Relation Definition and 1000 Threads

Recall that the Fibonacci sequence is defined by the initial conditions F0 = 0 and F1 = 1, and the recurrence relation Fn = Fn−1 + Fn−2 for n > 2. (a) Let F(z) = F0 + F1z + F2z 2 + F3z 3 + · · · be the generating function of the Fibonacci numbers. Derive a closed formula for F(z). (b) Consider...

Homework Statement hello all, I'm in the middle of solving a d.e using the series method. I have come across a weird pattern in part of my solution that I'm confused about: 6, (6)(10),(6)(10)(14),(6)(10)(14)(18),... Homework EquationsThe Attempt at a Solution I can see its 2(3), 2(3)*2(5)...

Why flowing current in wire creat magnetic field...if anybody say this is because of spin quantum number,... So i just want to say spin quantum number is because of wave nature of electron.i just want to know what effect of dual nature of electron on magnetic field.:rolleyes:

1. (16+x2)-xy'+32y=0 Seek a power series solution for the given differential equation about the given point x0 find the recurrence relation. So I used y=∑Anxn , found y' and y'' then I substituted it into the original equation, distributed, made all x to the n power equal to xn, made the...

Hi guys, first ever post. My question is if light travels at the same speed regardless of its wavelength, doesn't this statement seem to contradict itself? If the light simply traveled in a straight line then sure, but different wavelengths i would think mean that a greater distance would...

I am trying to conceptually connect the two formulations of quantum mechanics. The phase space formulation deals with quasi-probability distributions on the phase space and the path integral formulation usually deals with a sum-over-paths in the configuration space. I see how they both lead...

Homework Statement It is given in my book that: ΔStotal=ΔSsystem+ΔSsurrounding Where S is entropy. ΔSsurr=-ΔH/T Therefore: ΔStotal=ΔSsystem+[-ΔHsystem/T] As we can see here that ΔSsurrounding=-ΔHsystem/T is applied here . But is this relation correct? Homework Equations ΔS=qreversible/T Where...

Homework Statement for functions f: X -> Y and g: Y ->Z show that for all subsets C in Z , (g°f)^-1(C) ⊆ f^-1(g^-1(C)) (or find a counterexample) The Attempt at a Solution let z ∈ (g°f)^-1(C) such that (g°f)^-1(z) = x for some x∈X then z = (g°f)(x) z = g(f(x)) g^-1(z) = f(x) f^-1(g^-1(z) = x...

I'm trying to get my head around what this means exactly. I've plotted the graph to help verse me with the functions that I've derived. From the free electron model, the wavefunctions are treated as planewaves of the form \psi_\mathbf{k}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} Due to...

I am very confused about concepts of energy and work. I try to understand this way: there are many kinds of energy. every force is related with one kind of energy,but there is special one,the kinetic energy relate with the "sum force"

Homework Statement Give the equivalence classes of the relation aRb if and only if a^4 ≡ b^4 (mod 30) on the set {1, 2, 3, . . . , 15}. Homework Equations Definition of modular arithmetic. Definition of equivalence class. The Attempt at a Solution I can successfully do this problem using...

Hey all, I’ve scoured the internet in search of an answer to no avail, so it’s time to ask the experts!My background is more Chemistry and Biology, not Physics, or specifically fluid dynamics, so bear with me! Also, this is a little long, so I will do my best to make it easy to follow.The...

If H(x)= \int_c^x h(x)dx and H(a) = F(a) - G(a) = \int_c^a h(x)dx and H(b) = F(b) - G(b) = \int_c^b h(x)dx, then does that mean H(x) = F(x) - G(x)? Is the information provided sufficient enough to come to that conclusion?

Hey! :o How can we prove by induction the relation $A(x,y)>y, \forall x,y$ ?? (Wondering) When we have to prove a relation $P(n), n\geq 0$, we do the following steps: we show that it stands for $n=0$ we assume that it stands for n=k (Induction hypothesis) we want to shw that it...

Homework Statement If a relation R on N × N is (a,b)R(c,d) iff ad(b+c) = bc(a+d) Homework Equations -- The Attempt at a Solution I got the reflexive and symmetric parts but not the transitive part... here's what i have ## (a,b)(c,d)∈R and (c,d)(e,f)∈R## To prove ##(a,b)(e,f) ∈ R## .i.e...

Would this example be valid in satisfying a relation that is symmetric and anti-symmetric? The relation R = {(1,1),(2,2)} on the set A = {1,2,3} Also, I'm curious to know since relations can both be neither symmetric and anti-symmetric, would R = {(1,2),(2,1),(2,3)} be an example of such a...

