Property Definition and 608 Threads

If we have come to realize that energy conservation is not the most general conservation law in our spacetime, isn't it odd that we don't have a simple name for the "real deal"? I bumped into this thought through Noether's theorem, which relates symmetries in fields to conservation of all kinds...

Homework Statement An electromagnetic wave propagates through a gas of N free electrons per unit volume. Neglecting damping, show that the index of refraction is given by n^2 = 1 - \frac{\omega_P^2}{\omega^2}, where the plasma frequency \omega_P = \sqrt{\frac{Ne^2}{\epsilon_0m_e}}.\quad(1)...

Homework Statement [/B] example problem: 5 = [(x)(4+x)] / (4-x) answer: 5 Homework Equations Unsure what to use. 3. The Attempt at a Solution Not sure what my professor did, but I thought that if i multiply by the reciprocal of something, I have to balance by multiplying the other side as...

this is not a homework question, I just want to make sense of the equation here. Assuming matrix A is diagonal, If A_hat=T'AT where T' is an inverse matrix of T. e^(A_hat*t)=T'e^(At)T which implies, e^(T'AT*t)=T'e^(At)T we know that e^(At) is a linear mapping, therefore if we convert f to...

We know that catenation property decreases down the group... Then why oxygen exist as O2 molecule while sulphur exist as S8 molecule

Homework Statement Prove that in any vector space V, we have: ##\alpha \overrightarrow a = \overrightarrow 0 \Rightarrow \alpha = 0 \lor \overrightarrow a = \overrightarrow 0## Homework Equations I already proved: ##\alpha \overrightarrow 0 = \overrightarrow 0## ##0 \overrightarrow a =...

I could completely understand the fact it it was just a limit to our observations but how can it be a property of the microscopic particle itself? Here's how I understand about probabilities: Before a die is thrown, the probability of a certain number coming up is 1/6. But, it's before the die...

I am studying Classical Analysis with Marsden book. At very first chapter it covers sequence, field, etc... The book has theorems 1."Let F be an ordered field. We say that the monotone sequence property if every monotone increasing sequence bounded above converges." 2."An ordered field is said...

Hi PF! When proving ##\left(AB\right)^T = B^T A^T## I was thinking of writing ##\left(AB\right)_{ij} = A_{ik} B_{kj} = D_{ij}##. Then ##\left(D\right)^T_{ij} = D_{ji} = A_{jk} B_{ki} = A^TB^T## but clearly this is incorrect. Can someone tell me where my mistake is made? Thanks!

The mystery of dark matter seems to resist solution. Search after search comes up empty for the various hypothetical particles that could account for it. Is it possible that gravity itself in sufficient density, as on a galactic scale, has some multiplier effect we have not discovered and GR...

Homework Statement Is rotational inertia an intrinsic property of an object?[/B]Homework EquationsThe Attempt at a Solution So I know that rotational inertia is a property of an object that deals with a resistance to a change in the state of rotational motion but is it an intrinsic property? I...

We build a special number from ##5##, by squaring it, appending the next digit of the square to it and repeating the steps. ##5^2=25.## The next digit is 2, which is added to 5 to give 25. ##25^2=625.## The next digit is 6, which is added to 25 to give 625. ##625^2=390625.## The next digit is...

Homework Statement ' Here is the given problem Homework EquationsThe Attempt at a Solution a. For part a, I felt it was not continuous because of the sin(1/x) as it gets closer to 0, the graph switches between 1 and -1. Then I felt it might be continuous, therefore I am not sure. b. For part...

Homework Statement I need to show the attached function satisfies the Intermediate Value Property. Homework EquationsThe Attempt at a Solution I looked at the property definition, but I am really unsure what is being stated. I think if I knew what the property was stating, I could do the problem.

Homework Statement The signum function is defined by$$sgn(t)=\left\{\begin{matrix}-1, \ t<0\\0, \ t=0 \\ 1, \ t>0 \end{matrix}\right.$$It has derivative$$\frac{d}{dt} sign(t) = 2 \delta(t)$$Use this result to show that ##j2\pi \nu S(\nu)=2,## and give an argument why ##S(0)=0.## Where...

I am reading through a introductory algebra textbook and refreshing memory on this topic. In the matter of the Associative Properties, it is giving me the expression 3 + (8+x). (I'm skipping the graphs section because I'm leaving that for my tutor Saturday. But I'm moving to algebra because I...

