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 Annali dell'Universita di Ferrara   [SJR: 0.504]   [H-I: 14]   [0 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 0430-3202 - ISSN (Online) 1827-1510    Published by Springer-Verlag  [2352 journals]
• Remarks on the normal bundles of generic rational curves
• 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)

• Twisting Hopf algebras from cocycle deformations
• 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)

• Explicit div-curl inequalities in bounded and unbounded domains of
$${{\mathbb {R}}}^3$$ R 3
• 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)

• An extension criterion for the local in time solution of the chemotaxis
Navier–Stokes equations in the critical Besov spaces
• 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)

• Partition identities arising from Somos’s theta function identities
• 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)

• Some elementary examples of quartics with finite-dimensional motive
• 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)

• Height estimates and half-space type theorems in weighted product spaces
with nonnegative Bakry–Émery–Ricci curvature
• 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)

• On the qualitative behaviour of solutions to certain second order
nonlinear differential equation with delay
• 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)

• A regularity criterion for 3D Navier–Stokes equations via one component
of velocity and vorticity
• 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)

• On the growth and approximation of entire functions represented by
Laplace–Stieltjes’ transformation
• 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)

• Some singular value and unitarily invariant norm inequalities for Hilbert
space operators
• 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)

• Skew n -derivation on prime and semi prime rings
• 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)

• Klein–Gordon equations with homogeneous time-dependent electric
fields
• 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

• On local Gevrey regularity for Gevrey vectors of subelliptic sums of
squares: an elementary proof of a sharp Gevrey Kotake–Narasimhan theorem

• 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

• Existence of positive periodic solutions of nonlinear neutral differential
systems with variable delays
• 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

• q - Lupas Kantorovich operators based on Polya distribution
• 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

• Characterization of some derivations on von Neumann algebras via left
centralizers
• 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

• On the existence of the biharmonic Green kernels and the adjoint
biharmonic functions
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

• Bézier variant of the Jakimovski–Leviatan–Păltănea operators based
on Appell polynomials
• 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

• Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes
system in a half-space
• 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

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