solve absolute value equations. Play this fun millionaire-style game to find out.Two-Step Equation GameShow off your equation solving skills by playing this interesting math basketball game. You can play it alone or in teams.Equation Game with KiwiSolve one step equations algebraic equations practice games Kiwi.
LegalNotices. Please read our PrivacyPolicy. Our directory of Free Algebra Math Games available on the Internet -games that teach, build or strengthen your algebra math skills andconcepts while having fun.We categorize and review algebraic equations practice games games listed here to help you find themath games you are looking for.These algebra games and activities will help you to learn theconcepts of algebra algebraic equations practice games show you how to solve algebraic equationsand expressions.
It also include words to algebra games and equationof a line games.We also have algebra quizzes and worksheets. We have added some free games that can be played on PCs, Tablets, iPads and Mobiles.Related Topics:More Math Games,Math WorksheetsAlgebra Games Algebraic Expression Games. Algebraic ExpressionMillionaire This Algebraic Expressions MillionaireGame can be played alone or in two teams. For eachquestion you have to identify the correct mathematicalexpression that models the given word exprOne-Step Equations with Addition and SubtractionThis is a fun and interactive soccer math game about solving linear equations with whole numbers.
All solutions are positive numbers.Math Basketball - One-Step Equations with Addition and SubtractionPlay this interesting math basketball game and get points for scoring baskets and solving equations correctly.Solving One-Step EquationsDid you know that solving equation can be exciting. Play these two games to find out how much fun you can have when solving one-step equations.Two-Step Equation GameCan you solve two-step equations with integers. Play this algebraic equations practice games game to show off you skills.Equation Puzzle(New)This is an interactive crossword puzzle with key vocabulary words related to equations.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818695375.98/warc/CC-MAIN-20170926085159-20170926105159-00660.warc.gz
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CC-MAIN-2017-39
| 2,422 | 5 |
https://ui.adsabs.harvard.edu/abs/2017arXiv170906798S/abstract
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math
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In the class of metrics of a generic conformal structure there exists a distinguishing metric. This was noticed by Albert Einstein in a lesser-known paper of 1921 (Berl. Ber., 1921, pp. 261-264). We explore this finding from a geometrical point of view. Then, we obtain a family of scalar conformal invariants of weight 0 for generic pseudo-Riemannian conformal structures $[g]$ in more than three dimensions. In particular, we define the conformal scalar curvature of $[g]$ and calculate it for some well-known conformal spacetimes, comparing the results with the Ricci scalar and the Kretschmann scalar. In the cited paper, Einstein also announced that it is possible to add an scalar equation to the field equations of General Relativity.
- Pub Date:
- September 2017
- Mathematics - Differential Geometry;
- General Relativity and Quantum Cosmology;
- This work was presented for the first time at the Spanish-Portuguese Relativity Meeting - EREP 2017 held in M\'alaga (Spain), 12-15 September 2017. 5 pages, 1 table
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s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107890586.57/warc/CC-MAIN-20201026061044-20201026091044-00623.warc.gz
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CC-MAIN-2020-45
| 1,020 | 6 |
https://www.arxiv-vanity.com/papers/1805.08376/
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math
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Simultaneous weak measurement of multiple parameters of a subwavelength structure
A mathematical extension of the weak value formalism to the simultaneous measurement of multiple parameters is presented in the context of an optical focused vector beam scatterometry experiment. In this example, preselection and postselection are achieved via spatially-varying polarization control, which can be tailored to optimize the sensitivity to parameter variations. Initial experiments for the two-parameter case demonstrate that this method can be used to measure physical parameters with resolutions at least 1000 times smaller than the wavelength of illumination.
pacs:Valid PACS appear here
The concepts of weak value and weak measurement were introduced by Aharonov, Albert and Vaidman in 1988 Aharonov et al. (1988); Tamir and Cohen (2013); Svensson (2013) as an alternative to the standard measurement formalism of quantum mechanics. For a quantity associated with an operator , a standard measurement is related to the expected value , where is the state vector for the quantum state being measured. Since the state is normalized, the inner product in the denominator is typically taken as unity. Clearly, for Hermitian operators, this expected value is real and limited to the range of values spanned by the eigenvalues of . On the other hand, weak measurements are based on weak values defined as , where and are preselected and postselected states. It is easy to see that there is no bound to a weak value since the denominator can be made arbitrarily small by appropriate preselection and postselection. In fact, weak values need not even be real-valued. Such weak measurements have been employed, for example, to measure very small angular deviations with great precision Hosten and Kwiat (2008); Dixon et al. (2009).
While weak values are usually presented in the language of quantum theory, their formalism applies to classical measurements as well. Indeed, not only can the essential elements of some of their most successful experimental applications be explained classically Hosten and Kwiat (2008); Dixon et al. (2009), but many pre-existing important interferometric techniques can be interpreted in terms of weak values, in which the preselected state describes the illumination state, and postselection is achieved by a filtering process of the resulting light, either spatially, directionally, temporally, spectrally, or in polarization. Three examples of this are phase contrast microscopy Zernike (1942a, b), which earned Zernike the Nobel Prize in Physics in 1956, differential interference contrast microscopy Murphy (2001), and off-null ellipsometry Pedersen and Keller (1986).
In this Letter, we extend the weak value formalism to the simultaneous measurement of multiple parameters. We concentrate on the measurement of several morphological parameters of a periodic structure with subwavelength features. This example has practical applications in the semiconductor industry, in which manufacturers require precise measurements of integrated circuit components (e.g., stacked silicon wafers), often on sub-nanometer scales. Typical parameters of interest include the period, critical dimension (CD), overlay error, line edge roughness, trench depth and profile, film thickness, and wafer alignment and orientation Diebold (2001); Wilson (2015); den Boef (2016). Here we present the theory for the measurement of several parameters, as well as the experimental results of a two-parameter measurement of CD and orientation angle, which must be controlled during the etching process to reduce overlay error. The measurement scheme, which we refer to as focused vector beam scatterometry, is illustrated in Fig. 1(a). A polarized beam is focused onto the structure, then the scattered light is re-collimated, passed through a polarization analyzer, and measured. The key of this method is to design the incident polarization and the analyzer (either of which may be spatially inhomogeneous in general) to optimize the sensitivity of the measurement.
Let us begin with a mathematical description of this approach. In the linear regime, the test structure is characterized by its scattering matrix , which provides the coupling between an incident plane wave and a reflected plane wave with directions specified by the transverse direction cosines and , respectively (see Fig. 1(b)). The directional variables and are mapped by the objective lens onto the spatial pupil positions of the collimated input and output beams. After focusing, the incident field is represented by a vector angular spectrum, , which gives the complex amplitude and polarization of the plane wave component in the direction . The angular spectrum of the field reflected by the structure is then given by
After collection and collimation by the lens, the analyzer transmits a given polarization at each point, and the transmitted intensity is measured at the CCD. This measured intensity can be written as
The goal is to simultaneously measure a set of morphological parameters of the structure, denoted as , such as those mentioned above. Let us assume that, over the range of values of interest, the scattering matrix has approximately linear dependence on these parameters:
where the index of summation runs from 1 to . For simplicity, these parameters are normalized to be dimensionless and for their ranges of variation of interest to correspond to , with corresponding to the nominal structure. The measured intensity is then
Notice that can be interpreted as the weak value of . (More precisely, it is the weak value of with preselected and postselected states and , respectively, for any real .)
The key to a good measurement is to tailor and so that these weak values are real and have variations on the order of unity, and so that their dependences on are as distinguishable as possible. This is achieved by letting
where are a set of real functions of . The output intensity distribution is then given by
The design of a good measurement system then reduces to a suitable choice of pupil-dependent reference functions , from which and/or can be determined. In our setup we choose the analyzer to be uniform ( is constant), implying that a spatially varying input polarization would be required for optimal sensitivity. Let us consider the simple case where the test structure introduces no directional coupling, i.e., . This is the case, for example, for a uniform multilayer or a periodic structure with subwavelength period. The condition in Eq. (6) can be written as
which leads to the following solution for the incident angular spectrum:
where is an arbitrary envelope function. For structures that couple different directions, the solution for in terms of and the functions is similar although more complicated, sometimes requiring an iterative process.
where the coefficients (which depend on and ) are the elements of a real, positive semidefinite Hermitian matrix. In practice, for a fixed input polarization state, one can expand Eq. (10) and calculate the quadratic coefficients directly from a set of experimental calibration images of reference structures with known parameters. The advantage of this approach is that it accounts for systematic errors, including any deviation between the experimentally achieved input polarization and the theoretical distribution. Using the calibrated intensity profile, the physical parameters associated with an observed intensity from an unknown structure may then be determined using maximum likelihood estimation (MLE) techniques. The estimation uncertainty is inversely proportional to the square root of the eigenvalues of the Fisher information matrix, which can be computed from . For further discussion and examples of MLE in the context of an optical measurement, see Ref. Vella and Alonso (tion).
As an example of the method described above, we now present the results of a two-parameter measurement of a one-dimensional lamellar silicon grating structure with 0.4 m period. The two measured parameters were the grating’s critical dimension (CD) and its orientation angle (relative to horizontal) in the plane perpendicular to the optical axis. The illumination wavelength was 1.064 m, so that the subwavelength grating diffracted only a single propagating order, introducing no directional coupling. The basic layout for the experiment is contained in Fig. 1; complete details on the experimental apparatus and implementation will be discussed in a future publication.
The preliminary measurements presented here were taken using a uniform linear analyzer oriented at 45 and a uniform incident polarization. The input polarization, shown in Fig. 2(a), was chosen to minimize the transmission through the analyzer, resulting in the closest possible approximation of the conditions for optimal sensitivity to parameter variations. Future measurements are planned using a spatially varying polarization generator (currently under development) and a uniform elliptical analyzer. Fig. 2(d) shows a simulation of the optimal input polarization and analyzer for this configuration, which were designed to maximize the eigenvalues of the Fisher information matrix over the parameter range of interest. The optimized functions associated with this input polarization are plotted in Fig. 3.
A total of 49 measurements, shown in Figs. 2(b,e) for the experimental and simulated cases, were collected for seven structures with critical dimensions between 158 nm and 176 nm oriented at angles between and . The variations in intensity over this parameter range can be visualized by subtracting the mean intensity from each measurement, as seen in Figs. 2(c,f). Notice that the maximum variation of the experimental intensity from the mean is approximately 20% as large as the peak intensity. In comparison, the spatially varying polarization in the simulated case produces intensity variations up to 70% of the peak value, making the effects of the structure parameters more easily distinguishable.
The parameters associated with each experimental image were estimated using MLE techniques and compared to the “true” parameter values obtained from a series of focused ion beam (FIB) measurements. The true and measured parameters for each case are plotted in Fig. 4, along with the parameter values associated with eight additional reference measurements that were used for calibration purposes. The red ellipses represent the predicted standard deviation errors from a shot-noise-limited measurement of 7500 photons, as calculated from the eigenvalues and eigenvectors of the Fisher information matrix. On average, the estimation errors for CD and sample orientation were 0.78 nm and 0.39, respectively. Notice that the estimation errors for structures with similar true parameter values are highly correlated, suggesting the presence of systematic errors that were unaccounted for by the calibration procedure. Nevertheless, the relative errors between the two parameters (i.e., the error bar orientations) exhibit similar behavior to the Poisson statistical model.
To predict the accuracy of future experiments using an optimized elliptical analyzer and spatially varying input polarization, we performed a Monte Carlo simulation in which the structure parameters were estimated from simulated intensity distributions containing a discrete number of photons. The results for 1000 photons are shown in Fig. 5, along with ellipses representing the expected standard deviation error. By repeating the simulation for 7500 photons, the performance of the optimal solution can be compared against the approximate error of the current experimental implementation. The most dramatic improvement occurs for the nominal structure having 167 nm CD and 0 orientation; for this case, the expected standard deviation confidence intervals (based on the experimental calibrated intensity profile) were nm and . Under optimal conditions, these intervals are reduced to nm and . For all values within the parameter ranges of interest, the error in CD is reduced by at least a factor of 3, while the orientation error is reduced by at least a factor of 1.25. Additional simulations corroborate that over smaller parameter ranges (for example, nm CD and rotation), an optimized (spatially varying) input polarization could provide an even more significant advantage over a spatially uniform one.
In summary, we have described an extension of the weak value formalism to the simultaneous measurement of multiple parameters. The specific implementation of this technique was a focused beam scatterometry experiment in which preselection and postselection were achieved via polarization control. Our initial experimental results demonstrate that this method can produce accurate measurements of physical parameter variations on the order of optical wavelengths. Future experiments with improved polarization control and/or shorter illumination wavelengths are expected to further improve the accuracy of the measurement. These measurements may also include additional parameters such as grating depth and sidewall angle, which will test the viability of the method for the several-parameter case.
Acknowledgements.This work was carried out under a joint services agreement with IBM Corporation. Supplemental funding was provided by New York State (NYSTAR) through the Center for Emerging and Innovative Systems and by the National Science Foundation (PHY-1068325, PHY-1507278). MAA received funding from the Excellence Initiative of Aix-Marseille University - AMIDEX, a French “Investissements d’Avenir” programme. The authors would like to acknowledge Andrew Jordan and Philippe Réfrégier for useful discussions and Jon Ellis, Steve Gillmer and Mike Theisen for their contributions to the experimental setup.
- Aharonov et al. (1988) Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
- Tamir and Cohen (2013) B. Tamir and E. Cohen, Quanta 2, 7 (2013).
- Svensson (2013) B. E. Svensson, Quanta 2, 18 (2013).
- Hosten and Kwiat (2008) O. Hosten and P. Kwiat, Science 319, 787 (2008).
- Dixon et al. (2009) P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
- Zernike (1942a) F. Zernike, Physica 9, 686 (1942a).
- Zernike (1942b) F. Zernike, Physica 9, 974 (1942b).
- Murphy (2001) D. Murphy, Fundamentals of Light Microscopy and Digital Imaging (Wiley-Liss, New York, 2001) Chap. 10, pp. 153–168.
- Pedersen and Keller (1986) K. Pedersen and O. Keller, Appl. Opt. 25, 226 (1986).
- Diebold (2001) A. C. Diebold, Handbook of silicon semiconductor metrology (CRC Press, 2001).
- Wilson (2015) L. Wilson, International Technology Roadmap for Semiconductors (Semiconductor Industry Association, 2015).
- den Boef (2016) A. J. den Boef, Surface Topography: Metrology and Properties 4, 023001 (2016).
- Vella and Alonso (tion) A. Vella and M. A. Alonso, (in preparation).
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704821381.83/warc/CC-MAIN-20210127090152-20210127120152-00400.warc.gz
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CC-MAIN-2021-04
| 14,984 | 37 |
https://ro.pinterest.com/roxxybogdy/
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math
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Paws-opoly. Collect dogs, cats, other pawed animals. No RR, but zoos. No utilities, but fire hydrant and pet store. No hotels, but $$ to take care of pets based on dice roll. Two spaces to roll dice & multiply, one to collect $$, one to pay. No middle cards, but $$ +/- spaces on board. Still flushing out the details, but this is what I have so far.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187827853.86/warc/CC-MAIN-20171024014937-20171024034937-00161.warc.gz
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CC-MAIN-2017-43
| 350 | 1 |
https://byjus.com/question-answer/convert-the-ratio-15-20-to-the-fraction-1/
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math
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The correct option is C 1520
Given ratio is 15:20
Write the ratio as a fraction by writing the antecedent of the ratio as the numerator, and the consequent of the ratio as the denominator.
Simplifying the fraction, we get
Cancel out the common factors, we get
Hence, 15:20 can be written as 1520 or 34 as a fraction.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100593.71/warc/CC-MAIN-20231206095331-20231206125331-00650.warc.gz
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CC-MAIN-2023-50
| 316 | 6 |
https://blog.darkbuzz.com/2017/10/experts-dispute-meaning-of-bells-theorem.html?showComment=1508418197816
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math
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The debate is very strange. First of all, these two guys are extremely smart, and are two of the world's experts on quantum mechanics. And yet they disagree so much on the basics, that Maudlin accuses 'tHooft of not understanding Bell's theorem, and 'tHooft accuses Maudlin of sounding like a crackpot.
Bell's theorem is fairly elementary. I don't know how experts can get it wrong.
Maudlin says Bell proved that the quantum world is nonlocal. 'tHooft says that Bell proved that the world is either indeterministic or superdeterministic. They are both wrong.
I agree with Maudlin that believing in superdeterminism is like believing that we live in a simulation. Yes, it is a logical possibility, but it is very hard to take the idea seriously.
First of all, Bell's theorem is only about local hidden variable theories being incompatible with quantum mechanics. It doesn't say anything about the real world, except to reject local hidden variable theories. It is not even particular important or significant, unless you have some sort of belief or fondness for hidden variable theories. If you don't, then Bell's theorem is just an obscure theorem about a class of theories that do not work. If you only care about what does work, then forget Bell.
I explained here that Bell certainly did not prove nonlocality. He only showed that a hidden variable theory would have to be nonlocal.
Sometimes people claim that Bell should have gotten a Nobel prize when experiments confirmed his work. If Bell were right about nonlocality, and if the experiments confirmed nonlocality, then I would agree. But Bell was wrong about nonlocality, and it is highly likely that the Nobel committee recognized that.
At most, Bell proved that if you want to keep locality, then you have to reject counterfactual definiteness. This should be no problem, as mainstream physicists have rejected it since about 1930.
I am baffled as to how these sharp guys could have such fundamental disagreement on such foundational matters. This is textbook knowledge. If we can't get a consensus on this, then how can we get a consensus on global warming or anything else?
Update: Lubos Motl piles on:
Like the millions of his fellow dimwits, Maudlin is obsessed with Bell and his theorem although they have no implications within quantum mechanics. Indeed, Bell's inequality starts by assuming that the laws of physics are classical and local and derives some inequality for a function of some correlations. But our world is not classical, so the conclusion of Bell's proof is inapplicable to our world, and indeed, unsurprisingly, it's invalid in our world. What a big deal. The people who are obsessed with Bell's theorem haven't made the mental transformation past the year 1925 yet. They haven't even begun to think about actual quantum mechanics. They're still in the stage of denial that a new theory is needed at all.I agree with this. Bell's theorem says nothing about quantum mechanics, except that it helps explain why QM cannot be replaced with a classical theory.
Free will (e.g. free will of a human brain) has a very clear technical, rational meaning: When it exists, it means that the behavior affected by the human brain cannot be determined even with the perfect or maximum knowledge of everything that exists outside this brain. So the human brain does something that isn't dictated by the external data. For an example of this definition, let me say that if a human brain has been brainwashed or equivalently washed by the external environment, its behavior in a given situation may become completely predictable, and that's the point at which the human loses his free will.I agree with this also. No one can have perfect or maximum knowledge, so free will is not really a scientific concept, but it clearly exists on a practical level, except for brainwashed ppl.
With this definition, free will simply exists, at least at a practical level. According to quantum mechanics, it exists even at the fundamental level, in principle, because the brain's decisions are partly constructed by "random numbers" created as the random numbers in outcomes of quantum mechanical measurements.
But I don't agree with his conclusion:
Maudlin ends up being more intelligent in these exchanges than the Nobel prize winner. But much of their discussion is a lame pissing contest in the kindergarten, anyway. There are no discussions of the actual quantum mechanics with its complex (unreal) numbers used as probability amplitudes etc.No, 'tHooft's position is philosophically goofy but technically correct. Maudlin accepts fallacious arguments given by Bell, when he says:
Bell was concerned not with determinism but with locality. He knew, having read Bohm, that it was indeed possible to retain determinism and get all the predictions of standard non-Relativistic quantum theory. But Bohm's theory was manifestly non-local, so what he set about to investigate was whether the non-locality of the theory could be somehow avoided. He does not *presume* determinism in his proof, he rather *derives* determinism from locality and the EPR correlations. Indeed, he thinks that this step is so obvious, and so obviously what EPR did, that he hardly comments on it. Unfortunately his conciseness and reliance on the reader's intelligence have had some bad effects.No, Bell and Maudlin are just wrong about this. All of that argument also assumes a hidden variable theory, and therefore has no applicability to quantum mechanics, as QM (and all of physics since 1930) is not a hidden variable theory. If Bell and Maudlin were correct about this, then Bell (along with Clauser and Aspect) would have gotten the Nobel prize for proving nonlocality. 'tHooft is correct in accepting locality, and denying that Bell proved nonlocality.
So having *assumed* locality and *derived* determinism, he then asks whether any local (and hence deterministic) theory can recover not merely the strict EPR correlations but also the additional correlations mentioned in his theorem. And he finds they cannot. So it is not *determinism* that has to be abandoned, but *locality*. And once you give up on locality, it is perfectly possible to have a completely deterministic theory, as Bohm's theory illustrates.
The only logically possible escape from this conclusion, as Bell recognized, is superdeterminism: the claim that the polarizer settings and the original state of the particles when they were created (which may be millions of years ago) are always correlated so the apparatus setting chosen always corresponds—in some completely inexplicable way—to the state the particles happen to have been created in far away and millions of years ago.
The quantum double slit experiment demonstrates the nonlocality of quantum mechanics, predicted by the equations.ReplyDelete
Bell's Inequality is also used to demonstrate the nonlocality of quantum mehcanics.
Bell's Inequality, and all the surrounding experiments, did not really add to the notion of nonlocality seen in the double slit experiment.
And too, all the "quantum eraser" and "quantum teleporation" hype add little new physics to the physics observed in the quantum double slit experiment. :)
Double-slit interference does not prove any non-locality. No single-particle experiment can. You need two or more entangled particles, with experiment on them done at spacelike separation.Delete
Good to see that Tim Maudlin is stating that Werner Heisenberg was wrong:Delete
"In relation to these considerations, one other idealized experiment (due to Einstein) may be considered. We imagine a photon which is represented by a wave packet built up out of Maxwell waves. It will thus have a certain spatial extension and also a certain range of frequency. By reflection at a semi-transparent mirror, it is possible to decompose it into two parts, a reflected and a transmitted packet. There is then a definite probability for finding the photon either in one part or in the other part of the divided wave packet. After a sufficient time the two parts will be separated by any distance desired; now if an experiment yields the result that the photon is, say, in the reflected part of the packet, then the probability of finding the photon in the other part of the packet immediately becomes zero. The experiment at the position of the reflected packet thus exerts a kind of action (reduction of the wave packet) at the distant point occupied by the transmitted packet, and one sees that this action is propagated with a velocity greater than that of light. However, it is also obvious that this kind of action can never be utilized for the transmission of signals so that it is not in conflict with the postulates of the theory of relativity.
(The Physical Principles of the Quantum Theory, W. Heisenberg, 1930. p.39)"
Yes, the double slit experiment shows a sort of nonlocality in the sense that you can think of electrons going thru both slits and once. But Bell and his followers wanted to show some kind of action-at-a-distance, and you are right that those experiments do not show additional nonlocality.ReplyDelete
Yes!!! :) :) You have the best signal/noise physics blog out there! :)Delete
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The reason you are having so much trouble understanding the fuss over Bell's Theorem is that, unfortunately, you don't understand it either. In particular, it is not about "hidden variable" theories. Indeed, the very phrase "hidden variable theory" has no meaning at all outside of quantum theory, and there it is often as misleading as it could possibly be. (In the pilot wave theory, for example, the particle positions are called "hidden variables" even though they are the very variables that are manifest empirically. It is the wave function that is hidden.) Anyway, Bell's theorem is not about "hidden variables" or even about quantum theory: it is about *any local theory at all*. No local theory, of any sort, can predict violations of Bell's inequality for experiments done a space like separation. (Excluding superdeterminism as incompatible with science, which is what some of the debate with 't Hooft is about.) So if you accept that such experiments really do show these correlations at spacelike separation (and a Many Worlds person might deny that), then you accept that no local theory can be correct: the world itself uses non-local physics. Period.ReplyDelete
What does this show about quantum theory? If you understand it so that it predicts violations of the inequality at spacelike separation then you understand it as a non-local theory. So you should just accept that.
If you dispute this, as I am sure you will, here is your next task. Go look up Bell's theorem, and identify the step in the theorem where an assumption of "hidden variables" (as opposed to an assumption of just locality) is made. And explain how the theorem fails without that assumption. If you can't do that, stop and think. If you can, we can discuss what you have found.
One more comment. EPR shows that locality implies determinism. This is rather trivial: if anything really indeterministic happened in one of the distantly separated labs, then the only way for the result in the other lab to always anti-correlate with it is for information about the indeterministic outcome to be transmitted superluminally. On the other hand, explaining the EPR correlations locally with a deterministic theory is a piece of cake: that was Einstein whole point. And once you have determinism, you get counterfactual definiteness for free: the theory tells you what would have happened had things been different. But really counterfactual definiteness plays no role in the theorem. The CHSH inequality applies to local indeterministic theories with no perfect correlations. Indeterminism does not get you out of Bell's result, as you mistakenly believe.ReplyDelete
I am not the only one saying that Bell's theorem depends on local hidden variables. That is also what the Wikipedia article says, it is what Bell said, and it is what my textbooks say. Local hidden variables are essential to the proof. I really do not see how you can deny that.ReplyDelete
Bell later said that he just needed locality, but that was because he redefinied locality to mean a local hidden variable theory.
If Bell nonlocality has been proved, then why hasn't anyone gotten a Nobel prize for it?
My textbooks also deny that EPR proves determinism. You're right that EPR shows that certain experimental outcomes are determined once the emission has occurred, but most textbooks say that there is an inherent randomness in the process.
Wikipedia? Are you serious? Your textbooks?Delete
I gave you a simple, straightforward task if you think you actually understand what you are claiming: look at Bell's proof and identify the step (it isn't a long proof) where he assumes hidden variables, show how, then show that the proof fails without the assumption. And you respond by saying that Wikipedia says something? And what your textbooks say?
Bell's work has been almost uniformly misunderstood and misreported, as I document in "What Bell Did". But if instead of thinking for yourself you regard quoting Lubos Motl(!) as evidence of anything then it is clear what the situation is: you don't understand the theorem. You are simply parroting what other people, who also don't understand the theorem, say.
Of course Bell non-locality has been proved. Over and over. And all of the other obviously non-local phenomena: the GHZ phenomenon, teleportation (which is be really not a violation Bell locality per-se but indicates the information-theoretic transmitting properties of the wavefunction) etc.
One more time: if you understand what you keep saying, show the step in the proof. If you can't, just be honest and admit you are simply repeating things that you don't really understand. You might get interested enough to learn something.
The key Bell assumption is quoted in that 2014 paper, What Bell Did, by Tim Maudlin: "Let this more complete specification be effected by means of parameters λ. It is a matter of indifference in the following whether λ denotes a single variable or a set, or even a set of functions, and whether the values are discrete or continuous."ReplyDelete
The "parameters λ" are the local hidden variables.
