What is Conditions: Definition and 1000 Discussions
In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.
Allowing inequality constraints, the KKT approach to nonlinear programming generalizes the method of Lagrange multipliers, which allows only equality constraints. Similar to the Lagrange approach, the constrained maximization (minimization) problem is rewritten as a Lagrange function whose optimal point is a saddle point, i.e. a global maximum (minimum) over the domain of the choice variables and a global minimum (maximum) over the multipliers, which is why the Karush–Kuhn–Tucker theorem is sometimes referred to as the saddle-point theorem.The KKT conditions were originally named after Harold W. Kuhn and Albert W. Tucker, who first published the conditions in 1951. Later scholars discovered that the necessary conditions for this problem had been stated by William Karush in his master's thesis in 1939.
Is my resolution correct? I can't identify.
Calculate the line integral ∮C(2ydx+3xdy), where C is the circle x2+y2=1, using the Green's Theorem.
Green's Theorem:
Let M and N be functions of two variables x and y, such that they have continuous first partial derivatives in an open disk B in...
Optical pumping "is a process in which light is used to raise (or "pump") electrons from a lower energy level in an atom or molecule to a higher one".
In contrast, Rabi cycle "is the cyclic behavior of a two-level quantum system in the presence of an oscillatory driving field."
In the first we...
Since Ax = b has no solution, this means rank (A) < m.
Since ##A^T y=c## has exactly one solution, this means rank (##A^T##) = m
Since rank (A) ##\neq## rank (##A^T##) so matrix A can not exist. Is this valid reasoning?
Thanks
This is basically a physics problem but I will try my best to highlight the mathematics behind it.
Suppose I have two functions:
$$T(z,B)=\frac{\text{z}^3 e^{-3 A(\text{z})-B^2 \text{z}^2}}{4 \pi \int_0^{\text{z}} \xi ^3 e^{-3 A(\xi )-B^2 \xi ^2} \, d\xi },$$
$$\phi(z,B)=\int_0^z...
Suppose I'm looking at a bar of length L(t) in 1D and I have the conservation of mass:
\frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x}(\rho u)=0
In order to make things easier, I make the change of variable x'=x/L(t) so that in this frame of reference, the length remains constant...
I have a question related to the uncertainty principle in QFT and if it is related to the early universe conditions.
Do we still have four-vector momentum and position uncertainty relation in relativistic quantum theory?
I have been following the argument related to the early universe and the...
I'm studying "Semi-Riemannian Geometry: The Mathematical Langauge of General Relativity" by Stephen Newman. Theorem 4.4.4 in that book:
The proof of part 2 is given like this:
Seems a bit incomplete. I'd like to know if my approach is correct:
$$\langle A(v+tw),A(v+tw)\rangle=\langle...
I read there are 2 degrees of freedom in GR after boundary conditions specified. Does that mean 2 equations are enough for EFE equivalent? Those two seem like the amplitude and a phase.
TL;DR Summary: So I'm just confused when the question asks me to solve for the no load speed of DC motors and induction motors. Does no load condition mean that the output torque (Tout) is zero? This is what I was assuming so far for both DC and induction motor. Is no load condition the same...
We have inhomogenous dirichlet boundary conditions (well understood)....the laplace equation is a steady state equation and we can clearly see that in 2D..it will be defined by 4 boundary conditions and NO initial condition...having said that; kindly have a look at the continuation below...
I...
Prove that every surjective local homeomorphism ##\pi : \tilde{X} \to X## from a compact Hausdorff space ##\tilde{X}## to a Hausdorff space ##X## is a covering space.
U=U(x,t)
Ut=DUxx; 0<=x<=L, t>0
U(x,0)=0 0<x<=L
U(0,t)=a(t); t>0 *a(t) is known function*
(dU/dx)=0 for x=L
I have looked into many ways but not one is usable for diffusion equation with this boundary conditions.
The idea here (as I'm told) is to use the boundary conditions to get a transcendental equation, and then that transcendental equation can be solved numerically. So I'm making a few assumptions in this problem:
1. The potential ##V(x)## is even, so the wavefunction ##\psi(x)## is either even or...
I am unsure of my solutions and am looking for some guidance. a.)The real part of the wave in complex notation can be written as ##\widetilde{A} = A^{i\delta}##. Writing the Complex Wave equation, we have ##\vec E(t) = \widetilde{A}e^{(-kz-\Omega t)} \hat x##. Therefore the real part is ##\vec...
