Properties Definition and 1000 Threads

Are different electrical frequencies allocated to specific applications because of their properties or to regulate the spectrum so that each assigned frequency range is unique to one entity? I guess a related question is: Are we going higher in frequency ranges for things like automobile...

Hey, Ive a question in my textbook and I don't really know what to do! The question is: I know I need to prove that the relation is 1)Symmetric 2)Reflexive 3)Transitive But how do I prove this

Homework Statement I've solved a problem in my engineering homework to a point where I have the following data: ψ = arctan(3) = 71.57 (degrees) , inverse tangent of 3 δ = 30 degrees solve for gamma and chi (χ): tan(2gamma) = tan(2ψ)cos(δ) sin(2χ) = sin(2ψ)sin(δ) Homework Equations...

Homework Statement Use the Poisson distribution W=(λ^n/n!)*e^-λ to calculate <n> Homework Equations <n>=ƩW*n The Attempt at a Solution Since W = (λ^n/n!)*e^-λ I wind up with <n>=[(λ^n/n!)*e^-λ]*n But I really don't know where to go from here. Should I do a Taylor Series. I've...

I want to circulate cold water through copper tubing curled in a spiral about a fan. I'll cool the water with a large block of ice that I can remove and replace like a battery. To avoid making a mess I can freeze the ice inside of a copper housing, and pump the water in copper tubes around that...

Problem: Let $O$ be an $n \times n$ orthogonal real matrix, i.e. $O^TO=I_n$. Prove that: a) Any entry in $O$ is between -1 and 1. b) If $\lambda$ is an eigenvalue of $O$ then $|\lambda|=1$ c) $\text{det O}=1 \text{ or }-1$ Solution: I want to preface this with that although this is a 3-part...

Hi everyone, I'm trying to find a function of single variable f(x) with the following properties: -It is symmetric around zero -It is differentiable everywhere -f'(x)≥0 for all x>0 -f'(x)=0 when x=0 -f'(x)≤0 for all x<0 (I think these last two actually follow from the first three?)...

Hi, I am sort of hung up with a particular step in a derivation, and this has caused me to ponder a few properties of partial derivatives. As a result, I believe I may be correct for the wrong reasons. For this example, the starting term is (\frac{\partial}{\partial x}\frac{\partial...

I have written a short paper that addresses the question posed in the title. You can find a copy of the paper here: http://www.math.csusb.edu/faculty/pmclough/LP.pdf. I think the paper may have some pedagogical value. If you have any comments or suggestions regarding the paper or any different...

Three objects (A, B, and C) are brought close to each other one at a time. A and B attract, but B and C repel. Simple true/false question involving "is this one positive/negative/etc." What I'm unsure about is whether or not A could possibly be neutral, or more specifically, is there any way to...

Homework Statement Prove the following properties of relations: 1) If R is asymmetric then it's antisymmetric. 2) If R is asymmetric then it's irreflexive. 3) If R is irreflexive and transitive then it's asymmetric. The Attempt at a Solution 1) If R is asymmetric on a set X, then for all...

1.show that there is no axiom for set union that correspond to "Existence of additive inverses" for real numbers, by demonstrating that in general it is impossible to find a set X such that $A\cup X=\emptyset$. what is the only set $\emptyset$ which possesses an inverse in this sense? 2. show...

I'm interested in solutions of an equation f'(x) = -\frac{xf(x)}{Af(x)+ Bx^2} with some positive initial value f(x)>0, and with positive constants A,B>0. First question: Does an explicit formula exist? I couldn't figure it out. Second question: I see that f(x)>0\implies f'(x)<0, and on...

When a particle decays into two different particles, they are said to be entangled. If one of these is absorbed by an atom or there is a subsequent interaction with another particle, what happens to the previous or initial entanglement? Does it diminish or completely go away? For example...

