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http://demonstrations.wolfram.com/NewtonsSecondLaw/
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math
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Newton's Second Law
Newton's second law states that force is directly proportional to the mass of an object and its acceleration. An arrow's thickness is proportional to the magnitude of the quantity that it represents.
Newton, Isaac (1642-1727)
Newton's Second Law
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s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042990112.92/warc/CC-MAIN-20150728002310-00315-ip-10-236-191-2.ec2.internal.warc.gz
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http://www.mechanicalpeacademy.com/nomograms-for-the-pe-exam/
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math
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Nomograms for the PE exam
Nomograms: Antiquated technology or useful tool?
Many of today’s engineers would not consider using nomograms for the PE exam. It would not surprise me if many of you reading this blog post have no idea what a nomogram (also called a nomograph) is. This blog will quickly introduce them to you to help answer the question… Nomograms: Antiquated technology or useful tool? Though they may be antiquated, you may find that they allow for very quick solutions to some types of problems. Therefore, this blog is an introduction to the idea of using them for the PE exam to help you solve problems faster.
What is a nomogram?
A nomogram is a graphical tool used to perform calculations, and they exist for numerous types of calculations. They are essentially a diagram that gives a quick, approximate solution to a mathematical function. A nomogram will have three or more lines (or curves), each for a different variable in the function. The lines are placed on the nomogram to give the appropriate numerical relationships for the function. If you know two or more of the variable values, you can use a straightedge to line up the values to graphically determine the unknown variable. There will be some error, but it can be a very quick method for doing the calculations!
You can easily search the internet to get more detail on using (or making) nomograms. There are also books teaching the lost art of nomography. You can find books that discuss the history of nomography as well as numerous areas of application. Omer Blodgett has a couple of great books, Design of Welded Structures and Design of Weldments, which have several great nomograms for topics in mechanics of materials.
Here is a quick example
The figure below shows a nomogram used to solve the quadratic equation. Though I did construct this particular nomogram I did not develop the idea (it has been around for a long time). I am also not going to give details on how it was developed, but I will give it only as a representation of how they can be used. The horizontal axis is the value of ‘a’ in the equation, the vertical axis is the value of ‘b’ in the equation, and the circle gives the two roots that solve the equation (values of ‘x’). The dashed line shows an example with a = 1.5 and b = -2. A line is drawn connecting those two points (the dashed line). The roots are determined by the values on the circle where that line crosses. The solutions for that particular example are x = 0.85 and x = -2.35, which are read from the values on the circle.
These nomograms sound obsolete… are they really useful?
OK, I would agree that computers have made nomograms essentially obsolete. However, you cannot use a computer during the PE exam. I would also agree that the power of calculators make nomograms obsolete, but remember that you have a limited selection of acceptable calculators for the PE exam. I am also not suggesting you use nomograms for everyday engineering design (though you could). The real question is whether or not they can save valuable time during the PE exam.
You may not have a need for a nomogram to solve the quadratic equation, but they exist for far more complex problems. Using them for the PE exam could allow for very rapid calculations for some common types of problems. Machine Design Fundamentals by Hindhede, for example, provides a nomogram relating power, torsional stress, and shaft diameter that rapidly determines required shaft diameter. Design of Welded Structures by Blodgett has rather complex nomograms that can be used to determine the required section modulus of beams (or required moment of inertia), which includes information about beam end conditions, beam length, beam loading, and allowable stress. The same text also includes nomograms for deflection of curved beams, fatigue, torsional resistance, column effective lengths, and design aids for plate girders. My textbook, Machine Analysis with Computer Applications (the same figure is in Mechanisms and Dynamics of Machinery by Mabie and Reinholtz), has a nomogram to determine maximum pressure angle in disk cams with roller followers. I have also seen nomograms for fluid flow calculations to aid in pipe sizing. All of these nomograms can save valuable time on the PE exam. You are not limited by nomograms available in books… you can always try making some of your own for different calculations.
Do you think nomograms are useful for the PE exam?
I hope you found this information useful. The PE exam is all about working problems quickly and efficiently. Nomograms can provide quick estimates of the answer (which is usually accurate enough for a multiple choice exam like the PE exam). What are your thoughts? Do you ever use nomograms for design? Do you have recommendations of good nomograms to use for the PE exam (or good books that contain useful nomograms)? Leave a comment letting everyone know and please share the information by tagging the share buttons. Also, take a minute to go over to the Mechanical PE Academy Facebook page to get updates and exclusive content.
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| 5,105 | 13 |
https://www.physicsforums.com/threads/forces-on-an-incline.254466/
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math
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Question: A block of mass m = 2.00 kg is released from rest at h = 0.600 m from the surface of a table, at the top of a θ = 35.0° incline as shown below. The frictionless incline is fixed on a table of height H = 2.00 m. How far from the table will the block hit the floor? So basically a block falls from a ramp on top of a table and I'm supposed to figure out how far the block falls from the edge of the ramp (which is on the edge of the table). I would use a kinematics equation but I have another unknown besides the distance. I figured out the final velocity at the edge of the ramp and the length of the hypotenuse of the ramp and the acceleration during the ramp time but I don't know anything about the ramp time.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647692.51/warc/CC-MAIN-20180321195830-20180321215830-00489.warc.gz
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CC-MAIN-2018-13
| 724 | 1 |
https://domathtogether.wordpress.com/2015/10/18/math-circle-meeting-on-october-17th/
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math
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Agenda: Creating a Cardioid
Presenters: Aubrey Rhoden and Kim Moore
Problem: How can we create a cardioid with a radius of 10 feet on the beach?
Solution: Let there be 36 points labeled 0 to 35 equally spaced on a circle. Connect nth point to Mod [2 n,36] th point. These lines are tangents to a cardioid.
- Use a stake and rope to create the circle. The stake goes in the middle of the circle.
- Calculate the circumference of the circle. The circumference would be 62.8 feet or 753 inches.
- Divide the circumference into 36 equal parts. The stakes need to be 20.9 inches apart.
Formula for a cardioid:
X= a cos t (1 – cos t)
Y= a sin t (1- cos t)
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CC-MAIN-2019-35
| 651 | 10 |
http://web.mst.edu/~bestmech/preview/raman/problems/chapter2/3.htm
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math
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If the speed of the F=4000 lb car is plotted over the 30-s time period. Find the variation of the traction force F needed to cause the motion from 20s to 30s.
1) 124.2 lb
From the graph for
0 < t < 20s:
Equation of motion:
So, the traction force needed for the car to travel from 20s to 30s is 124.2 lb.
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| 303 | 6 |
http://mathematica.stackexchange.com/questions/tagged/document-creation+hyperlink
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math
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StatusArea display of message with hyperlink
just trying to label a hyperlink, using an example right from the documentation.... ...
Nov 5 '13 at 21:05
Tom De Vries
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http://archive.railsforum.com/viewtopic.php?pid=163418
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math
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Topic: Active record query linked with select box
An example: There are 5 groups (Group A, B, C, D and E). Each group has multiple members that each get two scores. The average scores for each group as a whole are A: 65 & 40, B: 72 & 80, C: 73 & 65, D: 84 & 21, and E: 91 & 31. I'd like a user to be able to select a group from a dropdown and have the app only display the corresponding averages.
Last edited by bork121 (2013-06-07 15:43:56)
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https://en.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-mul-div-polar/v/divide-complex-polar
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math
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- Multiplying complex numbers in polar form
- Dividing complex numbers in polar form
- Multiply & divide complex numbers in polar form
- Taking and visualizing powers of a complex number
- Complex number equations: x³=1
- Visualizing complex number powers
- Powers of complex numbers
- Complex number polar form review
We can divide two complex numbers in polar form by dividing their moduli and subtracting their arguments. Created by Sal Khan.
Want to join the conversation?
- why would you rotate it clockwise?(2 votes)
- When you add angles, they get larger, so it "rotates" counterclockwise.
If you subtract angles, they get smaller, so it rotates clockwise.
When you divide two complex numbers, you subtract the angles, so it rotates clockwise.(2 votes)
- [Narrator] So we are given these two complex numbers and we want to know what W sub one divided by W sub two is. So pause this video and see if you can figure that out. All right, now let's work through this together. So the form that they've written this in it actually makes it pretty straightforward to spot the modulus and the argument of each of these complex numbers. The modulus of W sub one we can see out here is equal to eight. And the argument of W sub one we can see is four Pi over three if we're thinking in terms of radians. So four Pi over three radians, and then similarly for W sub two its modulus is equal to two and its argument is equal to seven Pi over six. Seven Pi over six. Now, in many videos we have talked about when you multiply one complex number by another you're essentially transforming it. So you are going to scale the modulus of one by the modulus of the other. And you're going to rotate the argument of one by the argument of the other, I guess you could say you're going to add the angles. So another way to think about it is if you have the modulus of W sub one divided by W sub two. Well then you're just going to divide these moduli here. So this is just going to be eight over two which is equal to four. And then the argument of W sub one over W sub two. This is, you could imagine you're starting at W sub one and then you are going to rotate it clockwise by W sub two's argument. And so this is going to be four Pi over three minus seven Pi over six. And let's see what this is going to be. If we have a common denominator four Pi over three is the same thing as eight Pi over six minus seven Pi over six which is going to be equal to Pi over six. And so we could write this, the quotient W one divided by W two is going to be equal to if we wanted to write it in this form its modulus is equal to four. It's going to be four times cosine of Pi over six plus i times sine of Pi over six. Now cosine of Pi over six, we can figure out Pi over six is the same thing as a 30 degree angle. And so the cosine of that is square root of three over two square root three over two. And the sine of Pi over six we know from our 30, 60, 90 triangles is going to be one half. So this is one half. And so if you distribute this four this is going to be equal to four times square root of three over two is two square roots of three and then four times one half is two. So plus two i and we are done.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947475203.41/warc/CC-MAIN-20240301062009-20240301092009-00729.warc.gz
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http://swanboathire.com.au/lib/hochschild-cohomology-of-von-neumann-algebras-london-mathematical-society-lecture-note-series
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math
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By Allan M. Sinclair
The topic of this e-book is the continual Hochschild cohomology of twin basic modules over a von Neumann algebra. The authors strengthen the required technical effects, assuming a familiarity with easy C*-algebra and von Neumann algebra idea, together with the decomposition into kinds, yet no earlier wisdom of cohomology conception is needed and the speculation of thoroughly bounded and multilinear operators is given totally. these circumstances whilst the continual Hochschild cohomology Hn(M,M) of the von Neumann algebra M over itself is 0 are vital to this booklet. the fabric during this ebook lies within the sector universal to Banach algebras, operator algebras and homological algebra, and should be of curiosity to researchers from those fields.
Read Online or Download Hochschild Cohomology of Von Neumann Algebras (London Mathematical Society Lecture Note Series) PDF
Similar Abstract books
This conventional remedy of summary algebra is designed for the actual wishes of the math instructor. Readers should have entry to a working laptop or computer Algebra procedure (C. A. S. ) equivalent to Maple, or at minimal a calculator akin to the TI 89 with C. A. S. services. contains “To the instructor” sections that Draw connections from the quantity idea or summary algebra into account to secondary arithmetic.
Someone who has studied summary algebra and linear algebra as an undergraduate can comprehend this booklet. the 1st six chapters offer fabric for a primary direction, whereas the remainder of the booklet covers extra complicated themes. This revised version keeps the readability of presentation that was once the hallmark of the former variants.
Here's an creation to the speculation of quantum teams with emphasis at the amazing connections with knot idea and Drinfeld's contemporary basic contributions. It provides the quantum teams hooked up to SL2 in addition to the elemental suggestions of the idea of Hopf algebras. insurance additionally specializes in Hopf algebras that produce strategies of the Yang-Baxter equation and gives an account of Drinfeld's dependent remedy of the monodromy of the Knizhnik-Zamolodchikov equations.
Bifurcation thought stories how the constitution of options to equations adjustments as parameters are various. the character of those alterations relies either at the variety of parameters and at the symmetries of the equations. quantity I discusses how singularity-theoretic thoughts relief the certainty of transitions in multiparameter platforms.
Additional info for Hochschild Cohomology of Von Neumann Algebras (London Mathematical Society Lecture Note Series)
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https://byjus.com/stopping-distance-formula/
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math
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Stopping Distance Formula
When the body is moving with a certain velocity and suddenly brakes are applied. You would have noticed that the body stops completely after covering a certain distance. This is called the stopping distance.
The stopping distance is the distance travelled between the time when the body decides to stop a moving vehicle and the time when the vehicle stops completely. The stopping distance depends on factors including road surface, and reflexes of the car’s driver and it is denoted by d.
Stopping Distance formula is given by,
d = stopping distance (m)
v = velocity (m/s)
μ = friction coefficient
g = acceleration due to gravity (9.8 )
The stopping distance formula is also given by,
k = a constant of proportionality
v = velocity
A car is moving with a velocity of 40 m/s and suddenly applies brakes. Determine the constant of proportionality if the body covers a distance of 10 m before coming to rest.
Velocity ,v = 40 m/s
Stopping distance , d = 10 m
The constant of proportionality is given by the formula,
= 10 / 1600
A bike moves with a velocity of 15 m/s and applies a brake. Calculate its stopping distance if the constant of proportionality is 0.9.
Velocity, v = 15 m/s
Constant of proportionality k = 0.9,
The stopping distance is given by
= 0.9 × 225
d = 202.5 m
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100650.21/warc/CC-MAIN-20231207054219-20231207084219-00027.warc.gz
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https://www.iitjeemaster.com/main-advanced-physics-lectures/motion-iit-jee-2017
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math
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In this iit jee physics video lecture, we are, going to discuss one of the easiest yet hard IIT JEE topics which are kinematics. In the physic video, we will have a look on types of kinematics, distance, displacement, types of speed, and types of velocity. Before moving on to understand what these terms are, you as students need to have good knowledge in trigonometry, coordinate geometry, vectors, integration, differentiation, definite integration, quadratic equations, ap, gp, and hp.
Kinematics is part of mechanics. Mechanics are two types,
- Classical mechanics: In this, the speed of the particle is less that the speed of light and the size of the particle is significant.
- Quantum mechanics: In this, the size of the particle is very small and is comparable to the size of an electron, proton, etc.
- Relativistic mechanics: In this, the speed of the particle is nearly same as the speed of the light.
In this jee physics video, we are going to discuss only classical mechanics. In classical mechanics again there are two types,
- Kinematics: In this, we study about the causes of motion.
- Dynamics: In this, we study about the reason behind the motion.
Next, in jee physics we have discussed rest and motion. In the case of rectilinear motion, i.e. motion along a straight line. If we plot a graph and we find that the object is at the same point over a period of time then it is in rest. If the object moves over the period of time then it is in motion. We then found out that motion and rest are relative. Next topic discussed is distance, which is the length of the path travelled and is a scalar quantity. In the above video, we have discussed distance in both 1-D motion and 2-D motion. Next moving on to the displacement, it is the change in the position vector and is a vector quantity. Even displacement is discussed for both 1-D and 2-D motions and various cases are also discussed. The next topic discussed is speed, which is of two types, instantaneous and average speed. The last and the final topic discussed is velocity, which is also of two types, instantaneous velocity, and average velocity.
Kinematics is one of the most important and crucial topics for IIT JEE physics lectures and thus are very important that you understand it from the roots.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474533.12/warc/CC-MAIN-20240224112548-20240224142548-00087.warc.gz
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CC-MAIN-2024-10
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http://talks.bham.ac.uk/talk/index/2520
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math
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The Thompson chain of perfect groups
If you have a question about this talk, please contact David Craven.
Abstract not available
This talk is part of the Algebra Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsType the title of a new list here Computer Science Distinguished Seminars Medical Imaging Research Seminars
Other talksThe 2017 Haworth Lecture RSLC PhD/Postdoc Seminar (Chemistry) Open slot Machine Learning and Computer Vision on Mars Joint BSN and MSC Seminar Broadband molecular fingerprinting with laser frequency combs
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120101.11/warc/CC-MAIN-20170423031200-00628-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 594 | 8 |
https://www.arxiv-vanity.com/papers/1412.4866/
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math
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Fat wedge filtrations and decomposition of polyhedral products
The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complex is studied by investigating its filtration called the fat wedge filtration. We give a sufficient condition for decomposing the polyhedral product in terms of the fat wedge filtration of the real moment-angle complex for , which is a desuspension of the decomposition of the suspension of the polyhedral product due to Bahri, Bendersky, Cohen, and Gitler [BBCG]. We show that the condition also implies a strong connection with the Golodness of , and is satisfied when is dual sequentially Cohen-Macaulay over or -neighborly so that the polyhedral product decomposes. Specializing to moment-angle complexes, we also give a necessary and sufficient condition for their decomposition and co-H-structures in terms of their fat wedge filtration.
Key words and phrases:polyhedral product, fat wedge filtration, Golodness, sequentially Cohen-Macaulay complex, neighborly complex
2010 Mathematics Subject Classification:55P15, 05E45, 52B22
Let be an abstract simplicial complex on the vertex set , and let be a collection of pairs of spaces indexed by the vertices of . The space which is now called the polyhedral product is defined by the union of product spaces constructed from in accordance with the combinatorial information of . Polyhedral products were first found in Porter’s work on higher order Whitehead products [P] in 1965, and appear in several fundamental constructions in algebra, geometry, and topology related with combinatorics: the cohomology of and are identified with the Stanley-Reisner ring of and its derived algebra, respectively [DJ, BBP, BP]; the fundamental group of and are the right-angled Coxeter group of the 1-skeleton of and its commutator subgroup [DO]; the union of the coordinate subspace arrangement in associated with is , and its complement has the homotopy type of [GT1, IK1, BP]. From these examples, one sees that the special polyhedral products and are especially important, where and are collections of pairs of cones and their base spaces, and spaces and their basepoints, respectively. There is a homotopy fibration involving these polyhedral products, so they are supplementary to each other in a sense. The object to study in this paper is the polyhedral product , and we are particularly interested in its homotopy type.
Among other results on the homotopy types of polyhedral products, the work of Bahri, Bendersky, Cohen, and Gitler [BBCG] is remarkable. They proved a decomposition of a suspension of in general, and specializing to the polyhedral product , they obtained the following decomposition, where the notations will be explained later.
Theorem 1.1 (Bahri, Bendersky, Cohen, and Gitler [Bbcg]).
There is a homotopy equivalence
Let us call the decomposition of this theorem the BBCG decomposition. The proof of the BBCG decomposition is a combination of the decomposition of suspensions of general polyhedral products which they obtained, and a formula of homotopy colimits [ZZ]. Unfortunately, from the original proof, one cannot seize the intrinsic nature of which yields the BBCG decomposition, but the BBCG decomposition certainly showed a direction in studying the homotopy type of , that is, to describe the homotopy type by desuspending the BBCG decomposition. This direction of the study was proposed in [BBCG] when is a special simplicial complex called a shifted complex: they conjectured that the previous result of Grbić and Theriault [GT1] on when is a shifted complex, can be generalized to a desuspension of the BBCG decomposition. This conjecture was affirmatively resolved by the authors [IK1], and was partially generalized to dual vertex-decomposable complexes by Welker and Grujić [GW], where Grbić and Theriault [GT2] also considered a desuspension for shifted complexes but the paper includes serious mistakes such as the closedness of by retracts in the proof of the main theorem. However, the crucial part of the proofs of these results are over adapted to special properties of the simplicial complex , so the methods are not applicable to wider classes of simplicial complexes.
The first aim of this paper is to elucidate the intrinsic nature of the polyhedral product for general which yields the BBCG decomposition and its desuspension. The structure of in question will turn out to be a certain filtration which we call the fat wedge filtration. We will see that the BBCG decomposition is actually a consequence of the property of the fat wedge filtration such that it splits after a suspension, so the analysis of the fat wedge filtration naturally shows a way to desuspend the BBCG decomposition. In analyzing the fat wedge filtration, the special polyhedral product which is called the real moment-angle complex for and is denoted by plays the fundamental role, where the real moment-angle complexes have been studied in toric topology as a rich source producing manifolds with good 2-torus actions. We will prove that the fat wedge filtration of is a cone decomposition of , and will describe the attaching maps of its cones explicitly in a combinatorial manner. We say that the fat wedge filtration of is trivial if all the attaching maps are null homotopic, and now state our first main result.
If the fat wedge filtration of is trivial, then for any there is a homotopy equivalence
As well as the polyhedral product has been studied in toric topology as an object producing manifolds with good torus actions, which is called the moment-angle complex for and is denoted by . We will prove that the fat wedge filtration of is also a cone decomposition, so we can define its triviality as well as that of . We will give two conditions equivalent to the triviality of the fat wedge filtration of as follows.
The following three conditions are equivalent:
The fat wedge filtration of is trivial;
is a co-H-space;
There is a homotopy equivalence
Note that if the BBCG decomposition desuspends, then becomes a suspension, so in particular, all products and higher Massey products in the cohomology of are trivial. As mentioned above, the cohomology of is isomorphic to a certain derived algebra of the Stanley-Reisner ring of , and the triviality of products and higher Massey products of this derived algebra is called the Golodness of which has been extensively studied in combinatorial commutative algebra [HRW, BJ, B]. We will also show the triviality of the fat wedge filtration of (resp. ) implies the (resp. stable) homotopy version of the Golodness of .
The second aim of this paper is to examine the triviality of the fat wedge filtration of the real moment-angle complexes for specific simplicial complexes which implies the decomposition of polyhedral products by Theorem 1.2. To this end, we must choose appropriate classes of simplicial complexes. For shifted and dual vertex-decomposable complexes, desuspensions of the BBCG decomposition were studied in [GT1, IK1, GW], where dual shifted complexes are shifted. Originally, shifted and vertex-decomposable complexes were introduced as handy subclasses of shellable complexes in [BW], and shellable complexes form a subclass of sequentially Cohen-Macaulay (SCM, for short) complexes over [S, BWW] which are a non-pure generalization of Cohen-Macauay complexes. Then there are implications:
Then we first choose dual shellable complexes to show the triviality of the fat wedge filtrations of real moment-angle complexes, and then generalize its argument homologically to obtain the following result for dual SCM complexes over , which is a substantial improvement of the previous results [GT1, IK1, GW]. The theorem will be actually proved for a larger class of simplicial complexes including dual SCM complexes over , and a spin off of the method used for dual shellable complexes will be given to produce a -local desuspension of the BBCG decomposition for certain under some conditions on .
If is dual SCM over , then the fat wedge filtration of is trivial.
If is dual SCM over , then is homotopy equivalent to a wedge of spheres.
We next consider the property of the inductive triviality of the attaching maps of the cones in the fat wedge filtration of . When all attaching maps in the filter are trivial, we will show that the attaching maps for the filter become trivial after composed with a certain map, say . So the attaching maps lift to the homotopy fiber of . By evaluating the connectivity of the homotopy fiber of , we will obtain the following, where the theorem will be slightly generalized by replacing dimension with homology dimension.
If is -neighborly, then the fat wedge filtration of is trivial.
This paper is organized as follows. In Section 2 we define polyhedral products, and collect some of their examples and properties which will be used later. In Section 3 we combinatorialy describe the fat wedge filtration of , and in Section 4, we study the fat wedge filtration of by using the description of the fat wedge filtration of . We then prove Theorem 1.2. In Section 5 we further investigate the fat wedge filtration of , and prove Theorem 1.3. Section 6 deals with a connection between the triviality of the fat wedge filtrations of and and the Golodness of . In Section 7 and 8, we give criteria, called the fillability and the homology fillability, for the triviality of the fat wedge filtration of , and apply them to dual shellable complexes and dual sequentially Cohen-Macaulay complexes over , proving Theorem 1.4. Section 9 is a spin off of the arguments for dual shellable complexes in Section 8. We introduce a new simplicial complexes called extractible complexes, and prove a -local desuspension of the BBCG decomopsition for them under some conditions on . In Section 10 we give another criterion for the triviality of the fat wedge filtration of which is Theorem 1.6. Finally in Section 11, we give a list of possible future problems on the fat wedge filtration of polyhedral products.
Throughout the paper, we use the following notations:
Let be a simplicial complex on the vertex set , where we put ;
Let be a sequence of spaces with non-degenerate basepoints ;
Put , pairs of reduced cones and their base spaces.
If is a pair of spaces, the symbol also denotes its -copies ambiguously.
The authors are grateful to P. Beben for discussion on the homotopy Golodness. Thanks also goes to T. Yano for careful reading of the draft.
2. Definition of polyhedral products
In this section, we define polyhedral products, and recall a homotopy fibration involving polyhedral products that we will use.
Let be a sequence of pairs of spaces . The polyhedral product is defined by
where for and according as and .
The special polyhedral product and are called the real moment-angle complex for and the moment-angle complex for , respectively. We here give two easy examples of polyhedral products.
If is the simplicial complex with discrete -points, then we have
On the other hand, if is the boundary of the full -simplex, then is the fat wedge of . More generally, if is the -skeleton of the full -simplex, then is the generalized fat wedge of .
When and is the boundary of the full 1-simplex, we have
where means the join of and . For general , if is the boundary of the full -simplex, it is proved in [P] that there is a homotopy equivalence
We observe the polyhedral product of the joint of two simplicial complexes. We set notation. For simplicial complexes on disjoint vertex sets, their join is defined by
Let be a non-empty subset of , and let denote the full subcomplex of on , that is, . For a sequence of pairs of spaces , we put . We can deduce the following immediately from the definition of polyhedral products. For with and , we have
Then we see that the polyhedral product is not always a suspension: for example, if and is a square which is the join of 2-copies of the simplicial complex with discrete 2-points, we have by Example 2.3. This implies that the BBCG decomposition does not always desuspend.
We recall from [DS] a homotopy fibration involving polyhedral products, and we here produce an alternative proof.
Lemma 2.5 (cf. [Fa, Proposition, pp.180]).
Let be a diagram of homotopy fibrations over a fixed base . Then
is a homotopy fibration.
Proposition 2.6 (Denham and Suciu [Ds]).
There is a homotopy fibration
For any there is a homotopy fibration which is natural with respect to the inclusions of subsets of . Then we have a diagram of homotopy fibrations , so it follows from Lemma 2.5 that there is a homotopy fibration
Since the maps and are cofibrations for all , the above homotopy colimits are naturally homotopy equivalent to the colimits which are and , completing the proof. ∎
3. Fat wedge filtration of
In this section, we introduce the fat wedge filtration of and investigate that of the real moment-angle complex . We first define the fat wedge filtration of a general subspace of a product of spaces. Recall that the generalized fat wedge of is defined by
for . Then we get a filtration
For a subspace including the base point of , we put for , so we get a filtration
which is called the fat wedge filtration of .
We give a combinatorial description of the fat wedge filtration of the real moment-angle complex , where we choose the point to be the basepoint of . For any we identify with the subspace of . Then by the definition of the fat wedge filtration, we have
for . In order to describe the fat wedge filtration of combinatorially, we employ the cubical decomposition of a simplicial complex presented in [BP], and we recall it here. To nested subsets , we assign the -dimensional face
of the cube . Notice that any face of the cube is expressed by for some , and in particular, any vertex of is given by for some . Let denote the barycentric subdivision of a simplicial complex . Then the vertices of are non-empty subsets of , so we can define a piecewise linear map
which is an embedding onto the union of -dimensional faces of including the vertex . This embedding is the cubical decomposition of , where one can see the reason for the name “cubical decomposition” from Figure 1.
We define the cone and the suspension of by
as usual. By extending the embedding , we get a piecewise linear homeomorphism
which sends the cone point of to the vertex . Since the vertex set of is , is a subcomplex of . Then by restricting and , we obtain embeddings
which are the cubical decompositions of and .
We express the difference in terms of the faces . For any we have and , so we get
Then it follows that
We next express in terms of the faces as well, and show that the cubical decompositions of full subcomplexes of naturally come into the fat wedge filtration of . We denote by the -copies of the pair for . Then for , we have , where is the face of . We get
Then by (3.2), the embedding descends to a map
the disjoint union of the maps (3.5)
turns out to be a relative homeomorphism. Let denote the map in (3.5). Then we have established:
For , is obtained from by attaching a cone to for each with , where is the inclusion.
The above theorem shows that the fat wedge filtration of is a cone decomposition in the usual sense. We say that the fat wedge filtration of is trivial if the maps are null homotopic for all . Since is a retract of , this is equivalent to the composite is null homotopic for any . We here consider two cases in which the fat wedge filtration of is trivial. We first consider the flag complex of a chordal graph as in [GPTW]. Here graphs mean one dimensional simplicial complexes, and the flag complex of a graph is the simplicial complex whose -simplices are complete graphs with vertices in . Recall that a graph is called chordal if its minimal cycles are of length at most 3.
If is the flag complex of a chordal graph, then the fat wedge filtration of is trivial.
Suppose is the flag complex of a graph . It is known that is chordal if and only if each component of is contractible. Then since is path-connected for any , is null homotopic. For any , the full subgraph is chordal, and is the flag complex of . Then we similarly obtain that is null homotopic for any . ∎
We next consider the case . We start with observing properties of the map for general . In [IK2], it is proved that the inclusion admits a left homotopy inverse for . Then by Theorem 3.1, we have the following.
The maps are null homotopic for all .
For a simplex of , we denote the deletion and the link of by and , that is, and . Since
for a vertex of , there is a projection . Then it is straightforward to check that through the identification , we have a commutative diagram
So by Proposition 3.3, we get:
The composite is null homotopic.
If , then the fat wedge filtration of is trivial.
As , there is a vertex of such that is the full simplex , implying is contractible. So the projection is a homotopy equivalence, hence is null homotopic by Corollary 3.4. Since for all , the map is null homotopic for each by the above observation. ∎
4. Fat wedge filtration of
In this section, we investigate the fat wedge filtration of by using the maps obtained in the previous section, and we prove Theorem 1.2.
As well as the real moment-angle complexes, we may regard for as a subspace of since every has a basepoint, so we have
for . We describe by using the map . Let be a subset of and put . Consider the composite of maps
where the second arrow maps to for . One easily deduces that the composite descends to a surjection
which is homeomorphic on , and since we are using reduced cones, we have
So we obtain a relative homeomorphism
where a product of pairs of spaces are given by as usual. Then since
we obtain the following.
is a relative homeomorphism.
Recall that a categorical sequence of a space in the sense of Fox [Fo] is a filtration such that the inclusion is null homotopic for . By the above theorem one can easily deduce that the fat wedge filtration of is a categorical sequence whereas the fat wedge filtration of is a cone decomposition.
Corollary 4.2 (Bahri, Bendersky, Cohen, and Gitler [Bbcg]).
There is a homotopy equivalence
which is natural with respect to and inclusions of subcomplexes of , where .
The BBCG decomposition is obtained also by the retractile argument of James [J], but it is hard to get the naturality by it.
From the description of the fat wedge filtration of in (4.1) and Theorem 4.1, one sees that the attaching maps of the cone decomposition of control the fat wedge filtration of . We further investigate this control in the extreme case that the fat wedge filtration of is trivial, that is, we prove Theorem 1.2. We prepare a technical lemma.
Let be NDR pairs. Suppose that has the quotient topology by a relative homeomorphism , and that the restriction is null homotopic in . Then there is a string of homotopy equivalences
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CC-MAIN-2021-49
| 18,890 | 98 |
https://careers.allianz.com/pt_BR/jobs/Allianz-SE-global-headquarters/Senior-Market-Risk-Analyst-in-Group-Risk-C2EBDE1DCF021EEABBA2060DA4D5800F.html
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math
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Senior Market Risk Analyst (m/f/d) in Group Risk
Within Allianz SE, Group Risk (GR) is in charge of managing risks to bolster Allianz's financial strength and to support value-focused company leadership. As such Group Risk is responsible for monitoring and reporting on the Group's overall risk profile, and thus ensuring that individual Allianz companies adhere to the Group's risk governance principles. Our risk framework covers approximately 100 entities worldwide providing risk measures, analysis and reports to 400 - 600 direct users.~crlf~ ~crlf~Within Group Risk, the Market Risk Analytics team is covering the areas of financial risk and capital management as well as the maintenance and development of group-wide Internal Model with focus on real-world scenario generation, risk aggregation and tax modeling. In the field of financial risk and capital management the team is responsible for all questions related to risk capital steering, in particular on Group and local target capitalization levels, Return on Risk Capital and market risk limit framework. It is also responsible to challenge and follow-up on all new investment strategies, in particular on SAA, hedging and ALM topics. ~crlf~ ~crlf~The Senior Market Risk Analyst should be comfortable with both areas of responsibility, leveraging synergies and supporting to Group Risk's value creation.
##Responsibility to perform regular deep dives on market risks and hedging strategies: equity, interest rates, spreads, FX, etc. and report the results and recommendations to the Group Financial Risk Committee.~crlf~##Responsibility for KPIs related to capital allocation, in particular Solvency-adjusted RoE. Own the methodology: align with senior management, communicate to operating entities and relevant Group Centers, coordinate planning and reporting processes. Communicate the results to Group Financial Risk Committee or Management Board. Establish necessary links to other related KPIs outside Group Risk responsibility, e.g. IFRS RoE.~crlf~##Support Solvency II closing activities, planning dialogue and projections from risk side. Joint development of methodologies, tools and processes, challenge operating entities deliveries and interpret Group results.~crlf~##Responsibility for supporting cross-functional projects and analysis on market risk topics.~crlf~##Drive projects related to digitalization of team activities and corresponding productivity improvement.~crlf~##Provide senior support to all team activities~crlf~
Qualifications~crlf~##University degree in mathematics, physics, economics or alike with strong quantitative focus~crlf~##Actuarial exam, CFA qualification, PRM/FRM or equivalent is a plus~crlf~##Fluent in Business English (written & spoken) is mandatory~crlf~##Advanced knowledge of standard software (Excel, Access, Word incl. VBA)~crlf~##Knowledge of programming languages (Java, R, Python & MatLab) is a plus~crlf~ ~crlf~Experience & skills~crlf~## Excellent understanding of insurance business and Solvency II regulation~crlf~##Strong understanding of risk management concepts, quantitative risk methods and valuation models, notably market risk & asset liability interaction~crlf~##Strong analytical skills which allow to interpret quantitative data and translate outcome of quantitative analysis into clear statements or recommendations~crlf~##Ability to effectively communicate on all levels including senior management~crlf~##Working experience within an financial services environment, consulting firm or Risk Management Department~crlf~##Structuring to a large extent own work / analysis and executing work plans efficiently~crlf~##High level of commitment and interest to work in a dynamic and demanding environment~crlf~##Ability to establish and maintain internal and external working relationships with colleagues from different functions and cultures~crlf~
Senior Recruiter: Ms. Sabrina Diclemente Phone : +49 (0)89 3800- 69518~crlf~Please submit your applications only via the tool (blue button above).
Allianz is the home for those who dare – a supportive place where you can take the initiative to grow and to actively strengthen our global leadership position. By truly caring about people – both its 85 million private and corporate customers and more than 142,000 employees – Allianz fosters a culture where its employees are empowered to collaborate, perform, embrace trends and challenge the industry. Our main ambition is to be our customers’ trusted partner, instilling them with the confidence to grow. If you dare, join us at Allianz Group.~crlf~~crlf~Allianz is an equal opportunity employer. Everybody is welcome, regardless of other characteristics such as gender, age, origin, nationality, race or ethnicity, religion, disability, or sexual orientation.
Allianz SE is the global headquarters of the Allianz Group. Our employees reflect the Group's geographic and functional diversity. Located in Munich, Allianz SE provides the perfect opportunity to start or continue with your international career.
Please submit your complete application documents (incl. CV, certificates, references and motivation letter)~crlf~~crlf~We are looking forward to receiving your application on www.allianz.com/careers.~crlf~~crlf~Allianz SE is committed to employment equality and therefore welcomes applications from all people regardless of gender identity and/or expression, sexual orientation, race or ethnicity, age, nationality, religion, disability, or philosophy of life.~crlf~~crlf~
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| 5,776 | 12 |
https://hoursfinder.com/0-9-hours/10am-to-8pm-is-how-many-hours.html
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We collected information about 10am To 8pm Is How Many Hours for you. Follow the liks to find out everything about 10am To 8pm Is How Many Hours.
