Theorem Definition and 1000 Threads

Homework Statement Carnot theorem states that no engine working between two temperatures T1 of source and T2 of sink can have a greater efficiency than that of the Carnot engine. Second law of thermodynamics:it is impossible for a self acting machine to transfer heat from a body at a higher...

I cannot understand the the relation between Reynolds Transport Theorem and Volume Calculation. Volume calculation is an simple, straightforward process which, I think, have much connection between Reynolds Transport Theorem. We calculate volumes in thermodynamics, heat transfer and fluid...

Homework Statement Suppose that there are long-range interactions between atoms in a gas in the form of central forces derivable from a potential. $$V(r) = \frac k r^m $$ where r is the distance between any pair of atoms and m is a positive integer. Assume further that relative to any given...

I have encountered this theorem in Serge Lang's linear algebra: Theorem 3.1. Let F: V --> W be a linear map whose kernel is {O}, then If v1 , ... ,vn are linearly independent elements of V, then F(v1), ... ,F(vn) are linearly independent elements of W. In the proof he starts with C1F(v1) +...

I am reading Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with an aspect of the proof of Theorem 7.1.10 ...Theorem 7.1.10, and the start of its proof, reads as follows: In the above text from...

I am reading Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with an aspect of the proof of Theorem 7.1.10 ...Theorem 7.1.10, and the start of its proof, reads as follows: In the above text from...

I have proved for myself the following theorem, generalizing Galois theorem to general algebraic extensions. My question is: is it true, and is there some reference to this theorem in the literature? Theorem: Recall that a subfield ##M## of a field ##L## is a perfect closure in ##L## if there...

I am now looking at a physics problem that should be a use of stokes' theorem on a torus. The picture (b) here is a torus that the upper and bottom sides are identified as the same, so are the left and right sides. ##A## is a 1-form and ##F = dA## is the corresponding curvature. As is shown in...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 42: Field Extensions and Kronecker's Theorem ... I need some help with an aspect of the proof of Theorem 42.1 ( Kronecker's Theorem) ... Theorem 42.1 and its proof read as follows...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 42: Field Extensions and Kronecker's Theorem ... I need some help with an aspect of the proof of Theorem 42.1 ( Kronecker's Theorem) ... Theorem 42.1 and its proof read as follows: In the above...

What is the most motivating way to introduce Wilson’s Theorem? Why is Wilson’s theorem useful? With Fermat’s little Theorem we can say that working with residue 1 modulo prime p makes life easier but apart from working with a particular (p-1) factorial of a prime what other reasons are there for...

What is the most motivating way to introduce Wilson’s Theorem? Why is Wilson’s theorem useful? With Fermat’s little Theorem we can say that working with residue 1 modulo prime p makes life easier but apart from working with a particular (p-1) factorial of a prime what other reasons are there for...

What is the best way to introduce Fermat’s Little Theorem (FLT) to students? What can I use as an opening paragraph which will motivate and have an impact on why students should learn this theorem and what are the applications of FLT? Are there any good resources on this topic?

What is the best way to introduce Fermat’s Little Theorem (FLT) to students? What can I use as an opening paragraph which will motivate and have an impact on why students should learn this theorem and what are the applications of FLT? Are there any good resources on this topic?

If we consider a transformation of a field ##\Phi \rightarrow \Phi + \alpha \frac{\partial \Phi}{\partial \alpha}## which is not a symmetry of a lagrangian then one can show that the Noether current is not conserved but that instead ##\partial_{\mu}J^{\mu} = \frac{\partial L}{\partial \alpha}##...

Homework Statement There is a planet (spherical) with a hollow that is concentric with the planet.if the inner radius is r and outer radius is R and mass of the planet is M what would the gravity be outside of the planet at distance x from the center ? Homework Equations Shell theorem...

Homework Statement :[/B] Homework Equations W= \integral(Fxdx) W = \delta KEThe Attempt at a Solution I used the definition of work to find the final velocity at 2m, and then work theorem together with integration for the changing force. I ended up having different solutions at first but...

Homework Statement Consider a cylindrical solenoid(of radius a,and length h>>a,having n turns of wire for unity of lenght),The solenoid is connected to a resistance R and,at instant t=0 a current i(0)=i0 is flowing in the wire.Prove that poynting's theorem is verified for t>0[/B]Homework...

In the virial theorem the numerical value of the average potential energy within a system is exactly twice that of the average kinetic energy. I know the theorem is proved mathematically but to me it seems a coincidence that one value is exactly twice the other value. I find that interesting. I...

How would one prove the Stokes' theorem for general cases? Namely that $$ \int_{\partial M} W = \int_M \partial W$$ where ##M## is the manifold.

Homework Statement Find the point "c" that satisfies the Mean Value Theorem For Derivatives for the function ## f(x) = \frac {x-1} {x+1}## on the interval [4,5]. Answer - c = 4.48 Homework Equations ##x = \frac {-b \pm \sqrt{b^2 -4ac}} {2a}## ##f'(c) = \frac { f(b) - f(a)} {b-a}## The Attempt...

Hi. I was trying to translate the divergence theorem and the Green's theorem to tensor notation that we use in Relativity. For the divergence theorem, it was easy (please tell me if I'm wrong in the below derivation). I'm using the standard electromagnetic tensor ##F_{\mu \nu}## in place of the...

Great article showing you're never too old to do math: https://www.quantamagazine.org/20170328-statistician-proves-gaussian-correlation-inequality/

Most discussions about Bell's theorem meaning get at some point entangled in semantic and philosophic debates that end up in confusion and disagreement. I wonder if it could be possible to avoid this by reducing the premise, the basic assumption to its bare-bones math content in algebraic/group...

