for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

Let M(n) denote the group of orientation-preserving isometries of H. Classically, one uses the disk model for H to define the dynamical type of an isometry. In this model an isometry is elliptic if it has a fixed point on the disk. An isometry is parabolic, resp. hyperbolic, if it is not elliptic and has one, resp. two fixed points on the conformal boundary of the hyperbolic space. If in additi...

Information is usually related to knowledge. However, the recent development of information theory demonstrated that information is a much broader concept, being actually present in and virtually related to everything. As a result, many unknown types and kinds of information have been discovered. Nevertheless, information that acts on knowledge, bringing new and updating existing knowledge, is ...

Let M be a compact Riemannian manifold, and let ∆ = ∆M denote the Laplace– Beltrami operator of M acting on L2(M). The eigenvalue spectrum E (M) consists of the eigenvalues of ∆ listed with their multiplicities. Two manifolds M1 and M2 are said to be isospectral if E (M1) = E (M2). Geometric and topological constraints are forced on isospectral manifolds; for example if the manifolds are hyperb...

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

Experience in using ontologies and rules in applications has shown that in many cases we would like to extend their representational and reasoning capabilities to deal with vague or imprecise knowledge. For example, multimedia applications have highlighted the need to extend representation languages with capabilities which allow for the treatment of the inherent imprecision in multimedia object...