Condition Definition and 587 Threads

Hi, It is a well known fact that in an inverse linear problem low condition numbers have low noise amplification and therefore decrease the error. So I wanted to test this: I draw random (skinny) matrices A, calculate y=A*c where c is a known coefficient vector, add some noise and...

hi i'm using Matlab/simulink to create a microgrid model which simulate dynamic control of power based on the loads. the loads are changing based on the realtime. I use several voltage sources to power the loads. I would like to be able to turn on/off the generator based on the loads. for...

Homework Statement Find the deflection at x=L/4 and x=L/2 for the beam Homework Equations See attached pic. The Attempt at a Solution So I have the solution derived in class. Only 0<x<L/2 is derived because since the load on the beam is at L/2, the equation is valid for the...

Greetings! :biggrin: Homework Statement Starting from the Rodrigues formula, derive the orthonormality condition for the Legendre polynomials: \int^{+1}_{-1} P_l(x)P_{l'}(x)dx=(\frac{2}{2l + 1}) δ_{ll'} Hint: Use integration by parts Homework Equations P_l=...

Homework Statement A particle is in a 1D harmonic oscillator potential. Under what conditions will the expectation value of an operator Q (no explicit time dependence) depend on time if (i) the particle is initially in a momentum eigenstate? (ii) the particle is initially in an energy...

Homework Statement dy/dx =4yx^3-y y(1)=-3 dy/y = (4x^3-1)dx ln(y) = x^4-x+C y = e^(x^4-x+C) But an answer source says that after the integration I get ln(y) = x^4 - x + ln(C) so then.. ln(y/c) = x^4 - x y = Ce^(x^4 - x) which makes it much easier to solve for the constant given...

Hi, Given an over-determined system of linear equations y=A c, the condition number of matrix A essentially says how good vector c can be restored from measurements y. Changing the order of rows clearly does not change the condition number. But is there information/literature on how to...

Homework Statement 0<\left|x+3\right|<1/4 Homework Equations The Attempt at a Solution (-13/4)<x<(-11/4) and x\neq-3 Thanks in advance. This is my first post and I am unfamiliar with formatting this kind of stuff so I will work on getting better at that aspect.

Homework Statement now I have a PDE $$u_{xx}+u_{yy}=0,for 0<x,y<1$$ $$u(x,0)=x,u(0,y)=y^2,u(x,1)=0,u(1,y)=y$$ Then I want to know whether there are some method to make the PDE become homogeneous boundary condition. $$i.e. u|_{\partialΩ}=0$$

(If the equation below do not appear correctly, you can read all of the question in the attached file.) Solving the time dependent 1D Schrödinger equation, one can show that in all points (x,t), i\bar{h}\frac{\partial}{\partial t}\Psi(x,t)=-\frac{\bar{h}^2}{2m}\frac{\partial^2}{\partial...

What does it mean for a condition to be "open"? E.g. it is said that det(A)≠0 is an open condition for a matrix group. Furthermore, this implies that GL(n) has the same dimensions as the group of all nxn matrices as, and I quote, "the subgroup of matrices with det(A)=0 is a subset of measure...

Homework Statement Solve the following DE y'' + 8y' − 9y = 0, y(1) = 1, y'(1) = 0 Homework Equations Homogenous DE with constant coefficients The Attempt at a Solution Well, i solved it normally using a CE and having yH= c1 e^t + c2 e^(-9t) .. y' = c1 e^t -9 c2 e^(-9t)...

Hello guys! Homework Statement The question is like this: If ##z=\frac{a}{b}## and ##\frac{1}{a+b}=\frac{1}{a}+\frac{1}{b}##, find ##z##. The Attempt at a Solution This question is challenging for me because I don't know exactly where to start. The latter condition stated, the sum of...

As far as I know there is no explicit formulas but is this true? I've tested it in Matlab with random matrices and It seems true! cond(A+B) =< cond(A) + cond(B) Where can I find a proof for this hypothesis?

I would like to know if the second part of this question is asking something different. **Problem:** Consider the linear system $19x_1+20x_2=b_1, 20x_1+21x_2=b_2$. Compute the condition number of the coefficient matrix. Is the system well-conditioned with respect to perturbations of the...

Homework Statement They give me y ' = (xysinx)/ (y+1) , y(0) = 1 Homework Equations So I just separated and integrated The Attempt at a Solution I'm 99 percent sure I'm OK up till here. I just wanted to get an explanation for something. I was wondering my answer is y + ln(y)...

