Form Definition and 1000 Threads

is there any general way? i mean i know how to do it in integra form but the course I am taking right now requires me to do it in differential method

This seems to be the most interesting development in QG currently. I want to know what you think might present serious obstacles to completing the program. Where could it go wrong? The idea is that QFT and quantum statistical mechanics (QSM) need to be given a general covariant formulation...

I was fooling around with spreadsheet formulas, and created a series of rational approximations for the square root of 3: 7/4, 26/15, 97/56 etc. This is based on the continued fraction expansion for square roots. Each ratio N/D has the property that N^2 is one more than 3*(D^2)=K. I was curious...

$A=\overbrace{ 11-------1 }^{m}\underbrace{ 22-------2 }_{m}$ prove :$A=k\times (k+1),\,\, where\,\, k\in N$ (A can be expressed as the multiplication of two consecutive positive integers)

Robert Oeckl proposed this new formulation of QT in December of last year. http://arxiv.org/abs/1212.5571 I think it's important and worth learning about. It could replace Dirac form of QT for some (especially general covariant) quantizations. Historically it derives from 1980s work by Witten...

May you help me with finding the angle, and what is "line of sight"?(the final answer is 15°) Thank you in advance

I keep reading about polar unit vectors, and I am a bit confused by what they mean. In the way I like to think about it, the n-tuple representation of a vector space is just a "list" of elements from the field that I have to combine (a.k.a. perform multiplication) with the n vectors in some...

Help! Using 3 Points to Find Quadratic Equation in General Form I have a quadratic equation question that I have to solve, but I can't seem to understand it. The question is: "Using points (1,0);(3,0);(0,-6), find the quadratic formula in General Form (ax^2 + bx + c). My teacher says...

Hi Forum users I have a velocity autocorrelation code which was made to read a three component velocity vectors and I have modified to read a 9 component stress tensor data. I can compile it successfully but when I try to run it and compute a stress correlation function I get an error: i.e...

Hi Appologies for formatting issues this is the first time I have submitted something to the forum. I have a pretty simple problem, I am just going through the derivation of the First Fundamental Form and I think I am missing something in the derivation. If we have a point x = (x1,x2)...

Is there a way to express ##{n\choose k}{n\choose r}## in another form without n as the "top" of the binomial coefficient? I remember seeing it once but I forgot what it was.

Lets say Earths atmospheric pressure was reduced to 0.10 bar which is 10% Earths atmospheric pressure. The boiling point at this pressure is 113 degrees F. Due to the atmosphere being thinner there is a greater temperature difference with higher highs and lower lows in a 24 hour period. Lets say...

How does circular DNA wrap around a histone to form a chromosome? Or does it? I am having a hard time visualizing this for any sort of circular DNA: prokaryotes, mitochondria, etc. (This question was inspired by my reading about biology and reading that circular DNA does, in fact, form...

Hi all, I was just wondering, does the ionised form of a drug produce a pharmacological effect? I know that an ionised drug is lipid-insoluble so it cannot traverse across the membrane. However, my question is, what happens to them if they remain in the gastrointestinal tract? Does it still...

Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression: Z = Z1 X Z2 / Z1 + Z2 If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form. Homework Equations Multiplication and division of complex...

Homework Statement I want to derive the trig identities starting with rotation on the plane. Homework Equations One rotation through a given angle is given by $$x' = xcosθ - ysinθ $$ $$y' = xsinθ + ycosθ$$ The Attempt at a Solution What if I wanted to rotated through any...

Homework Statement For cable AD it is known that the magnitude is 14 kips, x-component has a value of -6.216, the direction angle in the z-direction is 83.63°, and Fy is less than zero. Find forces in Cartesian vector form, coordinates of point D if it lies on the x-z plane and point A is (0...

Odd Form Of Eigenvalue -- Coupled Masses This isn't strictly homework, since it's something I'm trying to self-teach, but it seems to fit best here. Homework Statement It's an example of applying eigenvalue methods to solve (classical) mechanical systems in an introductory text to QM...

