For a regular biordered set E, the notion of E-diagram and the associated regular semigroup was introduced in our previous paper (1995). Given a regular biordered set E, an E-diagram in a category C is a collection of objects, indexed by the elements of E and morphisms of C satisfying certain compatibility conditions. With such an E-diagram A we associate a regular semigroup RegE(A) having E as...

In this paper, we construct (a) a pair of two regular Cantor sets in higher dimension which exhibits $C^1$-stable intersection and (b) hyperbolic basic set $C^2$-robust homoclinic tangency the largest codimension for any dimensional manifold, using blenders. The former implies that an analog Moreira's theorem on real line does not hold dimension. latter solves question posed by Barrientos A.Rai...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defi ned by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

‎let $v$ be a vector space over a field $f$ of characteristic $pgeq 0$ and let‎ ‎$t$ be a regular subgroup of the affine group $agl(v)$‎. ‎in the finite dimensional case we show that‎, ‎if $t$ is abelian or $p>0$‎, ‎then $t$ is unipotent‎. ‎for $t$ abelian‎, ‎pushing forward some ideas used in [a‎. ‎caranti‎, ‎f‎. ‎dalla volta and m‎. ‎sala‎, ‎abelian regular subgroups of the affine group and r...

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

There is a concept in linear algebra called tridiagonal pair. The was motivated by the theory of $Q$-polynomial distance-regular graphs. We give tutorial introduction to pairs, working with special case as concrete example. totally bipartite, or bipartite (TB). Starting from first principles, we an elementary but comprehensive account TB pairs. following topics are discussed: (i) notion system;...

Let $M$ be an Alexandrov space collapsing to $X$ of lower dimension. Suppose has no proper extremal subsets and let $F$ denote a regular fiber. We slightly improve the result Perelman construct infinitely long exact sequence homotopy groups spectral cohomology for pair $(M,X,F)$. The proof is application good coverings spaces introduced by Mitsuishi-Yamaguchi. also extend this each primitive su...

In this paper, we consider central configurations of the planar 3n-body problem consisting n masses at vertices a regular n-gon inscribed in circle radius r and 2n second (not necessarily regular) concentric 2n-gon ar which are symmetric sense that set positions 3n corresponding invariant under action finite subgroup O(2). There two different types such configurations. first type, called bicirc...

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for L(R ) if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality principle extends to any dual pairs of projective unitary representations of countable groups. We examine the existence problem of dual pairs and establish some connectio...

We study the N-step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses the two-point correlators instead of the block probability, it makes it p...