arXiv subjects
Publications and source records attributed to Francesco Esposito.
We investigate qualitative properties of positive singular solutions of some elliptic systems in bounded and unbounded domains. We deduce symmetry and monotonicity properties via the moving plane procedure. Moreover, in the unbounded case, we study some cooperative elliptic systems involving critical nonlinearities in $\mathbb{R}^n$.
We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree $2$ in its Lie algebra. We translate the setup to a representation-theoretic context in the language of a symmetric quiver algebra. This makes it possible to provide a parametrization of the orbits via a combinatorial tool that we call symplectic/orthogonal oriented link patterns. We deduce information about numerology. We then generalize these classifications to standard parabolic subgroups for all classical groups. Finally, our results are restricted to the nilradical.
In this paper we consider positive solutions to quasilinear elliptic problem with singular nonlinearities. We provide a Höpf type boundary lemma via a suitable scaling argument that allows to deal with the lack of regularity of the solutions up to the boundary.
We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved moving plane procedure.
We consider positive singular solutions to semilinear elliptic problems with possibly singular nonlinearity. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure.
We provide a description of the orbit space of a sheet S for the conjugation action of a complex simple simply connected algebraic group G. This is obtained by means of a bijection between S/G and the quotient of a shifted torus modulo the action of a subgroup of the Weyl group and it is the group analogue of a result due to Borho and Kraft. We also describe the normalisation of the categorical quotient \overline{S}//G for arbitrary simple G and give a necessary and sufficient condition for S//G to be normal in analogy to results of Borho, Kraft and Richardson. The example of G_2 is worked out in detail.
Astronomy is undergoing through a methodological revolution triggered by an unprecedented wealth of complex and accurate data. DAMEWARE (DAta Mining & Exploration Web Application and REsource) is a general purpose, Web-based, Virtual Observatory compliant, distributed data mining framework specialized in massive data sets exploration with machine learning methods. We present the DAMEWARE (DAta Mining & Exploration Web Application REsource) which allows the scientific community to perform data mining and exploratory experiments on massive data sets, by using a simple web browser. DAMEWARE offers several tools which can be seen as working environments where to choose data analysis functionalities such as clustering, classification, regression, feature extraction etc., together with models and algorithms.
We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient of an affine subvariety of G modulo the action of a finite abelian 2-group. The affine subvariety is a closed subset of a Bruhat double coset and the abelian group is a finite subgroup of a maximal torus of G. We show that sheets of spherical conjugacy classes in a simple group are always smooth and we list which strata containing spherical classes are smooth.
Astronomy is undergoing through a methodological revolution triggered by an unprecedented wealth of complex and accurate data. The new panchromatic, synoptic sky surveys require advanced tools for discovering patterns and trends hidden behind data which are both complex and of high dimensionality. We present DAMEWARE (DAta Mining & Exploration Web Application REsource): a general purpose, web-based, distributed data mining environment developed for the exploration of large datasets, and finely tuned for astronomical applications. By means of graphical user interfaces, it allows the user to perform classification, regression or clustering tasks with machine learning methods. Salient features of DAMEWARE include its capability to work on large datasets with minimal human intervention, and to deal with a wide variety of real problems such as the classification of globular clusters in the galaxy NGC1399, the evaluation of photometric redshifts and, finally, the identification of candidate Active Galactic Nuclei in multiband photometric surveys. In all these applications, DAMEWARE allowed to achieve better results than those attained with more traditional methods. With the aim of providing potential users with all needed information, in this paper we briefly describe the technological background of DAMEWARE, give a short introduction to some relevant aspects of data mining, followed by a summary of some science cases and, finally, we provide a detailed description of a template use case.
Using different Lubin-Tate groups, we compare $(ϕ, Γ)$ modules associated to a Galois representation via Fontaine's theory.
In recent articles, the investigation of atomic bases in cluster algebras associated to affine quivers led the second-named author to introduce a variety called transverse quiver Grassmannian and the first-named and third-named authors to consider the smooth loci of quiver Grassmannians. In this paper, we prove that, for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable representation M is the set of points N in the quiver Grassmannian of M such that Ext^1(N,M/N)=0. As a corollary we prove that the transverse quiver Grassmannian coincides with the smooth locus of the irreducible components of minimal dimension in the quiver Grassmannian.
We show that the sheets for a connected reductive algebraic group G over an algebraically closed field in good characteristic acting on itself by conjugation are in bijection with G-conjugacy classes of triples (M, Z(M)^\circ t, O) where M is the connected centralizer of a semisimple element in G, Z(M)^\circ t is a suitable coset in Z(M)/Z(M)^\circ and O is a rigid unipotent conjugacy class in M. Any semisimple element is contained in a unique sheet S and S corresponds to a triple with O={1}. The sheets in G containing a unipotent conjugacy class are precisely those corresponding to triples for which M is a Levi subgroup of a parabolic subgroup of G and such a class is unique.
We study quiver Grassmannians associated with indecomposable representations of the Kronecker quiver. We find a cellular decomposition of them and we compute their Betti numbers. As an application, we give a geometric realization of the "canonical basis" of cluster algebras of Kronecker type (found by Sherman and Zelevinsky) and of type $A_2^{(1)}$.