Local Definition and 491 Threads

Homework Statement F(x)=(x^2)/(x+1) Find critical points Find local maxima & minima Homework Equations None The Attempt at a Solution F'(x) = x(x+2)/(x+1)^2 crit points: -2,0,-1 f(-2) = -4 f(0) = 0 f(-1)=undef My book is telling me that f(0) is the minima, and f(-2) is the...

Homework Statement ## f\left( x,y\right) =x^{2}-4xy+6x-8y+2y^{2}+10 ## ## f_{x}=2x-4y+6=0 ## ## f_{y}=-4x-8+4y=0 ## ## f_{y}=-4\left( x-y+2\right) ## -2=x-y, then solving fx and using this equality ## f_{x}=0=2\left( x-2y+3\right) =0 ## 2(-2 -y+3)=0 2(1-y)=0 y=1, then pluggin...

what does it mean.

Homework Statement see attachment The Attempt at a Solution I don't understand how they found fxy = 1 I understand how they found fxx, they used simultaneous equations, but I don't understand that notation.

I was wondering if anyone knows whether there exist strictly local interpretations of quantum mechanics. I understand that Bell's theorem tells us that any hidden variable theory must be non-local if it is to give QM. But what about other interpretations such as many worlds? It is obvious that...

According to this, if someone spins around at 2 revs per second when the moon is in the horizon, the moon seems to move at 4 times the speed of light. And this implies the moon is not in our local reference frame. And per this, local inertial frame applies to "small regions of a gravitational...

At the time Schwarzschild derived his solution (1915) he only had a version of the EFE that was not fully coordinate free, he used the equations in unimodular form, and therefore he could only consider the "outside of the star" part of the fully general covariant form we know now. So does a...

Consider an analytic function $f$ and non-constant defined on a set $\mathcal U\subset\mathbb C$ open and connected. Prove that the real-valued functions $|f|,\,\text{Re}(z),\,\text{Im}(z)$ can't achieve local maximum. This one looks hard, how to do it?

As I understand in SR light is always c in it's local reference frame regardless of a present gravitational field. Light would appear to be traveling slightly less than c in a gravitational field otherwise known as the Sharpio Delay in all non-local reference frames. Now, light must be traveling...

Homework Statement Theorem: Let f: M->R where M is a open subset of Rn Suppose f is C2(M) Let x E M such that "gradient of f at x" = 0 and the Hessian of f at x is positive definite Then x is a strict local minimum point of f. The above theorem is given in my textbook. If instead...

Hi all, I don't know if this is the right section, but I really need to solve this problem. I've been searching for the correct formula for two days. OK, here's the picture: The global rotation of all objects (rot_x, rot_y, rot_z): red object (0.00, 45.00, 0.00), blue object (45.00, 0.00...

Dear all, I would like to know from you the solution about this problem (which is not a homework, but a topic of my Master thesis!): I need the strain energy density related to a circle of radius r0 centered in an arbitrary point of a square plate, under the boundary conditions described in...

hi suppose i run Two notebook and in each of them i have matrix A and Constant B and a function C in each notebook these things have the same name. if in notebook 1 i assign B=10 then in notebook 2 B is 10 too , which is not my desire. how can i define these constants and matrices and...

Bonjour, I need to numerically compute the net electrical resistance of a given geometry. I know the shape of my object, it is relatively simple. It's close to this: http://2.imimg.com/data2/QX/UC/IMFCP-3019296/i-shape-big-1-250x250.jpg Actually my shape is even simpler because it's a...

I've learned Kg to Kgf this time I got another question.. I think it's another way around.. "The weight of an object is 25kgf. What is it's mass if local gravity is 9.6m/s^2" Tried this.. 25/(9.6)(9.8)= 25.5kg

Okay, so I have an astronomy/astrophysics exam tomorrow and I understand everything except for the local standard of rest. Could someone please explain it to me? Thanks!

Homework Statement The question provides a graph and asks for the local minimums. I attached a picture with the graph. 2. The attempt at a solution I said the local minima are when x=0,2,5. However the answer key suggests they are at 1,2,5. Could someone please explain why 1 is a...

what did bell show concerning the existence of a local hidden variable model for quantum physics?