I am doing a panel study with multiple linear regression. When I want to make sure that the residuals are normally distributed, as is a requirement for the regression model, can I assume so due the Central limit theorem (given the size is sufficient)? Or does it not apply when there is a time...

Homework Statement Homework EquationsThe Attempt at a Solution The correct answer is 0.25V. I'm getting 0.3335V[/B]

im trying to use angles on the same arc theorem

Homework Statement Verify the Divergence Theorem for F=(2xz,y,−z^2) and D is the wedge cut from the first octant by the plane z =y and the elliptical cylinder x^2+4y^2=16 Homework Equations \int \int F\cdot n dS=\int \int \int divF dv The Attempt at a Solution For the RHS...

Homework Statement Find all the numbers c that satisfy the conclusion of the Mean Value Theorem for the functions f(x)=\dfrac{1}{x-2} on the interval [1, 4] f(x)=\dfrac{1}{x-2} on the interval [3, 6] I don't need help solving for c, I just want to know how I can verify that the hypotheses of...

Homework Statement Can somebody explain to me how the first two steps are performed? The Attempt at a Solution I have no idea how to start the question. I tried using an equation for sin^6 x derived by (cos x + i sinx)^6 = cos 6x+isin 6x but the solution becomes way too hard.

Homework Statement Please see the following,I am confused by the word "only". Homework EquationsThe Attempt at a Solution I understand that the Compatibility theorem ensures we can find a basis of common eigenfunctions of \hat{A} ,\hat{B}.If each pair of eigenvalues {A_i,B_j} identifies...

It says that there is no value of a,b and c, with n>2 and all integer numbers that satisfies this: a^n=b^n+c^n I'm only going to use the cosine theorem. Let's consider three points A, B and C. They form the three sides of a triangle: a, b and c. The sides forms three angles, which can go from...

Background: I am taking an undergraduate fluid mechanics class. I seem to have a misunderstanding with my interpretation of Reynolds Transport theorem (RTT), which I have written below: $$\frac{DB_{sys}}{Dt} = \frac{\partial}{\partial t}\int_{CV}\rho bd V +\int_{CS}\rho b \vec{V}\cdot...

Anybody know how calculate the noise with equipartition theorem method? For a simple RC one order filter. The noise charge across the capacitor is Q. we have 1/2*k*T=1/2*C*(Q/C)^2 For a more complicated network as below. Can you help me on how to calculate the total noise charge or voltage...

Homework Statement A 2.90 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0360 m . The spring has force constant 860 N/m . The coefficient of kinetic friction between the floor and the block is 0.35 . The block and spring are released from rest...

In your opinion did Fermat have a proof for his theorem?

Homework Statement Verify Stokes' theorem ∫c F • t ds = ∫∫s n ∇ × F dS in each of the following cases: (a) F=i z2 + j y2 C, the square of side 1 lying in the x,z-plane and directed as shown S, the five squares S1, S2, S3, S4, S5 as shown in the figure. (b) F = iy + jz + kx C, the three...

Hello! I looked over a proof of Noether theorem and I am a bit confused about the last step. So they got that ##\delta q(t) p(t)## is constant (I just took the one dimensional case here) where ##\delta q## is a variation of the q coordinate and p is the momentum conjugate of q. I am not sure I...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.7 (Fermat's Little Theorem) ... Theorem 8.7 and its proof read as follows...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.7 (Fermat's Little Theorem) ... Theorem 8.7 and its proof read as follows: My questions regarding...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.6 ... Theorem 8.6 and its proof read as follows: In the above text, Anderson and Feil write the...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 8: Integral Domains and Fields ... I need some help with an aspect of the proof of Theorem 8.6 ... Theorem 8.6 and its proof read as follows: In the above text, Anderson and Feil write the...

One thing I find frustrating when trying to get a handle on this theorem is the number of different forms presented in the literature. I understand this to be due to it being very general theorem applicable to many different contexts. Not that the world needs a new, slightly different looking...

How can I derive that the work of a force perpendicular to velocity is always zero from the theorem of Noether? I have heard that there is a relation between these two but in Google I found nothing. Thank you very much

Homework Statement The sixth term of the expansion of (x-1/5)n is -1287/(3125)x8. Determine n. Homework Equations tk+1=nCkan-kbk The Attempt at a Solution tk+1=nCkan-kbk t5+1=nC5(x)n-5(-1/5)5 This is where I'm stuck. Do I sub in -1287/(3125)x8 to = t6? If so what do I do from here...

Homework Statement 1. Given the binomial (x2-x)13determine the coefficient of the term of degree 17. Answer = -715 2. Given the binomial (2x+3)10 determine the coefficient of the term containing x7. Answer = 414720 2. Homework Equations tk+1=nCkan-kbk The Attempt at a Solution #1 - What...

Whittaker (1st Edition, 1902) P.132, gives two proofs of Fourier's theorem, assuming Dirichlet's conditions. One proof is Dirichlet's proof, which involves directly summing the partial sums, is found in many books. The other proof is an absolutely stunning proof of Fourier's theorem in terms of...

Hi everyone, I use Wick's theorem to decompose expectation values of a string of bosonic creation and annihilation operators evaluated at the vacuum state. This can only be done when the time evolution is driven by a Hamiltonian of the form: H=\sum_{i,j}{\epsilon_{i,j} c^{\dagger}_{i}c_{j}}...

Hello, does anyone have reference to(or care to write out) fully rigorous proof of Stokes theorem which does not reference Differential Forms? I'm reviewing some physics stuff and I want to relearn it. I honestly will never use the higher dimensional version but I still want to see a full proof...

Homework Statement find the number of polynomials f(x) that satisfies the condition: f(x) is monic polynomial, has degree 1000, has integer coefficients, and it can divide f(2x^3 + x) i would very much prefer that you guys give me hints first. thanks Homework Equations remainder factor theorem...