Form Definition and 1000 Threads

I foolishly skipped most of my analogue electronics classes, and inevitably failed the exam. I'm now trying to revise for the resit but I'm so far behind that I just cannot understand any of the lecture slides, and I'm getting very stressed. The part of the module I am revising at the moment...

I would like to ask when can someone add the width in a scalar particle's propagator. In general the scalar propagator can be: \frac{1}{k^{2}-m^{2}+i \epsilon} (\epsilon \rightarrow 0) However I read somewhere that if necessary one can include a width for the propagator...

I was reading about Fermilab moving their new storage ring to the Muon Campus for the Muon g-2 experiment. I was curious about how the produce the Muons. I understand that protons hit a graphite target producing pions that quickly decay into Muons. How much energy are is required? How much...

The Maurer-Cartan one-form ##\Theta = g^{-1} dg## is though of as a lie algebra valued form. It arises in connection with Yang-Mill's theory where the gauge potential transforms as $$A \mapsto g Ag^{-1} - g^{-1} dg.$$ However, one also defines for lie-algebra valued differential forms...

Homework Statement How to get from Sum of 2(cos((3pi)/(2^(k+1)))sin(pi/(2^(k+1)))) from k = 1 to infinity to Sum of sin((4pi)/(2^(k+1))) - sin((2pi)/(2^(k+1))) from k = 1 to infinity The two expressions are equivalent. I need help getting from the first expression to the second.

Iam reading Julian Havil's book, The Irrationals: A Story of the Numbers You Can't Count On. In Chapter 3 Havil is writing about progress in the eighteenth century in determining the nature of $$\pi$$ and $$e$$ through the use of continued fractions. He writes (pages 92 - 93): Can someone...

I'm having a bit of difficulty conceptually understanding a problem. Hoping someone here can clear it up for me. In a simple circular condenser tube (which is cooled by water or air) what happens the tube wall temperature as the steam inside is condensed? Intuitively I would have thought that...

[SIZE="4"]Definition/Summary An algebraic function of a pair of numbers is an indeterminate form at a particular pair of values (which may include infinity) if the function does not tend to a unique limit at that pair of values. For example, \infty\ -\ \infty is an indeterminate form...

Homework Statement x*e^(y/x) + y dx = xdy, y(1) = 0 Homework Equations The Attempt at a Solution To solve, I divide everything by x dx to put everything in terms of v. e^v + v = dy/dx dy/dx = x dv/dx + v e^v + v = x dv/dx + v e^v = x dv/dx e^v / dv = x/dx Flip both sides. e^-v dv =...

Hi I am a new(ish) student of general relativity. I am currently reading 'Relativitiy DeMystified' However this guys explanation of one forms is completely mystifying to me. He says that basis vectors e_a = ∂_a = {\frac{∂a}{∂X^a}} And then says that this type of basis is...

(From another site) I think the answer is no, for ##i: S \rightarrow \mathbb R^n ## the inclusion/restriction, and ##w## any form, we have that ##i_{*}dw=d(i_{*}w )## , but the homology of ##\mathbb R^n## is trivial(i.e., every closed form is exact), so that we can write ##w= d(\alpha)##, for...

Hi everyone. Recently, I came across a closed form solution to ∫|cos(x)|dx as sin(x-∏*floor(x/∏+1/2)) + 2*floor(x/∏+1/2) I have no idea how to reach this solution but checking this for definite integral from 0 to 3∏/4 or ∏ seems to work. Using |cos(x)| as cos(x)*sgn(cos(x)) doesn't...

Homework Statement What the title says. There's a b part to the problem, but of course I can't move on to it until I understand what is going on here. Homework Equations A third degree polynomial is of the form f(x) = ax3 + bx2 + cx + d This information was not given in the...

I am guessing this is due to diffraction due to the small size of the molecules of air. But then, we never see diffraction effects (interference) for any arrangement or configuration of molecules in space?

Does anyone know of an online calculator that can form an equation of a curve with complex values and lots parameters? An advanced curve fitting calculator Y= C1(1/(1+C2e^C3x) for example

I am trying to figure out a method for using optical tweezers to manipulate individual atoms into new meta-material structures. I understand this would require a very complicated process. I thought of some general steps this process might use. This is roughly what I think it might require...

I'm reading about multlinear algebra and I'm stuck at differential form and outer product. The definitions involve tensor product and quotient set and I really cannot grab the concrete idea of the differential form. Can someone explain in a somewhat layman term what is differential form...

