Showing papers in "Ricerche Di Matematica in 2009"
TL;DR: In this paper, the problem of thermal convection was investigated for a layer of fluid when the heat flux law of Cattaneo was adopted, and the boundary conditions were those appropriate to two fixed surfaces.
Abstract: The problem of thermal convection is investigated for a layer of fluid when the heat flux law of Cattaneo is adopted. The boundary conditions are those appropriate to two fixed surfaces. It is shown that for small Cattaneo number the critical Rayleigh number initially increases from its classical value of 1707.765 until a critical value of the Cattaneo number is reached. For Cattaneo numbers greater than this critical value a notable Hopf bifurcation is observed with convection occurring at lower Rayleigh numbers and by oscillatory rather than stationary convection. The aspect ratio of the convection cells likewise changes.
30 citations
TL;DR: In this article, the first eigenvalue and corresponding eigenfunctions were studied for a fully nonlinear equation involving Hessian operators, and a Faber-Krahn inequality and a Payne-Rayner type inequality were proved for the p-laplacian operator and the Monge-Ampere operator.
Abstract: In this paper we consider the eigenvalue problem for a fully nonlinear equation involving Hessian operators. In particular we study some properties of the first eigenvalue and of corresponding eigenfunctions. Using suitable symmetrization arguments, we prove a Faber–Krahn inequality for the first eigenvalue and a Payne–Rayner type inequality for eigenfunctions, which are well known for the p-laplacian operator and the Monge–Ampere operator.
19 citations
TL;DR: In this article, the existence of multiple solutions for nonhogeneous singular elliptic equations involving critical Caffarelli-Kohn-Nirenberg exponent, by using Ekeland's Variational Principle and Mountain Pass Theorem without Palais Smale conditions, is established.
Abstract: In this paper, we establish the existence of multiple solutions for nonhogeneous singular elliptic equations involving critical Caffarelli–Kohn–Nirenberg exponent, by using Ekeland’s Variational Principle and Mountain Pass Theorem without Palais Smale conditions.
15 citations
TL;DR: Through simulations, it is found that, the cell-to-cell HIV transmission is very important for the final outcome of the HIV attacking.
Abstract: A four dimension ODE model is built to study the infection of human immunodeficiency virus (HIV) in vivo. We include in this model four components: the healthy T cells, the latent-infected T cells, the active-infected T cells and the HIV virus. Two types of HIV transmissions in vivo are also included in the model: the virus-to-cell transmission, and the cell-to-cell HIV transmission. There are two pos- sible equilibriums: the healthy equilibrium, and the infected steady state. The basic reproduction number R0 is introduced. When R0 1, the infected equilibrium exists and is globally stable. Through simulations, we find that, the cell-to-cell HIV transmission is very important forthefinaloutcomeoftheHIVattacking.Someimportantclinicalobservationsabout the HIV infection situation in lymph node are also verified.
11 citations
TL;DR: In this article, it was shown that a stable semistar operation of finite type ⋆ on a polynomial ring D[X] can be defined in a canonical way.
Abstract: Given a stable semistar operation of finite type ⋆ on an integral domain D, we show that it is possible to define in a canonical way a stable semistar operation of finite type ⋆[X] on the polynomial ring D[X], such that, if n := ⋆-dim(D), then n+1 ≤ ⋆[X]-dim(D[X]) ≤ 2n+1. We also establish that if D is a ⋆-Noetherian domain or is a Prufer ⋆-multiplication domain, then ⋆[X]-dim(D[X]) = ⋆- dim(D)+1. Moreover we define the semistar valuative dimension of the domain D, denoted by ⋆-dimv(D), to be the maximal rank of the ⋆-valuation overrings of D. We show that ⋆-dimv(D) = n if and only if ⋆[X1, . . . , Xn]-dim(D[X1, . . . , Xn]) = 2n, and that if ⋆-dimv(D) < ∞ then ⋆[X]-dimv(D[X]) = ⋆-dimv(D) + 1. In general ⋆-dim(D) ≤ ⋆-dimv(D) and equality holds if D is a ⋆-Noetherian domain or is a Prufer ⋆-multiplication domain. We define the ⋆-Jaffard domains as domains D such that ⋆-dim(D) < ∞ and ⋆-dim(D) = ⋆-dimv(D). As an application, ⋆-quasi-Prufer domains are characterized as domains D such that each (⋆, ⋆′)-linked overring T of D, is a ⋆′-Jaffard domain, where ⋆′ is a stable semistar operation of finite type on T. As a consequence of this result we obtain that a Krull domain D, must be a wD-Jaffard domain.
