Finite Definition and 1000 Threads

ive been given this question for a uni assignment: given the function: f (x) = 5(x^1.3) +1.5(7x − 3)+ 3(e^− x) + ln(2.5(x^3)) find the first derivative at all possible points within the interval [0, 6], with step length h = 1 for: forward difference aproximation, backward difference...

Does anyone know how to prove that any irreducible representation of a finite group G has degree at most |G|? Equivalently, that every representation of degree >|G| is reductible. Thx!

I am on a research project where I am finding the heat capacitance and thermal conductance of a material and would like to simulate it on a larger scale as material for heated flooring. Is there a program where I can do a looping heating pipe at a set temperature and show the conductance of the...

Homework Statement Assuming the mapping Z --> F defined by n --> n * 1F = 1F + ... + 1F (n times) is a ring homomorphism, show that its kernel is of the form pZ, for some prime number p. Therefore infer that F contains a copy of the finite field Z/pZ. Also prove now that F is a finite...

Homework Statement Let H be a finite subgroup of a group G. Verify that the formula (h,h')(x)=hxh'-1 defines an action of H x H on G. Prove that H is a normal subgroup of G if and only if every orbit of this action contains precisely |H| points. The Attempt at a Solution I solved the first...

Homework Statement If G is a finite group which acts transitively on X, and if H is a normal subgroup of G, show that the orbits of the induced action of H on X all have the same size. The Attempt at a Solution By the Orbit-Stabilizer theorem the size of the orbit induced by H on X is a...

Is there a distance where the curvature in spacetime created by an object's mass ends? Is it a finite gravity well or does the curvature just get infinitely weaker?

Does the 'Pauli exclusion principle' imply that the universe is only finitely creative? It's rather the philosophy than the physics behind it, I'm interested in. I just wanted to be sure I was interpreting this principle correctly. I thought it meant that there are only a discrete amount of...

Hi I have a question regarding unitary operators: If an infinitesimal operation (such as a rotation) is unitary does this guarantee that a finite transformation will also be unitary? thanks M

I found this problem, and I was wondering if I'm on the right approach. Let G be a finite group on a finiste set X with m elelements. Suppose there exist a g\inG and x\inX such that gx not equal to x. Suppose the order of G does not divide m!. Prove that G is not simple. Would it suffice...

When finding the angles for the finite length Biot-Savart formula of a filamentary conductor H = I*(cos(α2) - cos(α1))aΦ/(4πρ), is α1 supposed to be calculated at the start of the current, and α2 at the end? I'm just wondering because my book does it this way and vice-versa, so I'm not entirely...

If you make the length of a finite well shorter, then the energy levels should increase, because for example the uncertainty principle. But can the ground state, when squeezed, have such high energy that the energy is greater than the potential of the well? Does that even make sense?

I just started learning some basic measure theory. Could someone explain the difference between \overline{F(A \times A)} and \overline{F(A) \times F(A)} where A is a finite set. Also, how would this be different in A was an countably infinite set? Thanks!

I just started learning some basic measure theory. Could someone explain the difference between \overline{F(A \times A)} and \overline{F(A) \times F(A)} where A is a finite set. Also, how would this be different in A was an countably infinite set? Thanks!

please forgive my ignorance but, i was watching somthing in tv the other day about supermasive black holes, now my question is, if some black holes are more massive than others, how can their mass be infinite? if Blackhole A is more massive than black hole B then surly they can't both be...

I have to write a FD expilicit method, for temp dist on 2D plane. I am trying to mod the 1D solver to 2D solver, the code below is a 1D solver. Any possible suggestions how it can be done? I initially, derived u(i,j+1) for 2D for in that derivation i,j corresponds to x,y... where as in 1D...

Hello everyone: I am a C++ newbie; I am interesting in using C++ in my work on coupled fluid flow-chemical reaction problems. I apologize in advance for what is probably a very simple question. I would very much appreciate any help to get me on the right track! My goal is to come up with...

Homework Statement A rod with length L and section A has its extremities in contact with 2 springs of heat whose temperatures are T_A and T_B such that T_A>T_B. The rod is an environment where the temperature is worth T_0 (constantly). a)Determine the function T(x) that describes the...

