Theorem Definition and 1000 Threads

Homework Statement given the circuit shown below find the the vanin equivalent at resistance R. Homework Equations the resistances on the right side of the circuit can be simplified: 18 || (24+12) = 12 kΩ. The voltage can be found from 2 mA * 12 kΩ = 24 V. The voltage Va = 12-24 = -12 V...

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 an aspect of Theorem 1.8 ... Theorem 1.8 (preceded by its "proof") reads as follows...

Homework Statement The goal is to verify Stoke's Theorem. I've uploaded the image showing the problem and diagram. I'd like to get a double check on my work as I work on part b. Homework Equations Curl in cartesian coords and vector E. Integral of E dot dl = Integral of (Curl of E) dot dS The...

[FONT=verdana]Dear Everybody, I need some help to help the distance for part a. b) If the block comes back down after it was push, what is the speed back down. A 3.25 [FONT=verdana]kg block starts with a speed of[FONT=verdana] 15 m/s at the bottom of a plane inclined at...

Homework Statement Find the Taylor series for: ln[(x - h2) / (x + h2)] Homework Equations f(x+h) =∑nk=0 f(k)(x) * hk / k! + En + 1 where En + 1 = f(n + 1)(ξ) * hn + 1 / (n + 1)! The Attempt at a Solution ln[(x - h2) / (x + h2)] = ln(x-h2) - ln(x + h2) This is as far as I have been able to...

I have no idea if this is in the right direction. I know I am going to need the summation of the residues to use the theorem. I found the residues using the limit, but do I need to change these using the euler formula? We are supposed to be working problems at home and I am getting a bit lost...

Homework Statement Prove the continuity from below theorem. Homework EquationsThe Attempt at a Solution So I've defined my {Bn} already and proven that it is a sequence of mutually exclusive events in script A. I need to prove that U Bi (i=1 to infinity) is equal to U Ai (i=1 to infinity) to...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 7: The Riemann Integral ... I need help in fully understanding yet another aspect of the proof of Theorem 7.3.5 ...Theorem 7.3.5 and its proof ... ... read as...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 7: The Riemann Integral ... I need help in fully understanding an aspect of the proof of Theorem 7.3.5 ...Theorem 7.3.5 and its proof ... ... read as follows: In...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 7: The Riemann Integral ... I need help in fully understanding an aspect of the proof of Theorem 7.2.9 ...Theorem 7.2.9 and its proof ... ... read as follows...

I'm trying to expand the following using Newton's Generalized Binomial Theorem. $$[f_1(x)+f_2(x)]^\delta = (f_1(x))^\delta + \delta (f_1(x))^{\delta-1}f_2(x) + \frac{\delta(\delta-1)}{2!}(f_1(x))^{\delta-2}(f_2(x))^2 + ...$$ where $$0<\delta<<1$$ But the condition for this formula is that...

Here is an interesting little theorem - called Hall's Marriage Theorem: https://en.wikipedia.org/wiki/Hall's_marriage_theorem Well I am sitting here - simply flabbergasted. It's just a theorem - but guess what? A math student using it in a thesis at the University of NSW here in Aus had it...

This is related to vanhees71 statements (see bottom). I'll explain. First. The idea is very simple. As summary: Einstein showed that if reality was objective and quantum theory complete, then there had to be nonlocal effects. But since nonlocal effects can violate relativity, then there had to...

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 proof of Theorem 6.3.3 (L'Hospital's Rule ... ) ...Theorem 6.3.3 and its proof ... ... read as...

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 corollary to Theorem 6.2.1 ... Theorem 6.2.1 and its corollary ... ... read as follows: I am...

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 corollary to Theorem 6.2.1 ...Theorem 6.2.1 and its corollary ... ... read as follows: Can someone...

Let's consider a setup consisting of a table with friction, and a block on top of it. Suppose we drag the block across the table with a constant speed. The applied force ##f_{app}## acting through a distance ##d## does a work ##f_{app}d##. The frictional force ##\mu N## is equal to ##f_{app}##...

Can someone explain this article? https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-20170912/?utm_content=buffer4e481&utm_medium=social&utm_source=facebook.com&utm_campaign=buffer How is it related to the Cohen's theorem that continuum hypothesis is undecidable...

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 an aspect of the proof of Theorem 6.1.6 ...Theorem 6.1.6 and its proof ... ... reads as follows: In the...

Hello! (Wave) Which relation do the constants $a,b$ have to satisfy so that the implicit function theorem implies that the system of two equations $$axu^2v+byv^2=-a \ \ \ \ bxyu-auv^2=-a$$ can be solved as for u and v as functions $u=u(x,y)$ and $v=v(x,y)$ with continuous partial derivatives...

Hi! I'm currently reading "The Virial Theorem in Astrophysics" by G.W. Collins (the book is available as a free web edition at http://ads.harvard.edu/books/1978vtsa.book/) in which the author claims the importance of the ergodic hypothesis when applying the virial theorem to astrophysical...

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 5: Continuous Functions ... I need help in fully understanding an aspect of the proof of Theorem 5.3.2 ...Theorem 5.3.2 and its proof ... ... reads as follows:In...

https://en.wikipedia.org/wiki/PBR_theorem "The theorem was first published as an arXiv preprint with Pusey as the principal author,[1] a subsequent version published in Nature Physics,[2] that states the theorem that either the quantum state corresponds to a physically real object and is not...

Homework Statement I am working through a theorem on necessary and sufficient conditions for a set to be measurable and came across the following claim used in the proof: Let ##E## be measurable and ##m^*(E) = \infty##. Then ##E## can be written as a disjoint union of a countable collection of...

