Positive Definition and 963 Threads

If I parameterized a surface by the vector function r(a,b) I would then proceed to find the normal to the surface by crossing ra and rb. But how would I determine which normal raXrb or rbXra has the positive orientation? Im assuming you would first need to know if the concave side of the...

Hi, If A is some nonsquare matrix that is possible rank-deficient, then am I right to understand that (A^T)(A) is a positive semidefinite matrix? Does there exist an inverse (A^T A)^-1? Thanks for any help

The linear Diophantine equations: ax+by=c, a,b,c is natural numbers. If c is a multiple of gcd(a,b), there is infinite integer solutions, and I know how to find x,y. However, I wonder how to find positive integer solution x,y only.

Homework Statement Hello everyone. My problem is as follows: In a spontaneous process where two bodies at different temperatures T_{1} and T_{2}, where T_{1}>T_{2}, are put together until they reach thermal equilibrium. The number of atoms or molecules of the first is N_{1} and N_{2} for the...

Homework Statement How come A person picks a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The work done on the macaroni by the person is negative work however when person picks up a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a...

Homework Statement d=1352846320 The question asks for fxy. The rate of change of (the rate of change of f in the x direction) in the y-direction. We know fx is negative because as f moves in the x-direction, f decreases. But how do I know the rate of change of fx in the...

This post in influenced by 3 new threads in our cosmology forum. Recent observational data favors positive curvature of our Universe. The question I have, however, is why positive curvature implies spatially finite Universe? Yes, it might look quite obvious if we embed curved space into higher...

Homework Statement Show that if a 6x6 matrix A has a negative determinant, then A has at least one positive eigenvalue. Hint: Sketch the graph for the characteristic polynomial of A. Homework Equations Characteristic polynomial: (-\lambda)^n + (\text{tr}A)(-\lambda)^{n-1} + ...

Homework Statement Are there any positive integers n, a and b such that 96n+88=a^2+b^2 Homework Equations The Attempt at a Solution It resembles the Pythagorean theorem but I'm not sure how that would help me solve it. I factored the LHS 2^3((2^2)(3)n+11)=a^2+b^2 How do I...

Hello all! *please explain the terms 'positive definite function' and 'semi-definite function'.* CONTEXT: I am reading a book on the stability analysis of non-linear models. In the chapter for 'neighborhood stability analysis',I came across the "Lyapunov function V". V has the following...

A theorem from number theory states that, if a and b are nonzero integers, then there exists a smallest positive linear combination of a and b. This is my proof: Let S be a set such that S = {w\inNatural numbers : w=am+bn} , where a and b are positive integers, m and n are any integers...

Homework Statement Consider a Hilbert space with a (not necessarily orthogonal) basis \{f_i\} Show that G=\sum_i |f_i\rangle\langle f_i| has strictly positive eigenvalues. Homework Equations The Attempt at a Solution I know that G=\sum_i |f_i\rangle\langle f_i| is hermitian...

Let n be a positive integer and a be a positive divisor of n. Is there any general formula to find the number of positive divisors b of n such that (a,b)=1 ?.

Homework Statement Plot the waveforms for capacitor voltage VC, output voltage Vo, and diode voltage Vd given that Vs is a 20 Vpp triangle wave with period T. Use CVD model with diode VON = 0.7 V. Homework Equations KVLs? The Attempt at a Solution From my basic...

1. Three consecutive positive integers are such that the sum of the squares of the first two and the product of the other two is 46. Find the numbers. Variables: x. Three numbers: (x), (x + 1), (x + 2) 2. (I think, although I'm not sure.) x2 + (x + 1)2 + (x + 1)(x + 2) = 46 3. x2...

I am wondering if there is a systematic way to fix the phase of complex eigenvectors. For example e^{i \theta}(1,\omega,\omega^2) where e^{i \theta} is an arbitrary phase and \omega and \omega^2 are the cube roots of unity, is an eigenvector of the cyclic matrix \left(\begin{matrix}0&...

I know this is a basic question, but why are positive frequency modes so important when expanding a field operator. Furthermore, what do they represent?

Good Morning, The equations under investigation: Electrons: J = enμE + eD(dn/dx) Holes: J = epμE - eD(dp/dx) n or p = concentration of electrons or holes respectively D = diffusion constant μ = mobility The question in mind is as follows: If holes are...