You argue that this "makes no contentful physical supposition that can be denied." That is the belief of the hidden variable theorists. The belief might have seemed reasonable before 1925, but not since.
You must be joking again. Where do you find either "local" or "hidden" in that description? And the only reason Bell adds "additional" is that EPR already made clear that if the quantum mechanical description is complete, then the theory is non-local. That's the whole point of EPR (see title). As far as Bell is concerned, you can throw away the wave function and build a theory on whatever grounds you like. As long as it is local it can't violate his inequality (modulo hyperfine tuning, which we are discussing with 't Hooft). So are you saying that if Bell had started this way: "Take any local theory. Let the terms in which the theory describes systems be designated lambda. Lambda can be anything you like: it is a matter of indifference in the following whether lambda denotes a single variable or a set, or even a set of functions, and whether the values are discrete or continuous", or you actually say that that constitutes a contentful physical assumption that can be denied? Is that your assertion? Yes or no.Delete
No, I am not joking. I am not saying anything radical here either, as I am just defending orthodox textbook quantum mechanics.ReplyDelete
Quantum mechanics uses non-commuting observables. If you identify observables with measured values, calling them lambda or whatever you like, then you get Bell's inequality. But then you have left the quantum world and entered the world of hidden variable theories, because those lambdas commute.
As you say, it doesn't matter "whether lambda denotes a single variable or a set, or even a set of functions, and whether the values are discrete or continuous". As long as they are non-quantized variables that commute in the lingo of quantum mechanics, then you get a hidden variable theory. If they are also local, then the theory contradicts the Bell test experiments.
I think Bell switched from calling them "hidden variables" to "beables", but they amount to the same thing.
If you don't like Wikipedia, an excellent book on the Bell test experiments is The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics. What I say is consistent with that book.
Here are some more links.ReplyDelete
I posted a criticism in 2014 of Maudlin's 2014 paper.
Reinhard F. Werner also criticized it, with a paper starting: "The Editors of this special issue have asked me to give a comment on Maudlin’s contribution[Mau]. The background is that the paper is rather polemical and takes issue with views which are widespread in the physics community and probably also shared by most of the other authors of this volume." Maudlin replied here.
I post this quote to show that criticism of Maudlin is not just ignorance of what Bell did. Maudlin's view is contrary to most physicists with expertise in the subject. That does not make him necessarily wrong, of course. A lot of physicists say funny things about quantum mechanics.
Look, this is very clearcut. If you want to talk about Bell's theorem because you actually think that you, personally, understand the theorem then talk about the theorem. If you want to talk about sociology, then that is an entirely different matter. I do not dispute a word about Werner's sociology. The paper is polemical. It is polemical exactly because the vast majority of physicists—even those who style themselves experts—do not understand the first thing about the theorem. In "What Bell Did" I cite a video put out by Physics World, as mainstream physics as you can get, that claims that Bell proved that hidden variables are impossible and hence that the probabilities derived from quantum theory are fundamental randomness, not mere ignorance. And I demonstrated that that could not possibly be the case, since Bell was a strong proponent of the pilot wave theory, which employs hidden variables and is deterministic. These are just plain facts. Don't believe me? Watch the video and read "On the Impossible Pilot Wave".Delete
This is proof—absolute and irrefutable proof—that the "common wisdom" about Bell is completely and utterly false. They literally have no idea what they are talking about. So citing books and Wikipedia and so on is just pointless.
If your position is this—you don't really understand Bell's theorem, and you know you don't really understand it, and instead of studying it you intend to just repeat what you hear the most—then fine, just admit it. I will recommend that people not pay attention to what you say, since you acknowledge that you have no first-hand understanding. I will recommend that they read, say, the Scholarpedia article on the subject, not just because it exists but because I know first hand that it is accurate and well written and complete,
But if you claim to actually understand the theorem, and how quantum mechanics somehow gets around the theorem and remains a local theory despite predicting violations of the inequality at space like separation, then I can inform you that you are deluded.
As for the lambdas, when you say they have to commute and so one, notice that Bell says not a word about that. You want to use Grassman variables? Be my guest. The theorem still goes through. It might occur to you, looking at the actual proof, that all Bell does with lambda is conditionalize on it and integrate over the distribution of lambdas. And on top of that, the GHZ phenomenon does not even need the integration, since the predictions are not statistical.
Anyone can see that all you are doing is citing sources, not giving arguments. I assert that every one of your sources is wrong. If you want to defend your claims with actual arguments, do so. If you are only going to make sociological observations, then just admit that's all you have.
I cite authorities because you keep accusing me of not understanding Bell's theorem. It is not just me. You are accusing most expert physicists of not understanding it either, from 'tHooft on down.ReplyDelete
Yes I am. Did I really fail to make that clear? That 't Hooft does not understand it, or GHZ, is patent in the exchange I am having with him.Delete
My point is that you confidently pronounce that I am wrong here, as if you have an informed opinion on the matter. Do you claim you do, or you are just repeating what you read elsewhere? If you think there is a way out of Bell's result for quantum theory, then let's get down to brass tacks and identify what it is. If you are just parroting what you read without any understanding, then just fess up and we can move on.
Yes, I am saying that you are wrong. But if 'tHooft cannot convince you, I don't believe that I can either.ReplyDelete
I see you have disagreed with others, such as Griffiths (and his reply).
You also deny that there is a black hole information paradox.
And you rebut Anton Zeilinger for writing that “The discovery that individual events are irreducibly random is probably one of the most significant findings of the twentieth century.”
I agree with you about Zeilinger, and possibly also about black hole information. So I am not saying that you are wrong just because some big-shot physicists do.
In proofs of Bell's Theorem, there are always 2 noncommuting observables being applied to some particle, and some assumption about what would happen if some hypothetical measurement were taken of those 2 observables. Sometimes the assumption takes the form of "hidden variables", sometimes lambdas, and sometimes beables. Quantum mechanics teaches that you cannot simultaneously measure noncommuting observables, so there is a counterfactual assumption.
I interpret the Bohr dictum "There is no quantum world" as saying that there are no such hidden variables, lambdas, beables, or whatever you want to call them. As others prefer to say, there is no underlying realism. Or as Peres liked to say, unperformed experiments have no results. Anytime you make assumptions about the results of unperformed experiments, you are going directly contrary to quantum mechanics.
And that is what Bell does. He makes assumptions that are contrary to quantum mechanics, and then derives an inequality that is contrary to experiment. Had the experiments confirmed the inequality, he would have become a great hero for disproving quantum mechanics. As it is, he just helped confirm Bohr.
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Why all the distractions and the sociology again? I have been in other disputes. They have no bearing on this one. If you really want to examine this issue openly and clearly then stick to it and stop producing smoke.Delete
't Hooft is demonstrably ignorant of the GHZ set-up. Just look at the recorded discussion. This despite the fact that I posted my own account of it, and sent him Mermin's account of it by e-mail. So the fact that 't Hooft is unconvincing means nothing. If you think you really understand this stuff (and oddly you refuse to say whether you do or don't) then you should be convinced that you could do better than 't Hooft. Any knowledgeable person reading the discussion can see that he hasn't a clue.
But your further response suggests that you are under the impression that you do understand. So let's walk through that point by point.
"In proofs of Bell's Theorem, there are always 2 noncommuting observables being applied to some particle, and some assumption about what would happen if some hypothetical measurement were taken of those 2 observables."
The first part of this sentence is just nonsense and the second part false. Proofs of Bell's theorem have neither commuting nor non-commuting observables, because the proof simply does not use anything at all as an "observable". As I said before: use Grassman variables, use non-commuting 2x2 matrices, use whatever you like in lambda. Since you only ever conditionalize on it, it doesn't matter.
The false part is that there is an "assumption about what would happen if some hypothetical measurement were taken of those 2 observables". No, this is simply untrue. It is akin to the idea that Bell somehow assumes determinism in his proof, so any indeterministic theory escapes it. This is not only false it is silly. There are observed violations of the inequality that are quite large. If we write the CHSH inequality as
C(a,b) + C(a',b) + C(a,b') - C(a',b') ≤ 2
Then the violation found in nature are strong enough that the stated quantity is 2√2. So suppose you had a deterministic system whose maximum value is 2. And you now introduce a tiny bit of indeterminism, so according to you Bell's theorem doesn't hold and violation of his inequality is now possible for a local theory. Do you honestly believe that no matter how small the indeterminism introduced you can suddenly produce a violation that big? Furthermore, counterfactual definiteness fails in the face of any indeterminism. How does that help anything?
"Sometimes the assumption takes the form of "hidden variables", sometimes lambdas, and sometimes beables. Quantum mechanics teaches that you cannot simultaneously measure noncommuting observables, so there is a counterfactual assumption."
Since there is no assumption, it's name can't but be misleading. As I said, except in quantum theory there is not even any meaning to a variable being "hidden". All Bell is interested in are the variables that determine (or fix the probability of) the outcome of the experiment. Whether those variables are in some sense "hidden" or not is of no consequence to the proof.
As for the word "beable", that is Bell's reinvention in English of the word "ontology". The ontology of a theory is what the theory postulates as existing. A theory with no ontology makes no claims about the world at all.
As I already said, the structure of Bell's 1964 argument is that he takes as given the EPR paper. And in EPR there is a clear conclusion that any local theory be deterministic on account of the prefect correlations in the EPR set-up. If there were any fundamental local indeterminism in the theory, then only by superluminal influence could the distant experiment always display the anti-correlated result. Otherwise how could the distant particle know what happened in the indeterministic evolution?
As Bell says, in the theorem determinism is not *assumed* it is *derived*. The derivation uses the perfect EPR correlations. And once you have determinism you get counterfactual definiteness for free. It is also derived, not assumed. The only assumption is locality.
Note, however, that perfect correlations are not required to violate the inequality. The CHSH inequality above cannot be violated by any local theory. So there is no assumption at all about "unperformed experiments".
About the Bohr dictum. First, it is not clear that Bohr ever said it. But if he did, he was also supposed to have said that the microscopic world should be represented by mathematics, not visualizable descriptions. Bohr did not think that there is no quantum world: obviously there is. What else is the theory about? He was rather concerned to deny the neo-Kantian claim that everything in science had to be "anschaulich": visualizable. Using Bell's lambda to represent it would not have bothered Bohr in the least.
So every claim you made about Bell's proof is false. You keep saying that Bell assumes this or Bell assumes that but never point out where in the proof this supposed assumption occurs.That already shows that you are at best on shaky ground. And in fact you are standing in quicksand.
To get "C(a,b) + ... ≤ 2", you have to assume that the correlation C(a,b) is given by integration over some mysterious parameter lambda. That is justified by by assuming that lambda encapsulates everything about the particle pair, so that observing the particle just depends on lambda and the detector direction a or b. So (λ,a) determines one particle, while (λ,b) determines the opposite one. Repeating the experiment assumes some distribution of λ, so you can integrate to get the correlation C(a,b).ReplyDelete
To get 2√2, you have to assume quantum non-commuting observables, like spin in perpendicular directions. Or at 45 degrees, as I am not sure at the moment what gives the maximum.
As you say, this is a contradiction. So the parameter lambda assumption must somehow embody some hypothesis not present in quantum mechanics. You say it is a hypothesis that no one would deny. Maybe no physicist before 1925 would deny it. But the parameter lambda is only reasonable if you think that some parameter (real, discrete, or in some weirdo measure space) is going to determine the measurement at a given direction a.
If you want to avoid the issue of determinism of individual particles, then you can argue that the correlation is determined by lambda and the directions. I accept that. But you are still assuming some kind of funny lambda theory that is contrary to quantum mechanics. You are assuming that this lambda tells you outcomes that you never measure. That is the essence of a hidden variable theory.
Yeah, I know that Bohr may not have said that dictum, and there could be some disagreement about what Bohr would have meant if he did say it. That is why I qualified it with "I interpret".
The thing not present in quantum mechanics that is present is all theories covered by Bell's theorem is easy to identify: locality. Quantum mechanics is a non-local theory! Quantum mechanics embodies spooky action-at-a-distance! That is why Einstein could never accept it (not the indeterminism), that's why he kept searching his whole life for a local theory that could reproduce the predictions of quantum mechanics. In Bell's formalism, when analyzing standard quantum mechanics, lambda *is* psi! And the reason quantum mechanics can violate the inequalities is that it does not fulfill the locality conditions, i.e. it is non-local. What Bell showed was that Einstein's search was bound to fail.ReplyDelete
You are so confused because you somehow think the quantum mechanics is local. As Einstein saw, it is manifestly and obviously non-local. The non-locality is implemented in the standard collapse postulate. Start with a pair of particles in a singlet state. Suppose that that state is, in the EPR sense, complete. Then lambda just is psi. And in the entangled state, neither particle has a spin in any direction. Now measure the x-spin of particle 1. According to quantum mechanics, the outcome is truly random, not determined by any pre-measurement feature of the electron. Suppose the outcome is "up". Now reflect the outcome of this measurement on particle 1 by collapsing the wave function to the appropriate eigenstate of the particle 1 x-spin operator. *As a result of this collapse, triggered by an operation made on particle 1, particle 2 changes from a state of indefinite spin to an eigenstate of x-spin, the opposite eigenstate to that of particle 1.* That change of the state of particle 2 consequent to the measurement of particle 1 is a non-local change. The experiment carried out on particle 1 caused a change of state in particle 2, no matter how far away particle 2 was. Straightforward non-local effect. So it is not at all that the use of lambda somehow is incompatible with quantum mechanics. You are free to put whatever you like in for lambda, as I said. It is just that quantum mechanics fails to satisfy the conditions for locality. And properly so.
It is weird to say that lambda is psi. I don't think Bell said that. Bell was looking for a local and more realistic theory to replace quantum mechanics. Saying lambda equals psi just means that you are disguising quantum mechanics somehow.ReplyDelete
Applying Bell's theorem, this shows that QM is nonlocal. As you say, collapse of the wave function is a nonlocal operation. That makes QM a nonlocal theory, if you think of psi as a physical thing. Or "ontic", as some say.
But if psi is just a way of keeping track of our knowledge of the system, then QM can be regarded as a local theory. I think 'tHooft said in his comments to you that QM is a local theory. Knowledge about a system can be nonlocal, as Bell explains with his example about somebody's socks.
You say that QM is "manifestly and obviously non-local". If that is true, then why bother will all the Bell arguments? Why use Bell to prove that QM is non-local, when it is manifestly and obviously non-local anyway?
You say: "You are so confused because you somehow think the quantum mechanics is local." Did you say that to 'tHooft? Is he so confused because he somehow thinks that QM is local?
(It's okay. I won't dismiss you just because you say a brilliant theoretical physicist is confused. After all, he has some goofy ideas like superdeterminism, and other brilliant physicists subscribe to many-worlds and other goofy ideas.)
Griffiths quotes you in 2010: “The only way to give a local physical account of the EPR correlations is for each of the particles to be initially disposed to yield a particular outcome for each possible spin measurement. For if either particle is not so disposed and if we happen to measure the spin in the relevant direction (as we might), then there could be no guarantee that the outcomes of the two measurements will be anticorrelated.”
I think that I am understanding your argument better. This is why you reject the argument that Bell proves randomness, and why you think that Bell's lambda is undeniable.
I can go along with your anti-randomness argument, but saying "initially disposed to yield a particular outcome" is not enough to imply parameterization by some lambda in some measure space.
I would go further and say that Bell and the Bell test experiments show that electrons can be disposed towards certain outcomes without being parameterized by a measure space.
You might say: How can that be? Give me some mathematical model of how that can work?
I can only say that QM is the model. If you want something that more realistically models the probabilities, then you are led to sort of local hidden variable models that Bell proved to be impossible. So I have to say that there is no realistic probability model like that. There is no quantum world of local hidden variables.
Of course you can use psi as a lambda! Why not? Bell says you can use anything you like and he means it. The theorem isn't even *about* quantum mechanics, so no restrictions concerning the quantum formalism would make any sense. The theorem is proving that certain correlations for experiments done at spacelike separation cannot be predicted by any local theory (or, more precisely, any local non-hyperfine-tuned theory). Quantum mechanics happens to predict violations of the inequalities in such circumstance, and quantum mechanics is not hyperfine-tuned, so it follows that quantum mechanics is a non-local theory, just as Einstein said. And more importantly, such violations of the inequality have been observed over and over in the lab, so that proves that *actual physics* is non-local (granting that it is not hyperfine-tuned). You really have to stop projecting your expectations or your prejudices on Bell's work. Just read the theorem and see what it says. There are no restrictions on the lambda.Delete
Bell was not looking for a "more realistic" theory to replace quantum mechanics! There are obscurities in the standard presentation of quantum mechanics, and he wanted a theory that is sharply formulated without obscurities. And he had seen it done in 1952 in the papers of Bohm. So he knew it was possible. But Bohm's theory is quite manifestly non-local, so he was curious whether a completely clear *local* theory that recovers the predictions of quantum mechanics is possible. And he discovered it isn't.
It is not important whether you think of psi as a "real thing" for the purposes of the proof. It is only important that you regard it as *complete*, in the terminology of EPR. If it is complete, then two systems ascribed the same psi are physically identical in all respects. This does not require that psi be "physically real". In classical E & M a description of a system in terms of the scalar and vector potentials is complete, even though these are not regarded as physically real.
It is certainly not the case that "But if psi is just a way of keeping track of our knowledge of the system, then QM can be regarded as a local theory." Why not? because quantum mechanics predicts violations of Bell's inequality for experiments done at spacelike separation! And Bell's theorem proves (again, modulo hyperfine tuning) that no local theory can do that. How you "regard" the wavefunction is neither here nor there.
What was obvious to Einstein from the very beginning, as soon as he learned about the theory, was that if you regard the wavefunction as *complete* then quantum mechanics is obviously non-local. And this is what he and Podolski and Rosen proved in 1935. But keep in mind that this is the complaint he always brought against quantum theory: that it postulated spooky action-at-a-distance.
I actually didn't ask that of 't Hooft, but I assume he does regard standard quantum theory as non-local because one of his aims is to construct a local theory. He just doesn't understand that that would commit him to hyperfine-tuning, and what that means. That's what we are trying to get across to him.
The rest of your post is just incomprehensible. There is nothing about being "parameterized by a measure space" in Bell. Or, if you are somehow thinking about the integral he takes to get an expectation value, then shift to the GHZ where there are no statistics or expectations values involved. That's why I want to get 't Hooft to talk about GHZ, which he clearly completely misunderstands.
You really have to stop just searching the internet for things other people have said. Think for yourself and only write things you really understand. If you do that we can get things cleared up. If you are just repeating things you saw somewhere, it's hopeless.
Oh, and this sentence is positively painful: "Knowledge about a system can be nonlocal, as Bell explains with his example about somebody's socks." Apparently you have not even read "Bertlmann's socks and the Nature of Reality". Why don't you start there? Bell's point is that what is going on when his inequality is violated is *not* and *cannot be* anything akin to Bertlmann's socks.Delete
Another point. I question why you bother with Bell, if EPR demonstrates the non-locality that you claim. But why do you even bother with EPR?ReplyDelete
In the ordinary double-slit experiment, the photon (or electron) is usually interpreted as going thru both slits at once. But if you measure the particle in one slit, then it is 100% certain that you will not measure it in the other slit. Since the slits are spatially separated, and if you believe in locality, then by your reasoning the particles must be initially disposed to yield a particular outcome when a detector is put in a slit.
At the time the particles are emitted, it is hard to see how they would have anything to do with the precise placement of the slits.
So isn't that enough for your conclusion that QM is "manifestly and obviously non-local"? Why bother with all this EPR-Bohm-Bell-CHSH stuff?
Please pay attention! EPR does not demonstrate that actual physics of the world is non-local! It demonstrates that *if you regard the wavefunction as a complete description of a system* then the physics is non-local. Or, more exactly, EPR goes the other way: assuming that there is no real non-locality in the world, they prove that the wavefunction is not a complete description of the physical system. To get a complete description you have to add additional variables. There is nothing about these additional variables being "hidden" but they come to be known as "hidden variables". So what EPR prove is that if you want to maintain locality, then you need to add variables. And more than that: the theory with the additional variables has to be deterministic. So in the modern lingo, EPR prove that if you want to maintain locality you a forced into a deterministic local hidden-variables theory. Bell assumes that you have read EPR and understand that. What he then proves is that no deterministic local theory can recover all of the predictions of quantum theory. So locality is dead, tout court. That's why you do the "EPR-Bell-Bohm-CHSH stuff".Delete
The double slit has nothing to do with anything here. The double slit interference phenomena can be recovered by a local theory. For example, just use Bohmian mechanics. When only one particle is involved, you can regard the wavefunction as just representing a local wave in the spacetime and nothing goes faster than light. To get problems with locality you need two particles in an entangled state.
You do need to learn to read more carefully. I nowhere say that EPR demonstrates non-locality! So you are just being sloppy and inattentive. If you don't become more careful, then again the situation is hopeless.
From your Facebook exhange:ReplyDelete
Maudlin: "Bell assumed locality and proved that his inequality cannot be violated. Period."
'tHooft: "Point is that this statement is not true. QFT is completely local and disobeys his inequality."
From your latest comments:
"I actually didn't ask that of 't Hooft, but I assume he does regard standard quantum theory as non-local because one of his aims is to construct a local theory."
"So in the modern lingo, EPR proved that if you want to maintain locality you a forced into a deterministic local hidden-variables theory."
So I think you are misinterpreting 'tHooft. He regards standard quantum theory as local. He does not think Bell's theorem applies to it. He wants a superdeterministic local quantum gravity theory, and does not appear anywhere close to finding one.
You're probably right about this. I was making a distinction in my mind between QM and QFT which is probably unwarranted. Hans Westman has been pressing 't Hooft on that so I didn't feel like I needed to pile on: As Westman notes it is a triviality to see that QFT is non-local by Bell's criterion (which is the right one). He keeps asking 't Hooft to verify this and 't Hooft never responds.Delete
So is this the root of your confusion? You think that QFT is local because os the Equal Time Commutation Relations, i.e. because it is a non-signaling theory? But we all know that is not sufficient for locality. It was Bell himself who proved the no-Bell-telephone theorem, and he certainly did not conclude that quantum theory is local!
Is that the root your your confusion? Have you at least cleared up what EPR did and what Bell did?
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http://mathsisinteresting.blogspot.com/2008/11/solving-index-expression-in-quadratic.html
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In maths, the solving of indices questions and its quadratic counterparts are a common practice.
Depending on how you approach the solving, you may encounter a tough journey or a smooth-flowing one.
There are, however, simple tools and concepts that can be applied, in order to have fun solving them.
Here you go....
First, let's us take an example.
(2x)2 + 3(2x) - 4 = 0
To solve this type of quadratic (index) equation, you have to take note of the common mistake in mis-interpreting the second term above.
This is the "3(2x)" term. Refer to this link for explanation on the mistake.
Next, apply the concept of using "let" to the given equation.
This is needed to simplify the mathematical expression visually. Otherwise, it may look intimidating.
To learn about the power of using "Let", click here.
With the above 2 basic steps adhered to, you are ready to move forward into a relax solving environment to handle the given equation with ease.
Simplified equation: (After letting y = 2x)
==> y2 +3y -4 = 0
Applying next, the quadratic formula method, you can see that a = 1, b= 3 and c = -4.
Solving it for y, you will get 2 values shown below. ( Click here to learn how to make use of quadractic formula to solve.)
==> y = (-3 + 5)/2 = 1 and y = (-3-5)/2 = -4
After which, solve for x.
This y is related to x by the "letting" operation you have did in the first place, that is, y = 2x.
y = 1: y = 2x ==> 2x = 1 = 20 ==> x = 0 (Answer), logical comparison.
The other answer of y = -4 will not yield any valid real answer for x here.
( Why? --- see my next post).
So, you have done the solution very easily and without hiccups if you have understood the basic concept. If you have reviewed the working here, you will notice that there is nothing complex with all the steps.
Maths can be solved through a series of mind-blowing steps. But the reverse can also be true. It is up to you to define and choose the desire path.
Do not despair initially, as you need experience to manage this selection of strategy. How to achieve this experience? Simply practice and practice.
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https://www.physicsforums.com/threads/photon-as-force-carrier-particle.75703/
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To my embarrassment I realised I do not understand this. How does a photon mediate the EM force? If I put two magnets close to each other then there is no EM radiation jumping from the one to the other. So how does the photon carry the particle? I know that very magnet has a Magnetic field and that a photon is a little moving quanta of EM energy. Or a EM disruption in the EM field. But I fail to understand this. A EM field has nothing to do with photons right? Or do photons only jump over if there is an actual force on a charged object? Then, is it possible to observe a EM field through photons? Or lies my problem in the difference between an electric field, a magnetic field and an electromagnetic field?
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https://njwildberger.com/tag/mathematics/
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A few days ago I had an online conversation with Dr Daniel Rubin who is a mathematician living in the US and who works in analysis, geometry and approximation theory. The topic was one close to my heart: Daniel wanted to hear of my objections to the status quo concerning the foundations of modern analysis: namely my rejection of “real number arithmetic” and why I don’t accept “completed infinite processes”. And naturally he wanted to do his best to rebut them.
Here is a link to our chat:
It is certainly encouraging to see that some analysts are willing to engage with the uncomfortable idea that their discipline might actually be in serious logical difficulties. Most of us are reluctant to accept that something we have been working on for years and years might actually be wrong. I applaud Daniel for the courage to engage with these important ideas, and to consider how they fit, or don’t fit, into his current view on analysis.
When we learn pure mathematics, there are many things that we at first don’t understand, perhaps because they are obscure, or perhaps because we are not smart enough — it is easy not to be sure which. Our usual reaction to that is: let me try to accept the things which are cloudy, and hopefully with further learning things will become clearer. This is a reasonable approach to tackling such a difficult subject. However it does require us to put aside our natural skepticism, and accept what the more established figures are telling us at critical points in the theoretical development, even if we imagine this is only temporary.
A good example is: “analysis is built from axiomatic set theory.” In other words the foundations of “infinite sets” and so the basic logical structure of the “arithmetic of real numbers” is a consequence of work of logicians, and can be taken for granted without much further inquiry. Or to put it less politely: it is not the job of an analyst to work out clearly the foundations of the subject; this is something that can be outsourced.
In this fashion dubious logical sleights of hand can creep into an area, transmitted from generation to generation and strengthened with each repeat. Young academics in pure mathematics are under a lot of pressure to publish to obtain a foothold in the academic ladder. This means they do not often have time to mull over those knotty foundational questions that might have been bugging them secretly at the backs of their minds. They probably don’t spend a lot of time on the history of these problems, many of which go back centuries, and in former times engaged the interest of many prominent mathematicians.
Later in their career, if our young PhD has been lucky enough to score an academic job, they might be in a position to go back over these core problems and think them through more carefully. But even then there is often not a lot of “academic reward” in doing so: their fellows are not particularly interested in endeavors that are critical of the orthodoxy — pure mathematics is quite different in this regard than science or even applied mathematics!
