unsolved math problem solved

[daniel49]

So just out of curiosity why is this important and what applications might we see from it?
http://www.msnbc.msn.com/id/10617015/

 

[Yeraze]

Seems one obvious application would be the design of antennae & systems that can do radio transmissions through obstacles better, meaning better Wifi & Cell phone coverage through trees or buildings. Maybe Line-of-sight won't be such a huge deal in a few years...

 

[DrPizza]

For what it's worth, the title of your thread "unsolvable math problem solved" should be changed to "difficult math problem solved." Unsolvable means the problem can't be solved. There are, in fact, many math problems which are "unsolvable," and proven such.

 

[daniel49]

Originally posted by: DrPizza
For what it's worth, the title of your thread "unsolvable math problem solved" should be changed to "difficult math problem solved." Unsolvable means the problem can't be solved. There are, in fact, many math problems which are "unsolvable," and proven such.

Its not worth much, but technicaly you are correct. 🙂

 

[xtknight]

What is Kato's conjecture? All I get when I search for it is solutions to it.

Never mind. "Kato Conjecture" instead of "Kato's Conjecture" helps a bit but it would be nice if someone could provide a brief explanation of it.

 

[CycloWizard]

Never heard of it before this, but it has something to do with describing how waves move through multiple media. This solution will have very interesting implications in many fields, such as mechanical engineering (calculating natural frequencies of composites) or any sort of wave manipulation (radio, seismic waves). In my limited experience with trying to solve wave problems, the solution is valid only in a single material, as we were previously unable to describe how the waves might be transmitted into or behave in the adjoining medium. I suppose this solution will shed light on these issues, though I haven't read them yet to know for sure. In fact, I probably won't know for sure even after I read them, as mathematical journals use their own language altogether.

Edit:
I read one of them (The Solution of the Kato Problem for Divergence Form Elliptic Operators with Gaussian Heat Kernel Bounds, see listing here: link) and it seems that this problem has something to do with the L^2 norm of a term found in mass, energy, and momentum conservation equations, essentially stating that the norm is bounded by some constant multiplied by the L^2 norm of the gradient of the function of interest. In more layman's terms, this means that when numerically solving a problem of this form, one can predict a priori what the error might be by applying Kato's Conjecture to the particular problem at hand. This type of error prediction (or even error calculation) is really an essential step of numerical solutions to this form of problem, as without it you can have no confidence that the solution that you've produced is accurate. It seems to be analagous to the use of the energy norm in finite element analysis, where a famous theorem dictates that the error in energy norm is equal to the square root of the error in potential energy. This might not seem very important at face value, but it allows some very powerful techniques to be used to calculate certain output datas with very low error (called 'superconvergent extraction'), even if the overall error of the solution is large.

 

[bendixG15]

My quote for the new Year is going to be...thanks to daniel49


Its not worth much, but technicaly you are correct.

Instead of some snotty-ass comment

 

[daniel49]

Originally posted by: bendixG15
My quote for the new Year is going to be...thanks to daniel49


Its not worth much, but technicaly you are correct.

Instead of some snotty-ass comment

Sometimes I probably am but I don't like being a snotty-ass😉