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Zeros of irreducible characters lying in a normal subgroupFeb 08 2019Let $N$ be a normal subgroup of a finite group $G$. An element $g\in G$ such that $\chi(g)=0$ for some irreducible character $\chi$ of $G$ is called a vanishing element of $G$. The aim of this paper is to analyse the influence of the $\pi$-elements in ... More

On zeros of irreducible characters lying in a normal subgroupFeb 08 2019Feb 13 2019Let $N$ be a normal subgroup of a finite group $G$. An element $g\in G$ such that $\chi(g)=0$ for some irreducible character $\chi$ of $G$ is called a vanishing element of $G$. The aim of this paper is to analyse the influence of the $\pi$-elements in ... More

Clebsch-Lagrange variational principle and geometric constraint analysis of relativistic field theoriesDec 11 2018Inspired by the Clebsch optimal control problem, we introduce a new variational principle that is suitable for capturing the geometry of relativistic field theories with constraints related to a gauge symmetry. Its special feature is that the Lagrange ... More

Conjugacy classes, characters and products of elementsJul 10 2018Recently, Baumslag and Wiegold proved that a finite group $G$ is nilpotent if and only if $o(xy)=o(x)o(y)$ for every $x,y\in G$ of coprime order. Motivated by this result, we study the groups with the property that $(xy)^G=x^Gy^G$ and those with the property ... More

Discretized Fast-Slow Systems near Transcritical SingularitiesJun 18 2018We extend slow manifolds near a transcritical singularity in a fast-slow system given by the explicit Euler discretization of the corresponding continuous-time normal form. The analysis uses the blow-up method and direct trajectory-based estimates. We ... More

Space of isospectral periodic tridiagonal matricesMar 30 2018Dec 14 2018A periodic tridiagonal matrix is a tridiagonal matrix with additional two entries at the corners. We study the space $X_{n,\lambda}$ of Hermitian periodic tridiagonal $n\times n$-matrices with a fixed simple spectrum $\lambda$. Using the discretized Shr\"{o}dinger ... More

Manifolds of isospectral arrow matricesMar 28 2018An arrow matrix is a matrix with zeroes outside the main diagonal, first row, and first column. We consider the space $M_{St_n,\lambda}$ of Hermitian arrow $(n+1)\times (n+1)$-matrices with fixed simple spectrum $\lambda$. We prove that this space is ... More

Completely Baire spaces, Menger spaces, and projective setsMar 09 2018W. Hurewicz proved that analytic Menger sets of reals are $\sigma$-compact and that co-analytic completely Baire sets of reals are completely metrizable. It is natural to try to generalize these theorems to projective sets. This has previously been accomplished ... More

Zeros of irreducible characters in factorised groupsMar 01 2018An element $g$ of a finite group $G$ is said to be vanishing in $G$ if there exists an irreducible character $\chi$ of $G$ such that $\chi(g)=0$; in this case, $g$ is also called a zero of $G$. The aim of this paper is to obtain structural properties ... More

Convergence and quantale-enriched categoriesMay 24 2017Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched ... More

A family of singular ordinary differential equations of third order with an integral boundary conditionApr 03 2017We establish in this paper the equivalence between a Volterra integral equation of second kind and a singular ordinary differential equation of third order with two initial conditions and an integral boundary condition, with a real parameter. This equivalence ... More

Dynamical aspects of the total QSSA in Enzyme KineticsFeb 17 2017In this paper we prove that the well-known quasi-steady state approximations, commonly used in enzyme kinetics, which can be interpreted as the reduced system of a differential system depending on a perturbative parameter, according to Tihonov theory, ... More

Borel Circle SquaringDec 17 2016Jun 12 2017We give a completely constructive solution to Tarski's circle squaring problem. More generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If $k \geq 1$ and $A, B \subseteq \mathbb{R}^k$ are bounded Borel sets with the ... More

Finite 2-groups with odd number of conjugacy classesNov 28 2016In this paper we consider finite 2-groups with odd number of real conjugacy classes. On one hand we show that if $k$ is an odd natural number less than 24, then there are only finitely many finite 2-groups with exactly $k$ real conjugacy classes. On the ... More

Non-classical heat conduction problem with non local sourceOct 05 2016We consider the non-classical heat conduction equation, in the domain $D=\br^{n-1}\times\br^{+}$, for which the internal energy supply depends on an integral function in the time variable of % $(y , t)\mapsto \int_{0}^{t} u_{x}(0 , y , s) ds$, %where ... More

