Conditions Definition and 978 Threads

Hello all, I am currently in possession of two chemistry textbooks, Changs and Atkins, which I believe are both fairly new versions. Changs defines STP at 25 degrees Celsius and 1 atm, and Atkins defines STP at 25 degrees Celsius and 1 bar; I understand that numerically it would not make a...

The positive integers $a_1,\,a_2,\,\cdots,a_7$ satisfy the conditions $a_6=144$, $a_{n+3}=a_{n+2}(a_{n+1}+a_n)$, where $n=1,\,2,\,3,\,4$. Determine $a_7$.

Homework Statement How fast would a electric arc be when it ionizes through normal, unpressured air between say, two electrodes? Not the same as lightning as it is hypothetically from an artificial source. Homework Equations How would one calculate (please include your formula's and which...

Homework Statement Verify that diamond becomes more stable than graphite at approximately 15 kbars Homework Equations The Attempt at a Solution So, I understand that to show one substance is more stable than another at particular environmental conditions, I just have to show...

This is my first post so I hope this in the right place. I am fairly sure this is quite a straight forward question but I having trouble working out the details of it. "State the boundary conditions for an inviscid fluid at an impermeable fixed boundary x_3-h(x_1,x_3)=0 where we do...

How to solve this question. Please explain step by step.

Homework Statement Consider the RL circuit shown in the figure. Assume that the current ##i(t)## has reached a steady state with the switch at position ##A##. At time ##t = 0##, the switch is moved from position ##A## to position ##B##. http://imgur.com/dRIOrp0 If I use the image button...

Hi, it is easy solving these PDEs with the idealized homogeneous BCs they throw out in class, but I am having some difficulty solving the transient problem posed in the images below. I have tried working through it, but I don't have confidence in the result. I overlook the solution when the...

Homework Statement Let ##a>0## and y(x)=\left\{\begin{matrix} -x ;& x<-a\\ Cx^2+D;& -a<x<a\\ x;& x>a \end{matrix}\right. a) Find ##C## and ##D## so that ##y\in C^1(\mathbb{R})## b) For A>a calculate ##\int_{-A}^{A}(1-({y}')^2)dx## c) Is it possible to find ##C## and ##D## so that ##y\in...

Homework Statement Find the volume of an object bounded by x2 + y2 ≤ 1, x2 + z2 ≤ 1 and y2 + z2 ≤ 1. Homework Equations The Attempt at a Solution This stuff is very new to me (multiple integrals to find volume) so I am not entirely familiar with it. My first thought was to put...

How to show in details that the function |x| satisfies Dirichlet's conditions on $$[-\pi \pi]$$.; I know the Dirichlet's conditions, but facing problems to apply it on the given function.

Hi I am tutoring a pupil in high-school out of necessity (no other teachers avail), while I am not so acquainted anymore with chemistry. The pupil showed me a question concerning the calculation of the reaction enthalpy which looked somewhat as follows: 1. Problem statement, all variables...

Burgers Equation Question -- cannot satisfy initial conditions Homework Statement Use characteristics to solve u_t+uu_x=0 on half line x≥0 with u(x,0)=x^2 Homework Equations NA The Attempt at a Solution I think I have an issue with the initial condition. So solving via...

Hi! :o Given then following problem: $$ \min [-x_1 - (x_2 -9)^2]$$ subject to $$4x_1^2+x_2^2 \leq 400$$ I have to find the solution using the KKT conditions. I have found that the solution is $(0,9)$. Is my result correct?

I'm working on a student design project building a multirotor UAV to host a sensor array. The airframe supports arm beams with motors producing thrust at the end, a battery, a flight controller, payload, ESC's and needs to be custom made so that it is of a size that can support large blades and...

Hello, I am looking to solve the 3D equation in spherical coordinates \nabla \cdot \vec{J} = 0 using the Ohm's law \vec{J} = \sigma \cdot (\vec{E} + \vec{U} \times \vec{B}) where \sigma is a given 3x3 nonsymmetric conductivity matrix and U,B are given vector fields. I desire the...

Hi, All: I have a quotient map given by the mapping torus (S,h) , where S is a compact surface with nonempty boundary, and h: S→S is a homeomorphism. Let I=[0,1]. The mapping torus ## S_h## of the pair (S,h) is defined as the quotient q: $$ q:S \times I/~$$ , where (x,0)~(h(x),1), i.e., we...

