Consider a Doint set C in the complex plane whose complement K is connected and regular (i .e. K possesses a Green ' s function with pole at infini ty). Let denote the transfini te diameter of C . Recall that d m = l /U ' C®)! where <{>(z) irans >C onto tl ê exterior of the uni t circle. Equivalent ly , d^ = Lin | |T^(z) | Ij.] where | |g(z) | | c = max] <*(z) | ,zeC and T..(z) is t^e Tchebyche...

This paper gives a practical method of extending an n× r matrix P (z), r ≤ n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P (z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P (z) has rank r for each z ∈ T, it can be extended to a matrix with nonvanishing dete...

a method for the simultaneous determination of sulfamethoxazole (smx) and trimethoprim (tmp), based on a direct determination of smx after diazotization and coupling with 2-naphthol by visible spectrophotometry and an indirect determination of tmp in the uv region by difference was developed. by the suggested procedure, it was possible to analyze smx and tmp in pharmaceutical preparations witho...

This paper gives a practical method of extending an nr matrix P (z), r n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P (z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P (z) has rank r for each z 2 T, it can be extended to a matrix with nonvanishing determin...

Abstract Let $(z_k)$ be a sequence of distinct points in the unit disc $\mathbb {D}$ without limit there. We are looking for function $a(z)$ analytic and such that possesses solution having zeros precisely at $z_k$ , resulting has ‘minimal’ growth. focus on case non-separated sequences terms pseudohyperbolic distance when coefficient is zero order, but $\sup _{z\in {\mathbb D}}(1-|z|)^p|a(z)| =...

A well-known theorem by Becker states that if a normalized univalent function \(f\) in the unit disk \(\mathbb{D}\) can be embedded as initial element into Loewner chain \((f_t)_{t\geqslant 0}\) such Herglotz \(p\) Loewner-Kufarev PDE \(\partial f_t(z)/\partial f=zf'_t(z)p(z,t)\), \(z\in\mathbb{D}\), a.e. \(t\ge0\),satisfies \(\big|(p(z,t)-1)/(p(z,t)+1)\big|\le k&lt;1\), then admits \(k\)-q.c. ...

g l o b a l c o m p e t i t i v e n e s s h a s r e c e n t l y b e c o m e a b i g c h a l l e n g e f o r m a n y c o m p a n i e s a r o u n d t h e w o r l d, w h i c h a r e f o r c e d t o s e e k l o w e r c o s t s a n d h i g h e r q u a l i t y f o r w h a t t h e y p r o d u c e. t h e p r o s p e r i t y o f m a n u f a c t u r i n g f i r m s d e p e n d s o n s e l e c t i n g a n...

Weinstein’s[2] brilliant short proof of de Branges’[1] theorem can be made yet much shorter(modulo routine calculations), completely elementary (modulo Löwner theory), self contained(no need for the esoteric Legendre polynomials’ addition theorem), and motivated(ditto), as follows. Replace the text between p. 62, line 7 and p. 63, line 7, by Fact 1 below, and the text between the last line of p...

In this paper, we discuss stability and linear independence of the integer translates of a scaling vector = (1 ; ; r) T , which satisses a matrix reenement equation (x) = n X k=0 P k (2x ? k); where (P k) is a nite matrix sequence. We call P (z) = 1 2 P P k z k the symbol of. Stable scaling vectors often serve as generators of multiresolution analyses (MRA) and therefore play an important role ...