In this paper we prove that there exist 4—{k2; 1/2k(k—1); k(k—2)} SDS, regular Hadamard matrices of order 4k2, and SBIBD(4k2, 2k2 + k, k2 + k) for k = 47, 71, 151, 167, 199, 263, 359, 439, 599, 631, 727, 919, 5q1, 5q2N, 7q3, where ql, q2 and q3 are prime power such that ql ≡ 1(mod 4), q2 ≡ 5(mod 8) and q3 ≡ 3(mod 8), N = 2a3bt2, a, b = 0 or 1, t ≠ 0 is an arbitrary integer. We find new SBIBD(4k...

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the A (1) n−1 affine Lie algebra. We have classified them in two classes of solutions. The first class consists of n(n − 1)/2 K-matrix solutions with three free parameters. The second class are solutions that depend on the parity of n. For n odd there exist n reflection K-mat...

A problem of reducing intuitionistic fuzzy matrices is examined and some useful properties are obtained with respect to nilpotent intutionistic fuzzy matrices. First, reduction of irreflexive and transitive intuitionistic fuzzy matrices are considered, and then the properties are applied to nilpotent intutionistic fuzzy matrices. Nilpotent intuitionistic fuzzy matrices are intuitionistic fuzzy ...

We derive combinatorial necessary conditions for discrete-time quantum walks defined by regular mixed graphs to be periodic. If the walk is periodic, all eigenvalues of time evolution matrices must algebraic integers. Focusing on this, we explore which ring coefficients characteristic polynomials should belong to. On other hand, $\eta$-Hermitian adjacency have implications. From these, can find...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...

In this study we discuss about an application of fuzzy graph isomorphism. If we look two unequal fuzzy matrices on undirected fuzzy graphs, we cannot say either the fuzzy graphs of theses fuzzy matrices are isomorphic or not isomorphic. It is because two fuzzy matrices may look different even if the fuzzy graphs are isomorphic. In this study, by using the algorithm for fuzzy graph isomorphism i...

Path algebras are additively idempotent semirings and generalize Boolean algebras, fuzzy algebras, distributive lattices and inclines. Thus the Boolean matrices, the fuzzy matrices, the lattice matrices and the incline matrices are prototypical examples of matrices over path algebras. In this paper, generalized fuzzy matrices are considered as matrices over path algebras. Compositions of genera...

in this paper we define ( , ) k  q -fuzzy h -sub hemirings, ( , ) k  q -fuzzy h -ideals, ( , ) k  q - fuzzy     h -bi-ideals and ( , ) k  q -fuzzy h -quasi-ideals. we characterize h -hemiregular and h -intrahemiregular hemirings by the properties of their     ( , ) k  q -fuzzy h -ideals, ( , ) k  q -fuzzy h -bi-ideals and     ( , ) k  q -fuzzy h -quasi-...