Positive Definition and 963 Threads

I'm just learning but I can almost SWEAR that this is right, just reassure me?

Casus irredicibilis describes a situation where a cubic polynomial with integer coefficients has three distinct real roots, but you can't express those roots using just real numbers and radicals. Instead, if you want to only use radicals, then you must use complex numbers, even though the roots...

Homework Statement Find all the positive divisors of 10^n where n is a positive integer. The Attempt at a Solution can I factor this like 2^n5^n I notice that 10 has 4 divisors and 100 has 8 so it might seem that it has 4n divisors but I am not should how to give a nice...

how to prove that R(A)=\text{sum of} N(A-\lambda I)? \lambda is nonzero eignevalues of A

I have a matrix A, which contains only positive real elements. A is a differentiable function of t. Are the eigenvalues of A differentiable by t?

I'm having a argument with a mechanical engineer concerning positive pressure in a room. I was hoping someone could shed light on this. We both agree (of course) that pumping air into a room that will keep the room under positive pressure (relative to the outside) given that the room isn't...

Hello Everyone, In a course on field theory I was asked to calculate the first order correction for Lande g factor. I noticed that this comes out to be positive. ie g-2 > 0 I am wondering if there is a physical reason why this must be positive. Or is it just a matter of chance, that this...

I am trying to setup a circuit with an op-amp that is referenced to high rather than ground and has a positive gain less than one. So for instance, my circuite has power rails at ground and 3.3v. I want an input of 3.3v to give an output of 3.3v and i want an input of 0 to give an output of...

How to divide positive and negative charges from each other without them interacting with other matter or charge patterns. ,please answer I only need this to make my ultimate machine

Hello everyone, I am new to the forum and was wondering if someone can help explain something to me. I would like to understand the meaning of a positivly invariant system. I have checked the definition on wikipedia, http://en.wikipedia.org/wiki/Positive_invariance" and it is...

Say you have a magnet, one end of the magnet has a positive charge and the other end has a negative charge. What would happen to the magnet if you broke it in half?

Hi, I'm new in this forum. I have a problem i can't solve and searching on Google i couldn't find anything. It says: If D(g) is a representation of a finite group of order n , show that K = \sum^{i=1}_{n} D^{\dagger} (g_i) D(g_i) has the properties: b) All eigenvalues of K are...

dy/dx = (4x - y)/(x + 2y) for y(0) = 1 As not seperable us y = vx where v is a funciton of x method. If you follow it through you'll get y as a quadratic. According to the answer scheme, I should take the +ve square root because of y(0) = 1... why? Why can I discard the -ve square root...

A continuous-time markov chain is recurrent if and only if the embedded discrete time markov chain is recurrent. But, (as stated in several sources without proof or example that I can find) if the CTMC is positive recurrent the DTMC may be null recurrent and vice versa. Can someone provide an...

I have a question on the quantity -(dV/dP)T,N where V = volume, P = pressure, T = temp, N = number of moles and T, N are held constant. I see in textbooks that this quantity is always positive at equilibrium. It makes intuitive sense, as if it were negative, it would be unphysical. I've been...

Homework Statement For what b is the following matrix positive definite? (\stackrel{1}{b} \stackrel{b}{4}) (Sorry for the strange way I have that matrix represented) Homework Equations For a positive definite matrix x^{T}Ax for all nonzero x in \Re^n The Attempt at a Solution x^{T}Ax =...

1. The Problem: An elevator is hoisted by its cables at a constant speed is the total work zero, negative, or positive? 2. Homework Equations : g= -9.81m/s2 3. The Attempt at a Solution I'm thinking that since the weight of the elevator is in downward direction along with the acceleration of...

Find the form of all n in N satifying tow(n)=6. (sorry don't know how to write this Tex). What is the smallest positive integer n for which this is true? tow(n)=6 so 6=(1+a1)(1+a2)----(1+ak) where n=p1^a1p2^a2---pk^ak

A gas composed of nuclear fuel is undergoing fission, producing fast moving positive ions that I wish to remove from the system by use of a magnetic mirror. What field strength is needed to ensure the fragments follow the trajectory I need, and not interact with the surrounding material?

Homework Statement in screening for breast cancer, the probability that a mammogram will give a postive result, given that the in dividual has breast cancer is 0.95 (true positive). However the probability of a false positive is 0.1 (a) in a particular population of women, the likelihood...

Show that if n is a positive integer, then C(n,0) < C(n,1) <...<C(n, floor(n/2)) = C Homework Statement Show that if n is a positive integer, then C(n,0) < C(n,1) <...<C(n, floor(n/2)) = C(n, ceiling(n/2)) > ... > C(n, n) Homework Equations none The Attempt at a Solution Seems pretty...

I need to know if there is any relationship between the positive definite matrices and its eigenvalues Also i would appreciate it if some one would also include the relationship between the negative definite matrices and their eigenvalues Also can some also menthow the Gaussian...

I've recently been learning about how to tell if a matrix is positive definite and how to create a positive definite matrix, but I haven't been given a reason why they're useful yet. I'm sure there are plenty of reasons, I just haven't seen them yet. In what ways do the properties of a positive...

So i need to show if a matrix is positive definite or negative or neither I have a matrix 3x3 A so i compute xTAx I am left with an quadratic equation interms of x_1 x_2 and x_3 The Matrix is of the form A = [ 9 -1 2] |-1 7 -3| [2 -3 3] and solving xTAx i get...

[b]1. Which integers have exactly 3 distinct positive factors? Homework Equations [b]3. I would attempt this if I had any idea of what it meant. Can someone show me how to find one answer then I will find the other 2.