Looking at an exposition of Kripke semantics, the relationship ||- in a Kripke model is obviously supposed to be similar to the model relation |= . A possible world (a node) looks suspiciously like a model for second-order formulas. But of course it cannot be this simple. What is the connection...

Given the image: http://i.stack.imgur.com/EJ3ax.jpgand that $x_0 = 1, y_0=0$ and $\text{angles} \space θ_i , i = 1, 2, 3, · · ·$ can be arbitrarily picked. How can I derive a recurrence relationship for $x_{n+1}$ and $x_n$? I actually know what the relationship is, however, don't know how to...

Homework Statement prove that s_k <= 2s_{k-2}+3 for all ints k >= 3 if s1=1 and s2 = 3 and s2=5 and s4=9The Attempt at a Solution base case k = 3 s_3 <= 2s_1 + 3 5 <= 2+3 that is true. Now i must prove the inductive step. This is where I am having trouble. I assume that s_k <= 2s_{k-2}+3...

If we study model fit on a nonlinear regression model $Y_i=f(z_i,\theta)+\epsilon_i$, $i=1,...,n$, and in the Gauss-Newton method, the update on the parameter $\theta$ from step $t$ to $t+1$ is to minimize the sum of squares...

Is there a relationship between 1 and 2. If so, is it 1 implies 2, 2 implies 1, or if and only if. 1) $\operatorname{null}A=\operatorname{null}B$ 2) $\operatorname{col}\operatorname{rref}A=\operatorname{col}\operatorname{rref }B$

Homework Statement Given a Poincaré transformation, Lorentz+translation, I have to find the Poincaré generators in the scalar field representation and then prove that the commutation relations. I've done the first part but I can't prove the commutation relations. Homework Equations...

I have a designed feedback control system trying to minimize the overshoot and the setting time. The zeta I (think) ended up with is 0.94. According to this formula: I am supposed to have a very small overshoot. However the step response of the system looks like this: The poles are: 0.0000 +...

If three variables x,y and z are related via some condition that can be expressed as $$F(x,y,z)=constant$$ then the partial derivatives of the functions are reciprocal, e.g. $$\frac{\partial x}{\partial y}=\frac{1}{\frac{\partial y}{\partial x}}$$ Is the correct way to prove this the following...

While reading some articles on Wikipedia I came upon one interesting statement that essential says (I've rephrased for clarity; correct me if I'm wrong): "The Time-asymmetry of the second law of thermodynamics is due to the initial conditions of our universe" Can someone elaborate on what...

At the superconductor-superconductor point contact regime, two Andreev bound states carries supercurrent through the S-weak links-S interface. According to literature, current can be simply expressd Eq1) I_S=(1/Phi_0)*dE_A/d Phi here I_S : supercurrent, Phi_0 = flux quantum, E_A : Andreev bound...

Hi Everyone, I'm trying to understand dispersion relations in general. I know that for a simple wave like a light wave there is a 'constant phase' so the dx/dt is equal to the ratio of the angular frequency (omega) by the wave vector (k). However what does a 'constant phase' mean? How can I...

$$ T(n) = \begin{cases} 2 & \text{if } n = 2 \\ 2T(\frac{n}{2})+n & \text{if } n = 2^k \text{, for } k > 1 \end{cases}\\ \text{ } \\ \text{ } \\ \text{ } \\ \text{Prove } T(n) = n\lg(n) \text{ if } n = 2^k\text{, for } k > 1.$$ I am crawling through the "Introduction to Algorithms" textbook...

Hello! (Smile)I want to determine if $\sqrt{n}$ is $\Theta $ / $O$ / $\Omega$, $o$, $\omega$ of $n^{\sin n}$. To do so we could calculate the limit: $$\lim_{n \to +\infty} \frac{\sqrt{n}}{n^{\sin n}}$$ right? But how can we find the limit, although $\lim_{n \to +\infty} \sin n$ does not...

So as I understand Beer-Lambert, it describes the attenuation of intensity/flux/fluence. My question is, suppose you have: some set object of interest fixed at some far distance from a source (so the rays are ~parallel) a shield (e.g. layer of lead) is placed in front of the object, that...

