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 Subjects -> MATHEMATICS (Total: 864 journals)     - APPLIED MATHEMATICS (68 journals)    - GEOMETRY AND TOPOLOGY (19 journals)    - MATHEMATICS (643 journals)    - MATHEMATICS (GENERAL) (40 journals)    - NUMERICAL ANALYSIS (19 journals)    - PROBABILITIES AND MATH STATISTICS (75 journals) MATHEMATICS (643 journals)                  1 2 3 4 | Last

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 Bollettino dell'Unione Matematica Italiana   [SJR: 0.375]   [H-I: 19]   [1 followers]  Follow        Subscription journal  (Not entitled to full-text)    ISSN (Print) 1972-6724 - ISSN (Online) 2198-2759    Published by Springer-Verlag  [2335 journals]
• Homogenization of vector-valued partition problems and dislocation cell
structures in the plane
• Authors: Sergio Conti; Adriana Garroni; Stefan Müller
Pages: 3 - 17
Abstract: We consider target-space homogenization for energies defined on partitions parametrized by a discrete lattice $$\mathcal {B}\subset \mathbb {R}^N$$ . For a small $$\sigma >0$$ , the variable is a piecewise constant function taking values in $$\sigma \mathcal {B}$$ , and the energy depends on the jumps and their orientation. In the limit as $$\sigma \rightarrow 0$$ we obtain a homogenized functional defined on functions of bounded variation. This result is relevant in the study of dislocation structures in plastically deformed crystals. We review recent literature on the topic and propose our limiting effective energy as a continuum model for strain-gradient plasticity.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0083-z
Issue No: Vol. 10, No. 1 (2017)

• Recent results about the prime ideal theorem
• Authors: Giuseppe Molteni
Pages: 19 - 28
Abstract: Let $$\psi _{\mathbb {{{K}}}}$$ be the Chebyshev function of a number field $$\mathbb {{{K}}}$$ , and let $$\psi ^{(1)}_\mathbb {{{K}}}(x):=\int _{0}^{x}\psi _\mathbb {{{K}}}(t)\,\mathrm {d}t$$ and $$\psi ^{(2)}_\mathbb {{{K}}}(x):=2\int _{0}^{x}\psi ^{(1)}_\mathbb {{{K}}}(t)\,\mathrm {d}t$$ . Assuming the truth of Riemann’s hypothesis for Dedekind’s zeta function of $$\mathbb {{{K}}}$$ it is possible to prove explicit bounds for $$\psi _\mathbb {{{K}}}(x) - x$$ , $$\psi ^{(1)}_\mathbb {{{K}}}(x) - \tfrac{x^2}{2}$$ and $$\psi ^{(2)}_\mathbb {{{K}}}(x) - \tfrac{x^3}{3}$$ . These results can be used to prove the existence of many ideals with a small norms and to produce an extremely efficient algorithm for the computation of the residue of Dedekind’s zeta function.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0084-y
Issue No: Vol. 10, No. 1 (2017)

• Converse theorems: from the Riemann zeta function to the Selberg class
• Authors: Alberto Perelli
Pages: 29 - 53
Abstract: This is an expanded version of the author’s lecture at the XX Congresso U.M.I., held in Siena in September 2015. After a brief review of L-functions, we turn to the classical converse theorems of Hamburger, Hecke and Weil, and to some later developments. Finally we present several results on converse theorems in the framework of the Selberg class of L-functions.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0085-x
Issue No: Vol. 10, No. 1 (2017)

• A transportation approach to universality in random matrix theory
• Authors: A. Figalli
Pages: 55 - 74
Abstract: In this note we discuss a new recent approach, based on transportation techniques, to obtain universality results in random matrix theory.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0087-8
Issue No: Vol. 10, No. 1 (2017)

• A variational approach to Liouville equations
• Authors: Andrea Malchiodi
Pages: 75 - 97
Abstract: We consider a class of Liouville equations motivated by uniformization problems in a singular setting, as well as from models in Mathematical Physics. We will study existence from a variational point of view, using suitable improvements of the Moser-Trudinger inequality. These improvements allow to study the concentration properties of conformal volume, and to reduce the problem to studying explicit finite-dimensional objects.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0092-y
Issue No: Vol. 10, No. 1 (2017)

• On small modules for quantum groups at roots of unity
• Authors: Giovanna Carnovale; Iulian I. Simion
Pages: 99 - 112
Abstract: A conjecture of De Concini Kac and Procesi provides a bound on the minimal possible dimension of an irreducible module for quantized enveloping algebras at an odd root of unity. We pose the problem of the existence of modules whose dimension equals this bound. We show that this question cannot have a positive answer in full generality and discuss variants of this question.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0094-9
Issue No: Vol. 10, No. 1 (2017)