Homework Statement w is a function of three variables x, y, and z. Prove that \frac{\partial w}{\partial x}_{y,z} = \frac{1}{\frac{\partial x}{\partial w}}_{y,z} Homework EquationsThe Attempt at a Solution w=w(x,y,z) dx = \frac{\partial w}{\partial x}_{y,z}dx +\frac{\partial w}{\partial...

I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 4: Limits ... I need help in fully understanding an aspect of the proof of Theorem 4.2.9 ...Theorem 4.2.9 ... ... reads as...

Hey! :o I want to compute the integral $\oint_C \cos \left (x^{2017}\right )dx+\left (\frac{x^2}{2}+\sin y^{2018}\right )dy$, where $C$ is the boundary of the bounded field that is defined by the curves $y=2-x^2$ and $y=x$, with positive orientation. We have to apply Green's Theorem, or not...

Hi everyone, I was going through the derivation of the first Hohenberg-Kohn theorem (see here under eqn 1.31 for reference) when I noticed a once-obvious statement that didn't seem so obvious anymore. Namely, the proof requires that if you have two Hamiltonians ##H_1 \neq H_2##, then their...

A pendulum of mass m and length l is suspended from the ceiling of a trolley which has a constant acceleration a. Find the maximum deflection θ of the pendulum from the vertical. When I used work energy theorem, I got θ = 2 arctan(a/g). But when I took the equilibrium position and equated the...

Hi. My question is about nucleon-nucleon scattering. In David Tong's lecture note, he discusses Wick's theorem and nucleon scattering (page 58-60). My problem is that I don't know how to calculate the second line of eq(3.48): \begin{equation} <p'_1, p'_2|:\psi^\dagger (x_1) \psi (x_1)...

Hello! Recently I found this article: http://quantum-journal.org/papers/q-2017-07-14-13/pdf/ Being familiar with some basis of quantum formalism, I, nevertheless, experienced several difficulties with understanding of the theorem described in this paper. I would really appreciate if someone...

In his book: Introduction to Real Analysis, Manfred Stoll does not prove parts (a) and (b) of Theorem 2.2.6 on the limits to certain special sequences ... I am having trouble getting started on the proof of part (a) ... can someone please help me to make a meaningful start to the proof ...

Homework Statement consider a ski jumper moving down a track to acquire sufficient speed to accomplish the ski jumping task. The length of the track is L=25m and the track makes an angle of 45° with the horizontal if the skier starts at the top of the track with zero initial speed , determine...

Question: A) Derive the work - energy theorem for one particle. B) Check whether it is applicable for a system of particles and a rigid bodyWork - energy theorem for one particle system, total sum of work done by individual forces = work done by total force To show the above equality, let's...

I was thinking about why the buoyant force on an object should depend solely on it's volume and not shape. It seems loosely like the divergence theorem in that an integral over the surface is determined by the volume. There is a big difference though; in the divergence theorem we integrate...

Find product (1+3i)(2-2i) then change each to complex form and find product with DeMoivres theorem clueless!

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 Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the Nested Intervals Theorem ... ...

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 the proof of Theorem 2.1.38 ... Theorem 2.1.38 reads as...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Section 1.4: Entry 2: Axioms for the Integers ... In this section Bloch defines the integers as an ordered integral domain that satisfies the Well Ordering Principle ... rather than defining the...

So here's the question: You are given that F is a conservative vector field, except for singularities at the points (0,1), (2,0), (3,0), and (0,4). You are given the following information about line integrals around the following closed paths: 1) Around the curve C1 given by x^2 + y^2 = 2...

Hi, Our lecturer explained us the Reynold Transport theorem, its derivation , but I don't get where the - sign in control surface 1 comes from? He said that the Area goes in opposite direction compared with this system. I can't visualise this on our picture. Can you please help me understand...

This is the problem I'm currently working on: The pi groups I identified were h1, h2, d, D, g, t, and velocity, but when I looked at the solution, it selected Δh, D, t, ρ, d, ϒ, h1, with no explanation why those variables are needed. If I was solving with the Bernoulli equation, I wouldn't...

Hello! I have been doing a previous exam task involving the divergence theorem, but there is a minor detail in the answer which i can't fully understand. I have a figur given by ${x}^{2} +{y}^{2} -{z}^{2} = 1$ , $z= 0$ and $z=\sqrt{3}$ As i have understood this is a hyperboloid going from...

Hello everybody. I have to prove the fallowing theorem: The Cayley-Hamilton Theorem help me please...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.9 (6) ... Theorem 1.2.9 reads as follows: In the above proof of (6) we read the...

Charles Link submitted a new PF Insights post An Integral Result from Parseval's Theorem Continue reading the Original PF Insights Post.

Hello, today i was playing around with the pythagorean theorem and found out something that i can't really explaing or atleast explain it with probably a false answer. So i was putting every possible combination with the max digit of 10. For example 1^2+1^2=\sqrt{2}, 1^2+2^2=\sqrt{5}...

Hello, It is me again.So i was watching some math videos and i came across Fermat's Last Theorem which was very intersting.But i was confused because i wondered for a second and sayed "well if A,B and C are equal then they could be 0 to prove it" but at the same time i thought "well if it works...

Consider a continuous function f in [a,b] and f(a) < f(b). Suppose that \forall s \neq t in [a,b], f(s) \neq f(t). Proof that f is strictly increasing function in [a,b]. Homework Equations I.V.T: If f is continuous in [a,b] and \gamma is a real in [f(a),f(b)], then there'll be at least one c...