Points Definition and 1000 Threads

Hello, I have come across this sentence in a paper: "For a metal, the introduction of a finite temperature T can be of a more technical use: the Fermi surface of the system is no longer a sharp feature in the Brillouin zone, and the number of electronic wave vectors "k points" needed to...

Homework Statement Find the maximums, minimums, and saddle points (if any) of Z = 4Y3 + X2 - 12Y2 - 36Y +2 Homework Equations The partial derivatives with respect to X , and Y. The Attempt at a Solution I took the two partials, and set them equal to zero. The problem is...

Is there a formal way to measure the error between some arbitrary points and a non-linear curve in order to minimize it?

Homework Statement Find critical points. f(x,y) = (x-1)^4 + (x-y)^4 The Attempt at a Solution \frac{\partial f}{\partial x} = 4(x-1)^3 + 4(x-y)^3 \frac{\partial f}{\partial y} = - 4(x-y)^3 \frac{\partial f}{\partial x} = 0 , \frac{\partial f}{\partial y} = 0 , -...

If I specify the latitudes and longitudes of both point A and B on the surface of a unit sphere, how can I find the great circle angle between the two points? Say if Latitude and longitude of A is ##\epsilon_1 \;\hbox { and }\;\tau_1## respectively. Latitude and longitude of B is ##\epsilon_2...

Hello, I'm working on a design for an architectural structure, and I am choosing the material for the design. Are there any resources that will tell me the breaking point for like "1-inch" of material X. I need something that can support the weight of a car. Thanks! Carpetfizz

Homework Statement Determine the set of points at which the function is continuous. F(x,y) = arctan(x + √y) Homework Equations Perhaps the chain rule? The Attempt at a Solution I derived it, but the solution in the back of the book is nothing like what I expected. It involves e and...

Jordan writes:

U=kqoq/r ? Please look at the attachments. I was wondering if someone could please check my work. That is all. Thank you for your time!

Given a circle centered at the origin, how can one prove that the limit of the quotient of the number of lattice points on the circle over the radius goes to zero as radius goes to infinity?

for cos y the critical points are n*pi - 0.5*pi for cos 2x, the critical points should be n/2 * pi - 0.25*pi because if I set y=2x = n*pi - 0.5*pi , I get the eq in red for x. However if I do it graphically, I just get n*pi - 0.25*pi. The question: why algebraically I am constrained to use...

Homework Statement In the figure below, determine the point (other than infinity) at which the electric field is zero. (Let q1 = -2.45 µC and q2 = 6.50 µC.) Homework Equations The Attempt at a Solution Here is a little commentary my author gives on this problem: Each...

Homework Statement There are two parallel plates. The plate on the left has an electric potential of +60 Volts. The right plate has an electric potential of 0 Volts. The plates are 8.0mm apart. Between the two plates lies a point P 2.0mm from the left plate with a charge -3.5pC. Point R lies a...

I model arterial baroreflex data that I have collected in humans using the Kent equation which is: y=p1/(1+exp((x-p3)*p2))+p4; where Y=heart rate, X= estimated carotid sinus pressure, p1=range of Y, p2=slope coeff, p3=centerpoint on X, p4 = minimum Y. I use Sigma Plot to do a best fit line...

Homework Statement I was looking at the following tutorial http://mathworld.wolfram.com/Circle.html Homework Equations equations 31-34 o the link The Attempt at a Solution My question is just whether this means that for 31-34, the answers are determinants of 3x3 matricies...

Homework Statement How to find equilibrium points between four point charges? How do you determine whether these equilibrium points are stable, unstable, or neutral? I know the sum of the forces should equal zero, but that's it. How do you determine the stability of the equilibrium...

Can anyone give me some advice on where I should take my points of reference when using bernulli equation. I know the point will vary according to the problem, but can one say, always begin looking for this and that and apply the equation... Then move to this and that, etc

Not really a homework question, just the notes are confusing me. Homework Statement Let S be a functional. (Given without proof) If S is differentiable its derivative \delta S is uniquely defined as \delta S = \int_{x_{0}}^{x_{1}}\frac{\delta S}{\delta \gamma} \delta \gamma dx where...

