Explicit Definition and 138 Threads

Generate markdown code for a table of papers on string theory. Generate up to 5 rows, including at least columns for title, authors, and url. Make the urls clickable. Do not forget to prefix it with https: You can include papers from scientific journals or scientific repositories. For a given...

Hello everyone, I was looking at the light matter interaction Hamiltonian and I worked out a simple calculation where I was surprised to see that I had to introduce an explicitly non-local vector potential if I want to go further: $$\langle\psi|...

Hello, I am having trouble with deriving an explicit formula (if one exists) for S(a,n) such that for example $$S(a,5) = \sum_{i5=a}^{49} \sum_{i4=i5}^{49} \sum_{i3=i4}^{49} \sum_{i2=i3}^{49} \sum_{i1=i2}^{49}(1)$$ or $$S(a,4) = \sum_{i4=a}^{49} \sum_{i3=i4}^{49} \sum_{i2=i3}^{49}...

In the holonomic case, we can put the Lagrangian in the Lagrange equations to obtain the explicit form of the equations of motion. From Greenwood's classical dynamics book, the equations are Are there such general equations for the non-holonomic case?

I would like to discuss in detail an interesting aspect dealing with general considerations and methods to calculate the Q factor of oscillating systems on the example of this regenerative receiver. Althought it is closely related to the discussion here discussion here (especially Baluncore's...

I understand that a homotopy is a continuous deformation. The only thing I really remember is something in my notes like this: F(s, 0) = a(s) for 0≤s≤1 and F(s, 1) = a * Id(s). Basically I have to construct some sort of piece-wise function such that I go something like two loops half of the time...

Hi For a function f ( x , t ) = 6x + g( t ) where g( t ) is an arbitrary function of t ; then is it correct to say that f ( x , t ) is not an explicit function of t ? For the above function is it also correct that ∂f/∂t = 0 because f is not an explicit function of t ? Thanks

Derive an explicit expression for all ##f\in\langle q\rangle\subseteq \mathbb{Q}[x]##. I think it's doable and was wondering if there is a published formula?

I am tring to simulate impact of cricket ball on a bat. Whenever I try to simulate with custom materials it shows an error like 'Solver initialization failed. See the log file.' But when I carry out with steel as the material it works fine. Please help.

Hello everyone, I have to submit an assignment by Monday and there is only one part of the assignment missing, which is future developments of the Explicit Finite Difference Method. However, I can not do it because I really do not know what exactly he is asking me for on there. Could someone...

Homework Statement:: Discuss the limitation of the Explicit Finite Difference Model. Relevant Equations:: no formula Hello there, I have to discuss the limitations of using the Explicit Finite Difference model to calculate a 2D Heat Diffusion through an aluminium place, however, I really...

Suppose I had a Lagrangian $$L = q+ \dot{q}^2 + t.$$ This has explicit time dependence. Now consider another Lagrangian: $$L = q+ \dot{q}^2 .$$ Which has no explicit time dependence. But after solving for the equations of motion, I get $$\dot{q} = t/2 + C.$$ So I could now write my Lagrangian...

$$b_{k} = b_{k - 1}/2 +b_{k-1} $$ $$b_{0} = 1 $$ What would be the sequence for this expression, I calculated it to be 1, 2/3, 2/5, 2/7 ... Is it right? My explicit formula is $$b_{n} = 2/n+2 $$ What would be the explicit formula in your view and how can that formula be proved by...

I am wondering if it is possible to determine the covariance, ##\text{Cov}(a,b)##, of two fitted parameters given I know their explicit relationship ##a=a(b)##? I would like to construct the covariance matrix in the space of the parameters ##\left\{a,b\right\}##. Using the relationship...

I do not understand the following sentence (particularly, the concept of extra symmetry): 'If all ##\alpha^i## are the same, then there is extra symmetry and corresponding constants of motion'. OK so let's find the Lagrangian; we know it has to have the form: $$L(q, \dot q) = T(q, \dot q) -...

Hi everyone, I'm writing my statement of purpose for Masters/PhD programs in Physics (Condensed Matter Experiment, specifically superconducting quantum computing related). I've seen a lot of advice online for how to write SoPs, and I've made and answered a list of questions the statement has to...

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} =...

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...

