Condition Definition and 587 Threads

the solution for the infinite num case the problem is that i only could reach the condition that the coefficients are zero when i substituted n=0 , i am reaching two independent variables i am not sure what am i doing wrong that's preventing me from getting a similar result to them "that...

My attempt: $$ \begin{vmatrix} 1-\lambda & b\\ b & a-\lambda \end{vmatrix} =0$$ $$(1-\lambda)(a-\lambda)-b^2=0$$ $$a-\lambda-a\lambda+\lambda^2-b^2=0$$ $$\lambda^2+(-1-a)\lambda +a-b^2=0$$ The value of ##\lambda## will be positive if D < 0, so $$(-1-a)^2-4(a-b^2)<0$$ $$1+2a+a^2-4a+4b^2<0$$...

Let ##V## be a finite dimensional vector space over a field ##F##. If ##L## is a linear operator on ##V## such that the trace of ##L\circ T## is zero for all linear operators ##T## on ##V##, show that ##L = 0##.

I am going over the diffraction condition section in Kittle's Introduction to Solid State Physics physics and I am having a hard time understanding why the phase difference angle for the incident wave is positive while the phase angle difference for the diffracted wave is negative. Thank you...

The Euler method is straightforward to me; i.e ##y_{n+1}=y_n+ hf(t_0, y_0)## where the smaller the steps i.e ##h## size the better the approximation. My question is 'how does one go about in determining the initial condition ##y(0)=1## in this problem? am assuming that this has to be a point...

This is usual induced drag diagram. I have 2 questions: From Kutta–Joukowski theorem Fr is always perpendicular to effective airflow. 1. Does it mean for case without effective airflow(zero induced downward velocity), Fr is perpendicular to freestream airflow,so drag is zero? When effective...

This works: a=0.4 Select[ list, #[[2]] > a-0.025 && #[[2]] < a+0.025 & ] {{401803.,0.42485,3.33299,0.776904,0.277985},{402066.,0.40333,9.23462,0.381478,0.397121},{402872.,0.41899,3.47237,0.742789,0.27385}} But why doesn't this work? :- Select[ list, #[[2]] > b - 0.025 && #[[2]] < b +...

Hello, I try to better understand how and when I can apply the Born rigidity condition. So, for the following example: We've two space probes (Pa and Pb), that travel at an exact equal and same proper acceleration. At a given time tb0 in Pb, and as measured by Pb, the distance is Lba0 (it's...

The original differential equation is: My solution is below, where C and D are constants. I have verified that it satisfies the original DE. When I apply the first boundary condition, I obtain that , but I'm unsure where to go from there to apply the second boundary condition. I know that I...

I tried to solve this problem using the chart given below. But I get a different answer of ##\frac {2}{3}## rather than ##\frac {3}{4}##. Maybe the answer given is incorrect? I determine from the chart the number of ways in which A could win given that A has already won 2 of first 3 points...

I'm reading about Bloch states, these the are states of electrons in a periodic potential. What i know is that the electron in a Bloch state is shared between many ions and it is a stationary state. However, for a 1-dimensional model I've read that at the edge of the first Brillouin zone, when...

##f : [0,2] \to R##. ##f## is continuous and is defined as follows: $$ f = ax^2 + bx ~~~~\text{ if x belongs to [0,1]}$$ $$ f(x)= Ax^3 + Bx^2 + Cx +D ~~~~\text{if x belongs to [1,2]}$$ ##V = \text{space of all such f}## What would the basis for V? Well, for ##x \in [0,1]## the basis for ##V##...

Hi, (This question is part of the same example as a previous post of mine, but I have a question about a different part of it) I was looking at a question from an exam for a course I am self-teaching. There is a sub-question which asks us to find the values of a parameter for which the 2-cycle...

In two different textbooks, there are two different formulas with different derivation styles for the "No Fringe Formation" Condition. In approach (a), they use an amalgamation of bright and dark for 2 wavelengths having very minute difference in the following manner: 2dcostheta=n*λ(1)...

Hm I'm new to these concepts, and I want to make sure I am on the right track, would the relative condition number be: k=(x/2)((1/sqrt(x+1))-(1/sqrt(x))(1/(sqrt(x+1)-sqrt(x))). Or would I have to solve the limit as x approaches 0? Thank you.