Why is the solution to linear differential equations with constant coefficients sought in the form of Ce^kx ? I have heard that there is linear algebra involded here. Could you please elaborate on this ?

Hello everyone, I am re-reading the introductory section of Loomis and Sternberg's Advanced Calculus text. The sentence that I have come across which is giving me slight trouble is "Indeed, any valid principle of reasoning that does not involve quantifiers must be expressed by a...

Hi, I have an exercise whose solution seems too simple; please double-check my work: We have a product manifold MxN, and want to show that if w is a k-form in M and w' is a k-form in N, then ##(w \bigoplus w')(X,Y)## , for vector fields X,Y in M,N respectively, is a k-form in MxN. I am...

I don't how to proceed further Let $z=x+jy$ find in rectangular form: 1. $\text{Im}(z^3)$ this is where I can get to, $\text{Im}(x^3+3x^2jy+3xj^2y^2+j^3y^3)=\text{Im}(x^3+3x^2jy-3xy^2-jy^3)$ please help me.

While investigating more about complex numbers today I ran across the 2x2 matrix representation of a complex number, and I was really fascinated. You can read what I read here. As I understand it, you write z in its binomial form but instead of "1" you use the identity matrix, I, and for i...

If ##\omega## is an exact form ##( \omega = d\eta )## and ##\Omega## is the region of integration and ##\partial \Omega## represents the boundary of integration, so the following equation is correct: $$\\ \oint_{\partial \Omega} \omega = 0$$?

So this is some what of a silly question, I was bored and watching YouTube and there was a guy trying to say that the Earth is hollow ( crazy people are funny to watch) but it got me thinking could a planet form so that it was hollow? Or could a something like a small moon be hollowed out? I...

Hello everyone ,i have captured car positons at differents frames.http://www.imagesup.net/pt-7140205392313.png%5D%5BIMG%5Dhttp://www.imagesup.net/dt-7140205392313.png Suppose car's(left side car which is coming towards us) centroid is at video frame1 is P(x1,y1) and Q(x2,y2) at video frame4...

Let B be the non empty sets, B ={(x,y):y = e^x, x belongs to set of real numbers} Write the set in roster form.

I was studying a article that solves the cube and quartic equation in the inverse sense: ##x = \sqrt[3]{A} + \sqrt[3]{B}## ##x = \sqrt[4]{A} + \sqrt[4]{B} + \sqrt[4]{C}## https://www.physicsforums.com/attachment.php?attachmentid=70239&stc=1&d=1401676309I found this relationship too...

Here is my understanding, please correct me if I am wrong, thanks At the end of the giant stage of a star, it experiences a supernova explosion, and turns into a neutron star (could be pulsar) or black hole, the explosion releases a lot of its matter. Here is what I don't understand: 1...

Let say that I have hydrogen gas and oxygen gas mix together, is there any chance that some H2 and O2 will react to form water without doing anything to it? I know that there needs to be activation energy to start the reaction, but are there any chance of reaction happening without activation...

Homework Statement We are given a point A(1,1,1) and a vector v=(m-1,3m-5,2m-6). We are asked to write the parametric and continuous (I don't know if that's the appropriate term; in Spanish it's called "forma continua" but you'll see right away what I mean) equations of the line formed by these...

The situation is as such. you have a magnetic passing through a loop(loop 1)of wire as some time t, say you also have a larger loop of say one light year in radius surrounding loop 1, call this loop 2. at some time t the magnetic field is shut off. when this happens would loop 2 instantaneously...

For a homework assignment I need to find the determinant of: ##\left | \begin{array}{cccc} a^0 & b^0 & c^0 & d^0 \\ a^1 & b^1 & c^1 & d^1 \\ a^2 & b^2 & c^2 & d^2 \\ a^3 & b^3 & c^3 & d^3 \\ \end{array} \right | ## I've reduced my matrix, through linear combinations and column...

As we know photon's helicity are \pm1. Helicity is the projection of the spin S onto the direction of momentum, p, which is considered as Sz. What about Sx and Sy? They are both ZERO?

Hi all, I'm stuck on this incompatibility within the differential form of Gauss' thearem (or Maxwell's first equation) with dielectrics. \vec{\nabla}\cdot\vec{E}=\frac{\rho_{free}+\rho_{bound}}{\epsilon_{0}} \rho_{bound}=-\vec{\nabla}\cdot\vec{P} But with a linear, homogeneous...

