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Given two square matrices A, B of the same size, the two matrices AB and BA may have different ranks. A non-zero square matrix A is called a rankcommutator of a family L of n × n matrices if rank(AL) = rank(LA) holds for every L in L. Let L* denote the family of all rank-commutators of L. In this paper, we investigate the members of L* for the following families L of n×n matrices: all non-zero symmetric matrices; all diagonal matrices; all diagonalizable matrices. In the process, some new notions in linear algebra are created, such as "rank-symmetric matrices" and "determinant equivalent matrices", which might be useful for other study on ranks. A few problems for further study are posed at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, some subordination and superordination results for higher-order derivatives of certain p-valent analytic functions in the open unit disc are derived. Relevant connection of the results, which are obtained in this paper, with various known results are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we consider a set-valued implicit quasi-variational inequality problem in real uniformly smooth Banach space and show its equivalence with a fixed-point problem. Using this equivalence and Banach contraction principle for set-valued mapping, we prove the existence of solution for the set-valued implicit quasi-variational inequality problem. Further, we propose and analyze an iterative algorithm for the set-valued implicit quasi-variational inequality problem and discuss its convergence analysis and stability. The theorems presented in this paper generalize, improve and unify the results given in Noor [20,22] and the references therein. [ABSTRACT FROM AUTHOR]

In this paper, we present an Ekeland type variational principle, Takahashi type minimization theorem, Caristi type fixed point theorem and a generalized Oettli-Thera's equivalent form on complete D-metric space. We also prove that they are equivalent. The results present in this paper unify, improve and extend many known results due to Zhong, Ekeland, Takahashi, Caristi, and others. [ABSTRACT FROM AUTHOR]

Through out this paper, we assume that 0 < r. The Taylor transformations Tr are given by the positive,regular matrix defined by ank = (nκ)rκ-n(1 -- r)n+1 The purpose of this paper is to study these matrices as mappings into G. The necessary and sufficient conditions for Tr to be G -- G is proved. The strength of Tr in the G -- G setting is investigated. Also, it is shown that every G -- G Tr matrix is G -- translative. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notions of pseudo BL-algebra of fractions and maximal pseudo BL-algebra of quotients for a pseudo BL algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek - see [13], p.36). In this paper, we prove the existence of a maximal pseudo BL-algeba of quotients for a pseudo BL-algebra (Theorem 4.7) and we give an explicit description of the pseudo BL-algebra for some classes of pseudo BL-algebras. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider the isomorphic problem for type-W semigroups. Necessary and sufficient conditions when type-W semigroups are isomorphic will be given. In this paper, we generalize results of T.E. Hall in 1989 [9]. [ABSTRACT FROM AUTHOR]

In this paper, the notion of BCC-implicative ideal, BCC-commutative ideal, BCC-positive implicative ideal. Fuzzy BCC-implicative ideal and fuzzy BCC-positive implicative ideal and the quotient BCC-algebra induced by fuzzy BCC-ideal is introduced. The following results are obtained, for a BCC-algebra X: 1) BCC-commutative (resp. positive implicative) ideal must be a BCC-ideal. 2) fuzzy BCC-commutative (resp. positive implicative)ideal must be fuzzy BCC-ideal. 3) A fuzzy set µ in a BCC-algebra X is a fuzzy BCC-commutative (resp. implicative, positive implicative) ideal of X, if and only if, for each t ∈ [1, 1], t ≤ µ(0), µt = {x ∈ X, µ(x) ≥ t} is a BCC-commutative (resp, positive implicative, implicative) ideal of X, when µt ≠ Φ, 4) Let µ is a fuzzy BCC-ideal Of BCC-algebra X, and is not a constant, define a binary relation ∼µ on X by putting X ∼micro; y if and only if µ(xy) > 0 and µ(xy) > 0, then ∼micro; is a congruence relation on X. 5) In the end of this paper we give the construction of a quotient BCC-algebra X/µ via a fuzzy BCC-ideal µ. [ABSTRACT FROM AUTHOR]

The object of the present paper is to investigate several inclusion relationships and other interesting properties of certain subclasses of meromorphically p-valent functions, which are defined here by means of a family of linear operators. Relevant connections of the results presented in this paper with those obtained in earlier works are also indicated. [ABSTRACT FROM AUTHOR]

For a poser X, let TRE(X) denote the semigroup under composition of all regressive transformations α : X → X, that is, xα ≤ x for all x ∈ X. If X′ is a subposet of X, let TRE(X,X′) be the subsemigroup of TRE(X) consisting of all α ∈ TRE(X) whose ranges are contained in X′. In this paper, we intend to generalize Umar's isomorphism theorem stated that for chains X and Y, TRE(X) ≅ TRE(Y) if and only if X and Y axe order-isomorphic. It is proved in this paper that for chains X and Y and subchains X′ of X and Y′ of Y, if TRE(X, X′) ≅ TRE(Y, Y′), then X′ and Y′ are order-isomorphic. However, the converse need not be true. Moreover, some other interesting isomorphism theorems on such regressive transformation semigroups are also provided. [ABSTRACT FROM AUTHOR]