Homework Statement How much work is done by the electric field in moving a particle from (a,a,0) to (a,a,a) in a region where the electric field is: E = zye_x + yxey + xyezHomework Equations F=qE W = integral F dot dl V(2)-V(1)= - integral E dot dl The Attempt at a Solution I know how to do...

Question: Show that the derivative of f(x) = (x-a)m (x-b)n vanishes at some point between a and b if m and n are positive integers. My attempt: f(x) = (x-a)m (x-b)n f '(x) = m(x-a)m-1 (x-b)n + n(x-a)m (x-b)n-1 f '(x) = [(x-a)n-1 (x-b)n-1 ] [(m)(x-b) +(n)(x-a)] And this is as far as I got.

Homework Statement Why is weight positive if gravity is negative? Homework Equations W = mg The Attempt at a Solution So say there is some weight of an object, and the object's mass is multiplied by the acceleration due to gravity pointing downwards, so the weight becomes negative...

Homework Statement Two small beads having positive charges 3q and q are fixed at opposite ends of a horizontal insulating rod, extending from the origin to the point x=d. A third small charged bead is free to slide on the rod. At what point is the third bead in equilibrium? Explain whether it...

$$ P(r,\theta) = \frac{1}{\pi}\left(\frac{1}{2} + \sum_{n = 1}^{\infty} r^n\cos\theta\right) = \frac{1}{2\pi}\frac{1 - r^2}{1 - 2r\cos\theta + r^2} $$Prove that $P(r,\theta) > 0$ for all $r$ and $\theta$ where $0\leq r < 1$ and $-\pi\leq\theta\leq\pi$. How can I start this?

Prove that: d/dx x^-n = -nx^-n-1 Use the factorization of a difference of nth powers given in this section (not using quotient rule) My attempt gets me from the definition of the derivative to (1/n^(n-1)) n times... I need the negative. I get nx^(-n-1) instead of -nx^(n-1).

Homework Statement if M is dxd positive semi-definite matrix, then: M = L'(or L transpose) * L where L is a matrix of dimensions rxd How can I get L given M and the number of rows, r? for example, if M is 800x800 p.s.d, I want L such that it is a 30x800 matrix and so M (800x800) = L'...

Homework Statement Lifting a 20lb bucket of sand a distance of 100 ft at a rate of 2ft/s. I would assume: [W=F*d] = [W = MA*d] = [W = M(v/t)*d] and at a constant velocity: rate of v/t=0 so [W = M(0)*d] = [W = 0*d] = [W = 0] However, a video online shows that you'd take 20lb*100 ft...

1.Homework Statement BACKGROUND: A positive helium ion He+ (mass 6.7 x 10-27 kg, charge 2e) is released from rest from the surface of a +1000 V electrode, as shown in the diagram below. It crosses (in vacuum) the gap between the electrodes, passes through a small hole in a 0 V electrode...

For a positive integer $n$, let $$f_n(\theta)=\tan \frac{\theta}{2}(1+\sec \theta)(1+\sec 2\theta)(1+\sec 4 \theta)\cdots (1+\sec2^n \theta)$$ Find the value of (i) $f_2 \left(\dfrac{\pi}{16} \right)$ (ii) $f_3 \left(\dfrac{\pi}{32} \right)$ (iii) $f_4 \left(\dfrac{\pi}{64} \right)$ (iv)...

for the given circuit and waveform , i am not getting how output for ωt < π is Vs + E1 ? given Vs is input and equal to Vm Sinωt

Hi guys, So, these two formulas are making me very confused: UE=kQq/r ΔUE=-WE Ok, here is the problem: Let's imagine that we have two positive charges. One of them is static, the other one can move. If we place the positive charge close to the source charge, the movable...

Homework Statement (i) Show that if A is symmetric positive semi-definite, then there exists a symmetric matrix B such that A=B^2. (ii) Let A be symmetric positive definite. Find a matrix B such that A=B^2.Homework Equations The Attempt at a Solution For part 1, I used: B = Q\sqrt{\Lambda}...

Exploiting quasistatic approximation, if one wishes to calculate self-inductance of any loop, he is led to the following double line integral: \oint\oint\frac{d\vec{l_{1}}\cdot d\vec{l_{2}}}{r}, where r is the distance between the length elements \vec{dl_{1}} and \vec{dl_{2}}. Is this...

