Expression Definition and 999 Threads

Suppose we have a system with M nuclei and N electrons the electron density is defined as: \rho(\mathbf{r}) = \sum\limits_{\sigma = \uparrow, \downarrow} \sum\limits_{i}^N \psi^{*}_{i}(\mathbf{r\sigma})\psi_{i}(\mathbf{r\sigma}) i would like to know if it is valid...

Homework Statement Let n be a positive integer. Determine the smallest possible value of $$|p(1)|^2+|p(2)|^2 + ...+ |p(n+3)|^2 $$ over all a monic polynomials p with degree n. The Attempt at a Solution Let the polynomial be x^n+c_{n-1} x^{n-1} +...+ c_1x+c_0 p(1) =...

Hello Forum! I was wondering: In the rate law expressions, I could never find an example with a solid or a liquid in the reactants in my textbook (Chemistry by Zumdahl). I searched Chemistry (Raymond Chang) and Principles of Molecular Chemistry, without any success. What happens to...

I am ending with no operator in the end. So 1000 160 would be the answer or what. I do not know what to do from here. Please help!

hi all, Would it be possible for you to explain how to reach a solution for this question, or explain the process that you need to find the solution thank you

Homework Statement I try to derive the expression of ω with respect to t, but the problem is the armature current Ia or the flux is unknown. I don't know how to solve it. Anyone could give me ideas? Thanks a lotHomework Equations τ=J(ω/t) Vs=IaRa+Ea T=KEøIa Ea=KEøω

How to read this expression "A graph G = (V ,E)"

Hello I'm solving previous exams and there is this exercise that appears in almost every exam : Homework Statement Suppose v moles of a gas H2O are enclosed in a constant volume V at a low temperature so the gas is in aN undissociated state. At highest temperatureS, H2O molecules are...

Factorize the expression $(1+a+\cdots+a^n)^2-a^n$.

Hi, all. Here is an expression about kinetic energy from analytical dynamics of Haim Baruh which confuses me. "Consider a particle and the case which the kinetic energy is only quadratic in terms of velocity of the particle. We take the differential form of work-energy principle and remove...

Hello I just wanted to see if I did this right. I've come up with two trees and I'm pretty sure one of them is correct, I'm just not sure. Construct the Tree of the algebraic expression: ((x - 2) + 3) / ((2 - (3 + y)) x (w - 8))

State the differences between an expression and its simplified equivalent.

I'm looking for a proof of a validity of the inequation: (n-1)\sum_{i=1}^{n}x_{i}^{2}\neq 2\sum_{i=1,j=1,j<i}^{n}x_{i}x_{j} Assumptions: n\geq 2 \exists (i,j),x_{i}\neq x_{j} i=1,...,n j=1,...,n I have no idea how to prove those non-trivial expressions.

Homework Statement For vi(t) =V0 cosωt, obtain an expression for vout(t) in the circuit below and then evaluate it for V0 = 4 V, ω = 400 rad/s, R = 5 kΩ, and C = 2.5 μF. Homework Equations The Attempt at a Solution For this problem, I am having difficulty taking that second term...

Homework Statement find the general formula to calculate the sum Homework Equations 1+11+111+1111+11111+....upto n terms The Attempt at a Solution 100 + (101+100) + (102+101 + 100) + (103 + 102+101 + 100) + ... ==> (100+100+100+...upto n terms) + (101+101+101+...upto n-1 terms)...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement An N-turn circular coil of radius r with a total resistance of R is placed such that the normal to its plane is parallel to the +z axis. A uniform magnetic field varies with time according to B=B0sin(\omegat) where the amplitude B0 and angular frequency ω are constants...

Homework Statement Actually this is not from homework. It occurs in my brain this afternoon. Is it possible to derive the analytic expression of a function by its Taylor series expansion? For example, given the following expansion, how to derive the analytic expression of it? f(x) =...

Homework Statement Simplify sqrt(x^2+(y-sqrt(5))^2) = 8 - sqrt(x^2 + (y+sqrt(5))^2) The Attempt at a Solution I know squaring both sides, collecting like terms and simplifying gets the equation but in my solution manual they do it a different way that is a lot shorter and I need help...

Without the help of calculator, evaluate $\cos \dfrac{\pi}{7}\cos \dfrac{2\pi}{7}\cos \dfrac{4\pi}{7}$.

Hi Guys, I have an expression that i am struggling to manipulate into a laplace transform. This expression should fit one or a combination of the common transform pairs. I believe the transform the expression should be fitting is either a unit step 1/s a unit ramp 1/s^2 an exponential 1/s+a...

I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

Okay, This could be the easiest math question on here... but I'm going to ask the dumb question anyway. I have several coordinate points to solve for, and in each case I subtract the same amount from the previous "x" to get the next "x" value (X2...3...4...5...). The only point where I...

Q4.) Quadratic equation: \frac{-2x^2-14x-49}{x^3-7x^2}

given : $\dfrac {x}{m}+\dfrac{y}{n} +\dfrac {z}{p}=1$ $\dfrac {m}{x}+\dfrac{n}{y} +\dfrac {p}{z}=0$ find: $\dfrac {x^2}{m^2}+\dfrac{y^2}{n^2} +\dfrac {z^2}{p^2}=?$

simplify: $\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$

Hello! :) I have a question: Suppose that $\Sigma=\{0,1\}$.Is the language $\{0^{m}1^{n}:m+n \geq 2\}$ regular? I tried to find a regular expression.I checked the case $m+n=2$ and I found that the possible words are $00,01,11$ .But..how can I continue? :confused:

Homework Statement I need to obtain the minimum second order circuit of the function: Homework Equations The Attempt at a Solution I know that in order to get the minimum second order circuit, I need to use K-Map using both miniterms and maxiterm and compare them. My problem is to put the...

