Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Hörmander vector fields equipped with dilations: lifting, Lie-group construction, applications
No full textLet X = {X1, ... ,Xm} be a set of Hörmander vector fields in Rn, where any Xj is homogeneous of degree 1 with respect to a family of non-isotropic dilations in Rn. If N is the dimension of Lie{X}, we can either lift X to a system of generators of a higher dimensional Carnot group on Rn (if N>n, or we can equip Rn with a Carnot group structure with Lie algebra equal to Lie{X} (if N=n). We shall deduce these facts via a local-to-global procedure (available in the homogeneous setting), starting from more general results on the lifting of finite-dimensional Lie algebras of vector fields. The use of the Baker-Campbell-Hausdorff Theorem is crucial. Due to homogeneity, the lifting procedure is simpler than Rothschild-Stein\u27s lifting technique. We finally provide applications to the study of the fundamental solution Gamma for the Hörmander sum of squares Σj=1..m Xj2, including global pointwise estimates of Gamma and of its X-derivatives in terms of the Carnot-Carathéodory distance induced by X on Rn
Optimality conditions for sharp minimality of order in set-valued optimization
No full textSharp minimizers of order g are defined for set-valued optimizationproblems. Necessary and sufficient conditions are given for such mini-mizers, this allows us to extend the well known results obtained in thescalar and vectorial cases by Auslender [6], Studniarski [21], Ward [24]and Jim ´ enez [12, 13]
Complex Factorization by Chebysev Polynomials
Full text linkLet be real numbers for , and define a \textit{-periodic sequence} with initial conditions , and recurrences where ().In this paper, by aid of Chebyshev polynomials, we introduce a new method to obtain the complex factorization ofthe sequence so that we extend some recentresults and solve some open problems. Also, we provide new results by obtainingthe binomial sum for the sequence by using Chebyshev polynomials
An example of Berglund-Hübsch mirror symmetry for a Calabi-Yau complete intersection
Full text linkWe study an example of complete intersection Calabi-Yau threefold due to Libgober and Teitelbaum, and verify mirror symmetry at a cohomological level. Direct computations allow us to propose an analogue to the Berglund-H\"ubsch mirror symmetry setup for this example . We then follow the approach of Krawitz to propose an explicit mirror map
Parabolic problems in non-standard Sobolev spaces of infinite order
Full text linkThis paper is devoted to the study of the existence of solutions for the strongly nonlinear -parabolic equationwhere is a Leray-Lions operator acted from into its dual. The nonlinear term satisfies growth and sign conditions and the datum is assumed to be in the dual space $V^{-\infty,p\u27(x)}(a_\alpha,Q_{T})\>.
Regularity and Gr\"obner bases of the Rees algebra of edge ideals of bipartite graphs
Full text linkLet be a bipartite graph and be its edge ideal. Let be a bipartite graph and be its edge ideal. The aim of this note is to investigate different aspects of the Rees algebra \Rees(I) of . We compute its regularity and the universal Gr\"obner basis of its defining equations; interestingly, both of them are described in terms of the combinatorics of .
We apply these ideas to study the regularity of the powers of . For any we prove that \reg(I^{s+1})=\reg(I^s)+2 and that for an we have the inequality \reg(I^s) \le 2s + \MM(G) - 1
Controllability of impulsive neutral stochastic integro-differential systems driven by FBM with unbounded delay: Controllability results
Full text linkIn this paper we study the controllability results of impulsive neutral stochastic functional integrodifferential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are obtained by using stochastic analysis and a fixed-point strategy. In the end, one example is given to illustrate the feasibility and effectiveness of results obtained
Expansion formulas for Apostol type -Appell polynomials, and their special cases
Full text linkWe present identities of various kinds for generalized -Apostol-Bernoulli and Apostol-Euler polynomials and power sums, which resemble -analogues of formulas from the 2009 paper by Liu and Wang. These formulas are divided into two types: formulas with only -Apostol-Bernoulli, and only -Apostol-Euler polynomials, or so-called mixed formulas, which contain polynomials of both kinds.This can be seen as a logical consequence of the fact that the -Appell polynomials form a commutative ring. The functional equations for Ward numbers operating on the -exponential function, as well as symmetry arguments, are essential for many of the proofs.We conclude by finding multiplication formulas for two -Appell polynomials of general form. This brings us to the -H polynomials, which were discussed in a previous paper
Everywhere Surjections and Related Topics: Examples and Counterexamples
Full text linkThis paper deals with everywhere surjections, i.e. functions defined on a topological space whose restrictions to any non-empty open subset are surjective. We introduce and discuss several constructions in different contexts; some constructions are easy, while others are more involved. Among other things, we prove that there is a vector space of uncountable dimension whose non-zero elements are everywhere surjections from Q to Q; we give an example of an everywhere surjection whose domain is the set of countably infinite real sequences; we construct an everywhere surjective linear map from the Cantor set into itself. Finally, we prove the existence of functions from R to R which are everywhere surjections in stronger senses
Modules and the Second Classical Zariski Topology
Full text linkLet R be an associative ring with identity and Spec^{s}(M) denote the set of all second submodules of a right R-module M. In this paper, we present a number of new results for the second classical Zariski topology on Spec^{s}(M) for a right R-module M. We obtain a characterization of semisimple modules by using the second spectrum of a module. We prove that if R is a ring such that every right primitive factor of R is right artinian, then every non-zero submodule of a second right R-module M is second if and only if M is a fully prime module. We give some equivalent conditions for Spec^{s}(M) to be a Hausdorff space or T₁-space when the right R-module M has certain algebraic properties. We obtain characterizations of commutative Quasi-Frobenius and artinian rings by using topological properties of the second classical Zariski topology. We give a full characterization of the irreducible components of Spec^{s}(M) for a non-zero injective right module M over a ring R such that every prime factor of R is right or left Goldie