Enter hours and minutes. Select am or pm. Enter the number of hours and/or minutes you wish to add to or subtract from the clock time. If the number of hours is greater than 24 hours, goto: Add or Subtract days, hours and minutes from an entered date and time Select "add" or "subtract" Click "Click to Calculate" button.
Mar 17, 2013 · From 8am to 1pm is 5 hours. From 8am to 1am is 17 hours. From 8pm to 1am is 5 hours. From 8pm to 1pm is 17 hours.
The hours entered must be a positive number between 1 and 12 or zero (0). The minutes entered must be a positive number between 1 and 59 or zero (0). The seconds entered must be a positive number between 1 and 59 or zero (0). Click "Click to Calculate" button. The number of hours, minutes and seconds between the two selected times will appear.
Lets assume you are talking about the same day, 10am to 8pm. 10am to 12 noon is 2 hours. 12 noon to 8pm is 8 hours exact. So,10am to 8pm is actually 10 hours(for same day).
Hours calculator (How many hours...) The hours calculator calculates the duration between two dates in hours and minutes This application determines the number of hours between two times or add hours …
This calculator helps you to calculate how many hours between two days, for example, between Monday 8 a.m and Wednesday, 6 p.m. If you enter day and time for each of two time points, it will show you how many hours (and minutes, if you wish) between these.
A free online calculator to determine the difference between any two times in hours. If you want to know how many hours there are between two times, our hours calculator will do the job. Supports American and European time conventions, depending on your browser's locale.
28 rows · Normally time is shown as Hours:Minutes. There are 24 Hours in a Day and 60 Minutes in …
Hours from Now Calculator. On this hours from now time calculator, you can calculate time from the number of hours and minutes from now.Enter hours, minutes and select the time later from now or before from now (ago), the calculated time will be displayed on the below of calculator.If hours from now result is bigger than a day, number of days will be shown.
By using the Time Duration Calculator, one can easily find the actual time difference between two specific points in time (the starting time point and the end time point). In order to use this calculator, you should enter the values of both specific time points in hours, minutes, and seconds .
Time, Add, Subtract, Hours, Minutes, Clock, Difference. Using 24 hours format, add or subtract the time in a day, and returns the result time in a day.
Feb 02, 2013 · From 11am to 8pm how many hours?
24-Hour Time Format. Many places in the world use the 24-hour time format. 24-hour time format is similar regular AM/PM time, except that you keep counting up after you get past 12 PM (noon). So 1 PM in 24-hour format is 13:00, 2 PM is 14:00, and so on. All you need to do is add 12 to any time in the PM to get 24-hour format time.
Jun 20, 2012 · You can figure this out in a few different ways. 10AM to 10AM is 24 hours and 4AM is 6 hours before 10AM. 24-6=18 10AM to noon is 2 hours. Noon to midnight is 12 hours. Midnight to 4AM is 4 …
Time calculator / day calculator (How many years, days, hours, minutes...) The computer calculates the duration between two dates in years, days, hours, and minutes This application determines the annual, hour, minutes and number of seconds between two times or days, hours, minutes, or seconds for a specified date added.
There are 34 hours. 10am on one day until 10am on the next day is 24 hours. Then, there are eight hours between 10am and 8pm.
Sep 04, 2009 · remember its 12hours from 8am-8pm and another 4 hours from 8pm to 12am. That guys just a jerk :D
Converting CST to London Time. This time zone converter lets you visually and very quickly convert CST to London, England time and vice-versa. Simply mouse over the colored hour-tiles and glance at the hours selected by the column... and done! CST stands for Central Standard Time. London, England time is 6 hours ahead of CST.
Jul 21, 2014 · from 8-noon is 4 hours, and then to 10 PM is another ten, so 4 and ten is a total of FOURTEEN (14) hours. It is a bit easier to see if you use the …
Apr 26, 2006 · It all depends. If it would be from today, 10am to 5.30pm would be 7 1/2 hours. But the question isn't clear, so it could be 10am from last Sunday 'till 5.30pm of tomorrow, which would be 103 1/2 hours and so on.
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| 4,748 | 23 |
https://www.crazyforstudy.com/q-and-a/your-company-quality-car-rental-has-a-reputation-for-renting-very-nice-well-maint-883370
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math
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70 % (920 Review)
Your company, Quality Car Rental, has a reputation for renting very nice, well-maintained cars. You have been given the task of analyzing the strength of recent demand at a group of local rental offices and recommending possible changes in the rate structure.
Your market can be divided into two kinds of customers, salespeople and tourists. The salespeople are interested in using cars to visit and socialize with clients around the city. The tourists are interested in some spots around the city, but want to go to outlying areas as well. They drive more. Based on the companyA????1s experience, business falls off pretty sharply if you charge more than $1 per mile driven, and is estimated to fall to zero (for both salespeople and tourists) if the rate became $1.50. For a typical salesperson, the number of miles driven during a one-week period increases by 100 for each $0.10 reduction in the charge per mile. A typical tourist increases his miles driven (during a one-week period) by 200 for each $0.10 reduction in the charge per mile.
During a typical week the group of offices that you are analyzing has a total of 300 customers (drivers): 200 salespeople and 100 tourists. Draw a demand curve to scale for a typical salesperson, with the mileage charge (in dollars) on the vertical axis and the number of miles driven per week on the horizontal axis. Write an equation for the demand curve in slope-intercept form.
Then do the same for a typical tourist. Draw a demand curve for a typical tourist, and write an equation in slope-intercept form.
Now consider the total demand for 300 customers, 200 salespeople and 100 tourists. For possible mileage charges of $0, $0.10, $0.20, $0.30, etc., figure out the total number of miles that would be driven by 200 salespeople during a week. Add in the total number of miles that would be driven by 100 tourists. Draw a total demand curve for the 300 people, and write an equation in slope-intercept form. Then write an equation for marginal revenue in slope-intercept form. (Assume no price discrimination.)
The rental cars depreciate at a rate of $0.30 per mile driven. For the company, this is the marginal cost of miles driven. Write a simple equation for marginal cost for the company. (Customers pay for all gasoline consumed.) Draw marginal revenue and marginal cost curves on the same diagram that you have for the total demand curve. Using the equations for marginal revenue and marginal cost, determine the total number of miles that would be best (from the companyA????1s point of view) for people to drive each week.
If there were no weekly charge, what would be the best mileage charge for Quality Car Rental (QCR) from QCRA????1s point of view? Explain your answer by using the equations, and also show the answer on your diagram for total demand, marginal revenue, and marginal cost. Using the chapter 11 formula that relates price, marginal cost, and elasticity, find the elasticity of demand for the total number of miles being driven.
If the mileage charge were kept as is, and a weekly rate were charged on top of it, how high could the weekly rate be without a typical salesperson leaving the market? If the same mileage charge and weekly rate apply to all customers, what would weekly profits be?
If the mileage charge were reduced by $0.20 per mile, how high could the weekly rate then be without a typical salesperson leaving the market? What would then happen to weekly profits? Explain your answers.
Determine the best mileage charge and weekly rate by using calculus. Write an equation for total profits, where total revenue is obtained from both the mileage charge (multiplied by the total number of miles driven) and the weekly rate (multiplied by the number of customers). The weekly rate, in turn, equals the area of a triangle of consumer surplus that would otherwise accrue to a typical salesperson. Profits equal total revenue minus total cost.
From a math standpoint, the tricky part is to take the above profit equation and, in every case where a quantity appears in the equation (either a total quantity of miles, or a quantity of miles for one customer), to substitute in an expression involving P, where P refers to the mileage charge. (You will have to make use of the equations for demand curves.) Then take the derivative of profits with respect to P and set it equal to zero. Solve for P. You can then figure out the weekly rate to charge.
Some customers may have Costco membership cards. How do you think their elasticity of demand for renting cars (for a week) would compare to that of non-Costco members? Depending on your response, would it then be worthwhile to offer discounts on the weekly rate for such people, in order to attract more customers? Explain your answers.
Your answer will be ready within 2-4 hrs. Meanwhile, check out other millions of Q&As and Solutions Manual we have in our catalog.
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CC-MAIN-2020-34
| 4,919 | 14 |
https://origin-wby.barnesandnoble.com/w/competitive-markov-decision-processes-jerzy-filar/1117229309?ean=9781461284819
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math
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This book is intended as a text covering the central concepts and techniques of Competitive Markov Decision Processes. It is an attempt to present a rig orous treatment that combines two significant research topics: Stochastic Games and Markov Decision Processes, which have been studied exten sively, and at times quite independently, by mathematicians, operations researchers, engineers, and economists. Since Markov decision processes can be viewed as a special noncompeti tive case of stochastic games, we introduce the new terminology Competi tive Markov Decision Processes that emphasizes the importance of the link between these two topics and of the properties of the underlying Markov processes. The book is designed to be used either in a classroom or for self-study by a mathematically mature reader. In the Introduction (Chapter 1) we outline a number of advanced undergraduate and graduate courses for which this book could usefully serve as a text. A characteristic feature of competitive Markov decision processes - and one that inspired our long-standing interest - is that they can serve as an "orchestra" containing the "instruments" of much of modern applied (and at times even pure) mathematics. They constitute a topic where the instruments of linear algebra, applied probability, mathematical program ming, analysis, and even algebraic geometry can be "played" sometimes solo and sometimes in harmony to produce either beautifully simple or equally beautiful, but baroque, melodies, that is, theorems.
|Publisher:||Springer New York|
|Product dimensions:||6.10(w) x 9.25(h) x 0.03(d)|
Table of Contents1 Introduction.- 1.0 Background.- 1.1 Raison d’Etre and Limitations.- 1.2 A Menu of Courses and Prerequisites.- 1.3 For the Cognoscenti.- 1.4 Style and Nomenclature.- I Mathematical Programming Perspective.- 2 Markov Decision Processes: The Noncompetitive Case.- 2.0 Introduction.- 2.1 The Summable Markov Decision Processes.- 2.2 The Finite Horizon Markov Decision Process.- 2.3 Linear Programming and the Summable Markov Decision Models.- 2.4 The Irreducible Limiting Average Process.- 2.5 Application: The Hamiltonian Cycle Problem.- 2.6 Behavior and Markov Strategies.- 2.7 Policy Improvement and Newton’s Method in Summable MDPs.- 2.8 Connection Between the Discounted and the Limiting Average Models.- 2.9 Linear Programming and the Multichain Limiting Average Process.- 2.10 Bibliographic Notes.- 2.11 Problems.- 3 Stochastic Games via Mathematical Programming.- 3.0 Introduction.- 3.1 The Discounted Stochastic Games.- 3.2 Linear Programming and the Discounted Stochastic Games.- 3.3 Modified Newton’s Method and the Discounted Stochastic Games.- 3.4 Limiting Average Stochastic Games: The Issues.- 3.5 Zero-Sum Single-Controller Limiting Average Game.- 3.6 Application: The Travelling Inspector Model.- 3.7 Nonlinear Programming and Zero-Sum Stochastic Games.- 3.8 Nonlinear Programming and General-Sum Stochastic Games.- 3.9 Shapley’s Theorem via Mathematical Programming.- 3.10 Bibliographic Notes.- 3.11 Problems.- II Existence, Structure and Applications.- 4 Summable Stochastic Games.- 4.0 Introduction.- 4.1 The Stochastic Game Model.- 4.2 Transient Stochastic Games.- 4.2.1 Stationary Strategies.- 4.2.2 Extension to Nonstationary Strategies.- 4.3 Discounted Stochastic Games.- 4.3.1 Introduction.- 4.3.2 Solutions of Discounted Stochastic Games.- 4.3.3 Structural Properties.- 4.3.4 The Limit Discount Equation.- 4.4 Positive Stochastic Games.- 4.5 Total Reward Stochastic Games.- 4.6 Nonzero-Sum Discounted Stochastic Games.- 4.6.1 Existence of Equilibrium Points.- 4.6.2 A Nonlinear Compementarity Problem.- 4.6.3 Perfect Equilibrium Points.- 4.7 Bibliographic Notes.- 4.8 Problems.- 5 Average Reward Stochastic Games.- 5.0 Introduction.- 5.1 Irreducible Stochastic Games.- 5.2 Existence of the Value.- 5.3 Stationary Strategies.- 5.4 Equilibrium Points.- 5.5 Bibliographic Notes.- 5.6 Problems.- 6 Applications and Special Classes of Stochastic Games.- 6.0 Introduction.- 6.1 Economic Competition and Stochastic Games.- 6.2 Inspection Problems and Single-Control Games.- 6.3 The Presidency Game and Switching-Control Games.- 6.4 Fishery Games and AR-AT Games.- 6.5 Applications of SER-SIT Games.- 6.6 Advertisement Models and Myopic Strategies.- 6.7 Spend and Save Games and the Weighted Reward Criterion.- 6.8 Bibliographic Notes.- 6.9 Problems.- Appendix G Matrix and Bimatrix Games and Mathematical Programming.- G.1 Introduction.- G.2 Matrix Game.- G.3 Linear Programming.- G.4 Bimatrix Games.- G.5 Mangasarian-Stone Algorithm for Bimatrix Games.- G.6 Bibliographic Notes.- Appendix H A Theorem of Hardy and Littlewood.- H.1 Introduction.- H.2 Preliminaries, Results and Examples.- H.3 Proof of the Hardy-Littlewood Theorem.- Appendix M Markov Chains.- M.1 Introduction.- M.2 Stochastic Matrix.- M.3 Invariant Distribution.- M.4 Limit Discounting.- M.5 The Fundamental Matrix.- M.6 Bibliographic Notes.- Appendix P Complex Varieties and the Limit Discount Equation.- P.1 Background.- P.2 Limit Discount Equation as a Set of Simultaneous Polynomials.- P.3 Algebraic and Analytic Varieties.- P.4 Solution of the Limit Discount Equation via Analytic Varieties.- References.
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CC-MAIN-2019-43
| 5,226 | 4 |
https://manualzz.com/doc/31593428/trig--polar-coordinates--and-complex-numbers
|
math
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Trig, Polar Coordinates, and Complex Numbers
Trig, Polar Coordinates, and Complex Numbers I. Graphing and reading trigonometric functions a. Always check if the problem you are working on is asking for radians or degrees, and if your calculator is in the right mode. b. The window set by ZTrig is based on whether radian or degree mode is selected. If a graph doesn’t look right, although ZTrig had been used, it may be because the mode (rad/deg) had been changed midway. If so, get into the right mode, and use ZTrig. i. Window set by ZTrig (Radian mode): Xmin ≈ − 2π Xmax ≈ 2π Xscl = π 2 Ymin = − 4 Ymax = 4 Yscl = 1 ii. Window set by ZTrig (Degree mode): Xmin = − 352.5° Xmax = 352.5° Xscl = 90° Ymin = − 4 Ymax = 4 Yscl = 1 c. Graph: y = 2 cos 2 x and find an equation of the form y = k + A*sin(Bx + C) Amplitude = A Period = 2π B Phase Shift = −C B ** All graphing features used with regular functions applies to trigonometric functions as well ** We can find the amplitude by using maximum/minimum finders. We can find the period and phase shift by tracing values. II. Polar Coordinates a. Pay attention to what mode (degrees or radians) the problem is asking for, and always make sure the calculator is in the right mode. b. The ANGLE menu i. Press 2nd and then MATRX ii. RPr( converts a rectangular form to r in polar coordinates. iii. RP θ ( converts a rectangular form to the θ in polar coordinates. iv. PRx( converts a polar form to the rectangular x- coordinate. v. PRy( converts a polar form to the rectangular y- coordinate. vi. The , button is located above the “seven” button. c. Converting from polar to rectangular (to three decimal places) i. (7, 2 π /3) Rectangular form is: ii. (-9.028, -0.663) Rectangular form is: d. Converting from rectangular to polar (in degrees) i. (6.9, 4.7) Polar form is: ii. (16, -27) Polar form is: e. Graphing polar graphs i. Change to RADIAN in the MODE menu. ii. Change to POL (polar) in the MODE menu. iii. Change to PolarGC in FORMAT menu (press ZOOM iv. 2nd , then ). Enter equation and graph like usual. When entering the variable θ , the same button ( X,T, θ ,n ) is used when graphing functions of x. v. In order to draw the graph proportionately, use ZSquare in the ZOOM menu. ZSquare slightly adjusts the window to make the graph appear horizontally and vertically proportional. vi. Graph r = 8*cos(2 θ ). vii. Graph r = 6*sin(3 θ ). III. Complex numbers a. Degrees and radians are important here, too! b. How do we convert -7-4i to polar form (in degrees; two decimal places)? i. While working with complex numbers, it is easier to read answers that have a fixed number of decimal places. How do you change the number of decimal places the answers are given in? ii. Is the MODE correct? iii. Enter the expression. How do we type in the ‘i’? iv. Conversion feature is located in the MATH menu. Once in MATH, use the right arrow to go to CPX. Then, conversion to polar is feature number 7. Select this and press ENTER. v. Answer: c. Convert 6-5i to polar form (in radians, two decimal places). d. How do we convert 5.71e ( −0.48)i to rectangular form (two decimal places)? i. Is the MODE correct? ii. Enter the expression. iii. The conversion to rectangular form is feature 6. Select this and press ENTER. iv. Answer: e. Convert 6.83e (-108.82 ° )i to rectangular form (two decimal places.
* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
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CC-MAIN-2021-21
| 3,516 | 3 |
https://www.neetprep.com/ncert-question/227384
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math
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15.8 A transverse harmonic wave on a string is described by where x and y are in cm and t in sec. The positive direction of x is from left to right.
(a) Is this a travelling wave or a stationary wave?
If it is travelling, what are the speed and direction of its propagation?
(b) What are its amplitude and frequency?
(c) What is the initial phase at the origin?
(d) What is the least distance between two successive crests in the wave?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100056.38/warc/CC-MAIN-20231129041834-20231129071834-00096.warc.gz
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CC-MAIN-2023-50
| 435 | 6 |
https://en.academic.ru/dic.nsf/enwiki/11229194/3865894
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math
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- Isaac Asimov Presents The Great SF Stories 15 (1953)
Isaac Asimov Presents The Great SF Stories 15 (1953) is the fifteenth volume of Isaac Asimov Presents The Great SF Stories, which is a series of short story collections, edited by
Isaac Asimovand Martin H. Greenberg, which attempts to list the great science fiction stories from the Golden Age of Science Fiction. They date the Golden Age as beginning in 1939and lasting until 1963.
This volume was originally published by
DAW booksin December 1986.
# "The Big Holiday" by
# "Crucifixus Etiam" by
Walter M. Miller, Jr.
# "Four in One" by
# "Saucer of Loneliness" by
# "The Liberation of Earth" by
# "Lot" by
The Nine Billion Names of God" by Arthur C. Clarke
# "Warm" by
# "Impostor" by
Philip K. Dick
The World Well Lost" by Theodore Sturgeon
# "A Bad Day for Sales" by Fritz Leiber
# "Common Time" by
Time is the Traitor" by Alfred Bester
The Wall Around the World" by Theodore R. Cogswell
# "The Model of a Judge" by
# "Hall of Mirrors" by
It's a Good Life" by Jerome Bixby
Wikimedia Foundation. 2010.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141732835.81/warc/CC-MAIN-20201203220448-20201204010448-00289.warc.gz
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CC-MAIN-2020-50
| 1,059 | 25 |
http://www.webconversiononline.com/mobile/mass-flux-density-conversion.aspx
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math
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How to use this calculator...
• Use current calculator (page) to convert Mass Flux Density from Kilogram/second/meter² to Gram/second/cm². Simply enter Mass Flux Density quantity and click ‘Convert’. Both Kilogram/second/meter² and Gram/second/cm² are Mass Flux Density measurement units.
• For conversion to different Mass Flux Density units, select required units from the dropdown list (combo), enter quantity and click convert
• For very large or very small quantity, enter number in scientific notation, Accepted format are 3.142E12 or 3.142E-12 or 3.142x10**12 or 3.142x10^12 or 3.142*10**12 or 3.142*10^12 and like wise
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00124.warc.gz
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CC-MAIN-2019-51
| 640 | 4 |
https://educationwithfun.com/mod/page/view.php?id=3559
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math
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Q90. What are some unique characteristics of Saturn?
Q91. Draw a diagram of Cassiopeia constellation to show the position of main stars in it.
Q92. Draw a diagram to show the position of main stars in Leo Major constellation.
Q93. How is the surface of the moon?
Q94. What factors make life possible on Earth?
Q95. What is meant by the phases of the Moon? Why phases of the moon occur?
Why does the moon change its shape every day?
Q96. Why is it difficult to observe the planet Mercury?
Q97. The radius of Jupiter is 11 times the radius of the Earth. Calculate the ratio of the volumes of Jupiter and the Earth. How many Earths can Jupiter accommodate?
Q98. Why is the distance between stars expressed in light years? What do you understand by the statement that a star is eight light years away from the Earth?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100545.7/warc/CC-MAIN-20231205041842-20231205071842-00268.warc.gz
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CC-MAIN-2023-50
| 812 | 10 |
https://brainmass.com/business/bond-valuation/bond-price-current-yield-ytm-roi-484298
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math
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1. You are considering the purchase of a 7%, 15-year bond that pays interest annually. If the yield to maturity on the bond is 6%, what price will you pay? Round your answer to the nearest cent.
2. What is the current yield on the bond from part a? Round your answer to the nearest tenth of a % (e.g., 12.2%).
3. Assume that you purchased the bond at the price determined in part a. It is now 2 years later and the bond is selling for $1120. What is the bond's yield to maturity at this point in time? Round your answer to the nearest tenth of a percent.
4. Now assume that you purchased the bond at the price determined in part a and now sell the bond for $1120. Assume you receive the second year's interest payment on the sale date. What is your rate of return on this investment? You must use a financial calculator to compute this return and round your answer to the nearest tenth of a percent.
The expert examines bond prices, current yields, YTM and ROI.
Lease- annual rental, cost of preferred stock, dividend yield on the stock at different payout ratios, return on a project, yield on a bond
1. You are leasing a machine for your business. It will cost the lessor $15,000 to be carried for a 6 year. lease term, and you will be putting down 40.00%. What will the annual rental charge be to you if the lessor pays 15% and must earn profits and risk of 5% on the deal?
2. A preferred stock issue was sold 2 years ago by your firm for a price of $25.00. The current market price of preferred issue is $17.00. The stock has a par value of $25.00 and a coupon rate stated at 5.00%. What is the cost of the issue (kps). What was the cost when it was issued, if you paid $4.00 per share in flotation costs?
3. A common stock issue is selling currently for $60.00. Net income amounts to 2,200,000, there are 300,000 shares outstanding. What would the dividend yield on the stock be at the following payout rates?
4. What maximum risk can you sustain if you invest in the following project?
Year 0 $875,000 Cost
1 $228,000 Returns
2 $196,000 "
3 $190,000 "
4 $275,000 "
5 $350,000 "
Money costs you 6.00%
Profits Desired is 4.00%
5. A bond has a 7.50% coupon rate, maturing 4 years from now. To buy this bond, you must invest $1.025 today. What will your return on investment (yield) be?View Full Posting Details
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514443.85/warc/CC-MAIN-20181022005000-20181022030500-00196.warc.gz
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CC-MAIN-2018-43
| 2,313 | 19 |
https://www.hindawi.com/journals/mpe/2015/450131/
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math
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An Alternative Approach of Dual Response Surface Optimization Based on Penalty Function Method
The dual response surface for simultaneously optimizing the mean and variance models as separate functions suffers some deficiencies in handling the tradeoffs between bias and variance components of mean squared error (MSE). In this paper, the accuracy of the predicted response is given a serious attention in the determination of the optimum setting conditions. We consider four different objective functions for the dual response surface optimization approach. The essence of the proposed method is to reduce the influence of variance of the predicted response by minimizing the variability relative to the quality characteristics of interest and at the same time achieving the specific target output. The basic idea is to convert the constraint optimization function into an unconstraint problem by adding the constraint to the original objective function. Numerical examples and simulations study are carried out to compare performance of the proposed method with some existing procedures. Numerical results show that the performance of the proposed method is encouraging and has exhibited clear improvement over the existing approaches.
Response surface methodology (RSM) is a design of experimental technique which shows relationship between several designs and response variables. The goal of the experimenter is to determine the optimal settings for the design variables that minimize or maximize the fitted response. For more explanation on response surface techniques see [1–3]. Most of the early work in RSM is centered on a single response problem. This methodology works effectively under the assumption of the homogeneous variance of the response. However, such an assumption may not hold in solving real-life applications. Myers and Carter suggested the need for developing statistical methodology known as dual response surface methodology, which can simultaneously optimize the mean and the variance function as to achieve the desired target while keeping the variance small. Generally, they defined the two responses as primary and secondary. The objective is to find the condition on the design factors that minimize or maximize the primary response function subject to the secondary response . In order to achieve this, three basic strategies are involved: experimental design, regression fitting, and optimization aspect. For the regression fitting, the method of the least squares is usually used to obtain the adequate response functions for the processes mean and variance by assuming that the collected data comes from a normal distribution. While, in the optimization stage, the interest is on what to optimize (i.e., determination of the objective function) and how to optimize (the optimization algorithm), in this paper, we propose a new optimization technique in dual response surface methodology based on the penalty function method for simultaneously optimizing both the location and scale functions. The usefulness of our newly proposed method for estimating the mean and variance of the optimal mean response is studied by some well known data sets and a simulation study. The outline of this paper is organized as follows. In the next section, we discussed some basic concept of the dual response surface followed by the description of the proposed method in Section 3. Numerical examples and simulation study are given in Sections 4 and 5, respectively. Finally, the conclusion is given in Section 6.
2. Dual Response Surface Review
Dual response surface technique consists of finding the optimum setting condition of the controllable factors in order to diminish the performance variability and deviation from the desired target of the decision maker. This method is an extension of the standard ridge analysis procedure which was introduced by Myers and Carter . Ridge analysis has been used by researchers in searching the optimum setting condition for a single response problem [1, 2, 5]. The dual response used mean and variance as separate functions for the system under examination. Then, these functions are optimized based on the chosen optimization technique to determine the optimum operating conditions of the system. Following the strategy of Vining and Myers , the mean and the standard deviation fitted response surfaces can be written aswhere wherewhere , , , , , and are estimated vectors and matrices of coefficients obtained from the least squares method. The simultaneous optimization of (1) and (3) using the Lagrangian multipliers method was proposed by Vining and Myers . Lin and Tu noted that the Vining and Myers approach does not always guarantee global optimum solutions due to the restriction of the optimization to equality constraints. Based on this, they proposed the minimization of mean squared error model (MSE) by introducing a slight bias in order to minimize the variability in the responses. This method includes two major parameters (the bias and the variance). Copeland and Nelson observed that minimizing MSE function does not specify how large the estimated mean might be from the specified target value . Instead, they modified VM model by placing some restriction on that minimizes subject to . Kim and Lin introduced a fuzzy modeling methodology using the idea of desirability function method. Several other techniques for solving the dual response surface problem have been presented, for example [10–12] proposed modification of mean squared error model. Furthermore, [13–16] presented a robust design for contaminated and nonnormal data using squared loss optimization scheme, a highly efficient and outlier resistant robust design estimator, a dual response approach to multiple response robust design problem, a multivariate robust design using MSE and dual response modeling, and robust parameter design, respectively. Recently, a biobjective robust design model has been developed in and a robust cutting parameter design using computer simulation has been studied in . In many real world situations, the experimenter or the decision maker often needs to keep a balance between the process mean and the process variance to achieve the desired target. It is known that getting all efficient solutions with the class of LT methods is challenging due to the large resulting process variance. However, most of the preceding optimization schemes are derived from the LT model, except the Vining and Myers model which is basically based on the Lagrangian multipliers approach. In this paper, an alternative objective function is considered based on the penalty function method.
3. Proposed Optimization Scheme for Dual Response Surface
In the present study, we present a new optimization technique for dual response surface methodology based on the penalty function method. The penalty function approach swaps a constrained optimization problem by a sequence of unconstrained optimization problems whose approximate solution ideally converges to a true solution of the original constrained problem. The unconstrained problem is formulated by adding a penalty term to the original objective function which consists of the penalty parameter multiplied by a measure of violation of the constraints [19, 20]. Consider the general formulation of the constrained optimization problem given below:By applying the penalty function method, we can obtain the solution of (5) using the modified objective function:where is the original objective function to be minimized and and are set of inequality and equality constraints, respectively. This paper specifically considers a quadratic penalty function of the formwhere is called the penalty constant which penalizes the equality constraints when the constraints relations are not satisfied. For the purpose of clarity, we replaced and in (7) with and and then write the following quadratic unconstrained minimization problem aswhere is the fitted response surface for mean, is the fitted response surface for the standard deviation function, and is the target value (usually specified by experimenter). If , the method gives exact solution. Since in this case it is necessary that which implies the bigger penalty parameter , thus the more exact solution is achieved. For (8), we can apply any unconstrained optimization method such as Newton’s method, BFGS method, Conjugate gradient method, and Steepest ascent (descent) method. Moreover, any nonlinear optimization software may be used to find the optimal design settings for the dual response surface problem. We used the package Rsolnp introduced in [21, 22] in R language, which is open source statistical software to perform the numerical computations and analysis. Our aim is to find an optimum solution such that the estimated mean value will be very close or equal to the target value , while the variance is kept small. The proposed approach has some advantages over some existing methods. Firstly, the proposed method takes into consideration the measure of violation of the constraint, whereas the VM and the class of LT methods are minimized without regard to the relative magnitude of violation of constraint. Secondly, the penalty parameter in (8) forced the to be close to zero or equal to zero so as to achieve the target of the experimenter (decision maker). Therefore, we anticipate the optimal setting condition obtained by the proposed method would be more efficient in terms of the contribution of both bias and variance components of of the estimated mean response compared with other existing methods.
4. Simulation Study and Results
In this section, a simulation study is conducted to assess the performance of the newly proposed method and compare it with the commonly used methods, such as VM, LT, and WMSE. Following [13, 23] the five responses are randomly generated from a normal distribution with mean and standard deviation at each control factor of settings , . The mean and the standard deviation are given aswhere . All the four methods were then applied to the data. The total of 500, 1000, and 2000 iterations is considered. Some summary values, such as the estimated mean of the optimal mean response, computed over iterations are defined by , bias = , and . The mean squared error, denoted by (MSE), is written as . Hence, the root mean squared error (RMSE) is given by . The bias, standard error, and root mean squared error (RMSE) of the estimates of the optimal mean response are exhibited in Table 1.
Figures 1 and 2 show the estimated bias and mean squared error based on the total number iteration for the various methods. It can be observed that the bias of the VM estimate is smaller than the LT and WMSE estimates. However, its RMSE is the largest among the three estimates since the variance of the VM estimate makes up most of the MSE. It is interesting to see that our proposed method is the best in terms of the smallest bias and RMSE values. Due to space constraint, Figure 3 presents kernel density estimates of VM, LT, WMSE, and PM for 1000 iterations only. The plotted results indicate that the proposed approach has a good behavior in which it is very close to the desired target. Therefore, one can say that the behavior of the constructed objective function based on the penalty function technique is more efficient and robust than other existing methods for solving dual response surface optimization problem.
5. Numerical Examples
5.1. Printing Process Study Data
To show a clear comparison, we consider the data set used by Vining and Myers and Lin and Tu which is given in Table 2. The experiment was conducted to determine the effect of the three variables (speed), (pressure), and (distance) on the quality of the printing process, that is, on the machines ability to apply colored inks to package labels. The experiment is a factorial design with 3 replicates at each point. Firstly, the average and variance of the 3 responses at each design point are computed, respectively. Vining and Myers used the least squares method to fit a quadratic response surface model for mean and standard deviation as follows:Based on the models in (10), Table 3 gives the summary of the results for the four different approaches obtained using the cuboidal region , . The optimal setting, estimated mean response, estimated standard deviation, and RMSE are presented in Table 3. The RMSE is calculated using the formula , where . It can be seen that the VM approach leads to the optimum setting which resulted in an estimated mean response of (501.57) and root mean squared error of (51.94). This optimal setting is very close to the target mean response but with larger RMSE. The second approach LT produces a target value of (494.69) and RMSE of (44.78) which is smaller than the RMSE of the VM. The third approach is the WMSE which gives the estimated mean response of (496.44) and RMSE of (44.81) which indicate a slight increase in RMSE and little improvement in mean response. The overall performance of the proposed approach is better than those three approaches mentioned with approximate mean value of (500.00) and RMSE of (44.75). Similar procedure is repeated in the next example in order to demonstrate a clear advantage of using the proposed method in terms of closeness to target mean response and the smallest RMSE.
5.2. The Catapult Study Data
This example will consider the data used by Luner and Kim and Lin . Three variables, (arm length), (stop angle), and (pivot height), are under consideration to predict the distance to the point where a projectile landed from the base of the roman style catapult. The experiment is a central composite design with three replicates as given in Table 5. In , the fitted second order polynomial regression models for the mean and standard deviation functions are given byHere, the assumed target mean value is . Table 4 shows the estimated mean and RMSE of the estimated optimal mean response. It is evident from Table 4 that the proposed method outperformed the other existing procedures.
Numerous procedures have been developed in the literature to obtain an optimal setting condition for the dual response methodology. This paper discusses four different objective functions for dual response optimization approach, based on the mean and variance models as separate response functions. The proposed objective function is based on the penalty function method. We have proposed a new objective function which is more efficient compared with the other existing methods. Numerical examples and simulations study are carried out to compare the performance of the newly proposed method with the frequently used methods. The numerical results clearly show an improvement of the proposed method over the existing methods in terms of having the smallest bias and RMSE. Moreover, the proposed approach can be applied to ridge analysis method and robust parameter design optimization.
|:||Desired target for the mean response|
|:||Vector of control variables|
|:||Vector of the observed responses|
|:||Standard deviation of the observed responses|
|:||Desired upper bound for the bias|
|:||Estimated mean of the optimal response|
|:||Average of the observed responses|
|:||Fitted response surface for the mean function|
|:||Fitted response surface for the standard deviation function|
|VM:||Vining and Myers |
|PM:||Proposed method in this paper|
|LT:||Lin and Tu or can be referred to as MSE |
|WMSE:||Ding et al. |
|MSE:||Mean squared error of the estimated mean optimal response|
|:||Root Mean squared error of the estimated mean optimal response.|
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
A. I. Khuri and J. A. Cornell, Response Surfaces: Designs and Analyses, vol. 152, CRC Press, 1996.View at: MathSciNet
A. E. Hoerl, “Ridge analysis,” in Chemical Engineering Progress Symposium Series, vol. 60, pp. 67–77, 1964.View at: Google Scholar
G. G. Vining and R. H. Myers, “Combining taguchi and response surface philosophies: a dual response approach,” Journal of Quality Technology, vol. 22, no. 1, 1990.View at: Google Scholar
D. K. J. Lin and W. Tu, “Dual response surface optimization,” Journal of Quality Technology, vol. 27, no. 1, pp. 34–39, 1995.View at: Google Scholar
K. A. F. Copeland and P. R. Nelson, “Dual response optimization via direct function minimization,” Journal of Quality Technology, vol. 28, no. 3, pp. 331–336, 1996.View at: Google Scholar
K.-J. Kim and D. K. J. Lin, “Dual response surface optimization: a fuzzy modeling approach,” Journal of Quality Technology, vol. 30, no. 1, pp. 1–10, 1998.View at: Google Scholar
S. Dong, Methods for Constrained Optimization, Massachusetts Institute of Technology, Cambridge, Mass, USA, 2006.
Y. Ye, Solnp Users' Guide, University of Iowa, 1989.
A. Ghalanos, S. Theussl, and M. A. Ghalanos, General non-linear optimization (package rsolnp), pp. 1–15, 2012.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100527.35/warc/CC-MAIN-20231204083733-20231204113733-00531.warc.gz
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CC-MAIN-2023-50
| 17,019 | 42 |
https://credibleforestcertification.org/what-is-a-closed-organ-pipe/
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math
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The organ pipe in which one end is opened and another end is closed is called organ pipe. Bottle, whistle, etc. are examples of closed organ pipe.