Hello, Quick run-down: I am attempting to model thin film materials (e.g. Ti-Al-N) for thermal analysis. I am confused on how to figure out the number density of Nitrogen for a ceramic. All the tables I have in school textbooks are for gas (~0.0013 g/cm3). I can find density of...

in the following exercises, assume that x stands for an unknown real number, and assume that $x^2=x\times x$. which of the properties of real numbers justifies each of the following statement? a. $(2x)x=2x^2$ b. $(x+3)x=x^2+3x$ c. $4(x+3)=4x+4\times 3$ my answers a. distributive property b...

please help me break down this computations into the simplest possible steps using properties of real numbers. a. 5+37 b. 6*17 c. 12*16 d. 64+55 i'm not quite sure where to start.

Its been a while since I've done this stuff, and I don't have a text handy. I know that for sets, intersection distributes over union, I don't remember if the same will hold for vector spaces over addition? for example does A \cap (B + C) = A \cap B + A \cap C

Hello, I want to know what factors determine that a signal (radio wave, microwave, infra red) cannot be use for broadcasting but only point to point communication. I know that it has to do with frequency and the energy associated with it but cannot seem to have a concrete reason because of...

I have the following vector field:E=E_0(-sin(\phi),cos(\phi),0)^T and [/itex]E_0[/itex] is some constant. Does anybody here have an idea what this electric field does to a metallic sphere that is in it? Thereby I mean, does it create a dipole moment or does it create a current and so on?

justify each of the steps in the following equalities. i don't know where to start. what i know is i have to use properties of real numbers. please help! 1. $\displaystyle \left ( x+3 \right )\left(x+2\right)\,=\,\left ( x+3 \right )x+\left ( x+3 \right )2\,=\,\left ( x^2+3x \right )+\left (...

can you give an example of symmetric property of equality and transitive property of equality. the generalization of these properties are a bit abstract for me. thanks!

Hi, I'm wondering if there's any possible way to do voltage gating to a sample while observing it with a microscope, in order to measure its optical properties while changing its electrical parameters. Thanks

I would like to know if the Jordan Product carries along with it the same properties as that of the cross product (i.e. associativity, commutable, left/right distributive)? If you've taken LA, I'm sure you know that professors require us to complete a project and I've chosen the Jordan Product...

Dear all, i'm trying to understand geometry by studying the subject myself. i came across idea that I'm very much confuse of. it say's that 'geometry is a studies of geometric properties that is invariant under transformation' such as distance for euclidean geometry. my question is: why do...

Hi everyone, I would like to program water thermodynamic properties in C, C++ or Matlab in order to model a steam power plant. I'm particularly interested in getting the enthalpy of the fluid by knowing the temperature and the pressure. I recently found out the software Cantera...

Suppose you have the following definition of Dirac-delta function, or the so called sifting property: \int^{d}_{c}f(t)δ(t-a)dt =\left\{\begin{array}{cc}f(a),&\mbox{ if } c\leq x \leq d\\0, & \mbox{ if } x>d \mbox{ or } x<c \\ \mbox{undefined}, & \mbox {if } x = d \mbox{ or } x = c...

Hello, I am calculating the centroid of an area using this equation for composite bodies: sum(indivudual area times individual centroid)/sum(individual area) = distance from axis to centroid this is just y bar for a cross section that is symmetrical about the y axis I was under the...

Hi everyone I'd like to know what will happen to the magnetization and susceptibility of a given soil sample when it is denatured by heating.

\partialμgλρ - \partialρgμλ = 0 I have reaced to this statement. Is this true? How? What I thought is it looks like field strength tensor, but symmetric hence we can say it is true. Thank you.

I'm a fresher in PF. If I'm posting indecently, please forgive.. Vacuum is something empty. It contains nothing. Then why should it have properties like permeability, permittivity etc.?

Hello Can we consider the sentence “Adiabatic process cannot decrease entropy” (found for example here) to be true in any circumstances ? Here I do not want to focus on any particular situation. Hence the system is not necessarily a (perfect) gas; the transformation is not necessarily...

I'm working on a video game set in space, and I'd like my portrayal of the galaxy to be as scientifically accurate as is feasible. I've been looking into metallicity functions, but I can't make any sense of what I'm seeing, and I don't even know where to start on the subject of algorithms for...

Homework Statement Given f(x) = 1-x Show that 2f(3x + 1) = -6x Homework Equations The Attempt at a Solution I've tried many approaches, but I seem to be missing something. The latest approach was as follows and did not work. Divide by 2. f(3x + 1) = -3x f(3x) + f(1) = -3x...