Hi, I have to use a wide 5 point stencil to solve a problem to fourth order accuracy. In particular, the one I'm using is: u'' = -f(x + 2h) + 16f(x + h) - 30f(x) + 16f(x - h) - f(x - 2h) / 12h2 or when discretized u'' = -Uj-2 + 16Uj-1 -30Uj + 16Uj+1 -Uj+2 / 12h2 In addition to...

Hi, I'm trying to get my head around Schrödinger's equation and quantum wave theory. I'll try to shortly state how I understand it so you may see where I'm wrong and better answer the question. In classical mechanics if you solve a linear differential equation, the sum of the solutions is also...

Given a PDE of order 1 and another of order 2, you could show me what is, or which are, all possible initial conditions? For an ODE of order 2, for example, the initial condition is simple, is (t₀, y₀, y'₀). However, for a PDE, I think that there is various way to specify the initial condition...

Hello, I am graduate student in NE within the US. I am working on a grant that examines a small (10-100 microns) ceramic film region on the outside of the cladding region. I have assessed the neutronic impact, as well as a thermal impact (heat transfer coefficients, etc.) of the additional...

Hello! I have a nifty set of problems (or rather one problem, gradually building itself to be a great problem) that I like to collectively call "The final problem" as it is the last thing I need before I can take the exam in Numerical Methods.Information There is given a Laplace equation...

In Griffith's section about electrostatic boundary conditions, he says that given a surface with charge density \sigma , and take a wafer-thin Gaussian pillbox extending over the top and bottom of the surface, Gauss's law states that: \oint_{S} \mathbf{E} \cdot d \mathbf{a} =...

Hello. I'd like to know, does anybody know any information about finding boudary conditions for E, H vectors in case of rough interface, if phi(x) function is set. Maybe such kind of case ( 2D or 3D case) has been considered somewhere. Thank you in anvance.

I know that d^2<4mk for underdamped, d^2>4mk for overdamped and d^2=4mk for critically damped. This is true if there is only 1 mass and spring and damper. How to use these equations if I have 2 mass, 3 spring and 3 dampers. That is d,m,k are in 2x2 matrices. Please some one help me with this.

Hi, I'm having a problem with NDSolve in mathematica where it is interpreting my initial conditions as "True" or "False". Here is the code: soln = NDSolve[{eqn1[[1]], eqn1[[2]], x[0] == y[0] == 0, x'[0] == 1, y'[0] == 0}, {x, y}, t]; where eqn1 is determined by the following code...

Homework Statement Consider a charged particle, of mass m and charge q, confined in a device called a Penning Trap. In this device, there is a quadrupole electric field described in cartesian coordinates by the potential Phi[x,y,z] = U0 (2z^2 - x^2 - y^2) / (r0^2 + 2z0^2) Where U0 is...

Homework Statement We study the free electromagnetic field in a charge and current free cubic box with with edge length L and volume V. The vector potential in such a system is given via Fourier series: Homework Equations \vec{A}(\vec{r}, t) = \sum\limits_{k} \vec{A}_k(t) e^{i...

Given x = \left\{\begin{matrix} y \;\;\; case\;A\\ z \;\;\; case\;B\\ \end{matrix}\right. So, operate x means to operate the 2 cases of right side? For example: \int x\;dx = \left\{\begin{matrix} \int y\;dx \;\;\; case\;A\\ \int z\;dx \;\;\; case\;B\\ \end{matrix}\right. Correct?

In linearized gravity we can one sets $$(1) \ \ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}$$ where h is taken to be a small perturbation about the flat space metric. One common decomposition of h is to write the spatial part as $$ h_{i j} = 2 s_{ij} - 2\psi \delta_{ij} \ h_{0i} \equiv...

Homework Statement Just need some quick confirmation. For a beam which has a load applied to it, will its free end always have a shear force, bending moment and curvature of zero?

Homework Statement Determining two sets of boundary conditions for a double integral problem in the polar coordinate system. Is the below correct? Homework Equations The Attempt at a Solution There are two sets of boundary conditions that you can use to solve this problem in the polar...

What is the answer of this differential equation. ((d^2) r)/((ds)^2) +(m/(r^2)) -(nr/3)=0 the boundary conditions (i) r=a when s=0 and (ii) dr/ds =0 when r=b. m and n are constants.