I read that in string theory the Virasoro algebra contains an ##SL(2,R)## subalgebra that is generated by ##L_{-1}, L_{0}, L_{1}##. I read that this is the non-compact form of the ##SU(2)## algebra. Also, that as ##SU(2)## and ##SO(3)## have the same Lie algebra, so do ##SL(2,R)## and...

Hi, as I read in one of Hawking books, he predicted that a 2D life-form with an alimentary canal can not exist because it would fall apart. I was wondering about that, because I thought of an easy solution for this: with two movable chainings its still possible. I have made a graphic and...

Homework Statement Metric ansatz: ds^{2} = e^{\tilde{A}(\tilde{\tau})} d\tilde{t} - d\tilde{r} - e^{\tilde{C}(\tilde{\tau})} dΩ where: d\tilde{r} = e^{\frac{B}{2}} dr Homework Equations How to calculate second fundamental form and mean curvature from this metric? The Attempt at a...

Homework Statement A Triangle ABC has sides of length a, b and c labelled according to the usual convention. Forces of magnitude ka, kb and kc act along BC, CA and AB respectively, with the direction given by the order of the letters. By considering the vector sum of the forces, or otherwise...

Homework Statement Hi. I'm given a 3-dimensional subspace H that is made up of the states |1,-1\rangle, |1,0\rangle and |1,1\rangle with the states defined as |l,m\rangle and l=1 as you can see. The usual operator relations for L_{z} and L^{2} applies, and also: L_{+} = L_{x}+iL_{y} L_{-} =...

Homework Statement y(t) solves the following IVP y''(t) + 2y'(t) + 10y(t) = r(t) y(0) = 2 y'(0) = 3 r(t) = 0 if t < 0 t if 0 ≤ t ≤ 1 0 if t > 1 Demonstrate that the laplace transform of y(t) is Y(s) = \frac{2s+7}{s^{2}+2s+7} + \frac{e^{-s}}{s(s^{2}+2s+7)} +...

Homework Statement Use integration by parts to show that ∫(sqrt(1-x^2) dx = x(sqrt(1-x^2) + ∫ (x^2) / sqrt(1 - x^2) write x^2 = x^2 -1 + 1 in the second integral and deduce the formula ∫(sqrt(1-x^2) dx = (1/2)x(sqrt(1-x^2) + (1/2)∫ 1 / sqrt(1 - x^2) dx I actually found a...

Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...

In most of textbooks, the canonical quantization procedure is used to quantize the hamiltonian with a simple form, the quadratic form. I just wonder how should we deal with more complex form hamiltonian, such like the ones including interaction terms?

Homework Statement I was just curious about determinate form of a plane if anyone has any info. If you check out number 18 on wolfram I was pondering about this form. http://mathworld.wolfram.com/Plane.html Homework Equations The Attempt at a Solution I would like to know why if...

Homework Statement Let \vec{F}=<xy,5z,4y> Use Stokes' Theorem to evaluate \int_c\vec{F}\cdot d\vec{r} where C is the curve of intersection of the parabolic cylinder z=y^2-x and the circular cylinder x^2+y^2=36 Homework Equations Stokes' Theorem, which says that \int_c\vec{F}\cdot...

When finding lim(x->1) (1+2ln(x))^(1/(x-1)) = 1^(infinity) I let y = (1+2ln(x))^(1/(x-1)) then ln both sides giving ln(y) = ln(1+2ln(x)))/(x-1) Taking the limit of ln(y) gives 1/0, which is indeterminate and hence the limit does not exist. However, I typed this into MS Mathematics and got...

From the book of Nakahara "Geometry, Topology and Physics": A diffeomorfism ##f:\mathcal{M}\to \mathcal{M}## is an isometry if it preserves the metric: ## f^{*}g_{f(p)}=g_{p} ## In components this condition becomes: ## \frac{\partial y^{\alpha}}{\partial x^{\mu}}\frac{\partial...

I've been studying this kind of limits today and most of them were solved by the technique I mentioned in my previous topic, except for the one you just showed me how to solve and this one: $$\lim_{x->0} (1 - cos(x))^{1/x}$$ (It approaches 0 from the left, but I don't know how to write it...

Can someone explain how these are equivalent. sqrt((-3)^2) = (-3)^2/2 =sqrt(9) and (-3)^1 3 is not equal to -3 (-3)^2/2 can be expressed as: (-3^2)^1/2 and (-3^1/2)2 (9)^1/2 and (sqrt(-1)sqrt(3))^2...