11 citations
TL;DR: In this article, the strongly nonlinear boundary value problem was considered and the existence of weak solutions was shown under a certain sign condition of the Caratheodory function g without assuming any growth restrictions.
Abstract: We consider the strongly nonlinear boundary value problem,
$$Au+g(x,u)=f$$
where A is an elliptic operator of finite or infinite order. We introduce anisotropic weighted Sobolev spaces and we show under a certain sign condition of the Caratheodory function g without assuming any growth restrictions, the existence of the weak solutions.
8 citations
TL;DR: In this article, the authors describe minimal non-metabelian groups and minimal nonmetabased groups in a saturated formation and show that they are monotonically monotonous.
Abstract: Let \({\mathcal {F}}\) be a saturated formation. We describe minimal non-\({\mathcal {F}}\) -, minimal non-\({\mathcal{AF}}\) -, and minimal non-metabelian groups.
6 citations
TL;DR: The existence of solutions for many systems of integro-differential equations discovered and generalized in the process of applying the Galerkin method for some initial-boundary value problems is investigated in this article.
Abstract: The existence of solutions for many systems of integro-differential equations discovered and generalized in the process of applying the Galerkin method for some initial-boundary value problems will be investigated in this paper.
6 citations
TL;DR: In this article, decomposition theorems for modular functions on lattices and the relationship between such decompositions and lattice properties of a suitable system of uniformities are studied.
Abstract: We study decomposition theorems for modular functions on lattices and the relationship between such decompositions and lattice properties of a suitable system of uniformities. We give a purely topological characterization for the validity of a decomposition theorem of a certain type and examine when this topological condition is satisfied, namely when a system of lattice uniformities is a Boolean algebra consisting of permutable uniformities.
5 citations
TL;DR: In this paper, the authors consider a sample of i.i.d. times and interpret each item as the first-passage time (FPT) of a diffusion process through a constant boundary.
Abstract: We consider a sample $${\left\{T_n\right\}_{1\leq n\leq N}}$$
of i.i.d. times and we interpret each item as the first-passage time (FPT) of a diffusion process through a constant boundary. The problem is to estimate the parameters characterizing the underlying diffusion process through the experimentally observable FPT’s. Recently in Ditlevsen and Lanský (Phys Rev E 71, 2005) and Ditlevsen and Lanský (Phys Rev E 73, 2006) closed form estimators have been proposed for neurobiological applications. Here we study the asymptotic properties (consistency and asymptotic normality) of the class of moment type estimators for parameters of diffusion processes like those in Ditlevsen and Lanský (Phys Rev E 71, 2005) and Ditlevsen and Lanský (Phys Rev E 73, 2006). Furthermore, to make our results useful for application instances we establish upper bounds for the rate of convergence of the empirical distribution of each estimator to the normal density. Applications are also considered by means of simulated experiments in a neurobiological context.
4 citations
TL;DR: In this paper, the authors consider ideals arising from the intersection of hyperplanes of the projective space belonging to a partition, and determinate their generators and prove that they are Cohen-Macaulay.
Abstract: We consider ideals arising from the intersection of hyperplanes of the projective space \({\mathbb{P}^n}\) belonging to a partition. We determinate their generators and we prove that they are Cohen-Macaulay.
TL;DR: In this paper, a necessary and sufficient condition is given on the boundary datum in order to the Dirichlet problem for an elliptic equation in a two-dimensional exterior Lipschitz domain has a unique solution with a finiteDirichlet integral which converges uniformly at infinity to an assigned constant value.
