Example Definition and 879 Threads

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  1. Hamiltonian

    Real life example of the composition of two SHMs with same angular frequency

    Under the topic of simple harmonic motion comes the composition of two SHM's with the same angular frequency, different phase constants, and amplitudes in the same directions and in perpendicular directions. composition of SHM's in same direction: say a particle undergoes two SHM's described by...
  2. M

    B Looking for a good example of a naturally occuring compounding process

    She is not ready yet to understand the commonly-used example in the field of finance. I don't want to use the growth of a tree's trunk because the process is too slow. I have also told her the 'chess board and rice grain story', but in that story the growth rate is very fast, so doesn't have...
  3. John Greger

    A What are some example Feynman diagrams in Yang-Mills theory?

    Hi! So I have just been studying Yang-Mills theory advanced quantum field theory. In chapter 72 of Srednicki's book Quantum Field Theory they list the Feynman rules for non-abelian gauge theory. I was asked if I could show some sample allowed diagrams but I could not.. In standard particle...
  4. lakuzamalakuzam

    Statics example from Meriam ( SI improper )

    could not understand why it is partial constraints. Also, I don't understand how link works. Below here is what I am thinking i think it is totally wrong can someone explain what's wrong with my idea here.
  5. L

    B Basic Question: What are energy levels, of photons, for example?

    I often read of photons manifesting different levels of energy. I know that energy increases as wavelength decreases and frequency increases. Are there other ways particles gain or lose energy? As water boils heat energy is transferred to the water causing water molecules to move faster and to...
  6. cwill53

    Solving for Electrical Potential Energy: Durcell's Example

    This question is an example in Durcell's Electricity and Magnetism. The solution goes as follows: [In this case] there are four different types of pairs. One type involves the center charge, while the other three involve the various edges and diagonals of the cube. Summing over all pairs yields...
  7. Math Amateur

    MHB Smallest Sigma Algebra .... Axler, Example 2.28 ....

    I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help in order to make a meaningful start on verifying the first part of Axler, Example 28 ... The relevant text reads as follows: Can someone please help me to make...
  8. Math Amateur

    I Smallest Sigma Algebra .... Axler, Example 2.28 ....

    I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help in order to make a meaningful start on verifying the first part of Axler, Example 28 ... The relevant text reads as follows:Can someone please help me to make a...
  9. entropy2008

    Cauchy-Riemann Theorem Example in Physics

    I was thinking of the wavefunction in QM but I'm not sure how it's used and when.
  10. A

    Developing Algorithm to Recursively Walk Array: arr[4] Example

    I want to write code walk around the array recursively. For some reason I cannot share my code. Let's say I have a array like this: arr[4], I want to look 012 123 013 or 01 12 23 02 03 13. In code I write I can look 012 123 or 01 12 23 but I cannot look 013 or 02 03 13. What algorithm should I...
  11. T

    What is the proper grammar for my example sentence?

    I would like to know what the proper pronoun case is for a certain sentence. The following is my example sentence: Jessica thinks I was born for her. The example sentence uses the objective case for the pronoun. My guess is that the above example sentence uses the correct pronoun case, but...
  12. Math Amateur

    I The Indiscrete Topology is Pseudometrizable ... Willard, Example 3.2(d)

    I am reading Stephen Willard: General Topology ... ... and am currently focused on Chapter 1: Set Theory and Metric Spaces and am currently focused on Section 2: Metric Spaces ... ... I need help in order to fully understand Example 3.2(d) ... .. Example 3.2(d) reads as follows: and...
  13. Math Amateur

    MHB Open Sets in R .... .... Willard, Example 2.7 (a) .... ....

    I am reading Stephen Willard: General Topology ... ... and am currently focused on Chapter 1: Set Theory and Metric Spaces and am currently focused on Section 2: Metric Spaces ... ... I need help in order to fully understand Example 2.7(a) ... .. The relevant text reads as follows:My...
  14. S

    MHB Understanding Example from Topics in Banach Space Integration

    Hey Could you give me a hint how to explain this example? Need help to prove statement in red frame. Example from book (Topics In Banach Space Integration) by Ye Guoju‏، Schwabik StefanThank you
  15. Dada

    Comp Sci Find a Best-Case Example of QuickSort

    Hello to those who visit! Give a question "Construct a best-case example for Quicksort with n = 15", please explain how to get this case? Is there other special cases too if possible? The following images are the algorithm of Quicksort. My guess is that if I sort them in order or use number...
  16. Math Amateur

    I The Order Topology .... .... Singh, Example 1.4.4 .... ....

    I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 1, Section 1.4: Basis ... ... I need help in order to fully understand the order topology ... and specifically Example 1.4.4 ... ...Example 1.4.4 reads as follows: In order to...
  17. Z

    Reducing the Stable Matching (SM) problem: XOR secret sharing: Example?

    Hi, I am reading the following paper: Toward Practical Secure Stable Matching: https://encrypto.de/papers/RSSSK17.pdf. According to the paper: and at other place: Somebody please provide me an example for this model i.e reducing from multiparty data into 2-party data. Zulfi.
  18. Math Amateur

    I Convergence .... Singh, Example 4.1.1 .... .... Another Question ....

