Expression Definition and 999 Threads

Hello, I have an analytical expression E_{i} that I want to fit it to some data E(Ref)_{i} . I fitted this expression for N-points: I have calculated the value of chi-squared using the following formula: \chi^{2}=\frac{1}{N-1}\sum_{i=1}^{N}\frac{(E_i-E(Ref)_i)^{2}}{σ_{i}^{2}} where...

Hi, I am trying to understand the calculation of the characteristic impedance of a CPW ground. I need to get an analytical expression for the impedance. My first step was to read the book: "Coplanar_waveguide_circuits__components__and_systems" Here is what I don't understand: the...

A rope of negligible mass is wrapped around a uniform solid cylinder, of radius R, that can rotate freely about its axis, which is horizontal and fixed. A block hangs vertically from the rope and causes the cylinder to spin. The blocks mass, M_B is 4 times the mass, M, of the cylinder. Find an...

Homework Statement 1+2x+(4!x^(2))/((2!)^(2))+(6!x^(3))/((3!)^(2))+(8!x^(4))/((4!)^(2))+... Homework Equations Uhhhhh... The Attempt at a Solution Well, the denominator looks like it's going to be (n!)^2. And this expression appears to be using values of N≥0. But I'm not so sure...

Hello, My question is concerning how to compute the complex gradient of the following cost functional with respect to W: F=Ʃ_i=1:M ||y_i-Go*W_i||^2 + Ʃ_i=1:M ||W_i - X*(E_i - Gc*W_i)||^2 Where the summations go from i=1 to i=M and the dimensions of the diferent elements are: y: Nx1 Go: Nxn W...

Homework Statement Prove that sec^(2)(x/2) divided by 1 - tan^(2)(x/2) is sec x Homework Equations Trig identities. The Attempt at a Solution I used the identity: 1 + tan^2(x) = sec^2(x) I get for numerator: 1 + tan^2(x/2) I kept denominator same: 1 - tan^2(x/2) I get the...

problem solved, thanks

Hello, I am reading this paper about quantum gravity, trying and failing to follow along in the derivation of this, eq (204) p. 72, expression for the scale factor: a(t) = a_1 \left( 1 + \frac 3 2 ( 1 + \omega ) H_1 (t - t_1) \right)^{\frac 2 {3(1+\omega)}} (I'm not sure what the...

Hey guys, I was wondering how to get the expression for pauli matrices. I know that for one electron: S_i = \frac{\hbar}{2} \sigma_i But I also know that you can get to the above expression by explicitly calculating the matrix elements of the Sz, Sx and Sy operators (in the basis generated...

In Ramakrishna's paper, http://arxiv.org/ftp/arxiv/papers/1111/1111.1922.pdf , he derived equation (9), page 5. It is a difference of two square-roots using an approximation method. Can anyone help in how this is done? Thanks

hi, let's take something simple, for example: (a>b) && ((b>c) && c>d) || (d > c) Intuitively, it's easy to work out given the values of a, b, c and d and just evaluating the brackets in order of precedence. i.e. Is b > c?? then is c > d Then in addition to the above answer being...

I am trying to understand how, for a given physical system it is possible to come up with the correct expression for the lagrangian and thence the least action formulation from which the governing equations can be derived by application of the euler lagrange equation. From what I have seen so...

Homework Statement The ground state wave function for a particle of mass m moving with energy E in a one-dimensional harmonic oscillator potential with classical frequency omega is: u(subscript 0) (x)= N(subscript 0) exp((-alpha^2)(x^2)/2) and alpha=sqrt (m *omega/h-bar) where...

Homework Statement Reduce the expression to one that just contains xor and/or xnorHomework Equations (A'B'C')+(A'BC)+(ABC')+(AB'C)The Attempt at a Solution C'(A'B'+AB)+C(A'B+AB') C'(A\ominusB)+C(A\oplusB) not really sure what to do next.Do the C' and C cancel each other out?

Is there a simple way to find the integer values of f(x)=(a+5x)/(6x+1) with a, x integers.

Homework Statement With f(x)=-\lgroup\frac{a}{2}-\frac{x}{2b}\rgroup\ln\lgroup\frac{a}{2}-\frac{x}{2b}\rgroup-\lgroup\frac{a}{2}+\frac{x}{2b}\rgroup\ln\lgroup \frac{a}{2}+\frac{x}{2b}\rgroup and z=\frac{df}{dx}=\frac{1}{c} find an expression of x in terms of c. Homework...