I am going through these notes...they are pretty easy to follow. I would like more insight on the initial condition. In this problem, (attachment below), i guess the choice of initial condition is convenient as its easier to plug in the values of ##n=2## and ##b=3## (highlighted on the...
The given question from Electromagnetic Theory (which is based on Dielectric Boundary Conditions) is as follows:
Interface b/w two dielectric medium has a surface charge density (suppose xyz C / (m ^ 2) ). Using boundary condition find field in 1 (relative permittivity =xyz) if field in 2...
How did they impose boundary conditions here if "no end" is selected?
Here: https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html
I would like to do the same thing without changing the wave equation of the string.
Hello,
I' m trying to make a linear static analysis (Finite Element Analysis) on the following hand tool. I want to determine the boundary conditions. In order to do that I have decided to use a force couple to represent the forces that a bolt exerts on the jaws of this spanner.
Despite using...
In MOSCAP, why does the band stop bending as soon as the Si Fermi level touches either the conduction band (inversion) or the valance band (accumulation)?
Summary:: Conditions inside a protoplanetary disc.
I have just finished writing a fictional story that takes place inside a protoplanetary disc. Now I think I should determine how realistic it is.
My question -- Somewhere in a typical PP disc, the gas pressure would be in the range of one...
Hi, I am solving heat equation with internal heat sources both numerically and analytically. My graphs are nearly identical but! analytical one have problem at the beginning and at the end for my domain. Many people have used the same technique to solve it analytically and they got good answers...
Is the inability to exceed the speed of light a consequence of general relativity?
Is the fact that no energy is created from empty space a consequence of general relativity?
Or are they both constructions deriving from the energy conditions imposed to have solutions to Einstein's equations that...
Hi all,
I need some help with this one:There are 3 shapes of pasta: 1,2,3.
In a box there are 3 packages of pasta of shape 1, with different weights: 300 gr, 400 gr, 500gr.
In addition, there are 5 packages of paste of shape 2, with weights: 300gr, 350gr, 400gr, 500gr, 600gr,
and 4 packages...
Does setting up the problem symmetrically on this axis and the boundary conditions applied make sense? I don't believe I will have a problem solving for the potential inside, but i just want to make sure I have my B.C and axis correct before proceeding.
EDIT:
Or should this be a 2-D lapace...
I have attached an image of the pipe in the attachmnts. The pipe is parallel to z-axis form (-∞,∞) and sides of length a.
So my boundary conditions for this problem are as follows
1.) V=0 at y=0
2.)V=0 at y=a
4.)∂v/∂x=0 @ x=0
3.)V0 @ x=a
I am a little confused on the fourth boundary...
Problem Statement : I copy and paste the statement of the problem directly from the text.
Attempt : I wasn't able to go far into the solution. Below is a rough attempt.
##\begin{equation*}
\begin{split}
\sin^2A-\sin A\sin B+\sin^2B-\sin B\sin C+\sin^2C-\sin C\sin A & = 0\\
\sin A(\sin A -...
Let's give some context. I created a Mesh via snappyHexMesh and next I am setting the boundary conditions (BCs).
First I copied the patches folder "createPatchDict" to my system's folder via the command "cp $FOAM_ETC/caseDicts/mesh/manipulation/patches/createPatchDict ./system"
Taking into...
Since there is no free charge ##\int_S \vec{D} \cdot d\vec{a} = 0## and
##\rho_f = 0##
##\sigma_f = 0##
##\vec{nabla} \cdot \vec{P} = 0## since P is a constant
##\rho_b = - \vec{nabla} \cdot \vec{P} = 0##
For a simple surface we can find the boundary conditions for ##\vec{E}## using a Gauss'...
Hello,
I was reflecting on the functioning of a balanced Wheatstone bridge circuit:
Point C and D are at the same electric potential V (zero potential difference). Even if they are connected by an ideal zero resistance wire, current will not split at either node C or D to flow through that...
