Positive Definition and 987 Threads

Hi. I have a real tridiagonal symmetric matrix that comes from the discretization of a partial differential equation. The elements are given by: ##A_{i,j}=-\delta_{i-1,j}\kappa_{i-1/2,l}\frac{\Delta t}{h^2}+\delta_{i,j}\left[\frac{2}{c}+\frac{\Delta t}{2}\mu_{i,j}+\frac{\Delta...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as follows: n the above proof we...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as...

Is there a set of $2015$ consecutive positive integers containing exactly $15$ prime numbers?

Hi, While solving homework problems, I start by defining a positive-y direction and a positive-x direction. Let's say up and to the right. Until now, I've applied this same rule to all objects in each problem, no matter the direction the object moves. But it seems I have not understood this...

Homework Statement Prove that a 2x2 complex matrix ##A=\begin{bmatrix} a & b \\ c & d\end{bmatrix}## is positive if and only if (i) ##A=A*##. and (ii) ##a, d## and ##\left| A \right| = ad-bc## Homework Equations N/A The Attempt at a Solution I got stuck at the first part. if ##A## is positive...

Homework Statement The problem relates to a proof of a previous statement, so I shall present it first: "Suppose P is a self-adjoint operator on an inner product space V and ##\langle P(u),u \rangle## ≥ 0 for every u ∈ V, prove P=T2 for some self-adjoint operator T. Because P is self-adjoint...

Homework Statement Question: For ##\Lambda^3+\Lambda^2+A=0## , show that for ##A<0## there is some real positive ##\Lambda## which solves this Homework EquationsThe Attempt at a Solution [/B] Attempt: Write ##-A=\hat{A} ##, then ##\hat{A} \in (0,\infty)## and...

Hey How can i calculate the work done by a homogeneous electric field on a positive charge q = 7 × 10^-8 C when the charge moves from point 1 to point 2 . I have two cases: a) the charge is parallel to the Electric field; b) the displacement of the charge takes place at the angle α = 60 ° to...

I understand that if you have a function in which you want to determine the full (i.e. account for positive and negative values) integral you need to break down your limits into separate intervals accordingly. Is there any way in which you can avoid this or is it mathematically impossible? If...

I am trying to prove that $$ x^4+4096y^4+450x^2y^2-2304xy^3-36x^3y $$ is positive for all positive $x$ and $y$. I also have the condition $x>16y$ though I don't believe this is needed to prove positivity as I've plotted the function for varying $x$ and $y$ and it always seems to be positive...

I'm so confused, is the voltage reading of the meter gathered by: positive electrode charge - negative electrode charge = potential difference I don't get why there is a positive and negative electrode and what they do

Why do we get two answers when taking the square root? For example, let a = any positive number sqrt{a} = - a and a. Why is this the case? What about 0? Can we say sqrt{0} = - 0 and 0?

Homework Statement Given that ##f(x) = x^2 - bx + 1##, find the values of b for which at least one of the roots are positive Homework EquationsThe Attempt at a Solution So first I used the quadratic equation to find the roots: ##\displaystyle x = \frac{b \pm \sqrt{b^2 - 4}}{2}##. Now, given...

$x^2+y^2=1992---(A)$ pove $(A)$ has no positive integer solution

I am computing limit of detection of zinc of an electrolyte. Using standard additions method, I have obtained positive x intercepts for 6/8 samples all very close to zero. Positive x-intercepts imply final concentration values to be negative. if x-intercept taken to be zero, the concentration...

I need a flux of highly positive ions, at least penta-valent ions (5+ or more, 6+, 7+, ...); there are ion sources that can generate a proton flux, but I need 5+ ions; do you know how I can do that?

Hi, I am studying a positive sequence detector and have some trouble understanding it. I understand most of it, but the author in the book "Instantaneous Power Theory and Applications to Power Conditioning" writes: For extracting the fundamental positive-sequence voltage with the dual method...

if ## a,b,c,d,e ## are positive real numbers, minimum value of (a+b+c+d+e)( \frac{1}{a} +\frac{1}{b} +\frac{1}{c} +\frac{1}{d} +\frac{1}{e} ) (A) 25 (B) 5 (C) 125 (D) cannot be determined My approach : expanding the expression , i get 5+a( \frac{1}{b} +\frac{1}{c} +\frac{1}{d} +\frac{1}{e}...

