Authors:P. N. Agrawal; Pooja Gupta Pages: 1 - 23 Abstract: The purpose of the present paper is to introduce a Kantorovich modification of the q-analogue of the Stancu operators defined by Nowak (J Math Anal Appl 350:50–55, 2009). We study a local and a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness. Further A-statistical convergence properties of these operators are investigated. Next, a bivariate generalization of these operators is introduced and its rate of convergence is discussed with the aid of the partial and complete modulus of continuity and the Peetre‘s K-functional. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0291-1 Issue No:Vol. 64, No. 1 (2018)

Authors:Abderrahim Aslimani; Imad El Ghazi; Mohamed El Kadiri; Sabah Haddad Pages: 25 - 46 Abstract: We study the existence and the regularity of the biharmonic Green kernel in a Brelot biharmonic space whose associated harmonic spaces have Green kernels. We show by some examples that this kernel does not always exist. We then introduce and study the adjoint of the given biharmonic space. This study was initiated by Smyrnelis, however, it seems that several results were incomplete and we clarify them here. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0289-8 Issue No:Vol. 64, No. 1 (2018)

Authors:Tongkeun Chang; Kyungkeun Kang Pages: 47 - 82 Abstract: We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in \({\mathbb {R}}^n_+ \times (0,T)\) . We obtain new estimates of solutions including pressure in terms of mixed anisotropic Sobolev spaces. As an application, some anisotropic Sobolev estimates are presented for weak solutions of the Navier–Stokes equations in a half-space in dimension three. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0287-x Issue No:Vol. 64, No. 1 (2018)

Authors:Hocine Gabsi; Abdelouaheb Ardjouni; Ahcene Djoudi Pages: 83 - 97 Abstract: In this work we use some mixed techniques of the Mawhin coincidence degree theory and fixed point theorem to prove the existence of positive periodic solutions of delay systems. As a consequence, we offer existence criteria and sufficient conditions for existence of periodic solutions to the systems with feedback control. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0292-0 Issue No:Vol. 64, No. 1 (2018)

Authors:A. Hosseini Pages: 99 - 110 Abstract: Let \(\mathfrak {M}\) be a von Neumann algebra, and let \(\mathfrak {T}:\mathfrak {M} \rightarrow \mathfrak {M}\) be a bounded linear map satisfying \(\mathfrak {T}(P^{2}) = \mathfrak {T}(P)P + \Psi (P,P)\) for each projection P of \(\mathfrak {M}\) , where \(\Psi :\mathfrak {M} \times \mathfrak {M} \rightarrow \mathfrak {M}\) is a bi-linear map. If \(\Psi \) is a bounded l-semi Hochschild 2-cocycle, then \(\mathfrak {T}\) is a left centralizer associated with \(\Psi \) . By applying this conclusion, we offer a characterization of left \(\sigma \) -centralizers, generalized derivations and generalized \(\sigma \) -derivations on von Neumann algebras. Moreover, it is proved that if \(\mathfrak {M}\) is a commutative von Neumann algebra and \(\sigma :\mathfrak {M} \rightarrow \mathfrak {M}\) is an endomorphism, then every bi- \(\sigma \) -derivation \(D:\mathfrak {M} \times \mathfrak {M} \rightarrow \mathfrak {M}\) is identically zero. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0290-2 Issue No:Vol. 64, No. 1 (2018)

Authors:Ishwari Kunwar Pages: 111 - 144 Abstract: We obtain a generalized paraproduct decomposition of the pointwise product of two or more functions that naturally gives rise to multilinear dyadic paraproducts and Haar multipliers. We then study the boundedness properties of these multilinear operators and their commutators with dyadic BMO functions. We also characterize the dyadic BMO functions via the boundedness of (a) certain paraproducts, and (b) the commutators of multilinear Haar multipliers and paraproduct operators. PubDate: 2018-05-01 DOI: 10.1007/s11565-016-0260-0 Issue No:Vol. 64, No. 1 (2018)

