Bound Definition and 476 Threads

Hello, I have the following determinant: \text{det}\left(\mathbf{A}\mathbf{A}^H\right) where H denoted complex conjugate transpose, and A is a circulant matrix. I am looking for a lower bound for the above determinant. Is there one? Thanks in advance

Greetings. Let's say we have a bound state problem: two micro black holes in orbit around one other. Let us disregard Hawking evaporation, and solve this problem. The usual way of solving this problem is to do so quantum-mechanically by employing the Schrodinger equation, deducting the...

Can anyone suggest an upper bound for e^{-x^2} that can be integrated easily?

Hello, I have this quantity: \frac{1}{\sum_{m=1}^NX_m^{-1}}\geq\frac{1}{N\underset{m}{\text{max }}X_m^{-1}}=\frac{\underset{m}{\text{min}}X_m}{N} Is that true?

In non-relativistic QM, we spend a lot of time examining bound states--energy levels, spatial distributions, and all that. We can determine that an electron put into a Coulomb potential will have certain Hamiltonian eigenstates, which correspond to the orbitals of a hydrogen atom. However, in...

Find the error bound of approximation of f using the cubic spline want to find a cubic spline for f on the interval [a,b] suppose we have n nodes with n-1 different intervals I tried to find it using the Taylor expansion around any nodes say x_i \in [a,b] f(x) - S(x) = f(x_i)-S(x_i) +...

Hi, Despite decades of searching magnetic monopoles haven't been found. Could it be that they are existing as bound states of a North and South monopole? One could model such states as a Bohr atom. It seems that the ground-state binding energy would be much more negative than the...

I often hear something to the extent of, 1) "despite cosmological expansion, small-bound objects do not expand." and further, 2) "things like galaxies will aways remain bound, and will not expand." Pertaining to 1) Because cosmological expansion is a coordinate property, don't small scale...

The definition of 'Bounded above' states that: If E⊂S and S is an ordered set, there exists a β∈S such that x≤β for all x∈E. Then E is bounded above. The 'Least Upper Bound Property' states that: If E⊂S, S be an ordered set, E≠Φ (empty set) and E is bounded above, then supE (Least Upper...

Homework Statement I'm dealing with a dirac particle in an attractive spherical square well. I've solved for the transcendental equation to find energy, found the normalized wave function, and now I'm trying to explain what happens when the well becomes very deep, when V0 ≥ 2mc2. If I plug...

Free particle --> bound particle Homework Statement A free neutron meets a finite square well of depth V_{0}, and width 2a centered around origo. However, the probability that the neutron emits a photon when it meets the potential well, and thus decreasing its energy is proportional to...

Homework Statement For the following set if it has an upper bound, find two different upper bounds as well as the least upper bound (LUB), justifying your answer. If the set has no upper bound, state this and justify your answer. {x | 1 < x < √(7) and x is irrational} (a proof requires the...

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

I see equations of the form, y=\int_{-\infty }^{t}{F\left( x \right)}dx a lot in my texts. What exactly does it mean? From the looks of it, it just means there is effectively no lower bounds. I looked up improper integrals, but I can't say I really understand what is going on. So when...

Is there a theoretical upper bound for the density of matter? Given a proton (already almost as dense as a black hole, according to Wikipedia), can you theoretically compress it into any non-zero volume? Has any work been done that shows that matter can or cannot achieve certain levels of...

Homework Statement Use the Archimedean property of \mathbb{R} to prove that the greatest lower bound of {\frac{1}{n}:n\in\mathbb{N}}=0 the archimedean principle says that for any number y there is a natural number such that 1/n<y for y>0 The Attempt at a Solution since all of...

Homework Statement Hi, I just have a basic question regarding an asymptotic tight bound question. The question is : TRUE / FALSE http://latex.codecogs.com/gif.latex?3^{n+1} \text{ belongs to } \Theta(3^{n}) By definition of big theta: c_{1}g(n) \leq f(n) \leq c_{2}g(n) \text { }...

Why doesn't a dineutron system form a bound state? Why doesn't 2 neutrons with one spin up and the other spin down form a bound state but a neutron and proton with both spin up or down form a bound state

Homework Statement Give an example of a bounded subset of Q which has no least upper bound in Q. Explain why your answer has this property. Homework Equations The Attempt at a Solution [1/8, 1/4, 3/8, 1/2, 5/8, 3/4...infinity] is this correct?

