Authors:Philippe Rambour Pages: 159 - 178 Abstract: Using previous results we propose an asymptotic expression of the coefficients of the orthogonal polynomials on the unit circle with respect to a weight of type \(f_{\alpha _{1},\ldots ,\alpha _{M},\, \theta _{1},\ldots ,\theta _{M}}\) defined by \({ \theta \mapsto \prod \nolimits _{1\le j \le M} \vert 1 - e^{i(\theta -\theta _{j})}\vert ^{2\alpha _{j}} c}\) with \(\theta _{j}\in ]-\pi ,\pi ]\) , \(\theta _{i}\ne \theta _{j}\) , and \(-\frac{1}{2} < \alpha _{j}<\frac{1}{2}\) and c a sufficiently smooth regular function. As a corollary we give an asymptotic expansion of the entries of \(T_{N}^{-1}\big ( f_{\alpha _{1},\ldots ,\alpha _{M},\theta _{1},\ldots ,\theta _{M},\, \theta _{1},\ldots ,\theta _{M}}\big )\) for \(\max ( \alpha _{1},\ldots ,\alpha _{M})\in ]0, \frac{1}{2}[\) . PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0071-3 Issue No:Vol. 10, No. 2 (2017)

Authors:Binayak S. Choudhury; Samir Kumar Bhandari; Parbati Saha Pages: 179 - 189 Abstract: Cyclic contractions have received attention especially due to their uses in problems of global optimizations. In this paper we consider p-cyclic maps in 2-Menger spaces which are cyclic mappings between p-number of subsets of the space. We establish a fixed point result for these maps under the assumption of an inequality which is Kannan type and involves two control functions. Our results extends a previous results and is illustrated with an example. PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0073-1 Issue No:Vol. 10, No. 2 (2017)

Authors:Ismail Nikoufar Pages: 191 - 198 Abstract: In this paper, under certain conditions we find a double Jordan derivation near a certain function in a p-Banach algebra. Indeed, we prove the generalized Hyers–Ulam–Rassias stability and Isac-Rassias stability of double Jordan derivations in p-Banach algebras. PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0074-0 Issue No:Vol. 10, No. 2 (2017)

Authors:Andrea Cancedda Pages: 199 - 222 Abstract: We consider a Neumann–Robin spectral problem in a perforated domain \(\Omega _{\varepsilon }\) . By homogenization techniques we find the suitable homogenized problem and we discuss the asymptotics of eigenpairs, as the size of the perforation tends to zero. Our results involve an approach based on Višík lemma and the Mosco convergence of eigenspaces. We prove that eigenpairs of our problem converge to eigenpairs of the homogenized problem with rate \(\sqrt{\varepsilon }\) . PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0075-z Issue No:Vol. 10, No. 2 (2017)

Authors:Himashree Kalita; Azizul Hoque; Helen K. Saikia Pages: 223 - 228 Abstract: In this paper we introduce the concept of \(\xi \) -torsion module, \(\xi \) -torsion-free module and \(\xi \) -torsionable module. We investigate many properties of these modules. We characterize \(\xi \) -torsion modules and \(\xi \) -torsion-free modules using short exact sequences and module homomorphisms. PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0076-y Issue No:Vol. 10, No. 2 (2017)

Authors:Indrajit Lahiri; Imrul Kaish Pages: 229 - 240 Abstract: We consider in the paper the situation when an entire function shares a polynomial with its derivatives. Our results improve a result of Zhong. PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0077-x Issue No:Vol. 10, No. 2 (2017)

Authors:Michel Artola Pages: 241 - 269 Abstract: Methods developed by Lions and Peetre (Pub Math de l’IHES 19:5–68, 1964) are used to extend results derived in Artola (Bolletino UMI (9) V:125–158, 2012) for traces of weighted spaces. The weights are required to belong to the Hardy class H(p) defined in Artola (Bolletino UMI (9) V:125–158, 2012) to ensure that a necessary convolution product remains valid in weighted spaces. The restriction, apparently new, is necessary for the present treatment. PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0079-8 Issue No:Vol. 10, No. 2 (2017)