Homework Statement Simplify the following expressions (x'y'+xy'+x'y) (p+q'p)(p+qr) Homework Equations Laws of boolean algebra The Attempt at a Solution For the first one I've found many ways to solve it... something isn't right here (x'y'+xy'+x'y) =x'(y'+y)+xy' =x'+xy'...

Homework Statement Reduce, x(w+y'+z') + (w+x)y'z + wx'yz + wxy Homework Equations + stands for OR * (multiplication) stands for AND ' NOT The Attempt at a Solution I tried to combine some terms but I cannot find a good start... x(w+y'+z') + (w+x)y'z + wx'yz + wxy = xw + xy'+...

Homework Statement I need to simplify the boolean expression by algebraic manipulation as much as possible. (a+b+c)*(a'+c)*(a'+b') Homework Equations + stands for OR * stands for AND (or no operator between variables) ' Stands for NOT The Attempt at a Solution I tried but I do not...

Homework Statement A toy cart of mass M1 moves on frictionless wheels as it is pulled by a string under tension T. A block of mass M2 rests on top of the cart. The coefficient of static friction between the block and cart is μ. The cart is moving up a ramp at angle θ. Find an expression for...

A toy cart of mass m1 moves on frictionless wheels as it is pulled by a string under tension T. A block of mass m2 rests on top of that cart. The coefficient of static friction between the cart and block is μ. Find an expression for the maximum tension T that will not cause the block to slide on...

A flat, circular plate (mass Mp, radius Rp, thickness Tp) rotates parallel to the surface of the Earth on a frictionless axle. As it spins, a point on the top of the disc traces a circle each time the plate completes a rotation. in terms of the number of rotations per minute (N/min), create...

Homework Statement csc(cos^-1 u) Homework Equations Fundamental identities properties The Attempt at a Solution The book is incredibly vague on how to do this. I tried multiplying csc by (cosθ/cosθ) to get cotθ*secθ. I'm not sure if this is the right thing to do, or what to do...

I'm having trouble trying to decipher this: A number U is on the unit interval. Write the algebraic expression for "U differs from 0.5 by more than 0.25" This is what I did...am I doing this correctly? 0.5-U > 0.25 after doing the algebra U < 0.25

Homework Statement The position of an object of mass m is given by: http://imageshack.us/photo/my-images/62/20110920161443.jpg/ Find expression for the velocity and the acceleration and deduce the force components acting on the particle. Homework Equations W = vr, v = u+at , f = ma v = d/t...

Homework Statement A particle has mass m = 0.1 kg , has a velocity which is given as: v = 3.2i+4.3j+5.4k m/s It's acted by force f = 7.1i+8.2j+9.3k The questions which arise are: i) Find the speed of the particle. ii) Write down a unit vector in the direction of the velocity. iii)Find...

Hey folks its me again! The problem at hand gives me a potential energy function ( V(x) ) that defines the height of a particle in motion. Next to the problem is a picture of a curvy graph that is y vs x. It asks to find the expression for the horizontal acceleration. This is what I did...

1. a) Prove the following holds for A A is a matrix [a b, c d] I is identity matrix. A^2 = (a+d)A-(ad-bc)I. b) Assuming ad-bc not equal to 0, use a) to obtain an expression for A^-1. The Attempt at a Solution I proved the first equation, but I'm not seeing where it relates to...

Homework Statement consider the cascading of two non identical amplifiers stages, each having a low-pass STC frequency response. STage 1 has a low freqency gain of ALF1 and a 3 dB frequency of f1. Stage 2 has a low frequency gain of ALF2 and a 3 dB frequency of f2. Derive a polynomial...

Homework Statement Determine the expression for the variances in x (that is \sigma2) with respect to the appropriate variables for the following: a) X = \frac{wy}{z}, with variance in w,y,z Homework Equations I'm having trouble typing out the equation, but the equation I know for...

Hello, I'm prepping for a course I'm about to take and on the pre-course syllabus it said I should be able to: "Derive the equations for E and H fields in terms of magnetic current source M." It's been a long time since I've had an EM course, so I'm naturally lost. How would I go about...

Homework Statement Using Leibniz rule and integration by parts, solve \frac{\partial}{\partial x} \int_0^y u dy. Homework Equations u = U(x) f' (\eta) \eta = \eta(x,y) = y g(x)

Homework Statement I could not type it here, so i made a screenshot and posted it below. Homework Equations it's about complex numbers undergraduate level. I'm currently doing Euler's formula and De Moivre's theorem, although I'm not sure that the solution lies there. The Attempt at...

