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)

Authors:Sayed Saber Abstract: Let X be a Stein manifold of dimension \(n \ge 3\) . Let \(\Omega _{1}\) be a weakly q-convex and \(\Omega _{2}\) be a weakly \((n-q-1)\) -convex in X with smooth boundaries such that \(\overline{\Omega }_{2}\Subset \Omega _{1}\Subset X\) . Assume that \(\Omega =\Omega _{1}\backslash \overline{\Omega }_{2}\) . In this paper, we establish sufficient conditions for the closed range of \(\overline{\partial }\) on \(\Omega \) . Moreover, we study the global boundary regularity of the \(\overline{\partial }\) -problem on \(\Omega \) . PubDate: 2017-07-20 DOI: 10.1007/s40574-017-0135-z

Authors:Vincenzo Dimonte Abstract: This is a survey about I0 and rank-into-rank axioms, with some previously unpublished proofs. PubDate: 2017-07-15 DOI: 10.1007/s40574-017-0136-y

Authors:Pietro Caputo; Fabio Martinelli; Fabio Lucio Toninelli Abstract: We consider the \((2+1)\) -dimensional generalized solid-on-solid (SOS) model, that is the random discrete surface with a gradient potential of the form \( \nabla \phi ^{p}\) , where \(p\in [1,+\infty ]\) . We show that at low temperature, for a square region \(\Lambda \) with side L, both under the infinite volume measure and under the measure with zero boundary conditions around \(\Lambda \) , the probability that the surface is nonnegative in \(\Lambda \) behaves like \(\exp (-4\beta \tau _{p,\beta } L H_p(L) )\) , where \(\beta \) is the inverse temperature, \(\tau _{p,\beta }\) is the surface tension at zero tilt, or step free energy, and \(H_p(L)\) is the entropic repulsion height, that is the typical height of the field when a positivity constraint is imposed. This generalizes recent results obtained in [8] for the standard SOS model ( \(p=1\) ). PubDate: 2017-07-15 DOI: 10.1007/s40574-017-0137-x

Authors:Francesco Polizzi Abstract: We relate the existence of some surfaces of general type and maximal Albanese dimension to the existence of some monodromy representations of the braid group \(\mathsf {B}_2(C_2)\) in the symmetric group \(\mathsf {S}_n\) . Furthermore, we compute the number of such representations up to \(n=9\) , and we analyze the cases \(n \in \{2, \, 3, \, 4\}\) . For \(n=2, \, 3\) we recover some surfaces with \(p_g=q=2\) recently studied (with different methods) by the author and his collaborators, whereas for \(n=4\) we obtain some conjecturally new examples. PubDate: 2017-07-12 DOI: 10.1007/s40574-017-0131-3

Authors:Alessandra Bernardi; Grigoriy Blekherman; Giorgio Ottaviani Abstract: We study typical ranks with respect to a real variety X. Examples of such are tensor rank (X is the Segre variety) and symmetric tensor rank (X is the Veronese variety). We show that any rank between the minimal typical rank and the maximal typical rank is also typical. We investigate typical ranks of n-variate symmetric tensors of order d, or equivalently homogeneous polynomials of degree d in n variables, for small values of n and d. We show that 4 is the unique typical rank of real ternary cubics, and quaternary cubics have typical ranks 5 and 6 only. For ternary quartics we show that 6 and 7 are typical ranks and that all typical ranks are between 6 and 8. For ternary quintics we show that the typical ranks are between 7 and 13. PubDate: 2017-07-10 DOI: 10.1007/s40574-017-0134-0

Authors:Arthur W. Apter Abstract: We prove four theorems concerning the number of normal measures a non- \((\kappa + 2)\) -strong strongly compact cardinal \(\kappa \) can carry. PubDate: 2017-06-30 DOI: 10.1007/s40574-017-0133-1

Authors:Michel Artola 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 DOI: 10.1007/s40574-017-0130-4

Authors:M. Di Francesco; S. Fagioli; M. D. Rosini 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 DOI: 10.1007/s40574-017-0132-2

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