A question says; A particle moves along a straight line according to Eq s^2=at^2+2bt+c, s is distance traveled a, b , c are constamts . Then acceleration varies as what power of s? I have tried it but can't get anything out of it. Please help

Homework Statement What is the relation between the kernel of A and the kernel of (A^2 + A)? Homework EquationsThe Attempt at a Solution Break into A^2x = 0 and Ax = 0. We know Ax = 0 because that's the kernel of A, ker(A^2x) is subset of ker(A) so ker(A^2 + A) is a subset of ker (A)?

Homework Statement What is the relation between the image of A and the image of A2 + A? Homework EquationsThe Attempt at a Solution im (A^2 + A) for x (A^2+A) is within the image. Linear combination properties show A^2 x + A x. Not sure where to go from here

Hello, I have a question that is relevant to differential equations. Say for example I have two functions that are related to one anothers derivatives. For example, the voltage acrossed an inductor is proportional to the rate of change of current through that inductor. My question for you is...

Homework Statement The velocity of a particle is related to its position by: v2 = w2 (A2 - x2) where w and A are constants. Show that the acceleration is given by: a=-w2x[/B]Homework EquationsThe Attempt at a Solution a= v* dv/dt v=(A2w2-x2w2)1/2 dv/dt= 1/2 (A2w2-x2w2)-1/2 * -2xw2 v *...

Homework Statement Simplify the following commutator involving the creation and annihilation operators. [a^{\dagger}a,a \sqrt{a^\dagger a} ] Homework Equations I know that [a,a^\dagger] = 1. The Attempt at a Solution I think I should be trying to put the creation operators to the left...

in the case of information transfer or during reflex reaction, impulses pass through our body to brain. whether this has any relation with current in physics? whether vibrations are only passing? then how much is the speed through our blood?

relation between integration and differentiation ? how is instantaneous slope(differentiation) related to area under the curve(integration) ? thank you!

Hi. A very quick question. Why is it impossible for a wave to travel on a linear one-atomic chain if its wavelength equals the lattice constant? I.e. the lattice points vibrate with a wavelength equal to the distance between them? Here's what I mean...

... and its classical wave equation? Suppose in our double sit experimental setup with the usual notion of d,D we have a light of known frequency (v) and wavelength (L)- so its y=Asin(kx-wt). It passes through the two hole and move ahead doing the usual interference stuff, so final wave equation...

I was reading something and they said i was to decrease the rpm of a dc motor to increase the torque.. What i don't get is the equation for torque is T=(2*p*N)/60 So increasing the rpm should only increase the torque right.. Im a little lost here..please help

Homework Statement \omega (q)= \sqrt{( \frac{4f}{m})} sin\frac{qa}{2} Homework Equations N/A The Attempt at a Solution I don't understand the linear line given on the graph. For low q (or as q tends to zero) it says the relationship is linear. But as q tends to zero for the given equation...

When superposing waves in say double slit interference from two slits, I seem to have come across two approaches: 1. Sum the two waves in complex form to get the resultant amplitude, take the real part, and square to get the intensity, i.e I=[Re(A)]2 2. Sum the two waves in complex form to get...

Problem statement, equations, and work done: In quantum mechanics, there is a relation between momentum and wavelength and between energy and frequency. These are: ##p=\hbar k = \frac{h}{\lambda}## ##E = hf = \hbar \omega## A wave with an amplitude of 10cm is traveling on a string in the +x...

I am a little confused about how variables are related to distributions as one moves from descriptive statistics to inferential statistics. I know that a variable in descriptive statistics is some measurable characteristic of some phenomenon, and its distribution is some description (table or...

I need some help understanding how Newton's third law applies to field forces (namely gravitation). The third law in contact forces seems straightforward to me. Billiard ball A, which is moving, hits billiard ball B. The collision exerts a force on Ball B, resulting in its acceleration...

Hello all, I had clarified that refractive index of material such as(aluminium, copper, lead, teflon)changes with the temperature. the refractive index change even for this temperature range: -196 to 25°C ? I need to know like any law which gives a direct relationship between 1)the density and...

Homework Statement The maximum torque output from the engine of a new experimental car of mass m is τ . The maximum rotational speed of the engine is ω. The engine is designed to provide a constant power output P. The engine is connected to the wheels via a perfect transmission that can...

It is well known that quantum mechanics in the path-integral form is formally very similar to equilibrium statistical mechanics formulated in terms of a partition function. In a relatively recent, very readable and straightforward paper http://lanl.arxiv.org/abs/1311.0813 John Baez (a well known...

Me and and my friend were having discussion about the motion of molecules of gas.We talked about their velocity ,kinetic energy and much more. He asked me to derive a relation between pressure and energy. I was unable to explain him that... Can anyone explain the relation?