1. Unitary Geometry on Exceptional Cartan Domains In 1935, E.Cartan classified all symmetric bounded domains. He prived that there exit only six types of irreducible bounded symmetric domains in C. They can be realized as follows: RI(m,n) = {Z ∈ Cmn|I − ZZ ′ > 0, Z − (m,n) matrix} RIIp = {Z ∈ Cp(p+1)/2|I − ZZ ′ > 0, Z − symmetric matric of degree p} RIIIq = {Z ∈ Cq(q−1)/2|I − ZZ ′ > 0, Z − skew...

The retinal interphotoreceptor matrix (IPM) occupies the space between the neural retina and the retinal pigmented epithelium (RPE), two neuroectoderm-derived epithelia. While the IPM appears to be a major route by which photoreceptor cells receive vital metabolic factors, relatively little is known concerning its structure and function. The studies reported here describe the presence of specia...

We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms h...

The paper deals with the parallel computation of matrix factorization using graph partitioning-based domain decomposition. It is well-known that the partitioned graph may have both a small separator and well-balanced domains but sparse matrix decompositions on domains can be completely unbalanced. In this paper we propose to enhance the iterative strategy for balancing the decompositions from [...

This paper discusses fuzzification of crisp domains into fuzzy classes providing fuzzy domains. Relationship between two fuzzy domains, Xi and Xj , is represented by a matrix, wij . If Xi and Xj have n and m elements of fuzzy data, respectively, then wij is n × m matrix. The primary goal of the paper is to generate and provide some formulas for predicting interval probability in the relation to...

This paper discusses fuzzification of crisp domains into fuzzy classes providing fuzzy domains. Relationship between two fuzzy domains, Xi and Xj , is represented by a matrix, wij . If Xi and Xj have n and m elements of fuzzy data, respectively, then wij is n × m matrix. Our primary goal in this paper is to generate and provide some formulas for predicting interval probability in the relation t...

As well-known, De Rham's Theorem is a classical way to characterize vector fields as the gradient of scalar fields, it tool great importance in theory fluids mechanic. The first aim this paper provide useful rotational version theorem establish several results on boundary value problems field electromagnetism. Gurtin presented completeness Beltrami's representation smooth domains for symmetric ...

Fibronectin (FN) is an extracellular matrix protein that is assembled into fibrils by cells during tissue morphogenesis and wound healing. FN matrix fibrils are highly elastic, but the mechanism of elasticity has been debated: it may be achieved by mechanical unfolding of FN-III domains or by a conformational change of the molecule without domain unfolding. Here, we investigate the folded state...

Inclusion of absolute summability domains of matrices Factorable matrices Summability method of Cesàro a b s t r a c t In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely conve...

We prove general results that reduce the determination of the β–duals of matrix domains XT of triangles in certain FK spaces X to that of the β–dual of X, and the characterization of matrix transformations on XT to that of matrix transformations on X. AMS Mathematics Subject Classification (2000): 40H05, 46A45