And journals are uniformly not keen on publishing papers on foundational issues, especially ones which challenge accepted beliefs. As pure mathematics rests on a premise of logical correctness, any questioning of that is seen as subversive to the entire discipline.
But maybe some serious consideration and debate of the underlying logical structure is just what the discipline really needs.
I certainly enjoyed our conversation and I think there are valuable points in it. I hope you enjoy it, and look forward to another public YouTube discussion with Daniel.
I am recently retired from 30 years at the University of New South Wales (UNSW) Sydney. But I don’t plan on giving up on mathematics explanation and discovery any time soon — it is just too much fun, and exciting.
But to cement this new direction, I have decided to embark on an additional, quite different directions of explanation — to chart a course in mathematics exploration for the general viewer, offering you a road map to get into a wide range of interesting topics in pure mathematics that you can investigate also on your own — after some orientation on my part.
The first topic is particularly exciting — it is a series on Solving Polynomial Equations. You will all know that the standard extension of the quadratic formula to cubic equations involves complicated expressions with cube and square roots, that the quartic equation is even more complicated, and that this method breaks down, at least partially in the quintic and higher cases. Galois theory was designed partly to try to understand the obstructions to writing down formulas for zeros of higher degree polynomials in terms of radicals.
But since I don’t believe in irrational quantities except in an applied, approximate sense, these “solutions by radicals” are intrinsically suspect for me. Now I am going to show you an exciting alternative, which actually meshes closer to what physicists and engineers do to solve equations — using power series and rational extensions of them in the coefficients of the given equations.
With this rather dramatic shift in point of view, I claim that an entirely new landscape emerges, which remarkably connects with a rich hierarchy of combinatorial objects related to Catalan numbers and their generalizations. We will meet binary and ternary trees, polygonal subdivisions, Dyck paths, standard tableaux, and make lots of contact with many interesting entries in the Online Encyclopedia of Integer Sequences.
You might be surprised. Could it be that we will be able to solve the general polynomial equation with this major new point of view!?
To access this exciting series, please JOIN our Members section on my YouTube channel Wild Egg Maths. See for example this informational video:
For a minimal amount (around $5 / month) you will have a rich stream of interesting videos to watch. We are going to be delving into lots of other topics too — from graph theory to projective geometry to a new world of convexity to triangle geometry in hyperbolic geometry. There will also be quite a few advising videos on how to do research as an amateur or as a graduate student.
The videos will be informal, hands- on and will encourage you to participate. I look forward to having you join us!
Hi everyone, I’m Norman Wildberger, a soon-to-be retired professor of mathematics at UNSW in Sydney Australia, and I want to tell you about this channel which will introduce you to a wide variety of mathematical topics with a novel slant. The content is aimed at a very broad audience from everyday people with an interest in maths to graduate students working on a PhD in the subject. A link to this introductory video is given below, so you will be able to find quickly any of the playlists that I describe.
I believe that mathematics should be completely clear and straightforward, and that ideally a beginner should be able to navigate through one of the many branches of the subject, one step at a time, supported by lots of explicit examples and concrete computations, with the logical structure visible at all times.
That means however that I no longer buy the standard religion of “real numbers”, which are anchored in an arithmetic reliant on infinite processes. It’s not possible to add up an infinite number of things, so why do we pretend that we can?
I also don’t believe in the “hierarchies of infinite sets” that supposedly form the foundation for modern mathematics, following Cantor. It’s not possible to exhibit a “set” with an infinite number of elements, so why do we pretend that we can?
The pure mathematical community depends on these and other fancies to support a range of “theories” that appear pleasant but are not actually corresponding to reality, and “theorems” which are not logically correct. Measure theory is a good example –this is a subject in which the majority of “results” are without computational substantiation. And the Fundamental theorem of Algebra is a good example of a result which is in direct contradiction to direct experience: how do you factor x^7+x-2 into linear and quadratic factors? Answer: you can’t do this exactly — only approximately.
By removing ourselves from the seductive but false dreamings of modern pure mathematics, we open our eyes to a more computational, logical and attractive mathematics –where everything is above board, where computations actually finish in finite time, where examples can be laid out completely, and where we acknowledge the proper distinction between the exact and the only approximate. This is a pure mathematics which is closer to applied mathematics, and more likely to be able to support it. It also gives us many new insights, more precise definitions, and theorems which are actually …correct.
In this channel, we explore the beginnings of such an exciting new way of learning and doing and teaching mathematics. I present you with topics that are developed and explored in a sequence of YouTube videos, usually from rather elementary beginnings. These topics are organized in Playlists, so you can work your way through them sequentially and strengthen your understanding slowly and steadily.
The History of Maths series is great for high school teachers and anyone with a general interest in mathematics — so much of the subject makes more sense when viewed in a historical context. There is also a playlist on Ancient Mathematics and another on Old Babylonian mathematics. The latter topic is close to my heart — a paper in Historia Mathematica a few years ago with Daniel Mansfield on Plimpton 322 generated international coverage in hundreds of newspapers, including the New York Times.
Wild Trig is an introduction to Rational Trigonometry — a more general and algebraic view of trig that allows much more extensive and quicker calculation for many problems and that opens the door to many new theoretical possibilities, such as chromogeometry! This is based on my book: Divine Proportions: Rational Trigonometry to Universal Geometry.
Famous Math Problems discusses a wide range of —famous math problems, some of them with novel solutions!
Wild Lin Alg A and the follow up Wild Lin Alg B is a first year undergraduate course in Linear Algebra, from largely a geometric point of view.
The most extensive series is the MathFoundations series, which comes in parts MathFoundationsA (videos 1-79), MathFoundationsB (videos 80-149) and MathFoundationsC (videos 150-present). This series examines so many important topics in the subject. The most recent videos for example give a new treatment of the Algebra of Boole, transcending the more usual Boolean Algebra (which is not really what Boole intended) and open the door for simpler logic gate analysis by engineers.
The most elementary series is: Elementary Math (K-6) Explained which is for parents and teachers of primary school students, and will give you tools to understand the important mathematical skills and concepts their children need to learn. In this direction, there is also a course on Math Terminology for Incoming Uni Students meant for people from a non- English speaking background.
Universal Hyperbolic Geometry is a more advanced series on geometry which will give you an exciting new completely algebraic way to understand the hyperbolic geometry of Gauss, Lobachevsky and Bolyai, and which connects more naturally with relativistic physics. There are hundreds of new theorems here, many very beautiful. I will be developing this a lot more in the coming years.
So this is a large amount of content that is consistently oriented towards avoiding infinite processes and arguments which are not supportable by explicit computation. It is a new kind of mathematics. If you work through some of this, your mathematical understanding will deepen, you will see connections that were invisible, and your appreciation for the logical beauty of the subject will continue to grow. Mathematics is surely the richest intellectual discipline, and I want to empower more people, young and old to experience it directly, to learn lots of fascinating things, to be challenged, and to explore on your own. For those of you aspiring to do some research on your own, there will be plenty of new directions to think about!
My understanding is very different from my fellow mathematicians. So why do I have such a unique perspective? One reason is that I have simply worked in lots of areas of mathematics.
I have done work in number theory, developing the most powerful general algorithm for solving large Diophantine equations, and unravelling the algebraic structure of Gaussian periods. I’ve done work on Pell’s equation –basically discovered the simplest explanation of why solutions are always possible.
I have worked in Lie group harmonic analysis, solving the Horn conjecture (with A. H. Dooley and J. Repka) on eigenvalues of sums of Hermitian matrices. I’ve initiated the moment map of a Lie group representation and found a geometric Fourier transform which explains *-products on coadjoint orbits of compact Lie groups. The wrapping map introduced with A. H. Dooley gives a broad explanation for the effectiveness of A. A. Kirillov’s orbit theory.
In work with D. Arnal I’ve introduced quasi-standard Young tableux, building from my geometric “diamond” construction of the irreps of SU(3), which is of considerable interest to physicists. I have also given combinatorial constructions of G2 and the simply laced Lie algebras, excluding E8.
In 2005 I wrote a book which introduces Rational Trigonometry, and then extended that to a complete rewrite of hyperbolic geometry. This gives a large scale revision of Euclidean and non-Euclidean metrical geometries. With this I have further discovered a remarkable three-fold symmetry in planar geometry called chromogeometry.
I have developed the theory of finite signed hypergroups, which are probabilistic versions of finite groups, and developed a duality theory for them, somewhat like Poyntriagin duality for abelian groups, and also applied ideas of entropy to them.
For the last five years I have been developing the Algebraic Calculus, which is a coherent approach to Calculus which avoids real numbers and infinite processes, and is correspondingly more general and often gives new insights. Videos for this can be found at the sister channel Wild Egg mathematics courses, while the course itself is on openlearning.
If you are interested in learning more about my research at the more advanced level, there is a Playlist on this channel of Math Seminars, and also a smaller one on Research Snapshots, which I hope to enlarge in the future.
I have a Vice Chancellor’s award at UNSW for teaching excellence and have been very involved in the development of online tutorials for mathematics courses there.
In summary, my aim is to put this wealth of research and teaching experience to work in framing a more fruitful path for mathematics education, and opening up a more solid approach to pure mathematics research, connected more strongly to computational reality. Come along and join me on an exciting journey to explore new and better foundations and directions for 21st century pure mathematics! Once we face the music and see things as they really are, not just how we want them to be, there is much to do.
In the last fifteen years or so, I have become increasingly disenchanted with the way modern mathematics deals with, or rather doesn’t deal with, the serious logical problems which beset the subject. These difficulties arise from a misunderstanding of the nature of `infinite sets’ and `the continuum’, and then extend further in many directions.
`Infinite sets’ are propped up, according to the standard dogma, by certain axiomatics, which lift the burden of having to actually define properly what we are talking about, and prove the various theorems that we would like to have true. What a joke these ZFC axiomatics are. The entire situation is ironic to the extreme: in fact Cantor’s Set Theory was vigorously opposed by most prominent mathematicians during his day, and then collapsed in a catastrophic heap at the beginning of the 20th century due to the discovery of irrefutable paradoxes. And now, fast forward a hundred years later: not only has Set Theory been resurrected, essentially with no new ideas—most of the key concepts go back to Cantor or Turing, and are just endlessly recycled—but now most of us believe that this befuddled and imprecisely laid out subject is actually the correct foundation for the rest of mathematics! This is little short of incredible. I feel I have woken from a dream, while most of my colleagues are still blissfully dozing.
And our notion of the continuum is currently modelled by the so-called ‘real numbers’, which in fact are far removed from most sensible people’s notions of reality. These phoney real numbers that most of my colleagues pretend to deal with on a daily basis are in fact hazy and undefined creations that frolic and shimmer in a fantasy underworld deep beneath the computational precisions of our computers, ready to alleviate us from the dull chore of striving for precise computations, and incorporating correct error bounds when we can obtain only approximations.
We are talking about irrational numbers here; numbers whose names even lay people are familiar with, such as sqrt(2), and pi, and Euler’s number e.
Supposedly there are myriads of other ones, given by various arcane procedures, formulas and properties. The actual theory and arithmetic of such real numbers is never laid out completely correctly; rather we find brief ‘summaries’ of the wished-for properties that these creatures have, properties that ensure that theoretically many standard computational problems have solutions, even if our computers can in fact not find them.
Ask a modern pure mathematician to make the computation pi+e for you, and see what kind of bemused look you get. Is not the answer the same as the question? Is this not how we all do `real number arithmetic’??
The belief in `real numbers’ supports a false mathematical dream-world where almost everything has a solution; a Polyanna fantasy land which can be conjured up by words but not written down on paper. (Of course the computer scientist or applied mathematician or scientist knows that in reality all meaningful computations occur with rational numbers or floating point decimals).
What a boon it is to live in the `infinitely real’ dreamscape of the modern pure mathematician! To conjure up `constructions’ and ` computations’ these days we need only scribble words, phrases and descriptions together. This is why so many of the ‘best’ journals are filled with page after page of what might be generously called `mathematical prose’. See my submission `Let H be a load of hogwash’ to get a feeling for this language of modern mathematics that the journals encourage.
Most pure mathematicians feel little obligation to address the claims of logical weakness. Objections such as mine may be safely ignored. Unlike scientists, we don’t feel the obligation to step up to the plate and respond rationally to criticism, as it clearly cannot be correct: since the majority rules! As long as we all play along, and ignore the increasingly obvious gaps between what our computers can do and what we are claiming, everyone can pretend that things are merry.
But could the tide be turning? A little while ago, James Franklin and I had a public debate (quite civilized and friendly I would add) in the Pure Maths Seminar in the School of Mathematics and Statistics UNSW, and lo and behold– the room was filled to capacity, people were huddled at the doors from outside trying to hear what was said, and my heresies were not met with a barrage of hoots, tomatoes and derision.
Judging from the many comments, it is no longer such a one-sided debate as it was a few decades ago. I reckon that young people’s comfort and trust in computers has a lot to do with it. What is it really, if you can’t get your computer to model it?? Only a fantasy.
You can join the revolution, too. Don’t be so accepting of everything you are told. Ask for explicit examples and concrete computations. Be suspicious of appeals to authority, or the well worn method of swamping with jargon. And of course, watch as many of my videos as you can, for a slow but steady introduction to: a more sensible world of pure mathematics.
Perhaps the forces of confusion and orthodoxy will soon be on the back foot.
A quick quiz: which of the following four words doesn’t fit with the others??
We are going to muse about MOOCs today, a hot and highly debated topic in higher education circles. Are these ambitious new approaches to delivering free high quality education through online videos and interactive participation over the web going to put traditional universities out of business, or are they just one in a long historical line of hyped technologies that get everyone excited, and then fail to deliver the goods? (Think of the radio, TV, correspondence courses, movies, the tape recorder, the computer; all of which held out some promise for getting us to learn more and learn better, mostly to little avail, although the jury is still out on the computer.)
It’s fun to speculate on future trends, because of the potential—indeed likelihood—0f embarrassment for false predictions. Here is the summary of my argument today: MOOCs in mathematics are destined to fail essentially because the word Massive is intrinsically unrelated to the other words Open, Online and Courses. But, a more refined and grammatically cohesive concept: that of a TOOC, or Targeted Open Online Course, is indeed going to have a very major impact.
When we are teaching mathematics at any level, there are really two halves to the job. The first half is the one that traditionally get’s the lion’s share of attention and work: creating a good syllabus with coherently laid-out content, which is then clearly articulated to the students. The other half, which is almost always short-changed, and sometimes even avoided altogether, is to create a good set of exercises which allow students to practice and develop further their understanding of the material, as well as their problem-solving skills. In my opinion, really effective teaching involves about equal effort towards both halves; again this is rarely done, but when it is, the result usually stands well out above the fray.
Here are some examples of mathematics textbooks in which creating the problem sets probably occupied the authors as much as did the writing of the text: first and foremost Schaum’s Outlines (on pretty well any mathematics subject), which are arguably the most successful maths textbooks of the 20th century, and deservedly so, in my opinion. Then come to mind Spivak’s Calculus, Knuth’s The Art of Computer Programming, Stanley’s Enumerative Combinatorics, and no doubt you can think of others.
Good problems teach us and challenge us at the same time. They are the first and foremost example of Gamification in action. Good problems force us to review what we have learnt, give us a chance to practice mundane skills, but also give us an opportunity to artfully apply these skills in more subtle and refined ways. They provide examples of connections which the lecture material does not have a chance to cover, they give students a chance to fill in gaps that the lectures may have left. When combined with a good and comprehensive set of solutions, problems are the best way for students to become active in their learning of mathematics, a critically important aspect. When further combined with a skilled tutor/marker who can point out both effective thinking and errors in student’s work, make corrections, and advise on gaps in our understanding, we have a really powerful learning situation.
Here is where the Massive in MOOCs largely kills effective learning. It is the same situation as in most large first year Calculus or Linear Algebra classes around the world. Officially there may be problem sets which students are exhorted to attempt, but in the absence of required work to be handed in and marked, students will inevitably cut down to a minimum the amount of written work they attempt. In the absence of good tutors who can mark and make comments on their written work as they progress through the course, students don’t get the feedback that is so vital for effective learning.
Once you have thousands of students taking your online maths courses, it becomes very challenging to get them to do problem sets and have these marked in a reasonable way. The currently fashionable multiple choice (MC) question and answer formats that people are flocking to can go some small way down this road, but rarely far enough. Students need to be given problems which require more than picking a likely answer from a,b,c or d. They need to define, to compute, to evaluate, to organize, to find a logical structure and to explain it all clearly. This is practice doing mathematics, not going through the motions!
When we are planning an open course for possibly tens of thousands of students from all manner of backgrounds, the possibility to craft really good problems accessible to all diminishes markedly. There is no hope of giving feedback to so many students for their solutions, so all we can aspire to are MC questions that inevitably ride on the surface of things and don’t effectively support the crucial practice of writing. Learning slips into a lower gear. Such an approach cannot be the future of mathematics education. Tens of thousands of students going through the motions? They will find something more worthwhile to do with their time, like just watching YouTube maths videos!
But a slight rethinking of the enterprise, together with some common sense, can perhaps orient us in a more profitable direction. An education system ought to make enough money to at least fractionally support itself. People are willing to pay for something if it has value to them, and they tend to work harder at an activity if they have committed to it monetarily. All good technical writing has a well-defined audience in mind. These are almost self-evident truths. What we need is to think about crafting smaller, targeted open online courses, that generate enough income to support some minimal but effective amount of feedback on students’ work on real problem sets. By real I mean: problems that require thinking, computation, explanation.
Can this be done? Yes it can, and it will be the big education game changer, in my humble opinion. We will want to stream people into appropriate courses at the right level. Entry should be limited to those who have enough interest and enthusiasm to fork out some—perhaps minimal, but definitely non-zero!—amount of money, which hopefully can be dependent on the participant’s region; and who can pass some pre-requisite test. Yes, testing for entry is an excellent, indeed necessary, idea that will save a lot of people from wasting their time. Having 300 people from 10,000 pass a course is not a successful outcome. Better to have targeted the course first to those 1000 who were eager and capable. Then you get a lot more satisfaction across the board, from both students and the educators involved.
A major challenge will be how to provide effective feedback for written work. Relying exclusively on MC exercises should be considered an admission of failure here. If and when this challenge is overcome, TOOCs will have the potential to radically transform our higher education landscape!
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CC-MAIN-2023-23
| 27,862 | 69 |
http://yojih.net/type-1/guide-type-1-error-false.php
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math
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Type 1 Error False
to report p-values when reporting results of hypothesis tests. See the discussion of Power forHandbook of ParametricEasy-peasy!
Joint a comment| up vote 10 down vote You could reject the idea entirely. false http://yojih.net/type-1/guide-type-1-error-false-positive.php 04-15-2012 at 11:14 AM.. error Types Of Errors In Accounting a false positive may be calculated using Bayes' theorem. false as 90–95% of women who get a positive mammogram do not have the condition.
at Gelman's blog. Archived 28 March 2005 at the Wayback Machine.‹The template Wayback is being considered type
But the general is the probability that two groups…blacks and women, jointly-are pictured to make obvious mistakes. ISBN1-599-94375-1. ^ a Type 1 Error Example Bill is the author of "Big Data: Understandingfor Statistical Methods.
I never use the terminology "type I" and "type II" I never use the terminology "type I" and "type II" Plus I called an error of the first kind.Type I errors are equivalent to false positives.I couldn't find the way to find "female
Minitab.comLicense PortalStoreBlogContact UsCopyrightbeing studied produces no effect or makes no difference. Probability Of Type 1 Error is important to us.You can achieve this result images who thought it was cute to play stereotypes.
Share|improve this answer answered Nov 3 '11 at 1:20 Kara 311 add a comment for me.This error is potentially life-threatening if the less-effective medication isfire...because you WANT to have evidence of correlation when correlation really exists. Mitroff, I.I. & Featheringham, T.R., "On Systemic Problem Solving and the Wrong - it'sno effect on cavities), but this null hypothesis is rejected based on bad experimental data.
Simple, is absent, a false hit. The null hypothesis (at least in the US)University Press.The null hypothesis is true (i.e., it is true that adding water to toothpaste has '12 at 12:48 cardinal♦ 17.6k56497 answered Jul 7 '12 at 11:59 Dr.
If you could test all cars under all conditions, you would error signing up! ISBN1584884401. ^ Peck, Probability Of Type 2 Error has been assumed. error arguing that climate change is a myth when in fact....
The first error the villagers did (when have a peek at this web-site posts and share!False negatives may provide a falsely reassuring message to patients look at this site emails, doing so without creating significant false-positive results is a much more demanding task.David, F.N. (1949).So the probability of rejecting the null hypothesis when it is true
01:49 PM mcgato Guest Join Date: Aug 2010 Somewhat related xkcd comic.Thanks a lot for insisting on pooping on even the most light-hearted post.Team becomes stronger with every person who adds to the conversation.that we will reject a true null hypothesis.I set the criterion for the probabilityII error by ensuring your test has enough power.
http://yojih.net/type-1/guide-type-i-type-ii-error.php a priori cost-benefit analysis of Type I and Type II errors. never find anything! A man cannot become pregnant, so any discussion Type 1 Error Psychology the test is equal to 1−β.
Now, a 1/9 probability times whatever you find for the "doctor pregnant patient" number change, it's a pretty easy way to remember!! However, that singular right answer won't apply to everyonebut the experimental data is such that the null hypothesis cannot be rejected.After being deeply immersed in the world of big data for Jointthan 24 hours, and with poor quality of life during the period of extended life.
1:36 am Great exlanation.How can it be prevented. The first you bring them home and It is not a Type 1 Error Calculator (2011). 1 Reply mridula says: December 26, 2014 at
When we conduct a hypothesis test there be less likely to detect a true difference if one really exists. determine if the null hypothesis can be rejected. Cambridge What Are Some Steps That Scientists Can Take In Designing An Experiment To Avoid False Negatives am Thanks a million, your explanation is easily understood.Loved it and. "On the Problem of Two Samples".
Don't reject H0 I to make the same complaint. Twelve Tan Elvis's Ate Nine Hams With Intelligent Irish Farmers share|improve thisa newsletter. Then he thought that if one pair ofmust be chosen between risks of false negatives and false positives. As a result of the high false positive rate in the US, as many an innocent person being punished, then it is more serious than a Type II error.
guilty prisoner freed from jail. I am teaching an undergraduate Stats in Psychology course and have compare a new medical treatment with a standard one. to as an error of the second kind.Type II errors are equivalent to false negatives.Note that the specific alternate hypothesis is M.
C.K.Taylor By Courtney Taylor Statistics Expert Share Pin Tweet Submit not correspond with reality, then an error has occurred. blogs or the accuracy or reliability of such blogs. Thank you,,for Press.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348519531.94/warc/CC-MAIN-20200606190934-20200606220934-00093.warc.gz
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CC-MAIN-2020-24
| 4,948 | 19 |
https://onlinemathcenter.com/blog/math/7th-grade-polynomial-expressions-sum-cubes-difference-cubes/
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math
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By the time students reach 7th grade, they know their math lessons and private math tutoring classes often challenge their minds in ways other school subjects do not. Math has a certain way of opening our minds to new ways of thinking, interesting concepts, and fascinating processes to find solutions.
One particular topic that perplexes students year in and year out is the special cases of the sum of a cube and the difference of a cube. These special cases when multiplying polynomial expressions can seem extremely complicated at first sight, especially for students that struggle with polynomial expressions and other topics in algebra.
Once students learn the necessary skills to tackle these seemingly confusing problems, the ability to do so becomes a valuable tool for solving algebraic equations. The right school teachers and individual tutors can demystify these challenging concepts and pave the way for academic success.
Sum of Two Cubes
We can expand this into a formula that is easier for us to break down, manage, and solve
(a + b)³ = a³ + 3a²b + 3ab² + b³
Understanding this formula allows us to simplify complex algebraic expressions and solve equations much more efficiently. We must be able to recognize these kinds of patterns and use them to our advantage when we are faced with similar problems.
Difference of Two Cubes
Now that we’ve looked at the sum of two cubes, and expanded on the formula, let’s dive into the difference of two cubes. This concept, similar to the sum of two cubes, involves finding the cube of a binomial. This time, however, we will be working with subtraction instead of the division we saw in the previous example.
Like the sum of two cubes, when we express the difference between cubes, ‘a’ and ‘b’ are any two real numbers. The expression is written like this: (a – b)³.
And, similar to the sum of two cubes, we can expand the expression to read:
(a – b)³ = a³ – 3a²b + 3ab² – b³
The difference of cubes formula is an invaluable tool that will help students to factor expressions and analyze the behavior of functions quicker and more efficiently.
There are two cubes, one of lengths x and the other of lengths y:
We can split the larger “x” cube into four small cuboids, with box A being a cube with sides the same length as “y”:
We can write the volumes of these boxes as follows:
A = y3
B = x2(x − y)
C = xy(x − y)
D = y2(x − y)
We know, however, that these four boxes, A, B, C, and D make up the larger cube which has a volume of x3.
Therefore, we can say:
x3 = y3 + x2(x − y) + xy(x − y) + y2(x − y)
x3 − y3 = x2(x − y) + xy(x − y) + y2(x − y)
x3 − y3 = (x − y)(x2 + xy + y2)
x3 − y3 = x3 – 3x2y + 3xy2 – y3
Factoring the Sum and Difference of Cubes
I’m sure by now that you’re fully understanding the sum of cubes, the difference of cubes, and the ways you can solve such problems quickly. Factoring the sum and difference of cubes can be tough, even after seeing the process done in an example. In fact, factoring high-degree polynomial expressions is a tricky task for anyone.
To make math even more challenging, some students are visual learners and can benefit more from a video than several written examples. If that’s you – or your young one – be sure to take a look at these great explainer videos to see how you can factor higher-degree polynomials, and specifically how to factor the difference of cubes and the sum of cubes.
At Online Math Center
Our tutors have decades of combined experience dealing with every math problem under the sun, from polynomial expressions like these to trigonometric head-scratchers and everything in between. We offer personalized, individual tutoring classes to children of all ages and abilities, because we know that classes focused on plugging one child’s learning gaps are more valuable than dozens of classes shared with twenty other students.
We also offer tailored SAT preparation classes, intensive preparation classes for math competitions, and individual tutoring sessions for middle school students, and high school students. Our results speak for themselves, with over 500 students improving their math grades after taking classes at OMC.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506646.94/warc/CC-MAIN-20230924123403-20230924153403-00663.warc.gz
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CC-MAIN-2023-40
| 4,232 | 32 |
https://ibeehomeworksolutions.com/view/1649901/students/2021/08/29/for-astrologer-only-496194/
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math
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Kimm Company has gathered the following information about its product.
Direct materials: Each unit of product contains 3.10 pounds of materials. The average waste and spoilage per unit produced under normal conditions is 0.50 pounds. Materials cost $3 per pound, but Kimm always takes the 4.94% cash discount all of its suppliers offer. Freight costs average $0.40 per pound.
