Theorem Definition and 1000 Threads

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 the proof of Theorem 1.8.17 ... ... Duistermaat and Kolk's Theorem 1.8.17 and its proof (including the...

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 the proof of Theorem 1.8.15 ... ... Duistermaat and Kolk's Theorem 1.8.15 and its proof read as follows:In...

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 the proof of Theorem 1.8.8 ... ... Duistermaat and Kolk's Theorem 1.8.8 and its proof read as follows:In the...

Homework Statement Homework Equations Laplace and then inverse laplace. The Attempt at a Solution Laplace of U(t-to) = 1/s e^(-tos) x(t)-->X(s) Laplace inverse 1/s means integration. e^(-tos) means delay on x(t) by to. I think answer should be C Book answer is D. How am I wrong?

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 another aspect of the proof of Theorem 1.8.6 ... ... Duistermaat and Kolk"s Theorem 1.8.6 and the preceding definition...

In the book " Real Analysis: Foundations and Functions of One Variable" by Miklos Laczkovich and Vera T. Sos, Theorem 5.2 (Chapter 5: Infinite Sequences II) reads as follows:https://www.physicsforums.com/attachments/7722 Can someone inform me if there is an equivalent theorem that holds in...

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 the proof of Theorem 1.8.4 ... ... Duistermaat and Kolk"s Theorem 1.8.4 and its proof read as...

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 the proof of Theorem 1.6.2 ... Duistermaat and Kolk"s Theorem 1.6.2 and its proof read as follows:In the...

So as always I come here to make sure my maths homework is right and ask few questions to make sure I understand the topic. Here is my homework: Q.1 I'm fairly certain that this is correct, however, please check if I didn't do any stupid mistakes. Q.2 Same as above. Q.3 Now here is where the...

Homework Statement Griffiths Introduction to Electrodynamics 4th Edition Example 1.10 Check the divergence theorem using the function: v = y^2 (i) + (2xy + z^2) (j) + (2yz) (k) and a unit cube at the origin. Homework Equations (closed)∫v⋅da = ∫∇⋅vdV The flux of vector v at the boundary of the...

When using the work-energy theorem (Wnet=ΔE), when do you take gravitational potential energy into account? Change in energy implies all types of energy involved, but in what cases would PEg be a part of it?

Homework Statement Could someone illustrate why $$\int_{V} \nabla \cdot (f\vec{A}) \ dv = \int_{V} f( \nabla \cdot \vec{A} ) \ dv + \int_{V} \vec{A} \cdot (\nabla f ) \ dv = \oint f\vec{A} \cdot \ d\vec{a}$$ ? Homework EquationsThe Attempt at a Solution I understand that the integrand can...

The Fundamental Theorem of Quantum Measurements (see page 25 of these PDF notes) is given as follows: Every set of operators ##\{A_n \}_n## where ##n=1,...,N## that satisfies ##\sum_{n}A_{n}A^{\dagger}_{n} = I##, describes a possible measurement on a quantum system, where the measurement has...

I've published a paper on local hidden variables with surprising consequences for Bells Theorem. It is available on https://doi.org/10.1515/phys-2017-0106 The journal Open Physics is listed in T/R. To the background of Bell's argument, the following comments: Since Bell published his theorem...

Homework Statement 1. Homework Statement [/B] https://ibb.co/b263Pw Homework Equations [/B] Use thevenin method to find the intensity between A and B The Attempt at a Solution Well I tried a easier method but I just can't find the same answer[/B]

Some books argue that typical coordinate transformations such as space translations and rotations are represented in quantum mechanics by unitary operators because the Wigner's theorem. However I do not find any clear proof of this. For instance, suppose 1D for the sake of simplicity, by...

My question is, what is the BGV theorem? and what exactly does it say? I was watching A debate on cosmology where William Lane Craig uses the Borde, Guth and Vilenkin theorem to say the universe had a beginning. I was wondering if someone could possibly explain the case of the BGV theorem and...

