Recent content by phasic

Is there any way to prove this?

Sorry I'm a little rusty with my math and proof logic, and this feels like a dumb question, but oh well! The Euclidian norm of a vector in ℝ3 is \|{v}\| = \sqrt{x^2 + y^2 + z^2} where \|{v}\| \geq 0. I'm trying to show that there is always an infinite number of solutions for arbitrary...

I have stumbled upon an approximation to the average of integer square roots. \sum^{n}_{k=1}{\sqrt{k}/n} \approx \sqrt{median(1,2,...,n)} Sorry I am not very good at LaTeX, but I hope this comes across okay. Could anyone explain why this might be happening? In fact, I just discovered that...

This statement came from the book Convex Optimization by Boyd and Vandenberghe. I forget which page now, but the idea has come up again in Farkas' lemma, but in a different form. http://en.wikipedia.org/wiki/Farkas%27_lemma Let A be an n × m matrix and b an n-dimensional vector. Then...

So the column space of A transpose is the null space of A?

Edited the post so that it makes more sense. Does it now?

Actually, it means column space. This means that there is no linear combination of A's columns that gives b. This must mean that there is no x for which Ax = b, right?

Why is it that for arbitrary z, A^{T}z = 0 and b^{T}z ≠ 0 when there does not exist an x such that Ax = b, i.e. that b is not in the range space of A, where A is an n x m matrix?

I'm new to Riemann surfaces, but if there are indeed 2 branching points at -5 and 5, and the degree of w is 2, then the genus, g, for the surface is 2 = 2(g+2-1). So, g = 0. We're definitely looking at a sphere! If you're certain the path is figure 8 and encircles the branching points, I think...

Thanks! I just realized that using the unit disc is best. My final answer was 5*pi/2. Also, thanks for confirming that this is just for the flux through the open paraboloid, and that I also have to compute the flux through the cap at the bottom! The flux through the cap at the bottom is 0...

Homework Statement Consider the surface S with the graph z = 1-x^{2}-y^{2} with z≥0, and also the unit disc in the xy plane. Give this surface an outer normal. Compute: \int\int_{S}\vec{F}\bulletd\vec{S} where \vec{F}(x,y,z) = (2x,2y,z)Homework Equations \int\int_{S}\vec{F}\bulletd\vec{S} =...

Not lately. I just checked and it looks like how I remember it. Am I missing something?

First, he's sending the interval (a,b) to ((b-a)/2, (b-a)/2), which means sending (-2,1) to (-3,-3). If anything he's missing a negative sign.

The above suggestion seemed a little off, but I did find a function from (a,b) > (-1,1) using the Cartesian plane using slope and evaluating for the 'intercept' at -1. Then I dilated by pi/2 and stretched with tan, mapping (a,b) onto R with a composition of continuous bijections.

I found the answer to be 2*pi. I parameterized the sphere via spherical coordinates, x = cos(t)sin(s) y = sin(t)sin(s) and z = cos(s). This is a stretching of the (s,t) domain of (0<t<2*pi)X(0<s<pi) into the whole sphere. Using |Tt X Ts|, where Tt and Ts are tangent vectors on the surface...