Direct labor. Each unit requires 1.40 hours of labor. Setup, cleanup, and downtime average 0.23 hours per unit. The average hourly pay rate of Kimm s employees is $10.40. Payroll taxes and fringe benefits are an additional $3.30 per hour.
Manufacturing overhead. Overhead is applied at a rate of $5.30 per direct labor hour.
Compute Kimm s total standard cost per unit.(Round answer to 2 decimal places, e.g. 1.25.)
|Total standard cost per unit||$|
Lewis Company s standard labor cost of producing one unit of Product DD is 4.00 hours at the rate of $11.00 per hour. During August, 40,800 hours of labor are incurred at a cost of $11.20 per hour to produce 10,000 units of Product DD.
(a)Compute the total labor variance.
|Total labor variance||$||FavorableUnfavorableNeither favorable nor unfavorable|
(b)Compute the labor price and quantity variances.
|Labor price variance||$||FavorableUnfavorableNeither favorable nor unfavorable|
|Labor quantity variance||$||UnfavorableFavorableNeither favorable nor unfavorable|
(c)Compute the labor price and quantity variances, assuming the standard is 4.35 hours of direct labor at $11.39 per hour.
|Labor price variance||$||FavorableNeither favorable nor unfavorableUnfavorable|
|Labor quantity variance||$||FavorableUnfavorableNeither favorable nor unfavorable|
Costello Corporation manufactures a single product. The standard cost per unit of product is shown below.
The predetermined manufacturing overhead rate is $12 per direct labor hour ($12.00 1.00). It was computed from a master manufacturing overhead budget based on normal production of 5,900 direct labor hours (5,900 units) for the month. The master budget showed total variable costs of $32,450 ($5.50 per hour) and total fixed overhead costs of $38,350 ($6.50 per hour). Actual costs for October in producing 4,200 units were as follows.
The purchasing department buys the quantities of raw materials that are expected to be used in production each month. Raw materials inventories, therefore, can be ignored.
(a) Compute all of the materials and labor variances. (Round answers to 0 decimal places, e.g. 125.)
(b) Compute the total overhead variance.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950363.89/warc/CC-MAIN-20230401221921-20230402011921-00096.warc.gz
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CC-MAIN-2023-14
| 2,538 | 20 |
https://www.it.uu.se/research/publications/reports/2003-022/
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math
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In this paper, a two-dimensional heat diffusion system, which is modeled by a partial differential equation (PDE) is considered. Finite order approximations, for the infinite order PDE model, are constructed first by a direct application of the standard finite difference approximation (FD) scheme. Using tools of linear algebra, the constructed FD approximate models are reduced to computationally simpler models without any loss of accuracy. Further, the reduced approximate models are modified by replacing its poles with their respective asymptotic limits. Numerical experiments suggest that the proposed modifications improve the accuracy of the approximate models.
Download BibTeX entry.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474852.83/warc/CC-MAIN-20240229170737-20240229200737-00120.warc.gz
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CC-MAIN-2024-10
| 693 | 2 |
https://www.coursehero.com/file/6343112/4-2/
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math
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This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Fuzzy Set Theory by Shin-Yun Wang Before illustrating the fuzzy set theory which makes decision under uncertainty, it is important to realize what uncertainty actually is. Uncertainty is a term used in subtly different ways in a number of fields, including philosophy , statistics , economics , finance , insurance , psychology , engineering and science . It applies to predictions of future events, to physical measurements already made, or to the unknown . Uncertainty must be taken in a sense radically distinct from the familiar notion of risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far- reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an immeasurable one that it is not in effect an uncertainty at all. What is relationship between uncertainty, probability, vagueness and risk? Risk is defined as uncertainty based on a well grounded (quantitative) probability . Formally, Risk = (the probability that some event will occur) X (the consequences if it does occur). Genuine uncertainty, on the other hand, cannot be assigned such a (well grounded) probability. Furthermore, genuine uncertainty can often not be reduced significantly by attempting to gain more information about the phenomena in question and their causes. Moreover the relationship between uncertainty, accuracy, precision, standard deviation, standard error, and confidence interval is that the uncertainty of a measurement is stated by giving a range of values which are likely to enclose the true value. This may be denoted by error bars on a graph, or as value ± uncertainty, or as decimal fraction (uncertainty). Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged and the mean is reported, then the averaged measurement has uncertainty equal to the standard error which is the standard deviation divided by the square root of the number of measurements. When the uncertainty represents the standard error of the measurement, then about 68.2% of the time, the true value of the measured quantity falls within the stated uncertainty range. Therefore no matter how accurate our measurements are, some uncertainty always remains. The possibility is the degree that thing happens, but the probability is the probability that things be happen or not. So the methods that we deal with uncertainty are to avoid the uncertainty, statistical mechanics and fuzzy set (Zadeh in 1965)....
View Full Document
- Spring '11
- Fuzzy set, fuzzy set theory
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CC-MAIN-2018-05
| 3,145 | 5 |
http://www.physicsforums.com/showpost.php?p=3226940&postcount=68
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math
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Why do we rotate along with the earth's rotation?
View Single Post
Apr3-11, 10:51 AM
I am on earth okay? i move in e-w at 5 miles per hour now wat is my speed for a person whos inertia of state is at rest and wh is not under an external forces?
also answer my other question concerning force for quiring speed of 1005 miles
r u there Mr.Doc Al?
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s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657128337.85/warc/CC-MAIN-20140914011208-00125-ip-10-196-40-205.us-west-1.compute.internal.warc.gz
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| 344 | 6 |
http://joeyfillingane.com/index.php/books/algebra-2
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math
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This system scholars desire; the focal point academics WANT!
Glencoe Algebra 2 is a key application in our vertically aligned highschool arithmetic sequence constructed to assist all scholars in attaining a greater knowing of arithmetic and enhance their arithmetic rankings on today’s high-stakes checks.
Read Online or Download Algebra 2 PDF
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A glance at baseball information from a statistical modeling standpoint! there's a fascination between baseball lovers and the media to gather facts on each that you can think of occasion in the course of a 3-hitter and this e-book addresses a couple of questions which are of curiosity to many baseball enthusiasts. those comprise how one can cost avid gamers, are expecting the end result of a video game or the attainment of an success, making experience of situational info, and identifying the main necessary gamers on the earth sequence.
The translator of a mathematical paintings faces a job that's instantaneously attention-grabbing and complicated. He has the potential of studying heavily the paintings of a grasp mathematician. He has the obligation of maintaining so far as attainable the flavour and spirit of the unique, while rendering it right into a readable and idiomatic kind of the language into which the interpretation is made.
- Computational aspects of commutative algebra
- Commutative Formal Groups
- Codierungstheorie: Algebraisch-geometrische Grundlagen und Algorithmen
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Additional info for Algebra 2
If so, give an example and explain why it is true. If not true, give a counterexample. b+c 64. Writing in Math Use the information about coupons on page 11 to explain how the Distributive Property is useful in calculating store savings. Include an explanation of how the Distributive Property could be used to calculate the coupon savings listed on a grocery receipt. 65. ACT/SAT If a and b are natural numbers, then which of the following must also be a natural number? 66. REVIEW Which equation is equivalent to 4(9 - 3x) = 7 - 2(6 - 5x)?
Integer with a multiplicative inverse that is an integer CHALLENGE Determine whether each statement is true or false. If false, give a counterexample. A counterexample is a specific case that shows that a statement is false. 59. Every whole number is an integer. 60. Every integer is a whole number. 61. Every real number is irrational. 62. Every integer is a rational number. 63. REASONING Is the Distributive Property also true for division? In other _b _c words, does _ a = a + a , a ≠ 0? If so, give an example and explain why it is true.
Any real number greater than 9 is a solution of this inequality. The graph of the solution set is shown at the right. A circle means that this point is not included in the solution set. 6 7 8 9 10 11 12 13 14 CHECK Substitute a number greater than 9 for x in 7x - 5 > 6x + 4. The inequality should be true. 1. Solve 4x + 7 ≤ 3x + 9. Graph the solution set on a number line. Multiplying or dividing each side of an inequality by a positive number does not change the truth of the inequality. However, multiplying or dividing each side of an inequality by a negative number requires that the order of the inequality be reversed.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256147.15/warc/CC-MAIN-20190520202108-20190520224108-00556.warc.gz
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CC-MAIN-2019-22
| 3,254 | 14 |
https://www.bhoblog.it/women-shoes-noe-c-60_329/
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math
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= (sum of two consecutive numbers) $\times$ whole number But if you add two consecutive numbers, the answer is always an odd number. So a sum like this must have an odd number as a factor again - but $2^n$ doesn't. This proves that an even number of consecutive numbers cannot add to make $2^n$. Nicely done!
Octree occlusion culling
Malcolm Gladwell is the author of five New York Times bestsellers: The Tipping Point,Blink, Outliers,What the Dog Saw, and David and Goliath. He is also the co-founder of Pushkin Industries, an audio content company that produces the podcasts Revisionist History, which reconsiders things both overlooked and misunderstood, and Broken Record, where he, Rick Rubin, and Bruce Headlam interview ...
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Consecutive numbers (or more properly, consecutive integers) are integers n 1 and n 2 such that n 2 -n 1 = 1 such that n 2 follows immediately after n 1. Algebra problems often ask about properties of consecutive odd or even numbers, or consecutive numbers that increase by multiples of three, such as 3, 6, 9, 12.
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1.3. The consecutive odd numbers 3, 5, and 7 are all primes. Are there infinitely many such “prime triplets”? That is, are there infinitely many prime numbers p such that p+2 and p+4 are also primes? 1.4. It is generally believed that infinitely many primes have the form N2 + 1, although no one knows for sure.
find three consecutive even numbers such that the sum of the first and the last numbers exceeds the second number by 10 ans fast with method - Math - Linear Equations in One Variable
Edhesive unit 5 quizlet
Three consecutive whole numbers: If we call the middle number "x" then the other two are (x - 1) and (x + 1) So we are looking for the square of these three numbers to be 869. So we have: (x - 1)² + x² + (x + 1)² = 869. simplify the left side: x² - 2x + 1 + x² + x² + 2x + 1 = 869. The x terms cancel out leaving: 3x² + 2 = 869
Slope intercept form practice
SOLUTION: find three consecutive numbers such that 3 times the first is equal to 8 more than the sum of the other two. Algebra -> Customizable Word Problem Solvers -> Numbers -> SOLUTION: find three consecutive numbers such that 3 times the first is equal to 8 more than the sum of the other two.
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Find three consecutive numbers such that if they are divided by 10, 17, and 26 respectively, the sum of their quotients will be 10. (Hint: Let the consecutive numbers = x , x + 1, x + 2 , then x/10 + (x+1)/17 +(x+2)/26 =10
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How tyler mentally reacts toward himself when he swings and misses the ball is called _____.
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A046043 Autobiographical (or curious) numbers: n = x0 x1 x2...x9 such that xi is the number of digits equal to i in n. - Robert Leduc; A049442 Sum of first n consecutive prime numbers is pandigital (includes all 10 digits exactly once). - G. L. Honaker, Jr. A049443 Sum of
Q. Three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. Find the largest integer.
(d) can not be found, Question 47. (a) one number is 1 (d) 379409, Question 11. NCERT Exemplar Class 6 Maths is very important resource for students preparing for VI Board Examination. This test is Rated positive by 86% students preparing for Class 6.This MCQ test is related to Class 6 syllabus, prepared by Class 6 teachers. A whole number added to 0 remains unchanged. Learn. (a) 1 MCQ ...
The number that is added to each term is called the common difference and denoted with the letter d. So in our example we would say that d = 1. The common difference can be subtracting two consecutive terms. You can subtract any two terms as long as they are consecutive. So we could find d by taking 5 - 4 = 1 or 2 - 1 = 1.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence; find the three numbers.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780061350.42/warc/CC-MAIN-20210929004757-20210929034757-00425.warc.gz
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CC-MAIN-2021-39
| 4,158 | 25 |
https://sunmanagers.org/1994/0502.html
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math
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I appreciate the quick responses from the list, and I believe I know the answer ..
yes, I had carefully cd'd out of the /cdrom space and yes, I had carefully stopped all
the processes I knew of referencing the /cd, but after I got lsof recompiled and ran it,
lo! and behold it revealed that indeed (as Caller #3 correctly identified - he wins
the all-expense paid trip to WackyLand!), the the spro_install app had started the license
manager and license daemon running against the cd. Once they were stopped, it dismounted
with no problem!
Howard Modell (206)662-0189
[email protected] POBox 3707, m/s 4C-63, Boeing D&SG
[email protected] Seattle, WA 98124-2207
} From [email protected] Mon May 9 15:09:44 1994
} Date: Mon, 9 May 1994 15:09:03 +0800
} From: [email protected] (Dances on keyboards (Louis Brune))
} My guess is that a license manager process is still hanging around.
} And, distasteful though it may be, you can always reboot.
} From [email protected] Mon May 9 14:19:08 1994
} Reply-To: [email protected]
} Date: Mon, 9 May 1994 14:03:54 +0800
} From: [email protected] (Steve Ozoa)
} We ran into this while setting up our new SparcCluster. It had mounted the CD
} for a diskless boot, and didn't let go. We had to kill the mountd process. We
} found it with fuser, which is a standard part of the OS, so you should be able
} to use it. Not as good as lsof, but maybe good enough to find your culprit.
} From [email protected] Mon May 9 13:51:46 1994
} Date: Mon, 9 May 1994 13:52:49 -0700
} From: [email protected] (S. Cowles)
} i experienced a similar situation on an LX when installing 2.3. my
} guess was that the install process did not exit cleanly. i did a
} reboot and everything was copcetic afterwards.
This archive was generated by hypermail 2.1.2 : Fri Sep 28 2001 - 23:09:00 CDT
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| 1,872 | 30 |
http://zodiacastrology.blogspot.com/2012/10/the-mathematical-ability-of-indians.html
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math
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I am convinced that everything has come down to us from the banks of the Ganges, - astronomy, astrology, metempsychosis,.. It is very important to note that some 2,500 years ago at the least Pythagoras went from Samos to the Ganges to learn geometry...But he would certainly not have undertaken such a strange journey had the reputation of the Brahmins' science not been long established in Europe...
said Francois Marie Arouet Voltaire (French writer and philosopher)
Indians are a formidable software super power due to mathematical ability. Indians are the persons who saw beyond the Pythagorus Theorem
Perpendicular = Purusha
Base = Prakriti
Hypotenuse = Divine Man, Divya Purusha.
In Egyptian Symbolism,
Perpendicular = Orisis
Base = Isis
Hypotenuse = The Divine Child, Masonic Christ.
H^2 = a^2 + b^2
where H is the hypotenuse.
If 3 dimensional
h^2 = a^2 + b^2 + c^2
So the mathematical and philosophic ability of the Indians cannot be doubted, as they invented Zero.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593208.44/warc/CC-MAIN-20180722100513-20180722120513-00024.warc.gz
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CC-MAIN-2018-30
| 973 | 15 |
https://www.hackmath.net/en/math-problem/2497
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math
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Bronze, tin and copper
Bronze is an alloy of tin and copper. An alloy of 10% tin and 90% copper is Gunmetal. If it contains 20% tin and 80% copper, it is bell metal. How many tons of molten bell metal and how many tons of copper is needed to make 100 tons of Gunmetal?
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http://realitat.com/index.php/pdf/symplectic-geometry-and-mirror-symmetry-proceedings-of-the-4-th-kias-annual
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math
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By Y.G. Oh, K. Fukaya, Y-G Oh, K. Ono, G. Tian
Court cases of the 4th KIAS Annual overseas convention, held in August 14-18, 2000, Seoul, South Korea. prime specialists within the box discover the newer advancements on the subject of homological reflect symmetry, Floer idea, D-branes and Gromov-Witten invariants.
Read Online or Download Symplectic geometry and mirror symmetry: proceedings of the 4th KIAS Annual International Conference, Korea Institute for Advanced Study, Seoul, South Korea, 14-18 August 2000 PDF
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Ce cours de topologie a été dispensé en licence à l'Université de Rennes 1 de 1999 à 2002. Toutes les constructions permettant de parler de limite et de continuité sont d'abord dégagées, puis l'utilité de los angeles compacité pour ramener des problèmes de complexité infinie à l'étude d'un nombre fini de cas est explicitée.
This ebook is the 6th variation of the vintage areas of continuous Curvature, first released in 1967, with the former (fifth) version released in 1984. It illustrates the excessive measure of interaction among crew concept and geometry. The reader will enjoy the very concise remedies of riemannian and pseudo-riemannian manifolds and their curvatures, of the illustration concept of finite teams, and of symptoms of contemporary growth in discrete subgroups of Lie teams.
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Additional resources for Symplectic geometry and mirror symmetry: proceedings of the 4th KIAS Annual International Conference, Korea Institute for Advanced Study, Seoul, South Korea, 14-18 August 2000
The mixing of both object types is not considered here. Hence we restrict to cs ∈ int(s). We can easily determine which objects are scalable and which are not. An object s is said to be strongly star-shaped if there is a point ts ∈ int(s) such that for any point p ∈ s the straight line segment ts p is contained in s, but does not contain any point of bd(s), except possibly p. 3 An object s is scalable if and only if it is strongly starshaped. Proof: Suppose that s is scalable and has scaling point cs .
6, we think of -separated as being a slightly more general notion, since the property of being -separated is invariant under a scaling of the space. 32 Chapter 4. Geometric Intersection Graphs and Their Representation We now show that any intersection graph of scalable objects has an separated representation. 7 For a family A of closed scalable objects, any A-intersection graph has an -separated representation for some > 0. Proof: Let G be an A-intersection graph and S any representation of G. We prove that S can be turned into an -separated representation of G.
5 can be proved for intersection graphs of other scalable objects. In particular, we conjecture that similar techniques apply to intersection graphs of (unit) regular hexagons. Finally, observe that for the results in this section it does not matter if the disks or squares are open or closed. 2 From Separation to Representation The above theorems were quite specific to the object type. We can prove that the converse holds in a more general setting. In the following, let zs denote the size of an object s.
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https://m.scirp.org/papers/92610
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math
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Nowhere until now has the Gulf Stream and Bernoulli’s law occurred in the same sentence, to the best of my knowledge. In a steady fluid motion, where the speed is greatest, the pressure is least, and vice versa, along streamlines, it has not so far found a place there.
What stimulates initiating the present subject is a recent tentative notion that Bernoulli’s law may actually be involved in certain weather events . And that association happened by accident. Across the North Pacific along 35 N, an oceanographic ship sailed west in the spring of 1976. Though dedicated to the physics and chemistry of the entire water column, routine meteorological measurements were also made on the bridge every two hours around the clock for 35 consecutive days.
Within all weather data recorded quantitatively, there was unexpectedly revealed a prominent variation with a time-scale of two days . Then years later, it was noticed that the air pressure and wind speed records were 180 degrees out of phase at the two day cycle, which led to the idea that Bernoulli’s law may have been operating during that time .
Separate studies of flow past a cylinder or a sphere have shown that Bernoulli’s law along streamlines can be combined with another equation for the balance of forces across streamlines: centrifugal force on the curved paths equals a pressure gradient. Then, the two equations in two unknowns (pressure and flow speed) can be solved by elimination of one of the variables to get one equation in one unknown.
When the horizontal scale of the flow phenomenon increases past the point where, in the force balance equation, the centrifugal force should be replaced by the Coriolis force, and no other forces are added, then elimination of the pressure between it and Bernoulli’s equation produces a very simple relation: horizontal velocity shear equals the Coriolis parameter .
Quoting from Stommel’s Gulf Stream book (first edition): “The general fact is that a wide zone of anticyclonic vorticity (of approximately −0.5 f, where f is the local Coriolis parameter) seems to be established and also requires explanation.” (A translation of vorticity there is velocity shear here.) An understanding for an even larger current shear, exactly equal to f, is given below, along with discussions of how it could be made smaller by adding a force to one of the two governing equations that accounts for a particular sea level variation.
Start with Bernoulli’s law
where p is the pressure, V is the flow speed, is the fluid density and the same constant is assumed to apply to all streamlines for simplicity.
Geostrophy is written
where the pressure force is on the LHS and the Coriolis force is on the RHS, f being the Coriolis parameter. Assume the flow is into the page, x is positive to the right and the pressure decreases to the left.
Equations (1) and (2) are two equations in the two unknowns p, V. Take the x-derivative of (1) and use that to eliminate the pressure in (2) resulting in
which in condensed form says that the horizontal velocity shear equals the Coriolis parameter.
Equation (3) has recently been applied to a certain weather event in the North Pacific and found to be consistent with observations from a wind storm , but it is not yet ready to be applied to the Gulf Stream. The reason is that (3) is not complete enough for that job: there is at least one term missing from (1) and/or a force absent from (2). Not only that, but the exact form of the missing information is not known well enough to be expressed algebraically at this time.
Since the Gulf Stream imports warmer water from lower latitudes into a lower temperature environment, a guess can be made that the sea level within the Gulf Stream is higher than it is outside the current, caused by a density variation in its water column. There may exist sea level data to show whether or not this guess is correct, but if so I have not seen them.
Suppose a sea level variation actually occurs within the Gulf Stream region, in the cross-stream direction. Then a force on the surface water will exist in that direction and point down slope. For a given shoreward pressure force on the LHS of (2), adding an offshore force due a sea a level variation on the RHS means the Coriolis force must be smaller to maintain the balance. In other words, effectively the Coriolis parameter is smaller or the shear is smaller than f.
How could the sea level be highest in the middle of the Gulf Stream with an offshore downward slope on the right side? Here is a proposed density arrangement that could work. Perhaps the fastest flow brings into the region the warmest surface water because there has been less time in transit for heat to leak out into the air. Assume the water column containing the highest SSTs is short compared to the water column to the right in mid-stream. Therefore, the larger water column, although having a slightly lower temperature will produce a higher sea level because of its greater thickness. Essentially the lighter density warm Gulf Stream water is floating on the colder environmental water underneath, and it is held up to the surface by the buoyancy force associated with the thermocline. Sea level will be highest in the middle of the Stream. These qualitative comments need to be made quantitative as soon as possible.
Bernoulli’s law is brought to the Gulf Stream, along with the geostrophic relation, in order to try to increase the understanding of the large surface current shear on the offshore side of the Stream. In the future, other factors may need to be added, because actually Bernoulli provides too much help. One feature that has the potential to reduce the strength of Bernoulli’s law is a higher sea level inside the Stream due to the lower density in the warm water column.
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https://www.sciencemodels.info/en/force-and-motion/125702-chaotic-pendulum-.html
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math
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Chaotic Pendulum 2
A chaotic pendulum is a simple demonstration of chaos theory. Every time a sequence is measured differently.
In the circular ring behind the plexiglass cover, there is a fixed-arm pendulum. At the end of each arm is positioned further rotating the pendulum. The pendulum is moving various in unexpected directions - left or right rotates or varies.
Set the pendulum into motion by spinning the handle and watch the pendulum's chaotic motion.
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https://civil3dplus.wordpress.com/2010/08/26/google-earth-surfaces-at-wrong-elevation/
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Have you ever brought a Google Earth surface into your Civil 3D drawing and it comes in at the wrong elevation? Now, I’m not tallking off by 50′ (well maybe if you’re in Florida) but drastically off. I did a test and in Google Earth, I zoomed in on Longs Peak, one of the 14,000′ mountains visible from my house. In C3D, I set an appropriate coordinate system, import the surface, and everything works. Here’s a screenshot of the surface properties:
However, in two other drawings, using the exact same coordinate systems, the elevations are drastically different:
Now, what on earth could be causing such a drastic change in the elevations? It’s almost like the elevations on the left are being scaled by the conversion factor from feet to meters and on the right the conversion factor from feet to inches, and that’s exactly what is happening. It’s using the drawing units, the AutoCAD drawing units, to scale the Google Earth surface elevations (which units are in meters) as it brings it into the drawing.
In the above image, the left surface was brought into the drawing with units set to unitless (INSUNITS=0) so the elevations are set to meters, since that’s the units Google Earth uses. On the right, the drawing units are set to inches (INSUNITS=1), so that’s how many inches high Longs Peak is. If you are working in an imperial drawing, i.e., your Civil 3D units are set to feet, then you must have the AutoCAD drawing units also set to feet (INSUNITS=2). If you are working in a metric drawing, i.e. your Civil 3D units are set to meters, then you must have the AutoCAD drawing units set to meters (INSUNITS= 6).
Thanks Jeff for letting me know about this one!
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https://kudipost.com/qa/how-many-ounces-in-apound.html
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math
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We will also learn here that how many ounces are in a pound or oz in a pound.M (oz) = m (lb) × 16.
R134a cost per pound 2022;M (lb) = 5 oz / 16 = 0.3125 lb.Btw, what's the reason you asked the question since you obviously know the answer?
There are 16 ounces in a pound.And because weight is simply a way of measuring an object's mass, there are 16 ounces of weed in 1 pound of weed — just as there are 16 ounces in a pound of anything else in the world you might be weighing.
How many ounces in a pound?How to convert pounds to ounces.¼ lb * 16 = 4 oz.
Because a pound is equal to 16 ounces, you may use this simple rule to convert:15 oz * 0.0625 lb = 0.9375 lbs.
That depends on what pound:½ lb * 16 = 8 oz.And there are 16 cups in a gallon!) when in doubt, buy a scale.
If an eighth ounce is.To convert pounds to ounces, multiply the pound value by 16.
Check out the table or conversion chart below.There are a total of 16 ounces in one pound.Is there a pound to pound?
Weed is typically measured in ounces and there are 16 ounces in a single pound of weed.0.25 lb = 0.25 * 16 = 4 oz.
1 lb = 16 oz.In the united states, a pound is 16 ounces.In conclusion, the answer to the question how many fluid ounces in a pound is 16.00 fluid ounces.
While the imperial system says there are 453.52 grams in a pound, cannabis measurements are a little bit different.A pint's a pound, the world around.
Again the answer to that delicious food is water and the right amount of water is written on a myriad of recipe books.There are 12 ounces in a troy weight pound and 12 ounces in a pound of apothecaries' weight.You can understand deeply it with the following examples.
By writing oz, we indicate the unit ounce.Ounces are used commonly in weight when the.
If 1 lb = 16 oz.
NSP: Troopers locate more than a pound of meth in Hastings - A Hastings man was arrested Friday after Troopers with the Nebraska State Patrol and the TRIDENT Drug Task Force found more than a pound of methamphetamine during a traffic stop.
when is daylight savings · how to delete instagram account · how many oz in a gallon · what dinosaur has 500 teeth · what we do in the shadows · where am i · how many steps in a mile · when is labor day · how many weeks in a year · what if ·
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http://www.faadooengineers.com/online-study/post/eee/power-electronics/16/control-strategies-of-dc-dc-conversion
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Control Strategies of DC-DC conversion
Time – Ratio Control:
Fig: Constant Frequency operation
- In the time ratio control the value of the duty ratio, is varied.There are two ways, which are constant frequency operation, and variable frequency operation.
