Constraints Definition and 200 Threads

Problem: A = n by m matrix x = m by 1 vector y = n by 1 vector C = c by m matrix E = e by m matrix Alpha, gamma and theta are constants. norm(Ax-y) = min subject to: norm(Cx) = alpha norm(Ex) = gamma transpose(Cx)*Ex = (alpha^2)*(gamma^2)*cos(theta) I read a paper on how to do this with 1...

Homework Statement Consider the intersection of two surfaces: an elliptic paraboloid z = x2 + 2x + 4y2 and a right circular cylinder x2 + y2 = 1. Use Lagrange multipliers to find the highest and lowest points on the curve of intersection The Attempt at a Solution L = x^2 + 2x + 4y^2...

Homework Statement Given a vector z=<-12, 1, 1, 2, 7, 0> in R^6 and z=u+v, then find u and v such that u's coordinates are all equal to each other (like <0,0,0,0,0,0>) and v has coordinates that add up to 0Homework Equations z=u+vThe Attempt at a Solution i have no idea how to approach...

Hello everybody. I have a question about the physical meaning of the simplicity constraints that is often used in spin foams. For example, in http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.1780v4.pdf, eq. (34), it is written as K=-\gamma L where K are the boost and L the rotations. Is...

In hamiltonian formulation of GR there appears some constraints (it may be found e.g. in "Modern canonical quantum GR" by Theimann, ch. 1.2). I would like to find a Dirac algebra of the constraints (i.e. compute Poisson bracket between constraints), but my results are not consistent with...

How do pulleys help in carrying load? may be to reduce efforts.

Just read an article on Universe Today at: http://www.universetoday.com/77662/missing-milky-way-dark-matter/ The paper is at http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.1289v1.pdf . It introduces what seems to be rather tight constraints on the dark disc. Any cosmologists care to...

Homework Statement Which of these bodies has redundant constraints for the given loading conditions? F_1 and F_2 are applied, known forces. In the first choice, the support at A is fixed and a cable connects points B and C. In the second choice, the support at A is a smooth pin, and a cable...

Homework Statement A person who is properly constrained by an over-the-shoulder seat belt has a good chance of surviving a car collision if the deceleration does not exceed about 30 "g's" (1.0 g = 9.80 m/seconds squared). Assuming uniform deceleration of this value, calculate the distance...

Hello I am using Landau's mechanics Vol I for classical mechanics. On page 4 he mentions for Lagrangian of a system composed of two systems A and B which are so far away so that their interactions can be neglected. then for the combined system we have L = LA + LB I'm trying to...

Hi, I have a short question about gauge theories and constraints. Imagine I have a symmetry algebra, and I gauge it. With N generators in the algebra I get N gauge fields and N gauge curvatures. In realizing the algebra on the gauge fields I assume the gauge parameters are independent and...

Hi, I have a question about imposing constraints in order to obtain theories of gravity from gauge algebras. Let's take as a warming-up Poincare gravity. The procedure is as follows: * Gauge the Poincare group with generators P (translations) and M (rotations) to obtain the vielbein and...

How many constraints are there when the particle is moving in a plane and on three dimensional space and what are they?

Hi everyone. I have this problem which I am trying to formulate. Basically, I have the following linear constraints: p_{11} = 2 p_{22} = 5 p_{33}+2p_{12}=-1 2p_{13} =2 2p_{23} = 0 And these are for the symmetric matrix \mathbf{P} = \left( \begin{array}{ccc} p_{11} & p_{12} & p_{13}...

Why does a distribution function F_X have to be right continuous ? is'nt just making sure it is non-decreasing enough

1.Find a such that y=x2 - 2(x)1/2 + 1 is perpendicular to ay + 2x =2 when x=4 3.I have gotten as far as getting the slope of the normal line. I then rearranged the equation to y = (-2x+2)/ (a) and That is where I am stuck I am having a lot of trouble with these types of...

I'm trying to minimize a function over a rather complicated surface. I'm using an algorithm that takes an initial guess, finds the tangent plane at that point, minimizes using a linear programming algorithm, then (tries to) project back onto the complicated surface. More specifically, if \xi...

