Local Definition and 521 Threads

I considered posting this in the Food thread, but I think it might be better for it to be in its own separate thread. First of all, let me clarify that I love, LOVE ethnic cuisine and foods that are local to a particular region. I find that I learn a lot about groups of people or the local...

Homework Statement Find the local maximum and minimum values and saddle points of the function f(x,y) = x^2 + xy + y^2 + y Homework Equations Local max/min critical points saddle The Attempt at a Solution 1) partial derivative: fx = 2x+y fy = x+2y+1 from here, I'm a little confuse on...

Homework Statement Let f\colon\mathbb{R}^m\to\mathbb{R}. All partial derivatives of f are defined at point P_0\colon = (x_1, x_2, ... , x_m). If f has local extremum at P_0 prove that \frac{\partial f}{\partial x_j} (P_0) = 0, j\in \{1, 2, ..., m\} Homework Equations Fermat's theorem: Let...

Dear All: I'm very confusing with the relationship between photonic local density of states and the field intensity. In thermal equilibrium, the field intensity should be proportional to the photon's number (or squared) and also be proportional to the local density of states. We know that this...

Hello! (Wave) The local Lipschitz condition is the following:Let $c>0$ and $f \in C([a,b] \times [y_0-c, y_0+c])$. If $f$ satisfies in $[a,b] \times [y_0-c,y_0+c]$ the Lipschitz criterion as for $y$, uniformly as for $t$, $$\exists L \geq 0: \forall t \in [a,b] \ \forall y_1, y_2 \in...

I've ran into a problem where my local University, that I would be able to attend for no cost due to my close proximity (staying at home) and scholarships, does not offer physics as a major, only a minor. If I were to attend a different University, my scholarships wouldn't cover my costs due to...

Are many-particles systems theories like the Standard model of particle physics examples of local hidden variable theories?

Homework Statement I am trying to find a local inertial frame for the following metric: ds^2 = -(1+\Phi(x))dt^2 + (1-\Phi(x))dx^2 I can get the transformed metric to equate to η at any point, but I can't get the first derivates wrt the transformed coordinates to vanish. Homework Equations...

Is it okay to define a local operator as an operator whose matrix elements in position space is a finite sum of delta functions and derivatives of delta functions with constant coefficients? Suppose your operator is M, and the matrix element between two position states is <x|M|y>=M(x,y). It...

Hello everyone, I'd like to know if my understanding of local and integral quantities is clear. An integral quantity refers to the entire physical system, it is not defined point by point. A local one is defined point by point, for example ρ(x,y,z). Can I consider the charge dq as a local...

What do we mean by "there is no local construction for an action in terms of F^{\mu\nu}, or E and B"? So, I understand the construction "on-shell", once we solve Maxwell's equations to find F^{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}, and how we can then write an action which is both...

I am looking for a local field of positive characteristic, like Q22 was used in this article: http://8pic.ir/images/s9oiiuqqkq989w3posu9.png in fact, i need an another Example of a local field of positive characteristic like Q22 .

Homework Statement I need to confirm if I correct in saying the following: If f(x) is a function having the domain [a,b) as shown in the figure, then f(x) has several local maxima but none of them is global maximum, and f(x) does not have a global maximum. Homework Equations and...

In my, er, studies I've encountered descriptions of what I understand to be various ways to go from global to local coordinates. These are: tetrads, Riemann Normal Coordinates and Fermi Normal coordinates. Until now I haven't investigated much further than that, mostly because I've not been...

I saw a video recently by a Professor Jerry Mitrovica in which he claimed that the gravitational effect of the Greenland and Antarctic ice sheets is so substantial as to 'raise' local sea levels. He suggests this is in the order of 100 meters for Greenland. See this video - around the 14 minute...

Indicate whether you think it is a local maximum, local minimum, saddle point, or none of these? My solution: Point P = Local Max Point Q = Local Min Point R = None Point S = Saddle I got a 75% for first attempt, so one answer is not correct and I am not sure which one isn't.

One argument against Mach's principle is the speed of light restriction. How could the distant cosmic mass of the universe instantaneously have a local effect on an accelerating mass? But could we view this from the perspective of a field that is already presently locally at all points in...

