Given an integer n ~ 1, and the orthogonal polynomial1rn (· ; du) of degree n relative to some positive measure du, the polynomial system "induced" by 1rn is the system of orthogonal polynomials {7rk,n} corresponding to the modified measure dUn = 1r~du. Our interest here is in the problem of determining the coefficients in the three-term recurrence relation for the polynomials 7rk,n from the re...

An orthogonal approach to the fuzzification of both multisets and hybridsets is presented. In particular, we introduce $L$-multi-fuzzy and$L$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. In addition, we study the properties ofthese structures. Also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

In this paper, we introduce the concept of α-orthogonal patterns to mine a representative set of graph patterns. Intuitively, two graph patterns are α-orthogonal if their similarity is bounded above by α. Each α-orthogonal pattern is also a representative for those patterns that are at least β similar to it. Given user defined α, β ∈ [0, 1], the goal is to mine an α-orthogonal, β-representative...

Ternary complementary set based UWB signaling employing a set of orthogonal chip pulses is proposed. Each user transmits the same information bit over a set of parallel channels each characterized by an orthogonal pulse and a spreading sequence from a ternary complementary set. Ternary complementary sets assigned to two users are mutually uncorrelated in the complementary sense. Hence, the mult...

We show how to produce algebraically a complete orthogonal set of Latin squares from a left quasifield and how to generate algebraically a maximal set of self-orthogonal Latin squares from a left nearfield. For a left Veblen-Wedderburn system, we establish the algebraic relationships between the standard projective plane construction of a complete set of Latin squares, our projective plane cons...

an orthogonal approach to the fuzzification of both multisets and hybridsets is presented. in particular, we introduce $l$-multi-fuzzy and$l$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. in addition, we study the properties ofthese structures. also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...