Positive Definition and 963 Threads

sum(1/(n(n^2-1)^(1/2)),n=2,infinity) first derivative <0 for x>=2 I(1/(x(x^2-1)^(1/2)),x,2,infinity) x=secT, dx=secTtanT I(secTtanT/(secTtanT),T) ?

Homework Statement Suppose that T is a positive operator on V. Prove that T is invertible if and only if <Tv,v > is >0 for every v ∈ V \ {0}. Homework Equations The Attempt at a Solution If T is invertible, then TT-1=I.Now let v=v1+...+vn and let Tv=a1v1+...+anvn. Now <Tv...

positive operator proof Homework Statement Prove that if T ∈ L(V) is positive, then so is Tk for every positive integer k. Homework Equations The Attempt at a Solution Let v=b1v1+...+bnvn. Now since T is positive, T has a positive square root. T=S^2. <S^2v, v>=<S^2v1...

When a child does something favourable in the eyes of his parents, even something insignificant, and gets heaped with praise it gives me the creeps. I know that it's a useful educational tool but when every small action is rewarded it seems sort of like brainwashing. The kid is doing things to...

Homework Statement Prove that the sum of any two positive operators on V is positive.Homework Equations The Attempt at a Solution This problem seems pretty simple. But I could be wrong. Should I name two positive operators T and X such that T=SS* and X=AA*? I have a bad history of seeing a...

Does there exist a converging uncountable sum of strictly positive reals?

Please find an upper bound for P(X>=10) using Markov's and Chebyshev's Please state which is which. I'm not very good at stats and this is a homework problem :P Thanks!

Homework Statement Find a formula fo the sum of the fourth powers of the first n positive integers n ∑ i^4 (i=1) Justify your work using mathematical induction Homework Equations so i know the formula for the sum of the cubes of the first n positive integers k=n+1 ∑...

Hi everyone in this sub forum, I'm wondering if the following 'rule' (theorem?) is correct: For a hermitian Positive Semidefinite (PSD) matrix A=(a_{ij}), \max_{i,j\le n} |a_{ij}|=\max_{i\le n}a_{ii}. The reason for this intuition (It may be a well known result, I'm very sorry in this...

Hello, I've been quite avidly reading about one of the spectacular recent joint achievements of physics and pure math. The positive energy theorem [1,2,3] concerns the large-distance asymptotic behaviour of the gravitational field due to a localised distribution of mass-energy. I think I...

Homework Statement In quantum mechanics, how to show that the expectation value is always positive? Homework Equations The Attempt at a Solution

Calc. Angle between radius vector point and positive x axis? What does that mean? Homework Statement The cartesian coordinates of a point in the xy plane are x = −8.96 m, y = −1.75 m. Calculate the angle  between the radius- vector of the point and the positive x axis (measured...

Hi everyone The Hamiltonian of the Klein Gordon field can be written as H = \frac{1}{2}\int d^{3}E_p \left[a^{\dagger}(p)a(p) + a(p)a^{\dagger}(p)\right] and we have [H,a(p')] = -E_{p'}a(p') [H,a(p')] = +E_{p'}a^{\dagger}(p') The book I'm reading states that What does this mean? Thanks.

IT IS A POLL! I would like to learn if you've ever heard of the positive charge atomic form-factor before my asking this question. The positive charge atomic form-factor fnn'(q) stands at the nucleus charge Z and describes the positive charge cloud in atoms for elastic scattering at large...

Homework Statement Let R be a ring and suppose there exists a positive even integer n such that x^n = x for every x in R. Show that -x = x for every x in R. Homework Equations The Attempt at a Solution I solved the case where n = 2. Let x be in R. (x+x)^2= x+x = 2x...

Hi everyone, I know that for a matrix to be Positive semi-definite (A>=0) (PSD), the elements on the principle diagonal (upper left corner to right bottom corner) must be non-negative (i.e., d_ii>=0). But I wonder if there exists any condition to be satisfied by the elements on the secondary...

Firstly, I don't get why the at term on the exponential turned positive (red arrow).. can someone explain that please? And how do I start on this? How do I split it up such that I can do it for t>0 and t=<0? Do I just integrate e^2t between -inf and 0 and integrate e^-t...

