Form Definition and 1000 Threads

Good evening everybody. This is my suggestion for answer. The tensor is diagonal and the compression is a plane stress equilibre equation div(σ)=0 so: So, does that means that = f(y.z) = Ay+Bz and =f(x.z)= Cx+Dz A,B,C and D are constants. Is that what the question meant? Thank you in...

I've just been learning about Gauss' law which as far as I can tell states that the net electric flux through a surface equals the enclosed charge divided by the permittivity of free space, and is often expressed as the integral $$\int_S {\bf{E} \cdot d \bf{A}} = \frac{Q}{\epsilon_0}$$In some...

If I wanted to write ##\hat{r}##in terms of ##\hat{x}##and ##\hat{y}##, is it ##\frac{\hat{x} + \hat{y}}{\sqrt{2}}## ?

By working with the following definition of minimum of a quadratic form ##r(\textbf{x})##, ##\lambda_1=\underset{||\textbf{x}||=1}{\text{min}} \ r(\textbf{x})## where ##\lambda_1## denotes the smallest eigenvalue of ##r##, how would one tackle the above problem? It is clear that the diagonal...

I just ran this pretty quick at work. But this is the general outline. Sorry for the slop, it will get better with time. Thanks in advance and any additional info can be supplied. The material is from the Khan free course. ..... A student is fed up with doing her kinematic formula homework...

How did you find PF?: google Hi I have a scenario where I just cannot make up my mind when creating this joint and hinge at the same time. Obviously yellow is the hinge, red section to the left has two wings hanging off it held there by two hinges, 250 um. thinking about ultra sonics to...

Hey! :o I am looking at the following exercise: Construct a composite Turing machine $M$ that has a word $w$ over the alphabet $A = \{a, b\}$ tests to see if it's made up of two equal parts, that is, if $w = uu$ with $u \in {a, b}^+$. In this case, at the end of the method a $1$ has to be...

Hey! :o I am looking the follwong exercise: Using the method of Quine-McCluskey, determine the prime implicants for the following switching function and find a disjunctive minimal form. If available, also specify all other disjoint minimal forms. The switching function is...

According to this image, in the attached files there is the demonstration of the ampere's law in differential form. Bur i have some difficulties in understanding some passages. Probably I'm not understanding how to consider those two magnetic vectors oriented and why have different name. in...

Formula I have shows is probably for resulting harmonic? Does syntesizing mean writing the main formula? I havo no clue about effective value of signal and representation is probably done in excel or other graphing app.

As far as I know we can express the position and momentum operators in terms of ladder operators in the following way $${\begin{aligned}{ {x}}&={\sqrt {{\frac {\hbar }{2}}{\frac {1}{m\omega }}}}(a^{\dagger }+a)\\{{p}}&=i{\sqrt {{\frac {\hbar }{2}}m\omega }}(a^{\dagger }-a)~.\end{aligned}}.$$...

Lets take for example Gauss's law in integral form. Suppose at time ##t## we have charge ##q(t)## (at the center of the gaussian sphere) enclosed by a gaussian sphere that has radius ##R>>c\Delta t##. At time ##t+\Delta t## the charge is ##q(t+\Delta t)## and if we apply gauss's law in integral...

Hey guys, Sorry that it's been a decent amount of time since my last posting on here. Just want to say upfront that I am extremely appreciative of all the support that you all have given me over my last three or four posts. Words cannot express it and I am more than grateful for it all. But, in...

Hey guys, I'm kind of in a rush because I'll have to go to my classes soon here at USF Tampa, but I had one last problem for Intermediate Analysis that needs assistance. Thank you in advance to anyone providing it. Question being asked: "Let $A$ be a nonempty set of real numbers which is...

I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms...

The only thing tripping me up here is that the answer needs to be in vector form. If the question was asking for the scalar form, then I would just find the distance between the charges (plot the charges according to their vector coordinates, then use pythagorean theorem to find the distance...

Summary: could you explain why this equality is a quadratic form identity? i read this equality (4.26) here w depends on two variables. it is written that if B is bounded (L2) then it is a quadratic form identity on S. what does it mean? is it related to the two variables? next the author...

Backstory - I have not been in school for 5ish years, and am returning to take some grad classes in the field of Solid Mechanics. I am freaking out a bit about the math (am rusty). I have not started class yet, but figured I would get my books and start working through problems. This problem...