Hi Say I have two expressions of the form F(r, t) = \int{dr'\,dt'\,\,x(r,r',t,t')g(r',t')} and F'(r, t) = \int{dt'\,\,x'(r,t,t')g'(r, t')} It is clear that F' is local in space, whereas F is non-local in space. Is it correct of me to say that F' describes an isotropic...

Homework Statement f(x,y)=(1+xy)(x+y) Homework Equations The Attempt at a Solution I started out by expanding and got: x+y+x^2y+xy^2 Then I found all my partial derivatives and second derivatives: f_{x}=1+2xy+y^2, f_{y}=1+2xy+x^2, f_{xx}=2y, f_{yy}=2x, f_{xy}=2(x+y)...

It is an old idea that, at least in principle, hidden variables could be local if they are superdeterministic. However, so far this idea seemed too speculative for highly respectable journals such as Physical Review Letters to publish research on it. But now it seems that it has changed. The...

Please bring me out of my state of confusion if I need to be... The question is how to calculate the rate of an atomic clock (a pendulum clock may work otherwise) on board a vehicle traveling along the surface of the Earth at constant altitude, like a bus, a train or an aeroplane. This was first...

I heard in a conference that gravity forbids to construct local gauge invariants like Tr-\frac14 F^{\mu\nu}_aF_{\mu\nu}^a and only allows non-local gauge invariant quantities like Wilson Loops: Tr P e^{\oint_{\gamma} A_a dx^a}. Could someone explain me where does it come from? I have a basis...

I have a question I wanted to clear up. According to the definition of a "local inertial" frame in GR, you must use a coordinate system that locally looks Cartesian, right? I mean if you had a coordinate system with a basis that wasn't orthogonal, then it would not be considered a local inertial...

Hi, Let f :X-->Y ; X,Y topological spaces is any map and {Ui: i in I} is a cover for X so that : f|_Ui is continuous, i.e., the restriction of f to each Ui is continuous, then: 1) If I is finite , and the {Ui} are all open (all closed) , we can show f is continuous...

Hi everyone, Recently I faced a problem in calculating bending stress in a long UPN profile "flange" due to concentrated force. It seems that the regular/familiar formula for bending stress in a finite/short element does not applicable in local bending of long/infinite beam. See sketch...

I chanced upon an argument in Misner, Thorne and Wheeler to the effect that the energy/momentum of the gravitational field cannot classically be localised. Basic idea: you can make the Christoffel symbols vanish at any point, and hence the gravitational field at that point will vanish, taking...

One term I fully understand yet I have never seen how one actually does the calculation is the local gravity a particle feels in a gravitational field. Now, I honestly feel this is as stupid of a question as they come, but intuitively I'd say, if I wanted a(r), the acceleration as a function...

Is there a way in Mathematica to find the local maxima of a set of points? I have a fairly fine data set, and I can clearly see several peaks in it that I would like to know the numerical value of (as in, the highest point- I don't need a spline approximation or anything too fancy like that). I...

What is the meaning of the local gauge transformation exactly?? These days I'm studying. [D.J. Griffiths, Introduction to Elementary Particles 2nd Edition, Chapter 10. Gauge Theories] Here the Section 3. Local Gauge Invariance, the author gives the Dirac Lagrangian, \mathcal{L}=i \hbar c...

1. Show that the function F(x)=(sin(Nx)^2)/(sin(x)^2) has N-2 local maxima in the interval 0<x<pi Homework Equations 3. I am stuck after i have calculated the derivate, (2Nsin(Nx)cos(Nx)sin(x)^2-2sin(x)cos(x)sin(Nx)^2)/sin(x)^4 = 0 I am not sure how to simplify this equation, so...

Hi, All: I am trying to understand why covering maps have the local triviality condition, i.e., given a cover C:X-->Y, every point y in Y has a neighborhood Oy of y with p^-1(Oy)~ Oy x F, where F is the fiber. This seems confusing, in that fibers of covering maps are a (discrete)...

The local electric supply in our country is 415 volts. Our company recently imported plant and machinery. All the motors and electric panels that have been imported are on 220/110 volts specifications. The total load of the motors is 110 Kw. The motors are now tripping as soon as they are...