This paper deals with the way of solving inhomogeneous Cauchy-Fueter equations. An analogue of Mittag -- Leffler for regular functions of one quaternionic variable is proved in this paper, too. [ABSTRACT FROM AUTHOR]

This paper deals with the way of solving the inhomogeneous generalized Cauchy-Riemann systems in Quaternionic analysis. The Cousin problem is considered in this paper, too. [ABSTRACT FROM AUTHOR]

We define the Lie admissible non-associative algebra NAn,m,s in this paper. We show that NAn,m,s is simple. The corresponding Lie algebra of NAn,m,s is studied in the paper [4]. The matrix ring Mm(F) is a subalgebra of NAn,m,s We find all automorphisms of the algebra NA0,s,0 We define a Solid algebra by Theorem 4 in this paper. [ABSTRACT FROM AUTHOR]

Linear recurring sequences over semirings were introduced recently. In this paper, after investigating some properties on zero-sum strongly k-noetherian halfrings (briefly zero-sum SKN-halfrings), we study some properties of families of linear recurring sequences over zero-sum SKN-halfrings and relationships between families of linear recurring sequences and theirs annihilators. We also characterize the finitely generated subsemimodules of the S-semimodule of all linear recurring sequences over S. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity and M be an R-module. In this paper some properties of primary and classical primary submodules will be investigated. It is shown that if F is a faithfully flat R-module, then Q is a primary submodule of M if and only if F ⊗ Q is a primary submodule of F ⊗ M. Also some characterization of classical primary submodules are given. Furthermore, the existence of (minimal) primary submodules containing classical primary submodules are investigated. [ABSTRACT FROM AUTHOR]

The integral operator Lmp (λ, ℓ)(λ, ℓ > 0; p ∈ N; m ∈ N0 = N ∪ {0}, where N = {1, 2, ...}) for functions of the form f(z) = z-p + P∞k=p+1 akzk which are analytic and p-valent in the punctured open unit disc U∗ = {z ∈ C : 0 < |z| < 1} = U\{0} was introduced by El-Ashwah [7]. The objective of the present paper is to extend the definition of the operator Lmp (λ, ℓ)f(z) for m ∈ Z = {0, ±1, ±2, ...} and drive interesting argument results of p-valent meromorphic functions defined by this differintegral operator. [ABSTRACT FROM AUTHOR]

In this paper, we show that the number of members of Sn avoiding any one of five specific triples of 4-letter patterns is given by sequence A111279, which is known to count weak sorting permutations. By numerical evidence, there are no other (non-trivial) triples of 4-letter patterns giving rise to this sequence. We make use of a variety of methods [5, 6] in proving our result, including recurrences, the kernel method, direct counting, and bijections. [ABSTRACT FROM AUTHOR]

The quantum matrix algebra Mq(2) can be constructed through Ore extension. This is used to construct Mq(2)-modules from modules over its subalgebra. In this paper, we illustrate this approach and for a particular module over the subalgebra we determine all submodules of the induced Mq(2)-module for either q being a root of unity or not. [ABSTRACT FROM AUTHOR]

Let R be a semiprime ring and F : R → R a mapping such that F(xy) = F(y)x+yd(x) for all x, y ∊ R, where d is any map on R. In this paper, we investigate the commutativity of semiprime rings with a mapping F on R. Several theorems of commutativity of semiprime rings are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we identify the (0, *)-ideals of a demi-pseudocomplemented MS-algebra L as the kernel of the boolean congruences on L. In particular, we show that these ideals are precisely the kernels of the congruences # on L such that (L/v; *) is boolean, and that they form a sublattice of the lattice of ideals of L that is isomorphic to the interval [G, ι] of the congruence lattice of L where G is the Glivenko congruence and ι is the universal congruence. [ABSTRACT FROM AUTHOR]

In this paper, we define a Quasi Heyting ADL and derive some necessary and sufficient conditions for an SHADL to become a Quasi Heyting ADL.We also define the concept of an Almost Semi Heyting Algebra and derive some equivalent conditions for an ADL (L,⋁,⋀, 0) with a binary operation → and a maximal element m, to become an Almost Semi Heyting Algebra. [ABSTRACT FROM AUTHOR]

In this paper, the concept of essentially critically compressible modules are introduced, and related properties are investigated. The concept of essentially critically compressible modules are generalization of critically compressible modules discussed by Zelmanowitz. We have also provided some characterization of critically compressible modules in terms of CS modules, nonsingular modules, continuous modules and cyclic modules. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of 2-primal ideal in semiring and studied it. [ABSTRACT FROM AUTHOR]

