Authors:Saurabh Porwal; Shivam Kumar Pages: 1 - 8 Abstract: In the present paper, we investigate confluent hypergeometric distribution and establish some connections between \(\gamma -UCV\) , \(\gamma -ST\) , \(S^{*}_{\lambda }\) and \(C_{\lambda }\) with \(R^{\tau }(A,B)\) involving the operator \(\Omega (a;c;m)\) associated with the confluent hypergeometric distribution series. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0422-3 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Elmo Benedetto Pages: 23 - 27 Abstract: Very often, in physical exercises, it is necessary to differentiate an integral with respect to a parameter. Generally we differentiate after the integral evaluation but, occasionally, it is desirable, from theoretical point of view, to interchange the order of differentiation and integration. In this letter, we examine in a simple way the derivative under the flux integral getting the result in a very simple manner that could be useful from didactic point of view. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0424-1 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Saurabh Porwal; K. K. Dixit Pages: 29 - 34 Abstract: The purpose of the present paper is to introduce Mittag-Leffler type Poisson distribution. We obtain some properties of this distribution. It is worthy to note that the results of this distribution reduces to the result of Poisson distribution for \(\alpha =\beta =1\) . PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0427-y Issue No:Vol. 28, No. 1-2 (2017)

Authors:P. Sumati Kumari; I. Ramabhadra Sarma; J. Madhusudana Rao Pages: 35 - 43 Abstract: In this paper, we derive some implications and nonimplications among various kinds of convergence axioms derived in generalized metric space. Moreover, we prove an alternative proof for generalization of Banach contraction principle and illustrate this with a suitable example. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0425-0 Issue No:Vol. 28, No. 1-2 (2017)

Authors:E. Ballico Pages: 45 - 50 Abstract: Let X be a smooth n-fold, \(n\ge 3\) , and \(\mathcal {L}\) a spanned and ample line bundle on X with \(h^1(\mathcal {O}_X)=0\) . Let \(\mathcal {E}\) be a spanned rank r vector bundle on X with \(\det (\mathcal {E})\cong \mathcal {L}\) and no trivial factor. Here we prove that \(r\le h^0(\mathcal {L})-1\) and prove the existence of some \(\mathcal {E}\) for all r with \(n\le r \le h^0(\mathcal {L})-1\) . In the case \(n=3\) we show that if \(h^0(\mathcal {L}) -r\) is very small (in terms of the t-connectedness of \((X,\mathcal {L})\) ), then \(\mathcal {E}\) is obtained by a standard procedure from \(\mathcal {L}\) . If \(h^1(\mathcal {O}_X)>0\) we prove the upper bound for r substituting the integer \(h^0(\mathcal {L})-2\) with an integer \(\rho (\mathcal {L})\) with \(h^0(\mathcal {L})-2+ \max \{0,2h^1(\mathcal {O}_X)-h^1(\mathcal {L})\}\le \rho (\mathcal {L})\le h^0(\mathcal {L})-2+2h^1(\mathcal {O}_X)\) . PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0430-3 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Saranan Mondal; Lakshmi Kanta Dey Pages: 85 - 97 Abstract: In this article, we prove the existence and uniqueness of common best proximity point for a pair of non-self mappings satisfying weak P-property in a complete metric space. Moreover, we prove the same for Kannan type mappings and C-contractive mappings using weak P-property by changing non-self mappings to self mappings in a complete metric space. We take much weaker conditions on the mappings to prove our results. An example is presented here to support our main result. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0432-1 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Allahtan Victor Gnedbaye Pages: 109 - 118 Abstract: We factor the classical functors \({ As}\mathop {\longrightarrow }\limits ^{-} { Lie}\) and \({ Dias}\mathop {\longrightarrow }\limits ^{-}{ Leib}\) through the categories \({ Pre}\hbox {-}{} { Lie}\) and \({ Pre}\hbox {-}{} { Leib}\) of two new types of algebras. Thanks to Koszul duality for binary quadratic operads, we deduce two more categories of algebras \({ Perm}\) and \({ Ricod}\) giving rise to other factorizations. This yields a triangulation of Loday’s commutative diagram of functors on Leibniz algebras and associated operads. As an application, we define a notion of extended Leibniz algebras. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0431-2 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Yaya Sagna; Ahmadou Bamba Sow Pages: 151 - 163 Abstract: This paper is devoted to solving a real valued backward doubly stochastic differential equation with jumps where the time horizon may be finite or infinite. Coupling a linear growth condition and left continuity on the generator, we prove existence of a minimal solution. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0434-z Issue No:Vol. 28, No. 1-2 (2017)

Authors:Saurabh Porwal; Manish Kumar Pages: 165 - 170 Abstract: The purpose of the present paper is to study the mapping properties of an integral operator involving Bessel functions of the first kind on a subclass of analytic univalent functions. Relevant connections of the results presented here with various known results are briefly indicated. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0436-x Issue No:Vol. 28, No. 1-2 (2017)