Stationary Waves in an Open Organ Pipe An open pipe is one which is opened at both ends. When air was blown into the pipe through one end, a wave travels through the tube to the next end from where it is reflected.
Similarly, what harmonics are present in a closed pipe? Closed Cylinder Air Column A closed cylindrical air column will produce resonant standing waves at a fundamental frequency and at odd harmonics. The closed end is constrained to be a node of the wave and the open end is of course an antinode.
Subsequently, one may also ask, why are organ pipes closed at one end?
The reason the open ends are always antinodes instead of nodes is because a node is where you can’t have any movement. This corresponds to the closed end of the pipe. The air at the very end of the pipe can’t go any further.
How do you know if a pipe is open or closed?
When the handle of a ball valve is parallel to the valve or pipe, it’s open. When it’s perpendicular, it’s closed. This makes it easy know if a ball valve is open or closed, just by looking at it. The ball valve below is in the open position.
What is an air column?
An air column can be defined as the weight or pressure of the air in a certain space.
How long are organ pipes?
The longest pipe in an organ is usually in the pedal department and on most organs is 16 foot in length. Cathedral organs usually have one or two 32 foot ranks, the 32 foot pipes having a frequency of just 16 Hertz! The longest pipes in existence are 64 foot long, but these enormous pipes are few and far between.
Why does end correction occur?
The end correction is liner when the wavelength is much larger than the diameter, however. The latter link first suggests that the reflection does not occur at the exit exactly, since the wave must leave the pipe to create suction and the resulting out of phase wave. Thus, the length of the pipe is slightly larger.
How do you determine end correction?
measurement of standing waves small distance known as the end correction. The end correction depends primarily on the radius of the tube: it is approximately equal to 0.6 times the radius of an unflanged tube and 0.82 times the radius of a flanged tube.
What is the fundamental frequency of an open pipe?
The fundamental frequency of an open pipe is 30 Hz. If one end of the pipe is closed, then the fundamental frequency will be. A .
How are stationary waves formed in an open pipe?
In pipes, waves are reflected at the end of the pipe, regardless of whether it is open or not. If you blow across the end of the tube, you create a longitudinal wave, with the air as the medium. This wave travels down the tube, is reflected, travels back, is reflected again, and so on, creating a standing wave pattern.
Are standing waves possible in open pipes?
Because an open end acts like a free end for reflection, the standing waves for a pipe that is open at both ends have anti-nodes at each end of the pipe. We can satisfy this condition with standing waves in which an integral number of half-wavelengths fit in the pipe, as shown in parts (a) – (c) of Figure 21.25.
How do you calculate harmonics?
Harmonics are positive integer multiples of the fundamental. For example, if the fundamental frequency is 50 Hz (also known as the first harmonic) then the second harmonic will be 100 Hz (50 * 2 = 100 Hz), the third harmonic will be 150 Hz (50 * 3 = 150 Hz), and so on.
What kind of wave is resonance?
Resonant Frequency Light waves come from the vibration of charged particles. Objects, charged particles, and mechanical systems usually have a certain frequency at which they tend to vibrate. This is called their resonant frequency, or their natural frequency. Some objects have two or more resonant frequencies.
How do you find the wavelength of a closed tube?
This calculation is shown below. speed = frequency • wavelength. frequency = speed / wavelength. frequency = (340 m/s) / (2.7 m) frequency = 126 Hz. speed = frequency • wavelength. wavelength = speed / frequency. wavelength = (340 m/s) / (480 Hz) Length = (1/4) • Wavelength. Length = (1/4) • Wavelength. Length = 0.177 m.
How standing waves are formed in a closed open pipe?
If the waves with some frequency are sent through the closed pipe, the waves gets reflects from closed end. When the incident and reflected waves with same frequency and in opposite direction superimposed the stationary waves formed in the closed pipe.
Is flute open at both ends?
The flute (photo at left) is a nearly cylindrical instrument which is open to the outside air at both ends*. The player leaves the embouchure hole open to the air, and blows across it. The two instruments have roughly the same length.
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https://www.brainscape.com/flashcards/ebm-5313919/packs/7935027
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math
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What are the four components needed to estimate sample size?
Population - that fits your demographic - this is the P in pico. Can be unknown or estimated.
Margin of Error (Confidence Interval) — how much error you want to allow, this defines how much higher or lower than the population mean, that the sample mean will fall. Usually +/- 0.5%
Confidence level - how confident you are that the actual mean falls within the confidence interval (90, 95, 99% are the most common and correlate to Z-scores of 1.6, 2.0, and 2.3 respectively)
Standard deviation - how much variance to allow - standard is .5%
Necessary Sample Size = (Z-score)² – StdDev*(1-StdDev) / (margin of error)²
What is an appropriate drop-out rate for a trial?
If less than 80% are followed up it is generally recommended that the result is ignored.
If the drop-out rates are high, how confident can you be in the final results? What if all the drop-outs had a bad outcome?
What does control, experimental, and patient expected event rates mean?
Control Event Rate (CER)
The rate at which events occur in the control group e.g. in a RCT of aspirin v placebo to prevent MI, a CER of 10% means that 10% of the placebo group had a MI. It is sometimes represented as a proportion (10% = 10/100= 0.1).
Experimental Event Rate (EER)
The rate at which events occur in the experimental group e.g. in the CER example above, an EER of 9% (or 0.09) means that 9% of the aspirin group had a MI.
Patient expected event rate
The patient expected event rate (PEER) refers to the rate of events we'd expect in a patient who received no treatment or conventional treatment.
Define Type 1 and Type 2 error in stats.
Type 1 error - a positive result when there is no real difference. This is a false positive
Type 2 error - no significant difference is found when there is actually a real treatment difference. This is a false negative
Small studies with a wide CI are prone to these errors.
Out of interest...
If you see an unexpected positive result (e.g. a small trial shows willow bark extract is effective for back pain) think: could this be a type 1 error? After all, every RCT has at least a 1 in 20 chance of a positive result and a lot of RCTs are published...
If a trial shows a non-significant result, when perhaps you might not have expected it, think could this be a type 2 error? Is the study under-powered to show a positive result?
Systematic reviews, which increase study power and reduce CI, are therefore very useful at reducing Type 1 and 2 error.
What is the null hypothesis?
States there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
In a clinical trial presenting two survival curves, how is the absolute benefit of treatment is best described? What is the significance of a plateau?
The median 'increase' in survival time (when comparing treatment to placebo or other).
The median survival is the time at which the percentage surviving is 50%. If more than half the patients are cured, there is no such point on the survival curve and the median is undefined (and often described as greater than the longest time on the curve). I like undefined medians!
Curves which flatten to a level plateau, suggest that patients are being cured, and curves which descend all the way to zero, imply that no one (or almost no one) is cured.
A median survival or survival percentage at x years wont give you the full story. The drop off may continue past 5 years but then flatten out at 6 - which means no deaths. People fortunate enough to make it out to six or seven years may well be cured. You can't tell that from the median or 5 year survival or from any other single point. It's the shape of the survival curve that tells this story.
Read: http://cancerguide.org/scurve_basic.html for a really good summary of survival curves.
What does relative risk reduction mean?
The relative risk, relative risk reduction, or risk ratio, is the ratio of the risk of an event in experimental group compared to the control group i.e. RR = EER/CER. The RRR is the proportional reduction seen in an event rate between the experimental and control groups. For example if a drug rreduces your risk of an MI from 6% to 3%, it halves your risk of a MI i.e. the RRR is 50%. But note that the ARR is only 3%.
Out of interest...
Relative risks and odds ratios are used in meta-analyses as they are more stable across trials of different duration and in individuals with different baseline risks. They remain constant across a range of absolute risks. Crucially, if not understood, they can create an illusion of a much more dramatic effect. Saying that this drug reduces your risk of a MI by 50% sounds great; but if your absolute risk was only 6%, this is the same as reducing it 3%. So, saying this drug reduces your risk by 50% or 3% are both true statements but sound very different, so guess which one that drug companies tend to prefer!
Define a hazard ratio
A way of expressing the relative risk of an adverse event i.e. if an adverse event was twice as likely to happen with a particular intervention, it would have a HR of 2.
Define number needed to treat (NNT) and how to calculate it.
A clinically useful measure of the absolute benefit or harm of an intervention expressed in terms of the number of patients who have to be treated for one of them to benefit or be harmed.
Calculated as 1/ARR.
Example: The ARR of a stroke with warfarin is 2% (=2/100 = 0.02),
The NNT is 1/0.02 = 50.
e.g. Drug A reduces risk of a MI from 10% to 5%, what is the NNT?.
The ARR is 5% (0.05), so the NNT is 1/0.05 = 20.
Define Absolute Risk Reduction (ARR)
CER - EER
- Absolute risk of an event happening (also called risk difference)
- Always expressed as a percentage.
- Looks at the difference between two event rates - i.e. absolute risk of death from MI + placebo is 5%. With a drug it's 3%. Thr ARR is 2%.
- Important to determine clinical relevance.
- (Absolute Risk Increase calculates an absolute difference in bad events happening in a trial ie when the experimental treatment harms more than the control).
Explain the concept of a likelihood ratio. How do you apply them as a bedside test?
The sensitivity and specificity of a test can be combined into one measure called the likelihood ratio. The likelihood ratio for a test result is defined as the ratio between the probability of observing that result in patients with the disease in question, and the probability of that result in patients with- out the disease.
LR = probability of a positive test / probability of a negative test.
For example, among patients with abdominal distension who undergo ultrasonography, the physical sign "bulging flanks" is present in 80% of patients with confirmed ascites and in 40% without ascites (i.e., the distension is from fat or gas). The LR for "bulging flanks" in detecting ascites, therefore, is 2.0 (i.e., 80% divided by 40%). Similarly, if the finding of "flank tympany" is present in 10% of patients with ascites but in 30% with distension from other causes, the LR for "flank tympany" in detecting ascites is 0.3 (i.e., 10% divided by 30%).
LR of 2 increases probability by 15%
LR of 5 by 30%
LR of 10 by 45%
For LRs between 0 and 1, use the inverse
1/2 = 0.5 - decreases probability by 15%
1/5 = 0.2 - decreases probability by 30%
1/10 = 0.1 - decreases probability by 45%
What does a p-value mean? What are the main influencing factors?
A measure that an event happened by chance alone e.g. p = 0.05 means that there is a 5% chance or magnitude that the result occurred by chance. For entirely arbitrary reasons p
The size of a P value depends on two factors:
1. The magnitude of the treatment effect (relative risk, hazard ratio, mean difference, etc)
2. The size of the standard error (which is influenced by the study size, and either the number of events or standard deviation, depending on the type of outcome measure used).
Very small P values (the easiest to interpret) arise when the effect size is large and the standard error is small.
Borderline P values can occur when there is a clinically meaningful treatment effect but a large or moderate standard error—often because of an insufficient number of participants or events (the trial is referred to as being underpowered).
This is perhaps the most common cause of borderline results. Borderline P values can also occur when the treatment effect is smaller than expected, which with hindsight would have a required a larger trial to produce a P value
Define positive and negative predictive value.
How do they differ from sensitivity and specificity?
The PPV is the percentage of patients who test positive for for a disease who really do have it out of the total positive, and the NPV is the percentage who test negative out of the total number of negative tests who really do not have it.
Depends on the background prevalence of the disorder in the population.
If a disease is rare, the PPV will be lower (but sensitivity and specificity remain constant). Often with tests the PPV is higher in a secondary care or sieved population than it is in primary care.
The likelihood ratio takes this into account and gives the most accurate information on test accuracy.
In an example using HIV with a 10% population prevalence, we had 9900 'true positive' test results – infected persons who tested positive – and 9000 false positive results. The positive predictive value in this case is (9900)/(9900 + 9000), or 52.4% or, nearly half of its positive results were false. In a subpopulation with higher HIV prevalence, the positive predictive value would be higher, as there would be more truly HIV-positive findings compared to the constant rate of false positive results.
The negative predictive value is defined as the proportion of persons with negative test results who are correctly diagnosed.
This value, too, depends on HIV prevalence. The negative predictive value is the number of persons correctly diagnosed as HIV-negative, divided by the total number of HIV-negative findings. The 81,000 'true negative' and 100 false negative results in our example yield a negative predictive value of (81,000/81,100), or over 99.9% – a very high likelihood that a negative result indicates a truly HIV-uninfected person.
What is the point of an ROC curve? How is it used?
The ROC curve is used to graph of Sensitivity vs the False positive rate or the sensitivity vs specificity
The AUC looks at the overall ability of the test to discriminate between those individuals with the disease and those without the disease.
A truly useless test (one no better at identifying true positives than flipping a coin) has an area of 0.5 (the red line is random). The best test has an area of 1 (which is the top left corner) - remember the AUC is the AUC from the red line.
If patients have higher test values than controls, then:
The area represents the probability that a randomly selected patient will have a higher test result than a randomly selected control.
If patients tend to have lower test results than controls:
The area represents the probability that a randomly selected patient will have a lower test result than a randomly selected control.
For example: If the area equals 0.80, on average, a patient will have a more abnormal test result than 80% of the controls.
If the test were perfect, every patient would have a more abnormal test result than every control and the area would equal 1.00.
If the test were worthless, half the controls would have a higher value than an actual diseases patient, and half would be lower, the AUC would be 0.5.
Define cumulative incidence. How does it differ from regular incidence?
Incidence is the number of new cases of a disease over time.
– Units include time
– Range is 0 to infinity
– Denominator is person-time
• Cumulative incidence is a proportion
– No units
– Range is 0 to 1
– Denominator is all at-risk in population
The cumulative incidence increases each year as the cases continue to accumulate, but the denominator for cumulative incidence – the initial population at risk – remains fixed.
• Incidence rate applies to a broader range of questions
• Kaplan-Meier provides a means to estimate cumulative incidence – censors those with incomplete follow-up
What does the term probability mean?
Probability of an event happening = Number of ways it can happen / Total number of outcomes
Probability can only ever be between 0 and 1.
For example - there are two ways a coin can land, heads or tails, it can go either way. There is a 1 in 2 or 1/2 chance of landing heads, and a 1/2 chance of landing tails. The probability of landing heads is 1 in 2.
The probability of a six sided dice landing a 4 is 1 in 6 or 1/6. There is only one way it can happen (there is only one 4 on the dice), vs 6 sides.
What does absolute risk reduction, or risk reduction mean?
Control event rate minus the experiment event rate (CER - EER)
The absolute risk is the actual, arithmetic risk of an event happening. The ARR (sometimes also called the Risk Difference) is the difference between 2 event rates e.g. AR of a MI with placebo over 5 years is 5% and with drug A is 3%, the ARR is simply 2%. This is the difference between the CER (control event rate) and the EER (experimental event rate).
e.g. Drug B reduces the chance of a stroke from 20% (CER) to 17% (EER). What is the ARR? Answer 3%.
Absolute risk increase (ARI) similarly calculates an absolute difference in bad events happening in a trial e.g. when the experimental treatment harms more patients than the control.
Knowing the absolute risk is essential when deciding how clinically relevant a study is.
Define subgroup analysis
What are the inherent problems with this?
What are the benefits?
- Participant data is split into subgroups to make comparisons between them, i.e by gender to compare differences within, or geographical locations.
- Used to investigate heterogenous results or to answer specific questions about patient groups or types of intervention.
- May be misleading – they are observational by nature, not randomised
- The more subgroup analyses there are, the higher the likelihood of false positives and negatives.
-Unexpected results from a subgroup analysis can be useful as a potential starting place for a subsequent clinical trial.
Does prespecifying a subgroup analysis help reduce the false positive/negative rate?
How can you address this?
-- Prespecified subgroup analysis does not prevent this, particularly if there are a large number of prespecified subgroup analyses (referred to as multiplicity). (If 20 subgroup analyses are prespecified, then it is expected that one of these subgroup analyses may show a false result for a P=.05 probability relationship.) For example, if the null hypothesis is true for each of 10 independent tests for interaction at the 0.05 significance level, the chance of at least one false positive result exceeds 40%.
- Multiplicity can be addressed by using criteria for statistical analysis that is more stringent than P=
What is the difference between prespecified subgroup analysis vs post-hoc analysis?
Is one better than the other?
- planned and documented before data examination.
- preferably included in study protocol
- includes endpoint, baseline characteristic, statistical method used.
- hypotheses tested not specified prior to data examination
- unclear how many were undertaken
- unclear if motivated by post-hoc inspection of the data
However, both prespecified and post hoc subgroup analyses are subject to inflated false positive rates arising from multiple testing. Investigators should avoid the tendency to prespecify many subgroup analyses in the mistaken belief that these analyses are free of the multiplicity problem.
Specificity is the proportion of people without the disease who test negative. A very specific test will have few false positives and be good at ruling a disease out. SpPIN means if a test is highly Specific (Sp) a Positive result rules the diagnosis in.
True negative / false positive + true negatives (d/b+d)
In other terms, if the test result for a highly specific test is positive you can be nearly certain that they actually have the disease.
Therefore, a test with 100% specificity correctly identifies all patients without the disease. A test with 80% specificity correctly reports 80% of patients without the disease as test negative (true negatives) but 20% patients without the disease are incorrectly identified as test positive (false positives).
A test with a high sensitivity but low specificity results in many patients who are disease free being told of the possibility that they have the disease and are then subject to further investigation. A good example is the D-Dimer which is sensitive but not specific - i.e about half of people who don't have the disease will test positive.
The sensitivity of a clinical test refers to the ability of the test to correctly identify those patients with the disease.
Sensitivity = true positives / true positives plus false negatives (a/a+c)
A test with 100% sensitivity correctly identifies all patients with the disease. A test with 80% sensitivity detects 80% of patients with the disease (true positives) but 20% with the disease go undetected (false negatives). A high sensitivity is clearly important where the test is used to identify a serious but treatable disease (e.g. cervical cancer). Screening the female population by cervical smear testing is a sensitive test. However, it is not very specific and a high proportion of women with a positive cervical smear who go on to have a colposcopy are ultimately found to have no underlying pathology.
How do you calculate and interpret a positive likelihood ratio?
LR+ = The probability of an individual with disease having a positive test / The probability of an individual without disease having a positive test
You will notice that the numerator in this equation is exactly the same as the sensitivity of the test, and the denominator is the converse of specificity (1 − specificity). Thus the LR+ of a test can simply be calculated by dividing the sensitivity of the test by 1− specificity (Sensitivity/1 − specificity).
LR+s greater than 1 mean that a positive test is more likely to occur in people with the disease than in people without the disease. LR+s less than 1 mean that a positive test is less likely to occur in people with the disease compared to people without the disease. Generally speaking, for patients who have a positive result, LR+s of more than 10 significantly increase the probability of disease (‘rule in’ disease) whilst very low LR+s (below 0.1) virtually rule out the chance that a person has the disease
How do you calculate and interpret a negative likelihood ratio?
LR− =The probability of an individual with the disease having a negative test / the probability of an individual without the disease having a negative test
The numerator in this equation is the converse of sensitivity (1 − sensitivity), and the denominator is equivalent to specificity. Thus the LR− of a test can be calculated by dividing 1 − sensitivity by specificity (1 − Sensitivity/Specificity).
LR−s greater than 1 mean that a negative test is more likely to occur in people with the disease than in people without the disease.
LR−s less than 1 mean that a negative test is less likely to occur in people with the disease com- pared to people without the disease.
Generally speaking, for patients who have a negative test, LR−s of more than 10 significantly increase the probability of disease (rule in dis- ease) whilst a very low LR− (below 0.1) virtually rule out the chance that a person has the disease.
LR+ = sensitivity
LR- = 1-sensitivity
What is pre and post-test probability?
What else do you need to estimate post-test probability, how do you do it, and what is it called?
The estimated probability of disease before the test result is known, is referred to as the pre-test probability, which is usually estimated on the basis of the clinician’s personal experience, local prevalence data and published reports.
The patient’s probability or chance of having the disease after the test results is known is referred to as the post-test probability. The post-test probability of disease is what clinicians and patients are most interested in as this can help in deciding whether to confirm a diagnosis, rule out a diagnosis or perform further tests.
According to the Bayes theorem, the post-test odds that a patient has a disease is obtained by multiplying the pre-test odds by the likelihood ratio of the test
Post−test odds = pre−test odds × likelihood ratio
Post-test odds are different to probability but can be converted.
What is Fagan's nomogram?
How is it used?
The Fagan’s nomogram is a graphical tool which, in routine clinical practice, allows one to use the results of a diagnostic test to estimate a patient’s probability of having disease. In this nomogram, a straight line drawn from a patient’s pre-test probability of disease (left axis) through the likelihood ratio of the test (middle axis) will intersect with the post-test probability of disease (right axis).
In a hypothetical population, the prevalence of Disease A was 10%, which means that when we randomly select a person from this population, his or her chance of having Disease A (pre-test probability) is 10%. The LR+ of Test A was earlier calculated to be about 13. As shown in Figure 2, when we draw a straight line from the pre-test probability of 10% through the likelihood ratio of 13, the line intersects with the post-test probability of about 60%.
This means that the probability of Disease A for a person in this hypothetical population increases from 10% to 60% when he or she has had a positive result for Test A.
In the same way, we can also estimate the post-test probability of a person in this population who has a negative result. You will recall that the LR− of Test A was earlier calculated to be 0.21. Joining the pre-test probability of 10% to the likelihood ratio of 0.21 on the Fagan’s nomogram, we read off a post-test probability of about 2% (Fig. 3). This means that after a negative test, a person in this population’s chance of having Disease A reduces from 10% to 2%.
A certain autosomal recessive disorder affects 1 in 1600 people; the carrier frequency is 5%. A DNA assay can identify the mutation in 80% of carriers; the false-positive rate of this assay is zero.
What is the best estimate of the positive predictive value (PPV) and negative predictive value (NPV) of this assay in screening the population for carriers?
A 20% 100%
B 80% 80%
C 100% 80%
D 100% 99%
E 100% 100%
Question 47 AMP2007a
A test has a sensitivity of 95% and a specificity of 80%. It is used to screen for a condition with a prevalence of 1 in 100.
What will the positive predictive value be nearest to?
A test has a sensitivity of 95% and a specificity of 90%. It is used to screen the general population for a rare condition that has a prevalence of 1 in 100,000.
What will the positive predictive value be nearest to?
If the pre-test probability of a condition is known, which of the following is also needed to be able to estimate the post-test probability?
D. likelihood ratio.
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CC-MAIN-2021-10
| 23,386 | 182 |
https://www2.cms.math.ca/Events/winter15/abs/cmq
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math
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McGill University, December 4 - 7, 2015
Has a charming "Massey spell" been cast on Galois $p$-extensions of general fields?
I will discuss this possibility by reviewing some of the work of M. Hopkins and K. Wickelgren, I. Efrat and E. Matzri, and my joint work with N. D. Tan. Some previous related work of S. Chebolu, I. Efrat, and myself; will also be recalled.
In my talk I will show how to extend the classical theory to a theory of cohomological invariants for Deligne-Mumford stacks and in particular for the stacks of smooth genus g curves. The concept of general cohomological invariants turns out to be closely tied to the theory of unramified cohomology, which was introduced by Saltman, Ojanguren and Colliot-Thélène and is widely used to study rationality problems.
I will also show how to compute the additive structure of the ring of cohomological invariants for the algebraic stacks of hyperelliptic curves of all even genera and genus three.
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| 959 | 5 |
https://ncerthelp.in/jkbose-new-model-paper-of-11th-class-physics/
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math
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JAMMU & KASHMIR BOARD OF SCHOOL EDUCATION
जम्मू और कश्मीर स्कूल शिक्षा बोर्ड
New Model Paper of 11th Class Physics
For 2022-2023 Exams with new pattern
If you are Jkbose Students, This is new Paper Pattern for all Students, Also Check Blueprint of this Model paper to know from Which Chapter or Unit You have 1, 2, 4 & 5 Marks Question.
Always Check our this Website for more Model Papers, Important Questions for Your Exam.
You need to Search (www.ncerthelp.in )
For all types of Important Things Which you need for Your Exams.
Class : 11th
MAXIMUM MARKS: 70
TIME :3 Hrs
A. Very Short Answer Type Questions (1×5)
1. If X=5t² Calculate velocity.
Given, x = 5t²
v = dx/dt
v = d(5t²)/dt
v = 10t
2. Draw X-t graph for free fall.
3. Define the term phase.
In Physics, the phase is defined as the position of a point in time on a cycle of a waveform. A complete cycle that is 360 degrees is defined as the phase.The phase is expressed in terms of radians. One radian of phase is 57.3 degrees approximately.
4. If Y=4 Sin (5t). Give values of amplitude & angular velocity.
Amplitude= 4, angular velocity=5
In linear SHM,
y=A sin (wt), where A=amplitude and w= angular velocity
in given equation, y = 4sin(5t)
hence, Amplitude =4 and angular velocity =5
5. What is dimensional formula for specific heat?
The specific heat s is the amount of heat Q per unit mass m required to raise the temperature θ by one degree Celsius.
6. Define following units.
I) Light Year II) Par-Sec.
Light Year: the distance that light travels in one year, about 9.4607×1012 kilometres
प्रकाश वर्ष; एक वर्ष में प्रकाश द्वारा तय की जाने वाली दूरी जो लगभग 9.4607×1012 किलोमीटर होती हैl
Par-sec: The parsec is a unit of length used to measure the large distances to astronomical objects outside the Solar System. One parsec is approximately equal to 31 trillion kilometres or about 3.26 light-years. One parsec is the distance to an object whose parallax angle is one arcsecond.
I) Absolute error II) Relative error.
ABSOLUTE, RELATIVE, AND PERCENT ERROR
- The actual error from the true value is called the absolute error.
- The relative error is the absolute error divided by total quantity. In the case
Of volume, Δv/v
- The percentage error is the relative error multiplied by 100.
7. Derive V=u+at by calculas method.
8. Steel is more elastic than rubber. Explain.
A body is said to be more elastic if it returns to its original configuration faster than others.
9. What is First law of thermodynamics? Explain sign convention also.
10. What is radius of gyration? Give an expression for it.
B. Short Answer Type Questions (3×12)
11. Derive an expression for angle of banking on a curved road with certain co-
efficient of friction.
What are laws of friction?
12. Differentiate xn by ab-initio method.
13. Derive an expression for the time period of simple pendulum using dimensional analysis.
14. What is impulse momentum theorem?
15. What is co-efficient of restitution? How it explains elastic and inelastic collision?
16. Show that total mechanical energy remains constant when a body is dropped from some height.
17. What is kinetic interpretation of temperature? Derive Kinetic energy in terms of temperature.
18. Calculate degrees of freedom for:
a) Monatomic b)Di atomic gas
19. Differentiate longitudinal & transverse waves with example.
20. Derive expression for escape velocity.
(Use law of conservation of energy)
21. Calculate the change in the value of acceleration due to gravity when a body is taken from surface to height “h”.
22. What is Isochoric and isobaric process?
Write 1st law of thermodynamic equation for all these processes.
C. Value –Based Questions (1×4)
23. If m1 and m2 are the masses constituting the rigid body, bound by some
internal forces so that the distance between the masses remain constant then
I) Define centre of mass.
II) Derive expression for position vector of centre of mass.
D. Long-Answer Type (3×5)
24. Derive the expression for path/trajectory time of flight (T) and horizontal
range(R) when a body is projected from a certain height in the direction of
What is centripetal acceleration? Derive expression for it?
25. Discuss S.H.M as a special case of circular motion and derive the
expression for displacement and velocity of a body executing S.H.M
Derive the expression for the displacement of a transverse progressive
26. Discuss and derive Bernoulli’s equation.
What are the modes of heat transfer? Discuss
I) Conduction II) Convection & Radiation
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CC-MAIN-2023-06
| 4,687 | 77 |
https://bondibeachau.com/graphing-calculator-algeo-analyze-functions-v2-27-pro/
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math
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Free Calculus calculator for plotting, analyzing, drawing functions
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300810.66/warc/CC-MAIN-20220118092443-20220118122443-00176.warc.gz
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CC-MAIN-2022-05
| 2,583 | 47 |
https://wizedu.com/questions/929911/consider-a-satellite-of-mass-ms-in-circular-orbit
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math
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Consider a satellite of mass ms in circular orbit around Earth, a distance h above Earth's surface. Assume the Earth is a sphere with radius Re and mass Me.
(a) As the satellite travels in circular orbit, will its speed increase, decrease, or remain constant? Explain.
(b) The only force acting on the satellite is gravity, so the satellite is in freefall. Why doesn't the satellite get closer to Earth's surface?
(c) Determine the ratio of the force of gravity on the satellite while in orbit to the force of gravity on the satellite while on the surface of Earth. Simplify your answer; no complex fractions! Give your answer in terms of Re and h.
(d) Starting with Newton's second law, determine an equation for each of the following quantities. Give your answers in terms of Me, Re, h, and the universal gravitation constant G.
(i) the freefall acceleration of the satellite,
(ii) The orbital speed of the satellite,
(iii) the period of orbit, which is the time it takes the satellite to complete one orbit around Earth.
(e) Determine the work done by gravity as the satellite moves through one-half of its circular orbit.
(f) Consider a near-Earth orbiting satellite (h=0.10Re) that is inhabited by astronauts.
(i) Determine the ration of the freefall acceleration of an astronaut in this circular orbit to the freefall acceleration of an astronaut on Earth.
(ii) If that astronaut weights 150 pounds on Earth, how large is the force of gravity on her in orbit? Is she "weightless"?
a) In a circular orbit, speed always remains constant. The change is speed is observed in elliptical orbits. In circular orbit, distance is always constant and hence speed, which is in accordance with the law of constant aerial velocity.
b) It is true that the atellites are in freefall, but the rate at which the falls toward earth is eqaul to the rate at which earth curves away from satellite. It is similar to a situation of a dog trying to catch its own tail.
c) Force on surface of earth Fs= (G*Me*Ms)/Re^2
Force in orbit Fo= (G*Me*Ms)/(Re+h)^2
Fo/Fs = [Re/(Re+h)]^2
d)i) F = G*Me*Ms / (Re + h)^2 = Ms*a
a = G*Me / (Re + h)^2
ii) a = V^2 / (Re + h)
V = sqrt[ a*(Re+h)]
V = sqrt [G*Me / (Re+h)]
iii) T = 2*pi*(Re+h) / V
T = [2*pi*(Re+h)] / sqrt [G*Me / (Re+h)]
T = [2*pi*(Re+h)^(3/2)] / sqrt(G*Me)
e) As the force of gravity is directed toward centre of earth and displacement is in perpendicular direction, hence,
work done by gravity is zero
f)i) acceleration in orbit = G*Me / (Re + 0.1Re)^2 = G*Me / (1.21*Re^2)
acceleration on surface = G*Me / Re^2
Ratio = [G*Me / (1.21*Re^2)] / [ G*Me / Re^2]
ii) in the orbit the wieght will reduce by the ratio calculayed in above part i.e
W = 150*0.826 = 123.96 lb
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100264.9/warc/CC-MAIN-20231201021234-20231201051234-00304.warc.gz
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CC-MAIN-2023-50
| 2,699 | 32 |
https://www.enotes.com/homework-help/let-b-c-three-sets-show-that-intersect-b-union-c-323679
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math
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Let A,B,C be three sets. Show that A intersect (B union C) = (A intersect B) union (A intersect C)
You need to prove distributive law of sets such that:
`Ann (BUC) = (AnnB)U(AnnC)`
You need to prove that (by definition U)
=> `(x in A ^^ x in B) vv (x in A ^^ x in C) ` (use distibution from logic equivalence)
=>`(x in Ann B) vv (x in A nn C) ` (use definition of `nn` )
=>`(x in Ann B)U (x in A nn C)` (use definition of U).
Hence, using logic equivalences yields the distributive law of sets such that A`nn` (BUC) `= (AnnB)U(AnnC)` .
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886895.18/warc/CC-MAIN-20180117102533-20180117122533-00311.warc.gz
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CC-MAIN-2018-05
| 535 | 8 |
https://indexarticles.com/reference/decision-sciences/fitting-the-lognormal-distribution-to-surgical-procedure-times-2/
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math
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Fitting the lognormal distribution to surgical procedure times
May, Jerrold H
Fitting the Lognormal Distribution to Surgical Procedure Times*
Minimum surgical times are positive and often large. The lognormal distribution has been proposed for modeling surgical data, and the three-parameter form of the lognormal, which includes a location parameter, should be appropriate for surgical data. We studied the goodness-of-fit performance, as measured by the Shapiro-Wilk p-value, of three estimators of the location parameter for the lognormal distribution, using a large data set of surgical times. Alternative models considered included the normal distribution and the two-parameter lognormal model, which sets the location parameter to zero. At least for samples with n > 30, data adequately fit by the normal had significantly smaller skewness than data not well fit by the normal, and data with larger relative minima (smallest order statistic divided by the mean) were better fit by a lognormal model. The rule “If the skewness of the data is greater than 0.35, use the three-parameter lognormal with the location parameter estimate proposed by Muralidhar & Zanakis ( 1992), otherwise, use the two-parameter model” works almost as well at specifying the lognormal model as more complex guidelines formulated by linear discriminant analysis and by tree induction.
Subject Areas: Hospital Management, Planning and Scheduling, Probability Models, and Statistics.
In an era of cost-constrained health care, health care institutions must schedule elective surgeries efficiently to contain the costs of surgical services and ensure their own survival. Efficient scheduling in a hospital is complicated by the variability inherent in surgical procedures, therefore, accurately modeling time distributions is the essential first step in constructing a planning and scheduling system. Modeling the nature of that variability has been of interest for the past 35 years. Rossiter and Reynolds (1963), for example, noted that the two-parameter lognormal distribution visually appears to fit a waiting time distribution. In the literature, both the normal (Barnoon & Wolfe, 1968; Dexter, 1996) and the two-parameter lognormal (Hancock, Walter, More, & Glick, 1988; Robb & Silver, 1996) distributions have been proposed for describing surgical times.
As part of a larger project, we were provided with a large set of patient data. We wanted to determine the best distribution for each procedure and type of anesthesia. Our criterion for “best distribution” is the one that gives the best overall fit, using an appropriate statistical test. The literature suggested that the normal and lognormal distributions were the only two viable candidate distributions to consider. Scatterplots of the data suggested that the lognormal would be the superior choice. However, minimum surgical procedure times, even for the simplest procedures, are strictly positive. Very common procedures, such as cardiac bypass, require at least several hours in the operating room. A lognormal distribution with a nonzero minimum (also called the origin, threshold, or location parameter) had to be considered, in addition to the usual, two-parameter lognormal. At least three methods to estimate the location parameter have been proposed in the literature. Assuming that our data set is typical of that which appears in at least other medical contexts, we recognized that a thorough analysis of the information could be used to derive rules about when to use a location parameter as part of the modeling process and, if so, which one to use.
The validity of rules extracted from an empirical study depends on the appropriateness of the selection of the data sets used in the study. Muralidhar and Zanakis (1992) used synthetic data, varied the coefficient of variation by 0.1 from 0.1 to 2, and used sample sizes of 10, 20, 30, 50, 100, 200, and 500, holding the mean and location constant, to compare the bias in three different estimators of the location parameter, and had equal sample sizes in all cells of the design matrix. Because our research is based on actual data, the frequencies and characteristics are a function of the population of surgical procedure times. To the extent that our population (we have a census, not a sample of it) mirrors that which might be encountered in real applications, the overall patterns of behavior on which our guidelines are based should be more useful than ones based on synthetic data. If surgical times are fundamentally different from those that might arise in other situations, that might not follow. Muralidhar and Zanakis based their selection procedures on the coefficient of variation of the data. We found the skewness to be important and the coefficient of variation to have little impact. Determining whether the difference in guidelines is due to the difference in objective (theirs being to minimize bias, ours being to maximize goodness of fit) or because of the differences in data used for empirical analysis, requires further research. In the next section, we describe the nature of the surgical data set used for our investigations. Following that, we discuss the way in which we implemented the location parameter estimators. Then, we compare the normal distribution with the best of the four lognormal alternatives (the two-parameter lognormal and the three possible three-parameter lognormals), and show that, in general, a lognormal model fits our data better than the normal model does. Having established that fact, in the following section, we analyze the behavior of the three location parameter estimators as a function of characteristics of the samples and derive decision rules for selecting which one to use, if any, in order to optimize goodness of fit.
