Example Definition and 879 Threads

  1. JTC

    A Example of how a rotation matrix preserves symmetry of PDE

    Good Day I have been having a hellish time connection Lie Algebra, Lie Groups, Differential Geometry, etc. But I am making a lot of progress. There is, however, one issue that continues to elude me. I often read how Lie developed Lie Groups to study symmetries of PDE's May I ask if someone...
  2. Math Amateur

    MHB Linear Mappings are Lipschitz Continuous .... D&K Example 1.8.14 .... ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Example 1.8.14 ... ... The start of Duistermaat and Kolk's Example 1.8.14 reads as...
  3. Math Amateur

    MHB The Euclidean Norm is Lipschitz Continuous .... D&K Example 1.3.5 .... ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Example 1.3.5 ... ... The start of Duistermaat and Kolk's Example 1.3.5 reads as...
  4. Math Amateur

    MHB Orthogonal Projection .... .... D&K Example 1.5.3 .... ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Example 1.5.3 ... Duistermaat and Kolk"s Example 1.5.3 reads as follows:In the above example we read the...
  5. F

    Coriolis effect example: ball tossing on rotating carousel

    Hi all, I was reviewing the Coriolis effect and I came across the attached explanatory image (from the Italian version of a book on physics by Cutnell, Johnson, Young and Stadler). The idea is the following. two guys are facing each other on a rotating carousel; one of the guys on the throws...
  6. Math Amateur

    MHB Continuous Functions and Open Sets .... D&K Example 1.3.8 ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Example 1.3.8 ... Duistermaat and Kolk"s Example 1.3.8 reads as follows:In the above example we read the...
  7. rocdoc

    I Projective Representations: a simple example

    Could anyone help with providing a simple example of a projective representation of a small finite group ( order of group not greater than six )? My understanding is that, if the group has N elements, then I should see N matrices in the projective representation. I would prefer the example to...
  8. Ventrella

    A Examples of fractal structure in prime partition numbers?

    Regarding the recent discovery by Ken Ono and colleagues of the fractal structure of partition numbers for primes: a great lever of intuition would be to see a diagram, or any presentation of the numbers that reveals this fractal structure. Perhaps the fractal structure is somehow hidden in a...
  9. P

    Why is cos^-1 used in the first example but not the second?

    Mentor note: Thread moved from a homework section. I don't know if this is the right forum, but this isn't really a homework question that I have to solve, I am just trying to get better with vectors/trig and I looked at this for basic examples. I am okay with finding x and y components, but I...
  10. J

    Power Electronics controlled rectifier solved example

    Homework Statement Homework Equations Solved example The Attempt at a Solution I think the red part should be (alpha/firing angle) = 180 - 45 Here since the angle is 45, it makes no difference if you do 90 + 45 or 180 - 45, but i think it should be 180 - 45. Am I right?
  11. ORF

    B Is there any macroscopic example for the "mass excess"?

    Hello In nuclear physics, the mass excess is caused by the nuclear binding energy. Question: is there any macroscopic example where the "mass excess" is non-negligible? Thank you for your time. Regards.
  12. vanhees71

    The Homopolar Generator: An Analytical Example - Comments

    Greg Bernhardt submitted a new PF Insights post The Homopolar Generator: An Analytical Example Continue reading the Original PF Insights Post.
  13. E

    Example in chapter: Gravitation

    Homework Statement consider the motion of a comet in an elliptical orbit around a star. the eccentricity of the orbit is given by e= 0.20 and the distance between the perhelion and the aphelion is 1.0 × 10^power8 a- find the distances of nearest and farthest approaches of the comet. b- if the...
  14. K

    Why a book on a table is not an example of Newton's 3rd law?

    In a physics test in a Norwegian website of a school book, it says following: True or false? (1) According to Newton's 3rd Law, the weight of a book that is on a table is just as big, but opposite the force on the book from the table (normal force). FALSE. (2) According to Newton's 1st Law...
  15. J

    A Can you give an example of a non-Levi Civita connection?

    Hello! Since connections in general do not require that we have a Riemannian manifold, but only a smooth manifold, I find it kind of weird that the only examples of connections that I find in the internet are those which use the Levi-Civita connection. So, I wanted to know of any examples of...
  16. Math Amateur

    MHB Why Does Theorem 1.9 Use f(t) Instead of f(γ(t))?

    I am reading John B. Conway's book, "Functions of a Complex Variable I" (Second Edition) ... I am currently focussed on Chapter IV: Complex Integration ... Section 1: Riemann-Stieljes Integral ... ... I need help in fully understanding the first example on page 63 ... ... The the first...
  17. Math Amateur

    MHB Contour Integrals - Example 2.5, Palka, Section 2.2, Ch.4 .... ....

