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The purpose of the paper is to study the uniqueness of meromorphic functions sharing a small function with finite weight. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [21]. We also solve an open problem as posed in the last section of [21].

In this paper, we investigate the relationship between dual (Weak) Subtraction algebras, Heyting algebras and BE-algebras. In fact, the purpose of this paper is to show that BE-algebra is a generalization of Heyting algebra and dual (Weak) Subtraction algebras. Also, we show that a bounded commutative self distributive BE-algebra is equivalent to the Heyting algebra.

In this paper the authors introduced a new generalized differintegral operator for meromorphic univalent functions in U* = {z : z ∈ C, 0 < |z| < 1}. The objective of this paper is to establish certain results concerning the Hadamard product of functions in the classes ∑^{∗,m}_{μ,λ} (α, β , γ, k) and ∑^h_{μ,λ} (α, β , γ, k).

In this paper, we prove various existence results of a mild solution for a fractional nonlocal functional semilinear differential inclusion involving Caputo derivative in Banach spaces. We consider the case when the values of the orient field are convex as well as nonconvex. Moreover, we study the topological structure of solution sets. Our results extend or generalize results proved in recent papers.

This paper deals with the study of two-dimensional Saigo-Maeda operators of Weyl type associated with Aleph function defined in this paper. Two theorems on these defined operators are established. Some interesting results associated with the H-functions and generalized Mittag-Leffler functions are deduced from the derived results. One dimensional analog of the derived results is also obtained.

The paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interval. The paper also investigates a few properties concerning the convergence of powerseries, Taylor's expansion around a point and the order of a zero.

In this paper, we investigate the transportation problem with fractional objective function when the demand and supply quantities are varying. A set of mathematical programs is obtained to determine the objective value. Due to varying economic policies in the global world, it is hard to specify the supply and demand quantities for transportation problem. A transportation problem with fractional objective function is based on a network structure consisting of a finite number of nodes and arcs attached to them. After the derivation, we obtained the result in range, where the total transportation cost would appear. In addition to allowing for simultaneous changes in supply and demand values, the total cost bounds are calculated directly. This methodology would be very beneficial in the decision making. A numerical example has given in this paper for the support of theory.

In a paper in 2008, Herzog, Hibi and Ohsugi introduced and studied the semigroup ring associated to the set of minimal vertex covers of an unmixed bipartite graph. In this paper we relate the dimension of this semigroup ring to the rank of the Boolean lattice associated to the graph.

A famous conjecture by R. Stanley relates the depth of a module, an algebraic invariant, with the so-called Stanley depth, a geometric one. We describe two related geometric notions, the cover depth and the greedy depth, and we study their relations with the Stanley depth for Stanley-Reisner rings of simplicial complexes. This leads to a quest for the existence of extremely non-partitionable simplicial complexes. We include several open problems and questions.This paper is a report about a research project suggested by J. Herzog at the summer school P.R.A.G.MAT.I.C. 2008 at the University of Catania. In particular, the paper describes a direction where we expect that possible counterexamples can be found at least for a weaker version of Stanley’s conjecture.

Using the results in papers [2] and [3] in this paper we prove the existence of the interpolating spline-function by the null space dimension of operators A and T.

In the papers [9], [10] we introduced and studied M_λ -hypergroupoids; also, we obtained some results on the automorphism group of a G_ λ -hypergroupoid. In particular, given a group G and one of its element λ, we proved that the automorphisms of the corresponding G_λ -hypergroupoid are the one-one maps f : G → G which are λ-linea.A natural generalization of the notion of λ-linearity is the notion of (h, A, B)-linearity, introduced in the present paper. Theorem 1.7 provides the existence and uniqueness of a (h, A, B)-linear map. Theorem 2.3 gives the cardinality of the group Λ(G A ) of complete, bijective (h, A)-linear maps. In Theorem 2.7 we prove that Λ(G A ) is a semi-direct product.The notion of M_A -hypergroupoid is defned in the last section, via group actions on sets. We also study their homomorphisms and prove that the M_A -hypergroupoid is a hypergroup or a join-space according to the set A being a stable part or a subgroup of G.

In this paper we forward in the investigation of the matroidal M_λ -hypergrupoids introduced in [13]. We give necessary and sufficient conditions for such hypergrupoid to be matroidal; moreover, we find its cardinality and we analyse the properties of the corresponding omomorphisms. The paper gives also a characterization of the group Λ(G_λ), that is the one of the automorphisms of the hypergroupoid G λ ; this hypergroupoid is obtained by a given group G, an element of its λ and the action of G on G determined by the same operation of G.