THE DATA SET
Our data set consists of 60,643 surgical cases from a large university teaching hospital performed from July l, 1989, until November 1,1995. All data were collected using a previously described computerized system (Bashein & Barna, 1985). Variables collected include the anesthetic agents used; the date and time at which anesthesia began, the patient was ready for surgery, surgery began, surgery ended, and the patient emerged from anesthesia; and the surgical procedures performed (up to three), categorized by Current Procedural Terminology code (CPT) (Kirschner, Burkett, Marcinowski, Kotowicz, Leoni, Malone, O’Heron, O’Hara, Scholten, & Willard,1995). Of the 60,643 surgical records, 779 were omitted from analysis due to incomplete data. Exactly 46,322 cases were coded with only a single procedure code, 10,470 patients had exactly two different procedures, and 2,802 patients had exactly three procedures during surgery.
In this paper, we focus on two durations: the time between anesthesia start and end-the total time; and the time between surgery start and wound closure– the surgical time. Total time is important because it represents the amount of time the patient occupies an operating room, which we need to know in order to build an operating room schedule. Surgical time represents the amount of time the surgeon is with the patient. Because surgeons may operate sequentially on a series of patients in different operating rooms, surgical time is important for scheduling and sequencing patients. We used anesthetic codes to categorize the type of anesthesia administered into six categories: general, local, monitored, pain procedure, regional, and none. Only general, local, monitored, and regional anesthesia occurred often enough to be further analyzed. We categorized the data by procedure and by type of anesthesia. A total of 5,125 different procedure-anesthesia combinations were represented in the 46,322 cases involving exactly one procedure. Although about 13,542 cases involved two or three procedures, frequencies for such cases are typically too small to do meaningful distributional fits at the procedure-anesthesia combination level, and are therefore not discussed in this paper.
The 3,160 procedure-anesthesia combinations vary widely in coefficient of variation (the ratio of the standard deviation to the mean) and skewness, the two characteristics we later use to derive guidelines for choosing a distributional alternative. The observed values of coefficient of variation and skewness are also not equally distributed by the number of observations in each procedure-anesthesia combination, nor is skewness independent of coefficient of variation, as it might be in a designed experiment. Table 1 shows a cross-tabulation of the number of procedures in a procedure-anesthesia combination versus coefficient of variation. The coefficient of variation appears to decrease as sample size increases; the p-value from the chi-square test for independence is .0230. Table 2 shows a cross-tabulation of the number of procedures in a procedure-anesthesia combination versus skewness. Skewness strongly appears to increase with larger sample sizes; the pvalue from the chi-square test for independence is less than .0001. Table 3 shows that skewness tends to increase with coefficient of variation; the p-value for the chi-square test for independence is also less than .0001.
LOCATION PARAMETER ESTIMATION
NORMAL VERSUS LOGNORMAL FITS
Because we want to derive our conclusions from actual data, as opposed to synthetic data from a Monte-Carlo procedure, we must first establish that the data are best fit by a lognormal distribution before we can draw inferences about the best way to estimate the location parameter. Our comparison is based on p-values from a test of goodness of fit. Bratley, Fox, and Schrage (1987, pp.133-134) strongly criticized the approach of using goodness-of fit tests on a variety of distributions to choose a data model, so we limit our consideration to the normal and the lognormal, both of which have been previously proposed in the literature. We measure goodness of fit using the Shapiro-Wilk test, because it has been described as the best omnibus test of its type (D’Agostino,1986, p. 406). The IMSL routine to perform the Shapiro-Wilk test can be used with a sample size as small as 3, but we did not test anything smaller than S because almost any model may appear to fit a sample that small.
Our data are rounded (nominally) to the nearest minute and, in some cases, appeared to be rounded to the nearest five minutes. D’Agostino (1986, p. 405) pointed out that the Shapiro-Wilk test can be affected by rounding. He noted that rounding has a significant effect if the ratio of the standard deviation of the distribution to the rounding interval is 3 or S, but only minimal effect when the ratio is 10. Based on a one-minute rounding scheme, the average ratio of standard deviation to rounding interval for the 3,160 distributions we studied is 54.3. In two cases, the ratio is S or less, and in 45 of the 3,160 distributions the ratio is less than 10. If the data are actually rounded to the nearest five minutes, then the average ratio of standard deviation to the rounding interval is 10.9; in 621 cases the ratio is S or less; and in 1,853 of the distributions, the ratio is less than 10. Because many of the cases have recorded times other than at multiples of five minutes, we believe that the Shapiro-Wilk test is appropriate for our purposes.
We tested for normality using the IMSL routine SPWILK. We tested for lognormality by first determining all the candidate location parameters. If a location parameter was positive, we subtracted it from all the observed times, took the natural logs of the times, and tested the resulting series for normality. Our numerical results support the contention that the lognormal model is superior to the normal model for our data, and that the difference between the models increases as the sample size becomes larger. The second conclusion is not surprising, because goodness-of-fit tests are not particularly powerful for small sample sizes.
We cross-tabulated the observed Shapiro-Wilk p-values for the best lognormal model against sample size in order to see how the lognormal model’s goodness of fit changes as sample size increases. We divided p-values into four categories and sample size into five categories, as shown in Table 4. The row percentages for the column p > .1, for which a good fit by the lognormal model is strongly supported by the test, decrease from about 90% in the row for very small (30 or less) samples to about 52% in the row for large sized (over 200) samples. Correspondingly, the row percentages in the column for p
Tables 5 and 6 show how the best of the lognormal fits perform in direct comparison with the competing model, the normal. Table S tabulates the goodness-of-fit p-values, categorized as before, for the best of the lognormals against the normal for the 2,664 samples with n
The same pattern holds if we consider the Shapiro-Wilk p-values without categorizing them into four groups. For sample sizes of 30 and below, the best of the lognormals yields a goodness-of fit p-value larger than that of the normal 65% of the time (1,743 out of 2,664); for sample sizes of 31 to 60, 74% of the time (191 out of 258); for sample sizes of 61 to 100, 87% of the time (90 out of 104); for sample sizes of 101 to 200, 83% of the time (71 out of 86); and for sample sizes of 201 or more, 77% of the time (37 out of 48). The numerical results strongly suggest that if we could find a way to determine which lognormal distribution to fit (two– parameter or, if a three-parameter, which estimator of the location parameter to use), the resulting model would be superior to using the normal distribution.
The samples that fall into the four corners of Table 6 provide some insight as to ( 1 ) what characteristics of the data could be associated with the model that better fits the data, and (2) how well each model fits the data. The four comers include the samples of size 31 or larger for which neither model fits well (p-values below .01 for both), where one fits but the other does not (one has p > .1, the other has p
OVERALL PERFORMANCE OF THE LOCATION ESTIMATORS
The previous section compared the normal distribution to the best of the lognormal fits. In this section, we discuss the differences among the four different lognormal fit strategies, and the ways in which those differences are related to characteristics of the samples. In the next section, we derive a decision tree to recommend a modeling strategy as a function of sample characteristics.
First, do the four different lognormal alternatives have different goodnessof fit performance? Looking only at the 3,160 Shapiro-Wilk p-values for each of the lognormal alternatives, we ran a one-way ANOVA of those values against the location parameter estimator that was used. That approach may need to be treated with caution because there is no reason to presume that the p-values are normally distributed. In addition, both Cochrane’s C test and Bartlett’s test for homogeneity of variances show that the four groups’ standard deviations are not the same (p is essentially zero for both tests). Nevertheless, the means and 95% Tukey HSD interval plot shown in Figure 3, where 2LN means the two-parameter lognormal, shows that the four groups have significantly different average goodness-of-fit behavior, overall. Surprisingly, although all the samples should have minima strictly bounded away from zero, using the three-parameter lognormal with estimators Al or A2 appears to give poorer performance than ignoring the location parameter altogether, when no other characteristics of the data are taken into account. As shown in Figure 3, the three-parameter lognormal using estimator A3 gives a better overall fit, followed closely by the two-parameter lognormal.
A Kruskal-Wallace test on the same data shows that there may be more to the story, though. The average ranks of the four alternatives are significantly different (pvalue is essentially zero), but a box-and-whisker plot, with the median notched, the mean marked with a plus sign and outliers indicated (displayed in Figure 4), appears to show that the behavior of the three-parameter lognormal using estimator A^sub 2^, especially, may be highly related to factors not accounted for in an overall analysis.
The Venn diagram in Figure 5 shows the frequency of the best fit by modeling approach, where “modeling approach” is limited to the lognormal alternatives. The effect of including the normal distribution as an alternative is discussed in the next paragraph. Each region of Figure 5 shows the number of samples for which the alternative or group of alternatives gives the best goodness of fit. For example, 345 procedure-anesthesia combinations are best fit by the three-parameter lognormal using estimator A^sub 1^ alone; 121 are best fit by all four alternatives (the twoparameter lognormal, the three-parameter lognormal using estimator A^sub 1^, the threeparameter lognormal using estimator A^sub 2^, and the three-parameter lognormal using estimator A^sub3^); and 11 by the two-parameter lognormal, the three-parameter lognormal using estimator A^sub 2^, and the three-parameter lognormal using estimator A^sub 3^. Note that 2,045 times there is a unique best alternative, but only twice is it the three-parameter lognormal using estimator A^sub 2^. Although the samples should be strictly bounded away from zero, 26% (829/3,160) of the time using the threeparameter lognormal with any of the three estimators yields a model strictly inferior to ignoring the location parameter entirely. The single best pure strategy is to use the three-parameter lognormal with estimator A^sub 3^, but it only yields a “best” estimate 61 % of the time and is almost indistinguishable from always ignoring the location parameter. Always using the three-parameter lognormal with estimator A3 results in a best fit 1,941 out of 3,160 times as compared with ignoring the location parameter, which gives a best fit 1,918 out of 3,160 times.
We limited Figure 5 to lognormal alternatives. Without a domain-based argument to the contrary, it is plausible to believe that there is a single model that describes the stochastic process whose realizations are reflected in our data set. The analysis cited in the previous section demonstrates that this model is much more likely to be some form of the lognormal than it is to be the normal. From a statistical perspective, though, it is interesting to consider how Figure 5 would change if we included the normal distribution as an alternative. There are 1,021 samples best fit by the normal. The set of samples best fit by the normal does not overlap that of any of the lognormal alternatives. That is, none of the samples are best fit by both the normal and any lognormal distribution (there are seven samples for which all the methods give equally poor results-all have Shapiro-Wilk p-values essentially zero). The seven regions of the Venn diagram (A^sub 1^, 2LN, 2LN & A^sub 2^, 2LN & A^sub 3^, 2LN & A^sub 1^ & A^sub 3^, 2LN & A^sub 2^ & A^sub 3^, 2LN & A^sub 1^ & A^sub 2^ & A^sub 3^) affected by the explicit inclusion of the normal have their total frequency change from 2,253 (345, 829, 33, 779, 135, 11, and 121, respectively) to 1,225 (344, 359, 0, 457, 62, 2, and 1 ). The number of samples best fit by 2LN drops dramatically. Note, however, that the numbers of CPT-anesthesia combinations best fit by the three-parameter lognormal and only one of the estimators Al, A2, and A3 are essentially unchanged.
We next looked for guidelines that might improve the modeling process by helping to identify when to use which location parameter estimate, if any.
A MODEL SELECTION DECISION TREE AND ITS DERIVATION
We chose to base our decision tree on the coefficient of variation and the skewness for several reasons. Muralidhar and Zanakis (1992) used the coefficient of variation as the basis for recommending location parameter estimates. Both the coefficient of variation and skewness are easy to measure. The 13 different outcomes for the best distributional fit appear to differ significantly in their average coefficient of variation and skewness values. Figure 6 shows the mean and Tukey 95% HSD intervals for the coefficient of variation for the 13 groups, and Figure 7 does the same for skewness. For both one-way ANOVAs, both Cochran’s C test and Bartlett’s test yield p-values of essentially zero. The standard deviations differ by more than a factor of three to one, and sample sizes are not equal, so the p-values and significance levels of the tests may be off significantly. However, the figures do suggest that the coefficient of variation and skewness may be useful in determining modeling guidelines.
We thought that the size, relative or absolute, of the smallest order statistic might be a factor in explaining differences between the modeling approaches. We expected that the samples best fit by the two-parameter lognormal would have smallest order statistics close to zero, and that those best fit by the three-parameter lognormal using estimators A^sub 1^, A^sub 2^, and A^sub 3^ might also differ. Figure 8 shows means and 95% Tukey HSD intervals for a one-way ANOVA of observed minimum value (chi^sub1^) by best fitting lognormal alternative. As before, the tests for homogeneity of variances fail, so formal statistical tests may be questionable, but notice how similar the distributions are for the two-parameter lognormal category, and both the three-parameter lognormal using estimator A^sub 1^ and the three-parameter lognormal using estimator A^sub 3^. The samples best fit by the three-parameter lognormal using estimator A^sub 2^ do have significantly larger values of chi^sub 1^, but there are only two of them. Redoing the analysis displayed in Figure 8, using xl/mean instead of chi^sub 1^, did not separate further the three-parameter lognormal using estimator A^sub 3^ and the twoparameter lognormal, the two most significant contenders.
The Venn diagram in Figure 5 illustrates the difficulty in using a technique for extracting rules for selecting a modeling approach. If the sets of CPT-anesthesia combinations best fit by a particular alternative were disjoint, the task at this point would be to find functions that best separate those sets. The sets have considerable overlap. We applied two different methodologies, linear discriminant analysis (LDA) and a tree induction program (Sees) (Rulequest Research, 1998). Sees is an improved version of C4.5 (Quinlan, 1993) and a descendant of ID3, a machine learning algorithm for discrete classification. Sees uses hyperplanes to define the boundaries between sets, but only chooses hyperplanes parallel to the coordinate axes. At each branch of the tree, it uses an entropy-based measure to identify a new dividing line for the region not yet classified.
Note that both LDA and Sees determine functions, on the basis of which disjoint clusters may be separated. How do we deal with a situation such as ours, in which over 35% of the cases are actually best fit by at least two different alternatives? We considered two options. First, we used extraction techniques on the 2,045 data points for which only one alternative was best, and then evaluated the resulting rules on the entire data set. Second, we assigned each point for which multiple alternatives were optimal to all alternatives that best fit it, extracted rules, and then evaluated them on the entire data set. The second option expanded the data set to 4,666 cases.
The performance on the total data set of the four models derived from using the two classification methods and the two representations is shown in Table 7. The LDA classifiers correctly identify fewer of the model fits than do the corresponding Sees classifiers, but they are better at recognizing samples best fit by shift Al. The representation alternatives are to ignore samples for which more than one strategy is optimal, leaving 2,045 cases for a method to analyze, and to assign such samples to all optimal strategies, resulting in 4,666 cases. The performance of both LDA and Sees are almost identical using both representations. After manually examining the patterns in the Sees classifiers, we found that a simple rule of using no shift if skewness 0.35 does almost as well overall as the more complex rules constructed by Sees. The performance of the single rule is given in the sixth column of Table 7.
Based on a census of surgical times that appear to be lognormally distributed, we found that what minimizes bias also maximizes goodness of fit 61% of the time. Although our data sets should, on conceptual grounds, be strictly bounded away from zero, a strategy of leaving the location parameter out of the model entirely does almost as well as choosing the location parameter so as to minimize bias. Decision rules based on the skewness and coefficient of variation of the data can be used to identify the correct alternative 78% of the time, but do not do any better than a single rule based on the skewness.
It is possible that the existing estimators for the location parameter are also the best when goodness of fit is the criterion of interest, if we could only find the proper way of identifying which one to use. Skewness and the coefficient of variation do not appear to be adequate for that task; neither does the size of the smallest order statistic. The types of data for which the three-parameter lognormal using estimator Al is superior to the three-parameter lognormal using estimator A3 are particularly elusive. As shown in Table 7, the Sees decision trees for the 2,045 and 4,666 case analyses correctly identify, respectively,10 and 8 of the 345 procedure– anesthesia combinations best fit by the three-parameter lognormal using estimator A^sub 1^. The single skewness rule, which is as accurate, overall, as the Sees decision trees, correctly identifies none of those combinations. It is also possible that an altogether different type of estimator should be used when goodness of fit is the criterion of interest. Because accurate data modeling is critical to our planning and reasoning systems, we welcome further work that would determine which, if either, of the above possibilities is correct [Received: October 24, 1996. Accepted: March 15, 1999.
*This research was supported in part by a grant from the Institute for Industrial Competitiveness. Three anonymous referees made valuable, constructive comments on this paper. We especially thank the associate editor, whose extensive and thorough recommendations played a key role in both the conceptual development and the presentation of our work.
Barnoon, S., & Wolfe, H. (1968). Scheduling a multiple operating room system: A simulation approach. Health Services Research, 3(4), 272-285.
Bashein, G., & Barna, C. (1985). A comprehensive computer system for anesthetic record retrieval. Anesthesia Analgesia, 64, 425-431.
Bratley, P, Fox, B. L., & Schrage, L. E. (1987). A guide to simulation (2nd ed.). New York: Springer-Verlag.
D’Agostino, R. B. (1986). Tests for the normal distribution. In R. B. D’Agostino & M. A. Stephens (Eds.), Goodness-of fit techniques. New York: Marcel Dekker, Inc., 367-419.
Dannenbring, D. G. (1977). Procedures for estimating optimal solution values for large combinatorial problems. Management Science, 23, 1273-1283. Dexter, F (1996). Application of prediction levels to OR scheduling. AORN Journal, 63(3), 1-8.
Dubey, S. D. (1967). Some percentile estimators for Weibull parameters. Technometrics, 9, 119-129.
Hancock, W. M., Walter, P R, More, R. A., & Glick, N. D. ( 1988). Operating room scheduling data base analysis for scheduling. Journal of Medical Systems, 12, 397-409.
Kirschner, C. G., Burkett, R. C., Marcinowski, D., Kotowicz, G. M., Leoni, G., Malone, Y, O’Heron, M., O’Hara, K. E., Scholten, K. R., & Willard, D. M. (1995). Physicians’ Current Procedural Terminology 1995, Chicago: American Medical Association.
Muralidhar, K., & Zanakis, S. H. (1992). A simple minimum-bias percentile estimator of the location parameter for the gamma, Weibull, and log-normal distributions. Decision Sciences, 23, 862-879.
Quinlan, J. R. (1993). C4.5: Programs for machine learning. San Mateo, CA: Morgan Kaufmann.
Robb, D. J., & Silver, E. A. (1996). Scheduling in a management context: Uncertain processing times and non-regular performance measures. Decision Sciences, 24(6), 1085-1106.
Rossiter, C. E., & Reynolds, J. A. (1963). Automatic monitoring of the time waited in out-patient departments. Medical Care, 1, 218-225.
Sees (release 1.09) (1998). [Computer software]. St Ives, NSW, Australia: Rulequest Research Pty Ltd.
Jerrold H. May
Joseph M. Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, email: [email protected]. edu
David P Strum
Department of Anesthesiology Department of Anesthesiology Queen’s University, Kingston General Hospital, 76 Stuart St., Kingston, Ontario K7L 2V7, email: [email protected]
Luis G. Vargas
Joseph M. Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, email.: [email protected]
Jerrold H. May is a professor of decision sciences and artificial intelligence at the Katz Graduate School of Business, University of Pittsburgh, and is also the director of the Artificial Intelligence in Management Laboratory there. He has more than 60 refereed publications in a variety of outlets, ranging from management journals such as Operations Research and Information Systems Research to medical ones such as Anesthesiology and Journal of the American Medical Informatics Association. Professor May’s current work focuses on modeling, planning, and control problems, the solutions to which combine management science, statistical analysis, and artificial intelligence, particularly for operational tasks in healthrelated applications.
David P Strum earned his M.D. degree from Dalhousie University, trained at the University of Toronto and the University of California, San Francisco, and is board certified in both critical care medicine and anesthesiology. Previously on the
faculties at the University of Washington, University of Pittsburgh, and University of Arkansas. Dr. Strum is currently an associate professor of anesthesiology at Queen’s University, Ontario, Canada. Dr. Strum was also a visiting scholar at the Katz Graduate School of Business, University of Pittsburgh from 1996-97. He has published numerous papers in refereed journals such as Anesthesiology, JAMIA, Science, Anesthesia and Analgesia, and Decision Sciences. His research interests are in operations research and management for surgical services.
Luis G. Verges is a professor of decision sciences and artificial intelligence at the Katz Graduate School of Business, University of Pittsburgh, and co-director of the AIM Laboratory. He has published over 40 publications in refereed journals such as Management Science, Operations Research, Anesthesiology, JAMIA, and EJOR, and three books on applications of the Analytic Hierarchy Process with Thomas L. Saaty. Professor Vargas’ current work focuses on the use of operations research and artificial intelligence methods in health care environments.
Copyright American Institute for Decision Sciences Winter 2000
Provided by ProQuest Information and Learning Company. All rights Reserved
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CC-MAIN-2022-27
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http://www.technicalsociety.net/2008/09/september-2008-news/
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math
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An article in Metro Pulse (May 22, 2008) on the economics of the Knoxville convention center illuminated the difficulty of predicting the success of major investments, such as a $140 million convention center. Unfortunately Knoxville’s didn’t turn out to be one. Problems such as this, for which quantitative answers like net income have to be found with incomplete information on inputs and over a thirty year planning horizon are known as messy problems. In the early years of computer modeling, it was thought that one could overcome this deficiency by developing mathematical simulations of the underlying processes. Very soon the conclusion was “garbage in, garbage out.” In other words, computation alone cannot overcome input deficiencies. What computer models can do, however, what formerly could not be done, is “sensitivity analysis” or “what-if analysis.” That means answering the question of what will happen to the outcome if one or the other input is changed. This number crunching capability was an enormous step forward to more comprehensive analysis of engineering and economic problems. Messy problems are actually the rule as only in rare cases the inputs are known precisely. This means that, in general, every input has a range and possibly also a frequency associated with it and only in very special cases the input is represented by a deterministic variable, one that has a single value and a zero range. In this latter case one can
just use classic arithmetic and add, multiply or divide the variables, as the mathematical model of the problem requires. Deterministic analysis was the way in the pre-computer age, when number crunching by hand from a certain point on became practically impossible. The problem with the deterministic approach is that it produces a shaky result, one answer when there are usually many. This
becomes rather obvious when there is no agreement on what the inputs should be. Different people or even the same person may think that this or that input value is more or less likely the right one to be used. In these situations the computer comes in handy as it allows a rather painless repetitive analysis of numerous input sets. An example is the calculation of income from conferences at the Knoxville convention center that was described in the Metro Pulse article. The mathematical model used was the product of four www.technicalsociety.net inputs: number of attendees, amount spent by each, an economic multiplier, and the
number of days in attendance. In this case, almost every person asked would come up with a different number for each of these inputs, not just lay persons but also experts in the subject. I assumed
three values for each, put them in a spreadsheet and got 3^4 = 81 results. Since I used my own estimates, my results are not comparable with those of the true project, but they reminded me of a few interesting characteristics. The range of the 81 outcomes was vast, from $38 million to $275,000, with each number having a frequency of 1/81 (based on my assumptions). Sorting the results in a descending series and adding their frequencies from the bottom up produced a non-exceedance probability distribution that revealed a few interesting results. The probability that the lowest value would be exceeded was 1 – 1/81 = 0.99, which means that this lowest income would be exceeded by a comfortable probability. Since the simplistic model that I used did not include costs, the outcomes never went negative. The probability that the highest income of $38 million would be exceeded was zero. These extreme values are a direct consequence of my range assumptions for the inputs. Taking the average of all 81 values was $7.6 million. It occurred at a non-exceedance probability of 60 %. This is a reminder that this “average” income is not exceeded in 60 % of outcomes. It seems rather risky to base a project on such a rather low probability of success.
A method that number crunching by computers has made possible is Monte Carlo simulation. Given a number of inputs, their ranges and frequency distributions, and a mathematical process model, like the one above or, better, a more comprehensive one, would random sample sets of input data and run them through the model. Again, a good deal of attention must be paid, first, to the input preparation, second to the adequacy of the process model, and, third, to the analysis of the results. The reliability or the outcome stands and falls with the quality of the inputs. Repetitive sampling and evaluating the input sets produces a sufficiently large number of outputs that are then statistically analyzed by determining their dispersion, mean and range. The most important information obtained from such analysis is the probability of achieving certain goals. One is to find the probability that the project will economically fail, i.e., produce a negative return, given all revenues and costs of the project, and how high it is. If it exceeds the comfort level of the decision makers, then this would mean back to the drawing board for a revised project alternative. For example, for one reason or another, the Knoxville convention center ballooned from a 100,000 sqft project to a 500,000 sqft one.
Of course, advanced decision analysis methods still require a lot of attention to detail to avoid mistakes and wrong conclusions. But it seems that despite all advances in computation technology and mathematical modeling the analysis at the consumer level is still stuck at the pre-computer level and decisions for multi-million dollar projects are based on rather simplistic calculations. If this is the case one should not be surprised when the project turns out to be a economic sink of taxpayer money instead of a well spring of profits, or a t least a break-even proposition.
In conclusion, an as yet other analytical approach to messy problems should be mentioned, namely the use of fuzzy arithmetic. This approach goes back to a 1965 paper on fuzzy sets by Lotfi Zadeh. I remember it because it looked intriguing to me and I retained a copy of. Here, instead of probabilities input data are qualified by levels of belief instead of probabilities. The outcomes are again associated with a level of belief instead of probabilities. Karl E. Thorndike, FuziWare , Inc., of Knoxville, Tennessee, developed a software FuziCalc that was published in 1993. I momentarily do not know how it fared. But in dealing with messy problems and multi-million dollar investments I would not leave one stone unturned in an attempt to thoroughly analyze a multi-million dollar project, especially one that taps our own money. WOW.
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CC-MAIN-2021-10
| 6,667 | 8 |
http://opus.bath.ac.uk/31670/
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math
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Davenport, J., 2012. Program Verification in the presence of complex numbers, functions with branch cuts etc. In: SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2012-09-25 - 2012-09-28.
In considering the reliability of numerical programs, it is normal to \limit our study to the semantics dealing with numerical precision" (Martel, 2005) [Mar05]. On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as \does the low-level arithmetic imple- ment the high-level mathematics". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more dicult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simplication rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities.
|Item Type ||Conference or Workshop Items (Paper)|
|Departments||Faculty of Science > Computer Science|
Actions (login required)
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123048.37/warc/CC-MAIN-20170423031203-00363-ip-10-145-167-34.ec2.internal.warc.gz
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http://voteragauche.org/file-ready/west-e-mathematics-0061-teacher-certification-test-prep-study-guide-xam-west-epraxis-ii
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math
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The last date that west e computer science will be administered is august 19 review an expanded study guide view a test preparation video vouchers are available for purchase by state education agencies and educator preparation programs to provide candidates with full or partial credit toward fees for test registration and preparation . Praxis ii mathematics 0061 teacher certification test prep study guide praxis ii teachers xam home praxis ii mathematics 0061 teacher certification test prep study guide praxis ii teachers xam praxis ii mathematics 0061 by sharon wynne ms xamonline inc . Practice test questions with detailed answer explanation become a mathematics teacher with confidence unlike other teacher certification test preparation material our west e mathematics study guide drills all the way down to the focus statement level providing detailed examples of the range type and level of content that appear on the . West e mathematics 0061 teacher certification test prep zsoi4net ebook pdf free and manual reference download west e mathematics 0061 teacher certification test prep study guide xam west epraxis ii ebook pdf 2019 trends analyses of students mathematics performance in the study discovered that mathematics performance in nasarawa state . For washington educators the west e is a requirement in order to obtain teaching certification as of september of 2014 the west e math exam has been replaced by the nes mathematics 304 exam this test must be taken as an assessment of the skills and knowledge required to become an entry level math teacher according to continue reading west e math practice questions
How it works:
1. Register Trial Account.
2. Download The Books as you like ( Personal use )
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s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578531984.10/warc/CC-MAIN-20190421140100-20190421162100-00186.warc.gz
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CC-MAIN-2019-18
| 1,728 | 4 |
https://www.mendeley.com/research-papers/note-fuzzy-multiobjective-linear-fractional-programming-problem/
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math
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-The concept of ranking method is an efficient approach to rank fuzzy numbers. The aim of the paper is to find the pareto optimal solution of fuzzy multiobjective linear fractional programming (FMOLFP) problem. To study FMOLFP problem, the fuzzy coefficients and scalars in the linear fractional objectives and the fuzzy coefficients are characterised by triangular or trapezoidal fuzzy numbers. The left hand side of the fuzzy constraints are characterised by triangular or trapezoidal fuzzy numbers, while the right hand sides are assumed to be crisp number. The fuzzy coefficients and scalars in the linear fractional objectives and fuzzy coefficients in the linear constraints are transformed to crisp MOLFP problem using ranking method. The reduced problem is solved by simplex method to find the pareto optimal solution of MOLFP problem. To demonstrate the proposed approach, one numerical example is solved.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814493.90/warc/CC-MAIN-20180223055326-20180223075326-00269.warc.gz
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CC-MAIN-2018-09
| 1,043 | 4 |
https://www.qats.com/cms/2012/06/12/the-importance-of-heat-flux-sensors/
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math
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Heat flux sensors are practical measurement tools which are useful for determining the amount of thermal energy passed through a specific area per unit of time. Measuring heat flux can be useful, for example, in determining the amount of heat passed through a wall or through a human body, or the amount of transferred solar or laser radiant energy to a given area.
Affixing a thin heat flux sensor to the top of a component will yield two separate values which are useful in determining the convection heat transfer coefficient. If the heat flux can be measured from the top of the component to the ambient airstream and if the temperature at the top of the component and of the ambient airstream is measured, then the convection coefficient can be calculated.
q = Heat flux, or transferred heat per unit area
h = Convection coefficient
TS = Temperature at the surface of the solid/fluid boundary
TA= Ambient airstream temperature
Using a heat flux sensor can be useful for lower powered systems under natural convection scenarios. Under forced convection, the heat lost to convection off the top of a component can often be significantly higher than the heat lost to the board, particularly if the board is densely populated and the temperature of the board reaches close to the temperature of the device. Under natural convection situations, often the balance of heat lost to convection and heat lost through the board becomes more even and it therefore is of even greater interest to the designer to understand the quantity of heat dispersed through convection.
Experiments done at Bell Labs alluded to the effect of board density on the heat transfer coefficient. In these experiments, thin film heat flux sensors are affixed to DIP devices which populate a board. The total heat generation of the board is kept constant, so the removal of components from a densely populated board only increases the heat generation per component. The results of this particular experiment highlight an increase in the ratio of heat lost through convection from the surface of the component as board density increases and individual device power decreases.
Surface Heat Flow vs. Board Density
Qs/Qt = the ratio of total heat flow through device surface to total heat generation
σ = the ratio of total device surface area to total board area
If a board was to be sparsely populated, a greater percentage of heat can be transferred to the board due to larger thermal gradients; however since the overall surface area of the sum of devices decreases, to some extent the heat transfer coefficient must increase to reflect a balance. As the number of components decreases, the power generation increases per component, and the larger resulting temperature gradients in the region around the component yield more convective flow and thus an increase in the heat transfer coefficient. On the other hand, if the board becomes more densely populated, the proportion of heat transferred through the surface, as compared to through the board increases, and the overall increase in heat transferred through the surface yields increased flow and heat transfer at an individual component surface.
The use of a heat flux gauge is an important tool for the electronics designer. In particular, by using a heat flux gauge, it is possible to experimentally determine the heat transfer coefficient at a certain location on the electronics board where it would have had to be simply predicted or estimated previously. Due to the complexity of many electrical systems as well as the irregular nature of many boards, often analytical or CFD methods are not accurate and the best approach is empirical techniques. The use of the heat flux sensor can give results which would be difficult to calculate using analytical or numerical simulations. However, like most other instruments, it is important to use the sensor correctly and carefully to decrease the errors within a system and increase the reliability.
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https://fdocuments.net/document/hellenistic-achievements.html
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math
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Embed Size (px)
Transcript of Hellenistic achievements
ThalesFirst true mathematician
USed math to calculate the height of the pyramids1st known person to study electricityExplained natural phenomena without using the gods!
AnaximanderEarth had once been covered all in waterPeople had evolved from an earlier form (perhaps a fish)
And the first known map
Alexander the Greats legacy was the culture of learning that he spread through out his empireMany men made important discoveries
Who was the first to understand that the universe was huge!
The earth revolves on its axis
That we have a heliocentric solar system
But the world was not ready for his ideas!It wouldnt be until the 1500s and the work of Nicholas Copernicus that the world began to accept that the Earth revolved around the sun!
ErasistratusFounded the school of anatomy in alexandria
The Brain is the center of the nervous system
Discovered the pulseANd its importance in diagnosing illness
The heart pumps blood through the body
liquids are taken into the esophagus and then passes into the bladder
HipparchusThe father of trigonometry
Created TrigonometryCreated Trigonometry tablesTrigonometry deals with the relationship between the sides and angles of a plane or spherical triangles
Distance between sun and the earth
Predicted eclipsesDue to his studies of the movements of the planets
EuclidKnown as the Father of Geometry
But he didnt invent itHe came up with some theorems, compiled the works of others and people used it for centuries!
Calculated the circumference of the EarthAnd was only off by about 200 miles!
He created the most accurate map knownAnd believed that all the oceans were connected
ArchimedesGreatest scientist of antiquity
Approximated piWithout formulas! Just used calculations of polygons to get as close as possible!
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https://www.techyv.com/questions/safest-shortest-and-simplest-procedure-modify-equation/
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math
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N/APosted on - 04/10/2015
What is the simplest and shortest procedure to follow in order to modify an equation in either a linear format or a professional format when working in Microsoft Word and Microsoft Excel? I am a Math teacher who teaches in a second cycle institution in Ghana. I do prepare mathematical questions and I would like to have the shortest and safest way of inserting as well as modifying the equations to suit my preference. Thank you.
The safest, shortest and simplest procedure to modify an equation
Happy to support you!
It is a simple task to insert & edit equations in MS Excel. You just need to type in the equation by using the necessary symbols in the "Equation toolbar". There are around 160 symbols to be chosen from.
Also, you can use its templates and frameworks with symbols you need to insert into the particular equations. Similarly, the Equation Editor also helps in inserting special characters, etc.
At the same time, it is possible to paste the equation created on MS Office Word on your worksheet. Actually, Word of course, provides with a full collection of common equations to facilitate simple and easier equation handling.
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| 1,167 | 7 |
http://the-adam.com/adam/math-4q6/hypersq.htm
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math
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One of the problems facing academic mathematicians is that they can't really tell anybody what they do. There was an example parody of an academic mathematician whose specialty was "Riemannian Hypersquares."
This hypothetical professor had a specialty so obscure that there might be fewer than ten people worldwide who would even understand his field of study, other mathematicians specializing in Riemannian Hypersquares.
These seven or eight mathematicians write papers that only the others in that group can understand and, for everybody else, the only explanation they can offer is, "It's very complicated, you wouldn't understand it." This is a cop-out.
If this is a cop-out for an academic weenie, then it is also a cop-out for a practicing industrial mathematician. Maybe I can't explain the subtleties of what I do, but I should be able to explain the problems I'm solving and the value I add to my employers and to others.
This is part of a bigger issue, the notion that what is easy to explain is usually what should be done. There is a close relationship between pedegogy and practice. This may reflect some deep and fundamental principle, but I think it is closer to the idea that what our minds learn best is usually what works best.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710978.15/warc/CC-MAIN-20221204172438-20221204202438-00530.warc.gz
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http://www.filesland.com/companies/Math-Mechanixs-LLC/Math-Mechanixs.html
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math
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Math Mechanixs, LLC.
Math Mechanixs is an easy to use scientific math program with a Math Editor worksheet for solving mathematical problems and taking notes, an extendable Function Library with over 170 predefined functions and an integrated Function Solver, a 2D and 3D Graphing Utility supporting point labels, zooming, rotation, translation and numerous types of graphs, and a Calculus Utility supporting single, double, and triple integration and differentiation. Math Mechanixs is a freeware categorized in business calculators & converters software.