Hello, According to Stephen Hawking no boundary condition universe does not have any boundary in space time.If it is so then it is like earth.You can not go north to north pole.Earth does not have any edge or boundary.So universe is like closed structure like earth.Means after some times it...

For commutator, HQ-QH = 0 . But for this case as shown below, complex ψQHψ - HcomplexψQψ= 0? If the operator Q is in term of (∂/∂t) and (∂/∂x) ,then the HQ-QH may not be zero. Is there any restriction for Q operator?

It says that |xy| < p. But I don't understand why even after reading the proof. If I have a four state DFA, whose last state is the one that is going to repeat for a given input string of length p, |x| is already going to be four, since it represents the states necessary to reach the repetition...

Starting from the Cauchy definition of convergence of a series : \forall N,\epsilon>0,\exists N_0 | k>N_0\Rightarrow |\underbrace{\sum_{n=1}^{N+k}u_n-\sum_{n=1}^k u_n}_A |<\epsilon rewriting A in terms and considering a positive decreasing sequence : A\Rightarrow \epsilon>u_{N+k}+\ldots...

when we electric field between two conductors in certain direction the current density should pass in its direction why current density direction change at boundary although the direction of electric field is the same for both conductors

Although I understand the derivation of boundary condition in case of steady electric current but I did not understand, that the electric field which is in direction of J current density which is generated from permanent potential to have a current in a conductors that is applied between two...

Given \begin{align} L\phi &= \lambda\phi\\ \phi_t &= M\phi \end{align} where \(L\) and \(M\) are operators and \(\lambda\) a constant. I want to show the compatibily condition is \(L_t + [L,M] = 0\) where \([,]\) is the commutator. \[ (L\phi)_t = L_t\phi + L\phi_t = \lambda\phi_t = \lambda...

Hi All I am among the people who bought the nexus 7 without the data capability and pretty much the first generation of its kind when it first appeared at Google's store. After almost a year and a half I have noticed problems with the battery. It's not much of a problem as it is my annoyance...

Hi all, I'm asking a question about the number of the boundary conditions in high-order PDE. Say, we are solving the nonlinear Burger's equation \frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\nu \frac{\partial^2 u}{\partial x^2} subject to the initial condition u(x,0)=g(x)...

Hi all, It may be a trivial question. But, if I have a PDE of variable u(x,t) -------------------------------- \dot{u} = f(u,\partial_x{u},..) with boundary condition : u(0,t) = u(L,t) =0. -------------------------------- Now I need to calculate \partial_x{u} for that can I define the...

Measure Theory, Caratheodory condition The set E \subset ℝ^{p} satisfy Caratheodory's condition if: \forall A \subset ℝ^{p} m_e (A) = m_e(A \cap E) + m_e(A \cap E^c) Prove that if E is measurable then E satisfy the Caratheodory's condition. I know m_e (A) \leq m_e(A \cap E) + m_e(A \cap E^c)...

q)give the converse ,the contrapositive and inverse of these conditional statements a)if it rains today,then i will drive to work b)if |x|=x then x>=0 c)if n is greater than 3,then n^2 is greater then 9

Homework Statement A small rock is thrown vertically upward with a speed of 17.0m/s from the edge of the roof of a 30.0m tall building. The rock doesn't hit the building on its way back down and lands in the street below. Air resistance can be neglected. Homework Equations Acceleration...

I read from the PDE book about Laplace equation in static condition ie ##\frac {\partial U}{\partial t}=0##. But is it true that even if U is time varying ie ##U=U(x,y,z,t)##, you can still have Laplace and Poisson's equation at t=k where k is some fixed value. ie...

As per orthogonality condition this equation is valid: \int_0^b xJ_0(\lambda_nx)J_0(\lambda_mx)dx = 0 for m\not=n I want to know the outcome of the following: \int_0^b xJ_0(\lambda_nx)Y_0(\lambda_mx)dx = 0 for two cases: m\not=n m=n

Homework Statement I have applied separation of variables to a transient radial heat equation problem. T is a function of r and t. I have reached the following step: Homework Equations T_2(t,r) = \sum_{m=1}^ \infty c_m...