It has always struck me that extensive quantities (kinetic energy, volume, momentum, angular momentum, mass, entropy, ...) could be defined as measures (https://en.wikipedia.org/wiki/Measure_(mathematics)) whereas intensive quantities are fields. Are there known ressources that put emphasis on...

Homework Statement A pure substance is placed into two containers of the same volume. Container 1 has twice the mass of pure substance of Container 2. After the containers are shut and both reach thermal equilibrium with the surroundings, what do we know about: a) the pressure of Container 1...

Say I'm simulating the movements of two interacting atoms. Could this system have the markov property (the future positions of the atoms depend only on the current position, not the past)? What's got me on the fence are the atoms' momentums: it's a property of the present state (at time t, the...

Hi. I'm trying to proof the image formation property of a concave spherical mirror. I know you can do this easily with a particular choice of rays (namely one that hits the vertex and one that passes through the center of the sphere) but I would like to show that a generic ray yields the same...

Hello everyone! I am new in OrCad Capture Cis and apparently lack in fundamental knowledge. I have created this circuit so far but it appears that something (or everything) is wrong. The error is "Unconnected pin, no FLOAT property or FLOAT = e" in several parts of the circuit. Your answers will...

Homework Statement (a) If e is part of some MST of G, then it must be a lightest edge in some cutset of G. Homework Equations Cut property The Attempt at a Solution When the cutset has just one edge then yes it's true obviously. I am think I can do this by contradiction. Assuming e_i is part...

I was solving some examples and one of the examples states that pressure is a qualitative property, i searched a lot on the internet but i didn't find any explanation , i didn't even find any proof that this is true.

he definition of the limit of a function is as follows:[5] Let be a function defined on a subset https://upload.wikimedia.org/math/a/1/b/a1b67abab803e714098f3e69a33900da.png, let be a limit point of https://upload.wikimedia.org/math/f/6/2/f623e75af30e62bbd73d6df5b50bb7b5.png, and let be a...

Hello! (Wave) With use of algebra I want to prove the Lagrange property:For any real numbers $x_1, \dots, x_n$ and $y_1, \dots, y_n$, $$\left( \sum_{i=1}^n x_i y_i\right)^2=\left(\sum_{i=1}^n x_i^2 \right)\left(\sum_{i=1}^n y_i^2 \right)- \sum_{i<j} (x_i y_j-x_j y_i)^2$$ Could you give me a...

Homework Statement Find the Fourier transform of x(t) = 4 / (4 - i*t)^2 where i is imaginary Homework Equations Duality Property F(t) ↔ 2πf(-ω) when f(t) ↔ F(ω) The Attempt at a Solution I am not sure if duality property is the way to solve this. I look at a list of properties and this...

I was reading about this Fourier transforming property of lens,when I came by the experimental setup for Fourier optics(with laser and a 4f correlator system).Part of the setup was that of Fraunhofer diffraction and we get the Fourier transform of the aperture at the focal point of first lens...

Does the property of electric charge of an elementary or composite particle exist only within the context of gauge symmetry - of the complex phase of the wave function, i.e. does gauge symmetry define electric charge? Thanks in advance.

This truth table that represents statement p v (q ^ r) is equivalent to (p v q) ^ (p v r)Showing that this statement is not equivalent to (p v q) ^ r.. Now I need to what property of Boolean Algebra is being demonstrated by the fact that the first two statements were equivalentp q r q ^ r...

Hi, How can I prove direct band gap property of a Transition Metal Dichalcogenide electrically and optically through experimentation? I can use PL measurements to prove this for optical band gap. Is there any other equipment or technique to prove this? I can not use ARPES because channel length...

Consider a set X with |X|=n≥1 elements. A family F of distinct subsets of X is sad to have property P if there exist A and B in F, such that A is a proper subset of B and |B\A|=1. Determine the least value m, so that any F with |F|>m has property P. This is a problem asked by our Discrete...

Suppose that $u$ is the solution of the Laplace equation $u_{xx}+u_{yy}=0$ in $\{(x,y)\in \mathbb{R}^2: x^2+y^2<1\}$ $u(x,y)=x$ for all $(x,y)\in \mathbb{R}^2$ such that $x^2+y^2=1.$ Find the value of $u$ in $(0,0).$ Use the property of median value.