Homework Statement Here's the question : 1x1+ 2x2 +0x3 + 0x4 = 1 2x1+ 9x2 +1x3 + 0x4 = 6 0x1+ 1x2 +9x3 + 4x4 = 2 0x1+ 0x2 +4x3 + 3x4 = 8 I' m asked to solve this question using Choelsky method ( We need the symmetric positive definite matrix when we are using this method) Homework...

Homework Statement Is the group of positive rational numbers under multiplication a cyclic group. Homework EquationsThe Attempt at a Solution So a group is cyclic if and only if there exists a element in G that generates all of the elements in G. So the set of positive rational numbers would...

Homework Statement When is a Markov chain with double stochastic matrix positive recurrent? Homework Equations Double stochastic matrix is when the sum of the column vectors, and not just the row vectors, is 1. The Attempt at a Solution I know I have to show that the expected value of the...

Homework Statement Suppose B is a real nonsingular matrix. Show that: (a) BtB is symmetric and (b) BtB is positive definite 2. Homework Equations N/A The Attempt at a Solution I have managed to prove (a) by showing that elements that are symmetric on the diagonal are equal. However I have no...

Homework Statement Find the lewis structure for [CH3OH2]+ Homework Equations n/a The Attempt at a Solution I found the lewis structure to have a positive formal charge on the oxygen. I'm not sure why the oxygen would have the + f.c. since it is much more electronegative than fairly neutral...

I split off this question from the thread here: https://www.physicsforums.com/threads/error-in-landau-lifshitz-mechanics.901356/ In that thread, I was told that a symmetric matrix ##\mathbf{A}## with real positive definite eigenvalues ##\{\lambda_i\} \in \mathbb{R}^+## is always real. I feel...

proof ##\ln x##<=x-1 for positive x. if i show that at the start of the segment, the value in the start of the segment (0, +inf), of inx is smaller than x-1, and the derivative of inx is always smaller than x-1, is that suffice to proof that inx is always smaller than x-1? if not why?

does ever sound wave have a positive and negative frequency?

https://lh3.googleusercontent.com/0GOyZeQMdpLgYxYwwP4FMabe-Mk7QpADPC4ZK4PVpBGKvamcqjopOf3M0evdhE8PHZ3iTQ=s138 m1 is 4 kg and m2 is 8 kg. The kinetic friction coefficient on the table is 0.3. m1 is held in place. When m1 is released, m2 accelerates 1.2 m to the floor. Use conservation of...

$f(n)=\underbrace{111--1}\underbrace{222--2}$ $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,n$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,n$ prove:$f(n)$ is a product of two consecutive positive integers for all $n\in N$

Homework Statement Determine the Work done by the electric field E = axX - ay2y in moving a unit positive charge from position p1 (-2,0,0) to position p2 (5,-1,3) the distances are in m Homework EquationsThe Attempt at a Solution I'm not really experienced with forums therefore my attempted...

I know that in formus there are many answers about this question .I just want the value of g (will it be positive or negative) in this example which I am going to give , I threw a ball vertically upward the value of g at its max height (vi=0) ,what will be the value of g +10 or -10 m/s^2. I...

Is 23 = 5(-4)-3 gives a remainder -3 when divided by 5 ? is this statement true ? some of my colleagues said that remainder cannot be negative numbers as definition but I am doubt that can -3 be a remainder too?

Hi, I'm having trouble understanding this attached example in my physics textbook. It notes torque as being positive when substituted back into mg-Ft=-ma rather than being negative which I would think it would be because it is going in the clockwise direction. Can anyone help me understand why...