Let p[n] be the following property of Fibonacci numbers: p[n]: f_{n+1} * f_{n-1} - (f_{n})^{2} = (-1)^{n}. Prove p[n] by induction. This is the proof I wrote. i used regular induction. Is weak induction sufficient to prove it or do I need to prove this by strong induction? proof: BASE STEP...

What is the usage of the squareness in the thin film magnetic property studies?

Hi folks! I've encountered the matrix below and I'm curious about its properties; R= \begin{pmatrix} 0 & N-S\\ N+S & 0 \end{pmatrix} where R, N and S are real matrices, R is 2n by 2n, N is n by n symmetric and S is n by n skew-symmetric. Clearly R is symmetric so the...

When proving that x^m x^n = x^{m+n} and that (x^m)^n = x^{mn} for all elements x in a group, it's easy enough to show that they hold for all m \in \mathbb{Z} and for all n \in \mathbb{N} using induction on n. The case n = 0 is also very easy. But how does one prove this for n \in...

Homework Statement Hi, I am solving a system of differential equations and in one of my equations I have this, (D+2)X+(D+2)Y=0 where X and Y are variables, D is my differential operator. My question is, would it be mathematically correct to divide out (D+2) and thus getting X+Y=0, X=-Y ?

I am using FE package called ABAQUS, however my question is general, i read that the mesh should be uniform,so does that mean it should be square, also if i have different parts affect each other, does the nodes on one part need be connected to the other part at the edges(to achieve continuous...

One way to model the wavelike property of a trapped particle is to have it do something (say expand and contract) on a periodic basis as it travels though space. Assuming the periodic expansion and contraction matches the wavelength of the particle, it will "interfere" with other particles the...

Homework Statement Let S = {(a, b): a, b \in \mathbb{Z} and b ≠ 0}. An equivalence relation "~" on S is defined by (a, b) ~ (c, d) iff ad = bc. 1) For any b \in \mathbb{Z} \setminus {0}, show that [0/b] = [0/1] and [b/b] = [1/1]. 2) For any a, b \in \mathbb{Z} with b ≠ 0, show that...

Homework Statement A gauge transformation is defined so as to leave the fields invariant. The gauge transformations are such that \vec{A}=\vec{A'}+\nabla\Lambda and \Phi=\Phi'-\frac{\partial\Lambda}{\partial t}. Consider the Coulomb Gauge \nabla\cdot\vec{A}=0. Find out what properties the...

Pre-theoretically, we notice that objects have some property responsible for their varying dispositions to resist being pushed around in space, or to resist changes in motion given applied forces ("inertia"). So we introduce the term "inertial mass" to apply to the most physically interesting...

Is there a function f(x): \mathbb{R} \to \mathbb{R} such that \lim_{x \to 0} x f(x) = a \neq 0.

Hi, I'm a bit uncertain about the validity of my argument/approach to the following: I'm trying to prove that the solution to a partial differential equation \frac{\partial u(x,t)}{\partial t} + N[u(x,t)] = 0, where N is some nonlinear operator, CAN BE (not necessarily is) asymmetric...

We are going over magnetism in my Physics 2 course but we barely covered electromagnets. I was wondering what the math equation for field strength would be for an electromagnet. In other words, how is current related to field strength when you wrap a wire around a piece of metal. Also I was...

I sometimes hear that some aspects of the macroscopic world are emergent. That is, some people believe that certain properties and laws (for example crystal structure, superconductivity, the conservation laws, Maxwell's equations, the laws of thermodynamics, the existence of momentum) could not...

The title pretty much says it all, but let me elaborate on the source of confusion. VIM defines quantity as: Other definitions I found are extremely circular. They typically go like this, "a physical quantity is a property that can be quantified". In other words, they explain quantity with...

hello, i have been given two formulae for the entropy of an ideal gas undergoing a reversible process. the correct expression is: S = Nk(s0-ln({\frac{N_0}{N}})^{5/2} + ln({\frac{T}{T_0}})^{3/2} + ln({\frac{V}{V_0}})) where s_0 is a constant, N the number of particles, T the...