Newton flows for elliptic functions III Classification of $3^{\text{rd}}$ order Newton graphsSep 05 2016Feb 14 2018A Newton graph of order $r( \geqslant 2)$ is a cellularly embedded toroidal graph on $r$ vertices, $2r$ edges and $r$ faces that fulfils certain combinatorial properties (Euler, Hall). The significance of these graphs relies on their role in the study ... More

Newton flows for elliptic functions III Classification of $3^{\text{rd}}$ order Newton graphsSep 05 2016A Newton graph of order $r( \geqslant 2)$ is a cellularly embedded toroidal graph on $r$ vertices, $2r$ edges and $r$ faces that fulfils certain combinatorial properties (Euler, Hall). The significance of these graphs relies on their role in the study ... More

Newton flows for elliptic functions II Structural stability: Classification & RepresentationSep 05 2016In our previous paper we associated to each non-constant elliptic function $f$ on a torus $T$ a dynamical system, the elliptic Newton flow corresponding to $f$. We characterized the functions for which these flows are structurally stable and showed a ... More

Topological spaces with an $ω^ω$-baseJul 27 2016Jan 25 2017Given a partially ordered set $P$ we study properties of topological spaces $X$ admitting a $P$-base, i.e., an indexed family $(U_\alpha)_{\alpha\in P}$ of subsets of $X\times X$ such that $U_\beta\subset U_\alpha$ for all $\alpha\le\beta$ in $P$ and ... More

Topological spaces with an $ω^ω$-baseJul 27 2016Sep 09 2016Given a partially ordered set $P$ we study properties of topological spaces $X$ admitting a $P$-base, i.e., an indexed family $(U_\alpha)_{\alpha\in P}$ of subsets of $X\times X$ such that $U_\beta\subset U_\alpha$ for all $\alpha\le\beta$ in $P$ and ... More

Dimensions of multi-fan algebrasJul 13 2016Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and multi-fans. ... More

Dimensions of multi-fan algebrasJul 13 2016Dec 01 2016Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and multi-fans. ... More

Generic Torus CanardsJun 08 2016Torus canards are solutions of slow/fast systems that alternate between attracting and repelling manifolds of limit cycles of the fast subsystem. A relatively new dynamic phenomenon, torus canards have been found in neural applications to mediate the ... More

$\mathfrak G$-bases in free (locally convex) topological vector spacesJun 06 2016Jun 26 2016We characterize topological (and uniform) spaces whose free (locally convex) topological vector spaces have a local $\mathfrak G$-base. A topological space $X$ has a local $\mathfrak G$-base if every point $x$ of $X$ has a neighborhood base $(U_\alpha)_{\alpha\in\omega^\omega}$ ... More

Arithmetical structures on graphsApr 08 2016Jun 13 2017Arithmetical structures on a graph were introduced by Lorenzini as some intersection matrices that arise in the study of degenerating curves in algebraic geometry. In this article we study these arithmetical structures, in particular we are interested ... More

Finite orbits for nilpotent actions on the torusMar 13 2016A homeomorphism of the $2$-torus with Lefschetz number different from zero has a fixed point. We give a version of this result for nilpotent groups of diffeomorphisms. We prove that a nilpotent group of $2$-torus diffeomorphims has finite orbits when ... More

Finite orbits for nilpotent actions on the torusMar 13 2016Feb 09 2017A homeomorphism of the $2$-torus with Lefschetz number different from zero has a fixed point. We give a version of this result for nilpotent groups of diffeomorphisms. We prove that a nilpotent group of $2$-torus diffeomorphims has finite orbits when ... More

Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elementsJan 17 2016Jun 02 2016There are various results in the literature which are part of the general philosophy that a finite group for which a certain parameter (for example, the number of conjugacy classes or the maximum number of elements inverted, squared or cubed by a single ... More

Landau's theorem, fields of values for characters, and solvable groupsJun 26 2015When $G$ is solvable group, we prove that the number of conjugacy classes of elements of prime power order is less than or equal to the number of irreducible characters with values in fields where $\mathbb {Q}$ is extended by prime power roots of unity. ... More

Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomialsMay 21 2015Jul 12 2016We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by analytical methods. ... More

