Theorem Definition and 1000 Threads

Homework Statement attempt to derive the equation of centripetal acceleration using work energy theorem Homework Equations work done = Change in kinetic energy The Attempt at a Solution consider diametrically opposed points occurring in uniform circular motion - displacement = 2*R and let...

Moment of inertia is supposed to be defined with respect to a rotational axis such that for a system of point masses, I=∑miri2 where ri 's are the perpendicular distances of the particles from the axis. However, in some derivations of the virial theorem (like the one on wiki), the so-called...

Homework Statement Let S be the portion of the paraboloid ##z = 4 - x^2 - y^2 ## that lies above the plane ##z = 0## and let ##\vec F = < z-y, x+z, -e^{ xyz }cos y >##. Use Stoke's Theorem to find the surface integral ##\iint_S (\nabla × \vec F) ⋅ \vec n \,dS##. Homework Equations ##\iint_S...

Let me set up the question briefly. Emmy Noether's theorem relates symmetry to conserved quantities, e.g. invariance under translations in time => conservation of energy. A fundamental truth revealed. Massive gauge bosons, leptons and quarks all appear to acquire mass through the spontaneous...

So, I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields? I think not because in order to not have a Flux depending on distance but a constant one we need that r^2 of the...

Suppose we have equal and opposite charge densities on a parallel plate capacitor. Let the plates be separated some small distance d (small when compared with the plate size). Now slowly separate the plates so that their separation is now doubled to 2d. We have done work and the electrostatic...

Homework Statement [/B] Suppose we have a 2\pi-periodic, integrable function f: \mathbb{R} \rightarrow \mathbb{C} whose Fourier coefficients are known. Parseval's theorem tells us that: \sum_{n = -\infty}^{\infty}|\widehat{f(n)}|^2 = \frac{1}{2\pi}\int_{-\pi}^{\pi}|f(x)|^{2}dx, where...

Urs Schreiber submitted a new PF Insights post Why Supersymmetry? Because of Deligne's theorem. Continue reading the Original PF Insights Post.

I am trying to prove this function theorem: Let F:X→Y and G:Y→Z be functions. Then a. If F and G are both 1 – 1 then G∘F is 1 – 1. b. If F and G are both onto then G∘F is onto. c. If F and G are both 1 – 1 correspondences then G∘F is a 1 – 1 correspondence. Part a has already been...

Hello, I know a theorem that say that if ##F : \mathbb{R} \times \Omega \rightarrow E## is continuous and local lispchitziann in is seconde set value(where ##\Omega## is an open of a Banach space E.). we have that the maximum solution ##(\phi, J)##(where J is an open intervall and ##\phi : J...

The proofs of the Fundamental Theorem of Calculus in the textbook I'm reading and those that I have found online, basically show us: 1) That when we apply the definition of the derivative to the integral of f (say F) below, we get f back. F(x) = \int_a^x f(t) dt 2) That any definite integral...

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with a basic and possibly simple aspect of Theorem 2.3 ... Since the answer to my question may depend on...

71. Use the Comparison Theorem to determine weather the integral $$\displaystyle I=\int\frac{{x}^{2}}{{x}^{5}+2} \, dx$$ is convergent or divergent. Comparison Theorem Suppose that $f$ and $g$ are continuous with $f(x) \ge \, g(x) \ge 0 $ for $x\ge a$ (a) if $\displaystyle \int_{a}^{\infty}...

Homework Statement Let be ##f \in C^{1}(\mathbb{R}^{n}, \mathbb{R}^{n})## and ##a \in \mathbb{R}^{n}## with ##f(a) = a##. I'm looking for a suffisent and necessar condition on f that for all ##(x_{n})## define by ##f(x_{n}) = x_{n+1}##, then ##(x_{n})## converge. Homework Equations ##f(a) =...

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows: In the above text, in part 4...

I am reading T. S. Blyth's book "Module Theory: An Approach to Linear Algebra" ... ... and am currently focussed on Chapter 1: Modules, Vector Spaces and Algebras ... ... I need help with an aspect of Theorem 1.1 part 4 ... Theorem 1.1 in Blyth reads as follows:In the above text, in part 4 of...

