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In the present paper, we expand the domain of work on theconcept of semiderivations in 3-prime near-rings through the study ofstructure and commutativity of near-rings admitting semiderivations sat-isfying certain differential identities. Moreover, several examples havebeen provided at places which show that the assumptions in the hypothe-ses of various theorems are not altogether superfluous. 1. IntroductionThroughout this paper, N is a zero-symmetric left near ring. A near ringN is called zero symmetric if 0x= 0 for all x∈ N (recall that in a left nearring x0 = 0 for all x∈ N). N is called 3-prime if xNy = {0} implies x= 0or y = 0. The symbol Z(N) will represent the multiplicative center of N,that is, Z(N) = {x∈ N | xy= yxfor all y∈ N}.For any x,y∈ N; as usual[x,y] = xy−yxand x◦y= xy+yxwill denote the well-known Lie product andJordan product, respectively. Recall that N is called 2-torsion free if 2x= 0implies x= 0 for all x∈ N. For terminologies concerning near-rings we referto G. Pilz [7].An additive mapping d: N → N is said to be a derivation if d(xy) = xd(y)+d(x)yforall x,y∈ N, orequivalently, asnotedin [8], that d(xy) = d(x)y+xd(y)for all x,y ∈ N. An additive mapping d: N → N is called semiderivation ifthere exists a function g : N → N such that d(xy) = xd(y) + d(x)g(y) =g(x)d(y)+d(x)yand d(g(x)) = g(d(x)) for all x,y∈ N.Obviously, any deriva-tion is a semiderivation, but the converse is not true in general (see [6]). Therehas been a greatdeal of workconcerning derivations in near-rings(see [1, 2, 4, 5]where further references can be found). In this paper, we study the commuta-tivity of addition and multiplication of near-rings. Two well-known results forderivations in near-rings have been generalized for semiderivation. In fact, ourresults generalize some theorems obtained by the authors together with Rajiin [1].

In this paper we study the regularity of inside (or outside)(θ,φ)-derivations in BCI-algebras X and provethat let d (θ,φ) :X → Xbe an inside (θ,φ)-derivation of X. If there exists a ∈ X such thatd (θ,φ) (x)∗ θ(a) = 0, then d (θ,φ) is regular for all x ∈ X. It is alsoshownthatifX isaBCK-algebra,theneveryinside(oroutside)(θ,φ)-derivation of X is regular. Furthermore the concepts of θ-ideal, φ-idealand invariant inside (or outside) (θ,φ)-derivations of X are introducedand their related properties are investigated. Finally we obtain the fol-lowingresult: Ifd (θ,φ) :X → X isanoutside(θ,φ)-derivationofX,thend (θ,φ) isregularifandonlyifevery θ-idealofX isd (θ,φ) -invariant. 1. IntroductionThroughout the present paper X will denote a BCI-algebra unless otherwisementioned. Jun and Xin [4] defined the notion of derivation on BCI-algebrasas follows: A self map d : X → X is called a left-right derivation (briefly an(l,r)-derivation) of X if d(x ∗ y) = d(x) ∗ y ∧ x ∗ d(y) holds for all x,y ∈ X.Similarly, a self map d : X → X is called a right-left derivation (briefly an (r,l)-derivation) of X if d(x∗y) = x∗d(y)∧d(x)∗y holds for all x,y ∈ X. Moreover,if d is both (l,r)- and (r,l)-derivations, it is a derivation on X. Following [11],a self map d

The paper deals with the problem of meromorphic functionssharing a small function with its differential polynomials and improvesthe results of Liu and Gu [9], Lahiri and Sarkar [8], Zhang [13] and Zhangand Yang [14] and also answer some open questions posed by Kit-Wing Yu[16]. In this paper we provide some examples to show that the conditionsin our results are the best possible. 1. Introduction, definition and resultsIn this paper by meromorphic functions we will always mean meromorphicfunctions in the complex plane.Let f and g be two non-constant meromorphic functions and let a be a finitecomplex number. We say that f and g share a CM, provided that f − a andg − a have the same zeros with the same multiplicities. Similarly, we say thatf and g share a IM, provided that f −a and g−a have the same zeros ignoringmultiplicities. In addition we say that f and g share ∞ CM, if 1/f and 1/gshare 0 CM, and we say that f and g share ∞ IM, if 1/f and 1/g share 0 IM.We adopt the standard notations in Nevanlinna’s value distribution theoryof meromorphic functions such as the characteristic function T(r,f), the count-ing function of the poles N(r,∞;f) and the proximity function m(r,∞;f) (see[10]). For a non-constant meromorphic function f we denote by S(r,f) anyquantity satisfying S(r,f) = o(T(r,f)) as r → ∞, outside of a possible ex-ceptional set of finite linear measure. Let k ∈ N and a ∈ C∪ {∞}. We useN

In 1812, Gauss obtained fifteen contiguous functions rela- tions. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper (16) published in Com- puter & Mathematics with Applications 61 (2011), 620-629. In this paper, first we obtained 15 q-contiguous functions relations due to He- nie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting q- contiguous functions relations. These q-contiguous functions relations have wide applications.

