Positive Definition and 963 Threads

Show that for positive parameters $a$, $b$, and $c$, $$ \int_{0}^{\infty} \left( \frac{e^{-ax}-e^{-bx}}{x^{2}} + (a-b) \frac{e^{-cx}}{x} \ \right) \ dx = b-a + a \ln \left(\frac{a}{c} \right) - b \ln \left(\frac{b}{c} \right)$$

Homework Statement If a small positive and negative charge are created at rest at a point between electrodes as shown in the figure. In which direction will they move if one would neglect gravity? Ignore those weird arrows, those are for later questions. Homework Equations...

Under which conditions is a real positive definite matrix symmetric? I have crossposted here: http://math.stackexchange.com/questions/661102/positive-definite-matrix-symmetric

I am trying to find a matrix A such that $(1)$ can be written as $v^TAv=1$ where $v=(x, y)^T$. $(1)$: $$\left(\frac{x}{a_1}\right)^2 + \left(\frac{y}{a_2}\right)^2 - 2\left(\frac{xy}{a_1a_2}\right)\cos(\delta)=\sin^2(\delta)$$ $$a_1, a_2, \sin(\delta)\neq 0.$$ I am positive that $\cos(\delta)$...

Homework Statement So on my first day of intro to quantum physics my teacher assigned a lot of calculus problems as homework. One of them problems was a quite lengthy proof that one integral is the equivalent of another, and I am so close to getting the correct answer! All I need to do to...

Here is my task and my attempt of solution: How to use fact that C is positively orientated viewed from point (10,0,0)? I'm not sure I understand it.

I need an algorithm for LCM(k1, k2, ..., kn). Here's what I was thinking: any number ki that divides evenly into another number kj, set ki = 1 return k1*k2*...*kn I'm having trouble implementing it, though. int LCM(int* numsPtr, int size) { // assume size > 1 and that array only...

Hi this may sound like a simple question but I'm trying to find out the relative abundance of hydrogen in its various forms in space: H, H+, H-, H2, H2+, H2- I'd like to know these for our stellar neighborhood involving the solar wind and also for interstellar space outside the heliopause...

Object with positive mechanical energy in an attractive force field moves along a hyperbolic path and whose energy is zero, moves along parabolic path...isn't it?...But why?...Can't any object with ve energy move along the line joining centre of force?...If its radial component of kinetic...

What is the last three digits of the product of the positive roots of $\large\sqrt{1995}x^{\log_{1995} x}=x^2$.

Homework Statement Given $$y''+e^{-x}y=0. \qquad (*)$$ Let ##y(x)## be any nontrivial solution of ##(*)##, show that y has finitely many positive zeros. Hint: Consider ##z''+\frac{C}{x^4}z=0## where ##C>0## is sufficiently large, which has a solution ##z(x)=x\sin \frac{\sqrt C}{x}##. Homework...

Hello. A simple question.Solve in all positive integers, for: a^2=9555^2+c^2 Please, you show the way of solving it. Regards.

Determine the positive integers $z>y>x$ for which $\dfrac{1}{x}-\dfrac{1}{xy}-\dfrac{1}{xyz}=\dfrac{19}{97}$

Solve in positive integers for $577(bcd+b+c)=520(abcd+ab+ac+cd+1)$

Prove that if p and q are positive distinct primes,then $\log_p(q)$ is irrational. Attempt: Proof by contradiction: Assume $\log_p(q)$ is rational.Suppose $\log_p(q) = \dfrac{m}{n}$ where $m,n \in \mathbb{Z}$ and $\gcd(m,n) = 1$. Then, $p^{\frac{m}{n}} = q$ which implies $p^m = q^n$.

Does ##g(x,y,z)## (the equation of the surface) need positive z or negative z when doing a surface integral? The author specifies that ##g## either has ##z## or ##-z## depending on the orientation of the surface but doesn't specify which belongs to which orientation.

Homework Statement 2. The attempt at a solution So part a. makes sense to me, it basically comes down to A1 = 1 -1 -1 -1 1 1 -1 1 1 A2 = 1 -1 -1 -1 2 -2 -1 -2 11 I'm not sure how to approach part b. because the question doesn't make much sense to me...