I'm unclear on what exactly an annihilation or creation operator looks like in QFT. In QM these operators for the simple harmonic oscillator had an explicit form in terms of $$ \hat{a}^\dagger = \frac{1}{\sqrt{2}}\left(- \frac{\mathrm{d}}{\mathrm{d}q} + q \right),\;\;\;\hat{a} =...

Im trying to visualize what form the light cones take in Rindler coordinates. Below is my drawing + reasoning. Is it right?

The Minkowski metric for inertial observers reads ##ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2##. Is there a way to show that if it had off diagonal terms, the inertial observers would not see light traveling with the same speed?

Is it appropriate to say that within classical physics the general form of Newton II is the Cauchy momentum equation? This equation applies to an arbitrary continuum body. Therefore it is more general than the common form of Newton II which applies basically to point masses and centers of mass...

I want to make a small item in Stainless Steel Sheet of 1.2 mm thick, 18 inch width & 24 inch length, by "Metal Forming & Punching of Holes". Please suggest me, which grade of Stainless Steel Sheet is more soft or ductile? It has to be economical as well. Thank you.

The integral has the form: $$\frac{s^2\nu^4}{(2\pi)^2}\int_{-1}^1 u(1-u^2)k_f^5[|r_1\chi_1|^2+|r_1\chi_2|^2-|r_1|^2\chi_1^*\chi_2\cos(2k_f\sqrt{u^2-\nu^2}a)-|r_1|^2\chi_2^*\chi_1cos(2k_f\sqrt{u^2-\nu^2}a)]\, du$$ ##r_1,\chi_1## and ##\chi_2## are also imaginary functions of u, because the form...

I am studying a beginner's book on QFT. In a chapter on electromagnetic form factors, the authors have written, using normalized states, $$\begin{eqnarray} \langle \vec{p'}, s'| j_\mu (x) |\vec{p}, s \rangle \ = \ \exp(-i \ q \cdot x) \langle \vec{p'}, s'| j_\mu (0) |\vec{p}, s \rangle...

Given #11 $\quad\displaystyle xdx+ye^{-x}dy=0,\quad y(0)=1$ a. Initial value problem in explicit form. $\quad xdx=-ye^{-x}dy$ separate $\quad \frac{x}{e^{-x}}\, dx=-y\, dy$ simplify $\quad xe^x\, dx=-y\, dy$ rewrite $\quad y\,dy=-xe^x\,dx$ integrate (with boundaries) $\quad \int_1^y...

So I was reading the Charles&Wheeler book and this came out of nowhere: but how is it derived in the wholeness?

Hi, The following is called normal form of the conic section equation: x²+y²+2ax+2by+c=0 A circle is one of the conic sections when considered as a special of ellipse. I'm confused as to why the the given equation is called "normal form of the conic section equation" when, in my opinion, the...

From Thomas Moore A General Relativity Workbook I have the geodesic equation as, $$ 0=\frac{d}{d \tau} (g_{\alpha \beta} \frac{dx^\beta}{d \tau}) - \frac{1}{2} \partial_\alpha g_{\mu\nu} \frac{dx^\mu}{d \tau} \frac{dx^\nu}{d \tau} $$ as well as $$ 0= \frac{d^2x^\gamma}{d \tau^2} +...

Rewrite in logarithmic form: e^(-1) = c

Rewrite in exponential form: Log(6) 1294 = 4 Log(w) v = t Ln(1/4) = x Evaluate Log(4) 64 = ? Log(16) 4 = ?

Now that I think about this some more, nucleons can get close together if they are traveling at a very high speed. So maybe when the Earth first formed, stuff was moving fast (or at high temperature/pressure) and this forced nucleons together into nuclei? I don't really know what I'm talking...

Hello everyone, I'm trying to make lubrication out of paraffin, this is what I am doing, 1/3 melted paraffin wax, 1/3 paraffin oil, and 1/3 xylene. After melting the wax I add the oil, I then add the oil, mix it well to the correct consistency, I then transfer it to a glass container where I...

Determine if the set of vectors $\begin{bmatrix} x\\y\\5 \end{bmatrix}\in \Bbb{R}^3$ form a vector space ok if I follow the book example I think this is what is done $\begin{bmatrix} x_1\\y_2\\5 \end{bmatrix} +\begin{bmatrix} x_2\\y_2\\5 \end{bmatrix} +\begin{bmatrix} x_2\\y_2\\5...