Hi, Homework Statement Consider the vector potential, \vec{A}(\vec{x}), below. The problem is to calculate \vec{A}(\vec{x}) explictly, and show that it has components A_{r}, A_{\theta} and A_{\phi} Homework Equations \vec{A}(\vec{x}) = \frac{g}{4\pi} \int_{-\infty}^{0} \frac{dz'...

Homework Statement When pressure is applied to a liquid, its volume decreases. Assuming that the isothermal compressibility κ=-1/V(δV/δP) is independent of pressure, derive an expression for the volume as a function of pressure. Homework Equations The Attempt at a Solution I don't...

Hi, I've attached a screenshot in which a solution simplifies an expression given x>>a. I have been trying to simplify and express the equation as shown, but keep failing to recognize how they reached their solution. If anyone could provide a step-by-step breakdown that would be greatly...

Hello! Talking about propagation of an electro-magnetic field in a non-isotropic medium, I've got some troubles with the expression in object, used to show the Faraday rotation of the polarization of a field. Homework Statement An electro-magnetic field enters a particular medium...

Hi, (not homework/academic) Is a closed form of the following expression possible? Either way, some pointers in the right direction would be really helpful. H(s)=\sum_{n=-\infty}^\infty \frac{k^n}{k^n+a/s} Thanks, D

P and k are four-momentum of two particles. I read in a paper which said that [\slashed{P},\slashed{k}]=\slashed{P}\slashed{k} - \slashed{k}\slashed{P} is time-reversal odd. Why?

Hello! Tchebysheff polynomials are often defined with trigonometric functions: T_m (x) = \begin{cases} \cos(m \arccos (x)) & -1 \le x \le 1\\ \mathrm{cosh} (m \mathrm{arccosh} (x)) & x > 1\\(-1)^m \mathrm{cosh} (m \mathrm{arccosh} |x|) & x < 1 \end{cases} But they are also polynomials, and...

Hi MHB, I am completely clueless about how to tackle the problem below, given I noticed $y$ increases as $x$ increases, so there is no maximum point over the entire domain for that function, that is for $x \ge 0$, isn't that so?(Tmi) For what value of $x$ is the expression in...

In the attached image, I am having trouble with point 66. I realize the notation is a bit archaic, so I'll explain as much as I can. [(x,y)∈]a means "the set of solutions of the proposition a(x,y)." For example, the set of solutions to the proposition x < y. -= means "is not equivalent to"...

how does \frac{5700}{\sqrt{15,300}} turn into \frac{570}{\sqrt{153}} ??

Homework Statement I did an experiment investigating what effect height has on force and now i need a theoretical value to compare it to Homework Equations f=ma but i don't think acceleration is constant here The Attempt at a Solution f=ma f=0.104x9.8 f=1.01 i got 49 N with...

I would like to get an answer or pointers to suitable material, on the following question: I know that ∫|f(x)|2dx is finite. Can we say that lim x→±∞ x*(d/dx)|f(x)|2 is zero? Are there any theorems about such limits with unknown functions that have some known properties? Basically this question...

Homework Statement A solid flywheel of radius R and mass M is mounted on a light shaft of radius r so that the axis of rotation is horizontal. A light, inelastic rope is wound around the drive shaft and is connected, via a light, frictionless pulley to a mass m, which is suspended a height h...

Homework Statement In a triangle ABC let A,B,C denote the angles of the triangle. Then maximum value of the expression sinA/A + sinB/B + sinC/C is Homework Equations The Attempt at a Solution Applying Cauchy Shwarz inequality \dfrac{sinA}{A} + \dfrac{sinB}{B} + \dfrac{sinC}{C} \leq...

In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...

Hi, I'm reading a paper on foundations of QM where the expression below appeared \frac{1}{2}m\left(\frac{d^2 \overrightarrow{r}^2}{dt^2}\right)=m\left(\frac{d^2 \overrightarrow{r}}{dt^2}\right).\overrightarrow{r}+m\left(\frac{d \overrightarrow{r}}{dt}\right)^2 I cannot identify where it...

Hello, I have an array of length M. Some of the indices are non-negative. I need to derive a function/analytic expression (preferably linear or convex) that finds the span of indices for which the indices are non-negative. Example: Let p denote the desired vector. Let, p = [0 0 0.3 2.6...

Hello, This actually isn't a homework question, more of a curiosity, but since its a book problem I decided to post it here. Homework Statement An object is released from rest at time t=0 and falls through the air, which exerts a resistive force such that the acceleration a of the the...

Hello, using octave when I evaluate this expression (1+1/x)*x-x, with x = 10^(15) i get as result 1.125, I didn't undesrtood why, I know that octave show 15 digits in format long so when i evaluate (1+1/x)*x i get 1e15, the last digit is not visible and it is 1, so when i do substraction i get...

Homework Statement Find, using l'Hôpital's rule: lim x-> ∞ ((tan(ax)-atanx)/(sin(ax)-asinx)) Where a is a non constant greater than ± 1. Homework Equations -The Attempt at a Solution I can't work out anything from this point. I don't know how to change or factorize the expression (is there a...

Homework Statement In a triangle ABC, with usual notation, if ##a^2b^2c^2 (\sin 2A + \sin 2B + \sin 2C) = λ(∆)^x## where ∆ is the area of the triangle and x ##\in## Q, find (λx). Homework Equations The Attempt at a Solution The usual notation is: a,b,c are three sides of the...

Homework Statement So as a part of a very long question on homework for thermodynamics, I and some of my friends got into a debate about how to write an expression for entropy at a particular state. Homework Equations delS(state 1 to 2)= Cv*ln(T2/T1)+R*ln(V2/V1) (from constitutive...