Question: Given a1+a2+a3+...+an=0 and a1^2+a2^2+...+an^2=1, (all real numbers) find the maximal value of a1*a2+a2*a3+...+an*a1 Thoughts so far: I've treated the expression as a combination of n variables and differentiated - when it came to putting the constraints in it got to be a...

If I have a set of Probability distributions on a product space with marginal constraints, is there any way to (how to) express the same as a linear family of PD's ( i.e. all P s.t. E_P[ f_i] =a_i for some f_i, a_i )

Homework Statement By using the Lagrange multipliers find the extrema of the following function: f(x,y)=x+y subject to the constraints: x2+y2+z2=1 y+z=12. The attempt at a solution Using lambda = 1/(2x) I got x=y-z and y=1-z plugging that into the first constraint, I got: 6y^2-6y+1=0 which...

Hello everyone, I'd like to solve overdetermined system of linear equations (in fact to fit experimental data) (like y1=C1*X11+C2*X12+...+Cm1*X1m) y2=C1*X21+C2*X22+..+Cm*X2m ... yn=C1*Xn1+C2*Xn2+...Cm*Xnm) sometimes n>>m sometimes n>~m , yi and xij are...

The speed of light is fast but far from instantaneous. What constrains the speed of light to be what it is? e.g. c = f(xi) Life is good, d

MTd2 spotted this paper on arxiv and flagged it for us: Yes! I am very glad to get this one. This paper follows up on a March 2009 video seminar talk Giovanni A-C gave at Perimeter. I'll get the link. Yeah, it's easy to google: just say "Amelino Perimeter". This often works, google...

Why when doing a Lagrange Multipler with two constraints, why do you add the gradients of the two constriant funcions and set it parallel to the function to be maximized...

Homework Statement Find the maximum values of f(x,y,z)=xy+xz+yz-4xyz subject to the constraints x+y+z=1 and x,y,z>or equal 0. Homework Equations The Attempt at a Solution see attachment I found fgrad and ggrad and set fgrad equal to lambda*ggrad and used x+y+z=1 for my system of...

Homework Statement see problem 7 attachement Homework Equations The Attempt at a Solution see problem 7 attempt attachment I found the fgrad and ggrad and hgrad. I set fgrad equal to lambda*ggrad+mu*hgrad. using the two constraint equations I was able to solve for...

Suppose that you have a set of real variables {x1,x2,...,xn}. If x1 = f(x2,x3,...,xn) then this represents a constraint on all the variables. In this case, it's possible to find dx1/dxi as long as f is differentiable. But not all possible constraints among the xj are of this form. How might...

Homework Statement Consider the cylinder S in R3 defined by the equation x^2+y^2=a^2 (a). The points A=(a,0,0) \: and \: B = (a \cos{\theta}, a \sin{\theta}, b) both lie on S. Find the geodesics joining them. (b). Find 2 different extremals of the length functional joining A=(a,0,0)...

Hi, I've been learning about the calculus of variations this term, and we just covered the transversality condition for an optimization problem with the right end point free, as well as the first necessary condition on the augmented Lagrangian for a problem with integral constraints. I'm...

let be the Lagrangian (1/2)m( \dot x ^{2} + \dot y^{2}) - \lambda (x^{2}+y^{2}-R^{2}) with 'lambda' a Lagrange multiplier , and 'R' is the radius of an sphere. basically , this would be the movement of a particle in 2-d with the constraint that the particle must move on an sphere of...

Prove that if a, b, r, and s are positive reals and r + s = 1, then ar bs ≤ ra + sb.

I was just wondering... if a problem involved a particle which was constrained to move from x = -a/2 to a/2 and asked you to find it's properties (not position, though), could you just "shift" the entire system from x = -a/2, a/2 to x = 0 to a? Also, let's say that a question asked for the...

m equations of semi-holonomic constraints can be put in the form: fi=(q1,q2,...,qn,\dot{q}1,...,\dot{qn}) but "commonly appears in the restricted form: \Sigmaaikdqk +aitdt = 0 (i,k,t preceded by "a" should appear in subscript and the sum is over k) I don't understand this form. what are...