Is it possible to come up for a sequence property or sequence sum property for ΣnK=1K^-1 If so, what other sequence properties that are not commonly seen are there?

Homework Statement Show that no matrix A ∈ M3 (ℝ) exists so that A2 = -I3 Homework EquationsThe Attempt at a Solution This is from a french textbook of first year linear algebra. I'm quite familiar with properties of matrices but I don't have any idea of how to prove this. Thanks for the help!

Homework Statement Let |v> ∈ V with |v> ≠ |0>, and let λ, μ ∈ ℂ. Prove that if λ|v> = μ|v>, then λ = μ Homework Equations Vector Space Axioms The Attempt at a Solution I am struggling to begin with this one. I can think of tons of different ways to begin, but all seem to get into a hazy area...

$$ \frac{d^{2n}}{dx^{2n}}\left(x^2-1\right)^n = (2n)! $$

Self Teaching myself Machine Shop Math from book Technical Shop Math by Thomas Achatz. According to the examples given, a=a is a Reflexive Property while a+b=b+a is described as a Commutative Property of Addition. The quiz question is: Name the property illustrated in the example. a) x+1=x+1. My...

Hello, I need some aid to see if this true: $y^2+x*\sqrt{4x^2+y^2}=y^2+\frac{x}{y}*\sqrt{4(\frac{x}{y})^2+1}$ provide that y>0 and x>0.Thank you, Cbarker1

I don't know why this is possible To use delta function properties( sifting property) integral range have to (-inf ,inf) or at least variable s should be included in [t_0,t_0+T] but there is no conditions at all (i.e. t_0 < s < t_0+T) am I wrong?

So I'm currently renting a house out to a couple of my friends, but one is about to move into his own home and the other is moving out of state next spring. I've been thinking about either selling the house or getting a company to do property management for me since I'm out of state and don't...

Homework Statement Let A and B be n x m matrices, and λ and μ be real numbers. Prove that: (λA+μB)^T = λA^T+μB^t Homework Equations :/ The Attempt at a Solution I'm struggling to start here. If there was no λ and μ, I think I'd be able to reasonably solve this. How do I show that these...

Homework Statement [/B] Prove that \delta[a(x-x_1)]=\frac{1}{a}\delta(x-x_1) Homework Equations In my attempt I have used \delta(ax)=\frac{1}{a}\delta(x) but I'm not sure I'm allowed to use it in this proof. The Attempt at a Solution Some properties of Dirac delta function are proven using...

Suppose I work for a company and build an application for internal use, according to specifications I've been given by the company. Because I'm proud of how I implemented it, and because I believe it would be useful for many people to have, I build a generalized version of it during my free time...

Homework Statement 1. Let ε > 0. Determine how large n ∈ ℕ must be to ensure that the given inequality is satisfied, and use the Archimedean Property to establish that such n exist. a.) \frac{1}{n} < \epsilon b.) \frac{1}{n^{2}} < \epsilon c.) \frac{1}{\sqrt{n}} < \epsilon 2. Let ε > 0...

Can a particle have both a quantum property and not have that same quantum property?

the basic property of light is that ,it travels in a straight line but what causes it to travel in a straight line .in refraction of light ,what causes the refracted ray to bend towards the normal ,i am aware that it is related to velocity n material of medium but how does it influence the angle...

Two particles cannot be entangled in respect to position and momentum, I've read. But can particles be entangled by all other properties, including either position or momentum? For example by energy, momentum, spin and polarization (+some other(s)?) between two photons. I've read in some other...

Homework Statement understanding the following equation: ##(n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1##. I don't know from where the first ##n## on the RHS comes and how this is related to a single addition of ##(n+1)^n##. Homework Equations ##a(b+c)=ab+ac## The Attempt at a Solution My guess is...

This page (https://shiyuzhao.wordpress.com/2011/06/08/rotation-matrix-angle-axis-angular-velocity/), gives the following relation: \left[R\vec{\omega}\right]_{\times}=R\left[\vec{\omega}\right]_{\times}R^{T} Where: * ##R## is a DCM (Direction Cosine Matrix) * ##\vec{v}## is the angular...

Does the property that two bodies connected together and if one of them is accelerating with some acceleration the second also accelerates with the same acceleration, have a name? Like for example, if there is a person in an elevator and the elevator is accelerating with acceleration ##a##, then...