The object of the present paper is to introduce a new curva-ture tensor, named generalized quasi-conformal curvature tensor whichbridges conformal curvature tensor, concircular curvature tensor, pro-jective curvature tensor and conharmonic curvature tensor. Flatness andsymmetric properties of generalized quasi-conformal curvature tensor arestudied in the frame of (k,µ)-contact metric manifolds. 1. IntroductionIn 1968, Yano and Sawaki [27] introduced the notion of quasi-conformalcurvature tensor which contains both conformal curvature tensor as well asconcircular curvature tensor, in the context of Riemannian geometry. In tunewith Yano and Sawaki [27], the present paper attempts to introduce a newtensor field, named generalized quasi-conformal curvature tensor. The beautyof generalized quasi-conformal curvature tensor lies in the fact that it has theflavour of Riemann curvature tensor R, conformal curvature tensor C [8] con-harmonic curvature tensor Cˆ [9], concircular curvature tensor E [26, p. 84],projective curvature tensor P [26, p. 84] and m-projective curvature tensor H[15], as particular cases. The generalized quasi-conformal curvature tensor isdefined asW(X,Y)Z =2n−12n+1[(1−b+2na)−{1+2n(a+b)}c]C(X,Y )Z+[1−b+2na]E(X,Y)Z +2 n (b−a) P(X,Y )Z+2 n−12 n+1(1.1) (c −1){1+2 n(a +b)} Cˆ(X,Y)Zfor all X,Y,Z ∈ χ(M), the set of all vector field of the manifold M, where a,b and c are real constants. The above mentioned curvature tensors are defined

The aim of this paper is to present some properties of sT- continuous functions. Moreover, we obtain a characterization and pre- serving theorems of semi-compact, S-closed and s-closed spaces. The study of semi-open sets and semi-continuity in topological spaces was initiated by Levine (10). In 2009, Noiri et al. (13) defined the notion T-open sets and deduced some results. Quite recently, Al-omari et al. (1) have obtained some properties of T-open sets and characterizations of S-closed spaces. In this paper, we present some properties of sT-continuous functions. Moreover, we obtain characterizations and preserving theorems of semi-compact, S-closed and s-closed spaces. 2. Preliminaries Throughout this paper, (X,�) and (Y,�) stand for topological spaces on which no separation axiom is assumed unless otherwise stated. For a subset A of X, the closure of A and the interior of A will be denoted by Cl(A) and Int(A), respectively. Let (X,�) be a space and S a subset of X. A subset S of X is said to be semi-open (10) if there exists an open set U of X such that U ⊆ S ⊆ Cl(U), or equivalently if S ⊆ Cl(Int(S)). The complement of a semi-open set is said to be semi-closed. The intersection of all semi-closed sets containing S is called the semi-closure of S and is denoted by sCl(S). The semi-interior of S, denoted by sInt(S), is defined by the union of all semi-open sets contained in S. It is verified in (2) that sCl(A) = A ∪ Int(Cl(A)) and sInt(A) = A ∩ Cl(Int(A)) for any subset A ⊆ X. A point x ∈ X is said to be in the �-semiclosure of A, denoted by x ∈ �-sCl(A), if A ∩ Cl(V ) 6 � for each semi-open set V containing x. A subset A ⊆ X is said to be �-semiclosed (8) if A = �-sCl(A). The complement of a �-semiclosed set is called a �-semiopen

Let G be a cyclic group of prime power order. There is anatural embedding of Z[G] into a product of rings of integers of cyclotomicfields. In this paper the image of the embedding is determined, and wealso compute the index of the image. 1. IntroductionFor a finite abelian group Glet Z[G] be the integral group ring of G, andlet I G be the augmentation ideal. For each complex character χof Glet Q(χ)be the cyclotomic field generated by the values of χand Z[χ] be its ring ofintegers.ConsiderΦ : Z[G] −→Y χ∈Gb Z[χ]Φ(α) = (...,χ(α),...),where the domain of χis extended to Z[G] by linearity. The map Φ is aninjective ring homomorphism. The goal of this paper is to determine Φ(Z[G])when Gis cyclic of prime power order.For an elementβ= (...,β χ ,...) ∈Y χ∈Gb Z[χ],let us refer to its components β χ as the character values of β. We find that,when Gis cyclic of prime power order, we can express the necessary and suf-ficient condition for β∈ Φ(Z[G]) as congruence relations among the charactervalues of β. As a byproduct, we also compute the index of Φ(Z[G]) inQZ[χ].There are refined type of conjectures on the values of L-functions (cf. [1],[2], [4], [5]) which predict (among others) that certain elements ofQ

We study lightlike hypersurfaces of a semi-Riemannian spaceform fM(c) admitting a semi-symmetric non-metric connection. First, weconstruct a type of lightlike hypersurfaces according to the form of thestructure vector field of Mf(c), which is called a ascreen lightlike hyper-surface. Next, we prove a characterization theorem for such an ascreenlightlike hypersurface endow with a totally geodesic screen distribution. 1. IntroductionThe theory of lightlike submanifolds is an important topic of research in dif-ferential geometry due to its application in mathematical physics, especially inthe electromagneticfield theory. The study ofsuch notion wasinitiated by Dug-gal and Bejancu [3] and later studied by many authors (see up-to date resultsin two books [4, 5]). The notion of a semi-symmetric non-metric connectionon a Riemannian manifold was introduced by Ageshe and Chafle [1]. Recentlyseveral authors ([9]-[13]) studied lightlike hypersurfaces in a semi-Riemannianmanifold admitting a semi-symmetric non-metric connection. Most of authorsthat wrote on either lightlike hypersurfaces M of semi-Riemannian manifoldsMfadmitting semi-symmetric non-metric connections or lightlike hypersurfacesM of indefinite almost contact manifolds Mffail to treat with the case the struc-ture vector field ζ of Mfis not tangent to M, but studied only to the case ζis tangent to M (such M is called tangential lightlike submanifold ([9]-[13]) ofMf). There are few papers on non-tangential lightlike submanifolds of indefinitealmost contact manifolds studied by Jin ([6]-[8]).In this paper, we study non-tangential lightlike hypersurfaces of a semi-Riemannian space form admitting a semi-symmetric non-metric connection.There are several different types of non-tangential lightlike hypersurfaces ac-cording to the form of the structure vector field of the ambient manifold. We