Homework Statement I was given a sample of 5000 points from an ellipsoidal blob (in 3D) that has some orientation. Assuming that each point has equal mass, I was asked to calculate the inertia tensor of this blob, then find the principal axes to determine the orientation of this blob...

Hi all! This isn't actually a homework question, but thought this subforum is the place for this anyway. It's been some ten years since I last touched the topic of mechanics and I guess this is a real simple question, but what can you do when I don't get it! Any help is appreciated! How do...

Homework Statement For S \subset Rn, prove that S° is open. Homework Equations S° are all interior points of S. The Attempt at a Solution My class has only learned how to use balls to solve these types of problems (no metric spaces). So I need to choose an ε > 0 so that Bε(x) \subset...

Suppose we have 3 points in the plane given by: $\displaystyle (x_1,y_1),\,(x_2,y_2),\,(x_3,y_3)$ and we wish to find the area of the triangle whose vertices are at these points. We may let the base b of the triangle be the line segment between the first two points, and the altitude h of the...

Homework Statement Find the local maxima and minima and sketch: Critical points: (3, -4) and (6, 0) Interval of increase: (3, ∞) Interval of decrease (-∞, 3) I'm not quite sure if I graphed this correctly since I wasn't given the function to doublecheck. The Attempt at a...

i am facing difficulty in understading the following terms in fea 1. guass points and integration points 2. zero shear energy elements 3. Hourglassing 4. shear locking Please provide information about the four points in a much simpler way compared to what is presented in internet or books.

I would like to calculate (X,Y) coords on a circle with a 10" radius. I have some idea on how this can work but I'm not real solid on it. Say the center is (0,10) and I'd like to solve for Y given an arbitrary X. How would I do this? Obviously (10,0) and (-10,0) and (0,-10) and I know that sin...

I found one interesting example... We have a rectangle ABCD with his perimeter o. Where is the set of points when their (for each point) sum of distance lines AB, BC, CD, DA is 2/3o ? I tried it, but geometric problems is quite hard for me and I don't know how do it. So, have you got any...

Hi all, I am posting as a layman, whose 16 year old son has been issued with a court summons for criminal damage against a neighbour's car and driveway. A few weeks ago my son thoughtlessly emptied a small glass candle jar out of his upstairs bedroom window into what he thought was the...

This isn't really homework. I'm studying What Is Mathematics by myself. But I'm very stuck on one of its exercises. Homework Statement Prove that if for four complex numbers z_{1}, z_{2}, z_{3} and z_{4} the angles of \frac{z_{3} - z_{1}}{z_{3} - z_{2}} and \frac{z_{4} - z_{1}}{z_{4} -...

Hi I'm trying to study over break, this isn't an exact quote but its the part of the problem I need help with. Thanks. Homework Statement Draw the unit circle and plot the point P=(3,2). Observe there are TWO lines tangent to the circle passing through the point P. Lines L1 and L2 are...

in that at corners are not differentiable, does this mean that they also are not inflection points but at the same time a change in the rate. https://www.physicsforums.com/attachments/517 on the graph above f(x) for [0,7] at x=4 and x=5 what is f' and f'' or does it not exist thanks ahead(Dull)

Good Day, My professor historically has put more advanced questions on the final exams than can be found in our textbook. My supplements and extensive search engine use have not allowed me to get any further...Ive hunted through as many examples as I could find but cannot seem to find a...

Hi All, I'm struggling with finding a solution to an adjustment I'm working on. Thought someone else may have some thoughts? I have a kinematic time series of X,Y positions for two points (X1,Y1,X2,Y2). I know that the two points were a distance D (e.g., 100 m) apart from each other (the...

Good morning, I'm trying to compute the arclength (geodesic distance) between two n-dimensional points over a n-dimensional sphere (hypersphere). Do you know if it is possible? If yes, please, I'd be very pleased if you, as experts, provide me this knowledge. Thank you very much

A battery has a voltage of 107.5 V. We denote this battery with point B. Point C is the point after two resistors, which are parallel to one another. Immediately after point C we get one more resistor. Calculate the voltage between B and C. I calculated the total resistance between B and C...

