Properties Definition and 1000 Threads

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.

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...

can anyone please explain this property of silicon: An excellent oxide as the low-refractive-index cladding material. thanks

Over the past couple years, I have self-studied all of the basic mathematics (algebra, geometry, trigonometry, and calculus). When learning something new, my approach has always been to understand the underlying logic of why I was doing what I did. I have a bit of a proble, however. I never...

I am new in the field of science please can you help me. I would I appreciate it. I am not that knowledgeable.

Homework Statement A dissimilarity measure d(x, y) for two data points x and y typically satisfy the following three properties: 1. d(x, y) ≥ 0 and d(x, y) = 0 if and only if x = y 2. d(x, y) = d(y, x) 3. d(x,z) ≤ d(x, y) + d(y,z)The following method has been proposed for measuring the...

Homework Statement True/False: If true give a proof, if false give a counterexample. a) If A and B have the same eigenvector X, then A+B should also have the same eigenvector, X. b) if A has an eigenvalue of 2, and B has an eigenvalue of 5, then 7 is an eigenvalue of A+B...

Homework Statement Explain the difference in the following properties of dimethyl ether and ethanol: 1) Solubility in water 2) Rate of evaporation Homework Equations The Attempt at a Solution 1) Due to the oxygen being bonded to 2 carbon atoms none of the hydrogen atoms in the...

Did physicists ever try to put empirical constraints on the properties of the aether? I recall reading a popularization by Isaac Asimov in which he remarked that the aether would have had to have a very low density, and then to explain the high speed of light it would have had to have a...

Homework Statement Give a physicist's proof of the following statements regarding energy eigenfunctions: (a) We can always choose the energy eigenstates E(x) we work with to be purely real functions (unlike the physical wavefunction, which is necessarily complex). Note: This does not mean...

Could someone look over this and see if I have any mistakes? I'm trying to show that ∫ y' dx = ∫ dy through definitions. http://imgur.com/6zCHYo5 Thanks!

Homework Statement The problem states to find a unit vector that is orthogonal to \left\langle1, 1, -2\right\rangle, forms an angle of \frac{\pi}{4} with \left\langle1, 1, 1\right\rangle and has v1 > 0. Homework Equations cos\theta = \frac{\vec{u}\bullet\vec{v}}{|\vec{u}||\vec{v}|}...

I'm not entirely sure on the properties of limits, but this seems to work. Could someone look over this for me? http://imgur.com/6zCHYo5

I'm reading the second edition of John M. Lee's Introduction to Smooth Manifolds and he has a proposition that I'd like to understand better Let M, N, and P be smooth manifolds with or without boundary, let F:M→N and G:N→P be smooth maps and let p\inM Proposition: TpF : TpM → TF(p) is...

Homework Statement The Attempt at a Solution I am working a physics problem and want to make sure I'm not making a mistake in the math. Here is my math inquiry: Say you have (a*b)(c*d) where * indicates the dot product, and a,b,c, and d are all vectors. Can you say that (a*b)(c*d) =...

Hello, I am think of using chrome paint to create a uniquely shaped mirror. I was wondering if anyone has done studies to quantify how much light is reflected from different types of chrome and how much the light scatter. I realize chrome paint isn't the same as chrome, but I couldn't find...

Not sure if this is the right place to put this (sorry, first post here) Suppose I determine that the position angle (PA) of a galaxy, in one band - observed by SDSS - is -85.4 ± 8.9°, and is 84.7 ± 10.9° in another. Assuming - for now - that the errors have a Gaussian distribution, and that...

Homework Statement Could anyone help me with these two problems? The answer for the first one is 89.5%- 91.2% and the second one is 213 grams of glucose, but I didn't get those answers. 1. In making candy, a certain recipe calls for heating an aqueous sucrose solution to the "soft-ball"...

\frac{1}{998001} has some interesting properties. It will list out every 3 digit number except for 998. It has the form 0.001002003004... Here's a video on some more details if you're interested. 998001

Am i correct in thinking that in a simple ds^2 =dt^2 - a^{2}d\underline{x}^{2} metric that: g_{\mu\nu}=diag(1,-a^2,-a^2,-a^2) and g^{\mu\nu}=diag(1,-\frac{1}{a^2},-\frac{1}{a^2},-\frac{1}{a^2}) thx

Applications: garage door openers: 40.0 , standard cordless phones: 40.0 to 50.0 , baby monitors: 49.0 , FM radio stations: 88.0 to 108 , cell phones: 800 to 900 , Global Positioning System: 1227 to 1575 , microwave ovens: 2450 , wireless Internet technology: 2.4 to 2.6 . Which of the...

Hi, There are materials with almost any combination of properties. Turning to the combinations of chemical properties with others, such as mechanical, thermal and optical ones I can name a number of examples of materials (i.e. with mechanochemical, thermochemical and photochemical...

Hey everyone, In the process of wrapping my mind around the properties of metals for a realistic rpg combat system I'm working on, I made the following chart. Let me know what you think, if it's right (arrows pointing the right direction, covering the region, labeled correctly, etc), and if...

Homework Statement An amount of saturated steam at a pressure of 10 Bar, undergoes an isentropic (constant entropy) expansion. The final temperature is 30C. Find the final specific enthalpy and specific volume. Homework Equations Saturated Steam tables, Linear Interpolation methods? No...

Hello I have a mathematical problem that I could not solve. Could you please give me some hints how to solve it? Let f: [0,1] \rightarrow \mathbb{R} be a continuous and on (0,1) a differentiable function with following properties: a) f(0) = 0 b) there exists a M>0 with |f'(x)| \leq M...

Hello, simple question here! When a voltage is regulated down or up in a circuit by, let's say a DC/DC converter, does the corresponding current increase or decrease respectively so that the system remains consistent with the laws of conservation of energy? In other words, I want to know...