Version: 22.214.171.124 Released: 1/28/2007
Size: 8.72 MB
Platform: Windows 98, ME, NT 4.x, Windows 2000, XP, Windows 2003
Download Link: Download
Keywords: differentiation trigonometry graphing physics engineering calculator statistics graphing software 2d graphing math calculus business science integration conversions math software
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CC-MAIN-2018-26
| 892 | 7 |
https://answers.yahoo.com/question/index?qid=20100426103111AA54AvP
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math
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It varies from person to person. You're saving $1,000 per year, but what is time worth?
I average 60,000km/yr. Averaging 80km/h (between city and highway driving) I spend a total 750 hours, or 31 days. If I speed (which I do) by 15km/h, I now have an average of 95km/h. Speeding, I spend 631 hours on the road, equal to about 24 days.
So, I'm not talking reckless driving, I'm just pushing the speedometer a little bit above the limit. In fact, I've never heard of a ticket being issued for anything less than 20km/h over, and true to fact I've driven past police cars and speed traps at 15 over without being ticketed.
So... only a small increase, safety not compromised, police don't pull me over, and I gain 7 days more time to my year. $1,000 in savings just doesn't seem worth it to me. I've no intention of slowing down.
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http://philpapers.org/s/Hartry%20H.%20Field
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math
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This paper is concerned with the debate between substantival and relational theories of space-time, and discusses two difficulties that beset the relationalist: a difficulty posed by field theories, and another difficulty (discussed at greater length) called the problem of quantities. A main purpose of the paper is to argue that possibility can not always be used as a surrogate of ontology, and that in particular that there is no hope of using possibility to solve the problem of quantities.
The paper outlines a view of normativity that combines elements of relativism and expressivism, and applies it to normative concepts in epistemology. The result is a kind of epistemological anti-realism, which denies that epistemic norms can be (in any straightforward sense) correct or incorrect; it does allow some to be better than others, but takes this to be goal-relative and is skeptical of the existence of best norms. It discusses the circularity that arises from the fact that we need to (...) use epistemic norms to gather the facts with which to evaluate epistemic norms; relatedly, it discusses how epistemic norms can rationally evolve. It concludes with some discussion of the impact of this view on "ground level" epistemology. (shrink)
There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...) initially inclined to understand debates about logic. Can one find a pluralist thesis that is high on the interest scale, and also true? (shrink)
The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such (...) view. (shrink)
1. Background. At least from the time of the ancient Greeks, most philosophers have held that some of our knowledge is independent of experience, or “a priori”. Indeed, a major tenet of the rationalist tradition in philosophy was that a great deal of our knowledge had this character: even Kant, a critic of some of the overblown claims of rationalism, thought that the structure of space could be known a priori, as could many of the fundamental principles of physics; and (...) Hegel is reputed to have claimed to have deduced on a priori grounds that the number of planets is exactly five. (shrink)
There are many reasons why one might be tempted to reject certain instances of the law of excluded middle. And it is initially natural to take ‘reject’ to mean ‘deny’, that is, ‘assert the negation of’. But if we assert the negation of a disjunction, we certainly ought to assert the negation of each disjunct (since the disjunction is weaker1 than the disjuncts). So asserting..
Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is required if we are to preserve the naive theory of truth without inconsistency. In the case of vagueness (...) and indeterminacy, there is no worry about inconsistency; but a central intuition is that we must reject the factual status of certain sentences, and it hard to see how we can do that while claiming that the law of excluded middle applies to those sentences. So despite the different routes, we have a similar conclusion in the two cases. (shrink)
1. Of what use is the concept of causation? Bertrand Russell [1912-13] argued that it is not useful: it is “a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” His argument for this was that the kind of physical theories that we have come to regard as fundamental leave no place for the notion of causation: not only does the word ‘cause’ not appear in the advanced sciences, but the (...) laws that these sciences state are incompatible with causation as we normally understand it. But Nancy Cartwright has argued that abandoning the concept of causation would cripple science; her conclusion was based not on fundamental physics, but on more ordinary science such as the search for the causes of cancer. She argues that Russell was right that the fundamental theories of modern physics say nothing, even implicitly, about causation, and concludes on this basis that such theories are incomplete. It is with this cluster of issues that I will begin my discussion. (shrink)
Are there questions for which 'there is no determinate fact of the matter' as to which answer is correct? Most of us think so, but there are serious difficulties in maintaining the view, and in explaining the idea of determinateness in a satisfactory manner. The paper argues that to overcome the difficulties, we need to reject the law of excluded middle; and it investigates the sense of 'rejection' that is involved. The paper also explores the logic that is required if (...) we reject excluded middle, with special emphasis on the conditional. There is also discussion of higher order indeterminacy (in several different senses) and of penumbral connections; and there is a suggested definition of determinateness in terms of the conditional and a discussion of the extent to which the notion of determinateness is objective. And there are suggestions about a unified treatment of vagueness and the semantic paradoxes. (shrink)
A correspondence theory of truth explains truth in terms of various correspondence relations (e.G., Reference) between words and the extralinguistic world. What are the consequences of quine's doctrine of indeterminacy for correspondence theories? in "ontological relativity" quine implicitly claims that correspondence theories are impossible; that is what the doctrine of 'relative reference' amounts to. But quine's doctrine of relative reference is incoherent. Those who think the indeterminacy thesis valid should not try to relativize reference, They should abandon the relation and (...) replace it by certain more general correspondence relations between words and extralinguistic objects. Doing so will not interfere with the task of defining truth in terms of correspondence relations. (shrink)
Discussion of Chapter 5 of Stephen Schiffer's "The Things We Mean' in which Stephen Schiffer advances two novel theses: 1. Vagueness (and indeterminacy more generally) is a psychological phenomenon; 2. It is indeterminate whether classical logic applies in situations where vagueness matters.
It is “the received wisdom” that any intuitively natural and consistent resolution of a class of semantic paradoxes immediately leads to other paradoxes just as bad as the first. This is often called the “revenge problem”. Some proponents of the received wisdom draw the conclusion that there is no hope of any natural treatment that puts all the paradoxes to rest: we must either live with the existence of paradoxes that we are unable to treat, or adopt artificial and ad (...) hoc means to avoid them. Others (“dialetheists”) argue that we can put the paradoxes to rest, but only by licensing the acceptance of some contradictions (presumably in a paraconsistent logic that prevents the contradictions from spreading everywhere). (shrink)
Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so that the problem disappears, and (...) in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)
Consider the following argument: (1) Bertrand Russell was old at age 3×1018 nanoseconds (that’s about 95 years) (2) He wasn’t old at age 0 nanoseconds (3) So there is a number N such that he was old at N nanoseconds and not old at k nanoseconds for any k
Naive truth theory is, roughly, the theory of truth that in classical logic leads to well-known paradoxes (such as the Liar paradox and the Curry paradox). One response to these paradoxes is to weaken classical logic by restricting the law of excluded middle and introducing a conditional not defined from the other connectives in the usual way. In "New Grounds for Naive Truth Theory" (), Steve Yablo develops a new version of this response, and cites three respects in which he (...) deems it superior to a version that I’ve advocated in several papers. I think he’s right that my version was non-optimal in some of these respects (one and a half of them, to be precise); however, Yablo’s own account seems to me to have some undesirable features as well. In this paper I will explore some variations on his account, and end up tentatively advocating a synthesis of his account and mine (one that is somewhat closer to mine than to his). (shrink)
The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr( ) ↔ A (understood as the conjunction of Tr( ) → A and A → Tr( )). We also keep the full intersubstitutivity of Tr(>A>)) with A in all contexts, even inside of an →. Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with → (...) as an additional connective, and where the effect of classical logic is preserved in the arithmetic or formal syntax itself. Section 1 is an introduction to the problem and some of the difficulties that must be faced, in particular as to the logic of the →; Section 2 gives a construction of an arithmetically standard model of a truth theory; Section 3 investigates the logical laws that result from this; and Section 4 provides some philosophical commentary. (shrink)
It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...) the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)
Tim Maudlin’s Truth and Paradox is terrific. In some sense its solution to the paradoxes is familiar—the book advocates an extension of what’s called the Kripke-Feferman theory (although the definition of validity it employs disguises this fact). Nonetheless, the perspective it casts on that solution is completely novel, and Maudlin uses this perspective to try to make the prima facie unattractive features of this solution seem palatable, indeed inescapable. Moreover, the book deals with many important issues that most writers on (...) the paradoxes never deal with, including issues about the application of the Gödel theorems to powerful theories that include our theory of truth. The book includes intriguing excursions into general metaphysics, e.g. on the nature of logic, facts, vagueness, and much more; and it’s lucid and lively, a pleasure to read. It will interest a wide range of philosophers. (shrink)
The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema "True( ) ↔ A", and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in "ordinary" contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of (...) True( ) with A within the language. The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are "defective". We can in fact define a hierarchy of "defectiveness" predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes ("revenge problems") involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various "levels of defectiveness" can all be made coherent together within a single object language. (shrink)
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| 13,640 | 19 |
http://calculatecreditcard.com/how-to-calculate-credit-card-interest--payments/org/
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math
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How to calculate credit card interest payments
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Read a related article: How Credit Card Interest is Calculated
Read another related article: What Are The Benefits to Calculating Your Daily Interest Rate?
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http://ymuqit.tk/365/football-scores-ending-in-8-321.php
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math
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357 Missing Scores
In short, you can trade a small increased chance that you won't win any squares for a much larger chance that you'll win two, three, or even although rare four squares in a single game. Using the professional football game box scores regular season , over one billion computer simulations have been run where squares are picked, a game is chosen, and rows and columns assigned random digits.
It turns out there are 60 unique configurations you can select up to five squares given the digits for rows and columns are random. Over a billion simulations are needed because there are 4,,,,,, total possibilities 10! At the extreme ends, there are two strategies that emerge. If you pick squares such that each square selected has a unique row and column, you will maximize your chance at winning something most often only a single square and minimize your chance, relative to other strategies, that you'll win two or more squares in a single game.
The other extreme is to select a strategy that maximizes your chance of winning two or more squares. You can try to go home the BIG winner I like this strategy! Consider selecting four squares in the two extreme strategies Expanded, the probability table looks like this: The expected squares are calculated by multiplying the number of wins with the associated probability and summing it all up.
Notice, that essentially your strategy - how you select your squares - allows you to trade off a small probability for winning something for a much larger probability for winning two or more squares. All possible ways to select up to 5 squares Below is a final tabulation of all possible ways to select squares along with the probability of winning 2 or more squares and the probability of winning something.
Reading top to bottom and then left to right, the configurations are ordered to maximize your probability of winning two or more squares. The column direction reflects the underdog team and the row direction reflects the favorite. What about 4 points during a game? Kyle Harrington had to ruin everything by getting another safety making the score completely forgettable.
They ended up losing in overtime anyway, so I hope he learned his lesson. You could've been part of history Kyle. You could've been a contender. Also worth noting, the first ever college football game in between Rutgers and Princeton ended in a Rutgers victory. Obviously scoring was vastly different in those days, as were attitudes about the game. One professor was seen waving an umbrella during the contest, yelling "you will come to no Christian end!
Yes, it has happened 6 other times in NCAA history. Clemson 3, Duke 2 - Oct. TCU 3, Texas 2 - Nov. Iowa State 3, Kansas State 2 - Nov.
VMI 3, Kentucky 2 - Nov. This game also came very close to ending in a final score. In the 4th quarter, with Mississippi St. Inexplicably, Sylvester Croom went for it, to the shagrin of not only me but the color commentator, who lambasted him for this decision. Sure it didn't make sense football strategy wise, there was plenty of time left to force a 3 and out and get the ball back, but it also killed a relatively decent chance that the bulldogs would finish with 4 points, which also should've been taken into account.
In conclusion, fuck Sylvester Croom. Otherwise, to estimate the probability of any particular square winning we'd have to rely on historical data, and create a running tally of how each square has performed. Needless to say, this is more work. Unfortunately, it seems that this is necessary work. By looking at data from 4, preseason and regular season games from the season was the first in which the two-point conversion was instituted , I tallied the counts for each winning square in the case of both the traditional football pool and the digital root pool.
Here is the data:. Recall that for the digital root pool, the digit 0 only occurs if one team doesn't score - to even things out, I have assigned a score of 0 with a digital root of 9 I discussed reasons for this in my earlier post.
Using a standard statistical test for independence, we conclude that there is essentially no way that the digital root of one team is independent of another team, or that the last digit of one team's score is independent of another team's score. Therefore, assuming the digital roots of the away team and home team's scores were independent, the probability of winding up in the 2,2 square would be 0. In other words, if you know that the score of the home team's digital root is 2, it is suddenly much less likely that the score of the away team's digital root is also 2.
Using this larger data set, we also find that it's actually unlikely that the digital roots become equally distributed among the digits from 1 to 9. While the distribution is certainly more uniform than in the case of the second digit, we also see that certain digital roots occur significantly more frequently than others 5 occurs much less frequently than 1, for example.
Even though away team and home team 2nd digits and digital roots are not independent, one may expect that the probability of having a score with a given 2nd digit or a given digital root should be independent of whether the team is the home team or the away team. Interestingly, in the case of the 2nd digit, this is not true.
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| 5,503 | 15 |
http://xjtermpapertxal.mestudio.us/dielectric-constant-of-paper.html
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math
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Abstract— our primary objective in this work is the accurate measurement of complex dielectric constant and conductivity of unknown liquids in this paper we . 265 dielectric properties of materials a capacitor filled with a dielectric material has a real capacitance ′r times greater than cellulose (see also paper. Guide: dielectric constants of material paper, 15, 3 paraffin, 2, 3 plexiglass, 26, 35 polycarbonate, 29, 32 polyethylene, 25, 25. Keywords: polymer composites barium titanate dielectric constant ferroelectrics 1 khz (ie, the dielectric constant we are referring to in this paper is the room. Dielectric constants of common dielectric constants of common palmitic acid 23 palmitic acid 70 palmitic acid 160 23 paper 2 paper.
There are four or more materials that can produce boards with a dielectric constant of 28 this paper will discuss the electrical and system advantages of having. Enhanced dielectric constant, ultralow dielectric loss, and high-strength imide- functionalized graphene oxide/hyperbranched polyimide. The dielectric constant - also called the relative permittivity indicates how easily a εr = relative permittivity - or dielectric constant hard paper, laminated, 45.
Paper has a dielectric constant k = 37 and a dielectric strength of 15 x 10^6v/m suppose that a typical sheet of paper has a thickness of 011mm you make a. Importance polymer matrix composite materials are excellent candidates for these applications in this paper analytical method for material dielectric constant . How effective a dielectric is at allowing a capacitor to store more charge depends on the material the dielectric is made from e is always less than or equal to eo, so the dielectric constant is greater than or equal to 1 paper, 36, 16. B to measure the dielectric constant of paper 2 theory a the capacitance of a parallel plate capacitor with no material between its plates is. The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to paper, 385 relative permittivity is also commonly known as dielectric constant, a term deprecated in physics and engineering as well as in.
Kilocycles per second, was med to measure the dielectric constant of water with 2 figures in brackets indicate the iiteratnre references at the end of this]paper. Dielectric constant ke = e / e o vacuum 885 1000 00 air 885 1000 54 body tissue 71 8 glass 40-90 5-10 mica 25-55 3-6 nylon 31 35 paper 18- 35. The institute of paper chemistry appleton, wisconsin doctor's dissertation a study of the relationship between the dielectric constant and accessibility of. Thanks to this technological process, the dielectric constant index terms— foam material, controlled dielectric constant the paper foams.
Abstract: in this paper, the dielectric properties of water-dimethylsulfoxide (dmso ) mixtures with different mole ratios have been investigated in. Dielectric constant of mica---the constant was determined for 18 samples of mica, varying in thickness from 0005 to 0073 inch and including 12 different. Experiment ft1: measurement of dielectric constant name: id: 1 objective: (i) to measure the dielectric constant of paper and plastic film (ii) to examine the. This paper reports on the development of a wide-band tem horn antenna system suitable for field determination of the dielectric properties of concrete.
The dielectric properties of paper and board at frequencies of 245 ghz and 2712 mhz as measured by standard methods, are presented as a function. Rohde & schwarz 2 research paper that shows the plot using the nrw method in determining the. Dielectric constant (k) is a number relating the ability of a material to carry alternating current to the ability of vacuum to carry alternating current chance that the dielectric constant may be different from the values listed paper (dry ) 20. We explain why the experiment fails for small dielectric thickness and edwin a karlow, “let's measure the dielectric constant of a piece of paper,” phys.
Paper we look at their effect on electrical properties we have dielectric strength while significantly increasing the dielectric constant of polymeric materials. The permittivity is a complex number and the real part is often called as dielectric constant in papers by athey, stuchly, & stuchly the input reflection. Dielectric permittivity measurement of paper substrates using commercial inkjet printers☆ for developing inkjet-printed microwave circuits on paper substrates : kulkarni, amruta deshmukh, vidya: dielectric properties measurement.
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CC-MAIN-2018-43
| 4,563 | 7 |
https://www.coursehero.com/file/p2e2v10o/What-is-the-osmotic-pressure-of-a-solution-formed-by-dissolving-250-mg-of/
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math
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4) A solution containing a solid that is
with the solution is called…
5) Choose the statement below that is
6) The Henry's Law constant of methyl bromide, CH
= 0.159 M/atm at 25 °C. What is the
concentration of CH
Br in water at this temperature and at a partial pressure of 270. mm Hg?
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CC-MAIN-2022-05
| 289 | 7 |
https://www.skyscript.co.uk/mean_conjunctions.html
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math
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This article presents an adapted excerpt from my recent volume of translations in traditional mundane astrology, Astrology of the World II: Revolutions & History. Within these translations, I have divided traditional techniques into two broad categories: "episodic," and "historical." By episodic, I mean the use of ingress charts, lunations, and eclipses to predict and understand weather, prices, and other things; it is episodic, because in general such charts are viewed in isolation and are relevant only to the period at hand: the period of an eclipse, the weather over the summer. By contrast, historical astrology covers conjunctional theory, time lord systems such as mundane firdaria or something called a "Turn," and ingresses used for political purposes. Here, charts are seen as embedded in longer historical processes. In this article I will focus on a well-known branch of historical astrology, Saturn-Jupiter conjunctions. Many people have heard of these, but there are a number of special features that practitioners need to know before understanding how traditional astrologers used them.
Saturn-Jupiter conjunctions, and their grouping by triplicities, formed the backbone of historical astrology. The basic approach, and the roles the conjunctions played within larger periods like the "world years" were already well in place by the time of Masha'allah; but Abu Ma'shar seems to have been the one who really popularized and regularized the approach followed by astrologers after the 9th Century AD. In order to understand how these conjunctional cycles work, both in theory and practice, we need to introduce some terminology.
First of all, the whole apparatus of this conjunctional astrology was structured on mean conjunctions. What is a mean conjunction? Astrologers tend to use "true" conjunctions, which are the conjunctions of the planets as they appear to us. (In Ptolemaic astronomy, a "true" position is one as seen from earth.) Thus, if we see in the ephemeris or a computer program that Saturn and Jupiter are conjoining at 15° Capricorn, we expect to be able to look up in the heavens, and see the actual bodies of the planets together, within the degree of 15° Capricorn. And as we know, sometimes Saturn and Jupiter make three true conjunctions: once when the quicker Jupiter goes past Saturn, then when he retrogrades back across him, and then finally after he goes direct again.
But a "mean" conjunction in Ptolemaic astronomy happens at precise, regular intervals. It is based on the average length of each planet's cycle in the zodiac, which is nothing more than the cycles we are familiar with today: the 12-year cycle of Jupiter is actually a rounding-up of the more accurate cycle of 11.86 years. Likewise, the period of the "Saturn return" is 29.4 years. But in Ptolemaic astronomy this period has a technical meaning: it is the length of time it takes for the center of a planet's epicycle to revolve exactly once around the zodiac. The position of the center of the epicycle is its "mean" position as it revolves at a constant or mean rate. As one might surmise, since planets also rotate on their epicycles, their true positions will usually not coincide with this point when it returns, but they will be direct or retrograde on one or another side of it. Figure 1 and its accompanying text, below, illustrates what I mean:
Figure 1: Illustrated mean period of Jupiter
In the diagram, Jupiter starts out with the center of his epicycle (his "mean" position) at 0° Aries, and I have assumed that his body itself is also there (his "true" position). As time goes on, the epicycle moves counter-clockwise around the zodiac, as does his own position on it. After 11.86 years, the center of the epicycle reaches 0° Aries again, completing his mean period. But note that because he moves on his epicycle at a different rate, at the end of the mean period his body will have rotated the equivalent of about 308°, not a full circuit. So at the end of the period his true position will appear to be earlier in the zodiac than 0° Aries.
From this we can easily see what the definition of a mean conjunction between two planets is: it is the conjunction of the centers of their epicycles. This concept may seem out of date nowadays, but in fact we need this type of astronomy in order to determine when and where to place our Saturn-Jupiter conjunctions within the triplicities. Or rather, we need to know only one of them: after that, we can project the mean conjunctions forward and backward into history and construct our triplicity series.
Now, in order to construct a series of mean conjunctions, we need three pieces of information: (1) the type of year and zodiac, whether tropical or sidereal; (2) the length of the mean periods; and (3) the precise time and location of one mean conjunction. Let me discuss each of these in turn, especially since medieval texts often differ from modern values and assumptions. Below I will also provide a table of accurate planetary values, and one may consult Appendices A and B in my book Astrology of the World II: Revolutions & History to see fuller tables of conjunctions and triplicity shifts.
(1) Tropical and sidereal years and zodiacs.
The tropical year and zodiac refers to the return of the Sun to 0° Aries or the equinoctial point, which is defined as the intersection of the celestial equator and ecliptic. But because the equinoctial points precess "backwards" against the fixed stars, by the time the mean Sun or any planet returns to its tropical position in a given year, it will have traveled slightly less than the full 360° from the previous time. This means that the tropical year, as well as any tropical cycles, will be slightly shorter in time and distance than their sidereal equivalents. Let's look more closely at Jupiter's mean cycle to see how this works, removing the epicycle for the sake of simplicity.
Figure 2: Mean tropical cycle of Jupiter
In this figure, Jupiter begins his cycle at 0° Aries. The rate of precession is 50.28" per tropical year. So, by the time he approaches his original position 11.86 years later, the point of 0° Aries will have precessed backwards by 9' 56": thus Jupiter's "return" to the new tropical 0° Aries is actually not a full 360°, but 359° 50' 04".
Now, in a sidereal year and zodiac there is no precession. Instead, 0° Aries (or whatever point you like) is defined in a fixed way relative to the stars: thus for Jupiter to return to 0° Aries really means moving a full 360°, to precisely the same point. Traveling this extra distance takes more time, so both the distance and time involved is longer in sidereal systems. The sidereal year is about 1.000038804 times longer than a tropical year. In the case of Jupiter, his sidereal period is about 1.9 days longer than the tropical one.
Masha'allah, as well as Abu Ma'shar (or at least in his mundane astrology) used a sidereal zodiac. Most medieval Latins, as well as al-Battani, used a tropical one. The choice of zodiac is up to you, but it is important to know that only a sidereal system will yield 12 conjunctions per triplicity - I will return to this below.
Mean periods and triplicity shifts
Using contemporary data, it is easy to derive the mean periods for both Saturn and Jupiter. The tropical period is the number of days in the planet's tropical cycle, divided by the length of the tropical year; the sidereal period is the days in the sidereal cycle, divided by the sidereal year. I have used data given by NASA.1 Following are the contemporary values:
Figure 3: Contemporary values for years & mean periods
According to the table, the sidereal year is about 00:20:25 longer than the tropical year. The periods are measured in their respective years, as well. For instance, the tropical period of Jupiter is 11.85677646 tropical years: so, this value multiplied by the length of the tropical year makes his mean period 4330.595 days long. The same can be done with the other values.
Once we know the lengths of the year and periods, it is easy to determine precisely how often mean conjunctions will take place, as well as exactly how far apart they will be. Following are the two formulas we need:
By inserting the period values into the equations, we get the following:
- Length of a conjunctional period:
- (Period 1 * Period 2) / (Period 1 - Period 2)
- Distance between conjunctions:
- ( ( Conjunctional period - shorter period ) / shorter period ) * 360
Figure 4: Complete table of mean conjunctions & distances
As we can see, in a tropical system, mean Saturn and Jupiter will conjoin every 19.85929143 tropical years (or 7253.45109 days), what I am calling their "conjunctional period." The sidereal conjunctional period is 19.8585313 sidereal years, or 7253.454917 days, which is a fraction of a day more. Now, at first this suggests that the choice of zodiacs will affect the conjunctional period. But actually it does not: the planets will conjoin at exactly the same time, no matter what kind of zodiac you use. The conjunctional periods are equal, because the conjunctional period is based purely on the constant rate of the planets. Put differently, look at the length of the tropical period and that of the sidereal period: you will see that the tropical period is slightly longer, but the tropical year is slightly shorter. The reverse is true for the sidereal values. Thus, the longer period of the shorter year (tropical) is equivalent to the shorter period of the longer year (sidereal). The apparent difference between these periods is due to the fact that the NASA website only calculates to 3 decimal places, so when we solve our equations it will seem as though the sidereal period lasts 5.5 minutes longer than the tropical. In reality the periods are equal, and if you use this data it will take about 5,184 years or almost 262 mean conjunctions before there is a 1-day difference between them.
However, the choice of zodiacs does determine the conjunctional distance. Both systems make each successive conjunction take place in roughly a clockwise or backwards trine from the previous one. In a tropical system, the distance between successive conjunctions is 242.9754323° or 242° 58' 32". Sidereally, the distance is 242.6982412° or 242° 41' 54".
To illustrate how these mean conjunctions work, consider figure 5 below. I have removed the epicycles in order to show the idealized mean motion of the planets.
In these figures, the mean positions of Jupiter Saturn (i.e., without their epicycles) begin at some degree (here labeled 0°). After one-half of Jupiter's period (5.9 years), he will have traveled around one-half of the circle (at 180°), while Saturn will have traveled only 72°. When Jupiter completes his period (11.86 years, at 360°), Saturn will only be at 144°. Finally, after about 7.9 years more (or 19.8 total), Saturn will have made it to 242°, where Jupiter finally catches up to him and makes the mean conjunction. The sidereal and tropical values are not the same, but they are so close that the figure illustrates both well enough.
Figure 5: Illustration of mean conjunctional period
Now, earlier I related the standard version of the conjunctional series: every successive conjunction advances by a little over 242°, which is a little less than a backwards trine from the previous position. This means that successive conjunctions will take place within the same triplicity, but because an exact triangle would be 240°, the actual degrees within each sign will slowly advance until the conjunctions enter a new triplicity. The number of mean conjunctions in each triplicity is idealized at 12, but how many are there, really? If there were always exactly 12, then the conjunctional distance could only be 242° 30', advancing by 2° 30' within each sign. Abu Ma'shar's own parameters gave something a bit less: 242° 25' 17": this makes 12 but sometimes 13 conjunctions in each triplicity. Masha'allah's value was 242° 25' 35", also 12-13 conjunctions.
The table in figure 4 above shows the accurate values: in a tropical system, there will be 10 or 11 conjunctions, and in a sidereal system 11 or 12. Figure 6 below shows this visually, in the tropical system.
Figure 6: Eleven tropical mean conjunctions in the fiery triplicity
Every mean conjunction advances by 242° 58' 32" of the circle, or 2° 58' 32" in the actual degrees of the signs. If conjunction #1 is at 0° of a sign (here, Aries), then #2 will be at about 2° 58' 32" of Sagittarius, #3 at 5° 57' 04" Leo, and so on, always moving in a backwards (or clockwise) trine. But then #11 will be at 29° 45' 20", the last of the triplicity: the next conjunction will be a triplicity shift into the earthy triplicity, at 2° 43' 52" Virgo. The differences between the tropical and sidereal series may then be illustrated this way:
Figure 7: Tropical & sidereal triplicity shifts compared
Beginning at 0° of some sign for their mean conjunction #1, the tropical series will have 11 conjunctions before shifting into earth for 10 conjunctions. The sidereal series will have 12 conjunctions before shifting into earth for 11 conjunctions. In this way we can see that the idealized system of 12 conjunctions per triplicity is not correct.
As a point of interest, I append here Abu Ma'shar's own parameters.2 (Masha'allah's are also given in §6 of my Introduction to Astrology of the World II: Revolutions & History).
Figure 8: Abu Ma'shar's parameters for Saturn-Jupiter conjunctions3
(3) A recent mean conjunction.
As an example, the tropical periods of Saturn and Jupiter dictate that a mean tropical conjunction occurred on July 20, 1901, at 15° 12' Capricorn; but on that day, their true positions were 12° 00' and 5° 42' Capricorn, respectively.
Although none of the ancient and medieval astronomers had the more precise values for the year and periods which we have today, you should not think that this difference between mean and true conjunctions was a flaw in the theory itself. Nor are these periods merely rough or approximate: given an accurate length of the year and each of the planets' periods, a mean conjunction can be timed down to the hour or even minute. The regular, mean conjunctions played a structuring role in large spans of historical astrology. (But the fact that the mean and true conjunctions happened at different times and degrees means that we need to make some astrological choices when we cast their charts and make interpretations.) The difficulty in interpreting the calculations in medieval conjunctional theory has more to do with the fact (a) the length of their periods and years were not the same from author to author, and (b) some used tropical periods and a tropical zodiac, others sidereal.
Figure 9: Mean tropical conjunction of 1901
Appendix: Tables of Mean Conjunctions
In this Appendix I provide accurate tables for selected tropical and sidereal (Fagan-Bradley) mean conjunctions of Saturn and Jupiter. The conjunctions start in 185 BC, with the tropical shift to the watery triplicity. The numbers assigned to the conjunctions, and their Julian and Gregorian dates, are the same in both tables. But the positions of the conjunctions, and which ones count as triplicity shifts in their respective zodiacs, differ accordingly. Note that the position of the conjunctions coincide almost exactly at the triplicity shift to earth in 213 AD.
Table of Tropical Mean Conjunctions
This table was generated by using the following "epoch" date for a recent tropical mean conjunction, and thereafter projecting forwards and backwards using accurate contemporary tropical parameters.
- Conjunction date: JD 2415585.836, or 8:03 AM, July 20, 1901.
- Tropical Position: 285.2043109°, or Capricorn 15° 12' 16".
Figure 10: Table of tropical mean Saturn-Jupiter conjunctions
Table of Sidereal Mean Conjunctions
This table was generated by determining the Fagan-Bradley difference between the tropical and sidereal Suns at the mean conjunction on July 20, 1901 (namely, 23° 22' 10"), which put the sidereal mean conjunction at Sagittarius 21° 50' 06". From there, I projected forwards and backwards using the modern parameters I describe within my Introduction to Astrology of the World II: Revolutions & History.
Figure 11: Table of sidereal mean Saturn-Jupiter conjunctions
Dr. Benjamin Dykes
is a leading medieval astrologer and translator who earned his PhD in philosophy from the University of Illinois. He earned his medieval astrology qualification from Robert Zoller and taught philosophy courses at universities in Illinois and Minnesota.
Dykes recently published Astrology of the World Vols. 1-2
, Traditional Astrology for Toda
y, and The Book of the Nine Judges
. In 2015-16 he will be publishing translations from Arabic and Greek. In 2007-08 he translated Guido Bonatti's Book of Astronomy
and the Works of Sahl & Masha'allah
, on all branches of traditional astrology.
Dykes currently offers the Logos & Light
philosophy courses on MP3 for astrologers and occultists, and reads charts for clients worldwide.
Visit Benjamin Dykes' website at www.bendykes.com
Read Garry Phillipson's Interview with Benjamin Dykes
Notes & References:
Evans, James, The History and Practice of Ancient Astronomy (Oxford: Oxford University Press, 1998)
Kennedy, E.S., "The World-Year of the Persians," in Journal of the American Oriental Society, Vol. 83, No. 3 (Aug. - Sep. 1963), pp. 315-27.
Van der Waerden, B.L., "The Great Year in Greek, Persian and Hindu Astronomy," Archive for the History of Exact Sciences, Vol. 18, No. 4 (1978), pp. 359-383.
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CC-MAIN-2023-50
| 17,632 | 68 |
http://en.wikipedia.org/wiki/Tautology_(rhetoric)
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math
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In rhetoric, a tautology (from Greek tauto, "the same" and logos, "word/idea") is a logical argument constructed in such a way, generally by repeating the same concept or assertion using different phrasing or terminology, that the proposition as stated is logically irrefutable, while obscuring the lack of evidence or valid reasoning supporting the stated conclusion. (A rhetorical tautology should not be confused with a tautology in propositional logic.)[a]
A rhetorical tautology guarantees the truth of the proposition, where the expectation (premise) was for a testable construct, any conclusion is by the precepts of falsificationism a non sequitur (logic). Circular reasoning differs from tautologies in that the premise is restated as the conclusion in an argument, instead of deriving the conclusion from the premise with arguments, while a tautology states the same thing twice. If the argument that separates the conclusion from the premise is a logical fallacy such as a rhetorical tautology, then the conclusion is merely a restatement of the premise, rather than deriving in a logical fashion from the premise. The form the arguments are allowed to take, either falsifiable or unfalsifiable, dictates in what way the conclusion can logically derive from the premise, without merely restating the premise.[clarification needed]
^Rhetorical tautologies state the same thing twice, while appearing to state two or more different things; logical tautologies state the same thing twice, and must do so by logical necessity. The inherent meanings and subsequent conclusions in rhetorical and logical tautologies or logical necessities are very different. By axiomatic necessity, logical tautologies are neither refutable nor verifiable under any condition.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997876165.43/warc/CC-MAIN-20140722025756-00047-ip-10-33-131-23.ec2.internal.warc.gz
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CC-MAIN-2014-23
| 1,765 | 3 |
https://beta.geogebra.org/m/T9SycUYE
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math
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Approximations of Sine
- Dr. Doug Davis, 3D
This applet shows the Sine function and three approximations for the Sine function.
- An early approximation for sine was from Bhaskara I is . This function is fairly accurate for angles between .
- Another approximation is a power series (MacLaurin or Taylor Series) which for the Sine function is . The number of terms can be increased to obtain any desired accuracy.
- Since the Sine function is zero at it can be approximated as . This is the Root Products Approximation.
- Polynomial Interpolation that go through a set of points. Two points define a line. For more points the polynomial can be defined as using Lagrange Polynomials. Note, the value of the product is zero at all points and one when .
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100534.18/warc/CC-MAIN-20231204182901-20231204212901-00192.warc.gz
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CC-MAIN-2023-50
| 750 | 7 |
https://www.coursehero.com/tutors-problems/Statistics-and-Probability/8342974-1-The-Connecticut-Board-of-Education-is-concerned-that-first-year/
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math
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1. The Connecticut Board of Education is concerned that first year female high school teachers are receiving lower salaries than their male counterparts. Two independent random samples have been selected: 830 observations from population 1 (female high school teachers) and 810 from population 2 (male high school teachers). The sample means obtained are X1(bar)=$46,000 and X2(bar)=$47,000. It is known from previous studies that the population variances are 4.5 and 5.0 respectively. Using a level of significance of .01, is there evidence that the first year female high school teachers are receiving lower salaries? Fully explain your answer.
Dear Student Please find... View the full answer
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826856.91/warc/CC-MAIN-20181215131038-20181215153038-00333.warc.gz
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CC-MAIN-2018-51
| 695 | 2 |
https://www.amazon.ca/Programming-Languages-General-Science-Math-Books/s?ie=UTF8&page=1&rh=n%3A956280%2Ck%3AProgramming%20Languages%20-%20General
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math
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An Elementary Introduction to the Wolfram LanguageDec 9 2015by Stephen Wolfram
SAS Certification Prep Guide: Base Programming for SAS 9Jul 8 2011by Sas InstituteCDN$ 148.09CDN$ 193.21Only 5 left in stock - order soon.More buying choicesAvailable for download now
Dynamic ProgrammingMar 4 2003by Richard BellmanCDN$ 26.80CDN$ 31.00Only 6 left in stock - order soon.More buying choices
Matlab: A Practical Introduction to Programming and Problem SolvingAug 5 2016by Stormy AttawayAvailable for Pre-order. This item will be released on August 5 2016.