Hi folks -- does anyone know of a good survey article on the topic of whether local gauge invariance is a requirement of a fundamental theory within QFT -- hence of an asymptotically safe theory? I only have a few scattered remarks to this effect (by F. Wilczek mostly), so any good...

The double slit experiment is not known to violate any Bell inequality, and thus may have a local hidden variables description. Does Bohm-Dirac theory provide a local hidden variables description for the double slit? Are there other local hidden variables descriptions for the double slit? (If...

Hello, I was wondering what the exact definition of conformal transformations is. This is a question in the context of Shape Dynamics. In Shape dynamics, time is viewed as a global parameter of the universe, and as such is invariant under spatial coordinate transformation. Part of the...

Hello, I'm wondering what the exact definition of a local conformal transformation is, in the context of General Relativity (/Shape Dynamics) To be more precise: 1. Are local conformal transformations coordinate transformations or scalar transformations of the metric? 2. If they are...

Homework Statement Hello! I need to find a local linear increase in the field of the lens. I have Listing of Field Curvature Data. It contains vectors of - Y height, Tan Shift, Sag Shift, Real Height, Ref. Height, Distortion. I can not understand how these data get what I need. Homework...

Hey gang, I'm re-working my way through gauge theory, and I've what may be a silly question. Promotion of global to local symmetries in order to 'reveal' gauge fields (i.e. local phase invariance + Dirac equation -> EM gauge field) is, as far as i can tell, always done on the Lagrangian...

Let a\in\mathbb{R}, a>0 be fixed. We define a mapping \mathbb{Q}\to\mathbb{R},\quad q\mapsto a^q by setting a^q=\sqrt[m]{a^n}, where q=\frac{n}{m}. How do you prove that the mapping is locally uniformly continuous? Considering that we already know what q\mapsto a^q looks like, we can define...

I've posted a method below. I'm experimenting with local variable declarations in java. Actually, a compiler error in eclipse has made me reconsider what I understand about local variables. Why can't the local variable, String final, be created inside my if statement? Why, instead, would...

We work on project about mobile cellular networks. In a part of the project, we faced the problem about the proof of convergence of ...(Complete description is Available in attachment.Please download it) Please help me.It is very important!

Here is a new video, addressing a common question on this forum: https://www.youtube.com/watch?v=jlTVIMOix3I It's similar to that one, but has nice narration, and also shows an object thrown upward.

First I want to consider an example of 1D motion. Lagrange equation: $$ \frac{d}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0 $$ If we transform $$L \rightarrow L+a$$ with a is constant, the equation of motion remains unchanged. This is global symmetry. To obtain...

Hello everyone, I am currently reading chapter two, section 3 of Griffiths Quantum Mechanics textbook. Here is an excerpt that is giving me some difficulty: "Formally, if we expand V(x) in a Taylor series about the minimum: V(x) = V(x_0) + V'(x_0) (x-x_0) + \frac{1}{2} V''(x_0)(x-x_0)^2...

Hello everyone, I'm studying the finite strain theory and have come across the maximum dissipation principle. It implies a dissipation function defined as D=\tau:d-\dfrac{d\Psi}{dt} \tau denotes the Kirchhoff stress tensor, d the eulerian deformation rate and \Psi=\Psi(b_e,\xi) the free...

A rectangle with length L and width W is cut into four smaller rectangles by two lines parallel to the sides. Find the maximum and minimum values of the sum of the squares of the areas of the smaller rectangles. Unless I did incorrectly, the algebra is very very long... HELP

Hello all, I have this tricky question, I think I got the idea, just wish to confirm. If the function \[z=x\cdot ln(1+y)+a(x^{2}+y^{2})\] has a local minimum at (0,0), then: (choose correct answer) 1) a<-0.5 2) a>0 3) a>0.5 4) -0.5<a<0.5 5) a>0.5 or a<-0.5 What I did, is calculate the...

i have an autonomous system x'=f(x) and teh function f is loc lip on its domain, if x and y are sol of the system defined on (alpha, beta) and x(s)= y(s) for some s in (alpha, beta) then x= y on (alpha, beta) is the solution to prove this problem similar to this one...

Assume that f:\mathbb{R}^N\to\mathbb{R} is a differentiable function and that x_0\in\mathbb{R}^N is a local minimum of f. Also assume that N\geq 2 and that the gradient of f has no other zeros than the x_0. In other words \nabla f(x)=0\quad\implies\quad x=x_0 Is the x_0 a global minimum?