Homework Statement Both Q1 = Q2 = +5E-6 and are harnessed to screen and in a vacuum.----Q1---A----Q2------B--------P this is x axis, A and B are distances Homework Equations kQ/r^2 The Attempt at a Solution So the E field at point P is KQ1/(A+B)^2 + KQ2/(B)^2 My question is Why...

Here is the question: I have posted a link there to this thread so the OP can see my work.

[FONT='inherit']If $3^{n} +81$ is a perfect square, find a positive integer value of $n$. My Trail:: [FONT='inherit']When $n\leq 4,$ then easy to know that $3^{n} +81$ is not a perfect square. [FONT='inherit'] Now let $\displaystyle n = k +4 (k\in \mathbb{Z^{+}}),$ then $3^{N} +81 = 81...

Homework Statement Given two positive numbers calculate their weighted average(Note: This is not actually a homework question, but silly me have doubts, so I put it in this category) Homework Equations Two given positive numbers a,b. No separate weights are available to weigh each...

Hi everyone, :) I just want to know what "positive" means in this context? Is it positive definiteness or something? I mean, we cannot speak about the positivity or the negativity of the function \(f\) since it gives out complex values. Problem: Prove that the function \(f:\...

Hi MHB, This problem drives me crazy because first, I have not encountered a problem like this before (but this is only an excuse and it must be my incompetence that holds me back from cracking it successfully) and I called off the attempt because I don't think I can solve it. Problem...

I've just recently learned that protons do in fact have a charge, I was wondering if someone could explain this, as far as applying a positive charge, some real world examples. I've always studied current as a flow of electrons, never heard of a flow of protons before and have no idea what it...

when is g (9.8) negative or positive? i thought that g would be positive when its going towards the ground, and negative when it is being thrown in the air or against gravity.

I have a problem understanding whether a sign should be positive or negative when it comes to a spring. In my book, there is an example with a glider attached to a spring, and the glider is moving away from the spring so it expands. It says that in order to use the work-energy theorem, it has...

Q: Using Dirac notation, show that if A is an observable associated with the operator A then the eigenvalues of A^2 are real and positive. Ans: I know how to prove hermitian operators eigenvalues are real: A ket(n) = an ket(n) bra(n) A ket(n) = an bra(n) ket(n) = an [bra(n) A ket(n)]* =...

Homework Statement Let S ⊆ R be such that (i) a, b ∈ S ⇒ ab, a + b ∈ S (ii) for all x ∈ R exactly one of the following holds x ∈ S, x = 0, −x ∈ S. Show that S = {x ∈ R ; x > 0} (the set of positive numbers P) 2. Relevant theorems (T1) a² > 0 ∀ a ∈ R. (So a²∈P) (T2) All positive...

Homework Statement Homework Equations so i kno the formula for the for the sum of the first N positive integers when i = 1The Attempt at a Solution i kno the answer = [SIZE="4"]n^2(n+1)/2 but could someone explain step by step how you reduce it to get the final answer? as if I'm in...

Find the smallest positive integer $n $ for which $n^{16}$ exceeds $16^{18}$.

Hi How are you I have a question how we can know the work if - or + also heat energy please could see this question why in answer take work as - and heat as +

Homework Statement I am trying to understand when the positive or negative of a specific value in an equation (work-energy and momentum-impulse) is to be evaluated based off the motion diagram and when it is not? Homework Equations The ones in particular I am unsure about is...

I am building a positive peak detector circuit using AD829 opamps. I have attached my current circuit I built in multisim. I used a "superdiode" configuration on the charging circuit so that I simultaneously get the charging across the capacitor, no discharging during the falling edge, and...

Calculation of Total no. of positive integer ordered pairs $(n,r)$ in $\displaystyle \binom{n}{r} = 120$ My Try:: Clearly $\displaystyle \binom{n}{r} = 120 \Rightarrow \binom{120}{1} = \binom{120}{119} = 120$ So $(n,r) = (120,1)\;\;,(120,119)$ are positive integer ordered pairs which satisfy...