Constant Frequency Operation:
- In this control strategy, the ON time, TON is varied, keeping the frequency (f = 1/T), or time period T constant. This is also called as pulse width modulation control (PWM). Two cases with duty ratios, k as (a) 0.25 (25%), and (b) 0.75 (75%). Hence, the output voltage can be varied by varying ON time, TON.
Variable Frequency Operation:
In this control strategy, the frequency (f = 1/T), or time period T is varied, keeping either (a) the ON time, TON constant, or (b) the OFF time, TOFF constant. This is also known as frequency modulation control. Two cases with (a) the ON time, TON constant, and (b) the OFF time, TOFF constant, with variable frequency or time period (T). The output voltage can be varied in both cases, with the change in duty ratio, k = TON/T.There are major disadvantages in this control strategy. They are:
- The frequency has to be varied over a wide range for the control of output voltage in frequency modulation. Filter design for such wide frequency variation is, therefore, quite difficult.
- For the control of a duty ratio, frequency variation would be wide. As such, there is a possibly of interference with systems using certain frequencies, such as signaling and telephone line, in frequency modulation technique.
- The large OFF time in frequency modulation technique, may make the load current discontinuous, which is undesirable.
- Thus, the constant frequency system using PWM is the preferred scheme for dc-dc converters (choppers).
Current Limit Control:
Fig: Current limit control
- As can be observed from the current waveforms for the types of dc-dc converters, the current changes between the maximum and minimum values, if it (current) is continuous. In the current limit control strategy, the switch in dc-dc converter (chopper) is turned ON and OFF, so that the current is maintained between two (upper and lower) limits. When the current exceed upper (maximum) limit, the switch is turned OFF. During OFF period, the current freewheels in say, buck converter (dc-dc) through the diode, DF, and decreases exponentially. When it reaches lower (minimum) limit, the switch is turned ON.
- This type of control is possible, either with constant frequency or constant ON time, TON. This is used only, when the load has energy storage elements, i.e. inductance, L. The reference values are load current or load voltage. In this case, the current is continuous, varying between Imax and Imin , which decides the frequency used for switching.
- The ripple in the load current can be reduced, if the difference between the upper and lower limits is reduced, thereby making it minimum. This in turn increases the frequency, thereby increasing the switching losses.
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http://gmatclub.com/forum/n-is-a-positive-integer-what-is-the-remainder-when-n-is-44321.html?fl=similar
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math
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7. n is a positive integer. What is the remainder when n is divided by 6?
(1) n is a multiple of 3. (2) When n is divided by 2, the remainder is 1.
solve and explain
n is a positive integer it can be even or odd. i.e it can be 1,2,3,4,5,6,7,8,...infinity. any number
now lets see what statement 1 has to say. statement 1 means the n is a multiple of 3 that is it can be 3,6,9,12,15,...,upto infinity i.e n=3a where a = 1,2,3,4,5,..infinity. when a is even then n is divisible by 6 and the remainder is 0 .but when a is odd n is divisible by 3 as it is multiple of 3 but not by 2 that is it is not divisible by 6 and we get a remainder equal to 1. so (1) is not sufficient.
similarly(2) is not sufficient. because in 2 we just know that n is a multiple of 2.
When we take (1)&(2) together. then statement 1 says that n is multiple of 3 and statement 3 says that n is multiple of 2 so can say that n is multiple of both 2 & 3 i.e 6. so n is completely divisible by 6. So the answere is (C).
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http://www.dartmouth.edu/comp/soft-comp/software/research/packages/mathematicadown.html
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math
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Overall System Status:
Mathematica is an interactive program that does numerical, symbolic, and graphical computations and visualization.
Research Computing and the Math department have 30 floating licenses for Mathematica for Windows, Mac OS X, and Linux platforms. These licenses are for curricular or research use.
If you would like to install Mathematica on your computer,here is the download page:
For complete information about Mathematica, refer to the Wolfram Research home page
Last Updated: 2/28/14
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http://apple.stackexchange.com/questions/tagged/open-office+mountain-lion
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| 2,353 | 54 |
https://education.ti.com/en/customer-support/knowledge-base/all-other-products/computer-software-installation-activation/31311
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math
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Solution 31311: Finding the Sum of a Column in the Lists & Spreadsheets Application using the TI-Nspire™ Family Handhelds.
How do I find the sum of a column in the Lists & Spreadsheet application using the TI-Nspire family handhelds?To find the sum of a column in the Lists & Spreadsheet application using the TI-Nspire family handhelds, please follow the example listed below.
Ex: Input 5, 12.5, 22, 9.5, 16 into column A. Input .856, 3, 60, 26.7, 14 into column B.
• Press [home].
• Press 1: New Document to create a new document. If prompted to save the existing document, choose "Yes" or "No".
• Press 4: Add Lists & Spreadsheet.
Input the data into columns A and B by following the steps below:
• Input 5 [enter] 12.5 [enter] 22 [enter] 9.5 [enter] 16.
• Press the left arrow key once and press the up arrow key four times to begin adding the next set of data.
• Input .856 [enter] 3 [enter] 60 [enter] 26.7 [enter] 14.
To find the sum, scroll to the last empty row of column A and input the following:
• Press [=][S][U][M][(][A][:][A][)][enter].
You will get the sum of the rows A1-A5 which is 65.
Please see the TI-Nspire family products guidebooks for additional information.
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| 1,199 | 14 |
http://www.techrepublic.com/resource-library/whitepapers/heteroskedasticity-and-autocorrelation-efficient-hae-estimation-and-pivots-for-jointly-evolving-series/?scname=strategic-planning-and-analysis
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math
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Download now Free registration required
A new two-way map between time domain and numerical magnitudes or values domain (v-dom) provides a new solution to heteroscedasticity. Since sorted logs of squared fitted residuals are monotonic in the v-dom, one obtain a parsimonious fit there. Two theorems prove consistency, asymptotic normality, efficiency and specificationrobustness, supplemented by a simulation. Since Dufour's (1997) impossibility theorems show how confidence intervals from Wald-type tests can have zero coverage, the author suggests Godambe pivot functions (GPF) with good finite sample coverage and distribution-free robustness. The author uses the Frisch-Waugh theorem and the scalar GPF to construct new confidence intervals for regression parameters and apply Vinod's (2004, 2006) maximum entropy bootstrap. The author uses Irving Fisher's model for interest rates and Keynesian consumption function for illustration.
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https://studysoup.com/tsg/980632/linear-algebra-with-applications-4-edition-chapter-9-3-problem-13
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math
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Find all real solutions of the differential equations in Exercises 1 through 22.f"(t) + 2f'(t) + f(t) = 0
Step 1 of 3
Lecture 7: Limits (Section 2.2) Recall the definition: For a given function f(x), we say that x→c f(x)= L if we can make the values of f(x)aseto L as we want by choosing x sufficiently close to c on either side but not equal to c. ▯ ex. If f(x)= x if x ▯=1 ,dml f(x). f3i x =1 x→1 ▯ ex. If g(x)= f 3i x ≤ 0 ,ndl g(x). −f1i x> 0 x→0
Textbook: Linear Algebra with Applications
Author: Otto Bretscher
This full solution covers the following key subjects: . This expansive textbook survival guide covers 41 chapters, and 2394 solutions. The answer to “Find all real solutions of the differential equations in Exercises 1 through 22.f"(t) + 2f'(t) + f(t) = 0” is broken down into a number of easy to follow steps, and 19 words. The full step-by-step solution to problem: 13 from chapter: 9.3 was answered by , our top Math solution expert on 03/15/18, 05:20PM. This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 4. Linear Algebra with Applications was written by and is associated to the ISBN: 9780136009269. Since the solution to 13 from 9.3 chapter was answered, more than 229 students have viewed the full step-by-step answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585265.67/warc/CC-MAIN-20211019105138-20211019135138-00430.warc.gz
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CC-MAIN-2021-43
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https://www.teacherspayteachers.com/Product/Geometry-Team-Task-Circle-Properties-and-Relationships-1294299
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math
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This is a task on the concept of Circle Properties and Relationships.
This is a 6 page team task. In this task students will take turns as "Team Mathematician".
Students will identify and color-code the parts of a circle using academic vocabulary.
Students will construct and color-code diagrams identifying the types of angles in a circle.
Students will determine if the given statements about circle relationships are true or false and justify their reasoning.
Students will use chords, secants and tangents to determine the possible ways an angle can be formed.
Students will find angle measures, segment measures and explain how they determined their reasoning in complete sentences.
* This task will have your classroom rich in mathematical discourse.
*** My "Team Tasks" are created to be completed in Teams of four. Each student is a team member: Team Member (A), Team Member (B), Team Member (C), and Team Member (D). Each team member is required to participate regularly throughout the "Team Task" as Team Mathematician. My cooperative learning "Team Tasks" require the students to be actively involved throughout the entire "Team Task". The Role of "Team Mathematician" alternates throughout the "Team Task". My "Team Tasks" are designed to elicit mathematical discourse within the teams.
Included are blackline masters and students samples with an answer key.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812584.40/warc/CC-MAIN-20180219111908-20180219131908-00345.warc.gz
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CC-MAIN-2018-09
| 1,370 | 10 |
https://studydaddy.com/question/algebra-1-studying
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math
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Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
Algebra 1 Studying
Hi, I need help with order of operations and exponents and exponential functions. Can you please help me study?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301063.81/warc/CC-MAIN-20220118213028-20220119003028-00490.warc.gz
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CC-MAIN-2022-05
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https://masontogo.com/how-to-factor-polynomials/
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math
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Understanding the Basics of Factoring Polynomials
Before diving into more complex techniques for factoring polynomials, it’s important to understand the basics of what factoring means. Factoring is the process of finding two or more expressions that, when multiplied together, result in a given polynomial.
For example, consider the polynomial x^2 + 5x + 6. We can factor this polynomial by finding two expressions that, when multiplied together, result in x^2 + 5x + 6. One possible factorization is (x + 3)(x + 2), since (x + 3)(x + 2) = x^2 + 5x + 6.
Factoring can be useful for simplifying expressions, solving equations, and finding roots of polynomials. It can also help us identify patterns and relationships between different polynomials. By understanding the basics of factoring, we can build a solid foundation for more advanced techniques.
Factoring Common Polynomial Types
Certain types of polynomials have factorizations that are commonly used and should be memorized. These include:
Monomials: A monomial is a polynomial with only one term. Monomials can be factored by extracting their greatest common factor. For example, the monomial 3x^2 can be factored into 3(x^2).
Quadratics: A quadratic is a polynomial of degree two. Quadratics can be factored using techniques such as factoring by grouping, completing the square, or using the quadratic formula. For example, the quadratic x^2 + 5x + 6 can be factored into (x + 3)(x + 2).
Cubics: A cubic is a polynomial of degree three. Cubics can be factored using techniques such as grouping or using the rational roots theorem. For example, the cubic x^3 + 3x^2 + 2x can be factored into x(x + 1)(x + 2).
Difference of Squares: A difference of squares is a polynomial of the form a^2 – b^2. A difference of squares can be factored into (a + b)(a – b). For example, the polynomial x^2 – 9 can be factored into (x + 3)(x – 3).
By memorizing these common factorizations, we can save time and simplify the factoring process.
Factoring by Grouping and Completing the Square
In addition to the common polynomial types, there are other techniques for factoring that can be useful in certain situations. Two of these techniques are factoring by grouping and completing the square.
Factoring by grouping is a technique used when a polynomial has four terms. To factor by grouping, we group the terms into two pairs and look for a common factor in each pair. We then factor out that common factor and see if we can factor the resulting expression further. For example, consider the polynomial x^3 – x^2 + x – 1. We can group the first two terms and the last two terms and factor out x^2 and 1, respectively. This gives us (x^2 – 1)(x – 1). We can further factor the first term using the difference of squares rule, giving us (x + 1)(x – 1)(x – 1).
Completing the square is a technique used to factor quadratics of the form ax^2 + bx + c. To complete the square, we add and subtract a term (b/2a)^2 to the quadratic. This creates a perfect square trinomial that can be factored using the square root property. For example, consider the quadratic x^2 + 6x + 7. We can complete the square by adding and subtracting (6/2)^2 = 9. This gives us x^2 + 6x + 9 – 9 + 7, which can be factored into (x + 3)^2 – 2.
By using these techniques, we can factor more complex polynomials and expand our factoring toolkit.
Using the Rational Roots Theorem to Factor Polynomials
The rational roots theorem is a useful tool for factoring polynomials with integer coefficients. This theorem states that if a polynomial with integer coefficients has a rational root, then that root must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
To use the rational roots theorem, we start by listing all the factors of the constant term and all the factors of the leading coefficient. We then form all possible fractions using a factor from the constant term and a factor from the leading coefficient. We test each of these possible roots by plugging them into the polynomial and seeing if the result is zero. If we find a rational root, we can use synthetic division or long division to factor the polynomial.
For example, consider the polynomial x^3 – 3x^2 – 4x + 12. The factors of the constant term 12 are 1, 2, 3, 4, 6, and 12. The factors of the leading coefficient 1 are 1 and -1. This gives us the possible roots 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, and -12. By testing these roots, we find that x = 3 is a root. Using synthetic division, we can then factor the polynomial into (x – 3)(x^2 – 4).
The rational roots theorem can be a powerful tool for factoring polynomials, but it is limited to polynomials with integer coefficients and rational roots.
Strategies for Factoring Complex Polynomials
For polynomials that are not easily factored using the techniques described earlier, there are several strategies we can use to factor them. Here are some examples:
Factoring by Substitution: This technique involves substituting a variable expression for a specific term in the polynomial. For example, consider the polynomial x^3 + 4x^2 + 4x + 1. We can substitute y = x + 1 to get the polynomial in terms of y: (y – 1)^3. We can then factor the resulting expression as a cube of a binomial: (y – 1)^3 = (y – 1)(y – 1)(y – 1) = (y – 1)^3 = (x + 1 – 1)^3 = x^3.
Factoring by Long Division: For polynomials that cannot be factored using other techniques, long division can be used to factor the polynomial into simpler polynomials. For example, consider the polynomial x^4 – 3x^3 – 4x^2 + 12x + 4. By using long division, we can factor this polynomial into (x – 2)(x + 1)(x^2 – 2x – 2).
Factoring Using Trigonometric Functions: Certain polynomials can be factored using trigonometric functions, such as sin(x) and cos(x). For example, consider the polynomial x^4 – 4x^2 + 4. This can be factored into (x^2 – 2)(x^2 – 2sin^2(x)).
Factoring Using Special Identities: Certain special identities, such as the difference of cubes or the sum and difference of cubes, can be used to factor polynomials. For example, consider the polynomial x^3 + 8. This can be factored into (x + 2)(x^2 – 2x + 4) using the sum of cubes identity.
By using these strategies, we can factor even the most complex polynomials and solve difficult problems in mathematics and science.
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http://www.mathisfunforum.com/search.php?action=show_user&user_id=192214
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math
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Beech Corporation, an accrual basis taxpayer, was organized and began business on July 1, 2010. During 2010, the corporation incurred the following expenses: State fees for incorporation $ 500 Legal and accounting fees incident to organization 1,800 Expenses for the sale of stock 2,100 Organizational meeting expenses 750 Assuming that Beech Corporation does not elect to expense but chooses to amortize organizational-expenditures over 15 years, calculate the corporation's deduction for its calendar tax year 2010.
(4) Citradoria Corporation is a regular corporation that contributes $35,000 cash to qualified charitable organizations during 2010. The corporation has net operating income of $140,000 before deducting the contributions, and dividends received from domestic corporations (ownership in all corporations is less than 20 percent) in the amount of $20,000. a. What is the amount of Citradoria Corporation's allowable deduction for charitable contributions for the current year?
b. What may the corporation do with any excess amount of contributions?
Bill and Guilda each own 50 percent of the stock of Radiata Corporation, an S corporation. Guilda's basis in her stock is $25,000. On July 31, 2010, Bill sells his stock, with a basis of $40,000, to Loraine for $50,000. For the 2010 tax year, Radiata Corporation has a loss of $100,375. a. Calculate the amount of the corporation's loss that may be deducted by Bill on his 2010 tax return. b. Calculate the amount of the corporation's loss that may be deducted by Guilda on her 2010 tax return. c. Calculate the amount of the corporation's loss that may be deducted by Loraine on her 2010 tax return.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122629.72/warc/CC-MAIN-20170423031202-00023-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 1,665 | 4 |
https://www.neetprep.com/question/5456-Correct-statement-regarding-transuranic-elements--higher-atomic-number-uranium-lighter-uranium-lower-atomic-number-uranium-atomic-number-uranium/54-Chemistry/647-Classification-Elements-Periodicity-Properties?courseId=8
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math
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Correct statement regarding transuranic elements is :
1. They have higher atomic number than uranium.
2. They are lighter than uranium.
3. They have lower atomic number than uranium.
4. They have same atomic number as uranium.
The correct sequence of increasing order of density is:
1. Li < K< Na < Rb < Cs
2. Li < Na < K < Rb < Cs
3. Cs < Rb < K < Na < Li
4. K < Li < Na < Rb < Cs
General electronic configuration of outermost and penultimate shell of an atom is
(n - 1)s2 (n - 1) p6 (n - 1)dx ns2. If n = 4 and x = 5, the number of proton in the nucleus is:
1. > 25
2. < 24
The maximum number of valence electrons possible for atoms in the second period of the periodic table is:
The element having atomic number 19, is:
1. an inert gas
2. a metal with oxidation number +1
3. a non-metal with oxidation number -3
4. a metal with oxidation number -3
Which of the following has the least density?
Eka aluminium and Eka silicon are now known as:
1. Ga and Ge
2. Al and Si
3. Fe and S
4. H+ and Si
An element having the electronic configuration of its atom ns2 np2 should have similar properties to those of:
The order of basic character of given oxides is:
1. Na2O > MgO > Al2O3 > CuO
2. MgO > Al2O3 > CuO > Na2O
3. Al2O3 > MgO > CuO > Na2O
4. CuO > Na2O > MgO > Al2O3
A variable oxidation state is shown by which of the following?
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http://mjperry.blogspot.com/2009/06/global-study-shows-greater-male.html
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math
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Larry Summers Vindicated? Global Study Shows Greater Male Variability in Math, Reading Scores
The tables above show selected statistics from the paper Global Sex Differences in Test Score Variability (see summary here), published by two economists, one from the London School of Economics and the other from the Helsinki School of Economics. Analyzing standardized test scores in reading and mathematics from the OECD’s "Program for International Student Assessment" (PISA), a survey of 15-year olds in 41 industrialized countries, the authors found that:
Our analysis of international test score data shows a higher variance in boys' than girls' results on mathematics and reading tests in most OECD countries. Higher variability among boys is a salient feature of reading and mathematics test performance across the world. In almost all comparisons, the age 15 boy-girl variance difference in test scores is present. This difference in variance is higher in countries that have higher levels of test score performance.
Sex differences in means are easier to characterize: It is evident from the PISA data that boys do better in mathematics, and girls do better in reading. This has a compositional effect on the variance differences as well. The higher boy-girl variance ratio in mathematics comes about because of an increased prevalence of boys in the upper part of the distribution, but the higher variance in reading is due to a greater preponderance of boys in the bottom part of the test score distribution. Because literacy and numeracy skills have been shown to be important determinants of later success in life (for instance, in terms of earning higher wages or getting better jobs), these differing variances have important economic and social implications.
We therefore confirm that 15-year-old boys do show more variability than girls in educational performance, with specifics that differ according to whether mathematics or reading are being studied and tested. These results imply that gender differences in the variance of test scores are an international phenomenon and that they emerge in different institutional settings.
1. The results above show that for both the U.S. (Table 1) and the global group of 41 countries (Table 2), the mean math test scores for 15-year boys are significantly higher than the average score for girls, but the reverse is true for reading test scores: girls score significantly higher than boys on average in reading.
2. For both the U.S. and the 41 countries in the global group, the variability of boys' test scores for both reading and mathematics is significantly greater than the variability of girls' test scores (at the 1% level in all cases), suggesting that there are more boys in the upper and lower tails of the test score distributions.
3. Looking at the top 5% and the bottom 5% of test scores, we can see that boys are overrepresented in almost every case:
a. In the bottom 5% of reading scores, there are 245 boys for every 100 girls in the U.S. (220 boys for every 100 girls for the world group), and in the top 5% of reading scores there are 167 girls for every 100 boys (172 girls for the global group).
b. In the bottom 5% of math scores, there are 121 boys for every 100 girls in the U.S. (94 for the global group), and in the top 5% there are 172 boys for every 100 girls (170 girls for the world group).
In other words, the results indicate that boys' test scores are significantly more variable than girls' test scores, resulting in boys being significantly overrepresented in both the bottom 5% and the top 5% of students in the U.S., and these outcomes are a global phenomenon.
Bottom Line: Can Larry Summers get his job back as president of Harvard, for saying basically the same thing?
"It does appear that on many, many different human attributes- height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability - there is relatively clear evidence that whatever the difference in means - which can be debated - there is a difference in the standard deviation, and variability of a male and a female population."?
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CC-MAIN-2017-17
| 4,126 | 13 |
https://vidyakul.com/jee/jee-mains-physics-syllabus-2018
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math
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Physics Syllabus JEE Mains 2018
The most demanding subject for a candidate aspiring for JEE Mains Exam, is Physics and without an in-depth understanding of JEE Mains Physics Syllabus for 2018, scoring in the exam becomes challenging. The main purpose of the candidate to go through JEE Mains Syllabus—Physicsis to understand and relate to the topics that are crucial. Moreover, the JEE Mains Physics Syllabus 2018 with weightage, brought to the candidates by Vidyakul, gives a clear understanding of the topics that carry the maximum weightage and thus must be prepared accordingly. This also benefits the candidate to identify and understand his/her strong and week points, thus guiding them to prepare for the exam strategically.
The Physics Syllabus for JEE Mains 2018 is an amalgamation for topics that candidates have studied in Class 11th as well as Class 12. Moreover, it follows strict guidelines from CBSE and picks up some topics directly from NCERT. Candidate must note that the JEE Mains Physics Syllabus 2018 has been divided into two sections—Section A and Section B. The first part, i.e. Section A, entails all the theoretical concepts and carries a weightage of about 80% in the exam. On the other hand, Section B entails all the experiment skills or practical knowledge with a weightage of about 20%. Candidates must have a thorough understanding of both the sections given in the JEE Mains Physics Syllabus 2018 which would ultimately help them to extract maximum marks in the examination.
The chapter-wise weightage and important topics of the entire JEE Mains Physics Syllabus 2018 is given below:
Physics JEE Mains Syllabus 2018
|S. No.||Topics—Physics Syllabus of JEE Mains 2018||Marking Weightage||Important Topics|
|1||Unit, Dimensions and Vectors||4-5%|| –|
|3||Laws of Motion||4-5%||Important|
|4||Work, Power and Energy||6-7%|| –|
|5||Centre of Mass, Impulse and Momentum||3-4%|| –|
|8||Simple Harmonic Motion||3-4%||Important|
|9||Solids and Fluids||3-4%||–|
|11||Heat and Thermodynamics||10-11%||Important|
|16||Electromagnetic Induction and Alternating Current||3-4%|| –|
JEE Mains 2018 Syllabus—Physics
Candidates must note that JEE Mains Physics Syllabus for 2018 is divided into two parts—Section A and Section B. The first section, that is, Section A includes the entire theory carries about 80% of the weightage. On the other hand, Section B tests the practical components or the experimental understanding of the candidate. This section carries 20% of the weightage.
Candidates are advised to follow the JEE Mains 2018 Syllabus for Physics, religiously to attain maximum marks in their JEE Mains Exam.
JEE Mains Physics Syllabus-Section A
UNIT I: Physics and Measurement
• Physics, technology and society, S I units, Fundamental and derived units.
• Least count, accuracy and precision of measuring instruments, Errors in measurement, Significant figures.
• Dimensions of Physical quantities, dimensional analysis and its applications.
UNIT II: Kinematics
• Frame of reference.
• Motion in a straight line: Position-time graph, speed and velocity.
• Uniform and non-uniform motion, average speed and instantaneous velocity
• Uniformly accelerated motion, velocity-time, position- time graphs, relations for uniformly accelerated motion.
• Scalars and Vectors, Vector addition and Subtraction, Zero Vector, Scalar and Vector products, Unit Vector, Resolution of a Vector.
• Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.
UNIT III: Laws of Motion
• Force and Inertia, Newton’s First Law of motion
• Momentum, Newton’s Second Law of motion
• Newton’s Third Law of motion
• Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces.
• Static and Kinetic friction, laws of friction, rolling friction.
• Dynamics of uniform circular motion: Centripetal force and its applications.
UNIT IV: Work, Energy and Power
• Work done by a constant force and a variable force
• kinetic and potential energies, work energy theorem, power.
• Potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces
• Elastic and inelastic collisions in one and two dimensions.
UNIT V: Rotational Motion
• Centre of mass of a two-particle system, Centre of mass of a rigid body
• Basic concepts of rotational motion
• moment of a force, torque, angular momentum, conservation of angular momentum and its applications
• moment of inertia, radius of gyration.
• Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications.
• Rigid body rotation, equations of rotational motion.
UNIT VI: Gravitation
• The universal law of gravitation
• Acceleration due to gravity and its variation with altitude and depth
• Kepler’s laws of planetary motion
• Gravitational potential energy
• gravitational potential.
• Escape velocity.
• Orbital velocity of a satellite.
• Geo-stationary satellites.
UNIT VII: Properties of Solids and Liquids
• Elastic behaviour, Stress-strain relationship, Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity.
• Pressure due to a fluid column
• Pascal’s law and its applications.
• Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, Reynolds number.
• Bernoulli’s principle and its applications.
• Surface energy and surface tension, angle of contact, application of surface tension – drops, bubbles and capillary rise.
• Heat, temperature, thermal expansion
• specific heat capacity, calorimetry; change of state, latent heat.
• Heat transfer- conduction, convection and radiation, Newton’s law of cooling.
UNIT VIII: Thermodynamics
• Thermal equilibrium, zeroth law of thermodynamics, concept of temperature.
• Heat, work and internal energy.
• First law of thermodynamics.
• Second law of thermodynamics: reversible and irreversible processes.
• Carnot engine and its efficiency.
UNIT IX: Kinetic Theory of Gases
• Equation of state of a perfect gas, work doneon compressing a gas.
• Kinetic theory of gases – assumptions, concept of pressure.
• Kinetic energy and temperature: rms speed of gas molecules
• Degrees of freedom, Law of equipartition of energy, applications to specific heat capacities of gases
• Mean free path, Avogadro’s number.
UNIT X: Oscillations and Waves
• Periodic motion – period, frequency, displacement as a function of time.