Here is the question: I have posted a link there to this thread so the OP can view my work.

if a function ls locally lip then considering this diff eq x'(t)= f(x(t) where now x and y are solutions of the DE on some interval J and x(s)=y(s) for some s in J. then how can I prove that there exists a positive number delta such that x=y on (s-delta, s+delta)∩ J

Suppose ##f^{\prime\prime}## is continuous on an open interval that contains x = c 1. If ##f^{\prime}(c)=0## and ##f^{\prime\prime}(c)<0##, then ##f## has local maximum at x = c. 2. If ##f^{\prime}(c)=0## and ##f^{\prime\prime}(c)>0##, then ##f## has local minimum at x = c. 3. If...

I remember an argument, I think due to David Mermin, that refutes local hidden variables in a single measurement (as opposed to Bell's Inequality, which requires gathering statistics of many measurements). I know that's not a lot to go on, but I'm wondering if this rings a bell (no pun...

I fell upon another discord between realism and quantum mechanics while studying Bell's theorem : If we consider measurement of 2 spin 1/2 particles, with operators A, A', B and B' which are set respectively at 0, 45, 90 and 135 degrees (like in Bell experiment), we have...

While Planck time is usually regarded as the shortest unit of time, isn't the shortest unit of time that can exist is the time it took to go from absolute time, the big bang, to everything after that i.e. local time? Did local time exist at the instant of the Big Bang?

Does anyone know how to calculate Magnetic Local Time for a position on earth, given the current Universal Time, and the position in Geomagnetic latitude/longitude?

This paper - The Local Void: for or against ΛCDM?,http://arxiv.org/abs/1401.6459 - puts to the test the question of low galaxy counts in the vicinity of the Milky Way. It has been suggested this poses a problem for LCDM. Using the Millennium II supercomputer at the Max Planck Supercomputer...

Given a smooth vector field ##V## on a smooth manifold ##M## the uniqueness of differential equations assures that there exists a unique integral curve ##\phi^{(p)}: J \to M## for some open interval ##J \subseteq \mathbb{R}## for which ##0 \in J## and ##\dot \phi^{(p)} (0) = V_{\phi^{(p)}...

I've been working on a problem that I can't seem to get started on. Here is how it is posted: Metric of a space is: ds^2 = (1+2\phi^2)dt^2 - (1-2\phi)(dx^2+dy^2+dz^2), where |\phi | << 1 everywhere. Given a point (t_0 , x_0 , y_0, z_0) find a coordinate transformation to a locally...

Homework Statement Suppose we have f: \mathbb C^n \to \mathbb C^n with f(z_1, \cdots,z_n) = (\sigma_1(\mathbf z), \cdots, \sigma_n(\mathbf z)) where the sigmas are the elementary symmetric functions (i.e. \sigma_1 = \sum z_j \quad \sigma_2 = \sum_{i < j} z_i z_j \quad etc) Note if we look...

f(x) = { { 16 - x^2, if -4 <= x <= 0 { 2x - 3, if 0 <= x <= 4 I did the first derivative test and got zero but i don't think that's right. Any help?

1. If f(x,y)=e^{x}(1-cos(y)) find critical points and classify them as local maxima, local minima, or saddle points. The Attempt at a Solution I found the partials and mixed partial for the second derivative test as follows: f_{x}=-e^{x}(cos(y)-1) f_{y}=e^{x}(sin(y))...

Hey, Once again, I got a question about quaternions. Say I have an initial rotation Q1. I now want to rotate Q1 on the X and then on the Y axis. BUT: The Y rotation should apply to the local Y axis which was given in Q1. The problem is: If i rotate Q1 by the X-rotation Q2, then the Y...

Are Local Linear Approximation, Linear Approximation, and Linearization all the same thing? Question is, I learned about something called Local Linear Approximation in Calc 1. Now in Calc 2, the topic of Linearization from Calc 1 was mentioned. But I never did anything that was referred...

Homework Statement http://i.minus.com/jZdpOtdOiChOn.jpg Homework Equations Local extrema can be determined using the first derivative test. The Attempt at a Solution I ran the first derivative test to find the critical points, which were 0 and plus/minus 0.5. I plugged in the values into...