The object of the present paper is to study a semi-symmetricmetric connection in an (e)-Kenmotsu manifold. In this paper, we studya semi-symmetric metric connection in an (e)-Kenmotsu manifold whoseprojective curvature tensor satisfies certain curvature conditions. 1. IntroductionThe idea of a semi-symmetric linear connection on a differentiable manifoldwasfirstintroducedby Friedmannand Schouten[11] in 1924. Hayden[12] intro-duced a semi-symmetric metric connection on a Riemannian manifold. Yano[21] proved the theorem: A Riemannian manifold admits a semi-symmetricmetric connection whose curvature tensor vanishes if and only if Riemannianmanifold is conformally flat. Semi-symmetric metric connections on a Rie-mannian manifold have been studied by Amur and Pujar [1], Pravanovic [15],Binh [4], De ([6], [7]), De and Biswas [8], Sharfuddin and Hussain [16], Pathakand De [14], Jun, De and Pathak [13], Barman and De [2], Chaubey and Ojha[5], Singh and Pandey [17], Singh, Pandey and Pandey ([18], [19]) and manyothers.Duggal and Sharma [10] studied a semi-symmetric metric connection in asemi-Riemannian manifold. They studied some properties of the Ricci tensor,affine conformal motions, geodesics and group manifolds with respect to thesemi-symmetric metric connection. On the other hand, the study of manifoldswith indefinite metrics is of interest from the standpoint of physics and relativ-ity. Manifolds with indefinite metrics have been studied by several authors. In1993, Bejancu and Duggal [3] introduced the concept of (e)-Sasakian manifoldsand Xufeng and Xiaoli [20] established that these manifolds are real hypersur-faces of indefinite Kahlerian manifolds. Recently De and Sarkar [9] introduced

In recent years, more and more mathematicians have studied the existence of solutions for degenerate elliptic problems. This comes from the fact that they arise in many areas of applied physics, including nuclear physics, field theory, solid waves and problems of false vacuum. These problems are introduced as models for several physical phenomena related to equilibrium of continuous media which somewhere be perfect insulators (see [8, 19]). However, the study have essentially based on the Caffarelli-Kohn-Nirenberg inequalities and their variants, see for example [6, 7, 9, 11, 14, 26] and the references therein. In this paper, we will study the existence of solutions for degenerate elliptic problems involving Grushin type operator Gs = ∆x + |x| ∆y for s ≥ 0. To our knowledge, the Grushin type operators were firstly introduced in [10], and developed in [13, 15, 17, 22, 23, 24, 25]. Let Ω ⊂ R = R1 ×R2 be a bounded domain with smooth boundary ∂Ω, and 0 ∈ Ω. In this paper, we are interested in the semilinear elliptic system with Grushin type operator

This paper investigates mean square exponential dissipativ-ity of singularly perturbed stochastic delay differential equations. TheL-operator delay differential inequality and stochastic analysis techniqueare used to establish sufficient conditions ensuring the mean square expo-nential dissipativity of singularly perturbed stochastic delay differentialequations for sufficiently small e > 0. An example is presented to illus-trate the efficiency of the obtained results. 1. IntroductionSingularlyperturbed delaydifferentialequationsisordinarydifferentialequa-tions in which the highest derivative are multiplied by a small parameter andinvolving at least one delay term. These equations arise naturally in a widevariety of engineering applications, representative examples include catalyticcontinuous stirred-tank reactors [1], biochemical reactors [3], fluidized catalyticcrackers [15], flexible mechanical systems [5], electromechanical networks [2],etc. In recent years, in a number of papers [4, 8, 10, 18, 19, 20], the stabil-ity, dissipativity and other behaviors of singularly perturbed delay differentialequations are considered.However, in addition to delay effects and singular perturbation, stochasticeffects likewise exist in real systems. Many dynamical systems have variablestructures subject to stochastic abrupt changes, which may result from abruptphenomena such as stochastic failures and repairs of the components, changesin the interconnections of subsystems, sudden environment changes, etc. Mucheffort has been devoted to extend many fundamental results for determinis-tic systems to stochastic systems [9, 11, 12, 13, 14, 22]. In the past decades,increasing attention has been devoted to the problems of stability and other

Recently, Liu et al. [Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella function, Integral Transform Spec. Funct. 23 (2012), no. 7, 539-549] investigated, in several interesting papers, some various families of bilateral generating functions involving the Chan-Chyan-Srivastava polynomials. The aim of this present paper is to obtain some bilateral generating functions involving the Chan-Chyan-Sriavastava polynomials and three general classes of multivariable polynomials introduced earlier by Srivastava in [A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6], [A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117 (1985), 183-191] and by Kaanolu and zarslan in [Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), 625-631]. Special cases involving the (Srivastava-Daoust) generalized Lauricella functions are also given.

