Properties Definition and 1000 Threads

Def: A low discrepancy sequence is a uniformly distributed sequence with minimal discrepancy, O(logN/N). Question: Let <x> denote the fractal part of an irrational number x. Let (<x_n>) be an arbitrary low discrepancy sequence. Is it always true that : \lim_{n \to +\infty}|<x_n - x_{n-1}> -...

Thanks to those who participated in last week's POTW! Here's this week's problem. ----- Problem: Recall that the convolution of $f$ and $g$ is defined by the integral \[(f\ast g)(t) = \int_0^{t}f(t-\tau)g(\tau)\,d\tau.\] Establish the commutative, distributive, and associative properties of...

i need the derivation of orthogonal properties of associated laguerre polynomial (with intermediate steps). someone please tell me where can i get it (for easy understanding).

Homework Statement Let V = {RXR} with addition defined as (a1,a2) + (b1,b2) = (a1 + b1, a2b2) Show the vector space condition, for each x in V there exists a y in V such that x + y = 0, fails for the V defined above. Homework Equations The Attempt at a Solution a + d = (a1,a2)...

Hi! I'm currently re-reading Griffiths introductory QM book and plan to do most of the exercises. I got stuck on one problem and had to look for some hints and found two solutions that both claim that: \int_{-\infty} ^{\infty} \frac{\partial }{\partial x}\left[ \frac{\partial \Psi...

What properties of an inductor change in a low temperature environment. Specifically in the -100 through -70 degrees Celsius range?

Does the Higgs field of a fermion exclusively attract just like a gravitational field? Or can it also have repulsion? Is the Higgs field separate from the gravitational field or is the Higgs field the cause of gravity? If the Higgs field is separate from the gravitational field, then what is its...

If I sleep on copper would there be any beneficial release of negative Ions to improve my well being. In addition, will the thermal properties of copper stabilize my body temperature at 37.5c.

hi there! If ab > 0, then (a > 0 and b > 0) or (a < 0 and b < 0). This statement I can prove, just with the basic properties of numbers! Then, 1/b is defined as b^{-1} right? So, how does one prove that if \frac{a}{b} > 0, then (a > 0 and b > 0) or (a < 0 and b < 0)? Can you give me...

Do you people know any decent and simple (no fancy math) material for the atomic physics around diamagnetism, paramagnetism and ferromagnetism? Topics like wave-particle duality, energy levels, solids, why metals are conductors, relation between magnetic moment and effective mass of...

Hello, As known, any Lorentz transformation matrix \Lambda must obey the relation \Lambda^\mu~_\nu\Lambda^\rho~_\sigma g_{\mu \rho}=g_{\nu \sigma}. The same holds also for the inverse metric tensor g^{\nu \sigma} which has the same components as the metric tensor itself (don't really...

Homework Statement http://desmond.imageshack.us/Himg228/scaled.php?server=228&filename=theorem.png&res=landing Picked up Spivak's Calculus, 3rd ed. and just started. Got to this question and I'm honestly not sure how to start, I looked in the answer book which didn't really clue me in any...

Hello colleagues! I’d like to ask your opinion on the following information. I found an article where is talking about wonderful polymer that has very interesting properties to pick up parameters when applied on some surface including human body and to register information and to transfer...

Had some questions about wave-functions. Some of the questions might be invalid due to limited knowledge of the OP. 1. Are wave-functions real? i.e. do they exist in reality? Wave-functions are mathematical/probabilistic constructs. However if they can modify/change the behavior/path of a...

Do the absorptivity, reflectivity and transmissivity of a surface depend on the wavelength of the incident light?

Hello all, I am reading a paper and there is one bit in the paper that I am having a bit of trouble understanding. Say V(a) is a convex function and then the paper has the following line: [V(-2pi + a] + V(2pi + a]] >= 2V(a) I am sure this relationship is simple and falls out somehow...