I am trying to run explicit dynamics, but after AUTODYN PRE-SOLVER SETUP is complete the solution stops and the following message is displayed "A general failure occurred during the solution process." I have installed the same ansys version on another pc and everything works ok. RAM is the...

In most treatments of the mass renormalisation in dim reg, I see sources find the mass counter term by extracting the coefficient of e.g the ##m^2## term accompanied by a pole in epsilon. I know the mass counter term is found by placing an X on diagrams where there is usually a self energy...

Hey! :o We have the sequence $$0, \ 2 , \ -6, \ 12, \ -20, \ \ldots$$ Its recursive definition is \begin{align*}&a_1=0 \\ &a_{n+1}=(-1)^{n+1}\cdot (a_n+2\cdot n)\end{align*} or not? How can we convert that in the explicit form? (Wondering)

Hello, I would like to find explicit calculations of Chern classes on various bundles. I mean examples where the steps are worked out explicitly, in terms of explicit connections. I have only found abstract and non explicit "examples". I only really understand things when I can work out...

How would I go about solving for ##t_p## in the following equation:$$t_p - t + vy \cos {(2 \pi \omega t_p )} - vx \sin {(2 \pi \omega t_p )} = 0$$where our input is a point in ##ℝ^3## with coordinates ##t##, ##x##, and ##y##, and where ##v## and ##\omega## are constants. I’m pretty sure it...

(Not homework, just curious) Homework Statement Is there an explicit way to write the x which solves nx = e^x for constant n? Homework Equations nx = e^x Or equivalently, x = ln(x) + m The Attempt at a Solution For any n we could just find x numerically, but is there an explicit expression...

Hello, I understand that solving an equation like f(x)=0 means finding those values of x that make the equality true. In the case of some difficult trig equations (like sin(x)+tan(3x+2)+cos^2(x)=5 which I just made it) it may not be possible to find an explicit solution. What does that mean...

How do I figure whether to do implicit differentiation or just explicit?? Thanks for the answer.

I am doing guided wave simulation in ANSYS workbench. I applied a load (tone-burst signal) on the model and I ran the simulation successfully. Now, I want to extract the time waveform. Does anybody have any idea?

Homework Statement I am trying to wrap my head around what it means to find an explicit formula for the sequence of partial sums. Question: Find an explicit formula for the sequence of partial sums and determine if the series converges. a) sum from n=1 to n=infinity of 1/(n(n+1)) Homework...

Homework Statement Hi, I am trying to follow the working attached which is showing that the average energy is equal to the most probable energy, denoted by ##E*##, where ##E*## is given by the ##E=E*## such that: ##\frac{\partial}{\partial E} (\Omega (E) e^{-\beta E}) = 0 ## MY QUESTION...

Hello everybody, I´m simulating a problem of indentation of a tungsten needle tip on an aluminum layer. Before I was using just the module "Static Structural" from ANSYS, which is based on an implicit solver. Now I wanted to do the same simulation with the module "Explicit Dynamics" of ANSYS...

Homework Statement Use iteration to guess an explicit formula for u_k = u_{k−2} * u_{k−1}, for all integers k ≥ 2, u_0 = u_1 = 2 and prove it . Homework Equations Hint: Express the answer using the Fibonacci sequence. The Attempt at a Solution u_k = u_{k−2} * u_{k−1} and u_0 = u_1 = 2, so...

Homework Statement Solve the following initial value problem using Laplace transforms: y' + 4y = 3t3 e−4t ; y(0) = 0 . Useful information: Recall that the Laplace transform of y 0 is pY − y(0), where Y is the Laplace Transform of y. The Laplace transform of tk e−at is k!/(p + a)k+1 . Confirm...

Good Day Let's say I have developed a new method to extract, more efficiently (yes, "more efficiently" is ill-defined; but bear with me) the differential equations that describe a specific phenomena (please just assume it). So now I have a system of coupled second order differential...

Is there any research that was done on animal long and short term memories? And short of empirical analysis, if there is none, is there much we could conclude, based purely on what we know about their brains? For example, from knowing which brain parts deal with explicit and which with...

Homework Statement Show explicitly that ei*ε*κu * ei*ε*κv * e-i*ε*κu* e-i*ε*κv = Identity + ε2 [Kv,Ku + O (ε3) The Attempt at a Solution Kv,Ku = Kv*Ku - Ku*Kv I'm not sure exactly how to approach this problem. I know that U (tau) = ∏ ei*su*Ku and that for operators O --> O' = U O U†...

