Independent Definition and 745 Threads

does gravity effect viscosity ? is viscosity independent od gravity ?

Homework Statement I have a function V = kI where k is some constant I_err = 0.005 A V_err = 0.00005 V A fit was then made, but a problem occurs when I try to calculate the reduced chi^2. Since the error of the dependent variable V is so small, the resultant reduced chi^2 is fairly...

Homework Statement I need to argue this properly Let's say I have a matrix A and rref(A) is given as \begin{bmatrix} 1 & 0&-1 \\ 0& 1 & -1 \end{bmatrix} Since I have a pivot in every row, why isn't this linearly independent? Don't give me other arguments like "because there...

Prove this function satisfies the time independent schrodinger equation. When V is constant. Psi = A e^(i k x) + B e^(-i k x) Attempt: Time independent schrodinger equation : (- (hbar^2) / 2m) * (d^2 Psi / d x^2) + V Psi = E Psi Second order derivative of Psi : (-k^2 A e^(i k x)) + (-...

Special Relativity is just a special case where spacetime is flat and fixed. Meaning it is not really a correct picture of reality because nature chooses curved spacetime that is background independent. So quantum particles shouldn't be occurring in a flat fixed background but a dynamic...

Homework Statement Here is a really simple lin.alg problem that for some reason I'm having trouble doing. Assume that \left\{ v_i \right\} is a set of linearly independent vectors. Take w to be a non-zero vector that can be written as a linear combination of the v_i . Show that \left\{ v_i...

So I am taking a 1 credit independent study with a relatively new assistant professor who I am pretty sure only took me on to get a +1 on the his number of undergrads count and doesn't really have any time to advice me in anything or guide me. Ostensibly I am working on an experiment he's is...

What does it mean by "independent"(in gauge fixing of EM field) In my textbook, it gives the Coulomb gauge \phi = 0,\nabla A = 0 and says they will kill two degrees of freedom of the four potential and leave two independent components. I understand \phi = 0 will kill one degree of freedom...

Homework Statement Basically, the title says it all, I need to figure out whether these functions are linearly independtend on (-infinity, infinity) Homework Equations Wronskian (the determinant of the matrix composed of the functions in the first row, first derivative in the second...

Suppose X and Y are Uniform(-1, 1) such that X and Y are independent and identically distributed. What is the density of Z = X + Y? Here is what I have done so far (I am new to this forum, so, my formatting is very bad). I know that fX(x) = fY(x) = 1/2 if -1<x<1 and 0 otherwise The...

Homework Statement Well as the title describes, x and y linear independent in R^n S is a subspace in Rn spanned by x,y i.e S= span(x,y) define the matrix A as A=xy^T+yx^T This is actually a 3 part question 1 show that A is symmetrical 2 show that N(A)=S(Perpendicular) 3 show that the...

Hi Guys, I've used this forum as a great resource for a while now and it's always helped me out. Now I'm really stuck on something and was hoping you guys could help out. It's a pretty long question, but if you guys can just give me a general direction of what to do, I can go ahead and work it...

Homework Statement I need to prove that, if {u;v;w} is a linearly independent set in a vector space, then the set {2u + v + w; u + 2v + w; u + v + 2w} is also linearly independent. Homework Equations ... The Attempt at a Solution if {u;v;w} is a linearly independent set=>...

If a and 77 are relatively prime, show that for positive integers n, a^(10^n) modulo 77 is independent of n. I think I don't understand what this statement is asking. a^(10^n) modulo 77 independent of n means that a^(10^n) modulo 77 is always going to be the same or something?

How do I explain it?? Potential difference in the system discussed is independent Hi folks, - please view the attached image - my colleague and I had a major disagreement in the office. We both mutually put a lid on the discussion as we both felt that we needed more information in order to...

Homework Statement I'm trying to derive the second-order correction of energy in time independent perturbation theory. My professor did it the Landau's way so I'd rather use his notation (without bra and kets). I already derived the first-order correction: E_n^{(1)}=V_{nn}=\int...