Authors:Akhilesh Prasad; P. K. Maurya Pages: 189 - 198 Abstract: The wavelet transformation involving the fractional powers of Hankel-type integral transformation is defined and discussed on its some basic properties. An inversion formula of this transformation is also obtained. Some examples are given. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0438-8 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Nipen Saikia; Chayanika Boruah Pages: 199 - 206 Abstract: We prove some congruences for the number of bipartitions \(A_4(n)\) and partition triples \(B_4(n)\) of a positive integer n with 4-core. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0437-9 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Jeongmi Jeong; Chan-Gyun Kim Pages: 237 - 247 Abstract: In this paper, we are concerned with quasilinear elliptic equations with a Dirichlet boundary condition and two parameters. Using the truncation techniques and variational methods, the existence and/or multiplicity of positive solutions to the problems with a nonlinearity which satisfies either logistic growth rate or strong Allee effect growth rate are investigated. Also, a nonexistence result for nonnegative and nontrivial solutions is given. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0444-x Issue No:Vol. 28, No. 1-2 (2017)

Authors:Mijanur Rahaman; Rais Ahmad; Haider Abbas Rizvi Pages: 263 - 270 Abstract: In this paper, we introduce and study an over-relaxed scheme based on \(H(\cdot ,\cdot )\) -cocoercive operators for solving a generalized variational inclusion problem in Hilbert spaces. By using the resolvent operator technique associated with \(H(\cdot ,\cdot )\) -cocoercive operators, an existence and convergence result is proved. Our over-relaxed scheme seems to be more general and applicable for solving many related problems occurring in applied sciences. An example is provided in support of our main result. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0445-9 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Pakeeta Sookprasert; Poom Kumam; Dawud Thongtha; Wutiphol Sintunavarat Pages: 271 - 278 Abstract: In this work, we extend the concept of an almost generalized weakly contractive mapping in rectangular b-metric spaces. The establish of fixed point of such mappings is also provided. We give an example to support our results. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0443-y Issue No:Vol. 28, No. 1-2 (2017)

Authors:Fatma Gül Gurkan; Mehmet Acıkgoz; Erkan Agyuz Pages: 279 - 290 Abstract: By the same motivation Kim et al. (Adv Stud Theor Phys 8:745–754, 2014), the main aim of this paper is to define some new mixed type polynomials with connected to Boole and Tangent polynomials. Also, we obtain new and interesting identities from these polynomials. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0446-8 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Bernadette Faye; Florian Luca Pages: 291 - 294 Abstract: In this paper, we prove that there is no number with the Lehmer property in the sequence of Pell numbers. PubDate: 2017-03-01 DOI: 10.1007/s13370-016-0449-5 Issue No:Vol. 28, No. 1-2 (2017)

Authors:Akbar Paad Abstract: In this paper, we introduce the concepts of n-fold integral ideals and n-fold Boolean ideals in BL-algebras. With respect to concepts, we give some related results. In particular, we prove that an ideal is an n-fold integral ideal if and only if is an n-fold Boolean and (prime)maximal ideal. Also, we prove that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal \(\{0\}\) is an n-fold integral ideal. Moreover, we study relation between n-fold integral ideals and n-fold obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between n-fold Boolean ideals and n-fold positive implicative filters in BL-algebras. PubDate: 2017-03-25 DOI: 10.1007/s13370-017-0497-5

Authors:M. Pitchaimani; D. Ramesh Kumar Abstract: The aim of this paper to establish the existence and uniqueness of coincidence and common fixed points of Nadler type set-valued mappings under various generalized contractive conditions in the context of ultrametric spaces. Illustrative examples are provided to support our results. As an application, we have obtained well-posedness of the common fixed point problems. The presented results generalize several existing results in the literature in ultrametric space setting. PubDate: 2017-03-22 DOI: 10.1007/s13370-017-0496-6

Authors:A. Manimaran; B. Praba; V. M. Chandrasekaran Abstract: In this paper, we give a characterization of the rough semiring \((T,\Delta ,\nabla )\) . The order of a rough semiring is also derived. We present the idea of rough homomorphism on the set of all rough sets for the given information system together with the operations Praba \(\Delta \) and Praba \(\nabla \) . We illustrate these concepts through examples. PubDate: 2017-03-17 DOI: 10.1007/s13370-017-0495-7

Authors:Reza Aghayan Abstract: This paper is devoted to GM-sets and their applications in Lie theory from the theoretical and computational points of view. We consider the GM-set of a transformation group G acting on a smooth manifold M as the set of all associated G-equivariant maps and then investigate the relation between the concepts of G-conjugacy and G-invariance in Lie theory with respect to the associated GM-set. We will also have a look at the fundamental and constructive concept of moving frames through the GM-sets and apply this construction to carry out a detailed survey of some basic concepts in Lie algebra theory. PubDate: 2017-03-06 DOI: 10.1007/s13370-017-0481-0