Positive Definition and 987 Threads

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...

Homework Statement I meant for the title to be, Sum of all EVEN integers A formula to add all even integers between two given points. (i.e.) All integers from 6 to 2000 ? 6+8+10+12 .. + 2000 The Attempt at a Solution The reason I ask is because I derived such an equation that will work for any...

In a battery, why is the negative terminal at a lower potential than the positive terminal? And can we define absolute potential of a point? Potential means that the work done in bringing a charge from a given point to a given point on presence of the electric field created by another charge in...

Homework Statement In a symmetric positive definite matrix, why does max{|aij|}=max{|aii|} Homework Equations |aij|≤(aii+ajj)/2 The Attempt at a Solution max{|aij|}≤max{(aii+ajj)/2 max{|aij|}≤max{aii/2}+max{ajj/2} max{|aij|}≤\frac{1}{2}max{aii}+\frac{1}{2}max{ajj} then I...

Is it the absence and presence of an electrical fluid called as positive and negative charges?

Homework Statement A small, positively charged sphere is released from rest and moves directly away from a larger, positively charged sphere. During this process, the electrostatic force: a) does positive work and increases the kinetic energy of the small sphere b) does negative work and...

Hello all, I always read in texts that you can charge a body in air till the the electric field due to body does not exceeds the dielectric strength of air, which has a certain value. The question that is popping into my head is that, what if we charge the body in vacuum? I expect...

In SHM , we can only have negative acceleration, and maximum accelration is zero. Is that correct? What is the maximum acceleration here? http://answers.yahoo.com/question/index?qid=20110207103646AAij3SF Thank you.

Find all positive integers n for which \sqrt{n+\sqrt{1996}} exceeds \sqrt{n-1} by an integer.

The image bellow is the PN junction under equilibrium. I wonder why there are so many positive and negative ions in N and P types respectively. For me, I think that these ions should only exist in the depeletion region not outside the region. Thanks for help.

1. An elevator (mass 4700 kg) is to be designed so that the maximum acceleration is 6.80×10-2. What is the maximum force the motor should exert on the supporting cable? Force Diagram: Force Tension | elevator | mg 3. FT = ma + mg 4700[(0.068(-9.8)...

+++++++++++++++ charge here ------------------- Is the positive terminal always high potential, regardless of if an electron or proton is placed in the "charge here" area somewhere between the two plates, and the negative terminal is always low potential, no matter what...

what does the positive and negative half cycles in an ac represent?

Find all positive integers n such that $\phi(n)=6$. n>1 so we can write n as a product of primes, say $p_{1},...,p_{t}$ are the prime factors. Then, using the multiplicative property, we find that $n(1-p_{1})...(1-p_{t})=6p_{1}...p_{t}$. I've tried using odd/even arguments to deduce...

Homework Statement Note: this is actually my own question, not something from a book. So if I am wrong about some terminology please let me know In physics questions, they will tell you an electric field is |Some Value|. Since |Some Value| (lets call it X) is always positive, how do we know...

Homework Statement Two equal positive charges Q are fixed on the x-axis, one at +a and the other at -a. (a) The electric field E at the Origin O (b) The electric potential V at the origin O Homework Equations E=-dV/dr --> V=kQ/rThe Attempt at a Solution VNet = V0 + V1 I got V0 = -kQ/r...

I have a non-zero measured subset X\subseteq\mathbb{R}^{n} on which \sum_{i=1}^{n}\psi_{i}x_{i}=0 for all x=(x_{1},\ldots,x_{n}) in X. How can I show that \psi_{i}=0 for i=1,\ldots,n?

Homework Statement Is the set of all polynomials with positive coefficients a vector space? It's not. But after going through the vector space conditions I don't see how it can't be.

Homework Statement State what will happen when a positive particle has an initial velocity opposite to the direction of the electric field Homework Equations The Attempt at a Solution

Homework Statement Suppose U = T^2 + \alpha T + \beta I is a positive operator on a real inner product space V with \alpha^2 < 4 \beta . Find the square root operator S of U.Homework Equations The Attempt at a Solution Isn't this just the operator S \in L(V) such that S e_k = \sqrt{...

If I were to take a copper wire and shove it into the positive terminal of an electrical outlet and then stick the other side of the copper wire into the earth, will current flow??

I am preparing for an entrance and I came across this sum.The equation given is xyz=3000. we need to find how many positive integral solutions are there for x,y and z. Please help.

