Characterization Of Semigroups Research Articles

Characterizations of semigroups by their linear Diophantine anti-fuzzy bi-ideals

The purpose of this paper is to introduce linear Diophantine anti-fuzzification of algebraic structures. In this regard, we define linear Diophantine anti-fuzzy (LDAF) substructures of a semigroup and discuss some of its properties. Moreover, we characterize semigroups in terms of LDAF-ideals and LDAF-bi-ideals. Finally, we apply the linear Diophantine anti-fuzzification to groups and find a relationship between LDAF-subgroups of a group and its LDF-subgroups.

Yet another heat semigroup characterization of BV functions on Riemannian manifolds

Yet another heat semigroup characterization of BV functions on Riemannian manifolds

On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup

In this paper, we introduce the notions of interval-valued anti fuzzy prime (resp. strongly prime and semiprime) bi-ideals of semigroup. By using these ideas, we characterize those semigroup for which each interval anti-fuzzy bi-ideal is semiprime and strongly prime.
 
 Introduction: The theory of fuzzy sets proposed by Zadeh [6], in his classic paper of 1965, deal with the applications of fuzzy technology in information processing. Mordeson, Malik and Kuroki gave a systematic exposition fuzzy semigroups in [2], where one can find theoretical results on fuzzy semigroups. Shabir and Kanwal [5], introduced the concept of prime bi-ideal, strongly prime bi-ideals and semiprime bi-ideal of a semigroup and studied those semigroups.
 
 In this paper we introduced the concept of interval valued anti fuzzy prime, strongly prime and semiprime bi-ideal of semigroups and give characterization of semigroups in terms of these notions we characterize those semigroups for which each interval-valued anti fuzzy bi-ideal is semiprime and strongly irreducible.

Analysis of semigroups with soft intersection ideals

Abstract In this paper, semisimple semigroups, duo semigroups, right (left) zero semigroups, right (left) simple semigroups, semilattice of left (right) simple semigroups, semilattice of left (right) groups and semilattice of groups are characterized in terms of soft intersection semigroups, soft intersection ideals of semigroups. Moreover, soft normal semigroups are defined and some characterizations of semigroups with soft normality are given.

Capacity and the Corresponding Heat Semigroup Characterization from Dunkl-Bounded Variation

In this paper, we study some important basic properties of Dunkl-bounded variation functions. In particular, we derive a way of approximating Dunkl-bounded variation functions by smooth functions and establish a version of the Gauss–Green Theorem. We also establish the Dunkl BV capacity and investigate some measure theoretic properties, moreover, we show that the Dunkl BV capacity and the Hausdorff measure of codimension one have the same null sets. Finally, we develop the characterization of a heat semigroup of the Dunkl-bounded variation space, thereby giving its relation to the functions of Dunkl-bounded variation.

A Note on Gaussian BV Function and Its Heat Semigroup Characterization

A Note on Gaussian BV Function and Its Heat Semigroup Characterization

An approach to the study of fuzzy rough prime ideal extensions of semigroups

Fuzzy rough set is a pair of lower and upper approximations of fuzzy set in a fuzzy approximation space. This paper studies the extension of fuzzy rough prime and semi-prime ideals in semigroups. Then we introduce the composition theory on fuzzy rough set. Finally some new characterization of semigroups by the properties of composition on fuzzy rough ideal extension are given.

A characterization of semigroups through their fuzzy generalized $m$-bi-ideals

In this article, we initially present the concept of the fuzzy generalized $m$-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized $m$-bi-ideals, we give the important characterizations of the semigroups. We also characterize the $m$-regular and $m$-intraregular semigroups using the properties of the irreducible and strongly irreducible fuzyy generalized $m$-bi-ideals.

Direct integrals of strongly continuous operator semigroups

The goal of this article is to develop a theory for direct integrals of C0-semigroups on Hilbert spaces parallel to the recent approach by Lachowicz and Moszyński for direct sums of Banach spaces, diagonal operators, and semigroups. In it we deal with the existence and characterisation of semigroups, asymptotic rates, and questions of decomposability.

Frame decomposition and radial maximal semigroup characterization of Hardy spaces associated to operators

Let L be the generator of an analytic semigroup whose kernels satisfy Gaussian upper bounds and Hölder’s continuity. Also assume that L has a bounded holomorphic functional calculus on L2(Rn). In this paper, we construct a frame decomposition for the functions belonging to the Hardy space HL1(Rn) associated to L, and for functions in the Lebesgue spaces Lp, 1<p<∞. We then show that the corresponding HL1(Rn)-norm (resp. Lp(Rn)-norm) of a function f in terms of the frame coefficients is equivalent to the HL1(Rn)-norm (resp. Lp(Rn)-norm) of f. As an application of the frame decomposition, we establish the radial maximal semigroup characterization of the Hardy space HL1(Rn) under the extra condition of Gaussian upper bounds on the gradient of the heat kernels of L.

Poisson semigroup characterization and the trace theorem of a class of fractional mean oscillation spaces

In this paper, we use regular wavelets to study the Poisson extension of the fractional mean oscillation spaces . Via a distributional trace operator πφ, we establish a relation between and a class of harmonic function spaces .

