Relation Definition and 1000 Threads

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?

Homework Statement Given that the function f can be expanded in a power series of a and a^\dagger, show that: [a,f(a,a^{\dagger})]=\frac{\partial f }{\partial a^\dagger} and that [a,e^{-\alpha a^\dagger a}] = (e^{-\alpha}-1)e^{-\alpha a^{\dagger} a}aThe Attempt at a Solution I've tied using...

Homework Statement Pulsars are stars that have suffered gravitational collapse. They rotate rapidly and emit a narrow beam of radiation. The pulse lengths, at the earth, are ∼1ms and the periods are ∼1s. Within a few months of the discovery of pulsars distance estimates were obtained by...

Hello! (Smile) I want to find the exact solution of the recurrence relation: $T(n)=2T(\sqrt{n})+1$.$$m=\lg n \Rightarrow 2^m=n \\ \ \ \ \ \ \ \ \ 2^{\frac{m}{2}}=\sqrt{n}$$ So we have: $T(2^m)=2T(2^{\frac{m}{2}})+1$ We set $T(2^m)=S(m)$, so we get: $S(m)=2S \left( \frac{m}{2}\right)+1$...

can anyone convert the relation tan y=(Vsin(y)-gx)/Vcos(y) to an explicit function y=f(x) in terms of V, x and g? g is a constant V is the function V(x)= -aln(b/b-cx)-dx a,b,c,and d are also constants. Thanks!

Hello! (Smile) Let $R$ be an order of the set $A$. Then $R$ induces a strict order $S$ at the set $A$. $$$$ Let $S$ be a strict order of the set $A$. Then $S$ induces an order $R$ at the set $A$. The first sentence is proven like that in my notes: We define $S:=R-I_A$ and we can see that...

Homework Statement The radius for the inside of a curve is half the radius for the outside. With 2 cars of equal mass, car A travels on the inside and car B travels on the outside at equal speed. Which statement is correct? a. The force on A is half the force on B b. The force on B is half the...

Hello, I was wondering if H_{ii} (that is the ith diagonal element of a random matrix) has the same distribution with its corresponding eigenvalue, say \lambda_{i}. Thanks

Hi.. I want an explanation of the commutation relation. According to what I understand if two operators commute then they can be measured simultaneously. If they do not commute then the measurement of one depends on other as per the value of the commutator..I hope this is correct by far. In...

Homework Statement What is the commutation relation between the x and y components of angular momentum L = r X P Homework Equations None. The Attempt at a Solution I do r X p and get the angular momentum componants:L_{x} = (-i \hbar) (y \frac{d}{dz} - z \frac{d}{dy}) L_{y} = (-i \hbar) (z...

In the derivation of the generalized uncertainty principle (as pgs 1-2 of here), there is an anticommutator term that is dropped at the end, leaving just the commutator part...this is said to "strengthen" the relation, as both terms are positive. I don't understand this. So we basically have...

Hello! (Wave) I am looking at the proof of the proposition: $$\text{The relation } \epsilon_{\omega}=\{ \langle m,n \rangle \in \omega^2: m \in n\} \text{ is trichotomous on } \omega.$$ Proof: We define the sets: $T_m=\{ n \in \omega: m \in n \lor m=n \lor n \in m\},m \in \omega$ It suffices...

Hello! (Wave) Proposition Let $X$ be a set. The following are equivalent: $X$ is transitive Each element of $X$ is a subset of $X$ $\left( \forall x(x \in X \rightarrow x \subset X) \right)$ $X \subset \mathcal{P}X$ $\bigcup X \subset X$ Could you explain me why this: $X \subset...

Homework Statement [/B] Solve the recurrence relation (use iteration). an = an-1 + 1 + 2n-1 a0 = 0 Then prove the solution by mathematical induction. Homework EquationsThe Attempt at a Solution a1 = 2 a2 = 5 a3 = 10 a4 = 19 a5 = 36 The solution appears to be an = n + 2n - 1 How are we...

Homework Statement Find: Homework Equations The Attempt at a Solution

Homework Statement Let ##R## be an ordered relation on a set ##A## that is reflexive and anti-symmetric. If there is a chain of elements in ##R## that begins and ends with the same element, say the element ##x \in A## is it true that all the elements of ##R## sandwiched in between the ones...

1. Derive (∂U/∂P)V=-T(∂V/∂T)S 2. I must use dU=TdS-PdV 3. Derivations are my weakest part of math. I checked many wikis about Total differentials, partial derivatives, Maxwell relations and derivations. I can use the Thermodynamic Square, I know how to find different Maxwell relations but I am...

Hello! (Smile) Let $S(m)=S(m-1)+m$. I want to show that $S(m)=\Theta(m^2)$. That's what I have tried: We suppose a positive integer $m>0$. We suppose that $S(m-1)=\Theta((m-1)^2)$, so it holds that $\exists c_1, c_2>0$ such that : $$c_1 (m-1)^2 \leq S(m-1) \leq c_2(m-1)^2$$ We will show that...

Homework Statement The Hermitian operators \hat{A},\hat{B},\hat{C} satisfy the commutation relation[\hat{A},\hat{B}]=c\hat{C}. Show that c is a purely imaginary number. The Attempt at a Solution I don't usually post questions without some attempt at an answer but I am at a loss here.

Homework Statement http://postimg.org/image/i4p19540z/ Homework Equations Resultant force on the control volume = Mass flow rate (Velocity outlets -Velocity inlets) The Attempt at a Solution I am just wondering if the 4cm is called depth, then what is the term for the "into the paper"...

hi guys my question is if you have few grams of alkali metals and vapored it , what is the mathematical equation that links between these variables density vapor , the mass and the temperture ?? can you help me ?

Hii,i'm new in electrical and much confused bcoz of complicated relation between V,I, nd P. If P = VI = cons. and increasing V,decrease the value of I, but since P is also equal to I×I ×R and r is cons.,so decrease in I will always cause P to decrease which is supposed to remain constant. And i...

This is more a conceptual question. So i am doing some self review of multi variate calculus and i am looking at functinal relations of the form F(x, y, z,...) = 0 In the book they talk about implicit differentiation. Now i fully understand how to do the mechanics of it, but i was trying to...

I know they are directly proportional but how? could anyone explain it graphically ? thanks in advance

Hello! (Smile) It stands that $R[A \cap B] \subset R[A] \cap R[B]$, since: $$y \in R[A \cap B] \rightarrow \exists x \in A \cap B: xRy \rightarrow \exists x(x \in A \wedge xRy) \wedge (x \in B: xRy) \rightarrow y \in R[A] \wedge x \in R[B] \rightarrow y \in R[A] \cap R[B]$$ But, it doesn't...

Hi again! (Smile) If $\rho$ is an equivalence relation, could you explain me why the following relations stand? (Thinking) $I_A \subset \rho$ $\rho^{-1}=\rho$ $\rho \circ \rho \subset \rho$