For all positive integers m > n, prove that : \operatorname{lcm}(m,n)+\operatorname{lcm}(m+1,n+1)>\frac{2mn}{\sqrt{m-n}}

What happens if you combine both negative and positive feedback in one opAmp? assuming you only have unity gain in the negative configuration and no capacitors? I reckon adding capacitors would add some oscillatory behavior but would that be the case if both configurations are made only of...

Homework Statement The problem: Attached as TheProblem.jpg. Solution: Homework Equations xT A x The Attempt at a Solution I computed the product and got 9x22 + 4 x1x1 + 4x12. I'm thinking that I might need to show that that obtained polynomial must be below zero since we want...

Consider the quadratic function $\displaystyle q(\textbf{x}) = \frac{1}{2} \textbf{x}^T G \textbf{x} + \textbf{d}^T \textbf{x} + c$ on $\mathbb{R}^n$, where $\textbf{d}$ is a constant $n \times 1$ vector, $G$ is a constant $n \times n$ symmetric matrix and $c$ is a scalar. The gradient is...

I'm updating my CV and while browsing my documents I noticed a flattering official statement by two PIs that I worked for. I'd like to list it, but what is such a document called or what would be the best description? To get an idea of what it is, the second paragraphs states: "In general, we...

Hi everyone. Is there any way to set demands on least square solutions? I have an equation on the form Ax=b, which is solved for x as: x=(A'*A)^-1*A'*b I do know for a fact that all values in x should be positive, but the least square solution for my particular system contains a...

as a function f(z) = z^{\frac{1}{2}} why the real part is positive My work I looked into g(z) = z^2 , natural domain is the complex field we can see that g(z) = g(-z) , g is not 1-1 if z = r e^{i\theta} -z = e^{i\pi} z = re^{i(\theta + \pi)} so we will restrict the domain to...

Find all positive integer solutions of the equation $4x^3-12x^2+5x-10y+36y^2-18y^3+4x^2y+6xy-15xy^2=0$.

(I hope this is the right subforum) I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...

My question arises in the context of bosonic string theory … calculating the number of dimensions, consistent with Lorentz invariance, one finds a factor that is an infinite sum of mode numbers, i.e. positive integers … but it really goes back to Euler, and his argument that the sum of all...

I know that when there are excess positive charges in a conductor, for example, a metal sphere, the positive charges will spread out over its surface. However, I am confused about how this excess charge spreads out over the surface, if protons cannot move and only electrons can move. Can...

Normally the connection of supply voltage is +-V but now is +V and ground. What happen if Op-amp (ua741) with only positive supply voltage? The op-amp still function?

Homework Statement A nucleus contains Z protons that on average are uniformly distributed throughout a tiny sphere of radiues R. Suppose that in an accelerator experiment a positive pion is produced at rest at the center of a nucleus containing Z protons. The pion decays into a positive muon...

May sound trivial but I don't find it trivial from the things I am given as a definition of the exponential function: The exponential function satisfies f(a+b)=f(a)f(b), is the inverse to the ln and is restricted by the condition: exp(x)≥1+x I can't see how I can from this only proove...

x and k are positive integers ,satisfying : $ \text {x(x+1)=64} \text { k}^4 -48 \text{ k}^3 +16\text { k}^2-2\text{ k} $ please find x

In conductors, how does the excess of positive charge distribute itself across the surface of the material?

All right guys. A lil history bout me. in high school (10 years ago) i hated math, now i like it. Never went far with it in high school. Failed trig a year and a half ago. had to retake. Now I am in my first EVER calc2 class. Finished calc 1 with a high 80's (87 or so). Now I am in calc2 and i...

Homework Statement How to find the potential between two positive point charges? I don't know where I'm going wrong. ==I am adding V_1 and V_2. converted mC to C, cm to m, correct value of k. V1= kq1 / r1 v2= kq2/ r2. ==I am adding both of these, but I'm not getting...

For instance, say I have -ln(-∞) Does the negative sign on the natural log cancel with the negative sign on the infinity? Is this true? -ln(-∞) = ln(∞) Thank you -Drc

Homework Statement Two half-rings of charge of opposite polarity are brought together at the origin (so that the rings create a full circle against the y- and z-axis. Each half-ring has a charge of magnitude Q and radius a. Derive the net electric field at point P, located on the +x axis a...

I attached the circuit. I did kirkoff's voltage law (assuming current goes clockwise): -15+5-10,000I-40000I=0 where I=current I=-2*10^-4 A V_out=40,000*-2*10^-4A = -8V The way V_out is shown, it should solve to be negative, correct?

Is there a mathematical proof that the positive feedback makes the op-amp saturated? http://i.imgur.com/71PNh.png