• Regularized Euler- $$\alpha$$ α motion of an infinite array of vortex
sheets
• Authors: R. E. Caflisch; F. Gargano; M. Sammartino; V. Sciacca
Pages: 113 - 141
Abstract: We consider the Euler- $$\alpha$$ regularization of the Birkhoff–Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0097-6
Issue No: Vol. 10, No. 1 (2017)

• Some kinetic models for a market economy
• Authors: Marzia Bisi
Pages: 143 - 158
Abstract: We review the main results on some basic kinetic models for wealth distribution in a simple market economy, with interaction rules involving random variables to take into account effects due to market risks. Then, we investigate in more detail long time behavior of a model which includes the taxation phenomenon and the redistribution of collected wealth according to proper criterions. Finally, we propose a new class of kinetic equations in which agent’s trading propensity varies according to the personal amount of wealth.
PubDate: 2017-03-01
DOI: 10.1007/s40574-016-0099-4
Issue No: Vol. 10, No. 1 (2017)

• Affine lines in the complement of a smooth plane conic
• Authors: Julie Decaup; Adrien Dubouloz
Abstract: We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic Q. Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the plane consisting of birational endomorphisms restricting to biregular automorphisms outside Q, there are exactly two such lines: the restriction of a smooth conic osculating Q at a rational point and the restriction of the tangent line to Q at a rational point. In contrast, we give examples illustrating the fact that over fields of positive characteristic, there exist exotic closed embeddings of the affine line in the complement of Q. We also determine an explicit set of birational endomorphisms of the plane whose restrictions generates the automorphism group of the complement of Q over a field of arbitrary characteristic.
PubDate: 2017-03-18
DOI: 10.1007/s40574-017-0119-z

• Irrationality issues for projective surfaces
• Authors: Francesco Bastianelli
Abstract: This survey retraces the author’s talk at the Workshop Birational geometry of surfaces, Rome, January 11–15, 2016. We consider various birational invariants extending the notion of gonality to projective varieties of arbitrary dimension, and measuring the failure of a given projective variety to satisfy certain rationality properties, such as being uniruled, rationally connected, unirational, stably rational or rational. Then we review a series of results describing these invariants for various classes of projective surfaces.
PubDate: 2017-01-27
DOI: 10.1007/s40574-017-0116-2

• The number of real eigenvectors of a real polynomial
• Authors: Mauro Maccioni
Abstract: I investigate on the number t of real eigenvectors of a real symmetric tensor. In particular, given a homogeneous polynomial f of degree d in 3 variables, I prove that t is greater or equal than $$2c+1$$ , if d is odd, and t is greater or equal than $$\max (3,2c+1)$$ , if d is even, where c is the number of ovals in the zero locus of f. About binary forms, I prove that t is greater or equal than the number of real roots of f. Moreover, the above inequalities are sharp for binary forms of any degree and for cubic and quartic ternary forms.
PubDate: 2017-01-09
DOI: 10.1007/s40574-016-0112-y

• Canonical rings of Gorenstein stable Godeaux surfaces
• Authors: Marco Franciosi; Sönke Rollenske
Abstract: Extending the description of canonical rings from Reid (J Fac Sci Univ Tokyo Sect IA Math 25(1):75–92, 1978) we show that every Gorenstein stable Godeaux surface with torsion of order at least 3 is smoothable.
PubDate: 2017-01-05
DOI: 10.1007/s40574-016-0114-9

• On q -Bessel Fourier analysis method for classical moment problem
• Authors: Lazhar Dhaouadi
Abstract: In the first part of this paper, we give a sufficient condition for a particular case of the symmetric moment problem to be determinate using standards methods of q-Bessel Fourier analysis. This condition it cannot be deduced from any other classical criterion of determinacy. In the second part, we study the q-Strum–Liouville equation in the non-real case and we elaborate an analogue of the well known theorem due to Hermann Weyl concerning the Strum–Liouville equation. This emphasizes the connection between the moment problem associated to a particular class of orthonormal polynomials $$(P_n)$$ and the uniqueness of solution which belong to the $$L^2$$ space. The third part is devoted to the study of the q-Strum–Liouville equation in the real case and the behavior of solutions at infinity, which give more information about this type of orthonormal polynomials.
PubDate: 2017-01-04
DOI: 10.1007/s40574-016-0115-8

