An Extremal Problem Related to the Maximum Modulus Theorem for Stokes Functions

An Extremal Problem for Characteristic Functions

Suppose E is a subset of the unit circle T and H∞ ⊂ L∞ is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to znH∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of...

An extremal problem related to biplanes

The existence problem for biplanes has proved to be intractable: only finitely many are known. However, it can be turned into an extremal problem, on which some progress can be made. A biplane is a set of subsets (blocks) of {I, ... , n} such that (a) any two blocks meet in two points; (b) any two points lie in two blocks. It is easy to see that, for some integer k, every block of a biplane con...

AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM

In this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is r...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

A Strong Maximum Modulus Theorem for Maximal Function Algebras