1a) Determine the maximum value of f(x,y,z)=(xyz)1/3 given that x,y,z are nonnegative numbers and x+y+z=k, k a constant. 1b) Use the result in (a) to show that if x,y,z are nonnegative numbers, then (xyz)1/3 < (x+y+z)/3 Attempt: 1a) Using the Lagrange Multiplier method, I get that the...

I have been struggling with Part 3 of this question for some time: Computico Limited, currently operating in the UK, assembles electronic components at its two factories, located at Manchester and London, and sells these components to three major customers. Next month the customers, in units...

Hi, I have a convex function F(x,y) that I want to optimize. Since, derivative of F does not closed form, I want to use gradient ascent. The problem is, I have constrains on x and y. I don't know how to incorporate this into gradient search. If there was a closed form, I would use Lagrange...

This should be easy but I've not done this in years and I'm feeling dense: I need to fit a quadratic curve to three constraints, two of which are points, the third is an angle. I've found examples to do this but only if all three constraints are points, so if someone would kindly explain...

I'm trying to design a synchronous logic that uses a negative edge flop to shift data out of a chip (as part of the IEEE1149.1 standard). The input to this negedge flop is muxed from a whole bunch of shift registers within the chip, and these registers are all on posedges. Ideally, if...

[SOLVED] Variational calculus with bounded derivative constraints After learning about the calculus of variations and optimal control for a bit this semester, I've decided to tackle a "simple" (in the words of my professor) problem meant to illustrate a simplified example of highway...

I had a look at a simulation of galactic populations in the universe from the Max Plank university and realized it looked a lot like a population of neurons. The same branching and clustering occurs in both cases... in fact I found this comparison of the two images on the net... here they are...

My understanding is that in GR the way in which the components of the metric tensor can vary from location to location in spacetime is determined or constrained by a number of factors: (1) the choice of coordinates (a mathematical constraint); (2) the distribution of mass/energy (a physical...

Homework Statement In the figure, find an expression for the acceleration of m1 (assume that the table is frictionless). Homework Equations F=ma The Attempt at a Solution My biggest problem here is that I don't know what variables I am supposed to answer in (my homework is done on a...

My question is about the constraints in Hamiltonian viewpoint. I mean, where the constraints are put into the Hamilton's equations. Constraints are usually studied in Lagrange's equations in textbooks (such as Jose and Goldstein). However, I couldn't find anything about constraints in...

When we seek the extreaml value of the functional \Phi(\gamma) = \int_{t_0}^{t_1} L(x(t),\dot{x}(t),t)dt where x can be taken from the entire E^n then we come to the well-known Lagrange equations. Now when we are given a constraint, that x \in M, where M is a differentiable manifold and when...

How can I show that when a ball is rolling without slipping on a horizontal plane, the total horizontal force on the ball must be zero? I guess I should consider the ball as a rigid body and combine the equations describing the rotation with the rolling constraints, but how? Can someone give...

I was intrigued by this paper, and apparent implications for Smolin's cosmic natural selection [CNS] conjecture. http://arxiv.org/abs/astro-ph/0609644 Observational constraints on quarks in neutron stars Authors: Pan Nana, Zheng Xiaoping Comments: 16 pages,6 figures We estimate the...

Hi all, I'm having trouble with the following problem: It was given as a word problem from which to infer the mathematics but basically it is this: Maximize: f(x,y,z,t,w)= ln((y^2-x^2)(z^2-t^2)*w^3)+.8x-1.2y-20z/17+14t/17-w^3/(pi^3) Subject to the constraints: 0<= .5x+y+3z+3y+2.5w<+30...

http://www.arxiv.org/abs/gr-qc/0510011 "Recently the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single Master constraint. The MCP is designed to overcome the complications associated with the...

Marcus, you mentioned an interest in linguistics. I wonder what your neighbor would think about this. I have been interested for some time in tribal cultures in South America and New Guinea. This tribe, the Piraha, is the most unusual I have come across. I'd like to know what you and...

Pardon me if this should go elsewhere, but it seems like a problem with a linear algebra solution. I have a series of PDB files from a molecular dynamics simulation of modified DNA strands. I use the program Pymol (http://www.pymol.org) to visualize them as a "movie." But now I want to make a...