Showing papers in "Ricerche Di Matematica in 2012"

Basic properties of Hurwitz series rings

Abstract: This paper studies Hurwitz series rings and Hurwitz polynomial rings. Especially we characterize nilpotent elements, units, McCoy theorem, Noetherian, nonnil-Noetherian and S-Noetherian properties, PS and presimplifiable properties.

A note on the Schur multiplier of groups of prime power order

Abstract: By a well-known result of Green (Proc R Soc A 237:574–581, 1956) and the formal definition of Ellis and Wiegold (Bull Austral Math Soc 60:191–196, 1999), there is an integer t, say corank(G), such that \({|\mathcal{M}(G)| = p^{\frac{1}{2}n(n-1)-t}}\). In Niroomand (J Algebra 322:4479–4482, 2009), the author showed for a non-abelian group G, corank(G) ≥ logp(|G|)−2 and classified the structure of all non-abelian p-groups of corank logp(|G|)−2. In the present paper, we are interesting to characterize the structure of all p-groups of corank logp(|G|)−1.

Measure of weak noncompactness, some new properties in Fredholm theory, characterization of the Schechter essential spectrum and application to transport operators

Abstract: Measures of weak noncompactness have been successfully applied in topology, functional analysis and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We work with the notion of the measures of weak noncompactness in order to establish some results concerning the class of semi-Fredholm and Fredholm operators. Further, we apply the obtained results to prove, under some conditions on the perturbed operator, the invariance of the Schechter essential spectrum on Banach spaces. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator.

On a bilateral birth-death process with alternating rates

Abstract: We consider a bilateral birth-death process characterized by a constant transition rate λ from even states and a possibly different transition rate μ from odd states. We determine the probability generating functions of the even and odd states, the transition probabilities, mean and variance of the process for arbitrary initial state. Some features of the birth-death process confined to the non-negative integers by a reflecting boundary in the zero-state are also analyzed. In particular, making use of a Laplace transform approach we obtain a series form of the transition probability from state 1 to the zero-state.

Porous convection and thermal oscillations

Abstract: A theory is developed for thermal convection in a fluid saturated porous material when the temperature may propagate as a thermal wave. In particular, we are interested in the mechanism of thermal oscillation and so allow for Guyer–Krumhansl effects but employ a heat flux equation developed by Christov and Morro. The instability mechanism is investigated in complete detail and it is shown that stationary convection is likely to prevail under normal terrestrial conditions, but if the thermal relaxation time is sufficiently large there is a possible parameter range which allows for oscillatory convection. However, the presence of the Guyer–Krumhansl terms has the effect of damping the oscillatory convection and returning the instability mechanism to one of stationary convection.

Homogenization of unbounded singular integrals in W1

Abstract: We study homogenization by Γ-convergence, with respect to the L1-strong convergence, of periodic multiple integrals in W1,∞ when the integrand can take infinite values outside of a convex bounded open set of matrices.

On the long-time dynamics of nonautonomous predator–prey models with mutual interference

Abstract: The longtime behaviour of a nonautonomous bidimensional Hassell predator–prey model with mutual interference is investigated. The existence of an absorbing set in the phase space is shown, and necessary and sufficient conditions guaranteeing the nonlinear, global, asymptotic stability of the positive solutions have been found by using the Liapunov direct method.

The k-zero-divisor hypergraph

Abstract: The concept of a k-zero-divisor hypergraph of a commutative ring was introduced by Eslahchi and Rahimi (Int J Math Math Sci, Art ID 50875, 15 pp, 2007) In this paper we change the basic definitions of this concept, and we demonstrate that there are results about k-zero-divisor hypergraphs that parallel noteworthy results about zero-divisor graphs

On nonhomogeneous singular elliptic equations with cylindrical weights

Abstract: In this paper, we establish the existence of multiple solutions for nonhomogeneous singular elliptic equations with cylindrical weights, by using Ekeland’s variational principle and mountain pass theorem without Palais–Smale condition.

A Lagrangian approach to extended thermodynamics of relativistic fluids

Abstract: A Lagrangian approach to the fluid dynamics and fourteen moments extended irreversible thermodynamics of relativistic fluids is presented in a quite general formulation. According to the methodology developed here it is possible to deduce, starting from a suitable Lagrangian density L , the tensor structure of the fluxes governing the system, their relations with the production terms and the energy- momentum tensor. The main field Uand the four-vector generating function h � α are also evaluated under suitable assumptions concerning a non-equilibrium generaliza- tion of Gibbs relation. Convexity condition of the negative entropy density is provided for the privileged time direction w α parallel to h � α . A comparison with the results of

A total Steenrod operation as homomorphism of Steenrod algebra-modules

Abstract: Let p be an odd prime, M be an unstable locally finite module over the Steenrod algebra, and let $${\Phi_{S}}$$ be the localization out of the Euler class of the mod-p cohomology ring of the group Z/p. We prove that the Singer evaluation map $${d : \Phi_S^{GL_{1}} \otimes M \longrightarrow M }$$ is dually related to a total operation $${\chi P : M \longrightarrow \Phi_S^{GL_{1}} \otimes M}$$ . We determine the exotic $${\mathcal A (p)}$$ -module structure on the target which makes χ P an $${\mathcal A (p)}$$ -linear map, give a new proof of the Adem relations and find some new identities involving the Bockstein and the pth reduced powers.