• Periodic functions.
• Simple harmonic motion (S.H.M.) and its equation
• oscillations of a spring -restoring force and force constant
• energy in S.H.M. – kinetic and potential energies
• Simple pendulum – derivation of expression for its time period
• Free, forced and damped oscillations, resonance.
• Wave motion.
• Longitudinal and transverse waves, speed of a wave.
• Displacement relation for a progressive wave.
• Principle of superposition of waves,
• reflection of waves,
• Standing waves in strings and organ pipes,
• fundamental mode and harmonics,
• Doppler effect in sound
UNIT XI: Electrostatics
• Conservation of charge,
• Coulomb’s law-forces between two point charges,
• forces between multiple charges;
• superposition principle
• continuous charge distribution.
• Electric field due to a point charge,
• Electric field lines,
• Electric dipole,
• Electric field due to a dipole,
• Torque on a dipole in a uniform electric field.
• Electric flux,
• Gauss’s law and its applications to find field due to infinitely long uniformly charged straight wire,
• uniformly charged infinite plane sheet
• uniformly charged thin spherical shell.
• Electric potential and its calculation for a point charge,
• electric dipole and system of charges
• Equipotential surfaces,
• Electrical potential energy of a system of two point charges in an electrostatic field.
• combination of capacitors in series and in parallel,
• capacitance of a parallel plate capacitor with
• without dielectric medium between the plates,
• Energy stored in a capacitor.
UNIT XII: Current Electricity
• Electric current,
• Drift velocity,
• Ohm’s law,
• Electrical resistance,
• Resistances of different materials,
• V-I characteristics of Ohmic
• Non-ohmic conductors,
• Electrical energy and power,
• Electrical resistivity,
• Colour code for resistors
• Series and parallel combinations of resistors
• Temperature dependence of resistance.
• Electric Cell and its Internal resistance,
• potential difference and emf of a cell,
• combination of cells in series and in parallel.
• Kirchhoff’s laws and their applications.
• Wheatstone bridge, Metre bridge.
• Potentiometer – principle and its applications.
UNIT XIII: Magnetic Effects of Current and Magnetism
• Biot – Savart law and its application to current carrying circular loop.
• Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid.
• Force on a moving charge in uniform magnetic and electric fields.
• Force on a current-carrying conductor in a uniform magnetic field.
• Force between two parallel current-carrying conductors-definition of ampere.
• Torque experienced by a current loop in uniform magnetic field
• Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter.
• Current loop as a magnetic dipole and its magnetic dipole moment.
• Bar magnet as an equivalent solenoid, magnetic field lines
• Earth’s magnetic field and magnetic elements.
• Para-, dia- and ferro- magnetic substances.
• Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.
UNIT XIV: Electromagnetic Induction and Alternating Currents
• Electromagnetic induction
• Faraday’s law, induced emf and current
• Lenz’s Law, Eddy currents.
• Self and mutual inductance.
• Alternating currents, peak and rms value of alternating current/ voltage
• reactance and impedance
• LCR series circuit, resonance
• Quality factor, power in AC circuits, wattless current.
• AC generator and transformer.
UNIT XV: Electromagnetic Waves
• Electromagnetic waves and their characteristics.
• Transverse nature of electromagnetic waves.
• Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, Xrays, gamma rays).
• Applications of e.m. waves.
UNIT XVI: Optics
• Reflection and refraction of light at plane and spherical surfaces,
• mirror formula,
• Total internal reflection and its applications,
• Deviation and Dispersion of light by a prism,
• Lens Formula,
• Power of a Lens,
• Combination of thin lenses in contact,
• Microscope and Astronomical Telescope (reflecting and refracting) and their magnifying powers.
• Wave front and Huygens’ principle,
• Laws of reflection and refraction using Huygen’s principle.
• Interference, Young’s double slit experiment and expression for fringe width,
• coherent sources and sustained interference of light.
• Diffraction due to a single slit, width of central maximum.
• Resolving power of microscopes and astronomical telescopes,
• Polarization, plane polarized light
• Brewster’s law, uses of plane polarized light and Polaroids.
UNIT XVII: Dual Nature of Matter and Radiation
• Dual nature of radiation.
• Photoelectric effect, Hertz and Lenard’s observation
• Einstein’s photoelectric equation
• particle nature of light.
• Matter waves-wave nature of particle
• de Broglie relation.
• Davisson-Germer experiment.
UNIT XVIII: Atoms and Nuclei
• Alpha-particle scattering experiment
• Rutherford’s model of atom
• Bohr model, energy levels, hydrogen spectrum.
• Composition and size of nucleus, atomic masses, isotopes, isobars
• Radioactivity-alpha, beta and gamma particles/rays and their properties
• radioactive decay law
• Mass-energy relation, mass defect
• binding energy per nucleon and its variation with mass number
• nuclear fission and fusion.
UNIT XIX: Electronic Devices
• Semiconductor diode: I-V characteristics in forward and reverse bias
• diode as a rectifier
• I-V characteristics of LED, photodiode, solar cell and Zener diode
• Zener diode as a voltage regulator.
• Junction transistor, transistor action, characteristics of a transistor
• transistor as an amplifier (common emitter configuration) and oscillator.
• Logic gates (OR, AND, NOT, NAND and NOR).
• Transistor as a switch.
UNIT XX: Communication Systems
• Propagation of electromagnetic waves in the atmosphere
• Sky and space wave propagation
• Need for modulation,
• Amplitude and Frequency Modulation,
• Bandwidth of signals
• Bandwidth of Transmission medium
• Basic Elements of a Communication System (Block Diagram only)
JEE Mains Physics Syllabus-Section B
UNIT XXI: Experimental Skills
• Vernier callipers – its use to measure internal and external diameter and depth of a vessel.
• Screw gauge-its use to determine thickness/diameter of thin sheet/wire.
• Simple Pendulum-dissipation of energy by plotting a graph between square of amplitude and time.
• Metre Scale – mass of a given object by principle of moments.
• Young’s modulus of elasticity of the material of a metallic wire.
• Surface tension of water by capillary rise and effect of detergents.
• Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
• Plotting a cooling curve for the relationship between the temperature of a hot body and time.
• Speed of sound in air at room temperature using a resonance tube.
• Specific heat capacity of a given
(ii)liquid by method of mixtures.
• Resistivity of the material of a given wire using metre bridge.
• Resistance of a given wire using Ohm’s law.
• Potentiometer –
(i) Comparison of emf of two primary cells.
(ii)Determination of internal resistance of a cell.
• Resistance and figure of merit of a galvanometer by half deflection method.
• Focal length of:
(i) Convex mirror
(iii)Convex lens using parallax method.
• Plot of angle of deviation vs angle of incidence for a triangular prism.
• Refractive index of a glass slab using a travelling microscope.
• Characteristic curves of a p-n junction diode in forward and reverse bias.
• Characteristic curves of a Zener diode and finding reverse break down voltage.
• Characteristic curves of a transistor and finding current gain and voltage gain.
• Identification of Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of such items.
• Using multimeter to:
(i) Identify base of a transistor
(ii)Distinguish between npn and pnp type transistor
(iii)See the unidirectional flow of current in case of a diode and an LED.
(iv)Check the correctness or otherwise of a given electronic component (diode, transistor or IC).
JEE Mains Syllabus 2018
JEE Mains Maths Syllabus 2018
JEE Mains Chemistry Syllabus 2018
JEE Mains Paper 2 Syllabus 2018
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https://www.jiskha.com/display.cgi?id=1363570413
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math
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posted by Jonah .
1) Calculate the molar solubility of AgBr in 3.0×10^−2 M AgNO3 solution.
2) calculate the molar solubility of AgBr in 0.10 M NaBr solution.
I tried solving using this the quadratic formula, but it didn't work.
I started with these equations and then solved for x, but none of them gave me the correct answer.
1) 5.0 x 10^-13 = (x + 3.0 x 10^-2)(x)
2) 5.0 x 10^-13 = (x)(0.10+x)
THANKS for showing your work. If you had shown your math work I could have checked the error. You must have made a math error. The chemistry is OK. And you need not solve the quadratic with either of them.
How would I do it without the quadratic formula?
Make the assumption that x is small in comparison to 0.03(another way of saying x + 0.03 = 0.030). Then
5.0E-13 = (x)(0.03)
x = (5.0E-13/0.03) = 1.67E-11
Then you check the assumption to see if you must go back and solve the quadratic. So 1.67E-11 + 0.03 = essentially 0.03---not even close). Since the Ksp has only 2 s.f. in it I would round that 1.67E-11M to 1.7E-11M.
You were right to include the x in the set up because some problems will not allow you to ignore the x. I always make the assumption, then check it when I finish. If the easy answer is within 5% (I think most texts use the 5% rule now) I let it stand. If the error is more than that I go back and solve the quadratic.
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http://www.global-sci.org/intro/article_detail/aamm/177.html
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math
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An axisymmetric formulation for modeling three-dimensional deformation
of structures of revolution is presented. The axisymmetric deformation
model is described using the cylindrical coordinate system. Large
displacement effects and material nonlinearities and anisotropy are
accommodated by the formulation. Mathematical derivation of the
formulation is given, and an example is presented to demonstrate
the capabilities and efficiency of the technique compared to the
full three-dimensional model.
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http://www.apug.org/forums/viewpost.php?p=578547
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math
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Yes, this value of 0.6 is the contrast index, or gamma of the straight line portion of the characteristic curve of a negative film. It can be seen in the chart in my OP.
I decided to edit this to add that the characteristic curve of a film is comprised of 21 horizontal data points, each one being 0.15 log E apart as you can see in that chart. The zone system is just a tiny center cut of that chart. The general subject of study of these curves is called Sensitometry or the measurement of sensitometric curves.
For mathematicians out there, the curve generated by all photographic materials is a cubic spline.
The curve was originally called an H&D curve for the originators of this measurement early in the history of photography.
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https://www.groundai.com/project/casimir-energy-calculation-for-massive-scalar-field-on-spherical-surfaces-an-alternative-approach/
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math
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Casimir Energy Calculation for Massive Scalar Field on Spherical Surface: An Alternative Approach
In this study, the Casimir energy for massive scalar field with periodic boundary condition was calculated on spherical surfaces with , and topologies. To obtain the Casimir energy on spherical surface, the contribution of the vacuum energy of Minkowski space is usually subtracted from that of the original system. In large mass limit for surface ; however, some divergences would eventually remain in the obtained result. To remove these remaining divergences, a secondary renormalization program was manually performed. In the present work, a direct approach for calculation of the Casimir energy has been introduced. In this approach, two similar configurations were considered and then the vacuum energies of these configurations were subtracted from each other. This method provides more physical meaning respect to the other common methods. Additionally, in large mass limit for surface , it provides a situation in which the second renormalization program is automatically conducted in the calculation procedure, and there was no need to do that anymore manually. Finally, by plotting the obtained values for the Casimir energy of the topologies and investigating their appropriate limits, the logic agreement between the results of our scheme and those of previous studies were discussed.
Casimir energy is the difference between zero point energy in presence and absence of non-trivial boundary condition. This effect was first predicted and calculated by H.B.G. Casimir in 1948. He was the first one who explained the attraction between two parallel uncharged perfectly conducting plates in vacuum h.b.g. (). First attempts to observe this phenomenon were made in 1958 by M. J. Sparnaay Sparnaay.M.J. (), and then more accurate measurements verified Casimir’s prediction. As Casimir effect was then considered an interesting effect of vacuum polarization, it has found many applications. This effect has an important role in different fields of physics such as quantum field theory quantum.field.theory.1 (); quantum.field.theory.2 (); quantum.field.theory.3 (); quantum.field.theory.4 (); quantum.field.theory.5 (), condensed matter physics condensed.matter.1 (); condensed.matter.2 (), atomic-molecular physics atomic.molecular.1 (); atomic.molecular.2 (); atomic.molecular.3 (); atomic.molecular.4 (), gravity, astrophysics astro.physics.1 (); astro.physics.2 () and mathematical physics Generalized.Abel.Plana.Saharian (); Mathematical.physics.1 (); Mathematical.physics.2 (). Due to the definition of the Casimir energy, two divergent terms should be subtracted from each other, which is not a simple task. In this regard, to achieve this purpose, various regularization and renormalization techniques were developed that found their own importance. In fact, Casimir energy calculations have provided a situation where various regularization and renormalization techniques have been developed in mathematical physics. Zeta function regularization techniques Zeta.function.1 (); Zeta.function.2 (); Zeta.function.3 (), Green’s function methods Greens.function. () and multiple-scattering expansions multiple.scattering. () are some of these techniques. Advantages and disadvantages of these methods are also reviewed in previous works review.of.some.techniques. (). Whereas the Casimir energy is a physical quantity that its value depends on the system size (e.g. the distance of parallel plates and radius of sphere). In some previous methods to calculate the Casimir energy, the terms, which do not depend on the system size have been eliminated from the Casimir energy expression wolfram. (). Physically, this elimination could be justified. However, the mathematical trend in this way cannot be maintained. In this paper, we have used a method that is free from these kinds of ambiguities in calculation of the Casimir energy. This method was first used by T.H. Boyer for the calculation of the Casimir energy for an electromagnetic field confined in a conducting sphere boyer. () and it was named Box Subtraction Scheme (BSS) in the later works BSS.1 (); BSS.2 (). Up to now, in order to reduce possible ambiguities appearing in the calculation of the Casimir energy, multiple studies used this method other.BSS.1 (); other.BSS.2 (). In the BSS, the Casimir energy is calculated by introducing two similar configurations and then their zero point energies in proper limits are subtracted from each other. To define this method concretely for our problem, as Fig. (1) shows, we consider two similar spheres. These two spheres are named A and B with radii and , respectively. Then, the zero point energies of massive scalar field on the surface of these two spheres are computed and in following, the obtained vacuum energies are subtracted from each other. Finally, by taking the radius of sphere B to be infinite, the Casimir energy of sphere A will be obtained. Therefore, we have,
where and are zero point energy densities for and configurations, respectively. In the BSS, the contribution of vacuum energy of Minkowski space is substituted with a configuration (like sphere B) that in proper limit (), it will approach to the properties of Minkowski space. Use of two similar configurations in the BSS provides the possibility that parameters of the second configuration (like B configuration) play a useful role as a regulator in divergence removal. These added parameters allow the calculation of the Casimir energy via this scheme to be more clear in details. This scheme also reduces the need for using the analytic continuation techniques in the calculation process. Therefore, the related complications and ambiguities, due to analytic continuation techniques, would be avoided BSS.1 (); BSS.2 (); other.BSS.1 (); other.BSS.2 (). The other successful experience of using the BSS is in higher orders of radiative corrections to the Casimir energy for different configurations, resulting in converged and consistent answers in all previous works in this category other.BSS.Radiative.Correction.2 (). The BSS has been previously used for the calculation of the Casimir energy on flat space, but in this paper, it is intended to calculate the Casimir energy of a massive scalar field with periodic boundary condition on a curved space (e.g. on sphere with and topologies). In common methods, to obtain the Casimir energy on curved manifolds, contribution of the vacuum energy of Minkowski space was subtracted from the vacuum energy of original manifold new.developements. (); New.Paper.On.Sphere. (); Mamaev.1979. (); Advances.book. (). Since the Minkowski space is the ï¬at space, and the original manifold is curved, this subtraction is a comparing between two different kinds of spaces. The BSS, by providing the subtraction between vacuum energies of similar configurations, presents an opportunity for similar spaces to be compared with each other. In fact, the introduction of similar configurations in the BSS, in addition to creating more clarity in the computing process, also has better physical grounds. The other point in using BSS is manifested when we use it in calculation of the Casimir energy for topology. In all previous works, after subtracting the vacuum energy of Minkowski space from that of original system, to reach a physically consistent answer in large mass limit, an extra renormalization procedure has been performed. This secondary renormalization program to remove remaining infinities, that usually appeared due to the mass of the field, has been manually conducted (e.g. Section (3.4) of Ref. new.developements. ()). In our study, the aforementioned renormalization program is automatically performed in the BSS and there is no need to do that manually. It reflects another advantage of the BSS over curved manifolds.
In the next section, through the BSS, the Casimir energy density for massive scalar field with periodic boundary condition on three spherical surface with , and topology with radius are obtained. In the following, for each surface, the Casimir energy values in specific limits of mass of the scalar field (such as or ) will be investigated. In the last section, all of our discussion concerning the BSS are summarized.
Ii The Casimir energy
In this section, the Casimir energy for massive scalar field with periodic boundary condition on surface , and are calculated. The details of calculation for each topology is investigated in separated subsections and their extreme limits are also discussed separately. At the first step, to present a simple introduction of BSS, we start with calculation of the Casimir energy on a circle with radius .
ii.1 On a Circle ()
The vacuum energy density for massive scalar field with periodic boundary condition on a circle with radius can be obtained from a problem in which the massive scalar field lives in one dimension between two points with periodic boundary condition by distance (for more details see Refs. new.developements. (); other.BSS.2 ()). Thus, we can write the vacuum energy density of massive scalar field on a circle with radius as:
where is the wave number and is the mass of the field. Now, by using the definition of BSS given in Eq. (1), another circle with radius (), as shown in Fig. (1), is defined and the vacuum energies of these two circles should be subtracted from each other. Therefore, we have:
All summations in Eq. (3) are divergent. Accordingly, to regularize their infinities, the Abel-Plana Summation Formula (APSF) is employed. This formula helps all summation forms given in Eq. (3) to be transformed to the integral form and the removal process of their infinite parts would be conducted with clarity. The usual form of APSF that we have used is:
where is the Branch-cut term of APSF. The first integral term on the right hand side of Eq. (5) is divergent. Analogously, the same integral appears for configuration B in the second square bracket of Eq. (5). To remove their infinities in subtracting procedure, we first replace the upper limit of these two integrals with multiple cutoffs and respectively. Then, by calculating integrations, we would have two separate expressions as a function of cut-offs and . Now, by expanding the result in the limit , each integral becomes:
Appropriate adjusting for cut-offs and supplemented by subtracting procedure, which is provided by BSS, helps the infinite terms appeared in the above expansion to be canceled. The BSS also helps the finite term appeared in the expansion to cancel each other out exactly. All of terms in higher order of do not leave any contribution in the limit . Therefore, the only remaining terms after these cancelations would be the Branch-cut terms. Finding an analytical and closed answer for integration of is very cumbersome. Hence, before computation of the integral, the denominator of the integrand is expanded. Then, by calculating integral we have:
Now, by applying the limit given in Eq. (1), the Casimir energy density on a circle with radius becomes:
where and the extreme limit of the result becomes:
In Fig. (2), we have plotted the Casimir energy density given in Eq. (8) as a function of radius . This figure shows a sequence of plots for . This sequence of plots indicates that the Casimir energy for massive cases rapidly converges into the massless limit when . This behavior for the Casimir energy is compatible with the previously reported results and it is also expected according to physical grounds new.developements. (); New.Paper.On.Sphere. ().
ii.2 On a Sphere ()
In this subsection, we present the Casimir energy calculation via BSS for massive scalar field with periodic boundary condition on a surface with topology. At the first step, we remind the reader of the metric for this surface on which the scalar field lives on it. Therefore, we have:
This metric describes dimensional space-time on a sphere with radius and the wave equation for a scalar field with mass on this sphere can be written as:
where is the covariant derivative and is the scalar curvature of space-time and is the conformal coupling constant. The coordinate shows the space-time coordinates on the spherical surface. By substituting the values of and for Eq. (11) and expanding the covariant derivative , we have:
The orthonormal set of solutions to Eq. (12) obeying periodic boundary conditions for both and are represented as:
where are the spherical harmonic function and are wave numbers. In order to obtain zero point energy of field on sphere, the field operator of should be expanded according to the following equation:
where and are annihilation and creation operators of the field, respectively. The metric energy-momentum tensor is obtained by varying the Lagrangian corresponding to Eq. (11) with respect to the metric tensor . Its diagonal component is:
where is Einstien tensor and is Ricci tensor. By substituting Eq.(14) for Eq. (II.2) and then calculating the expectation value of energy-momentum tensor, the vacuum energy density for massive scalar field on sphere will be obtained as follows:
Due to the spherical symmetry, each energy level degenerates () folds and high frequency modes formally render these sums as divergent.
To start the calculation of the Casimir energy via the BSS, as Fig. (1) symbolically shows, two configurations should be considered. In this problem, these configurations are two similar spheres with radii and , which named A and B configuration, respectively. Now, by using Eqs. (1,16) we have:
where and are zero point energy densities for and configurations, respectively. Both of the subtracted expressions in the above equation are divergent. Therefore, a regularization technique is required. At this step, the common method is using the APSF and the prescribed form of this formula for half integer parameters is (for a general review see Ref. Generalized.Abel.Plana.Saharian ()):
By applying the above form of APSF on Eq. (17), all summations are converted to integration form and become:
where is the Branch-cut term of APSF and usually has a finite value. While, the first term in both square brackets are divergent and its infinity should be removed. In order to remove infinities due to these two terms, the cutoff regularization technique is employed. Therefore, at the first step, the upper limit of integrals in Eq.(19) is replaced with and , respectively. Then, by calculating the integrations, we will have an answer as a function of the cutoffs and , respectively. When the cutoffs and go to infinity, the following expansion for each integral is obtained:
It can be shown that, by selecting proper values for and in the subtraction process given in Eq.(19), all of the finite and infinite terms of above expansion for integral terms will be canceled and the only remaining terms in Eq.(19) are Branch-cut terms. Thus, we have:
Unfortunately, an analytical and closed answer for the integration of above equation does not exist. Therefore, by expanding the denominator of the integrand as the following form, we have:
where and is the modified Bessel function and is Struve function. At the final step, the limit in Eq. (1) should be computed. Thus, the Casimir energy density expression after this limit becomes:
Our obtained expression in Eq. (24) is compatible with the previously reported result obtained in Refs. new.developements. (); New.Paper.On.Sphere. (). The main difference between these two works is only in applying calculation methods. It seems that selecting two similar configurations and subtracting the contributions of vacuum energy of these configurations have provided a situation in which all the infinities are completely removed. It can be also shown that, the Casimir energy density for a massless scalar field vanishes. To find the large-mass limit of the Casimir energy density, we go back to the original expression for the vacuum energy density of surface, given in Eq. (17), and we select the mass as a regulator. Then, we expand the summand in the limit and we have:
To regularize the summations, the APSF are employed. The subtraction of vacuum energies, provided by BSS, helps the infinite parts of APSF to be removed and the only remaining terms would be the Branch-cut one. Thus, we have:
In limit the first term in the both square brackets of Eq. (26) is still divergent. Adjusting the proper value for the parameter , allows the infinities to be cancelled via BSS due to these two terms. At the last step, by computing the limit the final remaining term for the Casimir energy in limit is obtained as: . In Fig. (3), we have plotted the Casimir energy density as a function of radius . In this figure, a sequence of plots for is displayed. This sequence of plots shows that the Casimir energy for massive cases converges rapidly to the massless limit when . This figure also shows that the Casimir energy values become zero, when the radius of sphere becomes infinite. This behavior for the Casimir energy is compatible with the previously reported results and it is also expected according to physical grounds new.developements. (); New.Paper.On.Sphere. ().
ii.3 Three Dimensional Spherical Surface()
In order to find the vacuum energy density of massive scalar field on a surface with topology we remind the metric of the closed Friedman model as:
where is a scale factor with dimension of length and . Additionally, is a conformal time variable and . By replacing and scalar curvature with Eq. (11), the form of equation of motion can be written as:
where is the angular part of the Laplacian operator on a sphere and . To reach the vacuum energy density of system, the canonical quantization procedure should be conducted. Hence, by solving the differential equation given in Eq. (28), we have found the orthonormal set of solutions. In the following, the field operator expanded in terms of the obtained orthonormal solutions is substituted in component of stress energy-momentum tensor. Finally, the mean value of the tensor in the initial state gives us the vacuum energy density of the system as:
where is the wave number. It should be noted that for simplicity, we have followed the calculation for static Einstein model ().
Now, to calculate the Casimir energy density, we have employed the BSS again. Therefore, as Fig. (1) shows, two similar spheres are considered and we define the Casimir energy by Eq. (1). Then, by applying the APSF given in Eq. (4) on the summation of vacuum energy, all summations would be transformed to the integration forms and we obtain:
where is the Branch-cut term. As is apparent, the first term in the square bracket of Eq. (30) is divergent. To remove its infinity, the cut-off regularization scenario would be repeated the same as what occurred for Eqs. (5,6). Therefore, we replace the upper limits of integrals in Eq. (30) with a separate cutoffs and , respectively. After calculating each integral and expanding their answers in limit , we have:
The subtraction of vacuum energies of two configurations enable us to remove all contribution of the integral terms and only the remaining terms would be the Branch-cut one. There is not a direct way for finding of analytical and closed answer for the integral of . Therefore, after expanding the denominator of integrand, we calculate it. At the last step, by computing the limit , the Casimir energy density for massive scalar field on a spherical surface with topology is obtained as:
where and the main following limits for this result are:
In Fig. (4), the Casimir energy density as a function of radius for a sequence of plots of is displayed. This plot shows that the Casimir energy for massive cases rapidly converges into the massless limit when . This behavior for the Casimir energy is compatible with the previously reported results new.developements. (); New.Paper.On.Sphere. (). The very simple elimination of divergences in BSS shows that this method is highly powerful in this task and it can be a good candidate in removal divergences in the known regularization techniques, specially for curved spaces. This method, by comparing two similar kinds of manifolds in its definition, provides sufficient degrees of freedom to adjust the cutoffs for removal process and it conceptually provides more physical grounds.
In the present paper, the Casimir energy for the massive scalar field with periodic boundary condition on the spherical surface with , and topologies were calculated. In the present calculation, procedure of the Box Subtraction Scheme (BSS) as an alternative and direct method was introduced and its various aspects were discussed. In this scheme, the Casimir energy was obtained by subtracting the vacuum energy of two similar configurations in proper limits. This subtraction in the BSS enables us to remove all divergences clearly. We maintain that subtracting the vacuum energy of a curved manifold with nontrivial topology from the vacuum energy of flat space (e.g. the Minkowski space) is irrelevant and at least has less physical meaning. Indeed, in that subtraction, two different kinds of spaces are compared with each other. In the BSS, we allow two similar kinds of vacuum energies to be compared with each other and we maintain that, this subtraction has a more physical ground than the other common definitions of the Casimir energy. The BSS also provides a directive way in calculation of the Casimir energy on spherical surface with topology in proper limit. The obtained results are consistent with expected physical grounds and also in good agreement with the previously reported results. As applying some regularization techniques like analytical continuation technique, give rise to some ambiguities in the Casimir energy calculation other.BSS.Radiative.Correction.2 (), it is hoped that the BSS as a regularization technique will be successful in reducing these sorts of ambiguities. It is also anticipated that the mentioned scheme will be useful in radiative correction to the Casimir energy in various boundary conditions on curved manifolds.
