Theorem Definition and 1000 Threads

Homework Statement The moment of inertia for a perpendicular axis through the center of a uniform, thin, rectangular metal sheet with sides a and b is (1/12)M(a2 + b2). What is the moment of inertia if the axis is through a corner? The answer is given as this was a powerpoint lecture and it...

Homework Statement Find the remainder of ##4^{87}## in the division by ##17##. Homework Equations Fermat's Little Theorem: If ##p## is prime and ##a## is an integer not divisible by ##p##, then ##a^{p-1} \equiv 1 (\mod \space p)## or equivalently, ##a^p \equiv a (\mod \space p)## The...

Hello! I am a bit confused about the first Sylow theorem. So it says that if you have a group of order ##p^mn##, with gcd(n,p)=1, you must have a subgroup H of G of order ##p^m##. So, if I have a group G of order ##p^k##, there is only one subgroup of G of order ##p^k## which is G itself. Does...

Hello! (Wave) We consider the following problem. $$Lu=f(x) \text{ in } \Omega \\ u|_{\partial{\Omega}}=0$$ I want to show that if $c(x) \leq -c_0<0$ in $\overline{\Omega}$, then it holds that $\min\{ 0, \frac{\min_{\Omega}f(x)}{-c_0}\}\leq u(x) \leq \max_{\Omega} \{ 0...

Liouville's theorem states that the total time-derivative of the distribution function is zero along a system trajectory in phase-space. Where the system follows a trajectory that satisfies the Hamilton's equations of motion. I have a hard time getting an inuitive understanding of this...

Homework Statement Homework Equations Green's theorem The Attempt at a Solution DO I first parametrize? For 1st part, I have 3 parametrizations, which I can then find the normal vector, and use in the integrals?

Hawking area theorem says that area of black hole generally never decrease. Penrose process says that energy can be extracted from black hole. Energy extraction will decrease mass? if yes then if mass is decreased then will area also decrease? I am confusing things here :(

According to DeMorgan’s theorem (break the bar and change the sign), the complement of ܽa⋅b+c⋅d is a'+b'⋅c'+d' Yet both functions are 1 for ܾܽܿ abcd 1110. How can both a function and its complement be 1 for the same input combination? What’s wrong here?I honestly have no idea. I mean, shouldn't...

I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis ... ... I am currently focused on Garling's Section 1.7 The Foundation Axiom and the Axiom of Infinity ... ... I need some help with Theorem 1.7.4 ... and in particular with...

Homework Statement (See attachment: if it doesn't work, see below for poorer formatting)[/B] Theorem 6.1 (Centered Formula of Order O(h2)). Assume that f ∈ C^3[a, b] and that x − h, x, x + h ∈ [a, b]. Then (3) f (x) ≈ f (x + h) − f (x − h) 2h . Furthermore, there exists a number c = c(x) ∈ [a...

I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis ... ...At present I am focused on Chapter 1: The Axioms of Set Theory and need some help with Theorem 1.2.2 and its relationship to the Separation Axiom ... ... The...

I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis" ... ... At present I am focused on Chapter 1: The Axioms of Set Theory and need some help with Theorem 1.2.2 and its relationship to the Separation Axiom ... ... The...

Why is it possible that ∫∫∫ V f(r) dV ≠ 0 even if f(r) =0

Obviously ##\mathbb{R^2}## is convex, that is, any points ##a,b\in\mathbb{R^2}## can be connected with a line segment. In addition, ##f## is differentiable as a composition of two differentiable functions. Thus, the conditions of mean value theorem for vector functions are satisfied. By applying...

[FONT=Arial Black]The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. μx̄ = μ = 12,749 σ = 1.2 n = 35 For the given sample n = 35, the probability of a sample mean being less than...

I am wondering is someone could comment on a question I have recently answered. I have attached the question and my answer. Apologies for not following the standard procedure of Latex but there are drawings associated with this question. I answered section A and my results are written on the...

Homework Statement Using paper, pencil and the Virial theorem, calculate the position uncertainty (an estimate of the vibration amplitude) of the H atom in its ground state C-H stretching mode. In more precise language, calculate the bond length uncertainty in a C-H bond due to the C-H...