In this paper, we extend the concept of completely regular semirings and study some properties. Also we prove that, if S is a completely regular semiring and S is almost idempotent semiring, then S is an idempotent semiring. [ABSTRACT FROM AUTHOR]

Hv-structures are hyperstructures where the equality is replaced by the nonempty intersection. Therefore, this class of the hyperstructures is very large, one can use it in order to define several objects that they are not possible to be defined in the classical hypergroup theory. In the present paper we focus on the large classes of P-hyperstructures and ∂-hyperstructures. We introduce and study a property on inverse elements. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the concepts of several separation axioms between the T0 and T1 spaces. We also characterize the modules such as the pm-module, m-module, ε-module, ES-module, D-module and Y-module. Some new results of the prime spectrum of a module M over a commutative ring R are given. [ABSTRACT FROM AUTHOR]

In this paper, new proofs for Post's and Markov's examples of finitely presented semigroups with unsolvable word problem are presented by using Newman lemma and Composition-Diamond lemma. [ABSTRACT FROM AUTHOR]

In this paper, we give new common fixed point theorems on cone metric space. [ABSTRACT FROM AUTHOR]

In this paper, we give a characterization for a CR-submanifold of a Kaehler manifold to be a CR-warped product submanifold in terms of the canonical structures P and F. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class κ -- UCV(λ, γ, β, δ ) of analytic univalent functions with negative coefficients. This class is based on an integral operator Qβδ of the function f(z). We obtain some neighbourhoods results. Partial sums hm(z) of the functions f(z) in this class are considered. Also we study coefficient bounds, extreme points and radius of close-to-convexity, starlikeness and convexity of this class. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of the extension ≪ A; I ≫ of an ordered ideal I by a set A in a po-Γ-semigroup M and many properties of ≪ A; I ≫ are provided. Moreover, the equivalence relation ΦI on M defined by (x; y) ∈ ΦI ⇔≪ x; I ≫=≪ y; I ≫ is considered. It is shown that if M is commutative and I is an ordered s-semiprime ideal, then ΦI is an ordered semilattice congruence. Moreover, if I is an ordered prime ideal of M, then (x; y) ∈ ΦI ⇔ x; y ∈ I or x; y ∉ I. [ABSTRACT FROM AUTHOR]

We observe that a lobster with diameter at least five has a unique path H = x1, x2, . . . , xm with the property that, besides the adjacency in H, both x1 and xm are adjacent to the centers of at least one K1,s, where s > 0, and each xi, 2 ≤ i ≤ m-1, is at most adjacent to the centers of some K1,s, where s ≥ 0. This unique path H is called the central path of the lobster. We call K1,s an even branch if s is nonzero even, an odd branch if s is odd, and a pendant branch if s = 0. In this paper, we develop methods to get interlaced and graceful lobsters by joining smaller lobsters satisfying certain conditions. The interlaced and graceful lobsters we obtain here may have distinct features than those exist in literature [2], [5], [6], [7], [8], [9], and [11] that (i) some vertices on the central path need not be attached to any non-pendant branch and (ii) some vertices on the central path may have degree odd. We also prove that all diameter four trees other than the caterpillars are not interlaced. [ABSTRACT FROM AUTHOR]

In a recent paper, L.A. Bokut, V.V. Chaynikov and K.P. Shum have established a theorem of braid group Bn by applying Artin relations. For such a representation, it points out that all other compositions can be checked in the same way. In this note, we reconfirm such claim and check some more compositions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some necessary optimality conditions and sufficient optimality conditions of the bilevel multiobjective programming problems by using the theorem of alternative introduced by Z. Li in 1999 for set-valued maps, under the assumption of cone-subconvexlikeness for set-valued maps. [ABSTRACT FROM AUTHOR]

In the present paper, we study the rate of convergence in simultaneous approximation for the the recently introduced generalization of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the notions of weakly α-I-open sets and weakly α-I-continuous functions to obtain a new decomposition of continuity. We also investigate some fundamental properties of such functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the Kantorovich form of Stancu operators. As particular cases, we obtain similar properties for the Kantorovich form for Bernstein, Schurer and Schurer-Stancu operators. [ABSTRACT FROM AUTHOR]

Yamada first described the semidirect product structure of left (right, quasi-) inverse semigroups in 1973. Later, Sen, Ghost and Pal gave the structure and characteristics of LR-regular orthogroups. The subdirect product and dually-semidirect structure of LR-inverse semigroups were further given by Du and Guo. In this paper, we consider the subdirect product of the so-called WLR-inverse semigroups. This kind of semigroups forms a common generalization of left (right) inverses, LR-inverse semigroups and LR-regular orthogroups. [ABSTRACT FROM AUTHOR]