Hello I'm trying to show that the following upper bound on the matrix 2-norm is true: \left\|(AB)^+\right\|_2\leq\left\|A^+\right\|_2 \left\|B^+\right\|_2 where + is the matrix pseudoinverse and A\in\Re^{n\times m} and B\in\Re^{m\times p} are full-rank matrices with n\geq m\geq p...

Hi all, I would like to understand the mechanism by which a neutral impurity can bind an exciton. Because the impurity is neutral the attracation can not be simply electrostatic. I know that there must be a "neutralising electyron (or hole)" in the machanism but things are not clear enough...

This calc book that I am reading uses words like "upper bound" and "sup" a lot when proving theorems. I have never heared these terms before so it makes it hard for me to understand the proofs. I think it has to deal with max's values of a graph: For example given a set S of all elements c in...

Homework Statement Consider a particle with mass m and angular momentum l in the field of a central force F=\frac{-k}{r^{5/2}}. To simplify your equations, choose units for which m=l=k=1. a) find the value r_{0} of r at which U_{eff} is a minimum and make a plot of U_{eff}(r) for 0<r<5r_{0}...

Homework Statement I'm trying to learn the Branch and Bound method. For that, I need to master the Dual Simplex Method (DSA). I have tried and tried and tried to google examples but can't find any. Does anyone know where I can find any? How do you know the LPP has become infeasible with...

I am looking for a bound for the following expression S=\sum_{n=1}^N n^k e^{-an} where a>0 and k=1, 2, 3, or 4, apart from the obvious one: S\le \frac{n+1}{2} \sum_{n=1}^N e^{-an} = \frac{n+1}{2} \frac{1-e^{-Na}}{e^a-1}

Homework Statement I'm given that the function f(x) is n times differentiable over an interval I and that there exists a polynomial Q(x) of degree less than or equal to n s.t. \left|f(x) - Q(x)\right| \leq K\left|x - a\right|^{n+1} for a constant K and for a \in I I am to show that Q(x)...

Homework Statement An infinitely long cylinder, of radius R, carries a frozen-in magnetisation, parallel to the z-axis, M=ks k-hat, where k is a constant and s is the distance from the axis. There is no free current anywhere. Find the magnetic field B inside and outside the cylinder by two...

I have the following question: Let n\in\mathbb{Z}^{+} st. n is not a perfect square. Let A=\{x\in\mathbb{Q}|x^{2}<n\}. Show that A is bounded in \mathbb{Q} but has neither a greatest lower bound or a least upper bound in \mathbb{Q}. To show that A is bounded in \mathbb{Q} I have to show...

Homework Statement a) Prove that \ell_\infty \mathbb({R}) is a subspace of \ell \mathbb({R}) b) Show that \left \| \right \|_\infty is a norm on \ell_\infty (\mathbb{R}) The Attempt at a Solution For a) I guess we have to show that \vec{x} + \vec{y} \in \ell_\infty \mathbb({R})...

Homework Statement A particle moves in one dimension in the delta function potential V= αδ(x). (where that is an 'alpha' ... not 'a') An initial wave function is given \Psi = A(a^2-x^2) for x between -a and a and Psi=0 anywhere else What is the probability that an energy measurement will...

Hello all, the problem I have is the following: Suppose f \in C^1(0,1) and f(0) = 0, then f^2(x) \le \int_0^1 f^2(x) dx, but I was wondering if 1 is the best constant for the inequality. In other words, how do I determine the best bound for f^2(x) \le K \int_0^1 f^2(x) dx...

Homework Statement Problem as written in text (Eisberg, 2nd): If a particle is not bound in a potential, its total energy is not quantized. Does this mean the potential has no effect on the bahavior of the particle? What effect would you expect it to have? Homework Equations The...

Homework Statement Use part (a) to prove the Greatest Lower Bound Property. (a): If M is any upper bound for A, then: x\in(-A), -x\inA, and -x\leqM. Therefore x\geq-M, hence -M is a lower bound for -A. By the Least Upper Bound Property, inf(-A) exists. If inf(-A) exists, then...

upper bound of taylor! f(x) is two times diff. function on (0, \infty) . \lim\limits_{x\rightarrow \infty}f(x) = 0 satisfy. M=\sup\limits_{x>0}\vert f^{\prime \prime} (x) \vert satisfy . for each integer L , g(L) = \sup\limits_{x\geq L} \vert f(x) \vert, and h(L) = \sup\limits_{x\geq L} \vert...