Homework Statement Using the maximum power transfer theorem, find the value of R which will result in the maximum power being delivered to R. Homework Equations P_max= (V_oc)^2/4(R_th)) R_L=R_th P_RL=(V_th/(R_th+R_L))^2*R_L The Attempt at a Solution I have no clue where to even begin with...

I am having trouble doing this problem from my textbook... and have no idea how to doit. 1. Homework Statement I am having trouble doing this problem from my textbook... Show that the equation x + y - z + cos(xyz) = 0 can be solved for z = g(x,y) near the origin. Find dg/dx and dg/dy (dg/dx...

I know that for rigid bodies only the work-energy theorem states that the net work done on the body equals the change in kinetic energy of the body since a rigid body has no internal degrees of freedom and hence no other forms of energy such as potential energy. Is there a most generalized form...

Homework Statement Homework Equations Parallel axis theorem: Ip = Icm + Md^2 Icm = I = ML²/12 + 2 * mr² 3. The attempt Ip = Icm + Md^2 ==> wrong I = Md^2 ==> right Why don't I need to add "Icm"? Thanks.

Hello everyone. I need help on proofs. I have to proof the Angle-Angle-Side theorem. Can someone help me with this? The AAS states : If triangles ABC and DEF are two triangles such that angle ABC is congruent to angle DEF, angle BCA is congruent to angle EFD, and segment AC is congruent to DF...

Homework Statement I need to accommodate a dashpot in an intentionally simple work-kinetic energy analysis method. For example, for a box being dragged up a ramp via a rope while attached to a spring, I can deal with the work done by gravity, rope tension, spring force, and friction via the...

Hi I need a little help in my homework. It is not a direct problem to be solved. Rather I am supposed to find an application of Noether's theorem. All the article or papers I have found are very difficult for me to understand. In fact, I still don't understand any application of Noether's...

Homework Statement Use the Intermediate Value Theorem to prove that any continuous function with domain [0,1] and range in [0,1] must have a fixed point. Homework Equations Intermediate Value Theorem (IVT) states that if a function ##f(x)## of domain [##a,b##] takes values ##f(a)## and...

Hi, I wonder why wronskian must be constant. I know that p(x)W[u1(x),u2(x)]=constant, according to the Abel's theorem, but wouldnt there a special case that W[u1(x),u2(x)]=c/p(x). Then for this special case, W[u1(x),u2(x)]=/=c and satisfies Abel's theorem. Is it ok to ignore this special case?

I'm curious if anyone has ever simulated the infinite monkeys on typewriters using a computer, and managed to generate short sentences or phrases that have appeared in books/print media before. That would demonstrate the effectiveness of the infinite monkey theorem.

Hi All, I would like to know if is there any problem to present and prove a theorem and a Lemma (in this order) and after that use this theorem and this lemma to prove a corollary (which is simpler to prove and not so important as the theorem). I have looked up in some papers but with no...

I have been curious for some time, does the incompleteness theorem of mathematics have any consequences in physics? In order that I may understand your response you should know I'm was a senior math major at the university when last I was in school and my only physics background is the standard...

Hello,I had a discussion with my professor. He tried to convince me but I couldn't understand the idea. The Stokes Theorem (Curl Theorem) is the following: My professor says that the value of the equation should be zero whenever the area of integration is closed! (which will make a volume in...

Homework Statement An employee goes to work from 9 am to 4 pm. He takes a nap for an average of 2 hours if he starts napping before 1 pm and naps for an average of 1 hours if he starts napping after 1 pm. His boss randomly checks up on him once during his shift. If his boss finds him napping...

I was looking at the proof of Lagrange's theorem (that the order of a group ##G## is a multiple of the order of any given subgroup ##H##) in Wikipedia: I understand this proof fine, but I was wondering, instead of finding a bijection between cosets, is it enough to find a bijection between an...

I have read a proof but I have a question. To give some context, I first wrote down this proof as written in the book. First, I provide the recursion theorem though. Recursion theorem: Let H be a set. Let ##e \in H##. Let ##k: \mathbb{N} \rightarrow H## be a function. Then there exists a...

I wonder why projected area has been of much interest among physics communities, while the surface area could well be the solution unless any complex geometries are involved. The question popped up in my head when the surface tension in a water jet was derived. Clearly the jet has a circular...

