Form Definition and 1000 Threads

Homework Statement well this is not exactly a homework, i had an argument whith my teacher about my grade in a test, because i put a complex number in the form of R,theta and she claims that the form was costheta+isentheta, and i know that but i need to prove in a book that...

Few months back, in the final rounds of biology olympiad for Highschool students, i was asked, "Plants distributes sugar in the phloem as sucrose molecules, why did plant do this, and is there any advantages? Why not other form of sugar like glucose?"Can anyone help me? :3 Also i was wondering...

Homework Statement Find the Jordan canonical form of the matrix ## \left( \begin{array}{ccc} 1 & 1 \\ -1 & 3 \\ \end{array} \right)##. Homework EquationsThe Attempt at a Solution So my professor gave us the following procedure: 1. Find the eigenvalues for each matrix A. Your characteristic...

Hi all, I was doing some math and I stumbled upon a very interesting thing. When I do ln(-1), I get πi, and when I turn that into polar coordinates on the calculator, it gives me πeiπ/2 . Why is that? I'm very curious to know, because they are so intertwined! Thank you

Let $a, b \in \Bbb R$ and $u, v \in \Bbb R^2$, with $u = (0, 1)$ and $v = (1, 0)$. Show that every vector in $\Bbb R^2$ is of the form $au + bv$. Under what conditions is this true for general vectors $u = (u_1, u_2)$ and $v = (v_1, v_2)$? No idea where to begin. Would appreciate any help.

Hello all, I am posting this question here in this thread and not the homework thread since it is not a homework problem but something I have been working on myself. Let us imagine a fluid flowing through a pipe, we can measure pipe diameter and fluid velocity. The density of the fluid is also...

Homework Statement Write the density operator $$\rho=\frac{1}{3}|u><u|+\frac{2}{3}|v><v|+\frac{\sqrt{2}}{3}(|u><v|+|v><u|, \quad where <u|v>=0$$ In matrix form Homework Equations $$\rho=\sum_i p_i |\psi><\psi|$$ The Attempt at a Solution [/B] The two first factors ##\frac{1}{3}|u><u|##...

I have known what Ornstein-Zernike equation is. I try to plug in the form as follow to the isotropic materials: Still, I cannot show the pair correlation function as follow. Can anyone know what I have missed?

Homework Statement [/B] The door is held open by the means of 2 chains. If the tension in AB and CD is Fa = 300 N and Fc = 250 N, respectively, express each of these in Cartesian Vector Form Homework Equations Sin / cos / tan The Attempt at a Solution The angle of FA at B is...

I am unsure whether I am posting in the right place, but was hoping someone could help me out. I was wondering if anyone knows the shape of the material at the beginning of the manufacturing process of a stub axle, and how the shape will vary depending on the quantity of products being made...

Dear all, I have a question regarding the computation of the area of an ellipse. The parametric form of the ellipse with axes a and b is $$x(t) = a\cos{(t)}, \ \ \ y(t) = b\sin{(t)} $$ Using this to evaluate the area of the ellipse, usually one takes one halve or one quarter of the ellipse...

Homework Statement Using only NOT and XOR, construct a compound statement having the same truth table as: (a) p OR q (b) p AND q Homework Equations XOR is "exclusive OR." p XOR q = (p OR q) AND NOT (p AND q). I have been working under the assumption that I can use parentheses. The...

I thought that z= 7.5 was the maximum for galaxies to form after re ionization but this paper puts it at z=8.38, can galaxies have formed this early? arXiv:1703.02039 [pdf, other] Dust in the reionization era: ALMA observations of a z=8.38 Galaxy Nicolas Laporte, Richard S. Ellis, Frederic...

Homework Statement Homework Equations r=sqrt(a^2+b^2) θ=arg(z) tan(θ)=b/a The Attempt at a Solution for a)[/B] finding the polar form: r=sqrt(-3^2+(-4)^2)=sqrt(7) θ=arg(z) tan(θ)=-4/-3 = 53.13 ° 300-53.13=306.87° -3-j4=sqrt(7)*(cos(306.87+j306.87) I don't know if my answer is correct...

I cannot find any explanation of the mathematical form of the single-mode photon number states, i.e. the |n>. I take them to be functions with domain {0,1,2,3, …} and appropriate associated outputs. So |3> I take to have outputs {0,0,0,1, 0, …} , |0> to have outputs {1,0,0,0, 0, …} and...

Hello I was solving a problem in probability. Here is the statement. Seven terminals in an on-line system are attached to a communications line to the central computer. Exactly four of these terminals are ready to transmit a message. Assume that each terminal is equally likely to be in the ready...