Matter (deBroglie) waves is a concept and it's existence is not confirmed (?)..that said, We know that - The de Broglie equations relate the wavelength λ to the momentum p, and frequency f to the total energy E (including its rest energy) of a particle how closely do the properties of matter...

Hi, I am reviewing some material on refraction/Huygens' principle and I would like some help with a couple of technicalities. 1) Why does light slow down when it enters a denser material? (i.e details on scattering/ microscopic effects )Are the resultant wavefronts closer together? 2) Does it...

Hey I'm reading about relativity and I stumble across statements such as if a four-vector is timelike then it's always possible to find a reference frame for which the space-components vanish. Further if a four-vector is 'four-orthogonal' to a timelike four vector it must be spacelike. I...

Good day. Can anyone tell me what the difference is the value of magnetic induction B [T] when using the normal driver coil and the coil of superconductor? Thank you.

Why are cathode rays able to penetrate very thin metal films?

Homework Statement Simplify. \sqrt[3]{\frac{5}{4}} The answer according to the textbook is: \frac{\sqrt [3]{10}}{2} Homework Equations -- The Attempt at a Solution Separated numerator and deonominator into individual cube roots and multiplied both by \sqrt[3] {4} ...

Homework Statement Use the properties of the determinant of a matrix to show that\begin{vmatrix}1+x^2 & x & 1 \\ 1+y^2 & y & 1 \\ 1+z^2 & z & 1\end{vmatrix}=(x-y)(x-z)(y-z) Homework Equations Properties of determinants. There's 10 of them, according to my notes.The Attempt at a Solution I used...

Let us take a function defined by y=cx To differentiate that, we use the operator d/dx \frac{d}{dx} y = \frac{d}{dx} cx^{-1} By the chain rule/implicit differentiation on the left and normal differentiation on the right we get, \frac{dy}{dx} = -1c x^{-2} What confuses me is the proper...

Homework Statement The hamiltonian for a given interaction is H=-\frac{\hbar \omega}{2} \hat{\sigma_y} where \sigma_y = \left( \begin{array}{cc} 0 & i \\ -i & 0 \end{array} \right) the pauli Y matrix Homework EquationsThe Attempt at a Solution So from the time dependant schrodinger...

Hi, I am looking for the thermophysical (viscosity, thermal conductivity, diffusivity, linear expansion, dansity) values of gases and liquids at various pressure. Can anyone tell me any useful resource of finding this data. Thanks Misbah

Hello, I would like to check my arguments for this problem. Homework Statement Consider the relation R = \{(x,y) \in \mathbb{R} \times \mathbb{R}: x-y \in \mathbb{Z}\} on \mathbb{R} . Prove that this relation is symmetric, reflexive, and transitive. Homework Equations Supposing a relation...

Hey came across this question in my physics textbook. If the surface of a material is under compression, is it hot or cold relative to the body of the same piece of material? Unfortunately their explanation doesn't make any sense what so ever! Would anyone like to give an explanation that makes...

sir , my doubt is that are than any ordered fields other than Real numbers,rational numbers,integers...

This isn't really homework, but I figure this is the most appropriate place to post this... Please do say if you think there is a more likely place it will get answered - I'm new! Homework Statement I am trying to calculate the muzzle velocity of an air rifle. I can find the time of flight...

How is density an intensive property? If density= mass/ volume wouldn't the density increase as the mass increases seeing that they are directly proportional? I'm seeing this in my Uni lecture slides on thermodynamics; that density is an intensive property which means it is mass...

i need some conceptual help for my final year project... what are the thermal properties of ice cream?? Specifically the thermal conductivity and latent heat and the relation of it's variation with temperature... i'll be adding a copy of my abstract for better understanding. oh and yeah I'm a...

Hi i am carrying out CFD analysis on a valve and i would like to use a material of OIL as the fluid body. i have already carried out simulations with water and air, can anyone tell me were i can find the properties of oil (ie density 918kg/m³) in the materials library as at the moment this...