Hi experts, I still do not understand how positive charge is distributed inside a conductor. In case of extra electrons is it quite evident, as they are free to move and repel each other, so they go as far away as they can. But what exactly happens if electrons are removed from a conductor...

I am trying to understand the IR spectra of liquid. I can get the autocorrelation function of atoms' velocity, <v_{i}(0)v_{i}(t)> make a Fourier Transformation, the vibrational density of state (VDOS) can be obtained. Does the VDOS always be positive? Or it can also take negative value...

Can someone just confirm if I'm doing these two problems correctly ... 1. How much energy is needed to place 4 positive charges, each of magnitude +5mC, at the vertices of a square of side 2.5cm 2. Choose one way of assembling the charges and calculate the potential at each empty vertex as...

I just want to make sure I'm understanding negative work correctly. An example problem where there is a bullet with an initial velocity of x m/s and a final velocity of 0 m/s. It is stopped by a wood block and the question asks to determine the amount of work done on the bullet by the block. If...

Hi, Acceleration is defined as the change in velocity over the time interval. Is acceleration ever negative, or is it always positive? If I were to throw a rock up in the air, is it always accelerating at 10 m/s22 even up until it stops and starts falling back down? Thanks,

Homework Statement Assume that x is a positive multiple of 5 and is greater than 5. If 2x + 1 < 100, how many values for x are possible? Homework Equations The Attempt at a Solution How I solved the problem First manipulated inequality: 2x+1<100 => 2x < 99 => x <...

What is the fundamental premise of "positive thinking" The only quantifiable effect of positive or negative thinking that I can think of would be how each mindset influences your actual behavior. But do positive thinkers believe that it also somehow produces effects via some unknown mechanism...

Homework Statement I need to understand how signed multiplication is done in 2's to 10's complement.Homework Equations The complement D' of a number D with m digits in base r is rm - D. So, the complement of 010 in binary (2 in dec) is 1000 - 010 = 110 (-2, but 6 if it were unsigned). We add a...

Can anyone help me develop some insight as to what positive and negative voltage means? I've heard of the analogy to water flowing where amps are viewed as units of water flowing through a certain point per unit time and volts are viewed as how high the water is flowing downwards to the...

1. If the sun is reversing polarity where the northern part of the sun is showing signs of becoming positive and the southern part of the sun is already positive and if two like polarities repel could not the sun ? break in two. 2. question If the sun has two positives end and a negative...

Determine all solutions for \dfrac{a}{b} + \dfrac{b}{c} + \dfrac{c}{a} \ = \ 5, where \ \ a, \ b, \ and \ \ c \ \ are \ \ positive \ \ integers, \ \ and \ \ a <b < c.

Hello I am aware of what generates the electric charge of each particle, the virtual fotons around it that the particle generates, and that when two particle interact with each other a foton is exchanged and so forth. My question is though, what generates the positive and negative charge, and...

Homework Statement http://images.4chan.org/sci/src/1340320682704.jpg I am to write KCL equations for this circuit. Why is it that the current flowing AWAY from Node C is written as V2(t). I thought that when a current was flowing AWAY from a node, the current would be -V2(t)...

I am not sure if am suppose to consider this charge q, released in the space where there is no friction, or if it is released where there is friction... am I too far from the answer? Because I would assume that it will be in decreasing acceleration. Very confuse with all this topic. Thanks!

Okay, I have had a idea for some time and I want to see if it will work. first you get Magnesium 24 launch protons at 20 Mev then a decay happens. Now you have Na22 sodium 22 beta positive decays into a anti electron of 1 Mev with its counter particle they annihilation into 2 gamma rays which...

Show that the equation x^3-12x-7.2=0 has one positive and two negative roots: I know this can be solved by trial and error, and finding f(0),f(1-4),f(-1 - -4) I have shown that It has two negative roots and one positive however I'm wondering if there is another method on how to show it has...

What is the "first positive", "second positive", "first negative" systems of nitrogen Hello, I have been trying to catch up on spectroscopy theory, and I'm trying to get a grasp on what all the terms mean. I constantly seem the terms "first positive system", etc... coming up, and I'm not sure...

Does anyone know if I run 12 volts dc at 1 amp power for a distance of 250 feet and one wire is 12 gauge used for positive and other negative wire is 20 gauge will the smaller ground wire affect what the positive wire can carry? John