Example Definition and 845 Threads

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...

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...

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...

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...

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...

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?

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.

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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: "...

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 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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

Homework Statement If the centripetal force is at the left side of the equation; that means if we move it over to the other side, it'll have a negative sign, which means it is opposite in sense in relation to N and mg. But how is that possible, considering that the centripetal force always...

Hi just curious, What is the computing/networking model for a site with many users, say, as PF? Is it to grant access to each user to a shared drive? Sorry if this is too simple. I mean, I understand that first I login and I have to be first authenticated, then authorized to access certain...

Homework Statement Homework Equations [/B] Definition: A sequence X_1,X_2,\dots of real-valued random variables is said to converge in distribution to a random variable X if \lim_{n\rightarrow \infty}F_{n}(x)=F(x) for all x\in\mathbb{R} at which F is continuous. Here F_n, F are the...

https://www.theguardian.com/society/2016/apr/07/the-sugar-conspiracy-robert-lustig-john-yudkin Lots of important lessons here, for scientists, teachers, and the general public who consumes and often makes personal decisions based on science news.

Hi was reading about differential forms, when I tried to solve the example given in this pdf https://www.rose-hulman.edu/~bryan/lottamath/difform.pdf. According to it, the answer is that on the image above. But when I tried to solve this same example by following the expression for ##w## given...

Homework Statement Provide a counter example to the false assertion: Suppose that f and g are functions and f ◦ g is invertible. Then f and g are invertible. Homework Equations Definitions: An invertible function is 1-1 and onto If the image of g is not contained in the domain of f then f ◦...

Hi guys, I have a question to all of you. This question is based on the example which is located here: http://galileo.phys.virginia.edu/classes/252/time_dil.html I understand it but there is one thing is still unclear to me. So, here it is: Again we have Jill on the rocket and poor Jack on the...

Hello. I would like to check my understanding of how you transform the covariant coordinates of a vector between two bases. I worked a simple example in the attached word document. Let me know what you think.

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Chapter 5 ... I need some help with Example 5.2.1 in Section 5.2: Rings Generated by Elements ... In the Introduction to Section 5.2.1 (see text above) Lovett writes: " ... ...