Hi, I was just looking at an example for a certain problem and noticed that in the second step they went to arctan(epsilon). I know there's a form that is equal to arctan but am a little unsure. I've come across formulas on the web such as arctan(x) = ∫(dt)/(a2+t2) but nothing else that would...

Homework Statement Show that the set GL(n, R) of invertible matrices forms a group under matrix multiplication. Show the same for the orthogonal group O(n, R) and the special orthogonal group SO(n, R). Homework EquationsThe Attempt at a Solution So I know the properties that define a group are...

Homework Statement Show that every matrix A ∈ O(2, R) is of the form R(α) = cos α − sin α sin α cos α (this is the 2d rotation matrix -- I can't make it in matrix format) or JR(α). Interpret the maps x → R(α)x and x → JR(α)x for x ∈ R 2 Homework EquationsThe Attempt at a Solution So I know...

After series of algebraic simplifications, I ended up with the following integral: ##\int_0^\infty \exp(-Kx) \arctan(x) dx ## As far as I searched, there is no closed form solution for the integral. But, K is my design variable that I need to optimize later. To do this, I need to take K out of...

Is the Hubble's law(recessional velocity linearly proportional to distance) valid for all cases even when the spacetime is curved? Is there a nonlinear model for Friedman models or it's always linearly proportional?

From Courant's Differential and Integral Calculus p.13, In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral. Proof: Let ##A=(0,0)...

Homework Statement 3 charges are placed like shown: Q1 __4cm____ Q2 ______6cm___________Q3 Q1=-2nC Q2= 1nC Q3= 3nC Find the resultant force and its direction upon the charge Q3. Homework Equations F=k0*(Q1Q2)/r2 k0-constant, equals to 9*10^9 r-distance The Attempt at a Solution...

Homework Statement I need help when changing the formula of the yellow circled part to red-circled part ... Homework EquationsThe Attempt at a Solution I tried , but i didnt get what the author got ... Here's my working ... Which part of my working is wrong ?

Homework Statement [/B] Suppose a quadratic equation in 3 variables is put into a standard form represents a hyperboloid of one sheet. This hyperboloid has the property that: • the cross section through z= 0 is a circle of radius 1; • the cross section through x= 1 is the two straight lines...

Homework Statement Let |z+1| + |z-1| = 7 where z are complex numbers. Show that the solutions to this equation form an ellipse with foci at (+/-)1 Homework Equations (x^2 / a) + (y^2 / b) = 1 equation for an ellipse The Attempt at a Solution I set z = a + bi and so |z-1| = ((a-1)^2 + b^2)^1/2...

Homework Statement \frac{z-1}{z+1}=i I found the cartesian form, z = i, but how do I turn it into polar form?The Attempt at a Solution |z|=\sqrt{0^2+1^2}=1 \theta=arctan\frac{b}{a}=arctan\frac{1}{0} Is the solution then that is not possible to convert it to polar form?

This problem is driving me crazy and its the last one in an assignment I've been doing for the last week please help -i(5+2i) (Sleepy)(Sadface)(Angry)

Homework Statement Hi, As part of the proof that : the set of periods ##\Omega_f ## of periods of a meromorphic ##f: U \to \hat{C} ##, ##U## an open set and ##\hat{C}=C \cup \infty ##, ##C## the complex plane, form a discrete set of ##C## when ##f## is a non-constant a step taken in the...

I have recently been attempting to solve a problem that has been bugging me for quite some time. I've gotten back into calculus and integrals to attempt to solve a little formula I'm trying to build for a simulation test. Over-all, if I have ##\int _0^bv^2x\ dx## I'd expect the outcome to be...

I understand the concept of Kmaps, Quine method and forming a logic diagram but I'm lost at forming an equation from an addition and subtraction equation For example: a 2 bit plus a 3 bit binary integer. I would have a 4 bit sum and 3 carries. However, how does one form the appropriate equation...

Homework Statement Find the closed form of the impulse response of the system y[n] = 7y[n-1]-12y[n-2]+x[n] using the peel away and guess method. Ie, by using Python code to find the geometric ratios and amplitudes of the outputs as n grows large, then calculate residuals, and find the...

I have been studying the Higg's field and ran across a particular equation that made me realize I need to better understand Sturm-Liuoville. So naturally I went looking through my differential calculus textbooks but was surprised they didn't cover this detail. While the article covers how to get...