Homework Statement V is a subspace of Rn and S={v1,...,vk} is a set of linearly independent vector in V. I have to prove that any list of linearly independent vectors can be extended to a basis for V. Homework Equations None that I can think of. The Attempt at a Solution So to be...

Suppose X and Y are independent Poisson random variables, each with mean 1, obtain i) P(X+Y)=4 ii)E[(X+Y)^2] I m trying to solve this problem but have difficulty starting ... If some one could give me a some pointers

Question: If X and Y are independent poisson variates with mean λ1 and λ2 respectively, what is the probability that i) X + Y =k ii) X = Y Solution: Dont know how to solve this .

1. (a) If ^H_1 is a small perturbation to the Hamiltonian ˆH0, show that the first order correction to the ground state (gs) energy is: ∆E = ∫ψ*_0(x)ˆH1 ψ_0(x) dx between negative and positive infinity. where ψ0(x) is the gs wavefunction of the unperturbed system. B) (b) Take...

Let Xi, i=1,...,10, be independent random variables, each uniformly distributed over (0, 1). Calculate an approximation to P(\sumXi > 6) Solution E(x) = 1/2 and Var(X) = 1/12 [How should is calulate the approxmiate ]

Question : An infinite sequence of independent trails is to be performed . Each trails resulting in a success with probability p and failure with probability 1-p . What is the probability that i) atleast 1 success occurs in the first n trails ; ii) exactly k success occur in the first n...

Homework Statement when complex integral is independent of path? i heard that its for every function f(z) but when i have function f(z)=\left(x^2+y\right)+i\left(xy\right) its not independent, why?

Homework Statement integral: \int\limits_C\cos\frac{z}{2}\mbox{d}z where C is any curve from 0 to \pi+2i The Attempt at a Solution can i do this like in real analysis when counting work between two points, just count this integral and put given data in?

Hi everyone, here's a probability problem that seems really counter-intuitive to me: Find four random variables taking values in {-1, 1} such that any three are independent but all four are not. Hint: consider products of independent random variables. My thoughts: From a set perspective...

Say we consider the time independent Klein–Gordon equation, see: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation Lets impose the following boundary conditions, the function is zero at infinity and on some small ball of radius R centered on some origin the function is some...

Suppose we have time-dependent operator a(t) with the equal-time commutator [a(t),a^{\dag}(t)]=1 and in particular [a(0),a^{\dag}(0)]=1 with Hamiltonian H=\hbar \omega(a^\dag a+1/2) The Heisenberg equation of motion \frac{da}{dt}=\frac{i}{\hbar}[H,a]=-i\omega a implies...

hello :) i have a silly question and i keep confusing myself, hope someone can help me. my friend has two diseases and I want to calculate a number to represent the chance of success (i.e. him surviving both diseases for more than 5 years) disease A: chance of survival for more than 5...

Problem : Show that if event A is completely independent of Event B and C then A is independent of BUC?

http://nextbigfuture.com/2010/12/blacklight-power-announces-independient.html Can any physics buffs here make heads or tails of this? I really don't know what to think about this technology anymore :confused:...

Many textbooks make the statement that it's found experimentally that the electric force by a stationary charge on on a moving charge is independent of its velocity. Has this lead to any confusion for people here? Embarrassingly, I was using this to mean that in the proper frame of the...

I was talking to some friends last night and became interested in the topic of independent(ei. non-government or university affiliated) research institutes. While these sorts of things have typically been ruled out because of monetary concerns with the rapid advancement of cheap computing and...

Let t€R be fixed. Show that {u,v}CR^2 with u=(cost,sint), v=(-sint,cost) is a linearly inpedendent set.

Homework Statement Hello, I just want to know if I am going about this the right way. A and B are outcomes of a random experiment in a sample space \Omega such that \Omega = A\cupB. P(A) = 0.8 and P(B) = 0.5 Study if A and B, A and B^{c}, A^{c} and B, and A^{c} and B^{c} are independent...