    I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 4, Section 4.1: Sequences ... I need some further help in order to fully understand Example 4.1.1 ...Example 4.1.1 reads as follows: In the above example from Singh we read the...
  19. Math Amateur

    I Convergence in Topological Spaces .... Singh, Example 4.1.1 .... ....

    I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 4, Section 4.1: Sequences ... I need help in order to fully understand Example 4.1.1 ...Example 4.1.1 reads as follows: In the above example from Singh we read the following: "...
  20. N

    I Example of a Lie group that cannot be represented in matrix form?

    I am not sure if this is the right forum to post this question. The title says it all: are there examples of Lie groups that cannot be represented as matrix groups? Thanks in advance.
  21. B

    How to determine the angles using geometry (specific example)

    I'm trying to find angles α and β. No additional information except: d, h, a. I already tried to figure it out by using isosceles triangles, but this is only true when there is a equilibrium of forces. I thought there are similar triangles incorporated, but I get too many unknown variables...
  22. B

    B Interstellar Movie: Light Reflection on Planet Close to Event Horizon

    In the movie Interstellar we see a planet close to the event horizon so when the astronauts land and get stuck on the planet for over an hour, many years passes for the guy on the spaceship and when they return he is an old man. From what I understand, this is indeed what would happen and they...
  23. M

    Stokes' Theorem Example Question

    Summary:: This question is about a Stokes' Theorem question that I saw on Khan Academy and I am trying to attempt to solve it a different way. The problem is as follows: Problem: Let \vec{F} = \begin{pmatrix} -y^2 \\ x \\ z^2 \end{pmatrix} . Evaluate \oint \vec F \cdot d \vec {r} over the...
  24. B

    B Example on pg. 23 of Mathematics for the Million

    I'm trying to figure out this example on page 23 of the book Mathematics for the Million by Lancelot Hogben. (Here is a link to the online book: https://archive.org/details/HogbenMathematicsForTheMillion/page/n25 ) While I understand the concept that adding two and two does not always equal...
  25. S

    Mathematica DiracDelta function example from Wolfram documentation

    The page on the Wolfram function DiracDelta has this example: Integrate[DiracDelta[x] Cos[x], {x, -Infinity, Infinity}] It's the first example under Examples > Basic Examples. When I run it in Wolfram Cloud, it says "Invalid integration variable or limit(s) ..." and shows this result: What's...
  26. Math Amateur

    MHB An Example on Differentials .... Browder Proposition 8.12 ....

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... ... I need some help with an example based only on Proposition 8.12 ... and the material in...
  27. G

    I A one dimensional example of divergence: Mystery

    I am trying to understand “divergence” by considering a one-dimensional example of the vector y defined by: . the parabola: y = -1 + x^2 The direction of the vector y will either be to the right ( R) when y is positive or to the Left (L). The gradient = dy/dx = Divergence = Div y = 2 x x...
  28. G

    Manipulating exponents: not sure how this example is worked out

    Summary: An example problem on Brilliant.org leaves out a step in solving 2^3 + 6^3 I've spend a couple days trying to understand how the second step of solving the problem 23 + 63, which is 23 + 63 = 23 + (23 * 33) = 23(1 + 33). It is not clear how this problem gets to 23(1 + 33). I can see...
  29. Math Amateur

    MHB Complex Function Theory: Explaining Example 1.5, Section 1.2, Chapter III

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I have yet another question regarding Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III...
  30. Math Amateur

    MHB Complex Square Root Function: Qs from Bruce P. Palka's Ex. 1.5, Ch. III

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need further help with other aspects of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III...
  31. Math Amateur

    MHB Differentiating Complex Square Root Function: Bruce P. Palka, Ex. 1.5, Ch. III

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need help with an aspect of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III, reads as...
  32. Math Amateur

    MHB Exploring Theorem 4.29: Compact Metric Spaces & Inverse Functions

    I am reading Tom M Apostol's book "Mathematical Analysis" (Second Edition) ... I am focused on Chapter 4: Limits and Continuity ... ... I need help in order to fully understand the example given after Theorem 4.29 ... ... Theorem 4.29 (including its proof) and the following example read as...
  33. Math Amateur

    MHB Understand Example 3.10 (b) Karl R. Stromberg, Chapter 3: Limits & Continuity

    I am reading Karl R. Stromberg's book: "An Introduction to Classical Real Analysis". ... ... I am focused on Chapter 3: Limits and Continuity ... ... I need help in order to fully understand Example 3.10 (b) on page 95 ... ... Example 3.10 (b) reads as follows: My question is as...
  34. L

    BCH Formula Example: Solving with [b,b^{\dagger}]=I

    From [b,b^{\dagger}]=I it is easy to see that [b,[b,b^{\dagger}]]=[b^{\dagger},[b,b^{\dagger}]]=0. And from that e^be^{b^{\dagger}}=e^{b+b^{\dagger}}e^{\frac{1}{2}I} Using that I get exp(\beta b^{\dagger}-\beta^*b)=e^{\beta b^{\dagger}}e^{-\beta^*b}e^{-\frac{1}{2}|\beta|^2I}. So...
  35. Math Amateur

    MHB Compact Topological Spaces .... Stromberg, Example 3.34 (c) .... ....

