Periodic Definition and 437 Threads

Hi all! I'm trying to solve the following system of ODE's, but somewhat unsuccessful... \dot \vec x = [-i\omega(t)\sigma_z - \nu(t)\sigma_y]\vec x with sigma_i the Pauli matrices and w(t) and v(t) well-behaved functions of t (actually I also have that w = 1+v). Nevertheless, v(t+T) =...

• Can we create any of the periodic table elements? • Can we make it cost efficient in the future? • Can we synthesis H20 in the laboratory?

Homework Statement Sketch the function: f(x) = \begin{Bmatrix} \frac{-x}{a} & 0 \leq x \leq a \\ \frac{x-L}{L-a} & a \leq x \leq L where f(x) is an odd function and is periodic in 2L. And a is a constant less than L/2 Find the Fourier series for the function f(x). Homework...

Homework Statement Show that the following vector field on the cylinder has a periodic orbit, v' = -v Θ' = 1 Homework Equations Bendixson's theorem: Suppose D is a simply connected open subset of R^2. If the expression div(f,g) = ∂f/∂x + ∂g/∂y is not identically zero...

I've got several thoughts, but none of them is complete. A general explanation is that when a few atoms form a structure with lowest energy, then when the interfacial energy is low, these independent small groups of particles tend to gather together and form periodic structure. But why are...

Mathematicians are creating their own version of the periodic table that will provide a vast directory of all the possible shapes in the universe across three, four and five dimensions, linking shapes together in the same way as the periodic table links groups of chemical elements. The...

Homework Statement How do I find periodic points of a given function? I'm looking at discrete cases only (iterations of the function). Homework Equations A point is defined to be a periodic point of period n if f^n(x)=x, where f^n(x) is defined recursively as f(f^n-1(x)). [If this...

Homework Statement Is the following a vector space: The set of all periodic functions of period 1? ( i.e. f(x+1)=f(x) ) Homework Equations If v1 and v2 are in V then v1 + v2 is in V If v1 is in V then c*v1 is in V where c is a scalar The Attempt at a Solution I'm thinking no...

Homework Statement Suppose f is a periodic function of period 2pi and that g is a horizontal shift of f, say g(x) = f(x + a). Show that f and g have the same energy. Homework Equations n/a The Attempt at a Solution i can see that if f(x) is shifted by 'a' that it does not make the...

why aren't the lanthanide and actinide series included in the periodic table? is there some non periodicity in there elements?

I have found in physics literature a periodic function of time is many times written in complex form. For example,f(x,t)=g(x)e^{i\omega t} As a non-physicist this has proven a bit confusing. Is it generally understood that the function we are really interested in the real part of the...

Homework Statement If f be a periodic function as well as an odd function with period p and and x belongs to [-p/2, p/2]. Prove that is periodic with period p. The Attempt at a Solution In the solution, there is a step which I did not understand- I see no property of definite...

How did Dimitri Mendeleev know that some of the elements were missing/not discovered? How did he know that the missing elements existed? Did he find some sort of pattern when he created the Periodic Table?

Homework Statement Determine whether or not each of the following signals is periodic if signal is periodic determine the fundamental period (note that these are discrete not continuous signals) Show your solutions 1. x(n) = \cos^3(\frac{\pi(n)}{8}) 2. x(n) =...

Homework Statement Determine whether or not each of the following signals is periodic if signal is periodic determine the fundamental period (note that these are discrete not continuous signals) Show your solutions 1. x(n) = \cos^3(\frac{\pi(n)}{8}) 2. x(n) =...

Is a periodic curve still an immersed submanifold of a manifold M? Suppose y is the curve map an interval to a manifold M, and y is periodic, which means it is not injective. And immersed submanifold must be the image of a injective immersion.

M is a smooth manifolds, and X is a vector field on M, y is a maximal integral curve of X. Now suppose y is periodic and nonconstant, show that there exists a unique positive number T(called the period of y) such that y(t)=y(t') if and only if t-t'=kT for some integer k.(For this problem, What...

