Relation Definition and 1000 Threads

Let $U_1,\,U_2,\,\cdots$ be a sequence defined by $U_1=1$ and for $n>1$, $U_{n+1}=\sqrt{U_n^2-2U_n+3}+1$. Find $U_{513}$.

Homework Statement I've determined the dispersion relation for a particular traveling wave and have found that it contains both a real and an imaginary part. So, I let k=\alpha+i\beta and solved for \alpha and \beta I found that there are \pm signs in the solutions for both \alpha and \beta...

Hello! (Cool) Sentence The set, that does not contain any element, is unique. Proof: Let's suppose that $a,b$ are sets, so that each of these sets does not contain any element and $a \neq b$. From the axiom: Two sets, that have the same elements, are equal., there is (without loss of...

Homework Statement I have a homework problem in honors calculus III that I'm having a little trouble with. Given these three qualities of norms in Rn: 1) f(v)\geq0, with equality iff v=0 2) f(av)=|a|f(v) for any scalar a 3) f(v+w) \leq f(v)+f(w) we were given a set of 3 functions and told...

Homework Statement Differential equation: 2xyy' = x^2 + y^2 Relation: y^2 = x^2 - cx Homework Equations The Attempt at a Solution Hello, I can normally solve this problems with ease; however, I am having trouble with this particular problem. I have performed the implicit...

Hello, it is known that given a certain recurrence relation that describes a sequence of numbers, it is often possible to obtain a function f[n] that directly yields the n-th number of the sequence. This is usually accomplished by using powerful techniques involving generating functions or the...

When waves are propagated through medium, the displacement curve will move up and down. Do they have any relationship with propagated energy? For example, when energy is gained from other part the curve will rise up or fall down. And does energy in standing waves share similar principle?

I'm new to the concepts of quanum mechanics and the bra-ket representation in general. I've seen in the textbook that the compleatness relation is used all the time when working with the bra and kets. I'm a bit confused about how this relation is being used when applied more than once in a...

Dear all, If I have the value of photosynthetic photon flux in unit [ micro mole per meter square per second] as an output for ultra violet sensor. How can I know the corresponding wavelength of that radiation ? and can I know from that wavelength what is the type of the ultraviolet...

http://arxiv.org/abs/1409.0492 Is the Standard Model saved asymptotically by conformal symmetry? A.Gorsky, A.Mironov, A.Morozov, T.N.Tomaras (Submitted on 1 Sep 2014) It is pointed out that the top-quark and Higgs masses and the Higgs VEV satisfy with great accuracy the relations...

Hi ALL, On this forum, I found some really sensible answers to a few of my queries... posting one that's unanswered.. I want to understand how an engine or any power plant for that matter behaves under load... So I'm using a simple scenario to frame my questions... the values while made up...

Homework Statement The spin 1/2 electrons are placed in a one-dimensional harmonic oscillator potential of angular frequency ω. If a measurement of $$S_z$$ of the system returns $$\hbar$$. What is the smallest possible energy of the system? Homework Equations...

After being through with Newton's 3rd law of action reaction pairs, there arise a doubt regarding the categorization of force couple (related to torque) of being or NOT being an example of action reaction pairs.

Hi, what is the physics experiment that leads to the position-momentum commutation relation xpx - px x = i hbar What does it mean to multiply the position and momentum operators of a particle? What is the corresponding physical quantity?

I don't understand why we quantize the field by defining the commutation relation.What's that mean?And what's the difference between the commutation and anticommtation?

Hello, I read the Feynman's QED book, where I learned that a photon has a intrinsic property called frequency. This property affect, for example, the interference profile when we have a lot of photon together. Ok. Now, thinking on an conventional antenna. When we have a 100kHz signal on...

Homework Statement Greetings! I am reading section 2.8 of Jackson and trying to understand how completeness relation was derived. It starts with the orthonormality condition: ∫U_N ^*(ε) U(ε) dε =δ_{nm} We can represent a function as a sum of orthonormal functions if N is finite...

Hello everyone, this has been on my mind for a while and I finally realized I could just ask on here for some input :) I think in general, when most people start learning quantum mechanics, they are under the impression that the wave function \Psi represents everything you could possibly know...

