Recent content by Nebula

What happens in the very first step of the solution?

Homework Statement Suppose f is analytic inside and on the unit circle |z|=1. Prove that if |f(z)|\leqM for |z|=1, then |f(0)|\leqM and |f'(0)|\leqM. Finally, what estimate can you give for |f^n(0)|? Homework Equations This problem is in a section dealing with Cauchy's Integral Formula...

Homework Statement From Calculus on Manifolds by Spivak: 1-10 If T:Rm -> Rn is a Linear Transformation show that there is a number M such that |T(h)| \leq M|h| for h\inRm Homework Equations T is a Linear Transformation => For All x,y \in Rn and scalar c 1. T(x+y)=T(x)+T(y) 2...

Homework Statement From Calculus on Manifolds by Spivak: 1-7 A Linear Transformation T:Rn -> Rn is Norm Preserving if |T(x)|=|x| and Inner Product Preserving if <Tx,Ty>=<x,y>. Prove that T is Norm Preserving iff T is Inner Product Preserving. Homework Equations T is a Linear...

I’m an undergraduate student at an honors college. In order to get my degree I need to write a thesis. I need to find a topic soon. I’m going to talk to the professors here and see what things they have in mind but I’m trying to think of some ideas on my own. Thing is I’m really burnt out. I...

I wasn't sure where to drop this topic, so I figured General would be the best place. Anyway, here goes. I'm majoring in Physics/Mathematics and I need to begin work on my thesis soon. Only problem is I don’t have a topic. Whilst trying to find some problems and areas that link automata and...

I was asked to find a function that is continuous nowhere but its square is continuous everywhere but 0. The domain of the function is [0,1]. I can't come up with an example... Any help is appreaciated. Thanks

Did you think my l was a 1. Maybe I should write it differently. lim (x-> -oo) f(x) = lim (x-> oo) f(x) = a and a is even. Want to show f has either a minimum or a maximum.

I'm frustrated beyond belief with a proof. Suppose we have an continuous even function with a domain of all real numbers. Now this function has limit as x goes to negative infinty equal to l and the limit as x goes to positive infinty is also equal to l. I want to show that this function...

If all the elements have order two then doesn't each individual element generate a cyclic group? Either that or the identity paired with every element forms a group. How does that tell us anything about the product of elements?

Thats what I thought. Now as for the cyclic group part. I suppose it has a decomposition. It's very general. I'm not dealing with any specific group. Just a subset of the group in which all elements are order 2. ...I'm not sure here... I had thought about the cyclic group. Say you had a...

I've got a question. It pertains to a proof I'm doing. I ran into this stumbling block. If I could show this I think I could complete the proof. G is a finite Abelian Group such that there exits more than one element of order 2 within the group. more than one element of the form b not...

Can someone explain how to solve these types of things, my book gives one example and its useless: find a such that 0 < a < 73 a=9^794(mod 73) (= means congruent equals) solve x^86=6(mod 29) Thanks in advance :smile:

Right but what equations do I work with? Any ideas about 2?

A couple Blackbody Problems? I'm a little confused about these two problems involving blackbodies, hopefully someone could give me a bit of insight. Thanks in advance. 1. For a blackbody we there is a frequency peak and a wavelennght peak. Let's call em v and w respectively. Now consider the...