I want to know about applications of De Movire's theorem for root extraction.

A problem on geometry proof Hi (Smile), When considering the $$\triangle$$ ABM E is the midpoint of AB & EO //OM (given).I think this is the way to tell AO=OM , Help .Many Thanks (Smile)

According to Kirchoff $$e=J(T,f)A$$ ##e## is the power emitted and ##A## is the power absorbed If ##E## is the power supplied, can I say that $$e=E-A$$

Hello. I have a question about a step in the factorization theorem demonstration. 1. Homework Statement Here is the theorem (begins end of page 1), it is not my course but I have almost the same demonstration : http://math.arizona.edu/~jwatkins/sufficiency.pdf Screenshot of it: Homework...

Homework Statement Homework Equations Formula for Area of a retangle : A = L x W Pythagorean theorem: A2 + b2 = c2 The Attempt at a Solution So I am pretty sure I did it correct but I just want to be 100% certain I will get this right, By the way its a picture cause I found it easier to...

Hi,I have been stuck on this problem The midpoints of the sides AB and AC of the triangle ABC are P and Q respectively. BQ produced and the straight line through A drawn parallel to PQ meet at R. Draw a figure with this information marked on it and prove that, area of ABCR = 8 x area of APQ. I...

Homework Statement [/B] (a) Calculate the load current using Thevenin's Theorem (b) Calculate the load current using Superposition Homework Equations N/A The Attempt at a Solution There have already been a couple of historical posts of this question but those threads don't give me any...

This relates to a homework question which I have spent considerable time on and although I understand the concepts, the process of getting to the answer is difficult because of several different 'versions' of the right answer I see. The relevant threads are...

look figure (b) suppose that baseball deliver F through horizontal motion. imagine that the O point of the system is same line of F (+x is F direction) then before percussion, the angular momentum of the system is "0" because r and v of baseball are same direction (L = r x mv = 0) so after...

Homework Statement "Under mild continuity restrictions, it is true that if ##F(x)=\int_a^b g(t,x)dt##, then ##F'(x)=\int_a^b g_x(t,x)dt##. Using this fact and the Chain Rule, we can find the derivative of ##F(x)=\int_{a}^{f(x)} g(t,x)dt## by letting ##G(u,x)=\int_a^u g(t,x)dt##, where...

(Sorry for my bad English.) I was reading about the Green's theorem and I notice that the book only shows for the case where the function is a vector function. When learning about line integrals, I saw that we can do line integrals using "ordinary" functions. For example, the line integral of...

The math theorem to be proven We want to join three given points using any number of straight lines of any length while minimising the total length of the straight lines. Show that this is achieved by using three lines that are 120##^\circ## apart as shown above. The following is the answer to...

hi everyone, I would like say that there are lots of proofs related to pythagoras theorem in a flat space, but When I searched it's general form I have not found something worthwhile. Besides, I also involved myself to have a nice proof of it, as a result I have not any valuable or very close...

Homework Statement Find \int_{0}^{\infty} \frac{\cos(\pi x)}{1-4x^2} dx Homework Equations The residue theorem The Attempt at a Solution The residue of this function at $$x=\pm\frac{1}{2}$$ is zero. Therefore shouldn't the integral be zero, if you take a closed path as a hemisphere in the...

Hello, I have a question about Heine Borel Theorem. First, I am not sure why we have to show "gamma=Beta" gamma is the supremum of F(which is equivalent to H_squiggly_bar in the text ), and it has to be greater than beta. Otherwise, S contains H_squiggly_barSecond, for the case 1, why...

Use the squeeze theorem to show that $\displaystyle \lim_{{n}\to{\infty}} \frac{n!}{{n}^{x}}=0 \\ \text{have never used the squeeze theorem } \\ \text{but by observation the denominator is increasing faster}$

"Write out a series of three or more different whole numbers in geometric progression, starting from one, so that the numbers should add up to a square. So like, 1 + 2 + 4 + 8 + 16 + 32 = 63 (one short of a square)"(can't find an actual real life example) I can't seem to find an answer for this?

Homework Statement This theorem comes from the book "The Real Numbers and Real Analysis" by Bloch. I am having a hard time understanding a particular part of the proof given in the book. Prove the following theorem: There is a unique binary operation +:ℕ×ℕ→ℕ that satisfies the following two...