Show that for $|a| > |b| $, $$\int_{0}^{\infty} \frac{\sinh bx}{\cosh ax + \cosh bx} \ dx = 2 \ln 2 \ \frac{b}{a^{2}-b^{2}} .$$

Definition/Summary One of the most asked questions is concerning how to derive the Heisenberg Uncertainty Relation. Starting from almost basic concepts of Quantum Mechanics, a derivation is given here. Some details are left as minor exercises for the interested reader. The derivation...

Definition/Summary A recurrence relation is an equation which defines each term of a sequence as a function of preceding terms. The most well-known are those defining the Fibonacci numbers and the binomial coefficients. An ordinary differential equation can be considered as a recurrence...

Definition/Summary A relation on a set A is a set of ordered pairs (a,b) of elements ofA (a subset of A \times A). An equivalence relation \sim\ \subseteq A \times A is a relation which is reflexive, symmetric and transitive. In other words, the relation \sim on A is an equivalence...

Hi guys, I am still new to this forum, so I hope I can learn many things from this forum :) I am currently looking for my IB EE topic about the relation between temperature and natural frequency on an object. I have been researching about this topic, however I don't find any specific...

I'm having a brain fart so this is just another silly question but... when deriving the I-V relation for the capacitor: $$C=\frac{dq}{dV}$$ $$\frac{d}{dt}C=\frac{d}{dt} (\frac{dq}{dV})=\frac{d}{dt}C=\frac{di}{dV}$$ from here, normally we're supposed to do the following...

Hello! (Wave) I have to define an asymptotic upper and lower bound of the recursive relation $T(n)=5 T(\frac{n}{5})+\frac{n}{ \lg n}$. I thought that I could use the master theorem,since the recursive relation is of the form $T(n)=aT(\frac{n}{b})+f(n)$ $$a=5 \geq 1 , b=5>1 , f(n)=\frac{n}{...

Using the Hall-Petch relation, estimate the yield strength, σy, of a Cu-Zn alloy (brass) when the average grain diameter is 30 μm. where: σy = is the yield strength σ0 = 25 MPa is the internal friction stress ky = 12.5 MPa·mm1/2 is a material constant d = is the average grain size...

Is there a formal relation that links \int yxdx OR \int_{a}^{b}yxdx with \int xydy OR \int_{a}^{b}xydy where y=f(x) over the interval x\in\left[a,b\right].

Homework Statement suppose f~:~A \rightarrow B be a surjective map of sets. Prove that the relation a Rb \iff f(a)=f(b) is a equivalence relation whose equivalence classes are the fibers of f. Homework Equations The Attempt at a Solution I was able to easily prove that the...

Let's say we have a sealed container that has an adjustable volume, so the volume of the container can change from big to very small. When the volume is big, the container is filled with a certain amount of an ideal gas. After this the amount of gas is not changed but remains constant. Also we...

I'm learning ray optics and feeling so confused by the definition of "Hamiltonian of light". What I learned was that the "Hamiltonian of light" defined by H = n-|\vec{p}| = 0 indicates the momentum conservation, where n is refractive index and \vec{p} here is the canonical momentum. The...

Hey! (Wave) I have to find the primes $p$,for which $x^2 \equiv 13 \pmod p$ has a solution. That's what I have tried: $$\text{ Let } p>13:$$ We want that $\displaystyle{ \left ( \frac{13}{p} \right )}=1$ $$\left ( \frac{13}{p} \right )=(-1)^{\frac{13-1}{2} \cdot \frac{p-1}{2}}\left (...

'Slow-active suspensions realize small switching frequencies to control low-frequency body movements,such as roll pitch and lifting motions.Fully-active suspensions reach switching frequencies,like semi-active suspensions,greater than the natural eigen-frequencies of the vehicle.'- an excerpt...

Can anyone help explain this to me and solve this problem? I have gone over my textbook and I am having trouble understanding this. (Doh) Find the domain, range, and when A=B, the diagraph of the relation R. A={1,2,3,4,8}=B; a R b if and only if a|b. A.Domain {1,2,3,4,8} Range {1,4,6,9,15}...