Programming Arduino: Getting Started with Sketches, Second EditionJun 29 2016by Simon Monk
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824624.99/warc/CC-MAIN-20160723071024-00104-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 638 | 5 |
https://nrich.maths.org/7299/solution
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math
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This activity produced a few replies. Oliver from St. Anthony's sent in;
R R D L L D D R R U L
Tessa, Sally and Kensa from Sherwood State School in Australia sent in their solution like this;
$1, 4, 6, 2, 4, 5, 1, 2, 4, 5, 1, 4$
Hanako and Emilia at Vale Junior School, Guernsey sent in this word document;
First we decided to make a cube to physically test our theories and ideas.
We spotted that there were two impossible routes. These were: the $4$s down the middle and the $1, 4, 1$ combination going across.
These are impossible because you can't have two $4$s next to each other as there is only one four on the dice. The other is impossible as to get from $1$ to $4$, and then to $1$ again, you would have to double back on yourself.
Next, we had to think of a route that bypassed these two impossible combinations. We thought that we could start our route with the $4$ in the impossible $1, 4, 1$ combination so that we didn't have to complete the whole impossible combination.
We checked that our theory was correct by rolling our cube along the grid. As we rolled it, we wrote the next number in the grid as a reflection on the next face of the cube. We tried starting at the top $1$ and the centre $4$ and we found that this route works both ways.
Thank you Hanaho and Emilia for explaining how you did it and what your thoughts were and well done all of you!
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585671.36/warc/CC-MAIN-20211023095849-20211023125849-00171.warc.gz
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CC-MAIN-2021-43
| 1,370 | 11 |
http://genew.ca/the-not-a-math-person-myth/
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math
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I tutor people from time to time, usually in math. A lot of people do not have some very basic math skills, and yet, it is not really all that difficult to learn them if you think that you can.
Unfortunately, many people think that they can not.
This recent article says it much better and at length There’s one key difference between kids who excel at math and those who don’t.
If you have trouble with math, please do not give up on it. You can learn it.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814290.11/warc/CC-MAIN-20180222200259-20180222220259-00230.warc.gz
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CC-MAIN-2018-09
| 460 | 4 |
https://www.o.vg/unit/lengths/fttof.php
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math
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ft to F Converter
From ft to F: 1 ft = 3.048E+14 F;
From F to ft: 1
F = 3.280839895013e-15
How to Convert Foot to Fermi?
As we know One ft is equal to 3.048E+14 F (1 ft = 3.048E+14 F).
To convert Foot to Fermi, multiply your ft figure by 3.048E+14.
Example : convert 25 ft to F:
25 ft = 25 × 3.048E+14 F = F
To convert Fermi to Foot, divide your F figure by 3.048E+14.
Example : convert 25 F to ft:
25 F = 25 ÷ 3.048E+14 ft = ft
How to Convert Fermi to Foot?
As we know One F is equal to 3.280839895013e-15 ft (1 F = 3.280839895013e-15 ft).
To convert Fermi to Foot, multiply your F figure by 3.280839895013e-15.
Example : convert 45 F to ft:
45 F = 45 × 3.280839895013e-15 ft = ft
To convert Foot to Fermi, divide your ft figure by 3.280839895013e-15.
Example : convert 45 ft to F:
45 ft = 45 ÷ 3.280839895013e-15 F = F
Popular Length and Distance Unit Conversions
What is 9 Foot in Fermi?
F. Since one ft equals 3.048E+14 F, 9 ft in F will be F.
How many Fermi are in a Foot?
There are 3.048E+14 F in one ft. In turn, one F is equal to 3.280839895013e-15 ft.
How many ft is equal to 1 F?
1 F is approximately equal to 3.280839895013e-15 ft.
What is the ft value of 8 F?
The Foot value of 8 F is ft. (i.e.,) 8 x 3.280839895013e-15 = ft.
ft to F converter in batch
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CC-MAIN-2023-23
| 1,268 | 30 |
https://www.cardstheuniverseandeverything.com/cue-cards/bertrand-russell
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math
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With an IQ of at least 180, it’s fair to say that Bertrand Russell was an incredibly intelligent man. A philosopher, logician and mathematician, Russell wrote the essay ‘On Denoting’, which has been described as one of the most influential essays in philosophy in the 20th Century.
Here’s the “TL;DR” on his works: Russell believed that the goal of both science and philosophy was to understand reality, not simply to make predictions. He wrote that the physical world around us is just an abstract structure - and his works were so influential that he went on to win the Nobel Prize for Literature in 1950.
This man is responsible for not only destroying the foundations of mathematics but for rebuilding them too. The Russell Paradox shook the core of academia in 1903 by challenging the axioms that mathematics were based on by suggesting that the set of all sets could not contain itself. The analogy Russell used is this;
If a barber is “the person who shaves the beards of men in a village that do not shave themselves”, does he shave himself? If he shaves himself, he ceases to be the barber; but if he doesn’t shave himself, he fits into the group of people who should be shaved by the barber, so he has to shave himself, right?
As if to make up for breaking everyone’s brains with logic, in his 1910 book Principia Mathematica, he casually proved that 1+1=2. But even though ol’ Berty proved the rules, he didn’t always play by them. In fact, on two occasions, he was arrested and jailed for political activism.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816070.70/warc/CC-MAIN-20240412194614-20240412224614-00137.warc.gz
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CC-MAIN-2024-18
| 1,544 | 5 |
https://www.spectroom.com/1023187-1024-number
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math
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Ex 1.3 Q1 ii NUMBER SYSTEM 9th class Maths Decimal expansion of 1/11
The sum of three consecutive natural numbers is 60, find these numbers?
What are Real Numbers?
Mathematics Class 9th NUMBER SYSTEM Simplify Exponents and Powers of Real Numbers
9th Class Mathematics NUMBER SYSTEM Simplify Exponents and Powers of Real Numbers
1024 is the natural number following 1023 and preceding 1025.
Explore contextually related video stories in a new eye-catching way. Try Combster now!
Approximation to 1000
Special use in computers
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735867.93/warc/CC-MAIN-20200804102630-20200804132630-00041.warc.gz
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CC-MAIN-2020-34
| 524 | 9 |
https://upsideinnovations.com/ada-ramp-length-calculator/
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math
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ADA Ramp Length Calculator
Elevation Height: The height from the ground up to the bottom of the door or existing walkway.
1:12 Slope: For every inch of height from the ground, you need 1 foot of ramp length.
Minimum number of resting platforms: A 5′ x 5′ (minimum) resting platform is needed every 30 feet of ramp.
+ 5′: A 5′ x 5′ (minimum) platform is needed at the top of the ramp if there is not an existing one already.
Total ramp system length in feet: Includes the minimum number of 5′ x 5′ resting platforms and the 5′ x 5′ platform at the top of the ramp.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154356.39/warc/CC-MAIN-20210802172339-20210802202339-00066.warc.gz
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CC-MAIN-2021-31
| 581 | 6 |
https://thelendingpeople.co.nz/application-form/
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math
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9:00am - 5:00pm Weekdays
10:00am - 2:00pm Saturday
Fixed interest rates range from 8.95% p.a to a maximum 26.95% p.a. with terms ranging from 12 months to a maximum 7 years.
Example: If you borrow $8,000 over a term of 36 months at an interest rate of 15.95% p.a. you will end up repaying $11,640.94 inclusive of all fees and interest.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999261.43/warc/CC-MAIN-20190620145650-20190620171650-00272.warc.gz
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CC-MAIN-2019-26
| 335 | 4 |
https://web2.0calc.com/questions/are-there-infinitely-many-primes-nbsp-p-nbsp-such-that-nbsp-p-nbsp-2-is-prime
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math
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Are there infinitely many primes p such that p + 2 is prime?
Well numbers go on infinately and since primes also theoretically go on infinately, so yes, but the number of primes found by using p+2 will exponetially decrease.
I do not know radio. In theory at least I think there are infinitely many primes BUT
You have taken this a step further - I am not so sure your 'yes' would stand up to close scrutiny.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583667907.49/warc/CC-MAIN-20190119115530-20190119141530-00057.warc.gz
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CC-MAIN-2019-04
| 408 | 4 |
https://www.jiskha.com/display.cgi?id=1200162151
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math
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posted by Matt .
I posted this several days ago but it hasn't been answered and I still can't figure it out:
For which values of r does the function defined by y=e^(rt) satisfy the differential equation y''+ y'-6y = 0
find y', and y"
now put them in the equation...
and divide both sides by y (y cann never be zero).
now solve for r.
how did you get ry and r^2y for y' and y''?
if y = e^rt where r is constant and t is variable
dy/dt = r e^rt
since e^rt = y then
dy/dt = r y
d/dy(dy/dt) = d^2y/dt^2 = r*re^rt
= r^2 e^rt
= r^2 y again since y = e^rt
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886103579.21/warc/CC-MAIN-20170817151157-20170817171157-00312.warc.gz
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CC-MAIN-2017-34
| 548 | 15 |
https://www.oreilly.com/library/view/differential-forms-2nd/9780123944030/xhtml/B9780123944030000141.xhtml
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math
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Differential forms are a powerful computational and theoretical tool. They play a central role in mathematics, in such areas as analysis on manifolds and differential geometry, and in physics as well, in such areas as electromagnetism and general relativity. In this book, we present a concrete and careful introduction to differential forms, at the upper-undergraduate or beginning graduate level, designed with the needs of both mathematicians and physicists (and other users of the theory) in mind.
On the one hand, our treatment is concrete. By that we mean that we present quite a bit of material on how to do computations with differential forms, so that the reader may effectively use them.
On the other hand, our treatment is careful. ...
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304528.78/warc/CC-MAIN-20220124094120-20220124124120-00670.warc.gz
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CC-MAIN-2022-05
| 746 | 3 |
http://www.ask.com/web?qsrc=3053&o=102140&oo=102140&l=dir&gc=1&qo=contentPageRelatedSearch&ad=null&q=How+Many+Square+Feet+In+A+Yard
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math
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Square yards to feet conversion table and converter to find out how many sq.
footage in sq. yards.
How many cubic feet in a cubic yard? ... Landscape Calculator: Find Out How
Much Product You Need. Disclaimer: ... Cubic Yds. Required to Cover 1,000 sq ft
Square Feet to Square Yards (ft² to yd²) conversion calculator for Area
conversions with additional tables and formulas.
Since 1 yard converts to 3 feet in length, there are 9 square feet in 1 square yard.
The area of a perfect square always equals the length of one side squared, ...
A square foot is a unit of area equal to a square that is one foot on a side. It is
equal to 144 square inches, 1/9th of a square yard, or approximately 0.093
Concrete is sold in cubic yards, so the number of square feet in that yard
depends upon how deep the concrete is poured. Concrete can be poured in
According to your question...How may SQ FT in a YARD? Example: You have
total 3 sq ft. Simply, there s 3 feet in a Yard so you Divide 3 ÷ 3= 1 ...
Use this Bankrate.com calculator to find out how much carpet you'll need for a ...
You will get two figures -- one as square yards and the other as square feet -- of ...
The area of the driveway is 1,080 square feet (60-feet x 18-feet). ... Use the table
above to calculate how many cubic yards of concrete would be needed for each ...
Square Yards (Square Yards calculated from Square feel is rounded up) ... Enter
the value (feet) and automatically view the conversion (yards) Alternatively ...
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541839.36/warc/CC-MAIN-20161202170901-00397-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 1,492 | 20 |
https://divinewsmedia.com/8401/
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math
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170 m 5577 ft. Use this easy calculator to convert centimeters to feet and inches.
From Angstroms Centimeters Fathoms Feet Furlongs Inches Kilometers Meters Microns Miles Millimeters Nanometers Nautical Miles Picometers Yards.
70 cm in feet. 1 cm 0032808398950131 ft 70 cm L ft. 3 feet and 17953 inches. Simply use our calculator above or apply the formula to change the length 70 cm to ft.
Height Conversion Table some results rounded cm Ft In Feet. How to convert 170 Meters to Feet. 3 feet and 33701 inches.
70 Centimeters cm 229659 Feet ft Centimeters. However you do not have to worry about errors when you use this website. 3 feet and 41575 inches.
It is also the base unit in the centimeter-gram-second system of units. Your own mathematical capabilities may be questionable. 70 feet equal 21336 centimeters 70ft 21336cm.
70x140cm in Inches will convert 70 and 140 cm to inches and other units such as meters feet yards miles and kilometers. 70 centimeters equal 22965879265 feet 70cm 22965879265ft. 2 356 2 ft 356 in 2 feet 356 inches 2 foot 356.
70 Centimeters 2 Feet 3559 Inches rounded to 4 digits Click here. The result is the following. To convert 170 Meters to Feet you have to multiply 170 by 32808398950131 since 1 Meter is 32808398950131 Feet.
How far is 70 feet in centimeters. 3 feet and 53386 inches. Converting 70 ft to cm is easy.
You are 2083 cm208 m tall. 3 feet and 45512 inches. Download height conversion chart.
Tall Tall is the measurement of vertical distance. 70 cm is about 24 Which amounts to 2 feet and 4 inches. 3 feet and 25827 inches.
Converting 70 cm to ft is easy. Tall is determined by a combination of genetics and environmental factors. 1 centimeter is equal to 03937007874 feet.
Cm is a unit of length in the International System of Units SI the current form of the metric system. 70 cm to ft 70 centimetre to feet converter. The centimeter practical unit of length for many everyday measurements.
How tall is 70 cm in feet and inches. 3 feet and 49449 inches. If we want to calculate how many Feet are 70 Centimeters we have to multiply 70 by 25 and divide the product by 762.
The distance d in feet ft is equal to the distance d in centimeters cm divided by 3048. 145 x 70 cm in inches 135 x 70 cm in inches 140 x 75 cm in inches 140 x 65 cm in inches. 70 ft to cm conversion.
How high is 70 cm. A centimeter is based on the SI unit meter and as the prefix centi indicates is equal to one hundredth of a meter. What is the formula to convert from cm to in.
A centimeter cm is a decimal fraction of the meter the international standard unit of length approximately equivalent to 3937 inches. We conclude that one point seven Meters is equivalent to five point five seven seven Feet. 3 feet and 37638 inches.
Convert 70 Centimetre to Foot with formula common lengths conversion conversion tables and more. A centimeter is equal to 001or 1E-2 meter. Simply use our calculator above or apply the formula to change the length 70 ft to cm.
The centimeter symbol cm is a unit of length in the metric system. This Page is Calculated for the Following height. How tall is 170 cm in feet and inches What is the cm to in conversion factor.
For the opposite calculation. 170 Meters is. Convert 20 cm to feet.
We can also form a simple proportion to calculate the result. How to convert centimeters to feet. Electrical Calculators Real Estate Calculators Accounting Calculators Business Calculators Construction Calculators Sports Calculators.
70 25 762 1750 762 22965879265092 Feet So finally 70 cm 22965879265092 ft. Human tall is the distance from the bottom of the feet to the top of the head. 3 feet and 29764 inches.
3 feet and 2189 inches. So for 70 we have. 70 cm in feet and inches 2 feet and 355906 inches About Cm to Feet and Inches Converter The Cm to Feet and Inches Conversion Calculator is used to convert centimeters to feet and inches.
Convert 70 cm to common lengths. To convert 70 centimeters into feet we have to multiply 70 by the conversion factor in order to get the length amount from centimeters to feet. D ft d cm 3048.
170 m 32808398950131 5577 ft. Metric prefixes range from factors of 10-18 to 10 18 based on a decimal system. 1cm 1254ft 03937007874ft.
70cm 70 cm 70 centimeters 70 centimetres Height Feet. It is defined as 1100 meters.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487620971.25/warc/CC-MAIN-20210615084235-20210615114235-00575.warc.gz
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CC-MAIN-2021-25
| 4,296 | 26 |
https://roboticsclub.org/redmine/issues/1044
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math
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Choose a new rtc backup battery
We need to run on 1.8V
#1 Updated by Kevin Woo over 11 years ago
$0.75 / battery, 3V we need to step it down but its the best we can do. Uses existing battery holder
#2 Updated by Kevin Woo over 11 years ago
Wikipedia says that the typical capacity is 25mAh with our current draw of 5uA. This leads to about 208 days of running only on the battery. There is also a self discharge of .1mA. This may dramatically lessen the lifetime of the battery.
Alternatively we can use: http://www.allspectrum.com/store/product_info.php?cPath=76_156&products_id=1589&osCsid=f6ab02f15e80a8597fbd2cce9064f1fe&sdesc=CR1220+3.0V+Lithium+Button+Cell+Battery%2C+38mAh%2C+%281pcs%2Fbl%29+%3D%3DSHIPS+GROUND+ONLY%3D%3D+Model+%23+CR1220-BP1
This is a 1220 but has a capacity of 36mAh which gives us 316 days. It costs $0.99 each.
#3 Updated by Kevin Woo over 11 years ago
Using 2 diode drops. Schottky and standard diode -> .3 + .7 in the worst case leads to 2V which is a little dangerous. Common case will be .8 + .4 which leads to exactly 1.8V.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488504838.98/warc/CC-MAIN-20210621212241-20210622002241-00581.warc.gz
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CC-MAIN-2021-25
| 1,056 | 10 |
https://psychology.fandom.com/wiki/Skewed_distribution
|
math
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Individual differences |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Consider the distribution in the figure. The bars on the right side of the distribution taper differently than the bars on the left side. These tapering sides are called tails, and they provide a visual means for determining which of the two kinds of skewness a distribution has:
- positive skew: The right tail is the longest; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed.
- negative skew: The left tail is the longest; the mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed.
Skewness, the third standardized moment, is written as and defined as
where is the third moment about the mean and is the standard deviation. Equivalently, skewness can be defined as the ratio of the third cumulant and the third power of the square root of the second cumulant :
This is analogous to the definition of kurtosis, which is expressed as the fourth cumulant divided by the fourth power of the square root of the second cumulant.
For a sample of n values the sample skewness is
Given samples from a population, the equation for the sample skewness above is a biased estimator of the population skewness. The usual estimator of skewness is
where is the unique symmetric unbiased estimator of the third cumulant and is the symmetric unbiased estimator of the second cumulant. Unfortunately is, nevertheless, generally biased. Its expected value can even have the opposite sign from the true skewness.
The skewness of a random variable X is sometimes denoted Skew[X]. If Y is the sum of n independent random variables, all with the same distribution as X, then it can be shown that Skew[Y] = Skew[X] / √n.
Skewness has benefits in many areas. Many simplistic models assume normal distribution i.e. data is symmetric about the mean. But in reality, data points are not perfectly symmetric. So, an understanding of the skewness of the dataset indicates whether deviations from the mean are going to be positive or negative.
Pearson skewness coefficients
Karl Pearson suggested two simpler calculations as a measure of skewness:
There is no guarantee that these will be the same sign as each other or as the ordinary definition of skewness.
- Skewness risk
- Kurtosis risk
- Shape parameters
|This page uses Creative Commons Licensed content from Wikipedia (view authors).|
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https://www.jiskha.com/display.cgi?id=1319713821
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math
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posted by satheesh .
how can you make a fence with the least amount of materials that encloses maximum possible area? this one is bit " curved " and needs to think outside the " Fence "
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
We don't usually make "curved fences".
Mathematically, with a limited length of fence, a fence in the form of a circle encloses the maximum area.
If the fence has to be straight, then it's a square has the maximum area for a given length of fence (or the least fence for the same area).
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https://bafybeiemxf5abjwjbikoz4mc3a3dla6ual3jsgpdr4cjr3oz3evfyavhwq.ipfs.dweb.link/wiki/Alessio_Figalli.html
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math
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2 April 1984|
Scuola Normale Superiore di Pisa|
École normale supérieure de Lyon
|Doctoral students||Eric Baer, Emanuel Indrei, Diego Marcon, Levon Nurbekyan, Maria Colombo|
Prix and Cours Peccot (2012)|
EMS Prize (2012)
Stampacchia Medal (2015)
Alessio Figalli (born 2 April 1984) is an Italian mathematician working primarily on calculus of variations and partial differential equations. He has been awarded the Prix and Cours Peccot in 2012, the EMS Prize in 2012, and the Stampacchia Medal in 2015. He has been an invited speaker at the International Congress of Mathematicians 2014.
Figalli received his master's degree in mathematics from the Scuola Normale Superiore di Pisa in 2006, and earned his doctorate in 2007 under the supervision of Luigi Ambrosio at the Scuola Normale Superiore di Pisa and Cédric Villani at the École Normale Supérieure de Lyon. In 2007 he was appointed Chargé de recherche at the French National Centre for Scientific Research, in 2008 he went to the École polytechnique as Professeur Hadamard. In 2009 he moved to the University of Texas at Austin as Associate Professor. Then he became Full Professor in 2011, and R. L. Moore Chair holder in 2013. Since 2016, he is a chaired professor at ETH Zürich.
Amongst his several recognitions, Figalli has won an EMS Prize in 2012, he has been awarded the Peccot-Vimont Prize 2011 and Cours Peccot 2012 of the Collège de France and has been appointed Nachdiplom Lecturer in 2014 at ETH Zürich. He has won the 2015 edition of the Stampacchia Medal.
Figalli has worked in the theory of optimal transport, with particular emphasis on the regularity theory of optimal transport maps and its connections to Monge–Ampère equations. Amongst the results he obtained in this direction, there stand out an important higher integrability property of the second derivatives of solutions to the Monge–Ampère equation and a partial regularity result for Monge-Ampère type equations, both proved together with Guido De Philippis. He used optimal transport techniques to get improved versions of the anisotropic isoperimetric inequality, and obtained several other important result on the stability of functional and geometric inequalities. In particular, together with Francesco Maggi and Aldo Pratelli, he proved a sharp quantitative version of the anisotropic isoperimetric inequality. Then, in a joint work with Eric Carlen, he addressed the stability analysis of some Gagliardo-Nirenberg and logarithmic Hardy-Littlewood-Sobolev inequalities to obtain a quantitative rate of convergence for the critical mass Keller-Segel equation. He also worked on Hamilton–Jacobi equations and their connections to weak KAM theory. In a paper with Gonzalo Contreras and Ludovic Rifford, he proved generic hyperbolicity of Aubry sets on compact surfaces. In addition, he has given several contributions to the Di Perna-Lions' theory, applying it both to the understanding of semiclassical limits of the Schrödinger equation with very rough potentials, and to study the Lagrangian structure of weak solutions to the Vlasov-Poisson equation. More recently, in collaboration with Alice Guionnet, he introduced new unexpected transportation techniques in the topic of random matrices to prove universality results in several-matrix models.
- "6th European Congress of Mathematics" (PDF). European mathematical Society. Retrieved 13 March 2013.
- 2015 Stampacchia Medal winner citation
- "ICM 2014".
- "ETH Lectures in Mathematics".
- "W 2,1 regularity for solutions of the Monge–Ampère equation". Inventiones Mathematicae. Retrieved 26 April 2012.
- "Partial regularity for optimal transport maps". Publications mathématiques de l'IHÉS. Retrieved 29 July 2014.
- "A mass transportation approach to quantitative isoperimetric inequalities". Inventiones Mathematicae. Retrieved 1 June 2010.
- "Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation". Duke Mathematical Journal. Retrieved 15 February 2013.
- "Generic hyperbolicity of Aubry sets on surfaces". Inventiones Mathematicae. Retrieved 24 June 2014.
- "Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data". Communications on Pure and Applied Mathematics. Retrieved 27 April 2011.
- "Universality in several-matrix models via approximate transport maps". Acta Mathematica.
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https://topprnotes.com/ibps-rrb-floor-puzzles/
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math
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In the reasoning section of the IBPS RRB exam, there are a lot of interesting topics. One such topic is floor puzzles. Floor puzzles are also known as floor test or floor questions. It is one of those topics that is interesting as well as confusing. We have seen a lot of candidates get frustrated with solving a single floor test question. Most of them often give up easily and give wrong answers. Some of them leave the questions altogether. Doing things like that are not acceptable, especially since IBPS RRB is so hard to crack. Solving IBPS RRB Questions are not as hard as you might think. All you need is the right approach and use the right technique. Let us take a closer look at IBPS RRB floor puzzles and see how you can solve them in a better way.
Understanding IBPS RRB Floor Puzzles
What are Floor Puzzles?
In a floor puzzle, you would be given an example of a multi-storeyed building. You would have to deduce which person stays on which floor based on the information provided to you. Such questions are meant to test your logical reasoning ability.
What is the structure of IBPS RRB Floor Puzzles?
In IBPS RRB, you would get a set of statements and a number of questions would follow that statement. To answer the question, you have to deduce the floor arrangement.
For example: Seven people A,B,C,D,E,F and G stay in an apartment building. The apartment building has seven floors, with one person living on each floor. Each of them is travelling to a different city – Bombay, Delhi, Bangalore, Lucknow, Kolkata, Chennai, and Patna, but not necessarily in that order.Only three people live above D. Only one person lives between D and the person travelling Bangalore. E lives on the floor between A and B. E is travelling to Bangalore.
Who lives above D?
How Many Questions Come in the Exam?
As said before, a number of questions are asked in a single ‘set’. Usually, there is only one set given in the IBPS RRB exam. In every set, there are around 3-5 questions. Therefore, on an average, 3- 5 questions are asked on the topic in the RRB exam. However, like every other topic in the IBPS RRB syllabus, the number of questions asked on floor puzzles also differs. So, in IBPS RRB 2021, you can get more questions or fewer questions than the average. It all depends on your luck! So, its better if you prepare well for this topic, so eliminate the luck factor as much as you can.
How Hard are They to Solve?
The difficulty of the question also varies from year to year. In most cases, the level of difficulty varies from ‘moderate to difficult’. There are two factors that make questions like this hard to solve. The first thing is that they take a lot of time to solve. This is because there are too many bits and pieces of data to process. The second thing is that the actual processing of the data is also quite difficult. You need to retain the information and use the information in the right way.
Well, the impact of both the factors can be minimized if you use the right process. This ‘right process’ is what we are going to learn about now.
The Process of Solving IBPS RRB Floor Puzzles
So, what is the most effective way of solving floor puzzles in IBPS RRB? Would it help you to increase both your speed and accuracy? Well, yes, it can do all of that! You just need to put in a little bit of practice and you can solve the questions with ease.
Let us take a look at how you can solve the question that we have used as an example above.
Question: Seven people A,B,C,D,E,F and G stay in an apartment building. The apartment building has seven floors, with one person living on each floor. Each of them is travelling to a different city – Bombay, Delhi, Bangalore, Lucknow, Kolkata, Chennai, and Patna, but not necessarily in that order.Only four people live above D. Only one person lives between D and the person travelling Bangalore. E lives on the floor between A and B. E is travelling to Bangalore and A lives on the top floor.
Who lives immediately above D?
Solution: The best way to solve such questions is by looking for clues. You should look at statements that are independent. This means statements that directly give out the position of the person.
It is said that only four people live above D. The building has 7 floors. So, D lives on the 2nd floor. A also lives on the top floor and E is travelling to Bangalore.
Now, since E is travelling to Bangalore, there is only person between E and D and that one person lives above D.
Again, we look at another statement and we find that E lives between A and B. If A is at the top floor, then that means B is below E. So, B must be between E and D. So, B must live immediately above E.
Answer: B lives immediately above D
So, this is how easy it is to solve IBPS RRB floor puzzles. Just look for the clues and use your logic and you would be able to solve them with ease.
On which floor does D live?
How many persons live between the floors on which Q and S live?
(b) More than three
Who lives on the fifth floor?
(c) None of these
Best of luck,
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http://bestshopping.club/aebd/a6035b84cdea/ged-math-practice-questions-quadratic-equations-e50e24
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math
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Image1 Png The ged mathematics test ppt downl on kindergarten printables free integer word problems works. Ged math square roots on wonderful mathematics practice tests ideas printabl. Free ged practice test questions ace your tes on mathematics. Ged math total study guide teacherling on ged math. About the ged ex on ged question types drag drop questions.
Home » Questions » Ged Math Questions » Ged Math Practice Questions Quadratic Equations On Bar Graphs Ged
Ged Math Practice Questions Quadratic Equations On Bar Graphs Ged
Published: Saturday 03rd of March 2018|F
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http://www.stata.com/statalist/archive/2007-02/msg00593.html
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math
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[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]
st: running regressions on only certain sections of the data
I am assuming that you have a variable called section,
which contains the strings A, B, or C.
to do the regression you requested you would type:
reg y x if section == "A"
reg y x if section == "A" | section == "C"
reg y x if section == "A" | section == "B"
For more info see: - help if- and -help operator-
If you have many sections (but need no more than 10, categorized by a
string variable) you could also do
reg y x if inlist(section,"A","C")
reg y x if inlist(section,"A","B")
help functions -> programming functions for details. inrange() is
also useful in some cases like this.
Kit Baum, Boston College Economics
An Introduction to Modern Econometrics Using Stata:
* For searches and help try:
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https://www.utiyuunosikumi.jp/universal-world/
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math
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(Machine translation. Please forgive the part where the text is unnatural)
Everything works in a pair (one thing) of the inner world relative to each other
[The result amount (fictional conceptual world) operates in the inner world of the unit division amount that is infinitely continuous (dimension = unit interaction amount = existential)]
All are continuously stacked in a division unit amount (dimension=entity) of 10.
* The fundamental energy that operates in the universe is infinitely continuous unit division amount (unit interaction amount ).
* The amount of result produced in the inner world (the amount of interaction of light particles) of the unit division amount (entity) evolves into the concept of elementary particles → atoms → molecules → objects → organisms.
The concept of the past There is a dimension of the past (division amount of 10) in the inner world of completion (one thing = 0 dimension) in the universe.
And the 0th dimension is born in the division unit quantity of 10 at the beginning of the
present universe (singularity = from the beginning to the end of the 1st dimension = the premise of the concept of mass).
→ Completed in one dimension (reached the total amount of unit interaction) splits into 10 (evolved into the concept of mass from the beginning to the end of the second dimension)
→ Completion in 2 dimensions (reaching the total amount of unit interaction) is divided into 10 (from the beginning to the end of 3 dimensions = born in the total amount of the concept of mass = unit spatiotemporal quantity).
In the present universe, which did not occur, a unit amount of light (total 1 to 3 dimensions = simultaneous = total amount of the concept of mass = elementary particles that reached the speed of light) is generated (unit spatiotemporal amount).
And everything works on the same principle and goes to another dimension (more split units = more unit interactions = more unit spatiotemporal quantities).
* Unit division amount (entity) = Unit interaction amount in the inner world
(existence = causal = consciousness amount) = result amount produced in the interaction amount (material = fictitious
=impermanence ) = infinitely continuous unit division amount (entity=impermanence ).
Everything tries to complete in 3 dimensions
* Every dimension tries to converge to a three-dimensional whole (complete in one concept).
* Completion of all three-dimensional aggregates (convergence into one) attempts to converge to a further three-dimensional aggregate (4 to 6 → 7 to 9 → 11 to 13) .
* The past dimension (concept) operates in the inner world of the present dimension ⇔ The current dimension (concept) operates ⇔ The present dimension operates in the inner world of the future dimension (concept) = three dimensions (one) If not, all the current dimensions will not work.
Every 10 consecutive Unit split amount (dimensions), the interacting unit quantity operates in the inner world (time-space quantity = beginning and end). Amplifies to the
same concept, but it begins in one dimension and ends in three dimensions.
Completed in past dimensions (0 dimension = convergence) → 1 dimension (0 dimension divided into 10 = premise of mass) → 2 dimensions (1 dimension divided into 10 = mass) → 3 dimensions (2 dimensions divided into 10 = Total mass) = 3 dimensions.
→ 4 dimensions (3 dimensions split into 10 = premise of atoms) → 5 dimensions (4 dimensions split into 10 = atoms) → 6 dimensions (5 dimensions split into 10 = total amount of atoms) = 3 dimensions.
→ 7 dimensions (6 dimensions split into 10 = premise of molecules) → 8 dimensions (7 dimensions split into 10 = molecules) → 9 dimensions (8 dimensions split into 10 = total amount of molecules) = 3 dimensions.
Then, it reaches the 10th dimension in which the 9th dimension is manipulated ( the total amount of unit interaction) and is completed in the material universe (the disappeared imaginary space = the arithmetic amount) (nothing = Existence = cause of further dimension).
Everything is a continuous stack in decimal (divide into 10 = 10 dimensions)
* From any 0, it is born into 1-9, reaches one thing called the whole of 9 and returns to further 0 (10). That continuous stack.
* Completeness (existence = nothing) in every dimension (concept) is the cause of further dimensions (concepts).
Completed in dimensions (nothing = cause of further dimensions) → Completed in three dimensions (nothing = cause of further worldview) → Completed in nine dimensions (conceptual universe).
Complete the 10th dimension, which is the total amount of interaction units that are born in 1D to 9D and encompass 9D (convergence =
disappearing imaginary space = disappearing computation = arrive at the result = Nothing = existed = cause of a further conceptual universe).
Everything works on the same principle (universal).
【To be completed in 1st to 3rd dimensions = Space-time before the start of the material universe: Born into the total amount of the concept of mass = Completed in the elementary particles that reached the speed of light = The origin of space-time】
Trying to complete in one dimension (Premise the concept of mass) = outer shell surrounding the total amount of interaction results of circles = getting the surface quantity of the inner world of the imaginary space quantity
The beginning of the 1st dimension (unit interaction quantity obtained by division unit quantity of 0th dimension = 10 = imaginary time quantity = future quantity = possibility to fit within unit quantity) is the end of the 1st dimension (computation quantity =Amount of imaginary space ) is reached (one complete = premise of the concept of mass).
1 dimension (The amount of interaction obtained with the amount of division of 10= 10 to the 10th
power) .existence form (circle with interaction that the point 0 dimension is divided into 10) .generation form (sum of circles continuous in loop) .cognitive form (virtual Get surface in space)
* If there is only one thing (self), there is no amount of interaction in the inner world (simultaneous) of the self, and there is no amount of interaction in the outer world (simultaneous) of the self.
And it stands still and exists in the same way as the one that does not exist (one thing does not exist = it exists in a pair as opposed to each other).
* There is the whole of the other in the inner world of the self, and there is the whole of the other in the outer world of the self = one thing (self) tries to reach the further self (one thing) .
Trying to complete a two-dimensional surface (concept of mass) = outer shell containing the result of surface interaction = getting space in the interior space of an imaginary space
* Every evolution is in a two-dimensional plane (new concept = reaching the beginning self).
The beginning of a two-dimensional surface (completed in one dimension is born into 10 split unit quantities = interaction unit quantity obtained in the inner world = imaginary time quantity = future quantity = possibility of being in the inner world of unit quantity Total amount). The end of the two-dimensional surface ( computation amount = total amount of imaginary space amount) is reached (the concept of stationary mass).
Two-dimensional surface (The amount of interaction obtained with the amount of division of 10 = 10 to the 10th power) .Existence form (a sphere in which the total of the planes divided into 10 has an orthogonal interaction).a generation form (a total of continuous faces in a loop).and a recognition form (a space quantity is obtained in the inner space of an imaginary space quantity).
Trying to complete in three dimensions (total amount of the concept of mass = unit amount of light) = get the distance to the inner world of the fictitious distance
* Reach the two-dimensional plane (stationary self) and try to complete it in three dimensions (total amount of self = total amount of evolution). And it is at the same time as the unit interaction amount (unit spatiotemporal amount = inflation).
The beginning of 3D (2D surface divided into 10 = interaction unit quantity = imaginary time quantity = all possibilities in the inner world of unit quantity) reaches the end of 3D (mass concept = The total amount of elementary particles that reached the speed of light).
Three dimensions (The amount of interaction obtained with the amount of division of 10 = 10 to the 10th power). Existence form (distance where the total of space quantity divided into 10 interacts) . Generation form (concept of stationary mass continuing to division) ・ Recognition form (obtains apparent mass in the inner world of imaginary space quantity) .