On the Ekeland–Ghoussoub–Preiss and Stuart criteria for locating Cerami sequences

Abstract: A classical result of Ekeland, based on an idea of Ghoussoub and Preiss, asserts that under technical conditions, Cerami sequences for a real valued functional \({\Phi}\) on a Banach space X can be found in the vicinity of suitable closed subsets W of X. In this statement, “vicinity” is defined by means of an associated geodesic distance on X. Recently, under virtually the same hypotheses, Stuart discovered a similar property with a much clearer content since it can very simply be expressed in terms of the norm of X and the corresponding standard distance. In this paper, we prove that the Ekeland–Ghoussoub–Preiss and Stuart criteria are in fact equivalent. We also show that this equivalence need not be true when Cerami sequences are replaced by more general, yet admissible sequences, but that the equivalence is preserved, in part or in totality, under simple additional conditions. These results are also applicable to more general linking geometries than considered by Ekeland–Ghoussoub–Preiss or Stuart and to nonsmooth functionals.

The effective conductivity equation for a highly heterogeneous periodic medium

Abstract: We consider the homogenization of a conductivity equation for a medium made up of a set \({F_\varepsilon}\) (\({\varepsilon}\) being the size of the period of the medium) of highly conductive vertical fibers surrounded by another material (the matrix) assumed to be a poor conductor. The conductivity coefficients in the fibers behave as \({\frac{1}{\varepsilon^2}}\) while whose of the matrix behave as \({\varepsilon^2}\) . We show that the homogenized problem consists of an equality of the kind u(x) = m(x) f (x) where u denotes the macroscopic temperature, f the source term and m(x) a coefficient given by solving some cell equation.

Harmonic vector fields on compact Lorentz surfaces

Abstract: We study harmonic vector fields on a Lorentzian torus T 2 ie critical points of the total bending functional B : E → R were E consists of all unit timelike vector fields on T 2 We derive the first variation formula for B in terms of the Lorentz angle function associated to each X ∈ E and give applications on flat Lorentzian tori

A noise of new type and its application

Abstract: The purpose of this paper is to introduce a new noise depending on the space parameter and the construction of a space of generalized functional of the new noise. One of the significant applications is to give a concrete answer to the jump finding problem raised in [10] where the first step to the approach has been made. It is noted that the new noise, denoted by P′(u), is quite different from the time derivative Ṗ(t) of a Poisson process P(t).

Some new characterizations of solvable PST-groups

Abstract: A subgroup H of a finite group G is said to be τ-semipermutable in G if it permutes with all the Sylow subgroups Q of G such that (|H|, |Q|) = 1 and (|H|, |QG|) ≠ 1. A rather remarkable result of Lukyanenko and Skiba (Rend Semin Mat Univ Padova, 124:231–246, 2010) is: a finite solvable group G is a PST-group if and only if every subgroup of Fit(G) is τ-semipermutable. A local version of this result is established in this paper. A subgroup H of G is said to be τ-seminormal provided that it is normalized by all Sylow subgroups Q such that (|H|, |Q|) = 1 and (|H|, |QG|) ≠ 1. It is shown that a finite solvable group is a PST-group if and only if every subgroup of Fit(G) is τ-seminormal in G.

Strictly ascending HNN extensions in soluble groups

Abstract: We show that there exist finitely generated soluble groups which are not LERF but which do not contain strictly ascending HNN extensions of a cyclic group. This solves Problem 16.2 in the Kourovka notebook. We further show that there is a finitely presented soluble group which is not LERF but which does not contain a strictly ascending HNN extension of a polycyclic group.

A characterization of subgroup containment in direct products

Abstract: Using Goursat’s characterization of subgroups in a direct product, a characterization of subgroup containment in such a direct product is given. Applying this along with facts about p-groups we describe a process for obtaining the subgroup lattice of a direct product of p-groups. This process is implemented to portray the subgroup lattice of Q × Q, where Q is the quaternion group of order 8.

On radially symmetric solutions of the equation −Δu + u = |u|p-1u. An ODE approach

Abstract: Questions of the existence in a ball of radially symmetric solutions of the equation indicated in the title with the Dirichlet zero boundary conditions are studied in many publications and generally speaking, there was obtained more or less complete answer on these questions. It is known now that if the dimension of the space d ≥ 3 and 1 1, then for any integer l ≥ 0 this problem in a ball or in the entire space \({x \in \mathbb {R}^d}\) has a radially symmetric solution with precisely l zeros as a function of r = |x|. If d ≥ 3 and p ≥ (d + 2)/(d − 2), then the problem in the entire space has no nontrivial solution. For the first time, this problem was studied by a variant of the variational method. However, it is known to the specialists in the field that it is also interesting to obtain the same results by using methods of the qualitative theory of ODEs. In the present article, we shall give a simple proof of the result above in this way. An earlier proof of this result of the other authors is essentially more complicated than our one.