Abstract: A necessary and sufficient condition is given on the boundary datum in order to the Dirichlet problem for an elliptic equation in a two-dimensional exterior Lipschitz domain has a unique solution with a finite Dirichlet integral which converges uniformly at infinity to an assigned constant value.
TL;DR: In this article, a simple case of stationary one-dimensional flame propagation, modeled by the stoichiometric formula A → B, is considered, where the constituent A prevails before the flame while B outnumbers A behind the flame.
Abstract: We study the simple case of stationary one-dimensional flame propagation, modeled by the stoichiometric formula A → B To this aim we consider a binary mixture where the constituent A prevails before the flame while B outnumbers A behind the flame For the mathematical description of the problem, we refer to Mixture Theory and compare the predictions obtained by multi-temperature mixture balance laws with those (known in the literature) obtained by single-temperature equations
TL;DR: In this paper, it was shown that a finite solvable group possesses a transitive normality (permutability) relation if and only if it is a \({\fancyscript C}_p\) -group for all primes p.
Abstract: The class of groups G for which every subgroup of \({P\in {\rm{Syl}}_p(G)}\) is normal (permutable) in NG(P) is called \( \fancyscript{C}_p\) (\({\fancyscript X}_p\)). A finite solvable group possesses a transitive normality (permutability) relation if and only if it is a \({\fancyscript C}_p\) -group (\({\fancyscript X}_p\) -group) for all primes p. The classes \({\mathcal T}\) , \({\mathcal {PT}}\) , and \({\mathcal {PST}}\) denote, respectively, the classes of groups in which normality, permutability, and S-permutability are transitive relations. Our main result shows that the minimal non-\({\fancyscript C}_p\) -groups and the minimal non-\({\fancyscript X}_p\) -groups, respectively, are just the minimal non-\({\mathcal T}\) -groups and the minimal non-\({\mathcal {PT}}\) -groups. In addition, we arrive a new characterization of the solvable \({\mathcal {PT}}\) -groups and the solvable \({\mathcal {PST}}\) -groups.
TL;DR: Ben Nasr and Jarboui as discussed by the authors proved that if R is integrally closed with finite Krull dimension, then R is a maximal non-valuation subring of qf (R) iff R is not local and |[R, qf(R)]| = dim(R) + 3.
Abstract: In this paper we pursue and deep the study of ring extensions \({R \subset S}\) such that R is a maximal non-valuation subring of S [Ben Nasr and Jarboui in Houston J Math, 2009 (in press)]. It is proved in Ben Nasr and Jarboui [Houston J Math, 2009 (in press), Theorem 3.2] that if R is integrally closed with finite Krull dimension, then R is a maximal non-valuation subring of qf (R) iff R is not local and |[R, qf (R)]| = dim(R) + 3. This result encourages us to pose the following question: Let n be a nonzero positive integer greater than 2 and let R be a finite-dimensional domain such that |[R, qf (R)]| = dim(R) + n, does there exists an overring S of R such that R is a maximal non-valuation subring of S? This paper deals mostly with this question. We solve this question in case R is integrally closed.
SIDI1
TL;DR: In this paper, the Dirichlet problem for strongly nonlinear elliptic equations with degenerate coercivity and data in divergence form was considered and it was shown that some lower order terms have regularizing effects on solutions.
Abstract: We consider the Dirichlet problem for a class of strongly nonlinear elliptic equations with degenerate coercivity and data in divergence form. We show that some lower order terms have regularizing effects on solutions.
TL;DR: In this article, the authors consider several weaker conditions on the conjugates of cyclic subgroups and show that the strongest of which is equivalent to the FC-condition for many classes of groups.
Abstract: The following is clearly equivalent to the usual definition of FC-group. A group is an FC-group, if each of its cyclic subgroups has only finitely many conjugates. We consider several weaker conditions on the conjugates of cyclic subgroups, the strongest of which we show is equivalent to the FC-condition for many classes of groups.