Homework Statement Ax = 3m Ay = -4m Find the angle with respect to the x axis Homework Equations Tan = Ay/Ax The Attempt at a Solution Tan = Ay/Ax = -4m/3m = 1.333333 angle = -53 degrees Is -53 degrees a correct answer or should it be positive 53?

Homework Statement Suppose that k(t) is a continuous function with positive values. Show that for any t (or at least for any t not too large), there is a unique τ so that τ =∫ (k(η)dη,0,t); conversely any such τ corresponds to a unique t. Provide a brief explanation on why there is such a...

Hi All, Suppose I have the following system: A = 1 / (S + 1) (open loop) B = S / (2S + 1) (feedback path) I know that the positive feedback closed loop system will thus be: A / (1 - AB), and entering this manually in MATLAB (as well as doing it by hand), I get: 2 s^2 + 3 s...

Homework Statement lim [√(2x2 +1)]/(3x - 5) [SIZE="1"]x→-∞ I know that the answer is -√2/3. That is the answer my professor had on this example, and the math lab tutor also agreed, and so did my graphing calculator. But I keep getting √2/3 on paper. The math lab tutor explained yesterday why...

Determine the positive numbers $a$ such that $$\sqrt[3]{3+\sqrt{a}}+\sqrt[3]{3-\sqrt{a}}$$ is an integer.

The Friedmann solution(s) to the GR cosmological equations (without Lambda) assume pressure=0. What happens if we let p>0 ? It seems to me that there is no continuous solution to the cosmological equations in that case. Yet, if we include electro-magnetic radiation (such as MBR) in the energy...

I am not an engineer which is why I have come to this forum. I am currently working on a project for my business. I am trying to create a box that needs positive pressure. My basic requirements are to keep out dust and lint from contaminating my work. There will be an opening on this box...

Robert Oeckl proposed this new formulation of QT in December of last year. http://arxiv.org/abs/1212.5571 I think it's important and worth learning about. It could replace Dirac form of QT for some (especially general covariant) quantizations. Historically it derives from 1980s work by Witten...

Homework Statement If A is positive definite, show that ## A = C C^T ## where ## C ## has orthogonal columns. The Attempt at a Solution So, I've got the first part figured out. Because ## A ## is symmetric, an orthogonal matrix ## P ## exists such that ## P^TA P = D =...

Find the smallest positive integer $n$ such that for every integer $m$ with $0<m<1993$, there exists an integer $k$ for which $$\frac{m}{1993}<\frac{k}{n}<\frac{m+1}{1994}$$.

Can anyone give me some hints for this question please? Suppose A is positive definite and symmetric. Prove that all the eigenvalues of A are positive. What can you say of these eigenvalues if A is a positive semi definite matrix? Many thanks in advance.

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Consider the sequence of positive integers which satisfies $$a_n=a_{n-1}^2+a_{n-2}^2+a_{n-3}^2$$ for all $n \ge 3$. Prove that if $a_k=1997$, then $k \le 3$.

In QFT equations, there are not only positive energy solutions, but negative ones as well. Dirac had the hole theory. But the sea may have infinite charges and gravity effects. And then QFT textbooks just explain the negative solution as anti-particle. But in the lab, we measure the...

We know that the conservation of electromagnetic energy is expressed via the continuity equation below: \large{\frac{\partial u}{\partial t}}+\vec{\nabla}\cdot\vec{S}=-\vec{J}\cdot\vec{E} with u=\frac{1}{2}(\vec{E}\cdot\vec{D}+\vec{B}\cdot\vec{H}) and \vec{S}=\vec{E}\times\vec{H} . It...

This is from Lang's "A First Couse in Calculus". In chapter 1 he makes two statements regarding positivity: POS 1. If ##a##, ##b## are positive, so is the product ##ab## and the sum ##a+b##. POS 2. If ##a## is a number, then either ##a## is positive, or ##a=0##, or ##-a## is positive, and...