Dependence relation on a set is an important concept in universal algebra. In this paper, we prove the equivalence of three different kinds of dependence systems. [ABSTRACT FROM AUTHOR]

In this paper, we define β-insulator and strongly prime Γ-rings. We also prove that the following main results: (i) If a Γ-ring M is weakly semiprime then M is strongly prime if and only if its left operator ring L is right strongly prime and its right operator ring R is left strongly prime. (ii) If M is strongly prime Γ-ring,then their left and right operator rings are Morita equivalent. [ABSTRACT FROM AUTHOR]

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G)̲ satisfies s ≈ t. A graph G = (V;E) is called a right self-distributive graph if the graph algebra A(G)̲ satisfies the equation ((xy)z) ≈ ((xz)(yz)). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced by any term operations of A̲ of the appropriate arity, the resulting identities hold in A̲. In this paper, we characterize right self-distributive graph algebras, identities and hyperidentities in right self-distributive graph algebras. [ABSTRACT FROM AUTHOR]

For a group G, and a subset S of G such that 1G ∉ S, let Γ = Cay(G, S) be a Cayley graph. Then Γ is said to be arc-transitive, if Aut(Γ) is transitive on arc set. In this paper we give a complete classification for arc-transitive Cayley graphs of valency five on finite abelian groups. [ABSTRACT FROM AUTHOR]

The triangle groups Δ(2; 3; k) are infinite whenever k ≥ 6. Finite triangle groups are trivial, S3, A4, S4, and A5 for k = 1, 2, 3, 4, and 5 respectively. When k = 6, Δ(2; 3; 6) is an extension by the cyclic group C6 of a free abelian group of rank 2 and in particular is soluble. For k = 7, the triangle group Δ(2; 3; k) becomes a Hurwitz group. In this paper we develop a graphical technique to obtain these groups as permutation groups through the actions of PGL(2;Z) on the projective lines over finite fields Fq. [ABSTRACT FROM AUTHOR]

The structure theorem of strictly π-regular semigroups have been given by B.J. Yu in 1990. This structure generalized the structure theorem of a completely regular semigroup given by M. Petrich in 1974. In this paper we consider the isomorphism problem between two strictly π-regular semigroups. A necessary and sufficient condition for two strictly π-regular semigroups to be isomorphic is obtained. As a direct corollary of this result, we also obtain an isomorphism theorem for two completely regular semigroups to be isomorphic. [ABSTRACT FROM AUTHOR]

In this paper, we establish a set of necessary efficiency criteria and discuss several sets of global semiparametric sufficient efficiency conditions under various generalized (α, η, ρ)-V-invexity assumptions for a semiinfinite multiobjective fractional programing problem. [ABSTRACT FROM AUTHOR]

Let Ap(p ∈ N) be the class of functions ƒ(z) = zp + ap+1zp+1 + ... analytic in the unit disk. By usiug the Ruscheweyh derivative, we introduce a subclass Tp(c, α, λ, μ) of Ap which is relevant to the classes of starlike and convex functions. The object of the present paper is to discuss some properties of functions in the class Tp(c, α, λ, μ). [ABSTRACT FROM AUTHOR]

In this paper, we shall introduce ultra Bessel sequences in separable Hilbert spaces (i.e., Bessel sequences with uniform convergence property) and we shall see that no frame in an infinite dimonsional Hilbert space can be an ultra Bessel sequence, but each frame in a finite dimension Hilbert space is an ultra Bessel sequence . We shall also show that for each frame in a finite dimensional Hilbert space there exists a bound of frameness. [ABSTRACT FROM AUTHOR]

In this paper, as an application of π-partial characters of a finite π-separable group G, without using the well-known theorem of Schur-Zassenhaus, we show that if H1 and H2 are Hall π-subgroups of G, then for every conjugacy class K of G we have |H1 ∩ K| = |H2 ∩ K|. [ABSTRACT FROM AUTHOR]

The aim of the paper is to prove some existing results of random best approximation for R--subcommutaitve maps with affineness condition in the setting of convex metric space. As consequence, our works generalize the recent results of Nashine [13] and the result of Beg and Shahzad [2]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class Ap*(r, j, β, a, A, B) of meromorphic p-valent functions that satisfy z(Ip(r, λ)f(z))(j+1)/(Ip(r, λ)f(z))(j) ≺ (1 + A - B/a βz/1 + Bz) (p + j), z ∈ Δ*, where β is a complex number. Also we study coefficient inequalities and δneighbourhood and have found distortion bounds. We investigate some interesting properties on Ap* (r, j, β, a, A, B); too. [ABSTRACT FROM AUTHOR]