Homework Statement I'd like to know how to convert Maxwell's Equations from Differencial form to Integral form. Homework Equations Gauss' Law Gauss' Law for Magnetism Faraday's Law The Ampere-Maxwell Law The Attempt at a Solution Convert using properties of vector analysis (as Divergence and...

Why is i that two cones connected at their vertices is not a manifold? I know that it has to do with the intersection point, but I don't know why. At that point, the manifold should look like R or R2?

Hello. How can I verify that (u,v) = (x square - x, x+1) is a parametric form of a parabola? Thank you!

I am given the following set of 4x4 matrices. How can i justify that they form a basis for the Lie Algebra of the group SO(4)? I know that they must be real matrices, and AA^{T}=\mathbb{I}, and the detA = +-1. Do i show that the matrices are linearly independent, verify these properties, and...

Homework Statement For the following integral, find F and its partial derivatives and plug them into the Euler Lagrange equation $$F(y,x,x')=y\sqrt{1+x'^2}\\$$ Homework Equations Euler Lagrange equation : $$\frac{dF}{dx}-\frac{d}{dy}\frac{dF}{dx'}=0$$ The Attempt at a Solution...

hello this is my first topic here and i hope good discussion or answer to my question As i understand the Maxwell equation keep its form in all frames so why i need to make a covarient formulation form of electrodynamics ? for example what the covarient form of continuity equation give me !

Please see attached. I am trying to show that ## T_{p} f (\tau + 1) = T_{p} f (\tau ) ## ##f(\tau) \in M_k ## and so can be written as a expansion as ##f(\tau)=\sum\limits^{\infty}_{0}a_{n}e^{2 \pi i n \tau } ## ##f(\tau + 1) = f(\tau) ## since ##e^{2\pi i n} = 1## Similarly ##f(p\tau + p) =...

So I always thought that geometry is somewhat different from the rest of math. I mean, most of math is about numbers and relations. While geometry is about space. Does analysis connect the two? For example, the hypotenuse of a triangle is just a truncated portion of the number line that has...

Hello! This is my first post on these forums. So I was stuck with this question in my Mathematical Analysis exam, and it is as follows: ƒ(x) = 0 if x ∉ ℚ and (p + π) / (q + π) - (p / q) if x = (p / q) ∈ ℚ (reduced form). 1- Prove ƒ is discontinuous at all rational numbers except 1: This is...

##\theta(\tau, A) = \sum\limits_{\vec{x}\in Z^{m}} e^{\pi i A[x] \tau } ## ##=\sum\limits^{\infty}_{n=0} r_{A}(n)q^{n} ##, where ## r_{A} = No. [ \vec{x} \in Z^{m} ; A[\vec{x}] =n]## where ##A[x]= x^t A x ##, is the associated quadratic from to the matrix ##A##, where here ##A## is positive...

Homework Statement Let's say we have a mass of 5kg at a height of 3 m so it's potential energy is mgh = 147J/1.6e-19 = 9.19 e20 eV. Now we know that E = mc^2... so when finding the mass of this potential energy we get 10.2e3 kg. What the hell is that supposed to mean? Homework Equations None...

$\tiny{s6.12.25}$ $\textsf{If $v$ lies in the first quarter and makes an angle }\\$ $\textsf{$\pi/3$ with the positive x-axis and $\left| v \right|$=4} $ $\textsf{find $v$ in component form.}$ \begin{align} \displaystyle v&=\langle 2\sqrt{3},2\rangle \\ \end{align} this is probably correct...

can H2s form hydrogen bonds i read that H2s can , but I'm not so sure about it .

dy/dx = xe^(y-2x) , i am asked to form differential equation using this equation . the ans given is (e^-y) = 0.5(e^-2x)(x+0.5) + a , how to get the answer? btw , i have attached my working

Dear All It is known that pontryagin densities are defined in even dimension space, let's say i am concerned with 4 dim space time. We also have a certain group G. What is the formula of pontryagin densities for arbitrary group? Larger group?

The volume form on the unit sphere ##S^{n}## in ##\mathbb{R}^{n+1}## is given by $$i_{{\bf r}}\ dx^{1}\wedge \dots \wedge dx^{n+1}=\sum (-1)^{i-1}x^{i}dx^{1}\wedge\dots \widehat{dx^{i}} \dots \wedge dx^{n+1}.$$ Why must the volume form ##dx^{1}\wedge \dots \wedge dx^{n+1}## act on the vector...

I am pretty confused about how to write Navier-Stokes Equation into conservation form, it seems that from my notes, first, the density term with the pressure gradient dropped out. and second, du^2/dx seems to be equal to udu/dx. Why is it so? I attached my notes here for your reference.