Homework Statement Suppose that a matrix A has real entries (which we always assume) and a complex (non-real) eigenvalue  \lambda= a + ib, with  b not equal to 0. Let W = U + iV be the corresponding complex eigenvector, having real and imaginary parts U and V , respectively. Show that U...

Let x_1, x_2, ..., x_n be identically distributed independent random variables, taking values in (1, 2). If y = x_1/(x_1 + ... + x_n), then what is the expectation of y?

I've got a pretty good answer to this one already, yet I'd like to see how solid it is. I'll list the question first in quotes. Here's my work below. I credit http://arxiv.org/PS_cache/arxiv/pdf/0909/0909.1685v4.pdf" for the answer. X and Y are independent if and only if...

Homework Statement Show that every m×n matrix A with m linearly independent rows can be obtained from n × n matrix by deleting the last n − m rows. Homework Equations The Attempt at a Solution I have no idea of this question

Is it possible? Most of the resources I find are geared toward college class situations. I do not want to learn how to learn with a lecturer. Is there anything online free that can teach and quiz without acting as a supplement for an expensive course or school setting?

Homework Statement Let f:V\rightarrow V be a linear map and let v\inV be such that f^n(v)\neq0 and f^(n+1)(v)=0. Show that v,f(v),...,f^(n-1)(v) are linearly independent. The Attempt at a Solution I'm really stuck with this one. I know the definition of linear independence and...

Homework Statement Let T be a linear transformation of a vector space V into itself. Suppose x ε V is such that Tm(x)=0, Tm-1(x) not equal 0 for some positive integer m. show that x, T(x), …, Tm-1(x) are linearly independent. In regards to Tm and Tm-1 m and m-1 are upperscript on the...

Homework Statement if X and Y are independent random variables does it imply that X^2 and Y^2 are also independent? Homework Equations The Attempt at a Solution

An industrial hoist is being used in an emergency job where the weight exceeds the design limits of two of its components. For the amount of weight being lifted, the probability that the upper attachment hook will fail is 0.20. The probability that the lower hook will fail is 0.10. What is the...

Homework Statement y'' +(y')^2 = 6(y') -9 Homework Equations u = y' u' = y'' The Attempt at a Solution equation from 1 becomes u' + U^2 = 6u - 9 du/dx + u ^2 = 6u-9 du/dx = -u^2 + 6u -9 du/dx = -(u^2 +6u - 9) du/dx = -(u-3)^2 du/(u-3)^2 = - dx integrate...

Show this set of functions is linearly independent (e^(-x), x, and e^(2x)) Homework Statement f_{1}(x) = e^{-x}, f_{2}(x) = x, f_{3}(x) = e^{2x} Homework Equations Theorems and lemmas, which state that if vectors are in echelon form, they are linearly independent, and also that they are...

Hello, everyone I am studying Srednicki's "Quantum Field Theory", section 4 "The spin-statistics Theorem". Does anyone know how to show that "The time ordering of two spacetime points x and x' is frame independent if their separation is timelike."(P32), explicitly? And "Two spacetime points...

Hi, This has been bothering me for a while now.. The scalar wave equation is a 2nd order differential equation. So we would expect two independent solutions for it. However when you try to find the solution of the scalar wave equation (in spherical coordinates) by employing the separation...

Hi, I came across a question where I needed to prove that a set of vectors are linearly independent. The thing is, I am not sure how to reason the proof properly. Say you have three vectors x1,x2,x3 E R3, and prove that they are linearly independent. Put them into a 3x3 matrix A...

Hi, I have a question about counting (how difficult should that be ;) ) I have the set of tensors in D dimensions \{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\} with the relations H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho} T^{\mu}t_{\mu} = 1...

Hi all, I have learned that the hydrodynamic entrance length of a channel (to form fully developed laminar flow) is correlated to the Reynolds number, because the shear effects have to propagate inwards from the walls of the channel. However recently I found out that there is a 'minimum' to the...