Haelfix pointed out the paper http://arxiv.org/abs/1105.4733" , and Witten 2007 (discussed in that thread) expresses doubt that 4D gravity could be exactly solved, precisely because it has local excitations. And yet here Maloney et al have done it in 3 dimensions. Can something about their...

Homework Statement The streamlines of a fluid are as follows: x = (x0) + 3(y0)t^2 y = (y0)/(1 + 2t) z = (z0) + 5(x0)t Find the velocity and acceleration fields in the Eulerian description (local). Homework Equations Total/material acceleration: Dv/Dt = dv/dt + v.grad(v) The...

Hi all, (Also - if anybody could tell me how to get the latex to work on this page that'd be very handy!) While not technically homework this is a problem I've found I'm stuck on during my revision. Any help would be greatly appreciated. Homework Statement "By demanding that the covariant...

Hi, I'm reading a paper about acceleration and the author states the local coordinates of the observer (\tau,x) (for a non-uniformly accelerated observer) are specified (in relation to the inertial coordates (T,X))...

Hi, Everyone: Say f(z) defined on a region R , is a complex-analytic bijection. Does it follow that f:R--->f(R) is a diffeomorphism, i.e., is f^-1 also analytic? I know this is not true for the real-analytic case, e.g., f(x)=x³ , but complex- analytic...

Homework Statement This is less of a help me answer something question more a help me understand this question. I was reading though my hydrodynamics notes and there was a derivation that ended up with the follow equation \frac{D\psi}{Dt} = \frac{\partial\psi}{\partial{t}} +...

Hello, I'm been stuck on this problem and I've been staring blankly at it way too long. I stumbled upon here and thought I'd ask for help? :P Alright well, I'm looking for a local max/min, and I've already done the first partials and I got *f(x)=2x-y and f(y)=-x+2y+6; I'm sure those are right...

Hi I am analysing some piping which starts off as being aligned with the global axis system (X Y Z). So axially its X, laterally is Y and Z is vertically upwards. Due to bends etc. the end of the pipe is in a different orientation though still in the same plane - now the local axis system is x...

Is it possible that Lorentz invariance is just a lower limit of a larger manifold that has a priveleged frame? Even if Bell's experiments can't transmit signal faster than light. The spirit of relativity is still violated by say instantaneous correlation between 10 billion light years. As...

If we assume that an electron in an entangled pair has more than 2 plans (plans that determine if an electron go up or down through a magnet) to choose from, can we create a local hidden variable theory? If this is true, how many plans to choose from would an electron need for this to work...

Homework Statement Find the values of a and b if the function f(x) = 2x3 + ax2 + bx + 36 has a local maximum when x = −4 and a local minimum when x = 5. Homework Equations I'm not even sure how to start this, it's just baffling me for some reason The Attempt at a Solution i do...

I am confused as to exactly what a local base at zero (l.b.z.) tells us about a topology. The definition given in Rudin is the following: "An l.b.z. is a collection G of open sets containing zero such that if O is any open set containing zero, there is an element of G contained in O". Ok, great...

Hello to all. I'm having a few problems and would love to know how to do the following. 1. f(x) = 3x^2-8 2. Find the function's zeros, local max/min and the function's behaviour 3. My attempt at drawing the function ended with a downward curve intercepting at y=-8, x=0 But a...

Homework Statement Suppose F: Rn --> R has first order partial derivatives and that x in Rn is a local minimizer of F, that is, there exists an r>0 such that f(x+h) \geq f(x) if dist(x, x+h) < r. Prove that \nabla f(x)=0. Homework Equations We want to show that fxi(x) =0 for i = 1,...,n So...

Homework Statement if: H = Local Hour Angle Lat = Latitude. Dec = Sun Declination. cos(H) = -sin(a)-sin(Lat)*sin(Dec) / cos(Lat)*cos(Dec) I wand to get The value of Lat . The Attempt at a Solution I Tried to make it simple By : 1 - multiply both sides by the denominator 1-...

Im trying to calculate the ground state energy of Helium using a density functional theory approach combined with the local density approximation. So far I have set up universal functionals and I mainly need help with the actual algorithm the evaluation of the Hartree energy functional.