Hi so I'm really new to stats, like I know mean, median, mode, and t-testsish and that is it. However, this topic really resonates with me because I know it can have real world applications. So these are my questions. First off here is my real world problem. At my workplace, we sell food that...

There are two forms of the Maxwell equations, one is the differential form, the other is the integral form. Which one is more useful?

I know that the height before the first bounce will be ##y = g * t * t + v_0 * t + y_0##. After the first bounce, I can find y by pretending the ball was thrown from the ground with velocity ##e * -v_f## with ##v_f## being the velocity of the ball when hitting the ground, but I have to reset the...

Problem Statement: The effective charge density of the electron cloud in a hydrogen atom in its quantum mechanical ground state turns out to be given by pnot(e^-(r/rnot)), where pnot is a negative constant (the clouds charge density at r=0) and rnot is a constant (rnot=0.025nm). Use gauss's law...

Hello, For my homework I am supposed to get- into the form of a Bessel equation using variable substitution. I am just not sure what substitution to use. Thanks in advance.

nmh{896} mnt{347.21} consider th non-homogeneous first order differential system where $x,y,z$ are all functions of the variable t \begin{align*}\displaystyle x'&=-4x-3y+3z\\ y'&=3x+2y-3z+e^t\\ z´&=-3x-3y+2z \end{align*} write a system in the matrix form $Y'=AY+G$

Akio coaches the girls volleyball team. He needs to select players for the six different starting positions from his roster of 16 players. On Akio’s teams, each position has its own special responsibility: setter, front left-side and middle hitters, back right- and left side passers, and...

In my last post I asked about the general form of the Lorentz Transformation for time. Now I am trying to understand the final form of it, and how it makes sense based on what's happening physically. The final form for t is: t = γt1 + (γv/c2/)x1 It's the second part of this equation, the...

Hi. I've the following charge density: ## \rho = \rho_0 \frac {r}{R} ## I'm getting a trouble to calculate the potential inside a sphere of radius R located in the center of axis with the given charge density (using poisson equation): the Laplacian in spherical coordinates is: ##\frac {1}{r^2}...

Express -3-3i in polar form. I know that r=3√2. And I understand that now we take tan^-1(b/a) which I did. tan^-1(-3/-3) = π/4. So I put my answer as z = 3√2 [cos(π/4) + isin(π/4)]. However the answer manual told me this was incorrect I am unsure of where I went wrong...

one book example $\textsf{Suppose that A is a matrix whose characteristic polynomial is}$ $(\lambda-2)^2(\lambda + 1)^2, \quad \dim\left(E_2\right)=1 \quad \dim\left(E_{-1}\right)=2$ $\textsf{Find the Jordan Normal Form of A Find the Jordan Normal Form of A}$ $$\quad \dim\left(E_2\right)=1...

Homework Statement I learned that Covalent Bonds form between different specific atoms ( with similar electro-negativity ) with electrons. However, I wondered what type of bond would form between the different atoms if they had no electrons? Also , if I have 2 atoms with similar...

Do the Maxwell equations in the usual 3-vector form have the same form in any Lorentz frame? For example, the one that says ##\nabla \cdot \vec B = 0## will be valid in another, primed Lorentz frame? That is ##\nabla' \cdot \vec {B'} = 0##?

Homework Statement I want to manipulate an equation to suit a desired form. Homework Equations ##(-h^2/2uc)*(dp/dx)*ln((1+c*(x/h)^2)/(1+c))## becomes ##-(h^2/2u)*(dp/dx)*(1-(x/h)^2)## The Attempt at a Solution I have no idea, I'm not even sure how the natural log disappears. [/B]

Homework Statement ABC is an isosceles triangle such that AB = AC A has coordinates (4, 37) B and C lie on the line with equation 3y = 2x + 12 Find an equation of the line of symmetry of triangle ABC. Give your answer in the form px + qy = r where p, q and r are integers. Show clear...

The Biot-Savart law which describes a magnetic field created by a displacement current: $$\frac{dB}{dV}=\frac{\mu_0\epsilon_0}{4\pi}\frac{\frac{∂E}{∂t}×r}{r^2}$$ What's the relativistically co-variant form of this equation? Is the introduction of speed of light propagation delays enough, or...