In this paper, we introduce and study a new class of variational inequalities, which is called generalized set-valued variational inequality. The projection technique is used to establish the equivalence among generalized set-valued variational inequalities, fixed point problems and generalized set-valued Wiener-Hopf equations. This equivalence is used to study the existence of a solution of set- valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities. We also consider the auxiliary principle technique to study the existence of a solution of the generalized set-valued variational inequalities and to suggest a general and novel iterative algorithm. In addition, we have shown that the auxiliary principle technique can be used to find the equivalent differentiable optimization problem for the generalized set-valued variational inequalities. The results proved in this paper represent a significant refinement and improvement of the previous results.

This paper presents some preliminary results arising within a general framework concerning the development of software tools for fuzzy arithmetic. The program is in a preliminary stage. What has been already implemented consists of a set of routines for elementary operations, optimized functions evaluation, interpolation and regression. Some of these have been applied to real problems.This paper describes a prototype of a library in C++ for polynomial interpolation of fuzzifying functions, a set of routines in FORTRAN for fuzzy linear regression and a program with graphical user interface allowing the use of such routines.

In this paper we present quantitative analysis of the stability set of the first kind of stochastic multiobjective programming problems with random coefficients in the multiobjective functions. Using Kuhn-Tucker conditions and some statistical theorems, the authors determine the set of all random parameters that make the solution of our concerned problem be stable. An illustrative example is given to clarify the development theory in this paper.

If the collisions are redefined as a flux a kinetic conservation law can be written in divergence form. This can be handled numerically, in the framework of Finite Particle Approximation, using the CRF-method. In this paper we use the CRF-method for semiconductors' intravalley collision kernels. We extend the results obtained in a previous paper to the case of a 3D momentum space.

The paper is a review of shock wave propagation problems for inert and chemically reacting gases in the framework of discrete velocity models (Discrete Boltzmann Equation, DBE). The paper is divided in two parts. The former deals with the formulation of shock wave problems and with a review of results. The latter takes into account open problems and addresses the reader to future lines of research.

The problem of finding the splitting field for group characters is very old and important (see [4], Chapter 9). The most part of the papers on this subject are concerned with all irreducible characters of a group under certain conditions. It seems more difficult to obtain minimal splitting fields for only one character without strong conditions about the group. In this case, naturally,the number theoretical methods play an essential role. This paper concerns to prove that under certain circumstances if a rational character of a group has Q(21/2,i) as splitting field, then Q(i) or even Q(21/2) are splitting fields too.

This paper surveys various decidability results in the set theory. In the first part, we focus on certain classes of unquantified set-theoretic formulae involving the relations ∊ “membership”, = “equality”, and the operators ⋂ “intersection”, ⋃ “binary union”, \ “set difference”, ⋅ “singleton”, pow “powerset”, Un“general union”, η “choice operator”, etc. The unquantified theory basic to the results presented is the so called Multilevel Syllogistic (MLS) which is the set of all quantifier-free formulae in the language ∊, =, ⋂, ⋃ ,\ . The second part of the paper covers the quantified case and, among others, we consider: a quantified version of MLS, the class of formulae quantified over sets in which the membership predicate is not allowed, the class of prenex set-theoretic formulae having three quantifiers and the class having a prefix of the form ∀∀ ... ∀∃ . In the third part, some applications to domains different from pure set theory will be reviewed. Some undecidability results will be discussed in the last section. An appendix on Zermelo-Fraenkel set-theory concludes the paper.

This paper introduces a novel way to compute the membership function of a fuzzy set approximating the distribution of some observed data starting with their histogram. This membership function is in turn used to obtain a posteriori probability through a suitable version of the Bayesian formula. The ordering imposed by an overtaking relation between fuzzy numbers translates immediately into a dominance of the a posteriori probability of a class over another for a given observed value. In this way a crisp classification is eventually obtained.

In this paper we study different applications of the inclusion relationships, radius problems and some other interesting properties of p-valent functions which are defined by integral operator.

This paper examines the relationship between the concept of bounded index and the radius of equivalence, respectively p-valence, of entire bivariate functions and their partial derivatives at arbitrary points in C^2.

The object of this paper is to introduce a new special function, which will be called S-function. This function is an extension of the generalized Mittag-Leffler function due to Prabhakar [7], generalized Mittag-Leffler function introduced by Srivastava and Tomovski [14] and M-series given by Sharma and Jain [13], various integral transform of this function such as Euler transform, Laplace transform, Whittaker transform, K-transform are derived. The results obtained are useful in applied problems of science, engineering and technology.