Any official (scientific, verified) tracking of old weather conditions that one can look up? Say, I wanted to know what the weather was like in Kentucky in the city of Lexington on October 24th, 1983. Is there some kind of official recorded archive to look such information up?
I have been solving the constant coefficient 1D advection-diffusion equation ##\frac{\partial c}{\partial t} + v\frac{\partial c}{\partial x} = D\frac{\partial^2 c}{\partial x^2}## on ##0<x<L,t>0## with a variety of robin BC's.
Namely $$vc + D\frac{\partial c}{\partial x} = J^f ~~at~~ x=L $$...
Hello everybody,
Currently I am doing my master's thesis and I've encountered a physics problem which is very difficult for me to solve. The problem I have is finding equations for the magnetic scalar potential inside and outside a ferromagnetic wire for specific boundary conditions...
Assume we have a network consisting of a source with impedance ##Z_S## and load with impedance ##Z_L## and
we want to perform impedance matching on them in order to obtain the maximum power transfer:
Note that in practice there may occur sitations where causes more harm than profit (see eg...
Please correct me if I'm well off the fairway with the following theory.
We all know that atmospheric conditions (temperature, pressure, dewpoint, etc.) can affect many different bodies in motion, from aeroplanes to cars to golf balls. But in the case of a golf ball, exactly how big is the...
hello
I own mathematica 10.02
it is virtually impossible to solve PDE's ,even with NDSolve,if the initial conditions contain a derivative
I write
Derivative[1,0] [0,x] == f[x]
I mean
the first t derivative of u[t,x] for x at t=0 is f[x]
I own a book based on Mathematica 10.3
Even if a...
I am going through this notes, i can follow quite well...my only issue is on the highlighted part...i thought that we had two boundary conditions for ##y## ( of which one of them is non homogenous) and two boundary conditions for ##x##( of which both are homogenous)...kindly clarify on this part...
Hi, I have one question related to the boundary conditions I should apply in a Static Structural simulation for the following support.
The support is subjected to the following loading conditions shown below...
Hi!
This thread might well be similar to:
https://www.physicsforums.com/threads/thread-about-jacksons-classical-electrodynamics-3rd-edition.910410/
I'm self-studying Vanderlinde and having a great time. However, I think that I am conflating and confusing many different things. Let me just ask...
Below shows the generic V-N diagram for most of the civil aircrafts.
Now, I have the CFD results available for multiple combinations of angles of attack of the aircraft, with the deflection angle of the flap. I have to choose a couple, to input into my structural analysis of the flaps. How to...
Hi,
I'm not quite sure if I'm correct. I need to find the boundary conditions for 2 ropes ##T_1 \mu_1, T_2 \mu_2## fixed at ##x=0## to a massless ring with a massless damper of force ##F_d - -bv_y##
Here what I think, since the ring and the damper is massless ##\sum F_y = 0##. Thus, ##-T_1...
In a podcast with Sean Carroll and Roger Penrose (link :) ), it's briefly discussed that one can cook up certain unphysical examples of spacetimes in which SCC is violated. Indeed, in Harvey Reall's BH notes (link), it's written that:
What is a sufficient set of restrictions required in order...
Hello!
Consider this ODE;
$$ x' = sin(t) (x+2) $$ with initial conditions x(0) = 1;
Now I've solved it and according to wolfram alpha it is correct (I got the homogenous and the particular solution)
$$ x = c * e^{-cos(t)} -2 $$ and now I wanted to plug in the initial conditions and this is...
Hello everyone,
I am currently trying to understand periodic boundary conditions for the mechanical investigation of mechanical properties of a RVE. I found a good video explaining the theory behind it:
But something is unclear to me: At the above linked time step, the individual conical...
I have a differential equation of the form y''(t)+y'(t)+y(t)+C = 0. I think this implies that there are non-zero initial conditions. Is it possible to write a transfer function for this system?
This post...
For a 2D problem with unknown displacements u(x,y) and v(x,y), is it allowed to give such a set of BCs u(0,y)=1 and vy(0,y)=0, the former being a displacement BC, the latter being a force BC (vy is the y strain)?
How is this implemented in FEA software?