I'm self-studying A Book of Abstract Algebra, 2nd ed, by Pinter and I have two questions. First, the author says to consider the situation where ##K## and ##K'## are finite extensions of ##F##, and furthermore that ##K## and ##K'## have a common extension ##E##. Then he goes on to prove that if...

I don't know much about classical physics(such as lagrangian function), but as i was reading conservation of energy, i came to this theorem and it tells that if a system is symmetrical in certain transformations(such as translation, rotation etc) then it will have a corresponding law of...

I've been looking at the original work of Noether and I'm confused about this point. The transformation of fields and coordinates are supossed to form a group, then how the inverse of $$B^{\mu}=B^{\mu}(A^{\mu},\partial A^{\mu}/\partial x^{\nu},x^{\mu},\epsilon) $$...

The theorem says The probability that an event B occur after A has already occurred is given by P(B/A) =P(A intersection B) /P(A) But applying thus to a problem like the probability of occurrence of all 3 tails on 3 coins when tossed if 1 tail has already occurred is P(B/A) =(1/8)/(7/8)=1/7...

Hey! :o With appropriate conditions, I want to show that $$\iiint_{\Omega}(\nabla \phi)\cdot \textbf{f}\ dV=\iint_{\Sigma}\phi\textbf{f}\cdot \textbf{N}\ dA-\iiint_{\Omega}\phi\nabla\cdot \textbf{f}\ dV$$ With appropriate conditions, I want to prove Green's identities...

Homework Statement What is the remainder when -3x^3 + 5x - 2 is divided by x? The Attempt at a Solution Not sure how to complete this one, I would assume that it is the same as x+0? How would you divide the last term, (-2). Please show your steps as this will help me a lot! Thanks!

Hey! :o Using Gauss theorem I want to calculate $\iint_{\Sigma}f\cdot NdA$, where $\Sigma$ is the closed boundary surface of the pyramid with vertices $(0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0)$ and $f(x,y,z)=(x^2y, 3y^2z, 9xz^2)$ and the perpendicular vectors $N$ to the inside of the...

Hello, The well known no-clone theorem states that it is impossible to exactly copy the quantum state of a system. The explanation seems to reside in the uncertainty principle... But, for example, if we measure a photon with known polarization (say vertical) with a vertical linear polarizer...

Hey! :o I want to calculate $\int_{\sigma}\left (-y^3dx+x^3dy-^3dz\right )$ using the fomula of Stokes, when $\sigma$ is the curve that is defined by the relations $x^2+y^2=1$ and $x+y+z=1$. Is the curve not closed? Because we have an integral of the form $\int_{\sigma}$ and not of the form...

Homework Statement Show that Egoroff's theorem continues to hold if the convergence is pointwise a.e. and ##f## is finite a.e. Homework Equations Here is the statement of Egoroff's theorem: Assume that ##E## has finite measure. Let ##\{f_n\}## be a sequence of measurable functions on ##E##...

I have recently learned a bit about the Osterwalder-Schrader theorem. From my understanding, this tells you when a Euclidean path integral can be analytically continued to a valid relativistic Hermitian quantum field theory (one needs reflection positivity etc.). I am curious about...

Homework Statement A circular disc of radius 25 cm and mass 0.5 kg is revolving in its plane with an angular velocity of 4 radians per second. Find A) its kinetic energy of rotation, and B) its new angular velocity if a mass of 10 kg is suddenly fixed on the rim of the disc. Homework...

Here is problem I quickly made up: Suppose there is a ramp with a height of 6 meters and length of 12 meters. A block of 5 kg is pushed up to the top of the ramp with a constant velocity. The force of friction is 15 N. Here's the confusion: By using the non-conservative force work energy...

Homework Statement Evaluate the line integral of (sin x + y) dx + (3x + y) dy on the path connecting A(0, 0) to B(2, 2) to C(2, 4) to D(0, 6). A sketch will be useful. Homework Equations Sketching the points, I have created a parallelogram shape. I also know that green's theorem formula, given...

Homework Statement Homework Equations There are 5 equations we can use. We have the fact that Lagrangian is a constant for an affinely parameterised geodesic- 0 in this case for a light ray : ##L=0## And then the Euler-Lagrange equation for each of the 4 variables. The Attempt at a Solution...