• Argument estimates of certain meromorphic functions associated with the
generalized Bessel function
• Authors: H. E. Darwish; A. Y. Lashin; B. F. Hassan
Pages: 483 - 493
Abstract: The purpose of the present paper is to derive some inclusion properties and argument estimates of certain classes of meromorphic functions in the punctured unit disc, which are defined by means of Bessel function. Furthermore, the integral preserving properties in a sector are investigated.
PubDate: 2016-12-01
DOI: 10.1007/s40574-016-0063-3
Issue No: Vol. 9, No. 4 (2016)

• Degree of approximation of functions belonging to $$Lip(\omega (t),p)$$ L
i p ( ω ( t ) , p ) -class by linear operators based on Fourier series
• Authors: Soshal Saini; Uaday Singh
Pages: 495 - 504
Abstract: Fourier series and operators based on it are of great importance in both theoretical and applied mathematics because they can be considered as representation of a function or signal. In this paper, we estimate the degree of approximation of $$f \in Lip(\omega (t),p)$$ -class and its conjugate $$\tilde{f},$$ by matrix means of their trigonometric Fourier series by relaxing the conditions on $$\omega (t)$$ imposed by the earlier researchers. We also discuss some results which are analogous to our results.
PubDate: 2016-12-01
DOI: 10.1007/s40574-016-0064-2
Issue No: Vol. 9, No. 4 (2016)

• On the b -symplectic linear group
• Authors: Mohammad Shafiee
Pages: 505 - 511
Abstract: The set of all linear transformations on $$\mathbb {R}^{2m}$$ , preserving its b-symplectic structure, is a Lie group. This group has two components and its identity component contains the unitary group $$U(m-1)$$ as maximal compact subgroup. We obtain a unitary representation for the identity component. At last some results on embedding by this transformations are presented.
PubDate: 2016-12-01
DOI: 10.1007/s40574-016-0068-y
Issue No: Vol. 9, No. 4 (2016)

• On finite groups with nine centralizers
• Authors: Sekhar Jyoti Baishya
Pages: 527 - 531
Abstract: Given a group G, let $${{\mathrm{Cent}}}(G)$$ denote the set of distinct centralizers of elements of G. The group G is called an n-centralizer group if $${{\mathrm{Cent}}}(G) =n$$ and a primitive n-centralizer group if $${{\mathrm{Cent}}}(G) = {{\mathrm{Cent}}}(\frac{G}{Z(G)}) =n$$ . In this paper, we characterize the finite 9-centralizer and the primitive 9-centralizer groups.
PubDate: 2016-12-01
DOI: 10.1007/s40574-016-0070-4
Issue No: Vol. 9, No. 4 (2016)

• Gorenstein n -FP-injective and Gorenstein n -flat complexes
• Authors: C. Selvaraj; R. Saravanan
Abstract: In this paper, we introduce and study the notions of Gorenstein n-FP-injective and Gorenstein n-flat complexes, which are special cases of Gorenstein FP-injective and Gorenstein flat complexes respectively. We prove that over a left n-coherent ring R the class of all Gorenstein n-FP-injective (resp., Gorenstein n-flat) complexes is injectively (resp., projectively) resolving and we discuss the relationship between Gorenstein n-FP-injective and Gorenstein n-flat complexes.
PubDate: 2016-12-08
DOI: 10.1007/s40574-016-0113-x

• Free probability on $$W^{*}$$ W ∗ -dynamical systems determined by
$$GL_{2}(\mathbb {Q} _{p})$$ G L 2 ( Q p ) : generalized Hecke algebras
• Authors: Ilwoo Cho
Abstract: In this paper, we generalize classical Hecke algebras $$\mathcal {H}(G_{p})$$ over the generalized linear groups $$G_{p} = GL_{2}(\mathbb {Q}_{p})$$ induced by the p-adic number fields $$\mathbb {Q}_{p}$$ , for primes p. For a given group $$G_{p},$$ construct a suitable semigroup $$W^{*}$$ -dynamical system $$(M, \sigma (G_{p}), \pi ),$$ where M is a fixed von Neumann algebra, and $$\pi$$ is a semigroup-action of the $$\sigma$$ -algebra $$\sigma (G_{p})$$ of $$G_{p}$$ acting on M. By constructing the corresponding crossed product $$W^{*}$$ -algebra $$M \times _{\pi } \sigma (G_{p})$$ generated by $$(M, \sigma (G_{p}), \pi ),$$ we study free probability on the $$W^{*}$$ -subalgebra $$\mathcal {H}_{M}(G_{p})$$ of $$M \times _{\pi } \sigma (G_{p})$$ . One can understand our von Neumann algebra $$\mathcal {H}_{M}(G_{p})$$ as a generalized $$*$$ -algebra over both M and a Hecke algebra $$\mathcal {H} (G_{p}),$$ for a prime p.
PubDate: 2016-12-02
DOI: 10.1007/s40574-016-0111-z

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