Homework Statement So we have a string of N particles connected by springs like so: *...*...*...*...* A corresponding Hamiltonian that looks like: H= 1/2* \Sigma P_j^2 + (x_j - x_(j+1) )^2 Where x is transverse position of the particle as measured from the equilibrium position, and...

I am asked to prove that a real number is rational if and only if it has a periodic decimal expansion. I have shown that any periodic decimal expansion has an integer p such that multiplication returns an integer. For the case of showing that all rational numbers have a periodic decimal...

Homework Statement Let f be periodic with period P. Prove that 1/f is periodic with period P. The Attempt at a Solution f(s+P)= f(s) I know that is the equation for a periodic function. I am not sure how to prove the 1/f part though. Would I just do this: 1/f(s+P)=f(s)? I'm just...

letsa say my function is: x(n) = 1 + sin((2*pi)/N)*n + 3*cos((2*pi)/N)*n + cos( ((4*pi)/N)*n + pi/2); when i plot it inside a loop, with a loop variable being n, i have something llike increasing slope... even when i set a period N to be 8,4 or whateva.. on the other side... when i plot the...

aka "How to Rearrange the Elements Without Engaging in Alchemy" Below is one view on what the Periodic Table might look like if it were "callibrated" in geometric fashion to the Atomic Numbers of the Earth Alkaline Metals. (red cells) 4, 20, 56 and 120 are all 4 times the sum of squares (1 + 4...

Explain why the melting temperature increases from sodium to aluminium. Why does it have to do with ions and not atoms?

i think jordan wigner transform, when applied to open boundary system, can simplify a spin 1/2 system to a free fermion system but there is a difficulty in the case of periodic boundary condition in this case, we have to deal with terms like S_N^+S_1^-=(-)^{\sum_{k=1}^{N-1}n_k}...

Shall f be continuous function of two real variables. Proof that if equation x''=f(x,x') has not constant solutions, then neither it has periodic solutions.

A long time ago I took a number theory course and really enjoyed it. At one point we were shown the proof for the theorem that a number is rational if and only if it has a periodic decimal expansion. The (<=) direction is really easy if you know some Calculus, but I remember the (=>) direction...

Homework Statement Today i came across this one question where i had no clue of how to proove. it says f(x) = { 1, x rational ......{ ---------------------is periodic but have no period. (Proove it/Show it) .....{ 0, x irrational ignore the dots and dashes., just for indentation...

Homework Statement I am confused with why the author uses this form for periodic sound waves. Why did he use cosine instead? Later, he states Note he uses sin this time. I know that the difference between sine and cosine is the phase offset, by 90 degrees. But why did the...

Dear All, We have an voltage amplifier. The input is given in small square wave steps to check rise time and noise level of an output signal. The rise time looks good, but we see periodic (noise)oscillations after reaching the plateau. We measure signal voltage across capacitor (10 micro...

The problem is about mathematics but it originates from the self-gravitational instability of incompressible fluid, so let me explain the situation first. I have an incompressible uniform fluid disk that is infinite in the x-y direction. The disk has a finite thickness 2a along the...

Homework Statement A firework charge is detonated many meters above the ground. At a distance of 400m from the explosion, the acoustic pressure reaches a maximum of 10.0 N/m2. Assume that the speed of sound is constant at 343 m/s throughout the atmosphere over the region considered, that the...

Consider a dynamic system with a periodic trajectory. Given an arbitrary duration T of time, does there exist a chaotic trajectory of a similar system which approximates the closed orbit for the duration T with a given accuracy? Chaotic orbits which I've seen so far...

Homework Statement We are given a Hamiltonian dynamical system with a smooth Hamiltonian H:\mathbb{R}^2\to\mathbb{R} on \mathbb{R}^2, with canonical symplectic structure. Suppose this Hamiltonian has a periodic orbit H^{-1}(h_0). Prove that there exists an \epsilon>0 such that for all h\in...

Why do metals generally have lower ionization energies than non-metals? I mean, doesn't ionization energy depend on the atomic radius? And the atomic radius is in turn dependent on the shell and the protons. According to these factors, the atomic radius of Sodium should be smaller than...