In this paper, we obtain some fixed point theorems for dominated mappings satisfying locally contractive conditions on a closed ball in a left K-sequentially O-complete ordered quasi-partial metric space and in a right K-sequentially O-complete ordered quasi-partial metric space, respectively. Our results improve several well known results.

The effect of Marichev-Saigo-Maeda (MSM) fractional operators involving third Appell function on the $I$ function is studied. It is shown that the order of the $I$-function increases on application of these operators to the power multiple of the $I$-function. The Caputo-type MSM fractional derivatives are introduced and studied for the $I$-function. As special cases, the corresponding assertions for Saigo and Erd\'elyi-Kober fractional operators are also presented. The results obtained in this paper generalize several known results obtained recently in the literature.

The objective of this paper is to obtain an upper bound to the second Hankel determinant for the function f and its inverse belonging to the class of pre-starlike functions of order alpha (0 ≤ alpha ≤ 1), using Toeplitz determinants.

Bornological and b-bornological locally convex cones have studied in [D. Ayaseh and A. Ranjbari, Bornological Locally Convex Cones, Le Matematiche, Vol. LXIX (2014) Fasc. II, pp. 267-284]. In this paper, we obtain new results on bornological locally convex cones and present an example of nonbornological locally convex cone. We show that the projectivelimit of bornological cones is not bornological in general. Also, we present a bornological locally convex cone which is not b-bornological.

This paper is devoted to define the q^2-Sobolev type spaces on R_q by using the q^2-analogue Fourier transform and its inverse. In particular, we provide the readers for some embedding results with these spaces.The next part is devoted to the study of the related q^2-potential analysis and some of its properties.

In this paper, we define the q-analogue of Mellin Transform symmetric under interchange of q and 1/q, and present some of its main properties and explore the possibility of using the integral transform to solve a class of differential equations q-differences.

The purpose of this paper is to establish some types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit fractional-order differential equation.

An L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of non-negative integers such that |f(x)-f(y)|\ge 2 if x and y are adjacent and |f(x)-f(y)|\ge 1 if x and y are at distance 2, for all x and y in V(G). A k-L(2,1)-labeling is an L(2,1)-labeling f:V(G) to {0,...,k}, and we are interested to find the minimum k among all possible assignments. This invariant, the minimum k, is known as the L(2,1)-labeling number or λ-number and is denoted by λ(G). In this paper, we determine the λ-number for the coronas P_m \circ P_n, P_m\circ C_n, P_m \circ K_{1,n} and P_m\circ W_n and find an upper bound of the λ-number for the corona G_1 \circ G_2 where G_1 and G_2 are any two graphs such that G_2 has an injective L(2,1)-labeling and also we prove that the bound is attainable when G_1 and G_2 are complete. Also we present an upper bound of the $\lambda$-number for the corona G_1 \circ G_2 where G_1 and G_2 are any two graphs.

In the present paper, we define a generalized composite fractional q-derivative D^{\alpha,\beta,\nu}_q and obtain some results for it. These results are image of power function under D^{\alpha,\beta,\nu}_q, composition of Riemann-Liouville type fractional q-integral I^\alpha_q with D^{\alpha,\beta,\nu}_q and q-Laplace transform of D^{\alpha,\beta,\nu}_q. We also obtain solution of a q-difference equation with derivative as D^{\alpha,\beta,\nu}_q and discuss some special cases. A q-difference equation of D^{\alpha,\beta,\nu}_q is solved using q-Laplace transform and its inverse.

Let X⊂ P^n be a linearly normal elliptic curve. For any P in P^n the X-rank of P is the minimal cardinality of a set S ⊂ X such that P in \langle S \rangle.In this paper we give an almost complete description of the stratification of P^n given by the X-rank and the open X-rank.

Residuated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice.

In this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson's polynomials Φ_{n}^{(α)}(x,ν) of degree n and order α introduced by Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli polynomials B_n(x), generalized Bernoulli numbers B_n(a,b), generalized Bernoulli polynomials B_n(x;a,b,c) of Luo et al, Hermite-Bernoulli polynomials {_HB}_n(x,y) of Dattoli et al and {_HB}_n^{(α)} (x,y) of Pathan are generalized to the one {_HB}_n^{(α)}(x,y,a,b,c) which is called the generalized polynomial depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B_n, B_n(x), B_n(a,b), B_n(x;a,b,c) and {}_HB_n^{(α)}(x,y;a,b,c) are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli numbers and polynomials

In the present paper, authors introduce and study a new class of Salagean-type harmonic univalent functions that have fixed finitely many coefficients. We obtain coefficient conditions, extreme points, convolution condition, convex combinations for the above class of harmonic univalent functions.