Assume that a point x is an interior point of domain of some function f:[a,b]\to\mathbb{R}, and assume that the limit \lim_{(\delta_1,\delta_2)\to (0,0)} \frac{f(x+\delta_2)-f(x+\delta_1)}{\delta_2-\delta_1} exists. What does this imply? Well I know it implies that f'(x) exists, but...

I want to verify this, according to Griffiths p 557: \vec{F}(\vec r')=-\nabla U+\nabla\times\vec A ONLY if both ##\nabla U\; and \; \nabla\times\vec A\rightarrow\;0## faster than ##\frac 1 {r^2}## as ##r\rightarrow\;\infty##. But the requirement of ##\vec{F}(\vec r')## is only...

Can someone explained in simple language what is Lorent'z gauge or Lorent'z gauge condition, and can you give me example from practice or real life, can it maybe "carry" 2 different frequency at once let say.

Hi, I am working on a quite difficult, though seemingly simple, non-homogeneous differential equation in cylindrical coordinates. The main equation is the non homogeneous modified Helmholtz Equation \nabla^{2}\psi - k^{2}\psi =...

Hi, After reading several resources about work and energy, I am confused about the conditions that should be satisfied in order to be able to apply work energy theorem. It seems that textbooks have different arguments about this issue. I can summarize what textbooks say in three different...

The book states that ##P(x|y,t)## represents the probability density that the potential has a value x at time t, knowing that it had the value y at t=0. I understand this, the words are very clear. However I'd find much more intuitive the notation ##P(x,t|y,0)##, but I guess that's just me...

Homework Statement Let ##a,b,c## and ##m \in R^{+}##. Find the range of ##m## (independent of ##a,b## and ##c##) for which at least one of the following equations, ##ax^2+bx+cm=0, bx^2+cx+am=0## and ##cx^2+ax+bm=0## have real roots.Homework Equations The Attempt at a Solution I don't really...

How to test if a metric contain close timelike curve? I read somewhere that if the space coordinate change from positive to negative then it contain close timelike curve. For example, a metric gmn=-Adt2+Bdr2+Cdθ2+Ddz2, if C is negative, then it contain close timelike curve. Is that correct...

I am studying an article http://arxiv.org/abs/quant-ph/9907069 and having some problems understanding it. Is self adjointness of an operator a sufficient or necessary and sufficient requirement for its eigen vectors with the generalized eigenvectors (i don't know what are these) to form...

suppose function f is define on the interval [0,1] it satisfies the eigenvalue equation f'' + E f=0, and it satisfies the boundary conditions f'(0)+ f(0)=0, f(1)=0. How to solve this eigenvalue problem numerically? the mixed boundary condition at x=0 really makes it difficult

A rope is tied at one end then rotated in a vertical circle. Why do we take the tension at the free end of the rope as 0(Boundary Condition)?

##\phi:\mathbb R^4\to\mathbb R^4## is a smooth function such that ##J_\phi(x)^T\eta J_\phi(x)=\eta##, where ##J_\phi(x)## is the Jacobian matrix of ##\phi## at x, and ##\eta## is defined by $$\eta=\begin{pmatrix}-1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\end{pmatrix}.$$ I...

Hi, I have a question regarding the boundary condition present for a dielectric immersed in a static field. I hope one of you physics guru's can shed some light on this. Suppose we have a dielectric in space subjected to some external static electric field. I have read (without explanation)...

Homework Statement Given that x^{2}f(x)+f(\frac{1}{x})=0, then evaluate \int^{1.5}_{0.6}f(x)dx Homework Equations The Attempt at a Solution tried to replace f(x) using the provided equation...didn't help

the random value X takes values 1,2,3... and has the X has geometric distribution with p=0.20 (This means that X can be interpreted as the time the first crown to repeated throws a coin coin lands heads with probability p.) what is the expected value E(X/X>=6)=? i use this type ...

Homework Statement A wave function is given by: \Psi (x) = a cos(2\pi x) + b sin (2\pi x) for\: x<0 \\ and\\ \Psi (x) = Ce^{-kx} for\: x>0 \\ Determine the constant k in terms of a, b and c using the boundary conditions and discuss the case a >> b. Homework Equations...

Homework Statement I am working on chemical reaction engineering problem and it involves some math, which I am not able to figure out... I have to find the residence time for maximum production, which is in the case when : (dη_p)/dτ=0 I have to find the τ (residence time)...