Suppose we are given two functions: f:\mathbb R \times \mathbb C \rightarrow\mathbb C g:\mathbb R \times \mathbb C \rightarrow\mathbb C and the equation relating the Stieltjes Integrals \int_a^\infty f(x,z)d\sigma(x)=\int_a^\infty g(x,z)d\rho(x) where a is some real number, the...

Hey! :o I am looking at an example of the characteristic system of hyperbolic equations. One part of the example is the following: $\displaystyle{v=\text{ constant }, v=u_1+\sqrt{\frac{a}{b}}u_2}$, when $\displaystyle{\frac{dx}{dt}=\sqrt{ab}}$ $\displaystyle{x=\sqrt{ab}t+c \Rightarrow c=x-...

Hey there, This isn't a homework question, it's for deeper understanding. So I'm learning about unit normal/tangent vectors and the curvature of a curve. I have a few questions/points. 1) So my book states that we can express acceleration as a linear combination of the acceleration in the...

Do individual photons have some attributes which relate to EM wave frequency? In other words, is there any difference in photons composing a red and blue beam of light?

I'd like to know what exactly it's telling us. Does it mean that the more accurately we measure the energy of a system the less accurately we know for how long the system has been in that range of energies? Or does it mean that the more accurately energy is measured the less accurately we know...

So what if we have two thick lenses? Thanks in advance ,

Hello guys, Iam doing a project to find the tension of timing belt using a dial gauge indicator(consists of plunger and gear attached to it ie;rack and pinion mechanism) ,but i can't find a formula relating the displacement of the pointer and the tension (eg: 5° of dislplacement of pointer =...

Hi every one, Here is my question: In soil physics, knowing the relation between suction head, h, and the soil water content, S, one can derive the hydraulic conductivity, K, of that soil using a formula like: (ignore the superscripts "cap") where in my problem, τ=0.5, κ=1, β=2...

I'm in the first of 3 courses in quantum mechanics, and we just started chapter 4 of Griffiths. He goes into great detail in most of the solution of the radial equation, except for one part: translating the recursion relation into a form that matches the definition of the Laguerre polynomials...

(1) P_{l}(u) is normalised such that P_{l}(1) = 1. Find P_{0}(u) and P_{2}(u) We have the recursion relation: a_{n+2} = \frac{n(n+1) - l(l+1)}{(n+2)(n+1)}a_{n} I'm going to include a second similar question, which I'm hoping is solved in a similar way, so I can relate it to the above...

Homework Statement We say that two sets A and B have the "same powerfulness" if there is a bijection from A to B. Show that the relation "have the same powerfulness" is an equivalence relation between sets. Homework Equations An equivalence relation satisfy the following: xRx...

Homework Statement Estimate the magnitude of the fine structure splitting in H-α in THzHomework Equations Rydberg -- R_y \left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right) = \Delta E The Attempt at a Solution This isn't really a request for solution help, and more a justification. I know that if...

Hey! :o Having the following problem: $$(1): u_t=u_{xx}+f(x,t), 0<x<L, t>0$$ $$u(0,t)=u(L,t)=0, t>0$$ $$u(x,0)=0, 0<x<L$$ $$f(0,t)=f(L,t)=0, t>0$$ we do the following to find the general solution: We write the function $f(x,t)$ as a Fourier series: $$(2): f(x,t)=\sum_{n=1}^{\infty}{F_n(t)...

Hi all, Could someone please explain to me the process involved in converting an inhomogeneous recurrence to a homogeneous recurrence, I'm completely confused as to how it works.Thanks

Problem: Let $a_0$ and $b_0$ be any two positive integers. Define $a_n$, $b_n$ for $n\geq 1$ using the relations $a_n=a_{n-1}+2b_{n-1}$, $b_n=a_{n-1}+b_{n-1}$ and let $c_n=\dfrac{a_n}{b_n}$, for $n=0,1,2,\cdots $. Write a)Write $(\sqrt{2}-c_{n+1})$ in terms of $(\sqrt{2}-c_n)$. b)Show that...

My question is just to ask whether the operations like:- AUB is a relation or not? in our book it is written that the relations of two sets should be subset of the cartesian product of two sets but i think that relations are those which connects two sets and that can be AUB(A union B)...

We all know that quantum theory is based on the commutation relation and superposition principle. The trouble haunting me long time is that how to "get" the famous commutation relation? Could anybody give me an explanation?