Mapping Definition and 364 Threads

Mapping Rule Say I have the function y = 2 \sin 3(x - 20) and the corresponding mapping notation (x, y) \rightarrow (\frac{1}{3}x + 20, 2y) (which I assume is correct.) How come I take the inverse of the amplitude (2) and horizontal "compression" (3), and how come a negative phase shift moves...

Hi everyone, Let me set the scene. I'm writing a program to model the flow of an ideal fluid around various singularities using the complex potential and then using conformal transformations to map boundaries into new shapes. It's very nearly done but one of the transformations (what appears...

Greetings, This was posted in the Classic Physics section, reposted here in Quantum section in case someone here may have some experience in EMF mapping. I am currently working on an interesting experiment on crystalized metal and I need to find a way to get a detailed map of an...

Greetings, I am currently working on an interesting experiment on crystalized metal and I need to find a way to get a detailed map of an electromagnetic field when current is induced into a metal sample. I found the basic 2D approach of using conductivity paper and Ag ink to be useless as it...

Problem: I have a computer image of a grid "square" from an aviation chart. The "square" is actually approximately rectangular, but the left and right sides aren't quite parallel and the top and bottom sides are parallel but very slightly curved. I will assume/pretend that the top and...

I would appreciate if someone could explain Conformal Mapping using Complex Analysis using an example. I get the rough idea but have no clue how complex analysis comes into the picture. Thank You!

Mapping and functions... Why do were define one-one and many-one mappings as functions? Why do we separate them into a different group and make them special? Thanks in advance. :smile:

This makes for some interesting reading. http://www.foia.cia.gov/2020/2020.pdf The rise in economic power of China and India is pretty much a given. One prediction is really striking. They predict the world's economy to grow by 80 percent over 2000 levels. At that rate, the worst that...

I am interested in following the fate of cells in which a particular cytosolic receptor/transcription factor has been activated during development. Would something like a CRE recombinase transgenic work for this? Can anyone who worked with this system or has working knowledge of it give me a...

I have been speculating that the ancients believed in eternal life or re-incarnation because when you fall asleep you never actually remember the point at which you actually pass out...you just remember waking up. The ancients commonly believed certain gods had domain over natural elements...

Hi, can anyone tell me what a surjective mapping between Hilbertspaces is? That is: what does surjective mean? What about bijective? I mean what is special about a mapping if it is sujective or bijective?

I'm looking for a proof of the Riemann mapping theorem. If I'm not mistaking, there are differnet proofs and the original proof is quite difficult. I'd appreciate any information on where I can/might find a less complicated proof of this theorem.

Can a mapping from f:S->T associate an element of s into several elements of T? Also, how do you prove: A mapping f:S->T is bijective if and only if it has an inverse?

http://www.newscientist.com/news/news.jsp?id=ns99994434 This is what the internet looks like: http://www.newscientist.com/data/images/ns/9999/99994434F1.JPG