Please help with periodic motion problems! 1. What are the correct units for frequency? What are the correct units for angular frequency? 2. A grandfather clock keeps time by using a pendulum. If you want to design a pendulum to have a period of 1 s, estimate how long you should make the...

We may observe that cyclical or loosely periodic phenomena are extremely common in nature with phases varying over more than thirty orders of magnitude. Is there some overarching physical principle at work here; some deep line of code in the cosmic program as to why this should be so? This is...

I need to find if Sin(x^2) is a periodic function. As I think its not periodic but I need to proof that. I know that its possible to use f(x) = f(x+T), while T is the period frequency. But how to find out T ? and how to contradict this equation to say that the function is not periodic...

Homework Statement Hi guys Say I have an equation of the form f(x) = cos(x)+cos(0.2x), and I wish to find the solutions x. When I plot this graph, I see multiple solutions, but there is no apparent period for the solutions. Are all the solutions equally valid, or can some be discarded?

How does atomic radii decrease when we move left to right in a periodic table? Though the nuclear charge increase as a result of increase in number of protons,the same increase is occurring in number of electrons.

Homework Statement Consider the power series Σanxn = 1+2x+3x2+x3+2x4+3x5+x6+… in which the coefficients an=1,2,3,1,2,3,1,... are periodic of period p=3. Find the radius of convergence. Homework Equations The Attempt at a Solution My attempt at a solution was to first state...

Homework Statement A water-skier is moving at a speed of 13.3 m/s. When she skis in the same direction as a traveling wave, she springs upward every 6.2 s because of the wave crests. When she skis in the direction opposite to the direction in which the wave moves, she springs upward every...

Hi all - I would like to add a periodic inlet flow rate (Q(t) over an entire period T) as a BC in COMSOL. Does anyone know how to do this in 2D axisymmetric Transient Navier Stokes through COMSOL? I'm aware of the periodic boundary condition option available, but really just don't know how to...

Is an oscillatory motion always periodic ? 3 I think the answer is yes but the answer in my book was NO please explain

Homework Statement 1.If protons and two neutrons are removed from the nucleus of an oxygen-16 atom, a nucleus of which element remains? electron 2. If an atom has 43 electrons, 56 neutrons and 43 protons what is its approximate atoms mass? What is the name of this element? Technetium, 99...

quoted from Kittel text 8th edition page 170,171 the potential energy is U(x)=\SigmaU_{G}e^{iGx} but why it is also equal to-> U(x)=\SigmaU_{G}e^{iGx}+e^{-iGx} from text explanation, i couldn't get it why there is an extra term of e^{iGx} any 1 care to enlight me on this? thanks.

Hi all, let's say I have generated some discrete data as a function of time. And when I plot it, it looks like that it is periodic. Is there any scientific way to check whether or not the discrete data is really periodic? And determine the period, if possible? Many thanks.

Homework Statement Could \[F(s) = \frac{1}{{s(1 - {e^{ - s}})}}\] be the Laplace transform of some periodic function? Why? If so, find that periodic function The Attempt at a Solution If it was the Laplace transform of some periodic function, the the Laplace transform of the first wave...

Greetings, Can you match up the unearthly elements with their earthly counterpart based on the clues? After about 9 hours of work I am stumped. Take a look at the following page: http://www.scribd.com/doc/25315827/Alien-Periodic-Table Please feel free to download as a word doc. I am...

hi, i have a hard problem, i guess so, i am looking for any help g(x) is a bounded Lebesgue measurable function that is periodic i.e. g(x)=g(x+p). Then for every f \in L^1(\Re) lim_{n\rightarrow \infty}\int_{\Re}f(x)g(nx) dx=(\int_{\Re}f(x)dx)((1/p){\int_{0}^{p}g(x) dx) thanks for...

Homework Statement Fourier transform of scaled pulse train from -inf to +inf. Starting at 0 the first impulse is scaled at 2, the second impulse at 1 is scaled as 1, third at three scaled at 2, etc...Homework Equations Does my solution look correct?The Attempt at a Solution X(jw) =...