From Canards of Folded Singularities to Torus Canards in a Forced van der Pol EquationApr 15 2015We study canard solutions of the forced van der Pol (fvdP) equation in the relaxation limit for low-, intermediate-, and high-frequency periodic forcing. A central numerical observation is that there are two branches of canards in parameter space which ... More

The Real-rootedness of Eulerian Polynomials via the Hermite--Biehler TheoremJan 23 2015Apr 14 2015Based on the Hermite--Biehler theorem, we simultaneously prove the real-rootedness of Eulerian polynomials of type $D$ and the real-rootedness of affine Eulerian polynomials of type $B$, which were first obtained by Savage and Visontai by using the theory ... More

Perihelia reduction and global Kolmogorov tori in the planetary problemJan 19 2015Sep 20 2016We prove the existence of an almost full measure set of $(3n-2)$--dimensional quasi periodic motions in the planetary problem with $(1+n)$ masses, with eccentricities arbitrarily close to the Levi-Civita limiting value and relatively high inclinations. ... More

On the dynamics of endomorphisms of finite groupsSep 12 2014Dec 04 2014Aiming at a better understanding of finite groups as finite dynamical systems, we show that by a version of Fitting's Lemma for groups, each state space of an endomorphism of a finite group is a graph tensor product of a finite directed $1$-tree whose ... More

Global Kolmogorov tori in the planetary N-body problem. Announcement of resultJun 17 2014Jun 24 2014We improve a result in [L. Chierchia and G. Pinzari, Invent. Math. 2011] by proving the existence of a positive measure set of $(3n-2)$--dimensional quasi--periodic motions in the spacial, planetary $(1+n)$--body problem away from co--planar, circular ... More

Modeling of compressible electrolytes with phase transitionMay 26 2014A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist. In addition, ... More

Geometric properties of basic hypergeometric functionsApr 12 2014In this paper we consider basic hypergeometric functions introduced by Heine. We study mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex ... More

Aspects of the planetary Birkhoff normal formOct 01 2013Oct 28 2013The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the dynamics of ... More

On the Kolmogorov set for Many-Body ProblemsSep 26 2013Oct 01 2013I defended my PhD Thesis in Rome, Universit\`a Roma Tre, on April, 23, 2009, under the direction of Professor Luigi Chierchia. The judging committee was composed by Professors M. Berti, A. Celletti, C. Falcolini, J. F\'ejoz. Professors M. Berti and J. ... More

Triangulated categories of motives in positive characteristicMay 23 2013Dec 05 2013This thesis presents a way to apply this theorem of Gabber to a large portion of Voevodsky's work in order to lift the assumption that resolution of singularities holds. This gives unconditional versions of many of his and others' theorems provided we ... More

Special prime Fano fourfolds of degree 10 and index 2Feb 06 2013Feb 25 2014Mukai proved that most prime Fano fourfolds of degree 10 and index 2 are contained in a Grassmannian G(2,5). They are all unirational and some are rational, as remarked by Roth in 1949. We show that their middle cohomology is of K3 type and that their ... More

Orientation theory in arithmetic geometryNov 17 2011Jul 14 2018This work is devoted to study orientation theory in arithmetic geometric within the motivic homotopy theory of Morel and Voevodsky. The main tool is a formulation of the absolute purity property for an \emph{arithmetic cohomology theory}, either represented ... More

Orientation theory in arithmetic geometryNov 17 2011Dec 28 2014This work is devoted to study orientation theory in arithmetic geometric within the motivic homotopy theory of Morel and Voevodsky. The main tool is a formulation of the absolute purity property for an \emph{arithmetic cohomology theory}, either represented ... More

Closed forms and multi-moment mapsOct 29 2011We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For ... More

Legendre Duality Between Lagrangian and Hamiltonian MechanicsAug 29 2011In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (\rho,\eta)-tangent application of the Legendre bundle morphism associated to a Lagrangian L or Hamiltonian H is presented. Using that, a ... More

Multi-moment mapsDec 09 2010Mar 17 2011We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are ... More

Climate dynamics and fluid mechanics: Natural variability and related uncertaintiesJun 15 2010The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and reduction of the uncertainties in future climate-change projections. ... More

Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operatorJun 09 2010Feb 11 2013This article is concerned with conjugacy problems arising in homeomorphisms group, Hom($F$), of unbounded subsets $F$ of normed vector spaces $E$. Given two homeomorphisms $f$ and $g$ in Hom($F$), it is shown how the existence of a conjugacy may be related ... More