Hi there, I hold an engineering degree and I was just reviewing a page on Wikipedia. This image specifically demonstrates the impossibility of two theoretical heat engines having different efficiencies between two heat reservoirs. The full Wikipedia page can be found...

I understand that momentum, rest mass and energy can be put on the sides of a right triangle such that the Pythagorean Theorem suggests E^2=p^2+m^2. I understand that the Dirac equation says E=aypy+axpx+azpz+Bm and that when we square both sides the momentum and mass terms square while the cross...

Homework Statement Use Green's Theorem to find the area of the region between the x-axis and the curve parameterized by r(t)=<t-sin(t), 1-cos(t)>, 0 <= t <= 2pi Attached is a figure pertaining to the question Homework Equations [/B] The Attempt at a Solution Using the parameterized...

Homework Statement Hi I am trying to derive an expression for the deflection in a cantilever beam using castigliano's theorem. I have found and attached an example of the solution. I understand the most of what is going on in the attached solution but I don't know where the b^3 came from in the...

Hi I am trying to derive an expression for the deflection in a cantilever beam using castigliano's theorem. I have found and attached an example of the solution. I understand the most of what is going on in the attached solution but I don't understand where the b^3 came from in the last line.

Homework Statement You have inherited a tract of land whose boundary is described as follows. ”From the oak tree in front of the house, go 1000 yards NE, then 1200 yards NW, then 800 yards S, and then back to the oak tree. Homework Equations Line integral of Pdx + Qdy = Double integral 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 an aspect of the proof of Theorem 1.4 ... ... Theorem...

Hello, the work-kinetic energy theorem only considers kinetic energy KE and not potential energy PE. This theorem states that the work done by any force, be it conservative or non conservative, is equal to the change in kinetic energy of the body. I know that potential energy cannot be...

Hello! I am reading this paper and on page 9 it defines the De Rham's period as ##\int_C \omega = <C,\omega>##, where C is a cycle and ##\omega## is a closed one form i.e. ##d\omega = 0##. The author says that ##<C,\omega>:\Omega^p(M) \times C_p(M) \to R##. I am a bit confused by this, as...

I can't find the zeros to $$4x^5-10x^4-14x^3+49x^2-28x+4$$ I found my positive zeros, 2, 1/2 using synthetic division and possible zeros. But from there I'm stuck.

Does anyone know where I can find a proof of this theorem? Theorem: The Euclidean space ##\mathbb{R}^2## is not the union of nondegenerate disjoints circles.

I am reading John B. Conway's book, "Functions of a Complex Variable I" (Second Edition) ... I am currently focussed on Chapter III Elementary Properties and Examples of Analytic Functions ... Section 2: Analytic Functions ... ... I need help in fully understanding aspects of Theorem 2.29 ...

Homework Statement Show that the virial theorem holds for all harmonic-oscillator states. The identity given in problem 5-10 is helpful. Homework Equations Identity given: ∫ξ2H2n(ξ)e-ξ2dξ = 2nn!(n+1/2)√pi P.S the ξ in the exponent should be raised to the 2nd power. So it should look like ξ2...

To help me with this question, I think you'll need to have access to the proof, it's pretty involved and technical. I'm going the proof found in John M. Lee's "Introduction to topological manifolds", but I suspect that the proof will be the same no matter where you find it. Let ##U,V## be the...

Every even integer that is the square of an integer is a multiple of four. Prove by Contritidiction. Assume that n is even and n is square. I am lost to do next.

Hello, I am confused about the work energy theorem. If someone goes up the stairs at a constant velocity, is work being done on the person? After all, Wnet = change in kinetic energy, and that change is zero. This is the original problem that I am trying to solve, from David Morin's Problems...

Homework Statement If ##\{K_\alpha\}## is a collection of compact subsets of a metric space X, such that the intersection of every finite subcollection of {##K_\alpha##} is nonempty, then ##\cap K_\alpha## is nonempty. Generalize this theorem and proof the generalization. Why doesn't it make...

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...