In this paper we give a definition of the Hodge type Laplacian � on a non-commutative manifold which is the smooth dense subalgebra of a C ∗ -algebra. We prove that the Laplacian on a quantum Heisenberg manifold is an elliptic operator in the sense that (� + 1)−1 is compact. In non-commutative geometry, the Chevalley-Eilenberg complex is used to produce a cyclic cocycle in Connes' cyclic cohomology via a cycle over an algebra A where a Lie-group action on A is given. The most important result in this direction is the integrality of the pairing of a cyclic 2-cocycle and Rieffel's projection in the non-commutative torus A� (3, 6, 8). In this paper, using the same framework, we investigate a metric aspect of this complex. In fact, we define "Laplacian" on a non-commutative manifold which is slightly different with the one given in (10) and establish a Hodge- type theorem of the Laplacian on a quantum Heisenberg manifold. While the non-commutative torus is simpler, quantum Heisenberg manifolds with the non-commutative Heisenberg group action are tractable non-commutative man- ifolds given by the stirct deformation quantization of the classical Heisenberg manifold (7). We emphasize that if the group action is commutative and a C ∗ -algebra A is deformed from the group, this is not so interesting since the metric aspect on A is almost commutative as we observe the non-commutative torus case (3, 5). Thus it seems natural to consider the Heisenberg group action and a deformation from it. We show that in this case the Laplacian on zero forms or "functions" is diagonalizable and eigenvalues form a discrete set of R + which is well-known for a connected, oriented Riemmanian manifold (see, for example, (9)).

Let Λ be a robustly transitive set of a diffeomorphism f ona closed C ∞ manifold. In this paper, we characterize hyperbolicity of Λin C 1 -generic sense. 1. IntroductionA fundamental problem in differentiable dynamical systems is to understandhow a robust dynamic property (that is, a property that holds for a system andall C 1 nearby ones) on the underlying manifold would influences the behaviorof the tangent map on the tangent bundle. In this paper, we study the robustdynamic property for a transitive set. Let M be a closed C ∞ manifold, and letDiff(M) be the space of diffeomorphisms of M endowed with the C 1 -topology.Denote by d the distance on M induced from a Riemannian metric k·k on thetangent bundle TM. Let f ∈ Diff(M) and Λ be a closed f-invariant set. Theset Λ is transitive if there is a point x ∈ Λ such that ω(x) = Λ. Here ω(x) isthe forward limit set of x. Denote by f| Λ the restriction of f to the set Λ. Amaximal invariant set of f in an open set U, denoted by Λ f (U), is the set ofpoints whose whole orbit contained in U, that is,Λ

Let G =(V,E)beagraphwithchromaticnumber χ(G). Adominating set D of G is called a chromatic transversal dominating set(ctd-set) if D intersects every color class of every χ-partitionof G. Theminimumcardinalityofactd-setofG iscalledthechromatictransversaldomination number of G and is denoted by γ ct (G). In this paper wecharacterizetheclassoftrees,unicyclicgraphsandcubicgraphsforwhichthe chromatic transversal domination number is equal to the connecteddominationnumber. 1. IntroductionAll the graphs considered in this paper unless otherwise specifically statedare finite, connected and simple and are consistent with the terminology usedin Harary [4]. Let G = (V,E) be a simple graph of order p. For a subset Sof V, N(S) denotes the set of all vertices adjacent to some vertex in S andN[S] = N(S) ∪S.A vertex v of G is called a support if it is adjacent to a pendant vertex. Anyvertex of degree greater than one is called an internal vertex. A graph G iscalled a unicyclic graph, if G contains exactly one cycle.A subset D ⊆ V is a dominating set, if every v ∈ V − D is adjacent tosome u ∈ D. The domination number γ = γ(G) is the minimum cardinality ofa dominating set of G. A dominating set D is called a connected dominatingset if the induced subgraph hDi is connected. The minimum cardinality of aconnected dominating set is called the connected domination number and isdenoted by γ

We study biminimalcurves in 2-dimensional Riemannian man-ifolds of constant curvature. IntroductionElastic curves provide examples of classically known geometric variationalproblem. A plane curve is said to be an elastic curve if it is a critical point ofthe elastic energy, or equivalently a critical point of the total squared curvature[9].In this paper, we study another geometric variational problem of curves inRiemannian 2-manifolds of constant curvature. The Euler-Lagrange equationstudied in this paper is derived from the theory of biharmonic maps in Rie-mannian geometry.A smooth map φ : (M,g) → (N,h) between Riemannian manifolds is saidto be biharmonic if it is a critical point of the bienergy functional:E 2 (φ) =Z M |τ(φ)| 2 dv g ,where τ(φ) = tr ∇dφ is the tension field of φ. Clearly, if φ is harmonic, i.e.,τ(φ) = 0, then φ is biharmonic. A biharmonic map is said to be proper if it isnot harmonic.Chen and Ishikawa [3] studied biharmonic curves and surfaces in semi-Euclidean space (see also [6]). Caddeo, Montaldo and Piu [1] studied bihar-monic curves on Riemannian 2-manifolds. They showed that biharmonic curveson Riemannian 2-manifolds of non-positive curvature are geodesics. Proper bi-harmonic curves on the unit 2-sphere are small circles of radius 1/√2.Next, Loubeau and Montaldo introduced the notion of biminimal immersion[10].An isometric immersion φ : (M,g) → (N,h) is said to be biminimal if it is acritical point of the bienergy functional under all normal variations. Thus thebiminimality is weaker than biharmonicity for isometric immersions, in general.