I prefer to give investigators the benefit of the doubt, always, but I'm having a really hard time going along with this one. Beware that the link has a censored photo of the body from a distance in the air, and may upset some sensitive individuals...

Homework Statement Suppose that R is a partial order on A, B1 ⊆ A, B2 ⊆ A, x1 is the least upper bound of B1, and x2 is the least upper bound of B2. Prove that if B1 ⊆ B2, then (x1,x2) ∈ R.Homework Equations The Attempt at a Solution This problem has been stumping me. After assuming B1 ⊆ B2...

Homework Statement Okay, this is essentially the same question I had in an earlier thread, but i am trying to make my questions and uncertainties more clear for more accurate assistance: Suppose R is a partial order on A and B ⊆ A. Let U be the set of all upper bounds for B. a) Prove...

Homework Statement Suppose R is a partial order on A and B ⊆ A. Let U be the set of all upper bounds for B. a) Prove that every element of B is a lower bound for U. b) Prove that if x is the greatest lower bound of U, then x is the least upper bound of B. Homework Equations The...

Homework Statement Prove that there is no upper bound in A, where A = {x in Q | x2 < 2} The Attempt at a Solution My attempt has been to assume that there is an upper bound p in A and then I have been trying to find a way to show that there is a number that is larger than p but still in A...

Hello, I am working on a research project that requires me to write a solver for solving a particular problem. I could really use some math advice if anyone is willing to assist. I need to minimize a non-linear objective functions of 5 variables. It is a pretty complex function. Each of the...

Hi. In the book I'm reading I've come to a question regarding degenerate states in one dimension. It says that in one dimension there are no degenerate bound states. But say I have a stationary state with some energy E, and assume that it is normalizable. You can easily show that the complex...

Hi, I have sent this question a couple of days ago, but it seems that its latex form had problem. So, I decide to send it again. I will thank If somebody help me solving this problem. Consider a random variable k_1 with the given pmf as: Pr[k_1=l]=\sum_{l_1+2l_2=l}...

[SIZE="4"]Hi, I will thank If somebody help me solving this problem. Consider a random variable k_1 with the given pmf as: Pr[k_1=l]=\sum_{l_1+2l_2=l} \frac{N!}{(N-l_1-l_2)!l_1!l_2!}p_1^{l_1} p_2^{l_2} (1-(p_1+p_2))^{N-l_1-l_2}where l_1,l_2 \in [0,1,...,l] . but we don't have p_1 and p_2...

1. Which of the following is an allowed wave function for a particle in a bound state? N is a constant and α, β>0. 1) Ψ=N e-α r 2) Ψ=N(1-e-α r) 3) Ψ=Ne-α x e-β(x2+y2+z2) 4) Ψ=Non-zero constant if r<R , Ψ=0 if r>R Only one is correct. 2. What are the criteria for...

Homework Statement Does [0,1] \times [0,1] in the dictionary order have the least upper bound property?Homework Equations Dictionary Order. (on \mathbb{R}^2) Let x , y \in \mathbb{R}^2 such that x=(x_1 , x_2) and y = (y_1 , y_2). We say that x < y if x_1 < y_1, or if x_1 = y_1 and x_2 < y_2...

Hi everyone, The problem: Is this relation true? If so, how (or maybe where) it could be proved?P(A│B∪C)≤P(A│B)+P(A│C)-P(A|BC) and what about its possible generalization? thanks a lot in advance.

Homework Statement Find the volume bounded rho=5+2cosphi Homework Equations dV=rho squared drho d phi d theta The Attempt at a Solution I am guessing this is some cylindrical shape. Theta should be 0-2pi and phi=0 pi/2

Homework Statement Find the smaller volume bound by cone z=r and sphere z^2+y^2+x^2=4 using cylindrcal coordinates Homework Equations dV=r-dr d-theta dz The Attempt at a Solution Limits on r: z to sqrt (4-z^2) limits on theta: 2pi to 0 limits on z: 2-0 Did this and got 8...

Homework Statement Using spherical coordinares, find the smaller volume bounded by the cone z=r and the sphere z^2+y^2+x^2=4 Homework Equations x^2+y^2+z^2=4 ; rho=2, z=rhocosphi The Attempt at a Solution Shot in the dark: Tried function integrating (rho squared - rhocosphi)...