Add slack variables or subtract surplus variables, and set up the initial simplex tableau: Maximize z = 5x1 + 3x2 subject to: 2x1 + 5x2 ≤ 50 x1 + 3x2 ≤ 25 4x1 + x2 ≤ 18 x1 + x2 ≤ 12 with x1≥0, x2 ≥ 0 Please help.

A set S is countable if it is either finite or denumerable. What I don't understand is why S can be finite but not denumerable. Could anyone give an example?

meaning of "vanishes outside a set of finite measure" What does it mean when we say that a function vanishes outside a set of finite measure? As in the definition of the integral as a prelude to the Lebesgue integral in Royden's Real Analysis, 3rd ed. (p. 77). It said: If \phi vanishes...

Homework Statement I know this is probably fairly trivial, but for the life of me I cannot remember or reconstruct the proof for the proposition, "The sum of the lengths of a finite number of overlapping open intervals is greater than the length of their union." Homework Equations Not...

Homework Statement I am trying to find the coefficients in a Schrodinger equation approaching a finite potential. https://www.physicsforums.com/showthread.php?t=203385 It is a problem similar to this, except a little easier. In my case, though, there is no V1 as shown in the picture at the...

1. Homework Statement [/b] See attached 2. Homework Equations See attached 3. The Attempt at a Solution I know the answer is 6 or zero... but I can't figure out how to "show" this. When typing this equation into my calculator, I can clearly see that the number always ends in .0...

Homework Statement Let G be a finite group and H a subgroup of G having order m. Show that if H is the only subgroup of order m in G, then H is normal in G. Homework Equations A subgroup H of G is normal in G if and only if xHx^{-1} \subseteq H \forall x \in G The Attempt at a...

Homework Statement I want a general equation for the finite sum of n0 + n1 + n2... starting at n = 0 for the equation t = 64/(165+3n) so i have a sum of numbers: 64/165 + 64/168 + 64/171... i don't want you to think i am lazy and don't show work but this isn't for school. i want to figure...

Let S be a subspace of L^{2}(\left[0,1\right]) and suppose \left|f(x)\right|\leq K \left\| f \right\| for all f in S. Show that the dimension of S is at most K^{2} --------- The prof hinted us to use Bessel's inequality. Namely, let \left\{ u_1,\dots, u_m \right\} be a set of...

Homework Statement Prove that the group of order 175 is abelian. Homework Equations The Attempt at a Solution |G|=175=527. Using the Sylow theorems it can be determined that G has only one Sylow 2-subgroup of order 25 called it H and only one Sylow 7-subgroups called it K. Thus...

I'm trying to write a program to simulate the fields generated by a solenoid but I've hit a bit of a brick wall. There is a vast amount of examples and information on the field generated inside a solenoid however they all assume that the field outside is negligible and as such I have been having...

Suppose A is a finite abelian group and p is a prime. A^p={a^p : a in A} and A_p={x:x^p=1,x in A}. How to show A/A^p is isomorphic to A_p. I tried to define a p-power map between A/A^p and A_p and show this map is isomorphism. But my idea didnot work right now. Please give me some help. In...

Homework Statement If a finite connected graph G has minimal degree k, show there exists a path x_1, x_2, x_3,..., x_k so that G-{x_1,x_2,...,x_k} is still connected Homework Equations Minimal degree means every vertex has k or more edges connecting to it The Attempt at a Solution...

For a particle in finite potential well we can have several bound states depending on the height of potential well. Each bound state corresponds to definite energy En. Then corresponding to Each definite Energy there should be definite Momentum Pn. Since we have definite momentum--->...

Homework Statement this is part of a theorem for the error estimate for the model problem for finite element method. i have to prove the following inequality: \left|u'(x)-\tilde{u}'_h(x)\right|\leq max_{0\leq(y)\leq1}\left|u''(y)\right| Homework Equations \tilde{u_h} is the...

Homework Statement If G is a finite group and g is in G, then there exists a positive integer r with g^r=e. and in general, prove that, in any finite group G, the inverse of each element is a power of itself. Homework Equations The Attempt at a Solution I know if a group is...