Authors:M. Mursaleen; Md. Nasiruzzaman Pages: 271 - 289 Abstract: In this paper, we apply (p, q)-calculus to construct generalized bivariate Bleimann–Butzer–Hahn operators based on (p, q)-integers and obtain Korovkin type approximation theorem. Furthermore, we compute the rate of convergence for these operators by using the modulus of continuity and Lipschitz type maximal function. PubDate: 2017-06-01 DOI: 10.1007/s40574-016-0080-2 Issue No:Vol. 10, No. 2 (2017)

Abstract: The paper discusses uniqueness of solutions to stationary elliptic problems of the type $$\begin{aligned} A(u)+H(u)=f\in {\mathcal {D}}'(\Omega ), \end{aligned}$$ where \(\Omega \ \in R^{N},\ \) \(u\in W^{1,p}(\Omega )\ (1\le p\le +\infty ),\ A(u)\ \) is an elliptic operator, \(H(u)\ \) is an Hamiltonian that grows with \(\left {\nabla u}\right ^{p}\) and f is given. Methods introduced in Artola (Boll UMI 6(5-B):51–71, 1986), (Proceedings of the International Conference on Generalized Functions, (ICGF 2000). Cambridge Scientific Publishers, Cambridge, 51–92, 2004), (Ricerche di Matematica XLIV, fasc. 2:400–420, 1995) for quasilinear parabolic or elliptic equations, together with properties for some continuity moduli, are used to improve some results from Barles and Murat (Arch Ration Mech Anal 133(1):77–101, 1995) for bounded solutions and from Barles and Porretta (Ann Scuola Norm Sup Pisa Cl Sci 5(1):107–136, 2006), Lions (J Anal Math 45: 234–254, 1985) for unbounded solutions, when 1 \(\le p\le 2.\) Unilateral problems are considered and the case where f depends on the solution u is also discussed. PubDate: 2017-06-23

Abstract: In this paper we prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. The result is complemented with some numerical simulations. PubDate: 2017-06-20

Authors:Francesco Bastianelli; Ciro Ciliberto; Flaminio Flamini; Paola Supino Abstract: This short paper concerns the existence of curves with low gonality on smooth hypersurfaces \(X\subset \mathbb {P}^{n+1}\) . After reviewing a series of results on this topic, we report on a recent progress we achieved as a product of the Workshop Birational geometry of surfaces, held at University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained that if \(X\subset \mathbb {P}^{n+1}\) is a very general hypersurface of degree \(d\geqslant 2n+2\) , the least gonality of a curve \(C\subset X\) passing through a general point of X is \(\mathrm {gon}(C)=d-\left\lfloor \frac{\sqrt{16n+1}-1}{2}\right\rfloor \) , apart from some exceptions we list. PubDate: 2017-05-30 DOI: 10.1007/s40574-017-0129-x

Authors:Filippo F. Favale Abstract: In this paper we are interested in quotients of Calabi–Yau threefolds with isolated singularities. In particular, we analyze the case when X / G has terminal singularities. We prove that, if G is cyclic of prime order and X / G has terminal singularities, then G has order lower than or equal to 5. PubDate: 2017-05-25 DOI: 10.1007/s40574-017-0128-y

Authors:Vladimir Gol’dshtein; Valerii Pchelintsev; Alexander Ukhlov Abstract: In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains \(\varOmega \subset {\mathbb {R}}^2\) . This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal \(\alpha \) -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings. PubDate: 2017-05-17 DOI: 10.1007/s40574-017-0127-z

Authors:Luca Motto Ros Abstract: We survey some old and new results concerning the classification of complete metric spaces up to isometry, a theme initiated by Gromov, Vershik and others. All theorems concerning separable spaces appeared in various papers in the last twenty years: here we tried to present them in a unitary and organic way, sometimes with new and/or simplified proofs. The results concerning non-separable spaces (and, to some extent, the setup and techniques used to handle them) are instead new, and suggest new lines of investigation in this area of research. PubDate: 2017-04-27 DOI: 10.1007/s40574-017-0125-1

Authors:Margherita Lelli-Chiesa Abstract: We survey some results concerning Severi varieties and variation in moduli of curves lying on K3 surfaces or on abelian surfaces. A number of open problems is listed and some work in progress is mentioned. PubDate: 2017-04-22 DOI: 10.1007/s40574-017-0126-0