Authors:Poornapushkala Narayanan Pages: 145 - 164 Abstract: Let \(X=\mathscr {J}(\widetilde{\mathscr {C}})\) , the Jacobian of a genus 2 curve \(\widetilde{\mathscr {C}}\) over \({\mathbb {C}}\) , and let Y be the associated Kummer surface. Consider an ample line bundle \(L=\mathscr {O}(m\widetilde{\mathscr {C}})\) on X for an even number m, and its descent to Y, say \(L'\) . We show that any dominating component of \({\mathscr {W}}^1_{d}( L' )\) corresponds to \(\mu _{L'}\) -stable Lazarsfeld–Mukai bundles on Y. Further, for a smooth curve \(C\in L \) and a base-point free \(g^1_d\) on C, say (A, V), we study the \(\mu _L\) -semistability of the rank-2 Lazarsfeld–Mukai bundle associated to (C, (A, V)) on X. Under certain assumptions on C and the \(g^1_d\) , we show that the above Lazarsfeld–Mukai bundles are \(\mu _L\) -semistable. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0277-z Issue No:Vol. 64, No. 1 (2018)

Authors:Nipen Saikia; Chayanika Boruah Pages: 165 - 183 Abstract: We derive a new special case C(q) of a general continued fraction recorded by Ramanujan in his Lost Notebook. We give a representation of the continued fraction C(q) as a quotient of Dedekind eta-function and then use it to prove modular identities connecting C(q) with each of the continued fractions \(C(-q)\) , \(C(q^{2})\) , \(C(q^{3})\) , \(C(q^{5})\) , \(C(q^{7})\) , \(C(q^{11})\) , \(C(q^{13})\) and \(C(q^{17})\) . We also prove general theorems for the explicit evaluation of the continued fraction C(q) by using Ramanujan’s class invariants. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0283-1 Issue No:Vol. 64, No. 1 (2018)

Authors:Pierluigi Vellucci; Mattia Zanella Pages: 185 - 207 Abstract: We discuss a novel microscopic model for collective decision-making interacting multi-agent systems. In particular we are interested in modeling a well known phenomena in the experimental literature called equality bias, where agents tend to behave in the same way as if they were as good, or as bad, as their partner. We analyze the introduced problem and we prove the suboptimality of the collective decision-making in the presence of equality bias. Numerical experiments are addressed in the last section. PubDate: 2018-05-01 DOI: 10.1007/s11565-017-0280-4 Issue No:Vol. 64, No. 1 (2018)

Authors:Jonatan Floriano da Silva; Henrique Fernandes de Lima; Marco Antonio Lázaro Velásquez Abstract: In this paper we provide a characterization for stable hypersurfaces with constant anisotropic mean curvature immersed in the Euclidean space \(\mathbb {R}^{n+1}\) through the analysis of the first eigenvalue of the anisotropic Laplacian operator. PubDate: 2018-04-11 DOI: 10.1007/s11565-018-0301-y

Authors:Marco Andreatta; Claudio Fontanari Abstract: Here we investigate the property of effectivity for adjoint divisors. Among others, we prove the following results: A projective variety X with at most canonical singularities is uniruled if and only if for each very ample Cartier divisor H on X we have \(H^0(X, m_0K_X+H)=0\) for some \(m_0=m_0(H)>0\) . Let X be a projective 4-fold, L an ample divisor and t an integer with \(t \ge 3\) . If \(K_X+tL\) is pseudo-effective, then \(H^0(X, K_X+tL) \ne 0\) . PubDate: 2018-02-09 DOI: 10.1007/s11565-018-0300-z

Authors:T. M. Al-Gafri; S. K. Nauman Abstract: Let G be a finite group. A subgroup H of G is s-permutable in G if H permutes with every Sylow subgroup of G. A subgroup H of G is called an \(\mathcal {SSH}\) -subgroup in G if G has an s-permutable subgroup K such that \(H^{sG} = HK\) and \(H^g \cap N_K (H) \leqslant H\) , for all \(g \in G\) , where \(H^{sG}\) is the intersection of all s-permutable subgroups of G containing H. We study the structure of finite groups under the assumption that the maximal or the minimal subgroups of Sylow subgroups of some normal subgroups of G are \(\mathcal {SSH}\) -subgroups in G. Several recent results from the literature are improved and generalized. PubDate: 2018-02-05 DOI: 10.1007/s11565-018-0299-1

Authors:Luciana Mafalda Elias de Assis; Malay Banerjee; Ezio Venturino Abstract: In this paper two mathematical models are proposed and analyzed to elucidate the influence on a generalist predator of its hidden and explicit resources. Boundedness of the system’s trajectories, feasibility, local and global stability of the equilibria for both models are established, as well as possible local bifurcations. The findings indicate that the relevant behaviour of the system, including switching of stability, extinction and persistence of the involved populations, depends mainly on the reproduction rate of the favorite prey. To achieve full ecosystem survival some balance between the respective grazing pressures exerted by the predator on the prey populations needs to be maintained, while higher grazing pressure just on one species always leads to its extinction. PubDate: 2018-01-22 DOI: 10.1007/s11565-018-0298-2

