Search

This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It turns out that this generalization can be put in relation to a specific subordination of a homogeneous Poisson process by means of a subordinator for which it is possible to express the characterizing L\'evy measure explicitly. Moreover, the law of this subordinator solves a one-sided first-order differential equation in which a particular convolution-type integral operator appears, called Prabhakar derivative. In the last section of the paper, a similar model is introduced in which the Prabhakar derivative also acts in time. In this case, too, the probability generating function of the corresponding process and the probability distribution are determined.

Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species Sampling Sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, a class of generalized species sampling sequences that are conditionally identically distributed is introduced and studied: the Generalized Ottawa sequences (GOS). This class contains a '`randomly reinforced'' version of the P\'olya urn and of the Blackwell-MacQueen urn scheme. For the empirical means and the predictive means of a GOS, we prove two convergence results toward suitable mixtures of Gaussian distributions. The first one is in the sense of stable convergence and the second one in the sense of almost sure conditional convergence. In the last part of the paper we study the length of the partition induced by a GOS at time $n$, i.e. the random number of distinct values of a GOS until time $n$. Under suitable conditions, we prove a strong law of large numbers and a central limit theorem in the sense of stable convergence. All the given results in the paper are accompanied by some examples.

In this paper the existence of infinitely many eigenvalues for the non linear boundary value problem $$\left\{ \begin{gathered} - \Delta u - \bar \lambda u = \mu \alpha (u) \hfill \\ u|_{\partial \Omega } = 0 \hfill \\ \end{gathered} \right.$$ ΩtRn bounded and\(\bar \lambda \in \) (λ1, λ2)where λ1and λ2are the first and the second eigenvalue of — Δ respectively. The eigenvalues are characterized by the critical levels of a suitable functional on a smooth unbounded manifold. The usual method is not applicable because the functional is not positive definite and the Palais-Smale condition is not satisfied. We applies a technique introduced in a preceding paper [3].

An octagon quadrangle is the graph consisting of an 8-cycle ( x 1 , x 2 ,…, x 8 ) with two additional chords: the edges { x 1 , x 4 } and { x 5 , x 8 }. An octagon quadrangle system of order v and index ρ [ OQS ] is a pair ( X , H ), where X is a finite set of v vertices and H is a collection of edge disjoint octagon quadrangles (called blocks ) which partition the edge set of ρ K v defined on X . An octagon quadrangle system Σ = ( X , H ) of order v and index λ is said to be upper C 4 - perfect if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ -fold 4-cycle system of order v ; it is said to be upper strongly perfect , if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ -fold 4-cycle system of order v and also the collection of all of the outside 8-cycles contained in the octagon quadrangles form a ϱ -fold 8-cycle system of order v . In this paper, the authors determine the spectrum for these systems.

In this paper we study the gauge invariance of the time-dependent Ginzburg–Landau equations through the introduction of a model which uses observable variables. We observe that the various choices of gauge lead to a different representation of such variables and therefore to a different definition of the weak solution of the problem. With a suitable decomposition of the unknown fields, related to the choice of London gauge, we examine the Ginzburg–Landau equations and deduce some energy estimates which prove the existence of a maximal attractor for the system.

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate VAR(p) process) and we prove if the distance between the univariate ARMA models implied by the VAR representation is greater than a certain number that is a function of p, then Granger causality must exist in at least one direction in the variables.

Starting from the simplest recurrence relations of second order, in this paper are suggested direct solutions obtained from a generalization of Pascal’s Triangle. With some binomial formulas, it isn’t necessary anymore to calculate roots of associated equations, and the extension of parameters’ definition field to the complex field can be done without any difficulty. The general cases in which the coefficients are functions of an integer variable are studied, too.

A unified axiomatic scheme for both the Newtonian Mechanics and the Special Theory of Relativity is given, by setting two systems of Axioms that differ from each other in only one requirement about the possibility of measuring time-intervals by light reflections. The concept of «observer» is obtained as a derived concept, rather than a primitive one, as in some previous papers by other Authors. The status of Newtonian Mechanics as a «limiting case» of Special Relativity is rigorously deduced as a consequence of the result that the geometric structure of (neo)classical space-time is a limit of a family of relativistic geometric structures for the space-time.

In this paper we investigate the boundaries of applicability of the theory of the equilibrium states of Runge-Kutta schemes developed in [1], [2].

This paper deals with the existence of solutions for the implicit Cauchy problem F(t, x, x)=ϑB, x(t0)=x0 in a Banach space B. By using the Kuratowski and the Hausdorff measure of non compactness, we prove an existence theorem for the previous problem (Teorema 1.1) and its extension to non compact intervals (Teorema 2.1). These results generalize the previous ones by R.Conti [1] (in the case B=R), G.Pulvirenti [2] and T. Dominguez Benavides [3], [4] (in the general case). In particular, we relax a Lipschitz condition assumed by all of the abovementioned authors. Some applications of Teorema 2.1 are presented.

In this paper we continue our investigations (see[5]) devoted to transmission problems in consecutive angles, for elliptic operators. In[5] the above mentioned boundary value problems in the case of homogeneous constant coefficient operators and within the Sobolev weight spaces Ws1,s2r were investigated. This work is concerned with the problem for general operators, within the Sobolev weight spaces Ws1,s2r and Ws1,s2*r. Existence theorems and stability theorems for nullity, deficiency, index have been proved.