In this paper we introduce the notion of P-strongly regu-lar near-ring. We have shown that a zero-symmetric near-ring N is P-strongly regular if and only if N is P-regular and P is a completelysemiprime ideal. We have also shown that in a P-strongly regular near-ring N, the following holds: (i) Na+ P is an ideal of N for any a∈N.(ii) Every P-prime ideal of N containing P is maximal. (iii) Every idealI of N fulfills I+ P = I 2 + P. 1. IntroductionThroughout this paper, N denotes a zero-symmetric right near-ring. Aright N-subgroup (left N-subgroup) of N is a subgroup I of (N,+) such thatIN ⊆ I(NI ⊆ I). A quasi-ideal of N is a subgroup Q of (N,+) such thatQN ∩ NQ ⊆ Q. Right N-subgroups and left N-subgroups are quasi-ideals.The intersection of a family of quasi-ideals is again a quasi-ideal.Nis called regular, if for every element aof Nthere exists an element x∈ Nsuch that a= axa. Let P be an ideal of N. Then the near-ring N is said tobe a P-regular near-ring if for each a ∈ N, there exists an element x ∈ Nsuch that a= axa+ p for some p∈ P. If P = 0, then a P-regular near-ringis a regular near-ring. Here the notion of P-regularity is a generalization ofregularity. There are near-rings which are P-regular but not regular.V. A. Andrunakievich [1] defined P-regular rings and S. J. Choi [3] extendedthe P-regularity of a ring to the P-regularity of a near-ring. In this paper weintroduce the notion of P-strongly regular near-ring and obtain equivalent con-ditions for a near-ring to be P-strongly regular. We also introduce the notionsof P-prime ideals and P-near-ring in this paper. I. Yakabe [7] characterizedregular zero-symmetricnear-rings without non-zero nilpotent elements in termsof quasi-ideals. In this paper we characterize P-strongly regular near-ring interms of quasi-ideals. For the basic terminology and notation we refer to [6].

In the previous paper [8], the author gave a determinant for-mula of relative zeta function for cyclotomic function fields. Our purposeof this paper is to extend this result for more general function fields. Asan application of our formula, we will give determinant formulas of classnumbers for constant field extensions. 1. IntroductionLet pbe a prime. In 1955, Carlitz and Olson [2] provided an expression ofthe relative class number of p-th cyclotomic field in terms of a certain classicaldeterminant, which is known as the Maillet determinant. Many authors haveextended this result (cf. [5], [9]). In particular, Girstmair [3] gave a general-ization to an imaginary abelian field.In the function field case, several authors also gave determinant formulasfor class numbers. Let F q be the field with qelements. Let k= F q (T) be therational function field over F q , and A= F q [T] the associated polynomial ring.Let m∈ Abe a monic polynomial. We denote by Λ m the set of all m-torsionpoints of the Carlitz module (see Section 2). Let K

The purpose of this paper is to improve certain results proved in a recent paper of Soliman et al. (20). These results are the outcome of utilizing the idea of absorbing pairs due to Gopal et al. (6) as opposed to two conditions namely: weak compatibility and the peculiar condition initiated by Pant (15) to ascertain the common xed points of Lipschitzian mappings. Some illustrative examples are also furnished to highlight the realized improvements.

It is well known that plurigenus does not vanish for a suf- �ciently large multiple on a canonical threefold over C. There is Reid- Fletcher formula for plurigenus. But, unlike in the case of surface of general type, it is not easy to compute plurigenus. In this paper, we in- duce a different version of Reid-Fletcher formula and show that the con- stant term in the induced formula has periodic properties. Using these properties we have an application to nonvanishing of plurigenus. Throughout this paper X is assumed to be a projective threefold with only

The aim of this paper is to establish the well-known and veryuseful classical Saalschutz’s theorem for the series 3 F 2 (1) by following afft method. In addition to this, two summation formulas closelyrelated to the Saalschutz’s theorem have also been obtained. The resultsestablished in this paper are further utilized to show how one can obtaincertain known and useful hypergeometric identities for the series 3 F 2 (1)and 4 F 3 (1) already available in the literature. 1. Introduction and results requiredWe start with the following well-known and useful classical Saalschutz’stheorem [4, p. 87, Section 51] for the series 3 F 2 (1). If n is a non-negativeinteger and if a , b , c are independent of n ,(1.1) 3 F 2 [ n; a; bc; 1+ a + b c n ; 1]=( c a ) n ( c b ) n ( c ) n ( c a b ) n : As mentioned in almost all the standard books on generalized hypergeomet-ric series that this theorem can be established with the help of the followingEuler’s transformation formula [4, p. 60, Eq.(5)]. If

In this paper, we propose an algorithm for identifying ! j 2 (0 ;1 ), a j ;b j 2 C and N of the following trigonometric series f ( t ) = a 0 +∑ Nj =1 [ a j cos ! j t + b j sin ! j t ]by means of the nite number of sample values. We prove that the fre-quency components are shown to be the solutions of some characteristicequation related to the inverse of a Hankel matrix derived from the samplevalues. 1. IntroductionIn this paper we consider the problem of identifying ! j 2 (0 ;1 ), a j ;b j 2 Cand N of the following trigonometric series(1) f ( t ) = a 0 +∑ Nj =1 [ a j cos ! j t + b j sin ! j t ]by means of the nite number of values f ( t 1 ) ;:::;f ( t L ) where the number L of the values depends on N .In engineering, it is well known that a (sound) signal can be represented asa trigonometric series as in (1). The algorithm developed in this paper thuscan be applied to analyze the signals from the engineering point of view.The main idea of this paper is originated from the paper [1] and [2] by ElBadia and Ha-Duong. In those papers, the authors established an algebraicalgorithm to solve inverse source problems for elliptic equations in 2D and 3Dwhose source terms are assumed to be the combination of either monopolesor dipoles. Applying the concept of the

The purpose of this paper is to prove strong convergence theorems for common flxed points of two families of weak relatively non- expansive mappings and a family of equilibrium problems by a new mono- tone hybrid method in Banach spaces. Because the hybrid method pre- sented in this paper is monotone, so that the method of the proof is difierent from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive map- ping in Banach space l2. Our results improve and extend the correspond- ing results announced in (W. Takahashi and K. Zembayashi, Strong con- vergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Ar- ticle ID 528476, 11 pages; doi:10.1155/2008/528476) and (Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common flxed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616{5628) and some other papers.