Authors:Andrea Vaccaro; Matteo Viale Abstract: It is common knowledge in the set theory community that there exists a duality relating the commutative \(C^*\) -algebras with the family of \(\mathsf {B}\) -names for complex numbers in a boolean valued model for set theory \(V^{\mathsf {B}}\) . Several aspects of this correlation have been considered in works of the late 1970s and early 1980s, for example by Takeuti (Two Applications of Logic to Mathematics. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, Kanô Memorial Lectures, vol 3. Publications of the Mathematical Society of Japan, No. 13, 1978) and Fourman et al. (eds.) (Applications of sheaves. In: Lecture Notes in Mathematics, vol 753. Springer, Berlin, 1979), and by Jech (Trans Am Math Soc 289(1):133–162, 1985). Generalizing Jech’s results, we extend this duality so as to be able to describe the family of boolean names for elements of any given Polish space Y (such as the complex numbers) in a boolean valued model for set theory \(V^\mathsf {B}\) as a space \(C^+(X,Y)\) consisting of functions f whose domain X is the Stone space of \(\mathsf {B}\) , and whose range is contained in Y modulo a meager set. We also outline how this duality can be combined with generic absoluteness results in order to analyze, by means of forcing arguments, the theory of \(C^+(X,Y)\) . PubDate: 2017-04-12 DOI: 10.1007/s40574-017-0124-2

Authors:Benjamin F. Dribus; J. W. Hoffman; Sen Yang Abstract: We examine the tangent groups at the identity, and more generally the formal completions at the identity, of the Chow groups of algebraic cycles on a nonsingular quasiprojective algebraic variety over a field of characteristic zero. We settle a question recently raised by Mark Green and Phillip Griffiths concerning the existence of Bloch–Gersten–Quillen-type resolutions of algebraic K-theory sheaves on infinitesimal thickenings of nonsingular varieties, and the relationships between these sequences and their “tangent sequences,” expressed in terms of absolute Kähler differentials. More generally, we place Green and Griffiths’ concrete geometric approach to the infinitesimal theory of Chow groups in a natural and formally rigorous structural context, expressed in terms of nonconnective K-theory, negative cyclic homology, and the relative algebraic Chern character. PubDate: 2017-04-07 DOI: 10.1007/s40574-017-0123-3

Authors:Stefano Filipazzi Abstract: We show that there exist smooth surfaces violating Generic Vanishing in any characteristic \(p \ge 3\) . As a corollary, we recover a result of Hacon and Kovács, producing counterexamples to Generic Vanishing in dimension 3 and higher. PubDate: 2017-04-05 DOI: 10.1007/s40574-017-0120-6

Authors:Luca Migliorini Abstract: We give an introduction to non-abelian Hodge theory for curves with the aim of stating the \(P = W\) conjecture both in its original cohomological version and in the more recent geometric one, and proposing a strategy to relate the two conjectures. PubDate: 2017-03-30 DOI: 10.1007/s40574-017-0122-4

Authors:Giovanni Cimatti Abstract: The elliptic boundary value problem governing the steady electrical heating of a conductor of heat and electricity, the so-called thermistor problem, $$\begin{aligned}&{\nabla }\cdot ({\sigma }(u){\nabla }\phi )=0\ {\quad \hbox {in}\ {\Omega }}\quad \phi =\phi _b\ {\quad \hbox {on}\ {\Gamma }}\\&{\nabla }\cdot ({\kappa }(u){\nabla }u)=-{\sigma }(u) {\nabla }\phi ^2\ {\quad \hbox {in}\ {\Omega }}\quad u=0\ {\quad \hbox {on}\ {\Gamma }}, \end{aligned}$$ where \({\sigma }(u)\) is the temperature dependent electric conductivity and \({\kappa }(u)\) the thermal conductivity, admits a reinterpretation in the framework of general relativity if we choose \({\sigma }(u)=e^u\) , \({\kappa }(u)=1\) and, in addition, \({\Omega }\) is a domain of \({\mathbf{R}^3}\) axially symmetric whereas the function \(\phi _b\) , in a cylindrical coordinate system \({\rho },z,{\varphi }\) , is independent of \({\varphi }\) . The same analytical methods relevant in the thermistor problem can be used in this new context. PubDate: 2017-03-28 DOI: 10.1007/s40574-017-0121-5