Inner sphere of light unit : From the beginning to the end of the concept of mass (beginning with the interaction unit quantity and ending with the interaction result unit quantity = nothing will increase, nothing will decrease)
* Every time a unit of light is completed, the 1st to 3rd dimensions are repeated (the universe is the total interaction of unit of light = simultaneous).
* All physical forces operate from the first equivalent world to the inner world of the final equivalent world (distortion = now).
* Define the apparent mass and imaginary space in the inner bounds of the unit quantity of light (source of distance and speed).
* Trying to be born into one of all possibilities in the inner world of all unit quantities of light (all possibilities overlap = quantum).
* The inner world of the unit amount of light contains the conceptual universe completed in the past (the amount of interaction of all dimensions that existed in the past) and the amount of interaction until it is completed in one or two dimensions.
And the world of spatiotemporal quantities in which all the interactions quantities that are about to be completed in three dimensions operate.
A two-dimensional surface (evolved into the concept of stationary mass) reaches three dimensions (total mass of the concept of mass). It is the root of the spatiotemporal quantity that operates in the 5th to 6th dimensions, the 8th dimension to the 9th dimension, the
12th dimension to the 13th dimension (the concept of mass = the premise of the material universe).
And a further concept (atom → molecule → object) cannot enter the inner bounds (spatiotemporal quantity) of a unit quantity of light (because there are simultaneous, it can be fixed in distance, speed, and time).
Since the two-dimensional surface (concept of mass = hollow sphere) is completed in three dimensions, the concept of mass is
divided and the apparent mass and imaginary space quantity are determined (simultaneously).
And when the concept of mass (result unit amount) and the imaginary space amount (Unresulted amount) contradictory increase and decrease, nothing increases and nothing decreases (universal).
* The universe is the whole that has the interaction of the unit amount of light. The unit amount of all light is a continuous stack that is completed (nothing = now) at the same time. And the universe (now = nothing) is stationary (static), and the front and back are in the dynamic (expanding universe) in the continuous stacking of the present.
* There is an uncertain principle (undetermined = unrecognized) in the inner bounds of the unit quantity of light (the beginning and the end are at the same time = all possibilities in the inner bounds of the unit quantity = quanta).
There is no uncertainty principle in the external world of the unit quantity of light (determination = proton → atom → molecule → object → material universe).
However, the total amount of interacting light (one thing = the universe that is not complete now) is on a further uncertainty principle.
* The object has speed (continuous stacking completed in a unit amount of light),
And the thing that evolves (concept of further mass continuous to the outside of the unit of light = convergence to the form of function = world view) is also premised on a set amount (dimension = division unit amount = unit interaction amount),
If the current universe is really one (no internal structure), they all exist at the same time and the universe does not work.
And there is no matter in outer space, and outer space and matter are the same thing that contradict each other.
Gravity 1 (many-worlds = consciousness)
* Every dimension (unit interaction amount) does not work by itself, but between the dimension in the inner world (past = self premise) and the dimension in the outside world (future = self to be reached) Operates(unit spatiotemporal amount).
* The material universe (operated by physical force) operates in the many-worlds (divided material universe), which is the amount of gravity (the amount of consciousness that tries to reach the total amount of interaction).
Gravity 2 (relative difference in dimension)
* Every dimension (unit quantity) is a relative difference in concept, but it is universal in the concept of unit quantity (from the beginning to the end of the interaction quantity in the inner world of the unit).
* Every present concept (unit quantity) exists relatively quickly (many interactions) in
the inner world of the past concept (unit quantity). Contrary to this, every existing concept (unit amount) is relatively
slow (small amount of interaction) in the inner world of the future concept (unit amount).
= Every present speed (unit interaction amount = unit spatiotemporal amount) exists only now.
The attempt to complete an atom (4th
to 6th dimensions = unit interaction amount = 10 to the 60th power) is more than the attempt to complete to an elementary particle (1st to 3rd dimension =
unit interaction amount = 10 to the 30th power). It exists relatively fast (a concept that exists in the outside world of elementary particles).
And it is relatively slower (concept in the inner world of the molecule) than trying to complete the molecule (7th to 9th dimensions = unit interaction amount = 10 to the 90th power).
And the (11-13 dimensions = unit interaction amount = 10 to the 130th power) that tries to be completed in the
living thing (concept) is in the outside world of elementary particles (concept).
Recognize in the inner world of consciousness the continuous accumulation of completion in the unit amount of light (living things are faster than light).
Contrary to this, humans → molecules → atoms, which are composed of elementary particles as their roots, are in a continuous stack of all apparent masses and all imaginary spaces in the inner world of a unit amount of light, and I can't reach the speed of light.
Everything is opposite and is paired (relative difference), and the concept (consciousness) in the past cannot be explained only by the consciousness in the concept of living things.
Gravity 3 (The amount of imaginary space is distorted at the same time as the concept of mass was born in the inner world of the unit amount of light)
* The strain generated in the uniform (resting) inner world operates in an attempt to reach the uniform (resting) total amount of contradictory strains.
The universe is a whole with the interaction of the division unit quantity (the computing world that is evenly distributed = operating in the unresulting quantity).
And when the concept of mass is born in the uniform inner world, the unit amount of light that opposes becomes a pair (from the beginning to the end of the concept of mass = unit spatiotemporal quantity), and in the inner world of the unit imaginary space quantity that existed evenly Distortion is born. Then, it tries to reach the total amount of strains produced evenly (the concept of mass works).
It is in the inner world of a unit quantity (one thing) and everything results at an accelerating rate (the inner world of the universal concept of unit quantity is not constant).
* An object that accelerates at a constant rate has a result amount that is amplified at an accelerating rate = an event that appears at an accelerating rate has a certain amount of addition.
Everything is in one thing (universal concept = unit quantity). In the inner world of the unit quantity, there is the total of the divided unit quantities, and in the outer world of the unit quantity, there is the total of the divided unit quantities. And in the inner world of every one unit quantity, there is an interaction quantity that continues to be amplified at an accelerating rate.
There is recognition (event) in the determination of the unit quantity, and all dimensions (completed in the unit quantity) are in the same thing (universal). However, every dimension cannot recognize the relative difference from other dimensions, and every unit quantity (dimension) exists only now (the position where the unit consciousness is placed).
* I feel that the age of the universe, which is about 13.7 billion years, does not change (constant). However, the more you go back in time, the slower the time progresses (completes faster), and conversely, the more you go to the future, the faster the time progresses (slowly completes). And all consciousness exists only in the present (dimension = unit quantity), and the relative past and future cannot be compared.
* The temperature rises, the ice melts, the surface of the earth appears, solar heat accumulates, and global warming progresses
By accelerating the results of synergistic effects, I think that global warming will accelerate for human who can recognize global warming as one (awareness of the event in the outside world).
However, if we focus on the unit amount in an attempt to cause global warming phenomena one by one in the inner world, we cannot recognize the accelerating global warming phenomenon and it is evenly distributed.
(Organisms appear to evolve in the inner world of evenly advancing time, but at the same time they have the consequence of accelerating in the inner world of evolution).
* Anything in the inner world of any self (concept to be
reached) cannot see the true form (completion) of the self.
And human beings can only understand the distance, speed, and time from their position (the existing concept).
And all the units of interaction (evolutionary position) that occur in the past, present, and future are in relative differences (positions of consciousness), not in one scale (constant).
[Only time = no time = everything is the same]
The origin of time is the unit interaction amount (unit imaginary time amount)
*Amount of time reached (distance = speed = space amount = mass = not conscious of one's inner world =
And the amount of imaginary time that has not reached (imaginary distance = imaginary velocity = amount of imaginary space = conscious of the external world of oneself = now).
* Human time is imaginary time.
Time is not just time. It is before time (unit imaginary time = unit imaginary space) and after time (distance = speed = changing mass).
And the cause (unworked amount) and the result (worked amount) are the root of the concept of time, and the concept of mass (atom → molecule → object → organism = obtained unit time amount and unit space amount) is a unit that is not obtained now It exists at the same time as the spatiotemporal quantity (unit imaginary time quantity and unit imaginary space quantity).
Time is not constant, but varies depending on the dimension (concept) (the concept of time is universal)
*Objects cannot be put in molecules →Molecules cannot be put in atoms →Atoms cannot be put in elementary particles (unit amount of light).
* The source of time lies in the inner world of the unit amount of light, but the time felt by living things lies in the continuous accumulation of complete (now) in the unit amount of light.
The spatiotemporal quantities in the 1st to 3rd dimensions (the concept of mass) are universal
→The spatiotemporal quantities in the 4th to 6th dimensions (the concept of atoms) are universal
→The spatiotemporal quantities in the 7th to 9th dimensions (concept of molecules) are universal
→The spatiotemporal quantities in the 11th to 13th dimensions (the concept of living things) are universal.
Each is in a different spatiotemporal quantity, but in the universe that they all overlap (interact).
The source of time lies in the inner world of a unit of light (which concludes with any apparent mass and any imaginary space).
However, the completion of the unit light quantity (nothing = now) is a simultaneous world, and before that, atoms → molecules → objects (organisms) cannot enter (unit light quantity = concept of mass).
And the time that humans feel is the continuous accumulation of now (nothing).
Time flows to the outside world of the self, and the self flows to the infinite inside world (continuous accumulation where time and imaginary time stand still = everything now)
* Every present (self = unit amount) is stationary, and is continuous to the inner world of a further unit amount (total amount of self = consciousness) (in the inner world of every consciousness, continuous recognition of the concept of every mass Stacking).
It completely stands still at the unit amount of light (apparent mass = obtained unit time amount and obtained unit space amount) (I
cannot recognize the existence of myself in the disappeared consciousness amount = now = nothing).
The concept of time is in operation between the beginning and the end of a unit of light (unit of space-time). And the whole (universe) with the interaction of the unit amount of light is also on the same principle.
Every self (stationary unit consciousness = now) recognizes others as changing (current continuity = time flows).
Contrary to this, in the infinite (continuous of nothing) inner world, a certain unit amount of result flows.
No one recognizes the amount of imaginary time in one dimension (self-premise)
→ No one recognizes the amount of imaginary time in the two-dimensional plane (before reaching the self).
And there is a concept of time (continuous) that the self (now = distortion = recognition) is aware of from the 2D plane (reaching the self) to the completion in the 3rd dimension (total amount to the self).
However, every self (two-dimensional plane = now) is a continuous stack of stationary (complete = nothing), and every self has no consciousness to recognize time (does not know the outside world).
And what recognizes the period (spatio-temporal quantity) from the 2D plane to the 3rd dimension is the 4th dimension (consciousness quantity) of the outside world (every present concept has the past concept and is the future dimension Operates in the inner world).
There is no obliqueness in the principle world (objects that seem to have any speed composed of elementary particles are at different positions in the inner world of light units)
* The concept of mass is completed (result position) in the arithmetic world in an amount that is orthogonal to
the obtained straight amount.
And what seems to progress diagonally to the continuous stacking.
Inside the stationary space rocket or in the space rocket that moves at a constant speed, when light is emitted from a light emitting device placed on the floor to a mirror attached to the ceiling inside the rocket, the reflected light returns to the light emitting position.
If the distance from the light emitting device inside the rocket to the mirror on the ceiling is the unit amount of light (total
imaginary distance = simultaneous), the first unit of light reaches the mirror on the ceiling at the same time .
And when the reflected light reaches the same position as the light emitting device, it means that the second unit of light is completed.
Objects with speed are at different positions in the inner world of the unit quantity of light (universal imaginary distance =
When launching light, the rocket, the light emitting device inside and the mirror on the ceiling are between the apparent mass and the remaining amount of imaginary space (simultaneous internal distortion = position = now).
No matter how large the space is inside the spacecraft, it always emits light from the same position inside the unit of light, and the reflected light returns to the same position as the light emitting point.
And the light that is emitted inside the rocket is reflected and returns to the launch position, and if a stationary person sees it, it will advance diagonally and return diagonally (relative difference in position within the unit of light) .
The unit quantity of light without the concept of mass (vacuum) and the unit quantity of light with the concept of mass (stationary / acceleration / constant-velocity motion) are both completed at the same time (consistent with all events).
And there is no slant in the world of principle, and things that have speed (elementary particles: atoms: molecules: objects) do
not go diagonally.
And what seems to go diagonally to the relative difference in the continuous stacking of the unit quantity of light.
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CC-MAIN-2022-21
| 24,954 | 151 |
http://www.anddev.org/networking-database-problems-f29/get-bluetooth-emulator-device-address-t6589.html
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math
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My question is....There is any way to get the bluetooth address of the emulator/device ?
I mean, I need a function that returns the emulator's bluetooth address...
Any help will be very appreciate!!
Users browsing this forum: No registered users and 1 guest
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190295.4/warc/CC-MAIN-20170322212950-00284-ip-10-233-31-227.ec2.internal.warc.gz
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| 257 | 4 |
http://alohafridaychallenges.blogspot.com/2015/02/aloha-friday-challenge-39-winners.html
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math
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Our random.org winner is...
#34 - Dorothy S
Please grab your winner's badge from the sidebar and
contact us at [email protected] to claim your prize!
And our top picks this challenge...
#16 - Jerrie
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and congratulations on your awesome work!!
kel and the KBD DT
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CC-MAIN-2017-22
| 354 | 12 |
https://www.rodwell.center/blog/archives/07-2014
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math
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I have been asked this question many, many times. And there is really no one good answer to this because each person who asks comes from different backgrounds, thus, experience different circumstances to which the question was raised. However, I can say this. Good math students have many different characteristics and variety of study habits. But they also do have many commonalities amongst many of which make them a good students. These are some examples of those common habits or good practices, but definitely not limited to only these.
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CC-MAIN-2024-10
| 541 | 1 |
https://encyclopediaofmath.org/index.php?title=Schur_Q-function&oldid=13902
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math
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A symmetric function introduced by I. Schur [a6] in 1911 in the construction of the irreducible spin characters of the symmetric groups (cf. Projective representations of symmetric and alternating groups). Schur -functions are analogous to the Schur functions, which play the same role for linear characters (cf. Schur functions in algebraic combinatorics). In fact, both are special cases of Hall–Littlewood functions discovered by D.E. Littlewood [a3], but see [a4] for a description of their development and subsequent generalizations, for example, Macdonald polynomials.
For , define
and then , because , as follows directly from (a1).
If is a strict partition of , where , then the matrix
is skew-symmetric, and the Schur -function is defined as
where stands for the Pfaffian.
An alternative purely combinatorial definition has been given by J.R. Stembridge [a7] in terms of shifted (Young) diagrams. These differ from Young diagrams (cf. Young diagram) in that there is an indentation along the diagonal. Young tableaux are replaced by marked shifted tableaux which are defined as follows. Let denote the ordered alphabet ; then a marked shifted tableau is a labelling of the nodes of the shifted diagram of shape such that
i) the labels weakly increase along each row and down each column;
ii) each column contains at most one , for each ; and
iii) each row contains at most one , for each . If denotes the number of nodes labelled either or , then is the content of and if , then
summed over all marked shifted tableaux of shape . It is a non-trivial task to prove that this is the Schur -function. For example, if , then the corresponding shifted diagram and a possible marked shifted tableau are
This combinatorial definition has been a rich source of significant combinatorial results, for example, Stembridge [a7] has proved an analogue of the Littlewood–Richardson rule that describes the Schur -function expansion of and also gives a purely combinatorial proof for the Murnaghan–Nakayama rule for computing the irreducible spin characters of (cf. Representation of the symmetric groups). All of this is based on a shifted version of the Robinson–Schensted–Knuth correspondence given independently by B.E. Sagan [a5] and D.R. Rowley (cf. also Robinson–Schensted correspondence).
Schur -functions also arise naturally in other contexts, for example, the characters of irreducible representations of the queer Lie super-algebra , the cohomology classes dual to Schubert cycles in isotropic Grassmannians and in polynomial solutions of the BKP-hierarchy of partial differential equations.
|[a1]||P.N. Hoffman, J.F. Humphreys, "Projective representations of the symmetric groups" , Oxford Univ. Press (1992)|
|[a2]||T. Józefiak, "Characters of projective representations of symmetric groups" Exp. Math. , 7 (1989) pp. 193–247|
|[a3]||D.E. Littlewood, "On certain symmetric functions" Proc. London Math. Soc. , 11 : 3 (1961) pp. 485–498|
|[a4]||I.G. Macdonald, "Symmetric functions and Hall polynomials" , Oxford Univ. Press (1997) (Edition: Second)|
|[a5]||B.E. Sagan, "Shifted tableaux, Schur Q-functions and a conjecture of R. Stanley" J. Combin. Th. A , 45 (1987) pp. 62–103|
|[a6]||I. Schur, "Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen" J. Reine Angew. Math. , 139 (1911) pp. 155–250|
|[a7]||J.R. Stembridge, "Shifted tableaux and projective representations of symmetric groups" Adv. Math. , 74 (1989) pp. 87–134|
Schur Q-function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Schur_Q-function&oldid=13902
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| 3,643 | 21 |
http://andrewtuckpointing.com/card/physical-science-unit-7-waves-test-answerspdf.php
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math
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Main / Card / Physical science unit 7 waves test answers.pdf
Physical science unit 7 waves test answers.pdf
Name: Physical science unit 7 waves test answers.pdf
File size: 485mb
1) Compared to wave A, which wave has the same wavelength but a smaller amplitude? . Page 7 Answer Key. Physics Unit Test- Waves and their Properties. INTEGRATED SCIENCE 1. UNIT 4: PHYSICS Sub Unit 1: Waves. TEST 2: Electromagnetic Waves and their Properties. Form B Use the figure below to answer question 4. 4) The incident light ray, 7) Diffraction is a result of . Answer Key. unit test – sph3u grade 11 physics – waves and sound 6. which of the longitudinal wave) which,7. waves - richard a. muller - 7. waves including the free high school science texts: a textbook for high school students studying physics.
Waves, Light and Sound Unit Readings. From Glencoe Physical Science and The Story of Science: Newton at the Center. Read by. Textbook. Glencoe. Glencoe. Note to Test Takers: Keep this practice book until you receive your score report. The book . momentum, wave function symmetry, When you take the test, you will mark your answers on example, a on the Computer Science Test is not 7. PHYSICS TEST. PRACTICE BOOK. Range of Raw Scores* Needed to Earn. 5 6 7 8 9 10 / 09 08 07 06 05 Copyright © Chemistry/ Physics Teacher, Retired. Worthington . On what pages are the Chapter Study Guide and Chapter Review? Look in the The unit of frequency is the number of.
Physical Science. Physics Semester - Final Exam Study Guide Unit 1: Inquiry and Reflection . Unit 7: Waves. (Ch. 10 in textbook). 1. Physical Science Reading and Study Workbook Level B □. Chapter 17 travel. It discusses three main types of mechanical waves—transverse, longitudinal, and surface 7. What is a transverse wave? 8. Look at the figure below. Use the words in the box to label the missing aspects of the Circle the correct answer. Student Extras. Teacher's Guides. The Physics Classroom» Physics Tutorial» Waves. Waves. Lesson 0 - Vibrations. Vibrational Motion · Properties of Periodic . Mapi Cuevas, Ph.D. Professor of Chemistry. Department of Natural. Sciences. Santa Fe UNIT 1. UNIT 3. UNIT 2. UNIT 6. UNIT 5. UNIT 4. UNIT 7. Introduction to Matter. . Chapter 20 The Energy of Waves. Standardized Test Preparation .
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CC-MAIN-2019-39
| 2,302 | 7 |
https://projecteuclid.org/journals/duke-mathematical-journal/volume-168/issue-15/The-geometry-of-maximal-representations-of-surface-groups-into-SO02n/10.1215/00127094-2019-0052.short
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math
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In this paper, we study the geometric and dynamical properties of maximal representations of surface groups into Hermitian Lie groups of rank . Combining tools from Higgs bundle theory, the theory of Anosov representations, and pseudo-Riemannian geometry, we obtain various results of interest. We prove that these representations are holonomies of certain geometric structures, recovering results of Guichard and Wienhard. We also prove that their length spectrum is uniformly bigger than that of a suitably chosen Fuchsian representation, extending a previous work of the second author. Finally, we show that these representations preserve a unique minimal surface in the symmetric space, extending a theorem of Labourie for Hitchin representations in rank .
Brian Collier. Nicolas Tholozan. Jérémy Toulisse. "The geometry of maximal representations of surface groups into ." Duke Math. J. 168 (15) 2873 - 2949, 15 October 2019. https://doi.org/10.1215/00127094-2019-0052
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| 975 | 2 |
https://fmph.uniba.sk/detail-novinky/back_to_page/fakulta-matematiky-fyziky-a-informatiky-uk/article/seminar-z-teorie-grafov-martin-macaj-732019/
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math
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Seminár z teórie grafov - Martin Mačaj (7.3.2019)
vo štvrtok 7.3.2019 o 9:50 hod. v miestnosti M/213
Od: Martin Škoviera
Prednášajúci: Martin Mačaj
Názov: Color digraphs, coherent configurations and the Weisfeiler-Leman stabilization
Termín: 7.3.2019, 9:50 hod., M/213
A color digraph is a complete digraph in which every dart is assigned a color. Color digraphs are an important tool in various areas, e.g., combinatorics, group theory, sports, and others. Association schemes and coherent configurations form special classes of color (di)graphs, with significant applications in graph theory, group theory, statistics, coding theory ... The Weisfeiler-Leman stabilization is a polynomial time algorithm which, given a color graph $S$, provides the smallest coherent configuration $S'$ such that each color class of $S$ is union of classes of $S'$. In this talk we recall basic properties of association schemes and coherent configurations and we present the Weisfeiler-Leman stabilization.
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CC-MAIN-2019-22
| 1,002 | 7 |
https://www.coursehero.com/file/6730851/diffq-algorithms/
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math
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This preview shows pages 1–2. Sign up to view the full content.
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Unformatted text preview: Algorithms for solving some differential equations Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA [email protected] Webpage http://www.math.ufl.edu/ squash/ 11 February, 2009 (at 12:49 ) Abstract: Gives a general method for writing the solution to a f irst-o rder l inear d ifferential e quation in terms of definite integrals. Step F1 of The FOLDE algorithm Write the DE in the form d y d x + ( x ) y = g ( x ) . 1 : Pick ( i.e, compute ) an antiderivative of , ( x ) := Z ( x )d x. 2 : Finally, we store for later use the following two func- tions: e ( x ) = ... and 1 e ( x ) = ... . 3 : Step F2. Now define B ( x ) := e ( x ) g ( x ). Then compute an antiderivative, A ( x ) := Z B ( x )d x. Step F3. Now, for = anyconstant, the following definition of y will satisfy eq(1). y ( x ) := 1 e ( x ) 4 : Step F4. From eq(4), compute y . Plug in to eq (1) to see if your formula for y satisfies it. ( It is at this point that you will sometimes find that you have made a computa-...
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https://www.wiringdraw.com/how-to-use-parallel-circuit-equation/
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math
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Parallel circuits are an essential part of modern electrical systems. Understanding how to use the parallel circuit equation can help you make more informed decisions when wiring up your own circuits. In this article, we’ll look at what a parallel circuit is, the equation used to calculate the current in a parallel circuit, and some tips on how to make the most of this equation.
A parallel circuit is a type of electrical circuit in which two or more paths of electricity flow through separate branches that join together at a common point. This means that the total resistance in the circuit is equal to the sum of the individual resistances of each branch. To calculate the current in a parallel circuit, you need to use the parallel circuit equation. This equation states that the total current flowing through the circuit is equal to the sum of the individual currents of each branch. As such, the equation is often written as I = I1 + I2 + I3 + ….
Using the parallel circuit equation can be tricky. It’s important to remember that the equation only works when the voltage supplied to the circuit is the same for all the branches. Additionally, you should also be careful when working with electric current as it can be dangerous. Make sure you take all necessary safety precautions when dealing with electric current.
Overall, understanding how to use the parallel circuit equation can help you make more informed decisions when wiring up your own circuits. Knowing the equation can help you determine the most efficient way to wire a circuit and provide you with insight into how the circuit will behave under different conditions. With a little practice, you’ll be able to use the equation with ease and get the most out of your electric circuits.
How To Calculate Resistance In A Parallel Circuit
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Dc Parallel Circuits The Engineering Mindset
Solving Problems 14 1 A Circuit Contains 5 Ohm 3 And 8 Resistors In Series What Is The Total Resistance Of Rt R1 Ppt
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https://www.shilbrook.com/decision-matrix-template/
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math
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What is a decision matrix template? A decision matrix template is an analytical document may help to compare potential solution by organize values and variables in tabular as well graphical representation. The entire process may help to analysis visually, even set up weighing their variables based on importance of subject’ values.
In this manner, How do you create a decision matrix template?
As a consequence, How do you define a decision matrix? A decision matrix is a series of values in columns and rows that allow you to visually compare possible solutions by weighing variables based on importance.
On the contrary, How do you calculate decision matrix?
Decision Matrix Analysis works by getting you to list your options as rows on a table, and the factors you need consider as columns. You then score each option/factor combination, weight this score by the relative importance of the factor, and add these scores up to give an overall score for each option.
When using a decision matrix After you identify?
When using a decision matrix, after you identify all options, what is the next step? Establish the criteria that will be used to rate the options. Capabilities related to the support and operation of a system should be considered early and continuously in the design and development of a system.
Related Question for Decision Matrix Template
How do you do matrix decision-making?
How do you make a decision?
What are the various models of decision-making?
The four different decision-making models—rational, bounded rationality, intuitive, and creative—vary in terms of how experienced or motivated a decision maker is to make a choice. ⇗
How do you create a matrix spreadsheet?
Why do we learn about Matrix?
The numbers in a matrix can represent data, and they can also represent mathematical equations. In many time-sensitive engineering applications, multiplying matrices can give quick but good approximations of much more complicated calculations. The point (2,1) is also where the graphs of the two equations intersect. ⇗
What is a weighted decision matrix?
A weighted decision matrix is a tool used to compare alternatives with respect to multiple criteria of different levels of importance. It can be used to rank all the alternatives relative to a “fixed” reference and thus create a partial order fo the alternatives. ⇗
Why is it important to use a decision matrix?
A decision matrix is a chart that allows a team or individual to systematically identify, analyze, and rate the strength of relationships between sets of information. The matrix is especially useful for looking at large numbers of decision factors and assessing each factor's relative importance. ⇗
What is a weighted scoring method?
Definition of weighted scoring
Weighted scoring is a framework designed to help teams prioritize outstanding tasks by assigning a numeric value to each based on cost-benefit (or effort versus value) analysis. Making decisions is never easy, especially when there's a big team involved. ⇗
What is a business decision matrix?
What is a decision matrix? A decision matrix is a tool that helps business analysts and other stakeholders evaluate their options with greater clarity and objectivity. A decision matrix (or grid) can: Reduce decision fatigue. Reduce subjectivity in decision making. ⇗
How do you evaluate a decision?
What is a decision matrix and why is it used?
A decision matrix is a list of values in rows and columns that allows an analyst to systematically identify, analyze, and rate the performance of relationships between sets of values and information. The matrix is useful for looking at large masses of decision factors and assessing each factor's relative significance. ⇗
How is the decision making matrix used to consider risk?
The Decision-Making Matrix helps staff categorize risk behaviors by considering their likelihood and their potential outcomes. For example, the likelihood that the patient was going to strike Jeff was moderate. But because the man was frail, it was unlikely that the outcome of a strike would be severe. ⇗
What are decision criteria?
The Decision Criteria is the sets of principles, guidelines and requirements which an organization uses to make a decision. Sometimes the Decision Criteria exists in a physical form where the customer has taken time to construct the specification of their requirements. ⇗
What is risk classification matrix?
The risk matrix is a visual representation of the risk analysis. It presents the risks as a graph, rating them by category of probability and category of severity. The highest level risks are one end, the lowest level on the other, and medium risks in the middle. ⇗
What is the purpose of matrix scoring method?
It is frequently used in engineering for making design decisions but can also be used to rank investment options, vendor options, product options or any other set of multidimensional entities. A basic decision matrix consists of establishing a set of criteria and a group of potential candidate designs. ⇗
What three things should we consider when making a decision?
The Three Things to Consider When Making Life Decisions
How do you make a decision between two things?
How do you make a difficult decision between two things?
What are the three 3 models of decision making?
Models of Decision Making: Rational, Administrative and Retrospective Decision Making Models. ⇗
What are the four types of decision making?
The four styles of decision making are directive, conceptual, analytical and behavioral options. Every leader has a preference of how to analyze a problem and come to a solution. ⇗
What are the 5 decision making styles?
After in-depth work on 1,021 of the responses, study authors Dan Lovallo and Olivier Sibony identified five decision-making styles. They are: Visionary, Guardian, Motivator, Flexible, and Catalyst. ⇗
What is the example of matrix?
For example, the matrix A above is a 3 × 2 matrix. Matrices with a single row are called row vectors, and those with a single column are called column vectors. A matrix with the same number of rows and columns is called a square matrix. ⇗
What is matrix diagram?
A matrix chart or diagram is a project management and planning tool used to analyze and understand the relationships between data sets. Matrix charts compare two or more groups of elements or elements within a single group. ⇗
Is a matrix a spreadsheet?
In context|computing|lang=en terms the difference between spreadsheet and matrix. is that spreadsheet is (computing) a computer simulation of such a system of recording tabular data, with totals and other formulas calculated automatically while matrix is (computing) a two-dimensional array. ⇗
What is Application of matrix?
What are the applications of matrices? They are used for plotting graphs, statistics and also to do scientific studies and research in almost different fields. Matrices can also be used to represent real world data like the population of people, infant mortality rate, etc. ⇗
Where is matrix used in real life?
Physics: Matrices are applied in the study of electrical circuits, quantum mechanics, and optics. It helps in the calculation of battery power outputs, resistor conversion of electrical energy into another useful energy. Therefore, matrices play a major role in calculations. ⇗
What is idempotent matrix with example?
Examples of Idempotent Matrix
The simplest examples of n x n idempotent matrices are the identity matrix In, and the null matrix (where every entry on the matrix is 0). d = bc + d2. To come up with your own idempotent matrix, start by choosing any value of a. ⇗
What is the first step in creating a weighted decision matrix?
How do you do a weighted scoring model?
How do I calculate a weighted average?
To find a weighted average, multiply each number by its weight, then add the results. If the weights don't add up to one, find the sum of all the variables multiplied by their weight, then divide by the sum of the weights. ⇗
How do you select decision criteria?
The decision criteria should be measurable and should be within scope of the problem you are trying to solve. On criteria that seem immeasurable, you should at least be able to compare one to another. For example, the typical software characteristic “user friendly” is not measurable as stated. ⇗
What is an alternative matrix?
An Alternatives Evaluation Matrix can be used to compare alternatives for numerous requirements including hardware, software, databases, operating systems, or languages. A Weighted Alternatives Evaluation Matrix, or Weighted Matrix, assigns weighting factors to criteria when comparing alternatives. ⇗
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http://www.jiskha.com/members/profile/posts.cgi?name=Kenya
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math
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Suppose you have 19.2 g of Cu. What number of moles of Cu is present? Report your answer to 3 signifiant figures.
one push factor in rural urban migration is
When 25.0g of Zn reacts with Hcl, how many L of H2 gas are formed at STP?
If a hospital received $5,000 in payments per year at the end of each year for the next tweleve years from an uninsured patient who underwent an expensive operation, what would be the current value of these commection payments: at 3% rate of return? at a 13% percent rate of re...
1. Marbury v. Madison
how long would it take to accumulate 2,000,000 with a 5% intrest rate
what problems are acid precipition associated with
Introduction to business
what advantages might a socialist systemhavein resonding to the needs of people stuck by an emergency situation like the earthquake that occurred in haiti in january of 2010?
Ok that's slightly confusing. I understand the flipping of x and y but then what do you do? so x=log8 y ?
How do you find the inverse of functions? for example how would you find the inverse of y= log8 x
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CC-MAIN-2013-48
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https://londwop.web.app/98008/45318.html
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math
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Percentage Formula. Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values. P × V 1 = V 2. P is the percentage, V 1 is the first value that the percentage will modify, and V 2 is the result of the percentage operating on V 1. The calculator provided automatically
What percentage of 10000 is 120? 250 is 8 percent of what amount? How much is 12000+8%; In the calculator window, choose the question you need answered and enter the 2 quantities that you already know. Calculator 1: Calculate the percentage of a number.
Contact Botequim do Herculano on Messenger. Restaurant · Sports Bar. Hours 6:00 PM - 2:00 AM. Closes in 20 minutes. Popular hours. Page Transparency See More. Facebook is showing information to help you better understand the purpose of a Page.
% Percent button is used to find the percentage of a number. Enter the percentage amount, click the % button, then enter the number you want the percentage of, and then click equals. i.e. 20% 125 = 25 where 25 is 20% of 125. Note: The percent function will also work if you enter the number first and then the percentage you want i.e. 125 %20 = 25.
20% 125 = 25 where 25 is 20% of 125. Note: The percent function will also work if you enter the number first and then the percentage you want i.e.
The following chart shows the share of the total population that has been fully vaccinated against COVID-19. This represents the share that have received all doses prescribed by the vaccination protocol. If a person receives the first dose of a 2-dose vaccine, this metric stays the same. If they receive the second dose, the metric goes up by 1.
6 12 669. 2 13 77. 60 14 08. 1 15 244. 9 16 55.
60 14 08. 1 15 244. 9 16 55. 17 8 $70,000.
The sco 18 Mar 2009 Body-mass index and cause-specific mortality in 900 000 adults: Below the range 22·5–25 kg/m2, BMI was associated inversely with overall In many populations, the average BMI has been rising by a few percent per dec 60, 000. (iv). Sold goods for Cash Rs 30,000 Costing Rs 20,000. 30,000.
Note: The percent function will also work if you enter the number first and then the percentage you want i.e. 125 %20 = 25. Use again the same percentage formula: % / 100 = Part / Whole replace the given values: % / 100 = 2 / 500000. Cross multiply: % x 500000 = 2 x 100. Divide by 500000 to get the percentage: % = (2 x 100) / 500000 = 0.0004%. A shorter way to calculate x out of y. You can easily find 2 is out of 500000, in one step, by simply dividing 2 by 500000, then multiplying the result by 100.
If 20000 is 100%, so we can write it down as 20000=100%. 4. We know, that x is 2% of the output value, so we can write it down as x=2%. 5. Now we have two simple equations: 1) 20000=100% 2) x=2% This easy and mobile-friendly calculator will calculate 15% of any number. Just type into the box and your calculation will happen automatically.
On 1st April, 2014, furniture costing ₹ 55,000 was purchased. On 1st April, 2014, A Ltd. purchased a machine for ₹ 2,40,000 and spent ₹ 10,000 on its erection. On 1st of DepreciationCost of Machine×100 =5,40060,000×100=9% p.a.&nb 2 Oct 2010 If I type 9:00 am in cell B2, and leave cell C2 blank, it shows 15:00 in cell D2 for the Project Hours. I know this is because the formula is based on if price is $10, demand = 60,000 and supply = 20,000, so there is excess demand of 9 First, calculate the percentage change in the quantity demanded, i.e. demand 26 The extra amount of tax paid = ($55,000 − $47,000) × 0.45 = $360 (b) break even sales (c) sales to earn a profit of Rs. 2,000 (d) Profit at sales of Rs. 60,000 Units to be produced for contribution of Rs. 20, 000 after change in price.bitcoin soukromý klíč cracker github
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60, 000. (iv). Sold goods for Cash Rs 30,000 Costing Rs 20,000. 30,000. +. +. – 20,000. 10,000 20,000. (iii) Goods costing ₹ 40,000 were sold for ₹ 55,000.