In this paper, we study the behavior and sensitivity analysis of the solution set for a new system of generalized parametric multi-valued variational inclusions with (A,·)-accretive mappings in q-uniformly smoo- th Banach spaces. The present results improve and extend many known results in the literature. techniques. By using the projection method, Dafermos (2), Yen (12), Mukherjee and Verma (7), Noor (9) and Pan (10) studied the sensitivity analysis of solutions of some variational inequalities with single-valued mappings in finite-dimensional spaces or Hilbert spaces. By using the resolvent operator technique, Agarwal et al. (1), Jeong (3) stud- ied a new system of parametric generalized nonlinear mixed quasi-variational inclusions in a Hilbert space and in Lp(p ‚ 2) spaces, respectively. In 2008, using the concept and technique of resolvent operators, Lan (4) introduced and studied the behavior and sensitivity analysis of the solution set for a system of generalized parametric (A,·)-accretive variational inclusions in Banach spaces. Motivated and inspired by the research work going on this field, in this paper, we study the behavior and sensitivity analysis of the solution set for a new system of generalized parametric multi-valued variational inclusions with (A,·)-accretive mappings in q-uniformly smooth Banach spaces. The present results improve and extend many known results in the literature.

In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space. 1. Introduction and preliminaries Variational inequality problems have been found with an explosive growth in theoretical advances, algorithmic development and applications across all the discipline of pure and applied sciences, see (2-14) and the references therein. They combine novel theoretical and algorithmic advances with new domain of applications. Analysis of these problems requires a blend of technics from convex analysis, functional analysis and numerical analysis. As a result of in- teraction between dierent branches of mathematical and engineering sciences, we now have a variety of techniques to analysis various algorithms for solv- ing variational inequalities and related optimization. It is well known that the variational inequality problems are equivalent to the fixed point problems. This alternative equivalent formulation is very important from the numerical analysis point of view. In particular, solutions of the variational inequality problems can be computed using the iterative projection methods. It is well known that the convergence of the projection method requires the operator T to be strongly monotone and Lipschitz continuous. In this paper, we shall the equivalence to study a generalized variational inequality. Throughout this paper, we always assume that H is a real Hilbert space, whose inner product and norm are denoted by h·,·i and k · k. Let C be a nonempty closed and convex subset of H and A : C ! H a nonlinear mapping.

Even though there is a formula for h 0 ( X,O X ( nK X )) for acanonical threefold X , it is not easy to compute h 0 ( X,O X ( nK X )) be-cause the formula has a term due to singularities. In this paper, we finda way to control the term due to singularities. We show nonvanishing ofplurigenus for the case when the index r in the singularity type 1 r (1 ,− 1 ,b )is sufficiently large. Throughout this paper X is assumed to be a projective threefold with onlycanonical singularities and an ample canonical divisor K X over the complexnumber field C, i.e., a canonical threefold.It is well known that H 0 ( X,O X ( mK X )) does not vanish and generates abirational map for a sufficiently large m . When X is a surface of general type, H 0 ( X,O X ( mK X )) does not vanish for m ≥ 2 and H 0 ( X,O X ( mK X )) generatesa birational map for m ≥ 5.In a case of a threefold of general type, M. Reid and A. R. Fletcher de-scribed the formula for χ ( O X ( nK X )) (see [1]). Combining the formula for χ

This paper introduces a local non-positivity of two set-valued mappings (F,Q) and considers the existences and properties of solutions for set-valued mixed vector FQ-implicit variational inequality problems and set-valued mixed vector FQ-complementarity problems in the neigh- borhood of a point belonging to an underlined domain K of the set-valued mappings, where the neighborhood is contained in K. This paper generalizes and extends many results in (1, 3-7).

This paper ultimately aims to develop noninvasive techniques to identify the inside of a given electrical network. Based on the theory of the partial dierentiation equations and mathematical modeling, this paper devises the algorithms to find the locations of possible abnormali- ties. To ensure the certainty of the algorithms, this study restricted the forms of the network and the number of abnormalities, rendering it easy to prove the uniqueness of the position of the abnormalities.

In this paper, we investigate some fundamental properties and establish some results of f-derivations of BCI-algebras. Also, we prove Der(X), the collection of all f-derivations, form a semigroup under certain binary operation. 1. Introduction and preliminaries BCI-algebra has been developed from BCI-logic on the similar way as Bool- ean algebra was developed from Boolean logic which have a lot of application in computer sciences ((14)). Recently greater interest has been developed in the derivation of BCI-algebras, introduced by Y. B. Jun and X. L. Xin (8), which was motivated from a lot of work done on derivations of rings and Near rings (see (9, 11)). The notion was further explored in the form of f-derivations of BCI-algebras by J. M. Zhan and Y. L. Liu (15). In this paper, we prove some results on f-derivations of BCI-algebras. First, we show that an f-derivation of BCK-algebra is regular. However, we are able to show that under certain conditions namely, for a 2 X,f(a)⁄df(x) = 0 or df(x)⁄f(a) = 0, for all x 2 X the f-derivation, df, of a BCI-algebra X is regular and X is a BCK-algebra. Also, we study derivations in a p-semisimple BCI-algebra and show that if df,d 0 f are f-derivations in X, then df - d 0

