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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...

Same Yeah I'm having the exact same problem. I don't know what it is cuasing it. Greg, any ideas? Heeeeeelp! I use that address quite frequently. :cry: I don't know what to do. I'm having to use my school email for the time being, arg! :mad:

I have been doing some research concerning the prime number distribution, and basically have come to a point in which I'm not sure what direction to take. I'll breifly explain my work in hopes that someone may have some suggestions, or some conjectures which may spark new directions. My work...

The rate is droplets of fuel injected in the carburetor per second. As to how the heck C measures the fuel consumption from where he standing, I dunno. But I don't think it matters. What matters is that he is going to see a different distance which means his fuel assumptions arent going to work...

Thanks for the welcome everyone. :smile: You know Tom I'm really not sure. :confused: I guess I got cuaght up in life and all of its wild complexities. I'm at a new college this semester and have a pretty hefty workload that is math and physics related. So I'll be stoping by to stay sharp.

Well probably not. LOL But I came back. It's been about a year. I don't know where I've been all this time. Anyway, nice to see some old memebers still here running the show. Greg, the place looks mighty spiffy. Kudos indeed. Anyway just wanted to say hi to everyone. :smile:

Abstract Algebra Number Theory Calculus with Theory a.k.a. Advanced Calc. Modern Physics

I've got a little question here. Basically we've got this guy named "B" driving a straight track with a high constant velocity u. His buddy, "C" on the side of the track measures B's fuel consumption to be dn/dt. Now C filled the tank with just enough gas to make it the distance of the track...

Hello everyone. The Leonid Meteor shower is tonight for those people near the Atlantic coast of the United States. For the story check out www.spaceweather.com I'm not sure how good this years shower is going to be but hopefully we'll get somewhat of a show, and of course clear dark skies are...

Yikes! I didn't even realize that stuff was on there. I actually didn't bother to browse the site becuase I was having connection problems earlier. I only looked at the page with the news on it. Thats the link I posted. I wasn't aware (but I should have been) that other explicit and offensive...

WARNING: CONTAINS EXPLICIT CONTENT, VULGARITY, AND SADISM In case you want to view the bands site its http://www.hellonearth.net/news.htm

Yeah it's Tampa, I live in Tampa and this has been on the radio a lot lately. I think I overheard something on the radio this morning about the show being on October 4th and being broadcast over the internet. I can't remember though. It’s a second-degree felony in Florida to assist a suicide and...

I've heard mixed opinions on this. I've heard it causes all sorts of nuero-degenerative diseases and nausea and blindness among others. And I’ve also heard its all just a big urban legend. Could someone please clarify this for me? Thanks.

Another Lain Fan! I asked this question in these forums about a year ago. Sadly I never received a reply. Anyone interested in philosophy and religion should see Serial Experiments Lain, so I was hoping someone around here had seen this magnificent and deep anime. Alas I found another person...

I am wondering if anyone can give me some information on the chemistry of coral reef habitats particularly those in the south pacific. In general I am looking for information concerning temperature, salinity ranges as well as pH and local dissolved gasses and their corresponding abundance.

From PF2: Futurist Donde From PF: Way back in the day Feztaa Scandium Barry C. Detwiller a.k.a Powers of Light There are others, my mind has drawn a blank... Wow. PF Version 1, that seems like so long ago...

Main Entry: neb·u·la Pronunciation: 'ne-by&-l& Function: noun Inflected Form(s): plural neb·u·lae /-"lE, -"lI/; also -las Etymology: New Latin, from Latin, mist, cloud; akin to Old High German nebul fog, Greek nephelE, nephos cloud Date: circa 1738 1 : any of numerous clouds of gas or...

Thanks for the link Labguy. So essentially a neutron star isn’t made up entirely of neutrons. I completely overlooked the fact that the star might have various stratified layers particularly the “atmosphere” consisting primarily of iron nuclei. Thanks again for the info. :smile:

Jupiter near the Beehive Cluster Break out your binoculars folks because M44 also known as Beehive star cluster is near Jupiter in tonight’s sky. Binoculars are a great way to view this if you have a good clear sky. I wide field of view will let you get a good glimpse of the cluster and...

It is a known fact that neutron stars and pulsars, remnants of super nova explosions, have very strong magnetic fields. It is said that the collapse of the core amplifies the magnetic field of the progenitor. This is due to the fact that the magnetic fields lines are drawn closer together during...

Personally I think the super-symmetric theoretical particles have pretty goofy names. Quarks and leptons sound bad enough, how about their super-symmetric partners Squarks and Sleptons! That sounds even more ridiculous. Sneutrinos, Gauginos and the list goes on. In a tape-recorded lecture on...

Gravitational Waves This is a Gravitational Waves Class taught at the California Institute of Technology, January through May of 2002. This course was designed for physics graduate students or advanced undergraduates, and for scientists and engineers who have been working in other fields and...

LURCH was speaking mathematically. You see as far as we know a singularity is a zero dimensional point, it has no width, breadth or height. This knowledge comes directly from the mathematical constructs of General Relativity, Einstein’s Theory of Gravity. The Planck length as you mention is the...

I have confirmed PF mail is now fully operational! I repeat all systems are go!

I don't know if you would consider me a fanatic as my post count is no where near as high as other members (my post count on PF2 was over 500). But as long as I'm on the computer I've got a window open with PF on it. I'll refresh the window every now and then to see if anything new and...

In all my days of dreaming up wacky sci-fi ideas I’ve never seen or even considered the concept of a magnetic fluid spacecraft . When you say “Magnetic Fluid” what type of material are you talking about?

I don’t necessarily believe in UFO’s, but they are fun to talk about, and I like alien movies. Conspiracies also make for interesting discussions. Some conspiracies are quite outlandish while others might nearly be true. As far as conspiracies go I think the government holds a lot back from us...

I browsed around the Discovery Store and couldn’t find a scope that quite met your description. The Meade Autostar line has a motorized automatic finding capabilities but I don’t know of any that have a digital camera. If it is a Meade scope that has Autostar its probably a good buy. In general...

As far as I gather its not working yet. :frown: I attempted to send a couple e-mails to the address and they never went through.

Thanks Greg. We appreciate the time and effort.

Skills like those could help you get an engineering internship. There aren't to many Physics Labs and research facilities as there are various engineering firms. If you have a bit of engineering skills i.e. programming and design you should try to go after some engineering internships as well...

And it is for obvious reasons. The sound barrier was obviously theoretical possible however it simply was technologically inaccessible before 1947. Currently light speed is a theoretical maximum speed and technologically impossible to surpass. Tachyons have never been observed and relativity...

Hey longbusy you live in Daytona? Do you go to Embry Riddle Aeronautical University? Well even if you don't you are in for a treat, which you may or may not already know. Saturday March 29th at Embry Riddle Alan Guth author of The Inflationary Universe will be giving a talk as part of the day...

Absolutely. As far as we know now right now there is no useful information that can be encrypted in entangled states. But that does not rule out the possibility in it entirety. Future knowledge of more complex entangled states MIGHT lead to some type of useful FTL transmission. The key word is...

I think the only theoretical candidate is probably a wormhole. However as previously mentioned the ability to "prop" wormholes open depends on an exotic state of gravitational repulsion. Dark Energy/Matter (which we no little about) and also possible vacuum states that allow for negative energy...

I'm back. I was Nebula before and I'm still Nebula. Back on PF Version 1 I was Natas Sanchez. My post count on PF2 was over 500, my post count on PF1 was 250 or somthing like that. Its good to see everyone made the switch Cheers!