Someone please tell me what is wrong with this logic: i = √-1 i2= √-1√-1 = √(-1)(-1) = √+1 = 1 But also i2 = (√-1)1/2= -1

Homework Statement Prove that if ##\sigma## is the ##m##-cycle ##(a_1 ~ a_2 ... a_m)##, then for all ##i \in \{1,...,m\}##, ##\sigma^{i}(a_k) = a_{k+i}##, where ##k+i## is replaced by its least positive residue ##\mod m##. Homework EquationsThe Attempt at a Solution My question is...

I read that states are positive operators of unit trace - not elements of a vector space. Is it referring to quantum states or all classical states? I know operators are like minus, plus, square root and vectors are like rays in Hilbert space.. but why can't quantum states be vectors when in...

prove by induction for all positive integers n: 1+5+9+13+...+(4n-3)= n/2(4n-2) i tried this by trying to prove n/2(4n-2)+ (4(k+1)-3) = k+1/2(4(k+1)-2) but it did not work out for me.

Homework Statement Show, using the axiom of completeness of ##\mathbb{R}##, that every positive real number has a unique n'th root that is a positive real number. Or in symbols: ##n \in \mathbb{N_0}, a \in \mathbb{R^{+}} \Rightarrow \exists! x \in \mathbb{R^{+}}: x^n = a## Homework...

find lowest positive p such that $\cos(p\sin \, x) = \sin (p\cos\, x)$

Homework Statement Two equal positive charges are held fixed and separated by distance D. Find the electric field vector along their perpendicular bisector. Then find the position relative to their center where the field is a maximum There was another thread with this question but the...

Homework Statement Hi everybody! I'm preparing a maths exam so I run through a lot of problems, and I am unsure whether I tackled this one correctly or not: Prove that for every differentiable function ##f: \mathbb{R}^3 \to \mathbb{R}## and for every point ##x \in \mathbb{R}^3## the following...

I have the equation ##\sin 3x = \cos 7x##, and, in degrees, I have to find the smallest positive solution. Immediately, we can see that sin and cos are equal if their arguments are complements, so ##3x + 7x = 90##, which means that ##x = 9##. I know that that is a correct solution, but how do...

Hi, I have following two parameters with me a) Maximum three phase fault current in amperes (A) and phase angle in degrees (B). I want to calculate the positive sequence resistance (R) and reactance (X) from above two variables for a symmetric system. I couldn't figure out a way to find R and...

I am solving for the square root of a complex number, namely: ##\sqrt{5 -12i}## Let's assume for brevity's sake that I already have the solution ##3- 2i##. This is fine and well, but the book that I am reading goes on to say that "##- (3 -2i)## is an equally valid solution, since there is no...

given :$f(x)=x^3+ax^2+bx+1$ with $a\geq 0 \,\, and \,\, b\geq 0$ and also all of the three roots of $f(x)=0$ are real numbers, prove $f(2)\geq 27$

I know its very basic but still. From the school level we thaught that positive attracts negative. But i still don't know what is reason behind it. Why this work on atomic level? What is the reason behind the electrostatic attraction?

Homework Statement (22016+ 5)m + 22015 = 2n + 1[/B] find every n and m pairs as they are positive integersThe Attempt at a Solution (22016+ 5)0 + 22015 = 22015 + 1[/B] so one pair is m= 0 , n = 2015 if m =1 the equation is meaningless if m> 1 so there are really amount of powers that...

Consider an ideal gas following a thermodynamics cycle, represented on a ##P-V## plane. I read that if the cycle is "travelled" clockwise then ##W_{gas, cycle}>0## so the gas does positive work, while if the cycle is "travelled" counterclockwise then ##W_{gas, cycle}<0## but it seems to me that...

Homework Statement a positive definite matrix has eigenvalues λ=1 and λ=2. find the matrix Homework EquationsThe Attempt at a Solution I've used a 2x2 matrix with entries a0,a1,a2,a3 as the unknown matrix but no use. (As little as i know a0 and a3 should be 1 and 2 respectively...

I have the following problem: What is the sum of the first 40 positive odd integers? I look at the solution, and it says that "The sum of the first 40 positive odd integers is ##1 + 3 + 5 + \dotsm + 77 + 79##. And then it goes on with the solution. My question is, how do I find that 79 is...