Hi, I have a question that is very close the the one of the OP so I tough I should post in here instead of making a new thread. (Hope no one mind ) Let's say $$\lim_{x->\pm\infty}x(log \sqrt{x} - log(\sqrt{x}-y)-\frac{y}{\sqrt{x}} )=\frac{y^2}{2}$$ Now I could use taylor series to evaluate...

what changes does there occur in the result of the gaussian distribution "integration e^-alpha*x^2 dx=sqrt(pi/alpha) if i substitute that x^2 with some (x-a)^2? then what should be the integral result ?

Homework Statement I have a circuit with input source x(t), which contains also an inductor and a capacitor in series which I have found to be related to the output voltage y(t) (across the capacitor) like so: LC*d2y/dt2 + y(t) = x(t). I have also found its roots through the quadratic...

Here is the question: Here is a link to the question: What is the limit of (tanh(x))^x as x approaches infinity? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I've got a Fortran 95 program (which basically does few calculations) and I'd like to use it online. So that, the users will input data into a HTML form, the program will run, and it will display the results. Would it be possible to do it in the following way? To run a little program (e.g...

The basic equation of GR has a curvature constant Λ on the lefthand (geometric) side. The Friedman equation is derived from the Einstein Field Equation by making a simplifying assumption of uniformity. As a spacetime curvature Λ can be written either in units of reciprocal area or reciprocal...

I feel a bit silly asking this, but I've been working through some QM lately and there's one aspect of Schrodinger's equation that's puzzling me. I've typically understood the equation as i\hbar \frac{d|\psi\rangle}{dt}=\hat H |\psi\rangle, but I've also seen it written as i\hbar \frac{\partial...

I want to know why everything in the universe forms a Ball or Sphere? Is gravity the cause of this? If so why? For example, If we were to pick the sphere apart can we see the source of gravity? Is gravity also a ball or sphere and can we grasp and see it? Why do we not ever see square planets or...

Homework Statement A 90Ω resistor, a 32 mH inductor, and a 5μF capacitor are connected in series across the terminals of a sinusoidal voltage source Vs = 750cos(5000t + 30)V. Calculate the phasor current. Homework Equations phasor current i = V/Z V in polar form = (Magnitude)(cos a + j sin...

Homework Statement How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge e and mass m, with 4-momentum p^a and electromagnetic field tensor F_{ab} of a constant magetic field \vec B perpendicular to the plane of motion...

Predicting the functional form of solution of PDE How do you conclude that the solution of the PDE u(x,y)\frac{∂u(x,y)}{∂x}+\upsilon(x,y)\frac{∂u(x,y)}{∂y}=-\frac{dp(x)}{dx}+\frac{1}{a}\frac{∂^{2}u(x,y)}{dy^{2}} is of the functional form u=f(x,y,\frac{dp(x)}{dx},a) ? I know this...

I have some rather technical questions about the complex exponential form of the Fourier series: 1) What is the motivation behind the complex exponential form? Why not just use the real form (i.e. with sine and cosines)? 2) Surely the complex exponential form is an orthogonal set, i.e...

What is the most general form of the metric for a homogeneous, isotropic and static space-time? For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) signature) ds^2=dt^2+a^2(t)g_{ij}(\vec x)dx^idx^j Now the static condition. If I'm not mistaken...

Here is the question: Here is a link to the question: Express in the form a + bi, where a and b are real numbers.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hey. I want to use integrals-math to get from Gauss law in divergence form to the one in integral form. I know you can do it by simply accepting ∇*E dV = ρ/ε => ∫ ∇*E dV= ∫ρ/εdV = Q/ε = ∫E*dA, but I want to do it another way. I want to begin with ∫∇*E*dV and end up with Q/ε. So: E =...

When the sun is collapsed will it form a black hole?

I am creating a form using IBM Form Experience Builder. I want to create a survey as follows (content in [] denotes possible answers) Do you still require a specified asset? [yes/no/I'm not the owner] Do you know who the owner is? [yes/no] Specify: [] Survey is complete The...