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 4: Complex Integration, Section 2.2 Properties of Contour Integrals ... I need help with an aspect of Example 2.5,Section 2.2, Chapter 4 ... Example 2.5, Chapter 4 reads as follows:In...
  18. Math Amateur

    MHB How Can \dot{\gamma}(0) Fail to Exist in Palka's Example 1.3?

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 4: Complex Integration, Section 1.2 Smooth and Piecewise Smooth Paths ... I need help with some aspects of Example 1.3, Section 1.2, Chapter 4 ... Example 1.3, Section 1.2, Chapter 4...
  19. Math Amateur

    MHB Continuity of Complex Functions ....Palka, Example 1.5, Chapter 3 .... ....

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 3: Analytic Functions ... I need help with some aspects of Example 1.5, Chapter 3 ... Example 1.5, Chapter 3 reads as follows: In the above text from Palka Chapter 3, Section 1.2 we...
  20. Math Amateur

    MHB Limits of Complex Functions .... Example from Palka ....

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 2: The Rudiments of Plane Topology ... I need help with some aspects of a worked example in Palka's remarks in Section 2.2 Limits of Functions ... Palka's remarks in Section 2.2 which...
  21. Math Amateur

    MHB Why Does γ(t) = z(1-t) Represent the Same Curve in Reverse?

    I am reading "Complex Analysis for Mathematics and Engineering" by John H. Mathews and Russel W. Howell (M&H) [Fifth Edition] ... ... I am focused on Section 1.6 The Topology of Complex Numbers ... I need help in fully understanding a remark by M&H ... made just after Example 1.22 ... Example...
  22. Math Amateur

    MHB Remarks on Limit Superrior .... B&S Page 82 .... Example ....

    I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 3: Sequences and Series ... I need help in fully understanding an example given by B&S in some introductory remarks on Limit Superior and Limit Inferior ...The...
  23. A

    B What are some real world example of these equations?

    I am in Algebra one. I am curious to know the real world applications in some of the equations I'm learning. I asked my math teacher and he didn't know any answers. I am interested in using slope formula and linear inequalities in real life. How will I be using this in physics? I would like...
  24. A

    I Physics term for discussed example and calculations

    i thought of an example of a 2 system that would give anti torques for each other but i want to know how to properly calculate it and if there is a term for that kind of example: two manual treadmills placed infront of each other without any handles so nothing to grab on to. and for the...
  25. Math Amateur

    MHB What is the connection between sin and cos in Example 6.3.4?

    I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 6: Differentiation ... I need help in fully understanding the an aspect of Example 6.3.4 ...Example 6.3.4 ... reads as follows:The above example implies that...
  26. E

    Is this example of Bond Energy correct?

    Homework Statement [/B] (see attachments for example 2.9) Homework Equations [/B] The Attempt at a Solution As far as I have read and understood, most polymerizations (such as the one in this example) are exothermic. If this is the case, shouldn't this produce a negative (-) reaction...
  27. Math Amateur

    MHB Limits of Functions .... L&S Example 10.7 (2) ....

    I am reading "Real Analysis: Foundations and Functions of One Variable"by Miklos Laczkovich and Vera Sos ... I need help with an aspect of Example 10.7 (2) ... Example 10.7 (2) reads as follows: In the above text, we read the following: "... ... Since whenever \lvert x - 2 \lvert \lt...
  28. Math Amateur

    MHB Limits of Sequences .... Bartle and Shebert, Example 3.4.3 (b) ....

    I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 2: Sequences and Series ... I need help in fully understanding Example 3.4.3 (b) ...Example 3.4.3 (b) ... reads as...
  29. Math Amateur

    I Limits of Sequences .... Bartle & Shebert, Example 3.4.3 (b)

    I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 2: Sequences and Series ... I need help in fully understanding Example 3.4.3 (b) ... Example 3.4.3 (b) ... reads as follows: In the above text from Bartle and...
  30. D

    I How Can I Integrate the Equation for a Rocket's Velocity?

    Hi - I just thought of a (relatively) simple example: Here is the problem I can't solve due to my disability to integrate the resulting equation: I thought about a rocket that gets accelerated by a constant force F... Since the rocket is burning fuel and therefor losing mass at a conatnt rate...
  31. R

    I Actual example of a mixed state not part of entangled state

    A mixed state is when the system is actually in one state or another, but you just don't know which, and you use probabilities to describe your uncertainty. I'm referring to a mixed state of the entire system. I want an actual example. Can you think of some? Note I wasn't describing mixed state...
  32. Math Amateur

    MHB Galois Groups .... A&F Example 47.7 .... ....

    I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 47: Galois Groups... ... I need some help with an aspect of the Example 47.7 ... Example 47.7 and its proof read as follows: In the above example, Anderson and Feil write the following...
  33. Math Amateur

    B Galois Groups .... A&F Example 47.7 .... ....

    I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 47: Galois Groups... ... I need some help with an aspect of the Example 47.7 ... Example 47.7 and its proof read as follows: In the above example, Anderson and Feil write the following: "...
  34. Math Amateur

    MHB Finite Extensions - A&F Example 44.2 .... ....