How do we show the one point compactification of the positive integers is homeomorphic to the set K={0} U {1/n : n is a positive integer}? Say Y is the one point compactification of the positive integers. I know Y must contain Z+ and Y\Z+ is a single point. Also Y is a compact Hausdorff...

How does one integrate \int_0^\infty e^{-\beta x^2}\cos{(bx)} dx for positive beta and real b ? I was thinking maybe differentiation under the integral sign would do the trick, but I can't get anywhere.

Lets say you have a battery and connect wires to each of the terminals. Now you bring both of the wires together to create a spark. Is the spark jumping from positive to negative (current) or from negative to positive (electron flow). Thanks!

work done by spring forces -- positive or negative I have gotten the sign wrong on every single spring force-related problem. I'm pretty sure I'm working out the problems correctly, but the answer turns out to be negative when I have it positive, or positive when I have it negative. Of...

Homework Statement How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k, k+1, k+2, in the correct order: a) where these consecutive integers can perhaps be separated by other integers in the permutation? b) where they are in...

N is a seven digit base-8 positive integer having the form ABCDEFG that uses each of the nonzero base-8 digits 1 to 7 exactly once, and satisfies these conditions: (i) ABCDEFG is divisible by 7. (ii) ABCDEF is divisible by 6. (iii) ABCDE divisible by 5. (iv) ABCD is divisible by 4. (v)...

Hi, Apologies for the trivialness of the question, but I'm not so great at this. I was wondering why the square root of a real number is positive. Why is sqrt(9) = 3, and not -3 as well, since (-3)² would give 9. Is it just a condition you set, that the function values must be positive? At...

Homework Statement The curve y^2-3xy+2x^2=4 is a hyperbola with axes rotated from the standard position. Use Newton's Method to find the positive x-value to four decimal places for the point on the hyperbola where y=1. Homework Equations Newton's Method The Attempt at a Solution...

How do you make positive ions? I found a kit device that is made of a bunch of capacitors and diodes that's supposed to make negative ions (it says to reverse the diodes to make positive ions) how does this work? Wikipedia and HowStuffWorks weren't much help. Wikipedia explained what diodes...

Homework Statement There exists y > 0 such that [y^{2} = x if and only if x > 0]. This means that "there is some positive number whose square equals all positive numbers." - St. John College, Oxford The Attempt at a Solution I am not sure about this statement "- - some positive number whose...

1. Given that |\langle f|g\rangle|^2 \leqslant \langle f|f\rangle\langle g|g\rangle prove that |\langle f|H|g\rangle|^2 \leqslant \langle f|H|f\rangle \langle g|H|g\rangle where H is a Hermitian and positive definite operator. [b]3. I tried to identify H|g\rangle as a state and put...

Homework Statement Let A be a real symmetric positive definite matrix. Show that |aij|<(aii+ajj)/2 for i not equal to j. Homework Equations The Attempt at a Solution I really don't even know where to start with this. I think that aii and ajj must both be > 0 since they are on the...

Homework Statement In a fluorescent tube of diameter 3 cm, 10 *1018 electrons and 2.5 * 1018 positive ions (with a charge of +e) flow through a cross-sectional area each second. What is the current in the tube? Homework Equations Current is I = (delta Q)/(deta T) The Attempt at...

Does the positive electrode of a Daniel cell (the Copper electrode) actually have a net positive charge when the electrodes are not connected by a conducting material such as a wire? If not, does it have a net charge at all and how does this charge compare to the negative terminal? Finally...

Will a batteries get discharged if the positive one is connected to the negative Hi,yestrday i was told when a wire is connected between two bodies being charged oppositely 'and equally in magnitude' then a sudden discharge take place making the bodies uncharged.So what about the charged...

Homework Statement A kite string exerts a 12-lb pull (|F|) on a kite and makes a 45 degree angle with the horizontal. Find the horizontal and vertical components of F. Homework Equations Pythagorean The Attempt at a Solution 12*sqrt(2) for both horizontal and negative My question is...

