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:Alberto Alzati; Riccardo Re Pages: 211 - 220 Abstract: In this note we give a different proof of Sacchiero’s theorem about the splitting type of the normal bundle of a generic rational curve. Moreover we discuss the existence and the construction of smooth monomial curves having generic type of the normal bundle. PubDate: 2017-11-01 DOI: 10.1007/s11565-017-0276-0 Issue No:Vol. 63, No. 2 (2017)

Authors:Nicolás Andruskiewitsch; Agustín García Iglesias Pages: 221 - 247 Abstract: Let H be a Hopf algebra. Any finite-dimensional lifting of \(V\in {}^{H}_{H}\mathcal {YD}\) arising as a cocycle deformation of \(A={\mathfrak {B}}(V)\#H\) defines a twist in the Hopf algebra \(A^*\) , via dualization. We follow this recipe to write down explicit examples and show that it extends known techniques for defining twists. We also contribute with a detailed survey about twists in braided categories. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0264-9 Issue No:Vol. 63, No. 2 (2017)

Authors:Tahar Zamene Boulmezaoud; Keltoum Kaliche; Nabil Kerdid Pages: 249 - 276 Abstract: We give a constructive proof of some functional inequalities related to the div and curl operators in bounded and unbounded domains of \({{\mathbb {R}}}^3\) . Our new innovation consists in giving explicit constants in several geometric configurations. These inequalities are of a first use in solving div-curl systems and vector potential problems arising in physics. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0266-7 Issue No:Vol. 63, No. 2 (2017)

Authors:Hi Jun Choe; Bataa Lkhagvasuren Pages: 277 - 288 Abstract: We consider the Keller–Segel model coupled with the incompressible Navier–Stokes equations in the dimension three. Based on the wellposedness result in the critical Besov spaces, we present a result on the extension criterion for the local in time solution in the same functional setting, which is a new result for the model. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0265-8 Issue No:Vol. 63, No. 2 (2017)

Authors:B. R. Srivatsa Kumar; R. G. Veeresha Pages: 303 - 313 Abstract: In this paper, we establish certain partition identities for theta function identities of level 14 discovered by M. Somos. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0261-z Issue No:Vol. 63, No. 2 (2017)

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:Myong-Hwan Ri Pages: 353 - 363 Abstract: In this paper we show that a Leray–Hopf weak solution u to 3D Navier–Stokes initial value problem is smooth if there is some \(\alpha \in {{{\mathbb {R}}}}, \alpha \ne 0,\) such that \(\alpha u_3+(-\Delta )^{-1/2}\omega _3\) is suitably smooth, where \(\omega =\text {curl}\,u\) . PubDate: 2017-11-01 DOI: 10.1007/s11565-017-0274-2 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:A. Taghavi; V. Darvish; H. M. Nazari; S. S. Dragomir Pages: 377 - 389 Abstract: In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results. PubDate: 2017-11-01 DOI: 10.1007/s11565-017-0271-5 Issue No:Vol. 63, No. 2 (2017)

Authors:V. K. Yadav; R. K. Sharma Pages: 391 - 402 Abstract: Let \(n \ge 2\) be a fixed integer, R be a noncommutative n!-torsion free ring and I be any non zero ideal of R. In this paper we have proved the following results; (i) If R is a prime ring and there exists a symmetric skew n-derivation \(D: R^n \rightarrow R\) associated with the automorphism \(\sigma \) on R, such that the trace function \(\delta : R \rightarrow R \) of D satisfies \([\delta (x), \sigma (x)] =0\) , for all \(x\in I,\) then \(D=0;\,\) (ii) If R is a semi prime ring and the trace function \(\delta ,\) commuting on I, satisfies \([\delta (x), \sigma (x)]\in Z\) , for all \(x \in I,\) then \([\delta (x), \sigma (x)] = 0 \) , for all \(x \in I.\) Moreover, we have proved some annihilating conditions for algebraic identity involving multiplicative(generalized) derivation. PubDate: 2017-11-01 DOI: 10.1007/s11565-016-0259-6 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

Authors:Masaki Kawamoto Abstract: We consider a system associated to Klein–Gordon equations with homogeneous time-dependent electric fields. The upper and lower boundaries of a time-evolution propagator for this system were proven by Veselić (J Oper Theory 25:319–330, 1991) for electric fields that are independent of time. We extend this result to time-dependent electric fields. PubDate: 2017-10-20 DOI: 10.1007/s11565-017-0294-y

Authors:David S. Tartakoff Abstract: We study the regularity of Gevrey vectors for Hörmander operators $$\begin{aligned} P = \sum _{j=1}^m X_j^2 + X_0 + c \end{aligned}$$ where the \(X_j\) are real vector fields and c(x) is a smooth function, all in Gevrey class \(G^{s}.\) The principal hypothesis is that P satisfies the subelliptic estimate: for some \(\varepsilon >0, \; \exists \,C\) such that $$\begin{aligned} \Vert v\Vert _{\varepsilon }^2 \le C\left( (Pv, v) + \Vert v\Vert _0^2\right) \qquad \forall v\in C_0^\infty . \end{aligned}$$ We prove directly (without the now familiar use of adding a variable t and proving suitable hypoellipticity for \(Q=-D_t^2-P\) and then, using the hypothesis on the iterates of P on u, constructing a homogeneous solution U for Q whose trace on \(t=0\) is just u) that for \(s\ge 1,\) \(G^s(P,\Omega _0) \subset G^{s/\varepsilon }(\Omega _0);\) that is, $$\begin{aligned}&\forall K\Subset \Omega _0, \;\exists C_K: \Vert P^j u\Vert _{L^2(K)}\le C_K^{j+1} (2j)!^s, \;\forall j\\&\quad \implies \forall K'\Subset \Omega _0, \;\exists \tilde{C}_{K'}:\,\Vert D^\ell u\Vert _{L^2(K')} \le \tilde{C}_{K'}^{\ell +1} \ell !^{s/\varepsilon }, \;\forall \ell . \end{aligned}$$ In other words, Gevrey growth of derivatives of u as measured by iterates of P yields Gevrey regularity for u in a larger Gevrey class. When \(\varepsilon =1,\) P is elliptic and so we recover the original Kotake–Narasimhan theorem (Kotake and Narasimhan in Bull Soc Math Fr 90(12):449–471, 1962), which has been studied in many other classes, including ultradifferentiable functions (Boiti and Journet in J Pseudo-Differ Oper Appl 8(2):297–317, 2017). We are indebted to M. Derridj for multiple conversations over the years. PubDate: 2017-08-29 DOI: 10.1007/s11565-017-0293-z

Authors:Meenu Goyal; P. N. Agrawal Abstract: In this paper, we introduce the Bézier variant of the Jakimovski–Leviatan–Păltănea operators based on Appell polynomials. We establish some local results, a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness and also study the rate of convergence for the functions having a derivative of bounded variation for these operators. PubDate: 2017-06-08 DOI: 10.1007/s11565-017-0288-9