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: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:Hocine Gabsi; Abdelouaheb Ardjouni; Ahcene Djoudi 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: 2017-08-02 DOI: 10.1007/s11565-017-0292-0

Authors:P. N. Agrawal; Pooja Gupta 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: 2017-07-01 DOI: 10.1007/s11565-017-0291-1

Authors:A. Hosseini 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: 2017-06-21 DOI: 10.1007/s11565-017-0290-2

Authors:Abderrahim Aslimani; Imad El Ghazi; Mohamed El Kadiri; Sabah Haddad 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: 2017-06-20 DOI: 10.1007/s11565-017-0289-8

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

Authors:Tongkeun Chang; Kyungkeun Kang 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: 2017-06-06 DOI: 10.1007/s11565-017-0287-x