Hi everyone, I know that for a hermitian matrix to be PSD it is necessary that every principal minor [i.e, the minors obtained by deleting all the last i rows and columns for all i=(n-1)(-1)0]. I want to know if it is necessary that all minors of order>=2 be non-negative. Particularly, for...

I have two questions: 1. Let V be a finite dimensional inner product space. Show that if U: V--->V is self-adjoint and T: V---->V is positive definite, then UT and TU are diagonalizable operators with only real eigenvalues. 2. Suppose T and U are normal operators on a finite dimensional...

i. Write out the proper definition for lim f(x) x\rightarrowa+ ii. Let g(x)=x-1cos(x-1) Show that for every N and any b>0 there is a point t E (0,6) so that g(t)>N iii. Prove that for g as in (ii) we don not have lim g(x) x\rightarrow0+ I'm not sure what how to do...

Hi, I've got two related questions. You can decompose a (semisimple) lie algebra into root spaces, each of which are 1-dimensional. If X has root a and Y has root b then [X,Y] has root a+b. If the root space of a+b is not zero (i.e. there is a root a+b) then is it possible for [X,Y] to still...

Homework Statement Hi I have to say true or false, and then demonstrate my answer "if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign" For me its true, i was thinking of creating a triplet (x, y, z), where x=1 if "a" positive, x=0 if "a" negative, same for y...

ABCDEFGF is an 8-digit positive decimal integer, where each letter represents a different decimal digit from 0 to 9. The digits 1 and 9 do not appear. The nonzero even digits appear in ascending order, and the odd digits appear in descending order in ABCDEFGF. None of A and E can be zero...

Determine a 9-digit positive integer that uses each of the decimal digits from 1 to 9 exactly once, such that: (i) The sum of the digits 1 and 2 and all the digits between them is 9. (ii) The sum of the digits 2 and 3 and all the digits between them is 20. (iii) The sum of the digits 3...

I was thinking about and I think it might be possible, but before I do anything stupid, anything have an opinion about this?

Homework Statement Suppose 'a' and 'b' are real numbers such that the roots of the cubic equation ax^3-x^2+bx-1=0 are all positive real numbers. Prove that: i) 0<3ab<=1 ii) b>= 3^0.5 Homework Equations Let x,y,z be the roots: x+y+z=1/a xy+yz+zx=b/a xyz=1/a The Attempt at a...

question: let x_1,...,x_n positive real numbers. prove that \lim_{p\to \infty}\left(\frac{x_1^p+...+x_n^p}{n}\right)^{1/p}=max\{x_1,...,x_n\} can you give me some hints ?

so I have to prove that a^3-2b^3-4c^3 = 0 has no positive integer solutions. I have gotten through most of the proof but now I am stuck, and if you guys could give me a nudge in the right direction that would be great. work done so far: proof by contradiction, i assumed that...

Homework Statement Find the largest positive integer n such that n^3 + 100 is divisible by n + 10. Homework Equations The Attempt at a Solution The hint I've been given is to use (mod n + 10) to get rid of the n. but i don't quite see how it would work :S all my attempts...

Homework Statement (a) Determine the reflectivity spectrum R(E) of a free particle of mass m reflected from an infinite jump V(x), where V(x)=0 if x\leq0, V(x)=-\infty if x>0 The other similar problem is: (b) Determine the energy levels of a particle of mass m confined to an infinite...

I know that purely the acceleration due to gravity is positive because it accelerates things not decelerates or negative acceleration. But in some cases it can be negative but I'm not sure in which cases. For example if I'm just standing here on the ground is gravity working in a positive or...

hi! I'm new to the forums, and had a question that was more calculus-related than physics. i saw another post similar to this one, but it was incomplete and i couldn't get the answer with the information on it, any chance someone could help me out? The question is: "Find a unit vector with a...

Homework Statement (3xy^3)(4x^-3y^-2) Homework Equations ? The Attempt at a Solution = 12y ----- x^2

Homework Statement A point charge of 2.0 10-9 C is located at the origin. How much work is required to bring a positive charge of 4.0 10-9 C from infinity to the location x = 30.0 cm? and it requests the answer in J Homework Equations W=-q2(delta)V DeltaV = Ke q1/d where...