    I am reading Karl R. Stromberg's book: "An Introduction to Classical Real Analysis". ... ... I am focused on Chapter 3: Limits and Continuity ... ... I need help in order to fully understand an aspect of Example 3.34 (c) on page 102 ... ... Examples 3.34 (plus some relevant definitions ...)...
  36. Math Amateur

    MHB Why is the Series Absolutely Convergent for Sequences in l^2(N)?

    I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with an aspect of Example 2.3.52 ... The start of Example 2.3.52 reads as follows ... ... In the above Example from Sohrab we...
  37. Math Amateur

    MHB Uniform norm .... Garling Section 11.2 Normed Saces .... also Example 11.5.7

    I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help in order to understand some...
  38. R

    Example illustraing Quantum programming

    I'm interested in quantum programming. So far I've managed to use Java and Python inside Datamelt computation project for physics simulations and for various statistical plots. Now I want to make a simple code that illustates quantum computing, and maybe even to visualize its principles (for...
  39. sergiokapone

    A Index Juggling: Angular Momentum Tensor & Inertia Tensor in 3D-Space

    Lets consider the angular momentum tensor (here ##m=1##) \begin{equation} L^{ij} = x^iv^j - x^jv^i \end{equation} and rortational velocity of particle (expressed via angular momentum tensor) \begin{equation} v^j = \omega^{jm}x_m. \end{equation} Then \begin{equation} L^{ij} =...
  40. Math Amateur

    MHB Isometries .... Garling, Example 11.5.2 .... ....

    I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help in order to understand Example...
  41. user366312

    Need a layman's example of Linearizable Consistency model

    As far as I understand, Linearizable Consistency model is a Data-centric and Strong consistency model: Data-centric means: All clients experience the consistency All clients access the same data store All clients experience the same ordering Non-mobile clients. I.e. replica used doesn’t...
  42. Math Amateur

    MHB Open and Closed Sets .... Conway, Example 5.3.4 (b) .... ....

    I am reading John B. Conway's book: A First Course in Analysis and am focused on Chapter 5: Metric and Euclidean Spaces ... and in particular I am focused on Section 5.3: Open and Closed Sets ... Conway's Example 5.3,4 (b) reads as follows ... ... Note that Conway defines open and closed...
  43. Math Amateur

    I Open and Closed Sets .... Conway, Example 5.3.4 (b) .... ....

    I am reading John B. Conway's book: A First Course in Analysis and am focused on Chapter 5: Metric and Euclidean Spaces ... and in particular I am focused on Section 5.3: Open and Closed Sets ... Conway's Example 5.3,4 (b) reads as follows ... ... Note that Conway defines open and closed sets...
  44. nomadreid

    Medical PMC journals as source? Example on "ozone therapy"

    I am having a discussion with a friend who advocates "ozone therapy": re-injection of your blood after being enriched with ozone, done by a doctor. Since I am very skeptical of this fad (all I can see is that ozone destroys double bonds in carbon chains, which does not seem like a good thing--...
  45. sharinglanguage

    B Special Relativity Calc: Half Speed of Light - Jose

    Hello! I am trying to make some calculations on the Special theory of relativity over a practical example, considering the time dilation, but I may (more than likely..) be doing something wrong (probably with my assumptions). I would appreciate any comment on it. The example is that of a rocket...
  46. S

    I Griffiths: Intro To Quantum Example 4.3 clarification , <Sx> =

    Hello, In Griffiths Intro To Quantum (second edition) example 4.3 page 180 ... Calculating the expectation of <Sx>, equation 4.164. I'm sure I am wrong, but it seems like after using Euler's for the e^i terms there should be 2cos(yB0t)'s terms. I agree the sin's cancel (After using Euler)...
  47. L

    A Doubts in a lattice translation example

    I have two question about a exemple given in the Sakurai's quantum mechanics book, section 4.3. Let's consider an electron in a periodic potential ##V(x + a) = V(x)##, that has the form of a wave. We will take the potential to go to infinity between two latteces sites, such that its form change...
  48. Math Amateur

    I Parametrized Set .... McInerney, Example 3.3.3 .... ....

    I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.3: Geometric Sets and Subspaces of ##T_p ( \mathbb{R}^n )## ... ... In Section 3.3 McInerney...
  49. Math Amateur

    MHB McInerney Example 3.1.5: Multivariable Differentiation Q&A

    I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.1: The Derivative and Linear Approximation ... In Section 3.1 McInerney defines what is meant by...
  50. Math Amateur

    I Why is Mu Differentiable in McInerney Example 3.1.5?

    I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.1: The Derivative and Linear Approximation ... In Section 3.1 McInerney defines what is meant...
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