Iranian Journal of Mathematical Sciences and Informatics
Year:2019 | Volume:14 | Issue:1|Papers Count:15

In formal language theory, we are mainly interested in the natural language computational aspects of!-languages. Therefore in this respect it is convenient to consider fuzzy!-languages. In this paper, we introduce two subclasses of fuzzy regular!-languages called fuzzy n-local!-languages and B¨ uchi fuzzy n-local!-languages, and give some closure properties for those subclasses. We define a deterministic fuzzy automaton acceptance conditions on fuzzy!-languages and fuzzy n-local automaton. The relationship between deterministic fuzzy n-local automaton and two subclasses of fuzzy regular!-languages are established and proved that every fuzzy!-language accepted by a deterministic fuzzy automaton in 2-mode is a projection of a B¨ uchi fuzzy 2-local!-language.

A kind of approximation, called best coapproximation was introduced and discussed in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by several researchers in different abstract spaces. In this paper, we prove some results on the existence and uniqueness of best coapproximation in quotient spaces when the underlying spaces are metric linear spaces. We also show how coproximinality is transmitted to and from quotient spaces.

In network code setting, a constant dimension subspace code is a set of k-dimensional subspaces of Fn q. If Fn q is a nondegenerate symplectic vector space with bilinear form f, an isotropic subspace U of Fn q is a subspace for which U  U? . We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the property of being isotropic is used in decoding process, then we demonstrate the structure of an isotropic spread code. In network code setting, a constant dimension subspace code is a set of k-dimensional subspaces of Fn q. If Fn q is a nondegenerate symplectic vector space with bilinear form f, an isotropic subspace U of Fn q is a subspace for which U  U? . We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the property of being isotropic is used in decoding process, then we demonstrate the structure of an isotropic spread code.

In this paper, we investigate domination number as well as signed domination numbers of Cay(G: S) for all cyclic group G of order n, where n ϵ {pm, pq} and S = {k < n: gcd(k, n) = 1}. We also introduce some families of connected regular graphs 􀀀 such that S (􀀀 ) ϵ {2, 3, 4, 5}.

In this paper, the system of Fredholm integral equations of the second kind is investigated by using a modified degenerate kernel method (MDKM). To construct a MDKM the source function is approxi-mated by the same way of producing degenerate kernel. The interpolation is used to make the needed approximations. Lagrange polynomials are adopted for the interpolation. The equivalency of proposed method and Lagrange-collocation method is shown. The error and convergence analy-sis of the algorithm are given strictly. The efficiency of the approach will be shown by applying the procedure on some prototype examples.

Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with the subring R, characterizations of maximal fixed and maximal g-ideals in R of the form Mx(R) are given. Moreover, the classes of zR-ideals and z R-ideals are introduced in R which are topological generalizations of z-ideals and z-ideals of C(X), respectively. Various characterizations of these ideals are established. Also, coincidence of zR-ideals with z-ideals and z R-ideals with z-ideals in R are investigated. It turns out that some fundamental statements in the context of C(X) are extended to the subrings of RX.

The largest class of hyperstructures is the one which satisfies the weak properties. We connect the theory of P-hopes, a large class of hyperoperations, with the Lie-Santilli admissibility used in Hardonic Mechanics. This can be achieved by a kind of Rees, sandwich hyperop-eration.

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free R-submodules of a finite quasi-Frobenius ring R which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Gr¨ obner basis and we show that under certain conditions a linear code takes the maximum of minimum Hamming weight.

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems − div (ɑ (x, u, ru) +  (u)) + g(x, u, ru) = f − div F, in a bounded open set and u = 0 on @, in the framework of Orlicz-Sobolev spaces without any restriction on the M N-function of the Orlicz spaces, where − div (a(x, u, ru)) is a Leray-Lions operator defined from W1 0 LM( ) into its dual,  ϵ C0(R, RN)...

In this paper, first, we introduce the new concept of 2-inner product on Banach modules over a C-algebra. Next, we present the concept of 2-linear operators over a C-algebra. Our result improve the main result of the paper [Z. Lewandowska, On 2-normed sets, Glasnik Mat., 38(58) (2003), 99-110]. In the end of this paper, we define the notions 2-adjointable mappings between 2-pre Hilbert C*-modules and prove superstability of them in the spirit of Hyers-Ulam-Rassias.

Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the generalized mixed product ideals and show that Lk has a linear resolution if and only if Ik has a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal are again generalized mixed polymatroidal ideal.

In this paper, we classify the skew cyclic codes over Fp + vFp + v2Fp, where p is a prime number and v3 = v. Each skew cyclic code is a Fp+vFp+v2Fp-submodule of the (Fp+vFp+v2Fp)[x; ϴ ], where v3 = v and ϴ (v) = − v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.

Let R be a commutative ring with identity and M be an R-module. The zero divisor graph of M is denoted by 􀀀 (M). In this study, we are going to generalize the zero divisor graph 􀀀 (M) to submodule-based zero divisor graph 􀀀 (M, N) by replacing elements whose product is zero with elements whose product is in some submodule N of M. The main objective of this paper is to study the interplay of the properties of submodule N and the properties of 􀀀 (M, N).

Arenas et al. [1] introduced the notion of -closed sets as a generalization of locally closed sets. In this paper, we introduce the notions of -locally closed sets,  -closed sets and  g-closed sets and obtain some decompositions of closed sets and continuity in topological spaces.

We construct one− step iterative process for an  − nonexpan-sive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study 4− convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.