In my Physics class tonight (Physics for Scientists and Engineers 2), we have a quiz about the following topic: "Where to place a negative charge between two positive charges so that the negative charge has an equal force with each of the positive charges." I was hoping that someone could...

Say, all objects in a closed Universe are neutral, and there is only 1 (unbalanced) positive charge. Lines of an electric field started on a positive charge can end only on the negative charge or they go into infinity. But in a closed universe there are no negative charges nor they can go...

Hi everyone, this isn't really a homework question- this integral has come up during project work- but this seems like a sensible place to ask it nontheless. Homework Statement Compute I(t)=\int^{\infty}_{0} dx \frac{x^5}{(t+x^2)(1+(t+x^2)^4)} where t is real and positive. Homework...

I have a PDE test next week and I'm kinda confused. How do you prove that eigenvalues are all positive? I know Rayleigh Quotient shows the eigenvalues are greater than or equal to zero, but can someone explain the next step. Thanks in advance

When, let's say, a cylinder is rolling on a plane, and there is a rope coiled around the cylinder and the rope moves at an acceleration of A(rope) at the upper part of the cylinder to the right. Ok, so when I try to envision it, the cylinder is rolling in the CW direction. so R(alpha)= -...

Hi, Suppose we have: q_{ij}=\int_0^1x^{i+j}\,dx can we prove that \mathbf{Q}=[q_{ij}] is positive definite matrix? That is: \mathbf{d}^T\mathbf{Q}\mathbf{d}>0 for all d? Thanks in advance

how to determine which is the answer to positive sqrt and negative sqrt in this problem? substituting works but what if the equation is very long and you can't use calcu or computers http://i.imgur.com/SkcQZ.png also is there a way to solve this without squaring both sides?

Hi! If we have a 2x2 matrix [x y;y z] belonging to a positive semidefinite cone. Why is it equivalent to say x>=0, z>=0, and xz>=y^2? Thanks!

Homework Statement [PLAIN]http://img256.imageshack.us/img256/9025/93408370.jpg The Attempt at a Solution Shouldn't it be 2Q + x = -Q x = -3Q? My book say it is +Q

why positive or negtive polar of battery can not attract small objects ?

Homework Statement If b is added to c = 3.9i + 3.7j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of c. What is the magnitude of b? 2. The attempt at a solution I've probably just been staring at these problems for too long... First of...

greetings, consider a wire which is subjected to AC supply.now consider a point X anywhere on wire. now what will be the potential of that point during the positive and negative halfcycle of sinusoidal AC?what will be the direction of current? thanks

Homework Statement Let f be continuous at c and f(c)>0. Prove that there is an open interval (a,b) centered at c such that f(x)>0 for all x that are elements of (a,b) Homework Equations we are supposed to use the sign preserving property?? The Attempt at a Solution I tried...

Can an interval with all positive functions of x be proven?? f(x) has to always be greater that 0. How do you prove this?? f is continuous as c and f(c)>0. prove that there is an open interval (a.b) centered at c such that f(x)>0 for all x that are elements of (a,b)

Homework Statement http://img33.imageshack.us/img33/8751/49753333t.jpg Problem #2 [PLAIN][PLAIN]http://img121.imageshack.us/img121/5574/35712633.jpg My question is, why do they take positive x0? Shouldn't it be negative since it is that amount of x displacement away from the spring?

Homework Statement This is the conservation of energy in the absence of external forces ΔKE + ΔPE + ΔTE + ΔU= 0 TE is friction, U is other internal energy, like the spring So expand and disregard U and TE for a moment ½m(v² - v₀²) + mg(h - h₀) = 0 Now comes the...

Homework Statement Show that R^x/<-1> is isomorphic to the group of positive real numbers under multiplication. Homework Equations The Attempt at a Solution I know I need to show we have a homomorphism, and is one - to one and onto in order to be isomorphic. I know all...

Homework Statement Let {an}n≥1 and {bn}n≥1 be strictly positive series. If the limit n-> infinity (an/bn) = c /= 0, then the \sum an converges iff \sum bn converges, n≥1 Homework Equations The Attempt at a Solution Since we know that lim (an/bn) = c, then for all ε>0...

Homework Statement Go to http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_c_mech_frq.pdf Question two The solution is http://www.collegeboard.com/prod_downloads/ap/students/physics/ap08_physics_c_mech_sgs_rev.pdfThe Attempt at a Solution My question is part d) in the...

why do positive and negative charges attract each other?

Homework Statement \int ^b_0 cos(\frac{(n-m)\pi}{b}x) dx \int ^b_0 cos(\frac{(n+m)\pi}{b}x) dx n and m are positive integers. The Attempt at a Solution \int ^b_0 cos(\frac{(n-m)\pi}{b}x) dx = \frac{b\;sin[(n-m)\pi]}{(n-m)\pi} Obviously answer is zero if n not equal to...

Homework Statement Find an example with 2 * 2 matrices for which: 0 (= or < ) a (= or < ) b does not imply a 2 (= or <) b2. the trace and the determinant of both a and b matrices should be positive ! Homework Equations The Attempt at a Solution i just need to know 2 things : 1- is there...

Homework Statement This is a proof problem in the mathematical induction section of my textbook. I am having trouble with question (c). Result: 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6 for every positive integer n. (a) Use the result to determine the formula for 22 + 42 + 62 + ... + (2n)2 for...

I can't understand this and i would be appreciate if somebody help me. If in the metal we have a very big number of free electrons they should go to the positive therminal of the batery even if the other end of the wire is not conected to the negative therminal.What stops them.The copper wire...

Let A be a real nxn matrix. What are the requirements of A for A+AT to be positive definite? Is there a condition on eigenvalues of A, so that A+AT is positive definite? Also I am not sure about the definition of a positive definite matrix. In some places it is written that the matrix must be...