Markov processes with darning and their approximations

In this paper, we study darning of general symmetric Markov processes by shorting some parts of the state space into singletons. A natural way to construct such processes is via Dirichlet forms restricted to the function spaces whose members take constant values on these collapsing parts. They include as a special case Brownian motion with darning, which has been studied in details in Chen (2012), Chen and Fukushima (2012) and Chen et al. (2016). When the initial processes have discontinuous sample paths, the processes constructed in this paper are the genuine extensions of those studied in Chen and Fukushima (2012). We further show that, up to a time change, these Markov processes with darning can be approximated in the sense of finite-dimensional distributions by introducing additional jumps with large intensity among these compact sets to be collapsed into singletons. For diffusion processes, it is also possible to get, up to a time change, diffusions with darning by increasing the conductance on these compact sets to infinity. To accomplish these, we give a version of the semigroup characterization of Mosco convergence to closed symmetric forms whose domain of definition may not be dense in the L2-space. The latter is of independent interest and potentially useful to study convergence of Markov processes having different state spaces. Indeed, we show in Section 5 of this paper that Brownian motion in a plane with a very thin flag pole can be approximated by Brownian motion in the plane with a vertical cylinder whose horizontal motion on the cylinder is a circular Brownian motion moving at fast speed.

The ultimate rank of tropical matrices

A tropical matrix is a matrix defined over the max-plus semiring. For such matrices, there exist several non-coinciding notions of rank: the row rank, the column rank, the Schein/Barvinok rank, the Kapranov rank, or the tropical rank, among others. In the present paper, we show that there exists a natural notion of ultimate rank for the powers of a tropical matrix, which does not depend on the underlying notion of rank. Furthermore, we provide a simple formula for the ultimate rank of a matrix, which can therefore be computed in polynomial time. Then we turn our attention to finitely generated semigroups of matrices, for which our notion of ultimate rank is generalized naturally. We provide both combinatorial and geometric characterizations of semigroups having maximal ultimate rank. As a consequence, we obtain a polynomial algorithm to decide if the ultimate rank of a finitely generated semigroup is maximal.

Functions with bounded variation on a class of Riemannian manifolds with Ricci curvature unbounded from below

After establishing some new global facts (like a measure theoretic structure theorem and a new invariant characterization of Sobolev functions) about complex-valued functions with bounded variation on arbitrary noncompact Riemannian manifolds, we extend results of Miranda/the second author/Paronetto/Preunkert and of Carbonaro/Mauceri on the heat semigroup characterization of the variation of $$\mathsf {L}^1$$ -functions to a class of Riemannian manifolds with possibly unbounded from below Ricci curvature.

The abstract Cauchy problem for dissipative operators with respect to metric-like functionals

This paper is devoted to a characterization of semigroups of Lipschitz operators on a closed subset D of a Banach space X and the abstract Cauchy problem for an operator A in X satisfying the following condition: There exists a proper lower semicontinuous functional φ from X into [0,∞] such that the effective domain of φ is D(A) and such that limn→∞⁡Axn=Ax in X for any x∈D(A) and any sequence {xn} in D(A) satisfying two conditions limn→∞⁡xn=x in X and limsupn→∞φ(xn)≤φ(x). The main result asserts that a semigroup of Lipschitz operators on D can be generated by an operator A satisfying the above-mentioned condition, a dissipative condition with respect to a metric-like functional and a subtangential condition. The Kirchhoff equations with acoustic boundary conditions are solved by the method based on the abstract result with the construction of suitable Liapunov functionals and the use of a metric-like functional on a suitable set.

A semigroup characterization of well-posed linear control systems

We study the well-posedness of a linear control system Σ(A,B,C,D) with unbounded control and observation operators. To this end we associate to our system an operator matrix $\mathcal{A}$ on a product space $\mathcal{X}^{p}$ and call it p-well-posed if $\mathcal{A}$ generates a strongly continuous semigroup on $\mathcal{X}^{p}$ . Our approach is based on the Laplace transform and Fourier multipliers. The results generalize and complement those of Curtain and Weiss (Int. Ser. Numer. Math. vol. 91. Birkhauser, Basel, 1989), Staffans and Weiss (Trans. Am. Math. Soc. 354:3229–3262, 2002) and are illustrated by a heat equation with boundary control and point observation.

Endpoint bilinear estimates and applications to the two-dimensional Poisson–Nernst–Planck system

We study the Cauchy problem of the two-dimensional Poisson–Nernst–Planck (PNP) system in Besov spaces for r ⩾ 2. Our work shows a dichotomy of well-posedness and ill-posedness depending only on r. Specifically, when r = 2, combining the key bilinear estimates in with the heat semigroup characterization of Besov spaces, we prove the well-posedness of the PNP in , while for r > 2 we show that the PNP is ill-posed in in the sense that the difference of the charges must satisfy certain requirements, i.e. either the difference belongs to for r > 2 and the summation belongs to , or the difference belongs to and the summation belongs to for r > 2. Thus our results indicate that the difference of charges plays a crucial role and might provide some instability criterion for numerical analysis.

Characterizations of semi-groups that are semi-lattices of left groups

Zadeh in 1965 introduce the concept of a fuzzy set which now have a wide range of applications in various fields of Engineering Sciences, Computer Science and Management Sciences. It is worth mentioning here that for applications of fuzzy sets mostly associative algebraic structures are used such as in 2003, Mordeson, Malik and Kuroki have discovered the applications of fuzzy semigroups in fuzzy coding, fuzzy finite-state machines and fuzzy languages. We have applied fuzzy set theory to associative algebraic structures and have discussed related properties. Specifically we have characterized semigroups which are semilattices of left groups by the properties of generalized fuzzy ideals. Key words: -fuzzy ideals, -fuzzy bi-ideals, -fuzzy quasi ideals.

Some Characterizations of Semigroups by their Generalized Fuzzy Ideals

In this paper, we have characterized semigroups by the properties of their \((\in,\in \vee q_{k})\)-fuzzy ideals.

Characterization of Semigroups by Generalized Intuitionistic Fuzzy Quasi-Ideals

Characterization of Semigroups by Generalized Intuitionistic Fuzzy Quasi-Ideals