A contribution to stability theory for nonlinear Neumann problem

Abstract: In this paper we study the stability of the solutions of some nonlinear Neumann problems, under perturbations of the domains in the Hausdorff complementary topology. We consider the problem $${{\left\{\begin{array}{c}-\text{ div}\;\left(a\left( x, abla u_{\Omega}\right)\right)=0 \;\text{in}\; \Omega \\ {a\left( x, abla u_{\Omega}\right) \cdot u=0\; \text{on}\; \partial\Omega}\end{array}\right.}}$$ where \({{\mathbf{R}^n \times \mathbf{R}^n \rightarrow \mathbf{R}^n}}\) is a Caratheodory function satisfying the standard monotonicity and growth conditions of order p, 1 < p < ∞. If Ωh is a uniformly bounded sequence of connected open sets in Rn, n ≥ 2, we prove that if \({{\Omega_{h}^{c} \rightarrow \Omega^{c}}}\) in the Hausdorff metric, \({|\Omega_{h}| \rightarrow |\Omega|}\) and the geodetic distances satisfy the inequality \({d_{\Omega}\left( x,y\right) \leq \liminf_{h} d_{\Omega_{h}} \left( x,y\right)}\) for every \({x, y \in \Omega,}\) then \({ abla u_{\Omega_h} \rightarrow abla u_{\Omega}}\) strongly in Lp, provided that W1, ∞(Ω) is dense in the space L1, p(Ω) of all functions whose gradient belongs to Lp(Ω, Rn).

Lower semicontinuity for functionals with (p, q)-growth in Carnot groups

Abstract: Let Ω be a bounded open subset of \({\mathbb{G}}\), where \({\mathbb{G}}\) is a Carnot group, and let \({u: \Omega \rightarrow \mathbb{R}^d}\) be a vector valued function. We prove a lower semicontinuity result in the weak topology of the horizontal Sobolev space \({W^{1,p}_X(\Omega,\mathbb{R}^d)}\), with p > 1, of the integral functional of the calculus of variations of the type $$F(u)=\int\limits_\Omega f(Xu)\,dx$$ where f is a X-quasiconvex function satisfying a non-standard growth conditions and Xu is the horizontal gradient of u.

Reference frames in harmonic coordinates: Geometric and Physical aspects

Abstract: This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates Precisely, we express in relative form the harmonicity conditions and consider the so called “spatially harmonicity” of a reference frame in spherical symmetry The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions

Three solutions for a perturbed Navier problem

Abstract: In this paper we prove the existence of at least three distinct solutions to the following perturbed Navier problem: $$\left\{\begin{array}{ll}\Delta (|{\Delta u}|^{p-2}\Delta u) = f(x,u) + \lambda g(x,u) \quad{\rm in}\,\,\,\Omega \\ u=\Delta u = 0 \qquad\qquad\qquad\qquad\qquad\quad{\rm on}\,\,\, \partial \Omega,\end{array}\right.$$ where $${{\Omega \subset \mathbb {R}^N}}$$ is an open bounded set with smooth boundary $${\partial \Omega}$$ and $${\lambda \in \mathbb {R}}$$ . Under very mild conditions on g and some assumptions on the behaviour of the potential of f at 0 and +∞, our result assures the existence of at least three distinct solutions to the above problem for λ small enough. Moreover such solutions belong to a ball of the space $${W^{2,p}(\Omega)\cap W_0^{1,p}(\Omega)}$$ centered in the origin and with radius not dependent on λ.

Further variations on the theme of FC-groups

Abstract: Groups that are FC, or more generally satisfy any of the weakenings of the FC-condition considered in de Giovanni (Serdica Math. J. 28:241–254, 2002) and Robinson et al. (J. Algebra 326:218–226, 2011), have local systems consisting of normal finite-by-nilpotent subgroups. Apart from generalizing results from de Giovanni (Serdica Math. J. 28:241–254, 2002) and Robinson et al. (J. Algebra 326:218–226, 2011) to the more general context of locally (normal and finite-by-nilpotent) groups, we partially settle an open problem raised in Robinson et al. (J. Algebra 326:218–226, 2011) concerning the isomorphism of maximal p-subgroups, but in this more general setting of locally (normal and finite-by-nilpotent) groups.

A note on multivalued groups

Abstract: Buchstaber (Mosc Math J 6(1):57–84, 2006) defined multivalued groups. In this paper we will show that the first isomorphism theorem and Lagrange theorem dose not hold for multivalued groups. Finally we define stabilizer of an action and we show that orbit-stabilizer theorem is not true for multivalued-groups.