    I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 44: Finite Extensions and Constructibility Revisited ... ... I need some help in fully understanding Example 44.2 ... ...Example 44.2 reads as follows...
  35. Math Amateur

    I Finite Extensions - A&F Example 44.2 .... ....

    I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 44: Finite Extensions and Constructibility Revisited ... ... I need some help in fully understanding Example 44.2 ... ...Example 44.2 reads as follows: I am trying to fully understand EXACTLY...
  36. M

    A Can You Solve an ODE Using the Rayleigh-Ritz Method? - A Short Tutorial

    Hi PF! I'm trying to understand the Rayleigh-Ritz variational technique to estimate eigenvalues of an ODE. Could someone familiar with this technique either give me a good link to a worked example or write a BVP here and see if I can solve it under your guidance? Thanks!
  37. Hiero

    B Poisson's ratio, steel rod for example

    Steel has a "Poisson ratio" μ of 0.29 (in my book of problems at least). Am I understanding the meaning of this ratio correctly: if a steel cylinder is stretched along its symmetry axis by a factor p (something like 1.01 or 0.99) then the radius will change by a factor 1-μ(p-1)? [So then the...
  38. Math Amateur

    MHB Galois Theory - Structure Within Aut(K/Q) .... Lovett, Example 11.1.10 .... ....

    I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ... I need help with Example 11.1.10 on page 560 ... ...Example 11.1.10 reads as follows: My questions...
  39. Math Amateur

    MHB Automorphisms of Field Extensions .... Lovett, Example 11.1.8 .... ....

    I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ... I need help with Example 11.1.8 on page 559 ... ...Example 11.1.8 reads as follows: My questions...
  40. Math Amateur

    I Automorphisms of Field Extensions .... Lovett, Example 11.1.8

    I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ... I need help with Example 11.1.8 on page 559 ... ...Example 11.1.8 reads as follows: My questions...
  41. G

    Momentum Conservation & External Force: Explained with an Example

    Why ain't momentum conserved when external force acts on the system? Please explain with an example.
  42. Math Amateur

    MHB Example of an Inseparable Polynomial .... Lovett, Page 371 ....

    I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with Example 7.7.4 on page 371 ...Example 7.7.4 reads as follows: In the above text from Lovett we read the following:" ... ... The...
  43. Math Amateur

    I Example of an Inseparable Polynomial .... Lovett, Page 371 ...

    I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with Example 7.7.4 on page 371 ...Example 7.7.4 reads as follows: In the above text from Lovett we read the following:" ... ... The...
  44. A

    B Muon Time Dilation: Earth vs Muon Perspective

    From the reference frame of the earth, the distance between the surface of the Earth and the muon is longer, but the muon survives because time for the muon is slowed down. From the reference frame of the muon, the time experienced by the muon is not slowed down but the muon survives because...
  45. Math Amateur

    MHB Existence and Uniqeness of Finite Fields .... Example from D&F ....

    I am reading David S. Dummit and Richard M. Foote : Abstract Algebra ... I am trying to understand the example on Finite Fields in Section 13.5 Separable and Inseparable Extensions ...The example reads as follows: My questions are as follows: Question 1In the above text from D&F we read the...
  46. Math Amateur

    MHB Separable Polynomials - Paul E Bland's definition and example ....

    I am reading Paul E Bland's book: The Basics of Abstract Algebra and I am trying to understand his definition of "separable polynomial" and his second example ... Bland defines a separable polynomial as follows:https://www.physicsforums.com/attachments/6636... and Bland's second example is as...
  47. MARX

    Example 7-10 Lagrangian Dynamics Marion and Thornton

    Homework Statement A particle of mass m is on top of a frictionless hemisphere centered at the origin with radius a" Set up the lagrange equatinos determine the constraint force and the point at which the particle detaches from the hemisphere Homework Equations L=T-U The Attempt at a...
  48. Math Amateur

    MHB Splitting Fields - Example 3 - D&F Section 13.4, pages 537 - 538

    I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Section 13.4 : Splitting Fields and Algebraic Closures ... ... I need some help with an aspect of Example 3 of Section 13.4 ... ... Example 3 reads as follows: In the above text by Dummit and Foote, we read...
  49. Math Amateur

    I Splitting Fields - Example 3 - D&F Section 13.4, pages 537 -

    I am reading Dummit and Foote, Chapter 13 - Field Theory. I am currently studying Section 13.4 : Splitting Fields and Algebraic Closures ... ... I need some help with an aspect of Example 3 of Section 13.4 ... ... Example 3 reads as follows: In the above text by Dummit and Foote, we read...
  50. Math Amateur

    MHB Algebraic Extensions - Lovett, Example 7.2.7 .... ....

    I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with Example 7.2.7 ...Example 7.2.7 reads as follows: In the above example from Lovett, we read the following: " ... ... From our...
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