The Drinfeld modular function µ is a generator of the func-tion field of the Drinfeld modular curve X 0 ( T ) and has an t -expansionwith the integral coefficients at infinity. In this paper, we show that thecoefficients of µ has congruence properties modulo powers of T . 1. IntroductionVincent Bosser [1] showed that the coefficients of the Drinfeld modular in-variant j has congruence properties modulo powers of polynomials of degree 1in F q [ T ]. It can be applied for a generator µ of the function field of the Drinfeldmodular curve X 0 ( T ). The generator µ plays an important role in the study of X 0 ( T ) and the construction of class fields over function fields. Jeon and Kim[2] show that µ gives a plane model for X 0 ( T ) and the singular values of µ generate class fields over imaginary quadratic function fields.In this paper, by using tools of Bosser we show that the coefficients of µ hascongruence properties modulo powers of T .2. PreliminariesLet K be the rational function field F q

For F[e±x]{∂}, all the derivations of the evaluation algebra F[e±x]{∂} is found in the paper (see [16]). For M = {∂1, ∂2 1}, Dernon(F[e±x]M )) of the evaluation algebra F[e±x, e±y]M is found in the paper (see [2]). For M = {∂2 1 , ∂2 2}, we find Dernon(F[e±x, e±y]M )) of the evaluation algebra F[e±x, e±y ]M in this paper.

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)fuzzy subalgebras where α, β are any two of {∈, q, ∈ ∨ q, ∈∧ q} with α 6=∈∧ q was introduced, and related properties were investigated in [3]. As a continuation of the paper [3], in this paper, the notion of a fuzzy subalgebra with thresholds is introduced, and its characterizations are obtained. Relations between a fuzzy subalgebra with thresholds and an (∈,∈∨ q)-fuzzy subalgebra are provided.

In a recent paper, Domokos and [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].

We are interested in the distance problem between two objects in three dimensional Euclidean space. There are many dis- tance problems for various types of objects including line segments, boxes, polygons, circles, disks, etc. In this paper we present an iter- ative algorithm for flnding the distance between two given ellipses. Numerical examples are given. 1. Introduction and preliminaries The distance problem between two given objects in three dimensional space can be found often in computer-aided geometric design systems. Further, it is important to propose an e-cient algorithm for flnding the distance between two objects. There are many distance problems for various types of objects including line segments (5), boxes (6), polygons (8), circles (7), disks (1), etc. In the literature, many problems already have been studied and various numerical techniques to compute the optimal distance have been given. In this paper we consider the problem of flnding the distance between two given ellipses. The representation of an ellipse in three dimensional space can be given by using a geometric transformation of a standard ellipse in the xyiplane. This may simplify the distance function between the two ellipses. Thus, our problem is reduced to the distance problem between one standard ellipse and the other ellipse. We can present an iterative algorithm which is mainly based on computing the distance between a given point and a standard ellipse.

Several authors flnd all the derivations of an algebra (1), (3), (7). A Weyl type non-associative algebra and its subalgebra are deflned in the paper (2), (3), (10). All the derivations of the non- associative algebra WN0;0;s1 is found in this paper (4). We flnd all the derivations of the non-associative algebra WN0;s;01 in this paper (5).

Every non-associative algebra Lcorresponds to its sym- metric semi-Lie algebra L(;) with respect to its commutator. It is an interesting problem whether the equality Autnon(L) = AutsemiiLie(L) holds or not (2), (13). We flnd the non-associative algebra au- tomorphism groups Autnon (WN0;0;1(0;1;r1;:::;rp) ) and AutsemiiLie (WN0;0;1(0;1;r1;:::;rp)), where every automorphism of the automor- phism groups is the composition of elementary maps (3), (4), (7), (8), (9), (10), (11). The results of the paper show that the F-algebra au- tomorphism groups of a polynomial ring and its Laurent extension make easy to flnd the automorphism groups of the algebras in the paper.

In this paper, we introduce the SP-integral and the SPfi-integral deflned on an interval in the n-dimensional Euclidean space R n . We also investigate the relationship between these two integrals. It is well known (3) that the Perron integral deflned on an interval of the real line R by major and minor functions which are not assumed to be continuous is equivalent to the one deflned by continuous major and minor functions and that the strong Perron integral deflned on an interval of R by strong major and minor functions is equivalent to the McShane integral. In this paper, we introduce Perron-type integrals deflned on an inter- val of the n-dimensional Euclidean spaceR n using the strong major and minor functions, and investigate the relationship between these integrals. We shall call it the strong Perron integral, or brie∞y SP-integral. For a subset E of the n-dimensional Euclidean spaceR n , the Lebesgue measure of E is denoted by jEj. For a point x = (x1;x2;¢¢¢ ;xn) 2R n , the norm of x is kxk = max1•in jxij and the --neighborhood U(x;-) of x is an open cube centered at x with sides equal to 2-. For an interval I = (a1;b1)£(a2;b2)£¢¢¢(an;bn) ofR n with ai fi(fi 2 (0;1)), then the interval I is said to be fi-regular.

Throughout this paper, we will consider that R is a near-ring and G an R-group. We initiate the study of monogenic, strongly monogenic R-groups, 3 types of nonzero R-groups and their basic properties. At first, we investigate some properties of D.G. (R, S)-groups, faithful R-groups, monogenic R-groups, simple and R-simple R-groups. Next, we introduce modular right ideals, t-modular right ideals and 3 types of primitive near-rings. The purpose of this paper is to investigate some properties of primitive types near-rings and their characterizations.