A hypersurface being spacelike (a local condition - every tangent to the surface being spacelike) does not preclude that points on it cannot be causally connected (one is in the future or past light cone of the other). A classic example is a spacelike spiral surface. Typically, for foliating a...

The problem is a classical one, basically to find the equations of motion of cylinder of radius a inside a fixed cylinder of radius b, the cylinder that rolls rotate about its own axis in such way that it does not skid/slip. Now, the thing that is making myself confused is the constraint...

The K-L condition has projection operators onto the codespace for the error correction code, as I understand it. My confusion I think comes primarily from what exactly these projections are? As in, how would one find these projections for say, the Shor 9-qubit code?

1.4.1 Miliani HS Find all complex numbers x which satisfy the given condition $\begin{array}{rl} 1+x&=\sqrt{10+2x} \\ (1+x)^2&=10+2x\\ 1+2x+x^2&=10+2x\\ x^2-9&=0\\ (x-3)(x+3)&=0 \end{array}$ ok looks these are not complex numbers unless we go back the the...

Hi everyone, I'm trying to understand the rationale behind the boundary condition for the problem "Finite bending of an incompressible elastic block". (See here from page 180).Here we have as Cauchy Stress tensor (see eq. (5.82)): ##T = - \pi I + \mu (\frac{l_0^2}{4 \bar{\theta}^2 r^2} e_r...

I really have no idea as to how to attack the problem in the first place. I am here to ask for some generous help on how to start. The figure is shown below for reference.

Hi everyone, I am trying to solve the 1 dimensional diffusion equation over an interval of 0 < x < L subject to the boundary conditions that C = kt at x = 0 and C = 0 at x = L. k is a constant. The diffusion equation is \frac{dC}{dt}=D\frac{d^2C}{dx^2} I am using the Laplace transform method...

Now i am rather confused, the answer apparently is that ##(w-u) = \lambda(u-v)## But, i could find a way that disprove the answer, that is: Be u v and w vectors belong to R2, a subspace of R3: What do you think? This is rather strange.

The way I was taught to solve many quasi-linear PDEs was by harnessing the initial condition in the characteristic method at ##u(x,0) = f(x)##. What if however I need use alternative initial conditions such as ##u(x,y=c) = f(x)## for some constant ##c##? Can the solution be propagated the same way?

This is an iff statement, so we proceed as follows ##\Rightarrow## We assume that ##|\phi \rangle## is uncorrelated. Thus the state operator must be of the form ##\hat \rho = \rho^{(1)} \otimes \rho^{(2)}## (equation ##8.16## in Ballentine's book). The spectral decomposition of the state...

Hi, Question: If we have an initial condition, valid for -L \leq x \leq L : f(x) = \frac{40x}{L} how can I utilise a know Fourier series to get to the solution without doing the integration (I know the integral isn't tricky, but still this method might help out in other situations)? We are...

I read this paper where if you take the alcubierre metric calaculations while including torsion in GR you get positive energy spin requirements instead of exotic matter. Here is the link: https://arxiv.org/abs/1807.09745 Could it be because a spinning quantum vacuum will be less stiff like a...

Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1...

I'm a bit confused about the condition given in the description of the symmetry transformation of the filed. Usually, given any symmetry transformation ##x^\mu \mapsto \bar{x}^\mu##, we require $$\bar\phi (\bar x) = \phi(x),$$ i.e. we want the transformed field at the transformed coordinates to...

Question 1: I have used v= Aω*cos(ωt+δ) where A= 0.2 m, ω= π/3, t=1 and δ=0. Are the values right in this case? I am confused. Question 2: From question 1 I have got the value of V which is 9 m/s. By using v= ω√(A^2-x^2), I have got the value of x. Now, do I need to add it with 2.5(distance...

I have tried to write down the boundary conditions in this case and looked into them. As conditions i) and ii) were trivial, i looked into iii) and iv) for information that I could use. But all I got was that for the transmitted wave to have an angle, the reflective wave should also have an...

May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?

V=ir considering the whole circuit Now we knowV=E-ir Then ir=E-ir Therefore i=E/2r Therefore,V=E/2

Show $20a^2+20b^2+5c^2\ge 64$ if $y=x^4+ax^3+bx^2+cx+4$ has a real root.