Hi, I'm reading Baby Rudin and have a quick question regarding topology. Given a nonempty subset E of a metric space X, is it true that the only points in E are either isolated points or limit points? (b/c all interior points are by definition limit points, but not all limit points are...

Homework Statement find the slope of this line it contains these points: (-16, -1) , (-17, -7) Homework Equations y = mx + b The Attempt at a Solution i got y = 3/8x - .625 is that correct? my work i use -7 +1 / -17 + 1 ==-6/16 ==6/16 = 3/8 then i used -7 =...

Homework Statement A plane with equation xa+yb+zc=1 (a,b,c>0) together with the positive coordinate planes forms a tetrahedron of volume V=16abc (as shown in the Figure below) Find the plane that minimizes V if the plane is constrained to pass through a point P=(8,2,3) . Here is a...

Let $AB$ be the distance between the two points $A(x_{1} ~ x_{2})$ and $B(x_{2}, ~ y_{2})$ -- e.g. $AB = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$. Why is the point $P$ which divides $AB$ in the ratio $\lambda:\mu$ given by $\displaystyle ~~ \bigg(\frac{\lambda x_{2}+\mu x_{1}}{\lambda+\mu}, ~...

Homework Statement The Attempt at a Solution set x(t)=1+∫2cos(s(f^2(s)))ds(from 0 to t) then check x(0)=1+∫2cos(s(f^2(s)))ds(from 0 to 0)=1 then the initial condition hold, by FTC, we have dx(t)/dt=2cos(tx^(t)), then solutions can be found as fixed points of the map but for...

Continued from; Originally Posted by Jameson http://www.mathhelpboards.com/f2/understanding-how-deal-fractions-using-brackets-2596/#post11674 What is the full problem you are trying to solve? I can't make sense of your post until I know that. I have a circle problem and am trying to find...

Homework Statement Hello guys! I've never dealt with an ODE having 2 singularities at once, I tried to solve it but ran out of ideas. I must solve ##(x-2)y''+3y'+4\frac{y}{x^2}=0##. Homework Equations Not sure. The Attempt at a Solution I rewrote the ODE into the form...

The number of end points of the cantor set double each time an iteration is performed, therefore the total number of end points after infinite iterations is ~ 2^N where N is cantor's aleph null. 2^N is, however, c (the number of the continuum) and is therefore uncountable but we know that the...

Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that...

Homework Statement Determine all fixed points of: dx/dt = x(β-x-ay) dy/dt = y(-1+ax-y) β and a are parameters. I get what to do when there is just one differential equation, but not two.

In the context of families of seminorms I've come across these two definitions; i) a family of seminorms \{ p_I \} is separating if p_I = 0 for all I implies x=0. ii) for a family of seminorms, when for every x \in X / \{ 0 \} there is a seminorm p_I such that p_I (x) > 0. It is easy to show...

Hi guys I'm reading a book about linear programming and network flows. In chapter 2 when it talks about convex sets and their analysis it talks about extreme points and extreme directions of a convex set. I understand the definitions of extreme points and extreme directions, but I don't know...

Is there a nice closed-form for this?

Hello guys . I obtained a 3 dimensional dynamical system , how can I find its critical points with using software ? I tried it handy but its too involved to compute handy .

Why is Fourier sine series of any function satisfying Dirichlet's theorem, not defined on the discontinuous points whereas we define it for Fourier cosine series? ex - sine series of f(x) = cosx, 0<=x<=∏ is defined on 0<x<∏ whereas cosine series of f(x) = sinx, 0<=x<=∏ is defined on 0<=x<=∏

Homework Statement Points A B and C lie on the circumference of a circle where $$A =(-3,2)\\B=(-1,6)\\C=(7,2)$$ Show that AC is the diameter of the circle. Homework Equations The Attempt at a Solution Would it be sufficient to show that the angle ABC is a right angle and therefore...