This paper concerns the geometry of noncommutative domains and analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of noncommuting variables amongst which there are no relations they are free variables. Analytic free maps include vector-valued polynomials in free (noncommuting) variables and form a canonical clas...

A (bounded) manifold of circular type is a complex manifold M of dimension n admitting a (bounded) exhaustive real function u, defined on M minus a point xo, so that: a) it is a smooth solution on M \{xo} to the MongeAmpère equation (ddcu)n = 0; b) xo is a singular point for u of logarithmic type and eu extends smoothly on the blow up of M at xo; c) ddc(eu) > 0 at any point of M \ {xo}. This cl...

Syntrophins are scaffold proteins of the dystrophin glycoprotein complex (DGC), which target ion channels, receptors, and signaling proteins to specialized subcellular domains. A yeast two-hybrid screen of a human brain cDNA library with the PSD-95, Discs-large, ZO-1 (PDZ) domain of gamma1-syntrophin yielded overlapping clones encoding the C terminus of TAPP1, a pleckstrin homology (PH) domain-...

In image watermarking, the watermark’s vulnerability to geometric transformations has long been a difficult problem. Using invariant image features to carry the watermark is an effective approach to addressing this problem. In this paper, a multibit geometrically robust image watermarking algorithm using Zernike moments (ZMs) and pseudo-Zernike moments (PZMs) is proposed. Unlike its counterpart...

We consider the problem of estimating a function ( ) on the unit disk ( ): 2 + 2 1 , given a discrete and noisy data recorded on a regular square grid. An estimate of ( ) based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distinctive property of being invariant to rotation of axes about the origin of coordinates yielding therefore...

In broadband DS-CDMA uplink transmission using frequency-domain equalization (FDE) without cyclic prefix (CP) insertion, the transmission performance degrades due to inter block interference (IBI) and circular property loss. The schemes were proposed to solve the problems of IBI and circular property loss in our previous study with the assumption of perfect channel estimation. In this paper, th...

While the classical Schwarz method can only be used with overlap, optimized Schwarz methods can also be used without overlap, which can be an advantage when simulating heterogeneous problems, problems with jumping coefficients, or also for independent mesh generation per subdomain. The analysis of nonoverlapping optimized Schwarz methods has so far been restricted to the case of straight interf...

Optimized Schwarz methods are based on transmission conditions between subdomains which are optimized for the problem class that is being solved. Such optimizations have been performed for many different types of partial differential equations, but were almost exclusively based on the assumption of straight interfaces. We study in this paper the influence of curvature on the optimization, and w...