Conditions for a i-near-ring to be commutative areinvestigated. 1. IntroductionFor preliminary deflnitions and results related to near-rings, we referto Pilz [11]. The notion of a i-ring, a concept more general than a ring,was deflned by Nobusawa [8]. Barnes [1] weakened the conditions slightlyin the deflnition of i-ring in the sense of Nobusawa. Barnes [1], Kyuno[6], Luh [7] and Ozturk˜ (together with Jun) [9] studied the structure of˜i-rings and obtained various generalizations analogous to correspond-ing parts in ring theory. As a generalization of near-rings, i-near-ringswere deflned by Satyanarayana [13]. Recently, Booth, Groenewald andSatyanarayana studied several aspects in i-near-rings (see [2], [3], [12],[13], [14]). Also the third author (together with Cho and Kim) intro-duced the notion of i-derivations in i-near-rings and investigated basicproperties (see [4], [5]). In this paper, we investigate some conditionsfor a i-near-ring to be commutative.2. PreliminariesAll near-rings considered in this paper are left distributive. A i

In this paper, we establish almost stability of Ishikawa iterative schemes with errors for the classes of Lipschitz -strongly quasi-accretive operators and Lipschitz -hemicontractive operators in arbitrary Banach spaces. The results of this paper extend a few well-known recent results.

In this paper we explicitly compute the orders of am- biguous ideal class groups of layers of the basic Z3-extension of certain cubic flelds and give an example for Greenberg's conjecture. n +"p(k) for su-ciently large n: Greenberg's conjecture (3) claims that both "p(k);‚p(k) vanishes for the cyclotomic Zp-extension, contained in the fleld obtained by adjoining all p-power roots of unity to k; of any totally real number fleld k: In this paper we explicitly compute the orders of ambiguous ideal class groups of layers of the basic Z3- extension of certain cubic flelds and give an example for Greenberg's conjecture.

We introduce a fuzzy g-closure operator induced by a fuzzy topological space in view of the definition of ˇ (13). We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of fuzzy g-closure operators. 1. Introduction and preliminaries ˇ (13) introduced the fuzzy topology as an extension of Chang's fuzzy topology (2). It has been developed in many directions (3, 4, 7- 10). Balasubramanian and Sundaram (1) gave the concept of generalized fuzzy closed sets in a Chang's fuzzy topology as an extension of gener- alized closed sets of Levine (11) in topological spaces. In this paper, we introduce a fuzzy g-closure operator induced by ˇ fuzzy topological space. We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of (generalized) fuzzy continuous maps and fuzzy generalized irresolute maps. Moreover, we study the relationship between (resp. strongly) r-closed graphs and r-FT2 (resp. r-FT 2 1 ) spaces. Throughout this paper, let X be a nonempty set, I = (0;1), I0 = (0;1) and I X be the family of all fuzzy sets. For fi 2 I, fi(x) = fi for all x 2 X. For x 2 X and t 2 I0, a fuzzy point xt is defined by

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater (1). The error estimating function pro- posed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the mid- point.

In this paper, we introduce and study notions of average chain transitivity, average chain mixing, total average chain transitivity and almost average shadowing property. We also discuss their interrelations., 12 pages

WOS: 000401239400011 In this paper, a generalized boundary version of Caratheodory's inequality for holomorphic function satisfying f (z)

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

We derive a closed-form expression for the price of a Euro- pean quanto call option when both foreign and domestic interest rates follow the Vasicek's short rate model. A quanto is a type of financial derivative whose pay-out currency differs from the natural denomination of its underlying financial variable. A quanto option is a cash-settled, cross-currency derivative whose underlying asset has a payoff in one currency, but the payoff is converted to another currency when the option is settled. For that reason, the correlation between underlying asset and currency exchange rate plays an important role in pricing quanto option. Quanto options in this paper have both the strike price and the underlying asset price denominated in foreign currency. At exercise, the value of the option is calculated as the options intrinsic value in foreign currency, which is then converted to the domestic currency at the fixed exchange rate. This allows investors to obtain exposure to foreign assets without the corresponding foreign exchange risk. Pricing quanto options based on the classical Black-Scholes (1) model, on which most of the research on quanto options has focused, has a weakness of assuming a constant volatility and constant interest rates. To overcome such weakness, in valuing quanto option, it is natural to consider a stochastic volatility or stochastic interest rate models. Despite its importance, very few researches have been done on finding analytic solutions of quanto option prices under a stochastic volatility model primarily due to the sophisticated stochastic processes and inability to obtain the general closed form. However, by assuming constant interest rates, Giese (4) provided a closed-form expression for the price of a quanto option in the Stein-Stein stochastic volatility model, and then Y. Lee et al. (5) got a closed-form expression for the price of a European quanto

In this paper, we introduce the notion of symmetric bi-derivations of a B-algebra and investigate some related properties. We study the notion of symmetric bi-derivations of a 0-commutative B-algebra and state some related properties. © 2016 Korean Mathem Department of Mathematics, Faculty of Science, Yaşar University, Izmir, 35100, Turkey

The aim of this paper is to present the classical sets of sequences and related matrix transformations with respect to the b-metric. Also, we introduce the relationships between these sets and their classical forms with corresponding properties including convergence and completeness. Further we determine the duals of the new spaces and characterize matrix transformations on them into the sets of b-bounded, b-convergent and b-null sequences.