Hello, It's been puzzling for me to try to understand this issue. To begin with it is clear that there are basically two principles, the Position-Momentum uncertainty and the Time-Energy uncertainty. It is also clear that there are at least two different interpretations attached to both. One is...

Okay, I am studying Baby Rudin and I am in a lot of trouble. I want to show that a closed interval [a,b] is compact in R. The book gives a proof for R^n but I am trying a different proof like thing. Since a is in some open set of an infinite open cover, the interval [a,a+r_1) is in that open set...

Homework Statement I was given the problem of determining if the Converse of the Intermediate Value Theorem in my book was true. Below is my theorem from the book. Homework EquationsThe Attempt at a Solution I had looked at the converse and tried to draw some examples, and I am thinking it...

Hi... New to this forum. Be kind! I did not study physics at university, and consider myself an armchair physicist. I am a computer programmer by trade. I first came across Bells inequalities a few years ago, while working with a fello programmer who did have a PHD in physics. Its pretty...

So I have this question that goes like this, for a classical 1D system we are given an Hamiltonian of the form of an Harmonic Oscilator. However the term for the potential is infite when ##x\leq0## and the usual harmonical oscillator potential otherwise. The question is: is the equipartition...

Homework Statement in this problem , the author make π1 = D(dp/ dx) / ρ( V^2) , and make π3 as μ/ ρVD , how if i want to make μ/ ρVD (reciprocal of reynold number ) as π1 and make D(dp/ dx) / ρ( V^2) as π3 ? Homework EquationsThe Attempt at a Solution since we know that π1 is function of (...

Hi i am fatih from turkey.i am high school student.question is "how many squares are in an rectangle subdivided into unit squares?"(a<=b) My theorem about this question.Please write your comments.Thanks For your time, thanks all mathematicians !:)

Homework Statement A polynomial P(x) is divided by (x-1), and gives a remainder of 1. When P(x) is divided by (x+1), it gives a remainder of 3. Find the remainder when P(x) is divided by (x^2 - 1) Homework Equations Remainder theorem The Attempt at a Solution I know that P(x) = (x-1)A(x) +...

Homework Statement Suppose you're at a college campus. 3/4 of the people on the campus are students or professors from that college, and the rest 1/4 aren't. When asked a question, students and professors from that college will give you a correct answer every time, and those that aren't from...

Let's say there is a 5 sided cube that is missing the bottom face. Obviously, there is a boundary curve at the middle of this cube that goes around the 4 sides, front, right, back, and left. This boundary curve forms the boundary of the top half of the cube with the 5 faces and the bottom...

the first step of the Plancherel's Theorem proof found in: http://mathworld.wolfram.com/PlancherelsTheorem.html, says: let be a function that is sufficiently smooth and that decays sufficiently quickly near infinity so that its integrals exist. Further, let and be FT pairs so that...

Homework Statement why there is a need to change π3 to π3 ' (which is inverse of reynold number)? (in 2nd picture) Homework EquationsThe Attempt at a Solution why can we do so ? i was told that π1 = f( π2 , π3 , ...) if we use π3' , which is this will change the original meaning of π1 = f(...

I often read (for example, in Wikipedia on "Rosser's Trick") that in order for a proof of Gödel's First Incompleteness Theorem, one assumes an efficient consistent theory of numbers which includes a "sufficient fragment of elementary arithmetic". What minimum would qualify? Is Robinson's Q a...

Today I heard the claim that its wrong to use Stokes(more specificly divergence/Gauss) theorem when trying to get the Einstein equations from the Einstein-Hilbert action and the correct way is using the non-Abelian stokes theorem. I can't give any reference because it was in a talk. It was the...

Homework Statement http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/dimension/node9.html in the link above , the author stated that F / (rho)(D^2)(v^2) = f( (rho)(v)(D) / (μ) ) , Homework EquationsThe Attempt at a Solution can i rewrite in in anotgher way ...

Is this an abuse of Rolle's theorem? Rolle's theorem If a real-valued function f is continuous on a proper closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the open interval (a, b) such that f'(c) = 0. ##[x_1, x_1]##...