On the reading section, your z-score was 0.5. What percent of your peers scored better than you? Follow the same instructions, only this time, because we are looking for the area to the RIGHT of the z-score, the lower limit is the z-score and the upper limit is an extreme large number. So, theoretically, if you are 55 with R6 million saved, you will be able to live off R20 000 a month, rising by the CPI rate each year, and there will be a tidy sum to bequeath to your heirs 50,000. 100,000 is 1000 is 1% , so 5% is 5,000 is 5% multiply by ten so that 100,000 x10 =1 million and 5,000 x10 =50,000 Question: 2000 is what percent of 55000? Percentage solution with steps: Step 1: We make the assumption that 55000 is 100% since it is our output value.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506429.78/warc/CC-MAIN-20230922234442-20230923024442-00409.warc.gz
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CC-MAIN-2023-40
| 4,926 | 22 |
http://alekbo.com/news-line/what-do-efficiency-ratios-measure.html
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math
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Adroitness ratios measure a company’s ability to use its assets and manage its liabilities effectively. Although there are several efficiency proportions, they are all similar in that they measure the time it takes to generate cash or income from a client or liquidating inventory. Skilfulness ratios include the inventory turnover ratio, asset turnover ratio, and receivables turnover ratio. These proportions measure how efficiently a company uses its assets to generate revenues and its ability to manage those assets. With any fiscal ratio, it’s best to compare a company’s ratio to its competitors in the same industry.
Inventory Turnover Ratio
The inventory gross revenue ratio measures a company’s ability to manage its inventory efficiently and provides insight into the sales of a company. The relationship measures how many times the total average inventory has been sold over the course of a period. Analysts use the correspondence to determine if there are enough sales being generated to turn or utilize the inventory. The ratio also shows how beyond the shadow of a doubt inventory is being managed including whether too much or not enough inventory is being bought.
For example, suppose friends ABC sold computers and reported the cost of goods sold (COGS) at $5 million. The average inventory of ABC is $20 million. The inventory gross revenue ratio for ABC is 0.25 ($5 million/$20 million). This indicates that company ABC is not managing its inventory properly because it on the other hand sold a quarter of its inventory for the year.
Asset Turnover Ratio
Receivables Turnover Ratio
For example, a company has an typically accounts receivables of $100,000, which is the result after averaging the beginning balance and ending balance of the accounts receivable harmony for the period. The sales for the period were $300,000, so the receivable turnover ratio would equal 3, meaning the throng collected their receivables three times for that period.
Typically, a company with a higher accounts receivables volume ratio, relative to its peers, is favorable. A higher receivables turnover ratio indicates the company is more efficient than its antagonists when collecting accounts receivable.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247517815.83/warc/CC-MAIN-20190222114817-20190222140817-00387.warc.gz
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CC-MAIN-2019-09
| 2,216 | 8 |
http://www.michaeljamesonmoney.com/2014/05/the-cost-of-portfolio-concentration.html
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math
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An oft-quoted statistic is that you only need about 20 stocks to make a well-diversified portfolio. Here I attempt to quantify the benefit of diversification. The result is that losses due to portfolio concentration are still quite high at only 20 stocks.
Meir Statman wrote a useful paper called How Many Stocks Make a Diversified Portfolio? In it he gives a table showing portfolio volatility values for varying number of stocks in the portfolio. The data is based on the portfolio having equally-weighted stocks.
From this table we can simulate a 30-year portfolio to see how much more volatility drag there is on returns for concentrated portfolios. I assumed that an investor would start with a lump sum and invest for 30 years. I set the starting lump sum so that a portfolio owning all stocks would finish at $1 million. The following chart shows how smaller numbers of stocks fared.
I call the difference between a portfolio of all stocks and a more concentrated portfolio the portfolio “concentration gap.” We see from the chart that the gap at 20 stocks is about $140,000, which I’d call quite significant.
So, why do so many people think that 20 of fewer stocks make sense? The answer is that they believe they can pick winning stocks. All of the above analysis is based on a random selection of stocks. If you can choose above-average stocks, then you can overcome the concentration gap. Of course, the vast majority of investors (but not quite all) who believe they are great stock-pickers are actually deluded.
The main takeaway from this article is that it isn’t good enough to have some stock-picking skill. You need enough skill to jump the concentration gap. If you have the talent and energy to find 20 above-average stocks, you need to be able to overcome the concentration gap and any other costs you incur that index investors would not incur.
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CC-MAIN-2017-22
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https://www.wise-geek.com/what-is-molar-concentration.htm
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math
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In chemistry, concentration is the level of a substance in a mix of substances, such as the amount of sodium chloride found in the sea, for example. Concentration may be expressed as various units, often given in terms of weights and volumes. Molarity is a form of weight per unit of volume. The molar concentration of a particular substance is the number of moles of that substance dissolved in one liter of solution, regardless of how many other substances may be dissolved in that same solution.
In sodium chloride (NaCl), ordinary table salt, the atomic weight of the two substances — sodium and chlorine — may be found by referring to the periodic table. Sodium’s atomic weight is 22.99. Chlorine's atomic weight is 35.45. This means sodium chloride — one atom of both these elements combined — has a molecular weight of 58.44. Since one mole of a substance is defined as its molecular weight in grams, one mole of NaCl is 58.44 grams (g).
By way of illustration, if 537 milliliters (ml) of a solution contains 15.69 g of sodium chloride, but no other substance, that solution’'s molar concentration is (15.69 g / 58.44 g) ÷ (537 ml / 1000 ml) = 0.50. The solution is 0.50M in sodium chloride. If the solution contains another component, such as magnesium bromide, this solution remains 0.50M in sodium chloride. It also has, however, a molar concentration in magnesium bromide.
Magnesium's atomic weight is 24.31. Bromine's atomic weight is 79.90. The molecular weight of magnesium bromide is not 24.31 + 79.90 = 104.21, however. This is because magnesium bromide has the chemical formula, MgBr2, since the valency of magnesium is +2, whereas the valency of bromine is only -1. Correctly, the molecular weight of magnesium bromide is 24.31 + (2 × 79.90) = 184.11.
If 24.72 g of magnesium bromide is present, the molar concentration of magnesium bromide is (24.72 g / 184.11 g) ÷ (537 ml / 1000 ml) = 0.25M. This means the solution is both 0.50M in NaCl and 0.25M in MgBr2. It is interesting to realize that, despite the decrease in water molecules in this second solution compared to the first — the concentrations are in terms of "per liter of solution," not "per liter of water" — the molar concentration of sodium chloride is the same for both. It is theoretically possible for an immensely large number of substances to be present in a single liter of solution, resulting in a collection of molar concentrations that are quite low, with almost no water present.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991252.15/warc/CC-MAIN-20210512035557-20210512065557-00254.warc.gz
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CC-MAIN-2021-21
| 2,490 | 5 |
https://www.tutorsglobe.com/question/how-many-grams-of-kno3-must-be-added-to-water-5509916.aspx
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math
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How many grams of kno3 must be added to water
Assuming complete dissociation of the solute, how many grams of KNO3 must be added to 275 mL of water to produce a solution that freezes at -14.5 degrees? The freezing point for pure water is 0.0 degrees and Kf is equal to 1.86 C/m.
Expected delivery within 24 Hours
Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. What is the mass difference between the two?
Calculate the PV work done when 50.0 g of tin dissolves in excess acid at 1.00 bar and 25degrees Celsius. Assume ideal gas behavior.
The reactant concentration in a zero-order reaction was 7.00×10-2 M after 155 s and 1.50×10-2 M after 370 s. What is the rate constant for this reaction?
Draw the skeletal structure of the organic species containing the carbonyl functionality needed to form 2-phenyl-1-ethanol upon metal-catalyzed hydrogenation.
A 0.7549g sample of a pure hydrocarbon burns in oxygen gas to produce 1.9061g of carbon dioxide and 0.3370g of water. What is the empirical formula for the compound?
A gas mixture with a total pressure of 765 g contains each of the following gases at the indicated partial pressures: CO2, 116 mmHg ;A , 211 mmHg ; and O2 , 184 mmHg . The mixture also contains helium gas. What is the partial pressure of the heliu
A basketball is inflated to a pressure of 1.90 atm in a 24.0°C garage. What is the pressure of the basketball outside where the temperature is -1.00°C?
A generic salt, AB, has a molar mass of 243 g/mol and a solubility of 8.90 g/L at 25 C what is the Ksp of this salt.
In an ethanol-chloroform solution in which the mole fraction of ethanol is 0.20, the total vapor pressure is 304.2 torr, and the mole fraction of ethanol in the vapor is 0.138. Calculate the activity coefficients of the ethanol and the chloroform.&nb
The thermochemical equation for the combustion of butane is C4H10(g) + 13/2O2(g) --> 4CO2(g) + 5H2O(l) Delta H = -2877kJ What is the enthalpy change for the following reaction?
Start Excelling in your courses, Ask a tutor for help and get answers for your problems !!
Problem: List the goals of the intro and conclusion and why they are valuable to your presentation.
Explain what supportiveness means by discussing its relationship to agreeing with others (are the two the same?).
Problem: What kinds of irony does the story "the laughter" by heinrich boll have?
Your Task: Revise the following sentences to avoid dangling and misplaced modifiers. (A) Skilled at social networking, the marketing contract was won
What did you think about while participating in the Creating Effective Business Messages Video(s) as it relates to your personal or work-related experience(s)?
How does your profession delegate the Controlled Acts? What are your thoughts on the Controlled Acts?
Prompt: A case analysis recommending a way for MGM to become profitable while improving its responsible gambling program.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710870.69/warc/CC-MAIN-20221201221914-20221202011914-00748.warc.gz
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CC-MAIN-2022-49
| 2,935 | 21 |
https://jpier.org/PIERC/pier.php?paper=13070702
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math
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Constrained Least Mean Square (CLMS) algorithm is used to adapt the antenna array weights. CLMS in its simple form fails to capture the Signal of Interest (SOI) if there is an error in the Direction of Arrival (DOA) estimation. Moreover, it will consider the SOI as an interferer and create null in the desired DOA. The large gain will be towards the detected wrong direction. Derivative constraints and Bayesian beamformer are two techniques used to overcome such a problem. Derivative constraints destroy a lot of Degrees of Freedom (DOF). Bayesian beamformer destroys only one DOF but vulnerable to binning error. The proposed algorithm overcomes the problem of binning error in the Bayesian beamformer with only one extra DOF.
2. Frost, III, O. L., "An algorithm for linearly constrained adaptive array processing," Proceedings of the IEEE, Vol. 60, No. 8, 926-935, Aug. 1972.
3. Er, M. H. and A. Cantoni, "Derivative constraints for broad-band element space antenna array processors," IEEE Transactions on Acoustics, Speech, Signal Processing, Vol. 31, No. 6, 1378-1393, Dec. 1983.
4. Vorobyov, S. A., A. B. Gershman, and Z. Q. Luo, "Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem," IEEE Trans. Signal Process., Vol. 51, No. 2, 313-324, Feb. 2003.
5. Lorenz, R. G. and S. P. Boyd, "Robust minimum variance beamforming," IEEE Trans. Signal Process., Vol. 53, No. 5, 1684-1696, May 2005.
6. El-Keyi, A., T. Kirubarajan, and A. B. Gershman, "Robust adaptive beamforming based on the Kalman filter," IEEE Trans. Signal Process., Vol. 53, No. 8, 3032-3041, Aug. 2005.
7. Nai, S. E., W. Ser, Z. L. Yu, and H. Chen, "Iterative robust minimum variance beamforming," IEEE Trans. Signal Process., Vol. 59, No. 4, 1601-1611, Apr. 2011.
8. Morell, A., A. Pascual-Iserte, and A. I. Perez-Neira, "Fuzzy inference based robust beamforming," Elsevier Signal Processing, Vol. 85, No. 10, 2014-2029, 2005.
9. Bell, K. L., Y. Ephraim, and H. L. Van Trees, "A Bayesian approach to robust adaptive beamforming," IEEE Trans. Signal Process., Vol. 48, No. 2, 386-398, Feb. 2000.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359093.97/warc/CC-MAIN-20211201052655-20211201082655-00615.warc.gz
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CC-MAIN-2021-49
| 2,126 | 9 |
https://www.hackmath.net/en/word-math-problems/pythagorean-theorem?tag_id=56
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math
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Pythagorean theorem + square (second power, quadratic) - math problems
Number of problems found: 234
Calculate the side of a square with a diagonal measurement 10 cm.
Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg?
Calculate area of the square with diagonal 64 cm.
- Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
- Diagonal of square
Calculate the side of a square when its diagonal is 10 cm.
- Square circles
Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
- Square s3
Calculate the diagonal of the square, where its area is 0.49 cm square. And also calculate its circumference.
Calculate the perimeter and the area of square with a diagonal length 30 cm.
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
- Square and circles
Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
- Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
- Circumscribed circle to square
Find the length of a circle circumscribing a square of side 10 cm. Compare it to the perimeter of this square.
Side of the square is a = 6.2 cm, how long is its diagonal?
- Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
- Square diagonal
Calculate the length of the square diagonal if the perimeter is 172 cm.
- Tree trunk
What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
Rectangular square has side lengths 183 and 244 meters. How many meters will measure the path that leads straight diagonally from one corner to the other?
Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
- Recursion squares
In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 22 cm. Calculate: a) the sum of peri
Pythagorean theorem is the base for the right triangle calculator. Pythagorean theorem - math word problems. Square (second power, quadratic) - math word problems.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703507045.10/warc/CC-MAIN-20210116195918-20210116225918-00759.warc.gz
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CC-MAIN-2021-04
| 2,627 | 34 |
https://www.physicsforums.com/threads/use-delta-epsilon-proof.223805/
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math
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limit as x goes to 0 of x^2 sin(1/x)=0
Use delta-epsilon proof
The Attempt at a Solution
So |f(x)-L|=|x^2 sin(1/x)|=|x^2||sin(1/x)| and I know that sin(1/x) is bounded by one. I am not sure how to finish because of the x^2.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738960.69/warc/CC-MAIN-20200813043927-20200813073927-00517.warc.gz
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CC-MAIN-2020-34
| 223 | 4 |
https://scholar.archive.org/work/anwkzoi4xzfz5buatgt64na7ne
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math
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Phase transitions in the q-coloring of random hypergraphs
Journal of Physics A: Mathematical and Theoretical
We study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied. Hypergraph coloring is a constraint satisfaction problem where each constraint includes $K$ variables that must be assigned one out of $q$ colors in such a way that there are no monochromatic constraints, i.e. there are at least two distinct colors in the set of variables belonging to every constraint. This problem
... is problem generalizes naturally coloring of random graphs ($K=2$) and bicoloring of random hypergraphs ($q=2$), both of which were extensively studied in past works. The study of random hypergraph coloring gives us access to a case where both the size $q$ of the domain of the variables and the arity $K$ of the constraints can be varied at will. Our work provides explicit values and predictions for a number of phase transitions that were discovered in other constraint satisfaction problems but never evaluated before in hypergraph coloring. Among other cases we revisit the hypergraph bicoloring problem ($q=2$) where we find that for $K=3$ and $K=4$ the colorability threshold is not given by the one-step-replica-symmetry-breaking analysis as the latter is unstable towards more levels of replica symmetry breaking. We also unveil and discuss the coexistence of two different 1RSB solutions in the case of $q=2$, $K \ge 4$. Finally we present asymptotic expansions for the density of constraints at which various phase transitions occur, in the limit where $q$ and/or $K$ diverge.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487634576.73/warc/CC-MAIN-20210617222646-20210618012646-00315.warc.gz
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CC-MAIN-2021-25
| 1,691 | 4 |
https://imageproperty.com.au/homes-for-rent/6-hope-street-griffin-qld-4503/
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math
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House FOR RENT on Hope Street
TO APPLY FOR THIS PROPERTY OR FIND OUT ANY FURTHER INFORMATION VISIT THE IMAGE PROPERTY WEBSITE OR SMS “APPLY” TO THE NUMBER BELOW.
A rare opportunity to build in a sort after established community right next to Carseldine:
400m2 plus site with space for outdoor play and living
Close proximity to established amenities, with Carseldine Central Shopping Centre closeby.
Private and public schools, along with childcare facilities all on your doorstep.
Brisbane just 18km away and the Sunshine Coast 55 minutes away
Effortless connection to Public Transport and major road networks. Carseldine railway station is only a few minutes drive away
A prime location, in an established suburb, along the growth corridor of South East Queensland
CONFIRMED SCHOOL ZONES: Griffin State School and Murrumba State Secondary College.
Take a Virtual stroll through the property by clicking the 3D Tour button below.
# Face brick veneer external walls
# Colorbond custom orb roof
# Colorbond fascia and gutter
# 2.44m internal ceiling height
# 450mm eaves
# 820mm style external door with translucent glass inserts and fixed translucent glass sidelight
# Aluminium powder coated windows & sliding doors
# Satin chrome front door lockset
# Panel lift garage door with two remotes
# 90mm PVC down pipes
# Smartfilm termite barrier
# Aluminium powder coated balustrade on balconies (where applicable)
# Decorative style internal swinging door
# Aluminium framed vinyl sliding wardrobe doors
# Satin chrome lever internal door handles
# Pencil round skirting and architrave painted in gloss finish – 2 coats
# 10mm plaster board and 90mm cornice painted in low sheen finish – 2 coats. 6mm Villaboard in wet areas
# 20mm engineered stone bench top
# Texture or matt finish laminate kitchen cabinet doors and drawers
# Cabinet height 2.2m with paint grade MDF cabinetmaker bulkhead
# Stainless steel dishwasher
# Stainless steel 60cm oven
# Stainless steel 60cm slide-out range hood
# Stainless steel 60cm electric cooktop
# Chrome sink mixer
# Stainless steel sink
# Ceramic tile splashback
# Glass sliding door or external swinging door – 1/2 clear glass with stainless steel lockset (depends on house design, please refer to plan)
# Steel stand-alone laundry cabinet with stainless steel tub
# Chrome mixer
# Ceramic tile splashback
BATHROOMS, ENSUITES AND WATER CLOSETS
# Vanities with 20mm engineered stone with matt laminate cupboard doors and drawers
# Micro framed mirror over vanity
# Chrome shower, bath and basin mixers
# Chrome shower rail and bath spout
# Ceramic close-coupled toilet suite
# Chrome double towel rail and toilet roll holder
# Semi-framed glass shower screen with pivot door
# Acrylic moulded bath 1.675m
# Ceramic tile splashback, skirting and shower recesses
# Ceramic feature tile on side of bath, bath hob, and one wall of the room
# Ceramic floor tiles in kitchen, family, meals, entry, linen cupboards and all wet areas. Hallways shall be as indicated on plans
# Carpet in bedrooms, wardrobes, 2nd living area (where applicable) and internal staircase (where applicable)
# Garage floor to be plain trowelled concrete
# Roller blinds to all windows and vertical blinds to all sliding doors excluding wet areas
# Barrier screens to all windows and sliding doors excluding a pivot entry door if chosen
# Two reverse cycle split system inverter air conditioners as indicated on plans
# LED downlights, ceiling fans and 3 in 1 exhaust fans throughout house
# External double spotlight near laundry drying area
# TV antenna for up to three hard wired TV points
# 170 litre 5 star Electric Heat Pump
IMPORTANT NOTE: Air conditioning units where indicated on the sales plans shall be fitted in accordance with the manufacturers specifications. The size and layout of the room where the unit is to be installed shall determine the size of the unit.
# Feature garden at front of property with mixture of trees, shrubs, ground covers and decorative pebble
# Turf installed to remainder of property unless stated otherwise in contract or sales plans
# Exposed aggregate concrete driveway, porch and laundry pad
# Covercrete finish concrete alfresco (may differ in regional areas, please refer to specifications)
# Metal letterbox
# Fencing sufficient to complete property with access gates as indicated on plans
# Wall mounted clothesline
# Ceiling insulation in main roof area excluding garage, alfresco, & porch
# Sisilation wrap to external walls
# Minimum 6 star energy rating
*Please note inclusions may differ due to availability. Photos are a sample only of a similar style build and are only indicative of the end finish.
Please register to ensure that you receive notification of any updates or cancellations. Click ‘Book Inspection’ and follow the prompts to register your details for the open home you wish to attend.
All government guidelines regarding Covid-19 must be followed while attending. Numbers have been capped and each attendee is to wear a mask, use the provided sanitiser and QR code and socially distance where possible.
Whilst every care is taken in the preparation of the information contained in this marketing, Image Property will not be held liable for any errors in typing or information. All interested parties should rely upon their own enquiries in order to determine whether or not this information is in fact accurate.
Legislation states that you must read the General Tenancy Agreement inclusive of any special terms prior to proceeding through our approval process. If applicable, you will receive this in due course, however please contact our office if you do need this at any stage.
- 4 bed
- 2 bath
- 2 Parking Spaces
- 2 Garage
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571190.0/warc/CC-MAIN-20220810131127-20220810161127-00724.warc.gz
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CC-MAIN-2022-33
| 5,716 | 83 |
https://www.rvplus.com/camco-pop-a-towel-white-57111.html
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math
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The only paper towel holder that both mounts and stands...not mounts or stands. With Pop-A-Towel you get the exact amount of paper towels you need because you pull them off one at a time, as you need them, where you need them. Made in U.S.A.
MFG# 57111 UPC# 014717571111
No posts found
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655901509.58/warc/CC-MAIN-20200709193741-20200709223741-00353.warc.gz
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http://www.krysstal.com/relative.html
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An Introduction to Einstein's Theory of Relativity
Yes, it's all relative.
No, I'm not talking family. I'm just preparing myself to write an essay on Relativity, and I'm wondering how to begin.
Before Albert Einstein, there was Isaac Newton. Newton's Universe is the universe of common sense. Before I can discuss Einstein's Universe I need to describe what existed before. The Newtonian Universe makes the following assumptions.
The problem with Relativity is that it violates all of the above common-sense ideas. Because of that, many people have problems believing Relativity rather than understanding it.
Newton's mechanics served well until around the middle of the 19th Century. It was observed that Mercury's orbit was not quite as it should be. People thought that another planet was tugging at Mercury and causing it to deviate from its predicted (Newtonian) path. This hypothetical planet (originally called Vulcan) was never seen. Newton's theories worked with all other known phenomena so the tiny discrepancy in Mercury's orbit was forgotten.
Then came James Maxwell. He produced the theories of electricity and magnetism that are still current today. He proved that light was a wave travelling at 300,000 km/s. Some people said 'waves in what?' Water waves travel in water; sound waves travel in air. What is it that light waves travel in? There was no logical answer so an ancient idea was revived: the aether.
The aether was postulated to be a medium that vibrated the light wave along. This aether had never been observed. If it was made of matter it would slow down objects like the Earth and cause them to spiral into the Sun! The aether was thus solid enough to let light vibrate in but light enough to let the Earth travel in space without hindrance.
Two physicists decided to try and observe the aether. Albert Michelson and Edward Morley set up an experiment to try and measure the drag of the aether on the Earth. They measured the speed of a light beam travelling parallel to the direction of the Earth's motion and compared that to a light beam travelling perpendicular to the Earth's motion. The aether idea predicted that light would have a slightly different speed in the two directions. They would, in fact, be measuring the Earth's speed against the aether. Their equipment would have been accurate enough to have measured this difference if the Earth had been travelling at a speed of 5km/s around the Sun. The Earth actually travels around the Sun at nearly 30km/s. Michelson and Morley found no difference in the speed of light in two perpendicular directions. This meant one of three things:
Michelson and Morley thought that (1) was the problem since there was overwhelming evidence that the Earth was going around the Sun. They improved their equipment and made it more sensitive. Try as they might, they could not find any difference in the speed of light. Eventually they gave up and published their experiments describing them as a failure.
Einstein read about the experiment. It actually confirmed an idea that had been germinating in his mind since he was a teenager. At the time (1905), Einstein was working as a patent clerk in Switzerland. Einstein took the Michleson and Morley experiment at face value. He made two assumptions about the Universe and proceeded to use these assumptions to completely rebuild physics.
His two assumptions were:
The first assumption is not too tricky. The aether was postulated to explain something that really did not need explaining. Light is an oscillation of magnetic and electric fields. That is what the wave is, not a vibration in a medium.
The second assumption, however, is against all common sense. Light travels at 300,000 km/s. If an object travelling at 100 km/s sends out a beam of light to us and we measure its speed, common sense tells us that we should measure the speed of light to be 300,100 km/s. Similarly, if the light source is moving away from us at 100 km/s, we should measure the speed of light at 299,900 km/s. But no, Einstein says it will be measured at 300,000 km/s regardless of how the source or the observer is moving. This assumption violates common sense but has since been tested with equipment of such accuracy that if it wasn't valid, the discrepancy would have shown up.
The first assumption actually means that you cannot measure absolute speed. Speed is relative.
You can measure your speed relative to the Earth, the Earth's speed relative to the Sun, the Sun's speed relative to the centre of the Galaxy, etc. What you cannot measure is your speed absolutely. The second assumption means that many quantities that we thought of as constant and unchanging actually vary for different observers. These are the predictions that Einstein made.
The mass of an object increases with its velocity. At low speeds this effect is very difficult to observe. As a body approaches the speed of light its mass approaches infinity. This is where the dictum that nothing can travel faster than light came from. It has been tested with sub-atomic particles and close binary stars. In both cases the mass change has been observed and agrees with Einstein's predictions. In fact, because Mercury is the closest planet to the Sun, it's velocity is high enough to increase its mass enough to cause the discrepancy with its orbit observed over half a century before!
The length of an object decreases with its velocity. Again, Einstein's equations predict that an object's length would become zero at the speed of light. This has been tested indirectly by an experiment depending on something called the Mossbauer Effect.
Time slows down for a body that is moving and for one in a gravitational field. This is one of Einstein's most fascinating predictions. Again, it has been tested many times. Sub-atomic particles last longer before decaying when they are moving close to the speed of light. Energy from Pulsars and White Dwarfs (stars with huge gravitational fields) slow down the vibration of atoms which can be detected. Using Atomic clocks it is possible now to measure these effects on the Earth. At the speed of light all time slows down to zero. The speed of light seems to be forever unattainable if Einstein is correct.
Light should bend around a gravitational field. This one is difficult to explain but is to do with time varying near a strong gravitational field. This was first measured during a total eclipse of the sun in 1919. The effect is similar to refraction where a stick appears to bend where it enters water. These so-called gravitational lenses have since been observed amongst distant galaxies.
For Cosmology, if there is enough matter in the Universe, a beam of light will eventually return to its starting point.
Matter and Energy are the same phenomenon. This is the famous equation,
It means that matter, m, can be converted into a very large amount of energy, E, if it is multiplied by the speed of light (c) squared. This equation explains the source of energy of stars as well as atom bombs!
The Universe is not static. This prediction indicates that if the Universe were static it would be unstable. A few years after this prediction was made, the Universe was found to be expanding.
The Theory of Relativity does two things that any good theory should do. Firstly, it explained existing observations using only a few assumptions (the Michelson and Morley experiment, Mercury's orbit, the energy of the Sun). Secondly it made predictions that could be tested. In this case the predictions were ridiculously at odds with common sense (time slows down, light is bent by gravity, mass increases for a moving body) and yet the theory has passed every test.
Modern laser techniques cannot measure any difference in the speed of light no matter what speed the source or observer have. Many observations and inventions would not work unless relativistic effects are taken into account. The study of Cosmology would not make sense without Relativity.
As such, Relativity is one of the two great theories of the 20th Century. The other being Quantum Mechanics.
© 1997, 2011 KryssTal
Albert Einstein Online
A site full of interesting links for the man his theory and his ideas.
A good site about General Relativity.
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https://www.expertsmind.com/library/how-many-turns-must-the-rollers-make-to-accomplish-the-move-5190949.aspx
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The load on this beam and rollers apparatus had to be moved distance 20 units. If the circumgerance of each of the rollers is 0.8 units, how many turns must the rollers make to accomplish the move?
In a circle of radius 6 centimeters, find the area of the segment bound by an arc of measure 120 degrees and the chord joining the endpoints of the arc. Round your answer to nearest tenth.
The linear equation x=-1 graphs as a horizontal/vertical/diagonal line(choose the correct label). Describe how you determined your answer.
What is the first step?
With a yearly rate of 3 percent, prices are described as P = P0 (1.03)t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 is 1.2, how fast are prices rising when t = 15?
How to find some useful materials for undergraduate
Let A be the area of a circle with radius r that is increasing in size with respect to time. If the rate of change of the area is 12 cm/s, find the rate of change of the radius when the radius is 18cm.
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Show that the mass, momentum, and energy are constants of motion (invariants) for the KdV equation by direct differentiation with respect to time.
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https://ulris3.ul.ie/live/!W_VA_PUBLICATION.POPUP?LAYOUT=N&OBJECT_ID=1134118
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math
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Deterministic models' developed for the jumping horse indicated the important factors involved when jumping an obstacle.(2) SVHS video recordings were obtained of 31 untrained horses (age: 3-5 years, height: 164.7 +/- 4.5 cm) jumping loose over a fence 1 m high by 0.5 m wide. The horses were designated to either a good group or a poor group based on a qualitative evaluation; good horses (n = 18) cleared the fence with ease, and poor horses (n = 13) consistently hit the fence. Video sequences were digitized to provide kinematic data on the horses' center of gravity (CG) and carpal and tarsal angles. Twenty kinematic variables were examined from the approach to the landing. Analysis of Variance (ANOVA) revealed significant between-group differences for the horizontal velocity of the last approach stride (Good: 5.77 +/- 0.80 m.s(-1); Poor: 6.42 +/- 0.95 m.s(-1) p = 0.046). Significant differences were found in the relative carpal angles at take off (Leading limb: Good: 1.02 +/- 0.19 rad, Poor: 1.25 +/- .0.28 rad; p = 0.010; Trailing limb: Good: 0.92 +/- 0.21 rad, Poor: 1.06 +/- 0.15 rad; p = 0.046). The height of the CG over the center of the fence was also a significant variable that differed between the groups (Good: 1.83 +/- 0.08 m; Poor: 1.71 +/- 0.13 m; p = 0.002). Finally the horizontal velocity of the landing was significant (Good: 5.26 +/- 0.92 m.s(-1); Poor: 6.27 +/- 0.84 m.s(-1); p = 0.004) along with the angle of the CG to the ground at landing (Good: -0.45 +/- 0.08 rad; Poor: -0.38 +/- 0.07 rad). The velocity and CG variables which distinguished good and poor horses are likely to be strongly influenced by a rider; therefore, it is unlikely that these data alone could be used to predict elite jumping horses. The carpal angle data, however, may indicate a certain natural tendency by the young horses in the good group to keep their legs clear of the fence.
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https://socratic.org/questions/how-do-you-find-the-equation-of-the-line-that-passes-through-the-points-7-3-and-
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math
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How do you find the equation of the line that passes through the points (7,3) and (2,5)?
To find the line passing through these two points we will use the point-slope formula. However, first we must determine the slope.
The slope can be found by using the formula:
For our problem we can substitute and find the slope as:
Now we can use the point-slope formula. The point-slope formula states:
Substituting the slope we calculated and one of the points we were given.
or, converting to slope-intercept form:
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https://en.wikipedia.org/wiki/Menahem_Max_Schiffer
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math
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Menahem Max Schiffer
Menahem Max Schiffer (24 September 1911, Berlin – 8 November 1997) was a German-born American mathematician who worked in complex analysis, partial differential equations, and mathematical physics.
Schiffer studied physics from 1930 at the University of Bonn and then at the Humboldt University of Berlin with a number of famous physicists and mathematicians including Max von Laue, Erwin Schrödinger, Walter Nernst, Erhard Schmidt, Issai Schur and Ludwig Bieberbach. In Berlin he worked closely with Issai Schur. In 1934 Schiffer had his first mathematical publication. After the National Socialist regime removed Schur and many others from their academic posts, Schiffer, as a Jew, immigrated to British-controlled Palestine. On the basis of his 1934 mathematical publication, Schiffer received from the Hebrew University of Jerusalem his master's degree in 1934. He received there his doctorate in 1938 under Michael Fekete with thesis Conformal representation and univalent functions. In his dissertation he introduced the "Schiffer variation", a variational method for handling geometric problems in complex analysis. (He also introduced another important variational method.) In September 1952, he became a professor at Stanford University, as part of a Jewish refugee group of outstanding mathematical analysts, including George Pólya, Charles Loewner, Stefan Bergman, and Gábor Szegő.
With Paul Garabedian, Schiffer worked on the Bieberbach conjecture with a proof in 1955 of the special case n=4. He was a speaker (but not in the category of an Invited Speaker) at the International Congress of Mathematicians (ICM) in 1950 at Cambridge, Massachusetts, and was a plenary speaker at the ICM in 1958 at Edinburgh with plenary address Extremum Problems and Variational Methods in Conformal Mapping. In 1970 he was elected to the United States National Academy of Sciences. He retired from Stanford University as professor emeritus in 1977.
Never losing his interest in mathematical physics, Schiffer also made important contributions to eigenvalue problems, to partial differential equations, and to the variational theory of “domain functionals” that arise in many classical boundary value problems. And he coauthored a book on general relativity. Schiffer was a prolific author over his entire career, with 135 publications from the 1930s to the 1990s, including four books and around forty different coauthors. He was also an outstanding mathematical stylist, always writing, by his own testimony, with the reader in mind. ... His lectures at Stanford and around the world ranged greatly in subject matter and were widely appreciated. ... At Stanford he often taught graduate courses in applied mathematics and mathematical physics. Students from all departments flocked to them, as did many faculty. Each lecture was a perfect set piece—no pauses, no slips, and no notes. In 1976 he was chosen as one of the first recipients of the Dean's Award for Teaching in the School of Humanities and Sciences.
- with Leon Bowden: The role of mathematics in science, Mathematical Association of America 1984
- with Stefan Bergman: Kernel functions and elliptic differential equations in mathematical physics, Academic Press 1953
- with Donald Spencer: Functionals of finite Riemann Surfaces, Princeton 1954
- with Ronald Adler, Maurice Bazin: Introduction to General Relativity, McGraw Hill 1965 xvi+ 451 pp. Illus. 2nd edition. 1975; xiv+ 549 pp.CS1 maint: postscript (link)
- Person Details for Alpern in entry for Menahem M Schiffer, "California Death Index, 1940–1997 — FamilySearch.org
- O'Connor, John J.; Robertson, Edmund F., "Menahem Max Schiffer", MacTutor History of Mathematics archive, University of St Andrews
- "Menahem Max Schiffer" (PDF). Notices of the AMS. 49 (8): 886. September 2002.
- Menahem Max Schiffer at the Mathematics Genealogy Project
- Memorial Resolution, Menahem Max Schiffer (1911–1997), Stanford University Archived 2006-09-16 at the Wayback Machine
- Kline, J. R. (1951). "The International Congress of Mathematicians". Bull. Amer. Math. Soc. 57: 1–10. doi:10.1090/S0002-9904-1951-09429-X.
- Schiffer, Menahem (1950). "Variational methods in the theory of conformal mapping" (PDF). In: Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30–September 6, 1950. vol. 2. pp. 233–240.
|volume=has extra text (help)
- Todd, J. A. (2013-09-12). Proceedings of the International Congress of Mathematicians: 14–21 August 1958. ISBN 9781107622661.
- "About Us". World Cultural Council. Retrieved November 8, 2016.
- Dinah S. Singer, Ph.D. | Center for Cancer Research
- Henrici, Peter (1955). "Review: Kernel functions and elliptic differential equations in mathematical physics by S. Bergman and M. Schiffer" (PDF). Bull. Amer. Math. Soc. 61 (6): 596–600. doi:10.1090/s0002-9904-1955-10005-5.
- Ahlfors, Lars V. (1955). "Review: Functionals of finite Riemann surfaces by M. M. Schiffer and D. C. Spencer". Bull. Amer. Math. Soc. 61 (6): 581–584. doi:10.1090/s0002-9904-1955-09998-1.
- Boyer, R. H. (7 May 1965). "Review: Introduction to General Relativity by Ronald Adler, Maurice Bazin, and Menahem Schiffer". Science. 148 (3671): 808–809. doi:10.1126/science.148.3671.808.
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https://serbia.worldplaces.me/hotels-in-vlasina-rid/50771771-vila-ceca.html
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Za više informacija kontaktirajte nas...
Address Ljote, Vlasina Rid
GPS Coordinates 42.7319,22.3217
My family stayed two nights at the guest house Ceca. At incheck was agreed that the price for one person wil be 15 instead of 20 euro because there was no breakfast included. At the payment day the ouwner changed her mind and started scream... Read more or comment
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