The Algebraic Index Theorem and Fedosov Quantization of Lagrange-Finsler and Einstein SpacesMay 20 2010Jul 03 2013Various types of Lagrange and Finsler geometries and the Einstein gravity theory, and modifications, can be modelled by nonholonomic distributions on tangent bundles/ manifolds when the fundamental geometric objects are adapted to nonlinear connection ... More

Z[1/p]-motivic resolution of singularitiesFeb 15 2010May 02 2011The main goal of this paper is to deduce (from a recent resolution of singularities result of Gabber) the following fact: (effective) Chow motives with $Z[1/p]$-coefficients over a perfect field $k$ of characteristic $p$ generate the category $DM^{eff}_{gm}[1/p]$ ... More

Local/global analysis of the stationary solutions of some neural field equationsOct 12 2009Neural or cortical fields are continuous assemblies of mesoscopic models, also called neural masses, of neural populations that are fundamental in the modeling of macroscopic parts of the brain. Neural fields are described by nonlinear integro-differential ... More

Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, ISep 07 2007In this article and in its sequel we propose the study of certain discretizations of geometric evolution equations as an approach to the study of the existence problem of some elliptic partial differential equations of a geometric nature as well as a ... More

Hodge genera of algebraic varieties, IIFeb 13 2007Feb 20 2007We study the behavior of Hodge-theoretic genera under morphisms of complex algebraic varieties. We prove that the additive $\chi_y$-genus which arises in the motivic context satisfies the so-called ``stratified multiplicative property", which shows how ... More

Analytical properties and applications of the Wright functionJan 28 2007In this survey paper we consider some applications of the Wright function with special emphasis of its key role in the partial differential equations of fractional order. It was found that the Green function of the time-fractional diffusion-wave equation ... More

On energy functionals, Kahler-Einstein metrics, and the Moser-Trudinger-Onofri neighborhoodDec 15 2006Nov 02 2007We prove that the existence of a Kahler-Einstein metric on a Fano manifold is equivalent to the properness of the energy functionals defined by Bando, Chen, Ding, Mabuchi and Tian on the set of Kahler metrics with positive Ricci curvature. We also prove ... More

Semigroup-controlled asymptotic dimensionAug 29 2006We introduce the idea of semigroup-controlled asymptotic dimension. This notion generalizes the asymptotic dimension and the asymptotic Assouad-Nagata dimension in the large scale. There are also semigroup controlled dimensions for the small scale and ... More

Arithmetical Properties of Finite GroupsSep 16 2005Dec 01 2005Let $G$ be a finite group and $Ch_i(G)$ some quantitative sets. In this paper we study the influence of $Ch_i(G)$ to the structure of $G$. We present a survey of author and his colleagues' recent works.

Coarse dimensions and partitions of unityJun 27 2005Sep 15 2005Gromov \cite{Gr$_1$} and Dranishnikov \cite{Dr$_1$} introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships ... More

Advanced Determinant Calculus: A ComplementMar 24 2005Aug 10 2005This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous ... More

Puzzle geometry and rigidity: The Fibonacci cycle is hyperbolicMar 17 2002May 12 2002We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps which admits a ... More

Asymptotic analysis of two reduction methods for systems of chemical reactionsOct 15 2001This article concerns two methods for reducing large systems of chemical kinetics equations, namely, the method of intrinsic low-dimensional manifolds (ILDMs) due to Maas and Pope and an iterative method due to Fraser and further developed by Roussel ... More

K-area, Hofer metric and geometry of conjugacy classes in Lie groupsSep 11 2000May 16 2001Given a closed symplectic manifold $(M,\omega)$ we introduce a certain quantity associated to a tuple of conjugacy classes in the universal cover of the group ${\hbox{\it Ham}} (M,\omega)$ by means of the Hofer metric on ${\hbox{\it Ham}} (M,\omega)$. ... More

Advanced Determinant CalculusFeb 01 1999May 31 1999The purpose of this article is threefold. First, it provides the reader with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research. Second, it ... More

McKay correspondence and Hilbert schemes in dimension threeMar 25 1998Let $G$ be a nontrivial finite subgroup of $\SL_n(\C)$. Suppose that the quotient singularity $\C^n/G$ has a crepant resolution $\pi\colon X\to \C^n/G$ (i.e. $K_X = \shfO_X$). There is a slightly imprecise conjecture, called the McKay correspondence, ... More