Homework Statement Hi there. I have a simple RC circuit with a battery voltage of 10 V, R = 1 Ω, C = 1 F and a switch. I want to use the Explicit Euler (forward divided difference) to solve the equation and check for stability, rather than using a ODE. I am finding the equation for when the...

Hello, I have a typical 1D advection problem where a cold fluid flows over a flat plate. I did an energy balance to include conduction, convection and friction loss and I got the PDE's for the fluid and the solid. I used finite differences to solve the system as T(x, t) for both fluid and...

Homework Statement Solve the differential equation, explicitly. dy/dx = (2x)/(1+2y) The answer given by the book is... -1/2 + 1/2sqrt(2x - 2x^2 +4) Homework Equations Process for solving separable differential equations The Attempt at a Solution dy/dx = (2x)/(1+2y) (1 + 2y)*dy = 2x*dx...

I'm new with ansys if I can help it would be helpful. the problem is that two solids are shocked, but one of them is going through the other, have already implemented several things different tutorials but the answer is the same. the only question when I change the location fixed support the...

Find the solution of the given initial value problem in explicit form. Determine interval which solution is defined. (which i think is the same thing as saying find the interval of validity) $y' = (1-2x)y^2$ , $y(0) = -1/6$ So here is what I have so far.. $\int y^{-2}dy = x - x^2 + C$ $=...

When dealing with this separable equation for example, if I'm told to solve the given D.E. $y' = x^2/y$ so after manipulation and taking the integral I got $\frac{y^2}{2} = \frac{x^3}{3} + C$ This is the implicit form correct? Would the explicit form be $y = \sqrt{\frac{2}{3} x^3 + C}$

Find the explicit solution to $tyy' − 1 = 0$, $y(1) = 4$ and give the interval of validity. $ty \frac{dy}{dt} - 1 = 0$ $y \frac{dy}{dt} - 1 = 0$ ==> $ydy - {1/t} dt = 0$ $ydy = 1/t dt$ $\frac{y^2}{2} = ln(t) + c$$y = \sqrt{2ln(t) + c}$ applying $y(1) = 4$ so the explicit solution is: $C =...

Find the explicit solution to the IVP. $xdx + ye^{-x}dy=0$, $y(0) =1$ so I did some manipulation to get $ye^{-x}dy= -xdx$ ==> $\frac{dy}{dx}=\frac{-x}{ye^{-x}}$ but now I'm confused on what to do. What I found above is the implicit solution right? So do I just need to get $y'$ on the left side...

I am given a formula in explicit form and as a recurrence relation. It is asked to derive the recurrence relation from the explicit form. How is this done?

Hello all, hoping to get a bit of help with a diff eq problem that goes like this: Find an explicit solution of the given initial-value problem, x^2*(dy/dx)=y-xy ; y(-1) = -6 I separated my variables to get: S (1-x)/x^2 dx = S 1/y dy Integration of left via partial fractions: S 1/x^2 dx...

I've worked that out in my Mathematica notebook "Lie-Algebra Matrices.nb" in directory "Extra Mma notebooks" in SemisimpleLieAlgebras.zip, but I must concede that some of my derivations seem rather inelegant, not using features of the algebras very well. The last comment in How should I show...

Exercise 2.1.5 in Berrick and Keating: An Introduction to Rings and Modules reads as follows: Let $$M$$ be an abelian group with $$Mc = 0$$ for some positive integer $$c$$, and put $$c = ab$$ for coprime integers $$a,b$$. Write $$1 = ar + bs$$, and define endomorphisms $$\alpha$$ and $$\beta$$...

Let e_i be a unit vector with one 1 in the i-th element. Is the following expression has a recursive presentation? $$y_N = \sum_{k=0}^N {\frac{{{X^k} e_i}}{\|{{{X^k} e_i}\|}_2}} $$ where X is a n \times n square matrix, and {\| \cdot \|}_2 is a vector norm defined as {\|z\|}_2 =...

I've found this paper: [physics/9712033] Closed Expressions for Lie Algebra Invariants and Finite Transformations and I've attempted to interpret it. In some representation, a general Lie-algebra element A = aiLi for generators L (repeated dummy indices summed over, like i here). det(I -...

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 =...