Hello. I need help with some thermo basics. I can't understand the concept of constant volume compression/expansion. Please help me understand how it occurs. Also, I am not clear on how pressure is an intensive property. To my understanding it IS a quantity dependent on system size (eg...

Homework Statement A well lagged calorimeter of mass 120g contains 200g of water and 50g of ice, initial at 0°C. A jet of steam is blown through the water until the water temperature reaches 30°C. Calculate the mass of steam that must condensed. The specific heat capacity of Copper...

If two elements in a group operate together and can create more then 1 answer (this answer is still a part of set, not foreign) is it still a group, if so why?

Homework Statement Homework Equations The Attempt at a Solution I tried to see if the problem has any properties with determinants that i can apply but the properties i learned didn't involve the use of adjoint matrices so I'm kind of stumped on this one. Any hints would be...

Hello there. I have been reading G.H. Hardy's book "A Course of Pure Mathematics". It is a fantastic introduction to Analysis. I have no problems with the book so far, however, it does assume some knowledge in number theory. I just want to make sure that the following proofs for properties of...

Hey all, I'm doing an investigate into lock-in amplifiers and am looking for a book, or journal, which has a collection of properties/ characteristics for cables? For example, I'm particularily looking for a reliable source to quote the speed of propagation of a particular co-axial cable...

Is it known if space: 1. is "grainy" or smooth ?, 2. has singular points ?, 3. is like R^3 ?

Let p be an odd prime. Let f(a) be a function defined for a prime to p satisfying the following properties: (i) f(a) only takes the values ±1. (ii) If a=b (mod p), then f(a)=f(b). (iii) f(ab) = f(a)f(b) for all a and b. Show that either f(a) = 1 for all a or that f(a) = (\frac{a}{b})

Homework Statement Canada Post will deliver parcels only if they are less than a certain maximum size: the combined length and girth cannot exceed 297 cm (Girth is the total distance around the cross-section of the parcel). Canada Post delivers a crate with the smallest SA to your house. What...

Homework Statement 1 1 1 a b c = (b-a)(c-a)(c-b) a^2 b^2 c^2 (above is a 3x3 matrix equaling to a equation) question:"Show by applying property of the determinant"Homework Equations N/AThe Attempt at a Solution read through the whole chapter of...

Just a couple of numbers I'm having trouble finding. Does anyone know what a typical energy for a nuetrino ejected from the sun is? Any number on a guess-timate of what the density of nuetrinos is in deep space? Also, same two questions for electron nuetrinos and Tau nuetrinos. A 1...

i need the material properties of Tungsten Nitride. Here is a list of properties i need: 1.band gap at 300k 2.work function 3. electron and hole mobility 4. permittivity 5. thermal conductivity 6. heat capacity 7.SRH recombination rates(tau-n and tau-p) 8.density of states(conduction...

My friend and his brother were trying to work out what affects the size, power and height of a wave and why? Is it the moons gravity or fetch? Can anyone help?

Homework Statement the ques says: lim x tending to 0 [f(x)g(x)] exists. Then both lim x tending to 0 f(x) AND lim x tending to 0 also exist. True or False Homework Equations The Attempt at a Solution lim f(x)g(x) =lim f(x) * lim g(x) so if LHS exists then limf(x) and lim g(x) must exist so it...

Ok, so the wavelength is the length between two crests. Is it also the length of a complete wave? (sorry if I sound really stupid) The period is the time taken for one particle that makes up the wave to complete its oscillation, and it is also the time taken to make one complete wave. But I...

Homework Statement Suppose f is differentiable in \mathbb{C} and |f(z)| \leq C|z|^m for some m \geq 1, C > 0 and all z \in \mathbb{C} , show that; f(z) = a_1z + a_2 z^2 + a_3 z^3 + ... a_m z^m Homework EquationsThe Attempt at a Solution I can't seem to show this. It does the proof...

hi all, what happens if we employ two devices such that one measures position and another measures momentum but that they measure at the same time.