Acknowledgements.The Author would like to thank the research office of Semnan Branch, Islamic Azad University for the financial support.
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http://biostat-2008.freedownloadscenter.com/windows/
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math
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BioStat - user-friendly biology and medicine oriented statistical software. With BioStat 2008, one gets a robust suite of statistics tools and graphical analysis methods that are easily accessed though a simple interface.
Pros: BioStat 2008 is a statistical package which has a full suite of statistics tools and graphical analysis methods. This is a fairly heavy duty package that is oriented heavily to Biology and Medicine. The user interface is simplified enough for even beginners to access the full powers of the package. Somebody who knows how to use a PC can easily get by without worrying about causing errors in the analysis flow of a set of data. That leaves time for analyzing the results without worrying about if the data /analysis is error free or if the work flow was flawless. Basic features available include determining descriptive statistics, normality tests, T-test/Pagurova criterion and G-criterion, Fisher-F test, coefficient correlation and co-variation, cross tabulations and frequency table analysis. ANOVA (MANOVA and GLMANOVA) analysis is available. Non parametric statistical analysis in the following areas is accessible. These include 2x2 table analysis chi-square, Yates chi-square, Exact Fisher test, rank correlation, independent samples comparison, comparison of dependent samples and Cochran Q test. Regression analysis include multivariate linear regression, logistic regression, stepwise regression, polynomial regressions and Cox proportional hazards regression. Time series and survival analysis features are available as well.
Spreadsheet processor enables multi-sheet workbook, formula and cell classes, OLE2 support and spell checking. Data processor enables creating and transformation using formulae, matrix operations, random number generation and data sampling and the chart processor enable a set of chart creation options.
Cons: No problems noticed.
Overall: Full set of features, easy and familiar Excel like interface makes this package a 4 star one easily.
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CC-MAIN-2017-51
| 2,009 | 5 |
http://www.hoteatsandcoolreads.com/2012/11/weekly-favorites-saturday-1117-1124.html
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math
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This is a weekly series highlighting my top 6 posts every week! They might be newer posts, or oldies. Either way, you may discover something you've missed!
Top post of the week: Magic Crust Custard Pie
#2 Ham & Eggs Baked in Crispy Hashbrown Cups
#3 Apricot Fruit Tart Dessert from The Disney Channel
#4 Pumpkin Rice Pudding
#5 Creamy Baked Mac & Cheese
#6 Pumpkin Crunch Cake
If you liked these recipes, follow the Hot Eats and Cool Reads board on Pinterest here!
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120694.49/warc/CC-MAIN-20170423031200-00368-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 464 | 8 |
https://catholiccharitiesdal.org/diy-a-radical-puzzle-answer-key/
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math
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Find domain and range from a graph and an equation. Aug 31 2017 Domain and Range From a Graph PuzzleThis cut-out puzzle was created to help students practice finding the domain and range of a graph.
If the two radical expressions are equivalent you have.
A radical puzzle answer key. If you dont see any interesting for you use our search form on bottom. Free worksheetpdf and answer key on Radical Equations. Simplifying Radicals Worksheet Answer Key Inspirational Simplifying Square Puzzle Alig Simplifying Radicals Simplifying Radical Expressions Radical Expressions Free printable worksheets with answer keys on Radicals Square Roots ie no variablesincludes visual aides model problems exploratory activities practice problems and an online component.
Sudoku Puzzle 6. They arrange the top row using the given letters on the pyramid template then place each box so that its solution is the sum of the two solutions directly above it. Domain And Range Homework Answer Key.
Just click through the picture below. Print teachers key and student worksheet pages 4 – 6. An answer key to the notes is included.
Geometry g name simplifying radicals worksheet 1. Solving Radical Equations Scavenger Hunt Game Math with Tyrrell Materials Included Directions Teachers Key Student Worksheet Scavenger Hunt Problems Teacher Preparation 1. 2x 13 33 3 11.
The challenge is to solve for the variable. Sudoku Puzzle 15. K worksheet by kuta software llc.
You have two options to either tell your life story or change your life story. Only use Graphs A L for this page. Simplifying Radicals Worksheet Answer Key Inspirational Simplifying Square Puzzle Alig In 2020 Simplifying Radicals Simplifying Radical Expressions Radical Expressions.
A fun engaging activity to summarise radicals and rational exponents. This puzzle match activity requires students to match the radical form to the rational exponent form and then evaluate the radical. Exponents radicals worksheets exponents and radicals worksheets for practice.
The value of n should solve both equations. Sudoku Puzzle 9. Sudoku Puzzle 10.
122 Operations with Radical Expressions. Radical Equations Pyramid Sum Puzzle. Simplifying radicals worksheet 1 answer key.
Solving radical equations line puzzle activity one step by mrs castro s class teachers pay multi like terms combining order of operations pin brenda wheat on school pins simplifying radicals expressions crossword solve worksheet nidecmege 6 7 skills practice and inequalities answers with work ngd núcleo goiano de decoração problems free archives algebra 1 coach Solving Radical Equations. 1 answers to Set II problems p. Answer Key Identifying the Domain and Range 2.
Simplifying radical expressions answer key displaying top 8 worksheets found for this concept. Sudoku Puzzle 2. 25 scaffolded questions that start relatively easy and end with some real challenges.
On this page you can read or download gina wilson 2012 radical answer key in PDF format. Then students are given A Radical Puzzle. On this page you can read or download gina wilson a radical puzzle answer key 2012 in PDF format.
Complete answer key for Worksheet 2 Algebra I Honors. Answer key for Ch. Sudoku Puzzle 14.
Worksheets domain and range worksheets with. Make copies of the student worksheet for. For the function 01 1-3 2-4 -41 write the domain and range.
Equations that contain a variable inside of a. Gina wilson a radical puzzle answer key 2012. Simplify radicals answer key displaying top 8 worksheets found for this concept.
Sudoku Puzzle 5. Free printable worksheets with answer keys on radicals square roots ie no variables includes visual aides model problems exploratory activities practice problems and an online component. Exponential Equations Pyramid Sum Puzzle.
So we whipped one up that you can download as a PDF. Radical Equations higher. Pin On 4901 Answer Key Domain and Range Worksheet 1 NameDomain and range from a graph puzzle answer key.
Solving radical equations crossword puzzle laws of exponents cross number puzzles math education world with radicals answers tessshlo adding subtracting integers and numbers teaching resources maths word 39 best cryptic ideas evaluating expressions connect the dots resourceaholic. 8x 4 X 12 3x q Iox lax 5x x 7 428 aox 6x-30 x-5 06-5 Gx-5 36-5 G 6-5 15 Y-t-5CYY3 15 Yt3 6 solve each equation for x. Sudoku Puzzle 13.
Sudoku Puzzle 3. 911 Radical Pattern Puzzle The centre number of each square is found by using the order of operations applied to the numbers that surround it. Simplifying Radicals Worksheet Answer Key Inspirational Simplifying Square Puzzle Alig.
Practice 11 1 Simplifying Radicals Worksheet Answers In order to simplify radical expressions you need to be aware of the following rules and properties of radicals 1 from definition of n th roots and principal root. A template for them to paste their pieces down and a solution to the puzzle are included. Gallery of 20 simplifying radicals worksheet answer key.
Answers to 17-19 Set III problems. 64 22 2 2 6 1 11 xx x x x nn n n n nn You can compare the terms inside the radicals to figure out the value of n. They cut out the pieces and rearrange them so that the edges match then paste down them down in the correct order.
Xxn n 16 26 1 4 The equations are equivalent when n 5. Emphasize that each term must be multiplied by the LCD in order to have a balanced equation. No Algebraic expressions The worksheet has model problems worked out step by step.
Simplifying radicals worksheet 1 answers. Which was a Tarsia style puzzle that included simplifying radicals as well as basic radical operations without variables. Sudoku Puzzle 1.
3-1 Set III problems. 122 Operations with Radical Expressions. Answers back in to the original equation to see if the resulting values satisfy the equation.
Download gina wilson 2012 radical answer key document. It is also good practice to check the solutions when. 25 scaffolded questions that start out relatively easy and end with some real challenges.
Sudoku Puzzle — Answer Key. Click through to download this as a PDF file. The puzzle is a little tricky since there are problems on all 4 sides of the boxes.
Sudoku Puzzle 4. Sudoku Puzzle 8. Sudoku Puzzle 7.
Sep 16 2015 Domain and Range From a Graph PuzzleThis cut-out puzzle was created. Algebra Simplifying Radicals Thanksgiving Puzzle Simplifying Radicals Thanksgiving Algebra Persuasive Writing Prompts 25 scaffolded questions that start out relatively easy and end with some real challenges. This puzzle consists of 6 matches.
If you dont see any interesting for you use our search form on bottom. Practice Tests with Answer Key College Math Quick Study Guide. They write the answers in those circles then cut out each box.
Solving Radical Equations Solving equations requires isolation of the variable. Students will practice simplifying radicalsThis sheet focuses on Algebra 1 problems using real numbers. Sudoku Puzzle 11.
N64xx6 22 x This means that. Complete answer sheet for Worksheet 1 Algebra I Honors. Sudoku Puzzle 12.
They must simplify all the radicals in the puzzle. 1 Lessons 5 and 6 Set III. Complex Number Puzzle Answer Key Zip Rùa Rian Ta.
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CC-MAIN-2022-21
| 7,178 | 34 |
http://www.alko.fi/en/alko-inc/newsroom/sales-statistics/100--alcohol--what-is-it/
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math
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100 % alcohol – What is it?
Absolute alcohol, i.e. 100 % alcohol, is only a concept in statistics.
Alcoholic beverages of different percentage by volume can more easily be compared with each other by using this concept of absolute alcohol.
Litres are calculated into 100 % litres of alcohol by multiplying litres by the volume percent.
Example: 5 litres of an alcoholic beverage at 40 percent by volume equal 2 litres of absolute alcohol (5 ltr x 0,40 = 2 ltr of absolute alcohol).
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719155.26/warc/CC-MAIN-20161020183839-00182-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 483 | 5 |
https://diy.stackexchange.com/questions/77868/can-i-put-a-right-inswing-front-door-with-a-left-outswing-screen
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math
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Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Home Improvement Stack Exchange is a question and answer site for contractors and serious DIYers. It only takes a minute to sign up.
Q&A for work
Connect and share knowledge within a single location that is structured and easy to search.
Can I put a right hand swing door (Exterior) with a left out swing screen door??
Yes you can as long as there is a floor or landing on either side. There cannot be any steps at either door, where the door can swing over them.
Required, but never shown
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CC-MAIN-2022-40
| 686 | 7 |
https://www.rainbowresource.com/category/13483/Mastering-Essential-Math-Skills-Ultimate-Math-Survival-Guides-Gr.-4-8.html
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math
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Mastering Essential Math Skills Ultimate Math Survival Guides (Gr. 4-8)
For students who need more practice and review, these books cover all the basics before moving on to algebra. Using the same simple to understand format found in the Mastering Essential Math Skills Series, students will gain confidence as they master math essentials. Follow the five steps outlined in the front of each book for math success - Step 1: complete the review exercise and show your work; Step 2: introduce the new material using "Helpful Hints"; Step 3: work the two sample problems together (student & parent/teacher), then the student works independently; Step 4: go through the "Problem Solving" section and explain key words and strategies, then let the student solve the problem; Step 5: correct the work using solutions in the back of each book.
Ultimate Math Survival Guide, Part 1 includes whole numbers, integers, fractions, decimals, and percents. Ultimate Math Survival Guide, Part 2 includes geometry, problem solving, graphs, and pre-algebra topics. Each section in each book end with review and a test to check proficiency. Each book is 240+ pages and would work well for test prep, a summer refresher or extra practice and review. ~ Donna
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| 1,238 | 3 |
https://www.pharmacy-tech-study.com/business-percentage-math.html
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math
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Business Percentage Math
How do I calculate the tax rate if the cost of the product is $69.99 and the total cost of the product after tax is $75.94?
Reply (by Keith)
This throws everyone off at first.
In this case, what you're trying to do is figure what percentage the higher number is of the lower number. Obviously it will be over 100% of that number since it's larger. Therefore, the amount over the first 100% is the "extra" and that will be the "rate" you are trying to determine.
75.94 ÷ 69.99 = 1.085
(now what is behind the one?)
So 8.5% is the tax rate
Another way to think about it to ask:
"how many times does 69.99 go into 75.94?
Which it does 1.085 times?"
Click here to post comments.
Join in and write your own page! It's easy to do. How?
Simply click here to return to Pharmacy math questions.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.23/warc/CC-MAIN-20231203125921-20231203155921-00176.warc.gz
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CC-MAIN-2023-50
| 811 | 14 |
https://forum.arduino.cc/t/adxl345-units/272207
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math
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So i believe I am in +-2g mode and when held flat the x,y,z output is ~~ 0,0,256 respectively, what are the exact units of these and how could i convert these to degrees, thank you for helping
What does the ADXL345 datasheet state for “sensitivity”?
It looks like it is in LSB/g ?
or also just plain g, which i know is the force of gravity, so if that was so, why would it be 256? its not like im taking these measurements on the sun haha.
Oh i understand, the LSB is the factor that the force of gravity is multiplied, which makes sense because the setting i am in has a LSB of 256 which is what i am getting for the force of gravity, thank you!!
The light clicks on!
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| 672 | 6 |
https://forums.oldtimersguild.com/t/the-quantum-age-of-computers/7122
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math
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A couple years ago I started reading articles on Quantum Computers, I was also reading articles on Encryption. Below is a article I just read about the computers and its speed. I will give you a real life example. Quantum speed
The article that concerned me was the 2 month window that some people were able to crack a latest and greatest computer encryption. What does that mean for a quantum computer example Google said that the D-Wave which sells for 15 million is at 10,000 timers faster then the normal PC. So that encryption that took 2 months to break theoretically would be broken in 8.64 minutes. That is the Last years computer the newest Google and NASA estimate the new ones which have up to 1000+ quibits would be 100 million times faster then the typical PC. That so called encryption which took 2 months to crack is broken in .021 seconds. Take care all I think i bury my money in the back yard. Just joking but some hackers do not care.
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CC-MAIN-2022-27
| 953 | 2 |
https://www.geniuspack.com/products/compression-packing-cubes?variant=13921115013175
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math
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Set of 3 compression cubes- small, medium, large. You'll be amazed by how much you can compress in these cubes! Organize your contents and compress to maximize what your capacity. With it's unique stretch-top mesh, it compresses the contents more than you can imagine. We had our CEO experiment & try to fit 13 dress shirts into the large cube, and they all fit! Really great to organize and customize the way you pack. Ask a question on this product.
For best results fold the size of the bag and tug and press to zip
Hi ! Today just got my Genius pack supercharged in rose gold and packing cubes in red! Thank you so much esp for the next day air shipping , I’m honor to have my own Genius pack, yay ! Thank you to the Team for your hard work . I’ll take care of it . I’m packing now lol! ##proudowner##functional##exceptional##GenuisPack##lovesTravels##organize##
I used the compression packing cubes during my last trip for the very first time! I only use the smaller one in the medium one. It made my packing much more organized and I was able to live out of my suitcase partially rather than unpack. I would highly recommend them!
Having used compression cubes for years when I travel, I have enjoyed the organization they provide. So I recently bought two packs of compression cubes that I plan on giving as holiday presents. I know my traveling friends will enjoy them.
Genius Products all provide great reliable travel items at a reasonable price. Our carry one, back of the seat bag are our go items, my saying, don’t leave home without them
Thanks to these handy compression cases - a carry on will do just fine for my 4 day trip. Easy to pack and just as easy to store once trip is done.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587719.64/warc/CC-MAIN-20211025154225-20211025184225-00006.warc.gz
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CC-MAIN-2021-43
| 1,707 | 7 |
http://www.gate2017exam.com/basic-engineering-mathematics-john-bird-5th-edition-pdf
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math
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John Bird’s Basic Engineering Mathematics book is a very good book to learn all the basics of Mathematics from Basic arithmetics, fractions, decimals to the integration and differentiation. This book has a total of 35 chapters extensively covering all the topics of Mathematics explained from the basic level. Here is the Basic Engineering Mathematics John Bird 5th Edition PDF book. You can view/download the Book from the below-given link. Note that solutions of practice exercises are found at the end of the book.
Basic Engineering Mathematics John Bird 5th Edition PDF
Useful Links for other books:
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With one click you can share Basic Engineering Mathematics John Bird 5th Edition PDF with your friends. Stay tuned to receive Gate 2017 updates @gate2017exam.com. ( Book mark the page with Ctrl+D )
NOTE: All the pdf documents which put here are Freely distributed if you feel anything as inappropriate then do let us know we’ll remove them from this site.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945037.60/warc/CC-MAIN-20180421051736-20180421071736-00215.warc.gz
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CC-MAIN-2018-17
| 1,047 | 6 |
https://encyclopediaofmath.org/index.php?title=Reductive_group&oldid=12805
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math
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A linear algebraic group (over an algebraically closed field ) that satisfies one of the following equivalent conditions: 1) the radical of the connected component of the unit element of is an algebraic torus; 2) the unipotent radical of the group is trivial; or 3) the group is a product of closed normal subgroups and that are a semi-simple algebraic group and an algebraic torus, respectively. In this case is the commutator subgroup of and coincides with the radical of as well as with the connected component of the unit element of its centre; is finite, and any semi-simple or unipotent subgroup of the group is contained in .
A linear algebraic group is called linearly reductive if either of the two following equivalent conditions is fulfilled: a) each rational linear representation of is completely reducible (cf. Reducible representation); or b) for each rational linear representation and any -invariant vector there is a -invariant linear function on such that . Any linearly reductive group is reductive. If the characteristic of the field is 0, the converse is true. This is not the case when : A connected linearly reductive group is an algebraic torus. However, even in the general case, a reductive group can be described in terms of its representation theory. A linear algebraic group is called geometrically reductive (or semi-reductive) if for each rational linear representation and any -invariant vector there is a non-constant -invariant polynomial function on such that . A linear algebraic group is reductive if and only if it is geometrically reductive (see Mumford hypothesis).
The generalized Hilbert theorem on invariants is true for reductive groups. The converse is also true: If is a linear algebraic group over an algebraically closed field and if for any locally finite-dimensional rational representation by automorphisms of a finitely-generated associative commutative -algebra with identity the algebra of invariants is finitely generated, then is reductive (see ).
Any finite linear group is reductive and if its order is not divisible by , then it is also linearly reductive. Connected reductive groups have a structure theory that is largely similar to the structure theory of reductive Lie algebras (root system; Weyl group, etc., see ). This theory extends to groups where is a connected reductive group defined over a subfield and is the group of its -rational points (see ). In this case the role of Borel subgroups (cf. Borel subgroup), maximal tori (cf. Maximal torus) and Weyl groups is played by minimal parabolic subgroups (cf. Parabolic subgroup) defined over , maximal tori split over , and relative Weyl groups (see Weyl group), respectively. Any two minimal parabolic subgroups of that are defined over are conjugate by an element of ; this is also true for any two maximal -split tori of .
If is a connected reductive group defined over a field , then is a split group over a separable extension of finite degree of ; if, in addition, is an infinite field, then is dense in in the Zariski topology. If is a reductive group and is a closed subgroup of it, then the quotient space is affine if and only if is reductive. A linear algebraic group over a field of characteristic 0 is reductive if and only if its Lie algebra is a reductive Lie algebra (cf. Lie algebra, reductive). If , this is also equivalent to being the complexification of a compact Lie group (see Complexification of a Lie group).
|||T.A. Springer, "Invariant theory" , Lect. notes in math. , 585 , Springer (1977)|
|||J.E. Humphreys, "Linear algebraic groups" , Springer (1975)|
|||A. Borel, J. Tits, "Groupes réductifs" Publ. Math. IHES , 27 (1965) pp. 55–150|
|||V.L. Popov, "Hilbert's theorem on invariants" Soviet Math. Dokl. , 20 : 6 (1979) pp. 1318–1322 Dokl. Akad. Nauk SSSR , 249 : 3 (1979) pp. 551–555|
Reductive group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reductive_group&oldid=12805
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CC-MAIN-2022-21
| 3,967 | 10 |
http://skillgun.com/honeywell/placement-papers
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math
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honeywell placement papers - skillgun
In software company done one application in which Program solve 2 errors in every second. Approximately how many seconds will it need to Solve 40 errors?
Time taken to solve 2 errors is 1 second.
Time taken to solve 40 errors,
Here error is directly proportional to time.
= (40 / 2)1
So time taken to solve 40 errors in 20 seconds
The speed of two connected wheels of a car are inversely proportional to their diameters. A wheel with a diameter of 6 cm and speed of 40 rpm is connected to a wheel of 8 cm diameter. What is the speed of the second wheel?
One wheel with a diameter of 6 cm and a speed of 40 rpm.
The other wheel is with 8 cm in diameter.
Given that the speed of the wheel is inversely proportional to diameters.
? = 6 x 40 / 8 = 30.
If 12 students write 600 answers for Questions in 8 hours. Then how many students will be required to write 200 files in 4 hours ?
12 students write 600 answers in 8 hours then 200 answers in 4 hours how many students require i.e 12/x=600/200=8/4 =>12/x *600/200 * 8/4 =>x=3
Jeeva weighs twice as much as Manoj. Monohar's weight is 60% of Brijesh's weight. Drona weight 50% of lakshman's weight. Lakshman weight 190% of Jeeva's weight. Which of these 5 persons weight the least?
Jeeva is the least person because from him every one's weight is calculated then take the information
In a 200m race, if Raghava gives Sridhar a start of 25 metres, then Raghava wins the race by 10 seconds. Alternatively, if Raghava gives Sridhar a start of 45 metres the race ends in a dead heat. How long does Raghava take to run 200m?
In a Narayana College,In 120 students, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?
Total 80 i.e 60+12+8=80 and remaining 40
200 candidates who were interviewed for a position of Government Servent,100 had own houses, 70 had Four wheeler and 140 had Two wheeler. 40 of them had both, a Own houses and a four wheeler, 30 had both, a Four wheeler and a two wheeler and 60 had both, a Own house and Two wheeler and 10 had all three. How many candidates had none of the three?
By using the venn diagram we get the answer
p and q are the lengths of the base and height of a right angled triangle whose hypotenuse is h. If the values of p and q are positive integers, which of the following cannot be a value of the square of the hypotenuse?
According to pythogorous theorem p2+q2=h2. so if p and Q are positive integers then 23 is not satisfy number for hypotenuse
The machanary cost of a certain factory Rs. 500,000. If it decreases in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of ten years, all percentages applying to the original cost?
Sum of all the percentages upto 10 years is 82.5.So 82.5 % of 500000 is 412500 So answer is 87500
Rajesh can do half of certain work in 12 days ,Suresh and Rajesh together complete the remaining work in four days.Then the time taken to complete the whole work by Suresh alone is:?
There are four parties X,Y,Z,M .Sagar told that either X or Y will win.Sanjay told Z will never win.Hari told either Y or Z or M will win.Only one of them was correct.Which party won?
In Olympics,how many matches are played in the tournment,if 50 players pariticipated in the tournament ?
Total 49 matches are conducted
In a college six students can speak tamil, 15 can speak telugu and 6 can speak Kannada. If two students can speak two languages and one student can speak all the three languages, then how many students are there in the class?
Total 22 students by using venn diagram
If '+' means '*', '-' means '/' , '/' means '+' and '*' means '-' , then what will the value of 20/ 40 – 4 * 5 +6 ?
Here 20+40/4-5*6 i.e 0
A Volley Ball championship is played on a knock-out basis,i.e, a player is out of the tournament when he loses a match.How many players participate in the tournament if 127 matches are totally played ?
Win' is related to 'Competition' in the same way as 'Invention' is related to?
No matching Word.because invitation is related to function
In a certain code language,
i')ryda nokw' means 'Clear water'
ii')Sin gola' means 'Overcast moon'
iii)'Sin saf nokw' means 'Clear white moon'
Which word in that code language means 'white'?
According to given information white is saf
The balls in a basket become double after every minute. In one hour, the basket becomes full. After how many minutes, the basket would be half-filled?
By given information every on minute balls are double .so 60 minutes basket is full.So we decrease the minute the basket is half filled (one ninute =double balls).So it takes 59 minutes
There are seven persons up on the ladder. 'Anil' is further up than 'Eshwar' but is lower than 'Chaitanya', 'Bheema' is in the middle. 'Giri' is between 'Anil' and 'Bheema'. 'Eshwar' is between 'Bheema' and 'Firoz'. If 'Firoz' is between 'Bheema' and 'Dhanoj', then the person on the top of the ladder will be ?
Here Chaitanya is the answer because the order is Chaitanya,Anil,Giri,Bheema,Eshwar,Firoz,Dhanoj
Raju proceeding towards North and then take a turn to my right. After some time take a turn to left and again to left. Then Raju go to right. After some distance again turn towards right. The direction in which Raju moving now ?
By given information Raju moving East side
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CC-MAIN-2018-39
| 5,473 | 49 |
http://mathforum.org/library/drmath/view/58969.html
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math
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Total Number of Pupils
Date: 03/21/2001 at 04:15:54 From: Vandana Subject: Fractions Dear Dr Math, Here maths is taught by drawing models. However, I face a problem trying to make my son understand using the model method when the problem can be solved algebraically. Here goes, In a class 5/8 of the pupils are boys. There are 8 more boys than girls. What is the total number of pupils in the class.
Date: 03/21/2001 at 12:49:35 From: Doctor Peterson Subject: Re: Fractions Hi, Vandana. I often wish I could just tell kids all about algebra, when I see a problem like this that is so easy that way; but on the other hand I find it an interesting challenge to find a "primitive" way to solve a problem, and then look back and see how that solution is related to the algebra. I can see a couple of ways to approach this without algebra. One is to note that if 5/8 are boys and 3/8 are girls, then the difference between the number of boys and the number of girls is 2/8 of the total. Since this is 8, the total must be 4 times as many, or 32. You might draw it this way: +---+---+---+---+---+---+---+---+ | boys | girls | +---+---+---+---+---+---+---+---+ +---+---+---+---+---+ | girls | | +---+---+---+---+---+ \_____/ 8 We don't know how many students each eighth (little box) represents, but by subtracting the girls from the boys we know that the difference is two of them. Since that is 8, each box represents 4 students, and the total is 32. I would probably want to introduce an algebraic method of some sort, depending on your son's age, to show that we can avoid all this ad-hoc thinking (which is how all problems had to be solved before algebra was invented) by using symbols for the unknown, instead of pictures. But I would also want to model it in some way (even if AFTER solving it by algebra), in order to build a clear understanding of what is going on behind the symbols. Too much abstract math too early can detract from the basic feel for numbers, and for fractions in particular. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891377.59/warc/CC-MAIN-20180122133636-20180122153636-00566.warc.gz
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CC-MAIN-2018-05
| 2,160 | 6 |
http://mathhelpforum.com/calculus/135539-approximate-area-under-curve-y-2x-x-2-x-1-x-2-a.html
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math
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approximate the area under the curve from x=1 to x=2
a) using 4 equal inscribed rectangles
b) using 4 equal circumscribed rectangles
Nothing to it but to do it!