Hey I got an assignment where I have to get an expression of the current density to be: j = -e\int \frac{dk}{4\pi ^{3}} v_{x}f(k) It says k_{x} >0 underneath the intergrale. The current is flowing to the right (velocity of v_{x} > 0) Where f(k) is the fermi-dirac distribution function...

Homework Statement What will be the values of 'm' so that the range of the equation y= \frac{mx^2+3x-4}{-4x^2+3x+m} will be all real values i.e. y\epsilon (-\infty,\infty)given:x can take all real values. any help or hint will be appreciated. Homework Equations The Attempt at a Solution i...

The question states: Determine the negation of the expression. p -> q ^ r. I am having difficulty finding the negation. Below are the steps I have taken in an attempt to come to the solution. The - symbol will be the negate symbol. p -> q ^ r (-p OR q) ^ r -(-p OR q) ^ r...

Homework Statement 2/1+y-2 /2x^3+x its all over top of 2x^3+x Homework Equations The Attempt at a Solution should i multiply the top by 1+y, like the 2 and the -2.

Homework Statement simplify each expression: 2(4-h)^2-32/h Homework Equations The Attempt at a Solution I forget if I should multiply the 2 into the 4-h.

When we refer to terms in an equation, what EXACTLY are we referring to? Suppose for example we have: ab + bc + cd = A Suppose somebody refers to term "ab". Are they referring to the syntactical NAME "ab", the IMAGE of ab (i.e., it's value), or the ARGUMENT (a,b) which belongs to some...

[b]1. Homework Statement The swinging period T(θ) for a small amplitude simple pendulum, is given by T, a constant for a constant length pendulum. If the initial angle θ is large, then the amplitude becomes large and the period needs to be corrected. The correction to the large amplitude...

I have studied in my lower grades that work(w) done or energy is the product of force(f) and displacement(s).Till now I was thinking that this was true. I was not taught that it was the dot product of force and displacement. according to this definition, the work done when the force and...

Normally, integration means summing the infinitesimal rectangles of height f(t) and width dt. The differential dt appears as a multiplier behind the integration mark, \int, therefore. But, what do you think about summing non-standard infinitesimal pieces, like \int{1 \over 1/dt + 1}? For...

"Scientific Thinking Graphing" -Determining the Mathematical Expression Homework Statement Ok, so I recently got an assignment for "Scientific Thinking Graphing Practice". Basically, I need to take a data table that will produce a curve shaped graph and turn it into a straight lined graph...

Homework Statement A square loop with side-length a is positioned at the centre of a long thin solenoid, which has radius r (with r > a), length l and N turns. The plane of the loop is perpendicular to the 5axis of the solenoid. A current I = I0 sin ωt flows through the loop. Derive an...

Homework Statement k(x) = x^2(2x^3+x)^1/3 Homework Equations I used the product rule and the chain rule to get to the point that i did. The Attempt at a Solution dy/dx(x^2)(2x^3+x)^1/3 + dy/dx(2x^3+x)^1/3(x^2) = (2x)(2x^3+x)^1/3 + 1/3(2x^3+x)^-2/3(6x^2+1)(x^2) I can't...

Homework Statement The series, 1 / (1 x 2) + 1 / (2 x 3) + 1 / (3 x 4) + ... + 1 / [n(n + 1)] + ... is not a geometric series. (A) Use the identity 1 / [k(k + 1)] = 1 / k - 1 / (k + 1) to find an expression for the nth partial sum Sn and (B) use it to find the sum of the...

Suppose a particle in frame S moves with acceleration a_{x} and velocity u_{x} at a given instance in the x-direction. I wanted to find the acceleration in a frame S' moving with velocity v in the positive x-direction with respect to frame S. To do this I used the following approach...

Homework Statement Find the vertical asymptote, if there is one, of this rational function. \frac{\sqrt{16x^2 + 3x + 6} -5}{x-1} Homework Equations The Attempt at a Solution This was actually a Calculus problem, I had to find the limit at infinity. I was able to do that easily; an extra...

Homework Statement \frac{d^2y}{dx^2} + (y^4-1)\frac{dy}{dx} = 0 Homework Equations \frac{dy}{dx} + (y^4-1) = 0 The Attempt at a Solution \frac{dy}{dx} = (1- y^4) \frac{dy}{1- y^4} = dx Then I get a horrible expression involving logs and inverse tan functions...

Homework Statement If a polygon has n>=4 sides, what is the probability, in terms of n, that a triangle made up of vertices of the polygon shares at least one side with the polygon. Homework Equations The Attempt at a Solution Treating vertices of polygons as possible outcomes...