TL;DR: Di Gennaro and Franco as mentioned in this paper showed that the maximal integer for which there exists a threefold intersection of hypersurfaces of degree d and d − 1 such that X has only ordinary singularities of order m and |Sing(X)| = νm(d).
Abstract: Denote by νm(d) the maximal integer for which there exists for \({d \gg 0}\) a threefold \({X\subset \mathbb{P}^5}\) complete intersection of hypersurfaces of degree respectively d and d − 1 such that X has only ordinary singularities of order m and |Sing(X)| = νm(d). We prove that, \({
u_m(d)\ge \varphi(d)}\) where \({\varphi(d)\sim d^5}\) asymptotically. This result extends (Di Gennaro and Franco in Commun Contemp Math 10(5):745–764, 2008, Corollary 2.10).
TL;DR: In this paper, the third-order nonlinear difference equation is considered, and the rule of its trajectory structure is described, where the length of positive and negative semi-cycles of its nontrivial solutions are found to occur periodically with prime period 7.
Abstract: In this paper, the following third-order nonlinear difference equation
$$x_{n+1}=\frac{x_{n-1}^b x_{n-2}+1}{x_{n-1}^b + x_{n-2}},\quad n = 0, 1, 2,\ldots,$$
where \({b\in[0,1]}\) and the initial values \({x_{-2},x_{-1},x_{0} \in[0,\infty)}\) , is considered, and the rule of its trajectory structure is described. Mainly, the lengths of positive and negative semi-cycles of its nontrivial solutions are found to occur periodically with prime period 7. The rule is 3−, 2+, 1−, 1+ in a period. By utilizing this rule its positive equilibrium point is verified to be globally asymptotically stable. Some known results are included.
TL;DR: In this article, conditions under which a compact contractible polyhedron is strictly contractible to a point were studied, and conditions for the contractibility of compact polyhedra were established.
Abstract: In this paper we study conditions under which a compact contractible polyhedron is strictly contractible to a point.
TL;DR: In this article, a class of finite planar spaces with projective points is characterized, and the authors show that these spaces can be represented by a set of projective planes.
Abstract: In this paper a class of finite planar spaces with projective points is characterized.
TL;DR: In this article, it was shown that the flag-transitive plane of order 49 is not isomorphic to π, and that πt is obtained from π by replacement of a net of degree 25.
Abstract: Rao’s flag-transitive plane π of order 49 and πt, the plane obtained by transposing matrices of a representative set of π, has been studied. It is shown that πt is flag-transitive, πt is not isomorphic to π, and πt is obtained from π by replacement of a net of degree 25. Further, (1) the flag-transitive planes associated with 1-spread sets S2b and S2a in the classified list of translation planes of order 49 enumerated by Mathon et al, are respectively isomorphic to π and πt (2) The flag-transitive planes associated with the 1-spread sets of 0an* in the classified list of translation planes of order 49 enumerated by Charnes et al are isomorphic to π and πt in some order.
TL;DR: In this paper, the authors generalize this result to higher dimensions and thus answer to a question raised by Beckenbach and Rado, and discuss connections to reverse Holder inequalities and Muckenhoupt weights.
Abstract: Beckenbach and Rado characterized logarithmically subharmonic functions in the plane in terms of integral inequalities involving spherical averages. In this work we generalize this result to higher dimensions and thus answer to a question raised by Beckenbach and Rado. We also consider generalizations of integral inequalities suggested by Beckenbach and Rado and discuss connections to reverse Holder inequalities and Muckenhoupt weights.
TL;DR: In this article, the Hartshorne-Rao modules of minimal curves on a smooth rational scroll surface were studied and an upper bound for Betti numbers for any C was given.
Abstract: We study the Hartshorne-Rao modules M
C
of minimal curves C in $${\mathbb{P}^N}$$
, with N ≥ 4, lying in the same liaison class of curves on a smooth rational scroll surface. We get a free minimal resolution of M
C
for some of such curves and an upper bound for Betti numbers of M
C
, for any C.