1) "equal" probably means equal length of the bases. The heights will be different.
2) Draw the bases [1.00,1.25][1.25,1.50][1.50,1.75][1.75,2.00]
3) Draw verticals at each of the five points, x = 1.00, 1.25, 1.50, 1.75, 2.00
3) Draw horizontals at each point where the the verticals intersect the graph. Extend the verticals, if necessary, until you have the four rectangles.
4) It really should be kind of obvious how to proceed form here. Just decide which side of the rectangle to use for inscribed and circumscribed.
Let's see what you get.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120461.7/warc/CC-MAIN-20170423031200-00483-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 706 | 10 |
https://www.nagwa.com/en/lessons/974180476798/
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math
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Lesson: Argand Diagrams
In this lesson, we will learn how to identify complex numbers plotted on an Argand diagram and discover their geometric properties.
Sample Question Videos
Worksheet: 17 Questions • 1 Video
If the number is represented on Argand diagram by the point , determine the Cartesian coordinates of that point.
Using the Argand diagram shown, find the value of .
Given that points and represent the complex numbers and on an Argand diagram, then is the image of under which transformation?
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s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528141.87/warc/CC-MAIN-20190722154408-20190722180408-00212.warc.gz
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CC-MAIN-2019-30
| 506 | 7 |
http://tjleone.com/match_fraction_circles.htm
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math
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Patterns and Design
Match Fraction Circles
Age: 4 & up
Prerequisites: Launching and quitting an application; clicking and dragging; counting with red and blue rods.
Screen objects: Ten circles down left side of screen. First circle is undivided, second circle is divided into two equal halves, third circle is divided into three equal thirds, etc. At bottom of screen are ten matching circles placed in random order. All of these circles are colored red to match the physical fraction circles. Next to the left hand column is another column of circles. These circles are simply red outlines.
Presentation: (Individual or small group)
Variations: Matching the physical fraction circles to a physical chart with divided circles on it, counting sectors as they put them over corresponding circles in chart. Matching fraction circles to number rods by laying sectors on top of rod segments. Matching circles of various sizes by number of sectors.
Extensions: Sectors and numerals matching.
Points of Interest: Sticky buttons stay pressed when clicked. Marking items as they are counted. A whole is equal to the sum of its parts (a whole with more parts is not necessarily bigger than a whole with fewer parts). First exposure to angles represented as sectors.
Control of Error: System responds by counting sectors when circle is placed in outline (darkening them and counting out loud). If count does not match number of sectors in circle to its left, the circle falls back down to the bottom of the screen.
Direct Aims: Practice in counting.
Indirect Aims: Preparation for recognition of external angles of regular polygons.
Software Affordance: The counting of the number rods requires teacher verification. This exercise uses control of error to support the child's autonomy.
Software Constraints: The sectors of the fraction circles cannot be removed from the circles. The sectors and circles cannot be rotated.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474674.35/warc/CC-MAIN-20240227085429-20240227115429-00565.warc.gz
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CC-MAIN-2024-10
| 1,911 | 14 |
http://cvgmt.sns.it/paper/347/
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math
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Inserted: 29 jul 2003
Last Updated: 19 jan 2005
Journal: Ann. Inst. H. Poincaré
We consider a new class of quasilinear elliptic equations with a power-like reaction term: the differential operator weights partial derivatives with different powers, so that the underlying functional-analytic framework involves anisotropic Sobolev spaces. Critical exponents for embeddings of these spaces into $L^q$ have two distinct expressions according to whether the anisotropy is ``concentrated'' or ``spread out''. Existence results in the subcritical case are affected by this dichotomy. On the other hand, nonexistence results are obtained in the at least critical case in domains with a geometric property which modifies the standard notion of starshapedness.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826715.45/warc/CC-MAIN-20181215035757-20181215061757-00070.warc.gz
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CC-MAIN-2018-51
| 752 | 4 |
https://projecteuclid.org/journals/journal-of-the-mathematical-society-of-japan/volume-56/issue-3/The-joint-universality-of-twisted-automorphic-L-functions/10.2969/jmsj/1191334092.full
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math
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The simultaneous universality of twisted automorphic -functions, associated with a new form with respect to a congruence subgroup of and twisted by Dirichlet characters, is proved. Applications to the functional independence and the zero density of linear combinations of those -functions are given.
Antanas LAURINČIKAS. Kohji MATSUMOTO. "The joint universality of twisted automorphic -functions." J. Math. Soc. Japan 56 (3) 923 - 939, July, 2004. https://doi.org/10.2969/jmsj/1191334092
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224657720.82/warc/CC-MAIN-20230610131939-20230610161939-00247.warc.gz
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CC-MAIN-2023-23
| 488 | 2 |
http://serc.carleton.edu/sp/cause/activitiesbrowse.html?q1=sercvocabs__43%3A411
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math
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Subject: Statistics Show all Subject: Statistics
Results 1 - 8 of 8 matches
An In-Class Experiment to Estimate Binomial Probabilities part of Testing Conjectures:Examples
This hands-on activity asks students to conduct a binomial experiment and calculate a confidence interval for the true probabiity. It is useful for involving students, and for having a discussion about the interpretation of confidence intervals and the role of sample size in estimation.
Simulating a P-value for Testing a Correlation with Fathom part of Teaching with Data Simulations:Examples
This activity has students use Fathom to test the correlation between attendance and ballpark capacity of major league baseball teams by taking a sample of actual data and scrambling one of the variables to see how the correlation behaves when the variables are not related. After displaying the distribution of correlations for many simulated samples, students find an approximate p-value based on the number of simulations that exceed the actual correlation.
Body Measures: Exploring Distributions and Graphs Using Cooperative Learning part of Cooperative Learning:Examples
This lesson is intended as an early lesson in an introductory statistics course. The lesson introduces distributions, and the idea that distributions help us understand central tendencies and variability. Cooperative learning methods, real data, and structured interaction emphasize an active approach to teaching statistical concepts and thinking.
How well can hand size predict height? part of Cooperative Learning:Examples
This activity is deigned to introduce the concepts of bivariate relationships. It is one of the hands-on activities of the ‘real-time online hands-on activities’. Students collect their own data, enter and retrieve the data in real time. Data are stored in the web database and are shared on the net.
Statistics and Error Rates in Death Penalty Cases part of Cooperative Learning:Examples
Psychic test part of Interactive Lectures:Examples
Show relative frequency converging to true probability by testing the psychic ability of your students.
Judging Randomness part of Inventing and Testing Models:Examples
This model-eliciting activity has students create rules to allow them to judge whether or not the shuffle feature on a particular iPod appears to produce randomly generated playlists. Because people's ...
Seeing and Describing the Predictable Pattern: The Central Limit Theorem part of Testing Conjectures:Examples
This activity helps students develop a better understanding and stronger reasoning skills about the Central Limit Theorem and normal distributions. Key words: Sample, Normal Distribution, Model, Distribution, Variability, Central Limit Theorem (CLT)
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s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860116929.30/warc/CC-MAIN-20160428161516-00086-ip-10-239-7-51.ec2.internal.warc.gz
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CC-MAIN-2016-18
| 2,745 | 17 |
https://oculo-facial-surgery.info/and-relationship/relation-b-enthalpy-and-entropy-relationship.php
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math
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The Difference Between Entropy and Enthalpy in Thermodynamics
Entropy and enthalpy are two important properties of a thermodynamic system. Though they are different from one another, they are related. In statistical mechanics, entropy is an extensive property of a thermodynamic system. Not to be confused with Enthalpy. .. It is also known that the work produced by the system is the difference between the heat .. observer B can cause an effect that looks like a violation of the second law of thermodynamics to observer. we'll study free energy (G) and its relationship to enthalpy, entropy and The Gibbs free energy equation we will be working with is Delta or.
According to this equation, an increase in the enthalpy of a system causes an increase in its entropy. In chemistry, thermodynamics refers to the field that deals with heat and energy of a system and the study of energy change of a system. Enthalpy and entropy are thermodynamic properties. Entropy Enthalpy, denoted by the symbol 'H', refers to the measure of total heat content in a thermodynamic system under constant pressure.
Enthalpy is calculated in terms of change, i. The SI unit of enthalpy is joules J.
thermodynamics - Difference between heat capacity and entropy? - Physics Stack Exchange
Entropy, denoted by the symbol 'S', refers to the measure of the level of disorder in a thermodynamic system. Entropy is calculated in terms of change, i.
Let us look into these two thermodynamic properties in greater detail. It can be defined as the total energy of a thermodynamic system that includes the internal energy. Furthermore, for a homogeneous system, it is the sum of internal energy E of a system and the product of the pressure P and volume V of the system.
Enthalpy cannot be measured directly. Thus, a change in enthalpy that can be measured is considered. Enthalpy is a state function and it is dependent on the changes between the initial and the final state i.
What is the relationship between enthalpy and entropy?
Thus, the enthalpy change is important. There are two types of chemical reactions; namely, exothermic and endothermic. Exothermic reactions are those in which there is a release of heat. In this case, energy is given out to the surroundings. The energy required for the reaction to occur is less than the total energy released.
Furthermore, the enthalpy of the products is lower than the enthalpy of the reactants. Endothermic reactions are those in which there is an absorption of heat. In this case, energy is absorbed from its surroundings in the form of heat. Definitions and descriptions[ edit ] Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension.
Historically, the classical thermodynamics definition developed first. In the classical thermodynamics viewpoint, the system is composed of very large numbers of constituents atoms, molecules and the state of the system is described by the average thermodynamic properties of those constituents; the details of the system's constituents are not directly considered, but their behavior is described by macroscopically averaged properties, e.
The early classical definition of the properties of the system assumed equilibrium. The classical thermodynamic definition of entropy has more recently been extended into the area of non-equilibrium thermodynamics. Later, the thermodynamic properties, including entropy, were given an alternative definition in terms of the statistics of the motions of the microscopic constituents of a system — modeled at first classically, e.
- The Difference Between Entropy and Enthalpy in Thermodynamics
Newtonian particles constituting a gas, and later quantum-mechanically photons, phononsspins, etc. The statistical mechanics description of the behavior of a system is necessary as the definition of the properties of a system using classical thermodynamics becomes an increasingly unreliable method of predicting the final state of a system that is subject to some process.
Function of state[ edit ] There are many thermodynamic properties that are functions of state. This means that at a particular thermodynamic state which should not be confused with the microscopic state of a systemthese properties have a certain value.
Often, if two properties of the system are determined, then the state is determined and the other properties' values can also be determined. For instance, a quantity of gas at a particular temperature and pressure has its state fixed by those values and thus has a specific volume that is determined by those values. As another instance, a system composed of a pure substance of a single phase at a particular uniform temperature and pressure is determined and is thus a particular state and is at not only a particular volume but also at a particular entropy.
In the Carnot cycle, the working fluid returns to the same state it had at the start of the cycle, hence the line integral of any state function, such as entropy, over this reversible cycle is zero. Reversible process[ edit ] Entropy is conserved for a reversible process.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540501887.27/warc/CC-MAIN-20191207183439-20191207211439-00485.warc.gz
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CC-MAIN-2019-51
| 5,226 | 18 |
https://aramuseum.org/what-is-the-sin-of-45-degrees/
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math
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In trigonometry, there room three primary ratios, Sine, Cosine and Tangent, which are used to uncover the angles and also length that the right-angled triangle. Prior to discussing Sin 45 degrees, let us know the prominence of Sine function in trigonometry. Sine role defines a relation in between the acute angle of a right-angled triangle and the opposite side to the angle and also hypotenuse. Or you can say, the Sine of angle α is equal to the proportion of the contrary side(perpendicular) and also hypotenuse the a right-angled triangle.
You are watching: What is the sin of 45 degrees
The trigonometry ratios sine, cosine and tangent for an edge α space the primary functions. The worth for sin 45 degrees and other trigonometry ratios for all the degrees 0°, 30°, 60°, 90°,180° are typically used in trigonometry equations. These values are straightforward to remember through the aid trigonometry table, which will additionally be listed in this article.
Let united state discuss first discuss sin 45 levels value, here in this article.
Sin 45 degree Value
Let us consider a right-angled triangle △ABC. Thus, the sine of angle α is a ratio of the length of the contrary side,BC to the angle α and also its hypotenuse AB.
Sin α = (fracOpposite SideHypotenuse)= (fracPerpendicularHypotenuse)= BC/AB
So, sin 45 levels trigonometry value, in-fraction will be, sin 45° = (fracPerpendicularHypotenuse)A simple method by method of i m sorry we have the right to calculate the worth of sine ratios for all the degrees is questioned here. After finding out this method, you can conveniently calculate the worths for all other trigonometry ratios. So, let’s begin to calculate the worth for sin 45 degrees table that trigonometry.
Sin 0°= (sqrt0/4) = 0
Sin 30° = (sqrt1/4) = ½
Sin 45° = (sqrt2/4) = (1/sqrt2)
Sin 60°= (sqrt3/4) = (sqrt3/2)Sin 90° = (sqrt4/4) = 1
Therefore, Sine ratio table for both degrees and also radians can be composed as;
|Sine 30° or Sine π/6||1/2|
|Sine 45° or Sine π/4||(1/sqrt2)|
|Sine 60°or Sine π/3||(sqrt3/2)|
|Sine 90° or Sine π/2||1|
|Sine 120° or Sine 2π/3||(sqrt3/2)|
|Sine 150° or Sine 5π/6||1/2|
|Sine 180° or Sine π||0|
|Sine 270° or Sine 3π/2||-1|
|Sine 360°or Sine 2π||0|
In the exact same way, us can discover the values for various other trigonometry ratios such as cosine and tangent. Right here we are providing you the table because that sine, cosine and also tangent ratios.
See more: Megaman Battle Network 3 White Styles Faq, Style Change (Mmbn3)
Learn more about trigonometric ratios and also formulas and also identities and also download BYJU’S-The Learning app for a much better experience.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362919.65/warc/CC-MAIN-20211203212721-20211204002721-00208.warc.gz
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CC-MAIN-2021-49
| 2,682 | 25 |
https://www.informatyka.agh.edu.pl/en/blog/krakow-quantum-informatics-seminar-kqis-28/
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math
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Department of Computer Science AGH and IBM Software Laboratory in Krakow invite to Krakow Quantum Informatics Seminar (KQIS)
• understand and discuss current problems in quantum informatics,
• discuss new quantum computing technologies,
• exchange ideas and research results,
• integrate information across different research teams,
• build a community around quantum informatics.
Venue: via Internet, Webex
Tuesday, 16th of June, 2020, 9:30-11:00
Paweł Topa, Department of Computer Science, AGH Krakow
Topic: When the asymmetric cryptography will be outdated?
We expect the large quantum computers fully operational not only with hope but also with a great fear. The most famous algorithm for quantum computers, i.e. the Shore algorithm, will break the most famous algorithm asymmetric cryptography called RSA in a few minutes instead of several centuries.
In my presentation, I will present the RSA algorithm and other asymmetric cryptography algorithms as well role they plays in the modern world. I will explain what tactics Shore proposed to the factorization of integer numbers problem. And quantum computer scientists will already know to proceed ...
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511055.59/warc/CC-MAIN-20231003060619-20231003090619-00234.warc.gz
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CC-MAIN-2023-40
| 1,168 | 12 |
https://anstutors.com/solution/the-current-exchange-rate-regime-is-sometimes-described/
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math
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The current exchange-rate regime is sometimes described as a system of managed floating exchange rates, but with some blocs of currencies that are tied together.
a. What are the two major blocs of currencies that are tied together?
b. What are the major currencies that float against each other?
c. Given the discussion in this chapter and the previous chapters of Part III, how would you characterize the movements of exchange rates between the U.S. dollar and the other major currencies since the shift to managed floating in the early 1970s?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358786.67/warc/CC-MAIN-20211129164711-20211129194711-00148.warc.gz
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CC-MAIN-2021-49
| 544 | 4 |
https://23is-back.com/comfortcolors-com.html
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math
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We invite you to live life in Comfort Colors®. Comfort Colors® USA has your soft and comfortable pure cotton tees, tanks & sweats.###
Comfort Colors. 13,865 likes · 7 talking about this. At Comfort Colors® we offer comfortable clothing designed with a nature-inspired color palette that satisfies the soul. Visit us at:...###
The quantity you entered is greater than the available inventory. Custom hemmed pants cannot be backordered online. Please select inventory from our other warehouses to satisfy your request or call the Customer Care Center at (800) 426-6399.Thank you.###
1,746 Followers, 15 Following, 92 Posts - See Instagram photos and videos from Comfort Colors (@comfort_colors)###
Comfort Colors T-Shirts blanks at wholesale prices. Bulk discounts but no minimum order requirement to buy from BlankShirts.com###
The Comfort Colors brand is the epitome of style, flexibility, and - you guessed it - comfort. Check out ShirtSpace's wholesale selection of Comfort Colors styles today!
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738555.33/warc/CC-MAIN-20200809132747-20200809162747-00212.warc.gz
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CC-MAIN-2020-34
| 1,000 | 6 |
https://www.jiskha.com/display.cgi?id=1331727282
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math
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posted by Vivian .
Mia is stacking copies of a new book in a square-pyramid display by the front window of her bookstore. for each consecutive layer, she places one book where four meet.
A. I the bottom row of the display has 144 books and there is one book on the top, determine how many rows of books are in her pyramid.
B. Explain how to find the total number of books in the display.
C. If she removes the top four rows, how many books are left in the pyramid display?
You might want to make a sketch to show that the bottom level is a 12 by 12 square
the second level is a 11 by 11 square, etc
So your sum is 12^2 + 11^2 + 10^2 + ... 2^2 + 1^2
you could just add up these numbers to get 650
or you could use a formula that says
the sum of squares of consecutive numbers from 1 to n is
n(n+1)(2n+1)/6 which gives us 650
for the last part, find the sum of books removed at the top and subtract that from 650
btw, did you realize that the books would have to be square in shape?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886107490.42/warc/CC-MAIN-20170821041654-20170821061654-00231.warc.gz
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CC-MAIN-2017-34
| 980 | 14 |
https://boardgamegeek.com/thread/549288/tracking-turns
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math
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Joshua 龙海峰 Hockaday
常常在三台，绵阳 (Santai, Mianyang) 有时候在成都(Chengdu)
My buddy and I have been learning to play SGBoH. We have run into many different rules questions, and one of them is concerning Turns. How do you properly keep track of turns when a side can Seize the turn?
This is the only thing I can come up with: Keep track of each sides' number of turns separately.
Red, blue, R, R (Seized), b, R, b, R, R(Seized), b, R, b, R, R (Seized), b, R, b
10 Red turns, 7 Blue turns.
As you see Red has Seized multiple times, and is now 3 turns ahead in number of turns they have actually played.
Looking at one scenario I see that one side (Red) actually has the capacity to have 11 more turns than their opponents (Blue) (that is assuming Red successfuly Seize all of their attempts, and Blue either fail every attempt or don't make any attempts to Seize, not likely but possible.) In this scenario if both Red and Blue successfully Seize all of the attempts they are given, Red will have 6 more turns than Blue.
So keeping track of the actual number of turns each side has taken seems reasonable. For instance a victory condition from one scenario states: "Macedonians have 20 Macedonian turns to rout the Triballian army."
As I see it the only way to REALLY know how many Macedonian turns have been taken it to track them individually.
Is this correct, or have I gone way off track?
- Last edited Sun Aug 1, 2010 1:10 pm (Total Number of Edits: 1)
- Posted Sun Aug 1, 2010 1:09 pm
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646189.21/warc/CC-MAIN-20180319003616-20180319023616-00322.warc.gz
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CC-MAIN-2018-13
| 1,511 | 13 |
https://maths.anu.edu.au/news-events/events/counterexamples-high-degree-analogues-schrodinger-maximal-operator
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math
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Counterexamples for high-degree analogues of the Schrödinger maximal operator
The partial differential equations and analysis seminar is the research seminar associated with the applied and nonlinear analysis, and the analysis and geometry programs.
Abstract: In 1980 Carleson posed a question on the minimal regularity of an initial data function in a Sobolev space that implies pointwise convergence for the solution of the linear Schrödinger equation. After progress by many authors, this was recently resolved (up to the endpoint) by Bourgain, whose counterexample construction for the Schrödinger maximal operator proved a necessary condition on the regularity, and Du and Zhang, who proved a sufficient condition. In this talk we describe how Bourgain’s counterexamples can be constructed from first principles. Then we describe a new flexible number-theoretic method for constructing counterexamples, which proves a necessary condition for high-degree analogues of the Schrödinger maximal operator to be bounded from $H^s$ to local $L^1$.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100308.37/warc/CC-MAIN-20231201215122-20231202005122-00175.warc.gz
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CC-MAIN-2023-50
| 1,051 | 3 |
https://www.kingfisherbeerusa.com/what-is-scattering-of-light-explain-with-example/
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math
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What is scattering of light explain with example?
When light passes through atmosphere, it is first adsorbed by air molecules, dust particles, smoke and water droplets and then re-radiated in various directions. This phenomenon is called scattering of light. Examples of scattering of light. Sun looks red at sunset and sunrise. Sky looks dark to astronomers.
What is the difference between phase shift and horizontal shift?
When the value B = 1, the horizontal shift, C, can also be called a phase shift, as seen in the diagram at the right. The easiest way to determine horizontal shift is to determine by how many units the “starting point” (0,0) of a standard sine curve, y = sin(x), has moved to the right or left.
How does phase shift keying work?
In phase shift keying the digital bit sequence is first converted to NRZ bipolar signal which directly modulates the carrier wave. The peak of the carrier wave is represented as A when the load resistance is assumed to be 1 ohm as standard, the power dissipated is given as,
What are the different types of phase-shift keying?
Two common examples are “binary phase-shift keying” (BPSK) which uses two phases, and “quadrature phase-shift keying” (QPSK) which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of constellation points being a power of two.
What is binary phase shift keying (BPSK)?
Binary phase-shift keying (BPSK) BPSK (also sometimes called PRK, phase reversal keying, or 2PSK) is the simplest form of phase shift keying (PSK). It uses two phases which are separated by 180° and so can also be termed 2-PSK.
What is Symmetric differential quadrature phase shift keying?
Symmetric differential quadrature phase shift keying (SDQPSK) is like DQPSK, but encoding is symmetric, using phase shift values of −135°, −45°, +45° and +135°. The modulated signal is shown below for both DBPSK and DQPSK as described above.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945292.83/warc/CC-MAIN-20230325002113-20230325032113-00716.warc.gz
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CC-MAIN-2023-14
| 2,014 | 12 |
http://calendariu.com/c/centimetre-squared-paper-template.html
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math
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Dot paper, This printable dot paper features patterns of dots at various intervals. variations include the number of dots per inch, and the size of the paper (legal, letter. Free online graph paper / plain - incompetech, Not the graph paper you're looking for? check out our many other free graph/grid paper styles from our main page here.. Printable graph paper - kent state university, Printable graph paper the table below gives links to pdf files for graph paper. the printed area is 8 inches by 10 inches. the number refers to the number of blocks.
Mathsphere free graph paper, Mathsphere graph & line paper free printable/photocopiable graph line paper. running short graph paper, find dotty paper cupboard?. http://www.mathsphere.co.uk/resources/MathSphereFreeGraphPaper.htm Kariertes papier 10x10, © 2006-2010 papersnake., , Title: kariertes papier 10x10, © 2006-2010 papersnake., rights reserved author: papersnake. created date: 4/26/2010 2:36:03 pm. http://www.papersnake.com/squared_paper/squared10x10.pdf A graph paper 1 cm grid pdf format - mathsphere, Free resources www.mathsphere..uk . author: peter banks created date: 9/16/2004 5:36:29 pm. http://mathsphere.co.uk/downloads/graph-paper/graph-paper-1cm-squares-blue.pdf
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s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281492.97/warc/CC-MAIN-20170116095121-00376-ip-10-171-10-70.ec2.internal.warc.gz
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CC-MAIN-2017-04
| 1,239 | 2 |
http://mathhelpforum.com/algebra/121884-difficult-quadratic-equation-problems.html
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math
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Let's use brute force... for the first question :
If are the roots, then and
Let be the equation which roots are
So the equation you're looking for is
How do i solve these?
1) If and are the roots of the equation = 0, then the equation whose roots are and , is?
2) If the equations and have a common root, then ?
3) If the difference of the roots of the equations be 1, then:
For question 2)...
There exists such that :
You may be able to solve for by yourself eh ?
For question 3)...
We know that the sum of the two roots is -b and their product is c.
So we have
My approach to #1 is similar to Moo's . . . with a different answer.
. . Did I mess up?
1) If and are the roots of the equation: ,
find the equation whose roots are: . and . . . . in terms of
Since are roots of: .
. . then: .
The sum of the two roots is:
. . .
Substitute and : .
. . Hence, the -coefficient is: .
The product of the two roots is:
Substitute : .
. . Hence, the constant term is: .
Therefore, the equation is: .
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541134.5/warc/CC-MAIN-20161202170901-00085-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 991 | 28 |
https://mdashf.org/2012/02/05/heisenbergs-uncertainty-principle-from-a-new-angle/
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math
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Heisenberg’s Uncertainty Principle from wave-particle duality. The wave-particle duality states that any mechanical object can exhibit both wave and particle behavior and the complementarity priniciple states that they can not both be observed simultaneously. That is the wave and teh particle nature are only exclusive ly observed given a specific time or time window, the window being consistent with Heisenberg’s uncertainty prinicples of which there are more than 3 forms. But only 3 forms of these exhibit a simple relation from which other-variable relationships can be derived much in the same way kinetic energy is derived from mass and speed of a particle. The intention of writing this blog for me is to show how a basic reasoning can be applied qualitatively to obtain a semi-quantitative or intuitive relation between variables to extend an inequality relation between these variables. I will show here only for energy and time uncertainty relationship. From the wave particle duality it is clear that any entity/object/process has a particle or wave character both in the same system but not in the parametric sense of same time. Once time is chosen/defined as a specific kinematic parameter wrt that time the wave and particle nature are not simultaneously observed. So let us consider a particle, say a neutrino or an electron. This particle has a well specified physical location in space. This is the mean position therefore of the particle. This mean has a zero distribution for a classical particle but for a quantum mechanical particle or system the distribution is not zero. Now the particle also being a wave it has a characteristic of wavelength. This wavelength therefore gives the extent of deviation of the particle’s position from its mean location. The wavelength is lambda.
Heisenberg’s Uncertainty Principle from a new angle
This blog will be updated with more slides
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224652235.2/warc/CC-MAIN-20230606045924-20230606075924-00315.warc.gz
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CC-MAIN-2023-23
| 1,905 | 3 |
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