Authors:G. Chiaselotti; T. Gentile; F. Infusino Abstract: In this paper, we give a purely mathematical generalization of an information table. We call pairing on a given set \(\Omega \) a triple \(\mathfrak {P}=(U, F, \Lambda )\) , where U and \(\Lambda \) are non-empty sets and \(F:U\times \Omega \rightarrow \Lambda \) is a map. We provide several examples of pairings: graphs, digraphs, metric spaces, group actions and vector spaces endowed with a bilinear form. Moreover, we reinterpret the usual notion of indiscernibility (with respect to a fixed attribute subset of an information table) in terms of local symmetry on U and, then, we study a global version of symmetry, that we called indistinguishability. In particular, we interpret the latter relation as the symmetrization of a pre-order \(\le _{\mathfrak {P}}\) , that describes the symmetry transmission between subsets of \(\Omega \) . Hence, we introduce a global average of symmetry transmission and studied it for some basic digraph families. Finally, we prove that the partial order of any finite lattice can be described in terms of the above pre-order. PubDate: 2018-01-15 DOI: 10.1007/s11565-018-0297-3

Authors:Robert Laterveer Pages: 315 - 321 Abstract: This small note contains some easy examples of quartic hypersurfaces that have finite-dimensional motive. As an illustration, we verify a conjecture of Voevodsky (concerning smash-equivalence) for some of these special quartics. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0263-x Issue No:Vol. 63, No. 2 (2017)

Authors:Henrique F. de Lima; Márcio S. Santos Pages: 323 - 332 Abstract: We prove height estimates concerning compact hypersurfaces with nonzero constant weighted mean curvature and whose boundary is contained into a slice of a weighted product space of nonnegative Bakry–Émery–Ricci curvature. As applications of our estimates, we obtain half-space type results related to complete noncompact hypersurfaces properly immersed in such an ambient space. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0268-5 Issue No:Vol. 63, No. 2 (2017)

Authors:B. S. Ogundare; A. T. Ademola; M. O. Ogundiran; O. A. Adesina Pages: 333 - 351 Abstract: This paper establishes explicit criteria in form of inequalities for all solutions to a class of second order nonlinear differential equations (with and without delay) to be bounded, ultimately bounded and globally asymptotically stable using Lyapunov second method. Obtained results are new and they complement existing results in the literature. Some examples are given to illustrate the main results. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0262-y Issue No:Vol. 63, No. 2 (2017)

Authors:Chhaya Singhal; G. S. Srivastava Pages: 365 - 376 Abstract: In the present paper, we obtain the characterization of various growth parameters of an entire function F(s) represented by Laplace–Stieltjes transformation in terms of the rate of decrease of \(E_n ( {F,\beta } ),\) where \(E_n ( {F,\beta } )\) represents the error in approximating the function F(s) by exponential polynomials. PubDate: 2017-11-01 DOI: 10.1007/s11565-017-0272-4 Issue No:Vol. 63, No. 2 (2017)

Authors:Emmanuel Franck; Laurent Gosse Abstract: By applying Helmholtz decomposition, the unknowns of a linearized Euler system can be recast as solutions of uncoupled linear wave equations. Accordingly, the Kirchhoff expression of the exact solutions is recast as a time-marching, Lax–Wendroff type, numerical scheme for which consistency with one-dimensional upwinding is checked. This discretization, involving spherical means, is set up on a 2D uniform Cartesian grid, so that the resulting numerical fluxes can be shown to be conservative. Moreover, semi-discrete stability in the \(H^s\) norms and vorticity dissipation are established, along with practical second-order accuracy. Finally, some relations with former “shape functions” and “symmetric potential schemes” are highlighted. PubDate: 2017-12-06 DOI: 10.1007/s11565-017-0296-9

Authors:Lucio Guerra Abstract: We study the collection of homological equivalence relations on a fixed curve. We construct a moduli space for pairs consisting of a curve of genus g and a homological equivalence relation of degree n on the curve, and a classifying set for homological equivalence relations of degree n on a fixed curve, modulo automorphisms of the curve. We identify a special type of homological equivalence relations, and we characterize the special homological equivalence relations in terms of the existence of elliptic curves in the Jacobian of the curve. PubDate: 2017-11-23 DOI: 10.1007/s11565-017-0295-x