ELEMEN SIMETRIS DAN SIMETRIS DIPERUMUM PADA RING DENGAN INVOLUSI

The definition of symmetric element in a ring with unity and equipped with involution can be generalized to generalized symmetric elements. But the properties of symmetric element not automatically can be generalized to generalized symmetric elements. In this paper, we discuss the property of symmetric element which can or cannot be generalized to generalized symmetric elements. Because of at least there is an element of symmetric and generalized symmetric elements which have the generalized Moore Penrose inverse, so method in this paper is by establishing a relationship between symmetric element, generalized symmetric element and generalized Moore Penrose inverse of element.

Genetic Analysis in Japanese Kindreds of Congenital Type I Antithrombin Deficiency Causing Thrombosis

SummaryWe have identified two novel minor deletions (case 1; -TA or -AT at nucleotide 9831-3 in exon 5 and case 2; -A at nucleotide 7640-1 in exon 4), one novel nonsense mutation (case 3; TAT to TAA at nucleotide 7491 in exon 4), and one recurrent nonsense mutation (case 4; CGA to TGA at nucleotide 5381 in exon 3A) in Japanease kindreds with congenital type I antithrombin deficiency. The deletion detected in case 1 represented a symmetric element (CTCTGTCTC) and possessed a direct repeat (CTCTATGTCTC). The deletion in case 2 was recognized in a consensus sequence (TGAAT) and possessed a direct repeat (GATGAA). The nonsense mutation in case 3 formed a palindrome (CCGTTAACGG) and that in case 4 was caused hy a CpG dinucleotide mutation. These results confirm that the mutations of congenital type I antithrombin deficiency are not random events but are influenced strongly by DNA sequences.

Probabilistic factorization of a quadratic matrix polynomial

A purely algebraic result. We begin by stating the following theorem. Theorem. Let E be a finite set, and letdenote the set of real E × E matrices with non-negative off-diagonal elements and with non-positive row sums. Let A be a symmetric element of, and let V be a diagonal real E × E matrix. Then there exists a unique pair (H+, H−) of elements ofsuch thatI denoting the identity E × E matrix, and the superscript T signifying transpose. It is an immediate consequence that