Let R = S/I where S = k[T_1, . . . , T_n] and I is a homogeneous ideal in S. The acyclic closure R of k over R is a DG algebra resolution obtained by means of Tate’s process of adjoining variables to kill cycles. In a similar way one can obtain the minimal model S[X], a DG algebra resolution of R over S. By a theorem of Avramov there is a tight connection between these two resolutions. In this paper we study these two resolutions when I is the edge ideal of a path or a cycle. We determine the behavior of the deviations ε_i (R), which are the number of variables in R in homological degree i. We apply our results to the study of the k-algebra structure of the Koszul homology of R.

‎For a ring endomorphism α of a ring R, ‎Krempa called α a rigid endomorphism if aα(a)=0 implies a = 0 for a in R. ‎A ring R is called rigid if there exists a rigid endomorphism of R. ‎In this paper‎, ‎we extend the α-rigid property of a ring R to the upper nilradical N_r(R) of R. ‎For an endomorphism α and the upper nilradical N_r(R) of a ring R, ‎we introduce the condition (*): ‎N_r(R) is a α-ideal of R and aα(a) in N_r(R) implies a in N_r(R) for a in R. ‎We study characterizations of a ring R with an endomorphism α satisfying the condition (*), ‎and we investigate their related properties‎. ‎The connections between the upper nilradical of R and the upper nilradical of the skew Hurwitz series ring (HR,α) of R are also investigated‎.

In this paper, we introduce a new class of analytic p-valent functions defined in the open unit disc by using convolution and obtain some results including coefficient inequality, distortion theorems, Hadamard products, radii of starlikeness and convexity and closure theorems of functions in this class.

In the present paper we introduce Fibonacci difference sequence spaces l(F, Ƒ, p, u) and l_∞(F, Ƒ, p, u) by using a sequence of modulus functions and a new band matrix F. We also make an effort to study some inclusion relations, topological and geometric properties of these spaces. Furthermore, the alpha, beta, gamma duals and matrix transformation of the space l(F, Ƒ, p, u) are determined.

In this paper we construct vector bundles over a multiprojective space and study their properties. We first set out to establish the existence of monads on a multiprojective space X. Then, we study the vector bundles associated to these monads.

The fifth geometric-arithmetic index of a graph $G$ is defined to be GA_5(G). This index was introduced by A. Graovac et al. in 2011. In this paper, we give explicit formulas for the fifth geometric-arithmetic index of a family of Hexagonal Nanotubes namely: Armchair Polyhex Nanotubes.

The purpose of this paper is to prove that if the Pták function p is an operator norm, on \mathcal{B}(E), associated to a norm | . |, then (E, | . |) is a pseudo-Hilbert space. As a consequence, we obtain that if \mathcal{B}(E) is a C*-algebra, then E is a Hilbert space.

In this paper, we introduce and investigate two new subclasses of the functionclass\sigma of bi-univalent functions dened in the open unit disk, which are associated with thegeneralized Srivastava-Attiya operator, satisfying subordinate conditions. Furthermore, we ndestimates on the Taylor-Maclaurin coecients |a_2| and |a_3| for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

Our purpose in this paper is to define a linear operator F_{p,q,s}[\alpha_{1},m], then applying it to obtain some results on subordination and superordination preserving properties of holomorphic multivalent functions in the open unit disc. And sandwich-type result for these holomorphic multivalent functions is also considered.

In this paper, by making use of convolution, we obtain some interesting results for certain family of meromorphic p-valent functions defined by new linear operator.

In this paper, we derive several subordination results for a certain class of analytic functions defined by the generalized Al-Oboudi differential operator. Relevant connections of some of the results obtained with those in earlier works are also provided.

The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, and convex combinations for a new class of harmonic univalent functions in the open unit disc \ associated with the Salagean operator. We also discuss a class preserving integral operator. Relevant connections of the results presented here with various known results are briefly indicated.

In this paper, The author introduces the concepts of the GA-s-convex functions in the first sense and second sense and establishes some integral inequalities of Hermite-Hadamard type related to the GA-s-convex functions. Some applications to special means of real numbers are also given.

In this paper, we establish a q-analogue of Hermite-Hadamard inequalities for some convex type functions.