Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
Not a member yet
1189 research outputs found
Sort by
W01,1(Ω)-solutions for a degenerate double phase type operator in some borderline cases
No full textIn this paper we study the existence of W01,1(Ω)-solutions of the nonlinear problems which involves in its principal part the p-laplacian operator and a degenerate additional term that has a polynomial growth with respect to the gradient. The simplest model is −div (a(x)|∇u|p−2∇u) -div (|u|( r−1)q+1|∇u|q−2∇u) = f in Ω, and u = 0 on ∂Ω, where Ω is a bounded open subset of RN(N>2), 1 < q ≤ p < N, r > q-1/q and f is a function with poor summability
Littlewood-Paley characterization of discrete Morrey spaces and its application to the discrete martingale transform
Full text linkThe goal of this paper is to develop the Littlewood–Paley theory of discrete Morrey spaces. As an application, we establish the boundedness of martingale transforms. We carefully justify the definition of martingale transforms, since discrete Morrey spaces do not contain discrete Lebesgue spaces as dense subspaces. We also obtain the boundedness of Riesz potentials
Extremal functions and uncertainty principles for fourier multipliers on the Laguerre hypergroup
Full text linkThe main purpose of this paper is to introduce the Fourier multipliers operators on the Laguerre hypergroup and to give some new results related to these operators as Parseval’s, Plancherel’s, Calder´on’s reproducing formulas and Heisenberg’s, Donoho-Stark’s uncertainty principles. Next, using the theory of reproducing kernels we give best estimates and an integral representation of the extremal functions related to these operators
Some new iterative schemes for solving general quasi variational inequalities
Full text linkSeveral new classes of general quasi variational inequalities involving two arbitrary operators are introduced and considered in this paper. Some important cases are discussed, which can be obtained by choosing suitable and appropriate choice of the operators. It is shown that the implicit obstacle boundary value can be studied via these quasi variational inequalities. Projection technique is applied to establish the equivalent between the general quasi variational inequalities and fixed point problems. This alternative formulation is used to discuss the uniqueness of the solution as well as to propose a wide class of proximal point algorithms. Convergence criteria of the proposed methods is considered. Asymptotic stability of the solution is studied using the first order dynamical system associated with variational inequalities. Second order dynamical systems associated with general quasi variational inequalities are applied to suggest some inertial type methods. Some special cases are discussed as applications of the main results. Several open problems are indicated for future research work
Totally inert subgroups of a rank two group constructed by Zassenhaus
No full textA subgroup H of an abelian group G is totally inert if, for every non-zero endomorphism φ of G, H is commensurable with φ(H), that is, H ∩ φ(H) has finite index in H and in φ(H). In this paper we provide necessary and sufficient conditions for the existence of rank two subgroups which fail to be totally inert of a particular torsion-free group of rank two G such that End(G) = Z[i], the ring of Gaussian integers, obtained by a classical construction of Zassenhaus. The results obtained here partially solve a problem raised in a recent paper by Brendan Goldsmith and the author, where totally inert subgroups of general abelian groups are investigated
Formal (q-)Euler integrals over the unit hypercube and over triangles in higher dimensions for multiple (q-)hypergeometric functions
Full text linkThis article contains both multiple hypergeometric functions and cor- responding q-analogues. First we present integral expressions for multi- ple hypergeometric functions over the unit hypercube and over triangles in higher dimensions. Then we extend these integrals to the q-case by using the q-real number R⊞q . The q-binomial theorem, the q-beta integral and their generalizations to higher dimensions are used in the proofs. Also confluent forms with the Euler q-exponentoial function are proved. Reduction for- mulas for Kampe ́ de Fe ́riet functions are proved by using Euler integrals, Beta integrals and hypergeometric transformations. Finally, Euler integral representations for Horn functions and q-Euler integral representations of q-Kampe ́ de Fe ́riet functions are proved
Renormalized solutions for some non-coercive quasilinear elliptic problem in Musielak-Orlicz space
Full text linkIn this paper, we study the existence of renormalized solutions for the following non-coercive quasilinear elliptic problem: −div(a(x,u,∇u))+g(x,u) =f−div(φ(u)) in Ω, and u=0 on ∂Ω. in the Musielak-Orlicz-Sobolev space W10Lφ(Ω), where−diva(x,u,∇u) is a degenerate Leary Lions operator and g(x,u) is a Caratheodory function that satisfies the sign condition with φ(·) ∈ C0(R,RN) and f ∈ L1(Ω).The Musielak-Orlicz function φ(x,t) is regular and does not necessarily satisfying the ∆2−condition
Algorithm substitution attacks on symmetric encryption: a survey
Full text linkIn 2014, Bellare, Paterson, and Rogaway suggested formalizing Algorithm Substitution Attacks (ASAs), a new type of attack against symmetric encryption methods. These attacks replace the conventional encryption algorithm with a subverted one, enabling the attacker, known as Big Brother, to decrypt messages without the user\u27s collaboration. The formal definitions of these attacks highlight the user\u27s capacity to identify the subversion (i.e., the replacement of regular encryption with a malicious one) and the Big Brother\u27s capacity to gather data about encrypted messages. In recent years, the cryptographic community has developed several definitions, attacks, and possible defenses to increase its awareness of this potential issue.In this paper, we will explore the algorithm-substitution attack concepts and assaults available in the literature, comparing them with a critical eye
On the formulation of extended thermodynamics in the case of fractional exclusion statistics.
Full text linkWe consider the non-equilibrium theory for the fractional exclusion statistics (FES) by using the Maximum Entropy Principle and the Entropy Principle. The entropy balance equation is determined and the statistical consequence of theory are discussed. Both the entropy and its flux are computed explicitly in terms of the non-equilibrium Lagrange multipliers while, by using a general expression for the energy dispersion relation, some thermodynamic properties connected with the convexity conditions of the entropy are explicitly analyzed. Finally, for an ideal gas subject to FES, the construction of an arbitrary set of closed hydrodynamic equations, in the context of Extended Thermodynamics, is briefly illustrated
Some properties for ν-zeros of parabolic cylinder functions
Full text linkLet Dν(z) be the Parabolic Cylinder function. We study the ν-zeros of the function ν → Dν(z) with respect to the real variable z. We establish a formula for the derivative of a zero and deduce some monotonicity results. Then we also give an asymptotic expansion for ν-zeros for large positive z