Hey! :o We have a matrix $A\in \mathbb{R}^{m\times n}$ which has the rank $n$. The condition number is defined as $\displaystyle{k(A)=\frac{\max_{\|x\|=1}\|Ax\|}{\min_{\|x\|=1}\|Ax\|}}$. I want to show that $k_2(A^TA)=\left (k_2(A)\right )^2$. We have that...

h and s can be obtained from "Saturated refrigerant-134a—Pressure table" however, how to get h2? it is not on the curve, and neither p or dV is given in the question. Thank you

Hello! In Optical fibers, let ##k_1## and ##k_2## be respectively the propagation constants in core and cladding, ##\beta## the propagation costant of a mode along the direction ##z##, ##a## the radius of the fiber. Using the normalized quantities ##u=a \sqrt{k_1^2 − \beta^2}## and ##w=a...

Assume there is a boundary separates two medium with different heat conductivity [κ][/1] and [κ][/2]. In one medium, the temperature distribution is [T][/1](r,θ,φ) and on the other medium is [T][/2](r,θ,φ). What is the relationship between [T][/1] and [T][/2] ? Is it - [κ][/1]grad [T][/1]=-...

Homework Statement:: F is not conservative because D is not simply connected Relevant Equations:: Theory Having a set which is not simply connected is a sufficient conditiond for a vector field to be not conservative?

253 Which of the following is the solution to the differential equation condition $$\dfrac{dy}{dx}=2\sin x$$ with the initial condition $$y(\pi)=1$$ a. $y=2\cos{x}+3$ b. $y=2\cos{x}-1$ c. $y=-2\cos{x}+3$ d. $y=-2\cos{x}+1$ e. $y=-2\cos{x}-1$ integrate $y=\displaystyle\int 2\sin...

While determining the condition for the pair of straight line equation ##ax^2+2hxy+by^2+2gx+2fy+c=0## or ##ax2+2(hy+g)x+(by^2+2fy+c)=0 ## (quadratic in x) ##x = \frac{-2(hy+g)}{2a} ± \frac{√((hy+g)^2-a(by^2+2fy+c))}{2a}## The terms inside square root need to be a perfect square and it is...

Clarification: The statement in the title is actually from the solution to the homework question, as given by the textbook (you can see the whole thing below under "Textbook solution"). The solution doesn't explain everything, which is where my confusion comes from. Usually in my classes we...

Hello. I've recently been reading this paper... https://arxiv.org/pdf/gr-qc/0001099.pdf ...in the hope that I can begin to understand some the role of the energy conditions in General Relativity. But I'm not making much progress and so I've turned to this paper...

While deriving continuity equation in Fluid mechanics, our professor switched the order of taking total time derivative and then applying delta operator to the function without stating any condition to do so(Of course I know it is Physics which alows you to do so) . So,I began to think...

Namaste I seek a clarification on the periodicity condition of discrete-time (DT) signals. As stated in Oppenheim’s Signals & Systems, for a DT signal, for example the complex exponential, to be periodic, i.e. ej*w(n+N) = ej*w*n, w/2*pi = m/N, where m/N must be a rational number. Above is...

As far as I know when a function is extremized its partial derivatives are all equal to 0 (provided we aren't dealing with a constraint) ##\left(\frac{\partial f}{\partial x} \right)_{yz} = \left(\frac{\partial f}{\partial y}\right)_{xz} = \left(\frac{\partial f}{\partial z}\right)_{xy} =0##...

Let ##f:\mathbb{R}^n\rightarrow\mathbb{R}^n##. Is there any class of function and some type of "growth conditions" such that bounds like below can be established: \begin{equation} ||f(x)||\geq g\left( \text{dist}(x,\mathcal{X})\right), \end{equation} with ##\mathcal{X}:= \{x:f(x)=0\}## (zero...

I first tried by assuming the matrices but it was becoming complicated so i tried taking transpose on both sides,it also did not help.So now i could not think of what to do further.Help please.

As homework, I shall show that the retarded scalar potential satisfîes the Lorentz gauge condition as well as the inhomogenous wave equation. We saw in class how to do it. But I was thinking about this, and it seems to me that it's redundant to prove both of those things. For, if the scalar...

Hello! I have some data points generated from an unknown distribution (say a 1D Gaussian for example) and I want to build a neural network able to approximate the underlaying distribution i.e. for any given ##x## as input to the neural network, I want the output to be as close as possible to...