I am trying to prove that there is always one bound state for a finite square well using variational method, and I am stuck. I've tried using e^(-bx^2) as my trial wave function, but I am left with E(b)=(hbar^2)b/2m - V, where V is the depth of the well. In this equation, taking the derivative...

Homework Statement Give an example of an open cover in R^n which has no finite subcover. Homework EquationsThe Attempt at a Solution {x ε Q | x < sqrt(3)} U {x ε Q | x > sqrt(3) }

Homework Statement This problem is insanely intuitive. Define f : (0,1) \rightarrow \Re by f(x)=\begin{cases} 1/q&\text{if } x \neq 0 \text{, is rational, and }x = p/q \text{in lowest terms}\\ 0&\text{otherwise }\end{cases} Suppose \epsilon > 0. Prove that there are at most a...

Homework Statement for n\inN and \phi: {1,...,n} \rightarrow {1,...,n}. Prove \phi is 1-1 if and only if it is onto. The second part of this is to prove that if E is a finite set and f:E\rightarrowE then f is 1-1 iff f is onto. Homework Equations There are several (many) theorems...

Hello, I was just reading about implicit vs explicit finite element solvers and have a question about the difference between them. I understand that the implicit solver has a linear approximation step that is used to force equilibrium. My question is does that make the explicit solver...

Hi all. I have here a reference with a representation of the Lie algebra of my symmetry group in terms the fields in my Lagrangian. In order to calculate Noether currents, I would like to use this representation to derive formulae for the infinitesimal forms of the symmetry transformations...

Homework Statement Express the 3D charge density \rho for a thin wire with length Z and uniform linear charge density \lambda along the z-axis in terms of a two-dimensional dirac-delta function. Homework Equations The three dimensional charge density is the total charge over a...

Homework Statement Express the 3D charge density \rho for a thin wire with length Z and uniform linear charge density \lambda along the z-axis in terms of a two-dimensional dirac-delta function.Homework Equations The three dimensional charge density is the total charge over a volume.The...

I am trying to make a program that solves elasticity problems with finite element method and I don't understand how to bring in boundary conditions. Constant displacement boundary conditions seem simple: replace variables that represent the displacements at surface nodes with the prescribed...

I'm relatively new to calculus, and this question was bugging me, so I have decided to ask it. We have the function y=1/x with domain x\geq1 and we rotate the curve around the x-axis in order to form a solid of revolution. (Gabriel's Horn) The integral is V=\pi\int^{z}_{1}1/x^2 dx and we...

Homework Statement Let G be a finite group and let I ={g in G: g^2 = e} \ {e} be its subset of involutions. Show that G is abelian if card(I) => (3/4)card(G). Homework Equations The Attempt at a SolutionI don't really know how to proceed with this problem and to make use of 3/4. I know that...

Is every finite metric space imbeddable in a manifold? That is, for every finite metric space (X,d), does there exist some manifold such that there are |X| many points on it which is isometric (with the length of geodesics as metric) to (X,d)?

Homework Statement A rod of length 25 cm has a uniform linear charge density of 7 μC/m. Determine the Electric Field at a point P located at a perpendicular distance 69 cm along a line of symmetry of the rod. Homework Equations E=k*charge density(integral(dx/(d^2+x^2)^3/2) The...

How do I use the finite difference method with M = N = 20 to obtain a plot of the solution of \nabla2u = 1, 0 < x < 1, 0 < y < 1, u(x,0) = x(1-x), u(x,1) = x(1-x), 0 \leq y \leq 1, u(0,y) = 0, u(1,y) = 0, 0 \leq y \leq 1.

I have a question. I’m 74 and have taught science to high school students for much of my life. I only have a lowly Bachelor of Education degree so my knowledge of the subject is pretty limited. I did manage to get through a second year physics class, though. Since retiring I have read Brian...

Hello, As we know, the wave function of infinite potential wells form a complete orthogonal base. I have tried now to solve out the wave function for finite potential well, checking the orthogonality, I found that they are no longer orthogonal to each other (I mean the wave function...