If I want to verify an electric field E is possible in free space, do I just need to check ∇xE =0?

Homework Statement http://imgur.com/Mwin7dB http://imgur.com/Mwin7dB Homework Equations The Attempt at a Solution This is a fairly simple problem. My issue is that I can't identify the second initial condition. The first one is simple. At t=0, the voltage on the capacitor is...

Mod note: Reinstated problem after poster deleted it. [/color] Homework Statement Just wondering if I did this correctly: ##y''+4y'+4y=e^{x}## and initial conditions ##y(0)=0; y'(0)=1## Homework Equations The Attempt at a Solution So I found the characteristic equation to be...

HI I study some thing about fierz and paulli conditions In massive gravity and Higher spin particle, what's difference between them? the conditions in massive gravity and higher spin are similar. are they related to them? thanks

Homework Statement Ignore the text in German. You just need to see the picture. 2 conductors both with potential 0 are given. \alpha is the angle between the conductors. (r, \varphi) are polar coordinates pointing to a point in the plane. Homework Equations What we need to do is...

Homework Statement This is what I understand about Alternating Series right now: If I have an alternate series, I can apply the alternative series test. \sum(-1)^{n}a_{n} Condition 1: Nth term test on a_{n} Condition 2: 0 < a_{n+1} ≤ a_{n}If condition 1 is positive or ∞, convergence is...

Homework Statement solve the heat equation over the interval [0,1] with the following initial data and mixed boundary conditions.Homework Equations \partial _{t}u=2\partial _{x}^{2}u u(0,t)=0, \frac{\partial u}{\partial x}(1,t)=0 with B.C u(x,0)=f(x) where f is piecewise with values: 0...

Homework Statement Consider a 1-dimensional linear harmonic oscilator. Any measurement of it's energy can either return the value of ħw/2 or 3ħw/2, with equal probability. The mean value of the momentum <P> at the instant t=0 is <P> = (mħw/2)1/2 Find the wave function ψ(x,0) for this...

I want to show that if G is a smooth manifold and the multiplication map m:G×G\rightarrow G defined by m(g,h)=gh is smooth, then G is a Lie group. All there is to show is that the inverse map i(g)=g^{-1} is also a smooth map. We can consider a map F:G×G\rightarrow G×G where F(g,h)=(g,gh) and...

Make up an equation that satisfies the given conditions: must have x-intercepts at (-1, 0) and (2, 0). It must also have a y-intercept at (0, 4). Is it correct to say that the equation with x-intercepts would look like this: y = (x - 2) (x + 1)How do you factor the y-intercept?

Homework Statement (A) The damped oscillator is described by the equation mx''+bx'+kx=0. What is the condition for critical damping expressed in terms of m,b,k. Assume this is satisfied. (B) For t<0 the mass is at rest (x=0). This mass is set in motion at t=0 by a sharp impulsive force so...

What are the boundary conditions of the universe?

For any element x \in A_5, we have that [A_5:C_{A_5}(x)]=\begin{cases} [S_5:C_{S_5}(x)], & \text{condition 1} \\ \frac{1}{2}[S_5:C_{S_5}(x)], & \text{condition 2} \end{cases} Basically I want to know what the conditions are. Note that C is the centralizer.

Homework Statement Denote the ground state and the first excited state of a 1D quantum system by ##\psi_{0}## and ##\psi_{1}##. If it is given that $$\psi_{1}(x) = x \psi_{0}(x)\,\,\,\text{and}\,\,V(0)=0$$ find the potential V(x). Homework Equations TISE The Attempt at a Solution If I sub...

What is the least restrictive set of conditions needed to utilize the formula ##\int\limits_{\Omega}\mathrm{d}\alpha=\int\limits_{\partial\Omega} \alpha##?

Homework Statement Given: A sealed, rigid container (cannot change shape or size) containing steam at the shown conditions has heat added until it reaches the final shown state. Determine: a) heat added, b) work performed, c) change in internal energy of the system, and d) final system...

Given that the function $f(x)$ is defined on the set of natural numbers, taking values from the natural numbers, and that it satisfies the following conditions: (a) $f(xy)=f(x)+f(y)-1$ for any $x,y \in N$. (b) the equality $f(x)=1$ is true for finitely many numbers. (c) $f(90) = 5$...