If i have an arbitrary ket then i know it can always be expressed as a linear combination of the basis kets.I now have an operator A which has 2 eigenvalues +1 and -1. The corresponding eigenvectors are | v >+ = k | b > + m | a > and | v >- = n | c > where | a > , | b > and | c > are...

Hi guys, So just wondering - the fact that the force is always the negative derivative of potential with respect to distance: F=-\dfrac{\partial V}{\partial x} Where does this come from and does it have a name or something? like a theorem perhaps? Thanks!

NO TEMPLATE BECAUSE MOVED FROM ANOTHER FORUM Hello, I've been trying to figure out how it works for complicated problems, I know how to use long division, but I'm not understanding how this process is done for a problem like I have. Instructions: Write the function in the form ƒ(x) = (x -...

Hello I am struggling with proving theorem 1, pages 98-99, in Spivak's Calculus book: "A function f cannot approach two different limits near a." I understand the fact that this theorem is correct. I can easily convince myself by drawing a function in a coordinate system and trying to find two...

Homework Statement Consider the Klein-Gordon equation ##(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0##. Using Noether's theorem, find a continuity equation of the form ##\partial_\mu j^{\mu}=0##. Homework Equations ##(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0## The Attempt at a Solution...

Hi, One silly thing is bothering me. As per one lemma, If a, b, and c are positive integers such that gcd(a, b) = 1 and a | bc, then a | c. This is intuitively obvious. i.e. Since GCD is 1 'a' does not divide 'b'. Now, 'a' divides 'bc' so, 'a' divides 'c'. Proved. What is bothering me is ...

Can someone please explain the progression of topics I would need to study in order to tackle Noether's Theorem? I keep hearing how important it is and am setting a self-study goal for myself to eventually understand it with enough rigour that I can appreciate it's beauty. I have a feeling I...

Homework Statement F(x) = (integral from 1 to x^3) (t^2 - 10)/(t + 1) dt Evaluate F'(x) Homework Equations Using the chain rule The Attempt at a Solution Let u = x^3 Then: [((x^3)^2 - 10) / (x^3 + 1)] ⋅ 3x^2 *step cancelling powers of x from fraction* = (x^3 - 10)(3x^2) = 3x^5 - 30x^2 I am...

Hi everybody! I'm currently studying Noether's theorem, but I'm a bit stuck around a stupid line of calculation for the variation of the symmetry. The script of my teacher says (roughly translated from German, equations left as he wrote them): "V.2. Noether Theorem How does the action change...

I am reading the book, Basic Abstract Algebra by P.B. Bhattacharya, S.K. Jain, and S.R. Nagpaul ... ... and am currently focused on Chapter 2: Integers, Real Numbers and Complex Numbers ... I need help with an aspect of the proof of the Fundamental Theorem of Arithmetic in Section 1.3 ... ...

I am reading the book, Basic Abstract Algebra by P.B. Bhattacharya, S.K. Jain, and S.R. Nagpaul ... ... and am currently focused on Chapter 2: Integers, Real Numbers and Complex Numbers ...I need help with an aspect of the proof of the Fundamental Theorem of Arithmetic in Section 1.3 ... ...The...

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 5.1 Prime Ideals and Maximal Ideals ... I need some help with understanding the proof of Theorem 5.12 ... ...Theorem 5.12 reads as follows: In the above text Rotman writes the following:"...

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 5.1 Prime Ideals and Maximal Ideals ... I need some help with understanding the proof of Theorem 5.12 ... ...Theorem 5.12 reads as follows: In the above text Rotman writes the following:"...

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 5.1 Prime Ideals and Maximal Ideals ... I need some help with understanding the proof of Proposition 5.9 ... ...Proposition 5.9 reads as follows: In the proof of Proposition 5.9, Rotman...

I am reading Joseph J. Rotman's book: Advanced Modern Algebra (AMA) and I am currently focused on Section 5.1 Prime Ideals and Maximal Ideals ... I need some help with understanding the proof of Proposition 5.9 ... ...Proposition 5.9 reads as follows: In the proof of Proposition 5.9, Rotman...

Bell's theorem states that super-luminal communication exists between particles that are separated by space-like separation viz. faster than light transmission of information. There is spontaneity in this. Relativistically this would amount to going back in time. The state of creation of...