Homework Statement A water tank is formed by sliding four identical cubical blocks together. All edges are watertight. Each block has mass M and is L meters on each side. You wish to fill the tank to its brim, i.e. to depth L. What is the minimum coefficient of static friction between the...

I am trying to write down a compact form of S = A+L/(B+C)+L/(B-C), does it make sense in general to write down S = A+L/(B\pmC)? Update: I have simplified it too much in the minimal working example, the denominators is actually more complicated, let me elaborate...

Is there any way to write the Dirac lagrangian to have symmetric derivatives (acting on both sides)? Of course someone can do that by trying to make the Lagrangian completely hermitian by adding the hermitian conjugate, and he'll get the same equations of motion (a 1/2 must exist in that...

I am doing a project in Chemistry and I need to use Hess' Law to cancel two equations and if in one equation the NH4NO3 is solid and in the second one the NH4NO3 is aqueous. The equations are: 1: NH4NO3 (s) + HCl (aq) --> HNO3 (aq) + NH4Cl (aq) 2: NH4OH (s) + HNO3 (aq) --> H2O (l) + NH4NO3...

Given the following diff equation: ##(1 - D)y(x) = f(x)##, being D = d/dx, the "implicit" solution is: ##y(x) = \frac{1}{1-D}f(x)##, so, for "explicit" the solution is necessary to expand the fraction 1/(1-D) by identity: ##\frac{1}{1-x}=\sum_{0}^{\infty}x^n \Delta n##, but this infinity series...

Hello, What is the most general cylindrically symmetric line element in the canonical form? Best regards.

A second order differential equation form d2y/dx2 = f(x,y,dx/dy) How do I read the language on the right hand side?

Hi, I am numerically solving the 2D effective-mass Schrodinger equation \nabla \cdot (\frac{-\hbar^2}{2} c \nabla \psi) + (U - \epsilon) \psi = 0 where c is the effective mass matrix \left( \begin{array}{cc} 1/m^*_x & 1/m^*_{xy} \\ 1/m^*_{yx} & 1/m^*_y \\ \end{array} \right) I know that...

Hi, (hope it doesn't seem so weird), I'm looking for a general expanded form of (x+y+z)^{k}, k\in N k=1: x+y+z k=2: x^{2}+y^{2}+z^{2}+2xy+2xz+2yz k=3: x^{3}+y^{3}+z^{3}+3xy^{2}+3xz^{2}+3yz^{2}+3x^{2}y+3x^{2}z+3y^{2}z+6xyz k=4: x^{4}+y^{4}+z^{4}+4xy^{3}+4x^{3}y+4xz^{3}+4x^{3}z+4yz^{3}...

Homework Statement The displacement, y(x; t), of a tight string of length, L, satisfies the conditions y(0, t) = \frac{\delta y}{\delta x}(L,t) = 0 The wave velocity in the string is v. a) Explain what is meant by a normal mode. Give the form of the displacement, y(x; t), for the normal...

This is related to a homework problem but I want to understand it as well. How can a proton break up into a positron and neutron when a neutron clearly has a greater mass than a proton?

Hey! :o I have the following exercise and I need some help.. $"\text{The eigenvalue problem } Ly=(py')'+qy=λy, a \leq x \leq b \text{ is of the form Sturm-Liouville if it satisfies the boundary conditions } p(a)W(u(a),v^*(a))=p(b)W(u(b),v^*(b)). \text{ Show that the boundary conditions of the...

Collision -- a ball and string form a pendulum... 1. A 1.0-kg ball is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point in its swing when it is moving horizontally, the ball collides elastically with a...

Hey! :o I have the following exercise: Write in the normal form the differential equation $$u_{xx}+\frac{2y}{x}u_{xy}+\frac{y^2}{x^2}[(1+y^2)u_{yy}+2yu_y]=0$$ Hint: You can suppose that the one new variable is given by $\xi=x$ I have done the following: $a=1, b=\frac{y}{x}...

Homework Statement A measuring cylinder collects 475 mL of this water in a minute. At the top the diameter of the stream is 0.700 cm. Homework Equations What is the velocity of the stream 20.0 cm below the top? The Attempt at a Solution im not sure which formula to use? i was...

Homework Statement Hello all, This is a problem on a worksheet I was given and I am stumped! Statement: Will a ppt form when 35.00 mL of 1.0x10^-3 M CoSO4 is mixed with 15.00 mL of 7.50x10^-4 M Al2(SO4)3 and 200 ml of a buffer which is .200 M NH3 and .200 M NH4Cl? I do not need the answer...