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It is a singular fact that the first and pithy de Finetti’s essay on exchangeability has not earned the same reputation as that of others of his papers about the same subject. In fact, this paper contains, on the one hand, all the main results on sequences of exchangeable events, together with the right subjectivistic interpretation of the role they play in the study of the connections between probability and frequencies. On the other hand, the paper makes use of mathematical methods abandoned, immediately after its publication, by de Finetti himself. The center of this methods is the so–called characteristic function of a random phenomenon. Independently of the destiny of the paper, we think that, apart from its undoubted historical value, it contains ideas susceptible of interesting new developments. Therefore, we have deemed it suitable to give here a detailed and faithful account of its content, for the benefit of the colleagues who are not in a position to understand Italian. Moreover, to emphasize the value of the paper at issue, we develop de Finetti’s brief hint to the extendibility of exchangeable sequences of events, to obtain a new explicit necessary and sufficient condition of an algebraic nature.

Strong convergence theorems that approximate common fixed points of two nonlinear mappings are presented. Our method is based on the Martinez-Yanes–Xu iteration, which extends Nakajo and Takahashi’s CQ method. In this paper, by exploiting the mean-valued iteration procedure, we further develop Nakajo and Takahashi’s CQ method and Takahashi, Takeuchi, and Kubota’s shrinking projection method. The approach of this paper does not require that the two mappings be continuous or commutative. The types of mappings considered in this paper include nonexpansive mappings and other well-known classes of mappings as special cases.

The purpose of this paper is to establish necessary and sufficient optimality conditions and some duality results for weakly efficient solutions of a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. Using parametric approach, the problem (P) is first equivalently transformed into a parametric problem (P µ) with µ ∈ Rp, for which we construct then a dual problem. This is achieved in terms of conjugate duality theory. Under appropriate assumptions, the weak and strong duality results for (Pµ) are presented. These results permit us to give dual characterizations for the weakly efficient solutions of the problem (P).

The first author to construct a non-normal bicanonical threefold in P 4 was L. Godeaux in 1936 [5]. This threefold has degree 8. In the first part of the present paper, starting from a normal threefold of general type where q1 = q2 = pg = 0, P2 = P3 = 5, of degree 6 (cf. [11]), we construct Godeaux’s example and two examples of tricanonical threefolds in P 4 . One of the tricanonical threefolds is normal. In the second part of the paper, we construct (starting from the beginning) a normal bicanonical threefold of degree 8 that has the birational invariants given by q1 = q2 = pg = 0 and P2 = 5. No other examples of bicanonical and tricanonical threefolds in P 4 are known.

In this paper, we focus on some class of Stefan type problems. We prove the existence and uniqueness of renormalized solution in anisotropic Sobolev spaces with data belonging to L1 -data, based on the properties of the renormalized solutions and the generalized monotonicity method in the functional spaces.

Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the existence of a formal smoothing as defined by Tziolas. In this paper we address the reverse question giving sufficient conditions on X that guarantee the converse, i.e. formal smoothability implies geometric smoothability. This is useful in light of Tziolas’ results giving sufficient criteria for the existence of formal smoothings.

In this paper, a new family of rotationally symmetric planar graphs is described based on an edge coalescence of planar chorded cycles. Their local fractional metric dimension is established for those ones arisen from chorded cycles of order up to six. Their asymptotic behaviour enables us to ensure the existence of new families of rotationally symmetric planar graphs with either constant or bounded local fractional dimension.

In this paper we develop two approaches for studying a large family of generalized Bernoulli–Euler polynomials. For the determinental approach, using Little Fermat’s Theorem, we establish a congruence identity and we give an explicit formulas of the generalized Bernoulli–Euler polynomials in terms of the Stirling numbers. The linear recursive approach allows us to formulate some properties of the generalized Bernoulli–Euler numbers and the generalized Bernoulli–Euler polynomials. Moreover, combinatorial formulas for these polynomials are provided.

Abstract. This paper is concerned with the study of the non-coercive p(x)-parabolic problems. We prove the existence of entropy solutions for this parabolic equation, and we will conclude some regularity results.

This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions, which are particularly nice cofibrations. The cobar construction of a locally conilpotent cocommutative coalgebra is shown to be an example of semifree DG-Lie algebra. We also give an example of a non-cofibrant DG-Lie algebra whose underlying graded Lie algebra is free; this cannot occur in the bounded above case, where DG-Lie algebras of this form are always cofibrant.

We consider a one-species plasma moving in an infinite cylinder in R3, in which it is confined by means of a magnetic field diverging on the walls of the cylinder. In a recent paper [4] we have supposed that the plasma satisfies the Vlasov equation with a Yukawa mutual interaction (i.e. Coulomb at short distance and exponentially decreasing at infinity). Assuming that initially the particles have bounded velocities and are distributed according to a bounded density without any hypothesis on its decreasing at infinity, we have proved the global in time existence and uniqueness of the time evolution of the plasma and its confinement. In the present paper we extend this result to a Coulomb interaction, making on the initial density some assumption of slight decreasing on average at infinity, which however does not imply that the density belongs to any Lp space. The proof is similar, but slightly simpler.

In this paper a new class of bivariate refinable functions is constructed by means of the directional convolution product between the tensor product of two univariate refinable functions belonging to a particular class, shortly recalled in this paper, with a third one in the same class. The new functions have many properties useful in applications, such as compact support, positivity, central symmetry, refinability and linear independence of the integer translates. Moreover, the so constructed functions turn out to be suitable for solving the cardinal interpolation problem.

We consider a convex body in R^3, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that the gas particles interact with the body by means of elastic collisions. Giving to the body an initial velocity V_0, we prove that, for |V_0| small enough, |V (t)| ≈ C t^{−5} for large t, being C a positive constant depending on the medium and on the shape of the obstacle. The power law approach to the equilibrium V = 0, instead of the exponential one (typical in viscous friction problems), is due to the long memory effect of the recollisions. This paper completes the analysis made in previous papers (see [7] and [8]), in which for simplicity the body was assumed to be a disk.

In this paper we determine the number of connected components of moduli spaces of both marked and polarised irreducible holomorphic symplectic manifolds deformation equivalent to generalised Kummer varieties

We consider an abstract Cauchy problem of an evolution inclusion with a singlevalued perturbation on a real Hilbert space. The evolution inclusion contains subdifferentials of time-dependent, proper, lower semicontinuous, convex functions which depends on a solution itself of the Cauchy problem. Moreover, the subdifferentials are taken with respect to inner products, which also depend on a solution of the Cauchy problem. Such structures are sometimes called quasi-variational structures for convex functions and inner products. The main purposes of this paper are to show the existence of strong solutions to the Cauchy problem of an evolution inclusion with a perturbation and to apply this result to a mass-conservative tumor invasion model with a degenerate cross diffusion.

Many papers discuss the problem of recovering a function when a set of data is known on a domain Ω ⊂ R^2. Most of these papers assume that the size of the data set is large. At our knowledge, little or practically nothing is said about the case in which the sample has a size that is moderate. In this paper we tackle this problem. We indicate a way for its solution and hence we give a concrete example. Some numerical experiments are shown.

We consider the numbers Br,s = (B + 1)r Bs (in umbral notation Bn = Bn with the Bernoulli numbers) that have a well-known reciprocity relation, which is frequently found in the literature and goes back to the 19th century. In a recent paper, self-reciprocal Bernoulli polynomials, whose coefficients are related to these numbers, appeared in the context of power sums and the so-called Faulhaber polynomials. The numbers Br,s can be recursively expressed by iterated sums and differences, so it is not obvious that these numbers do not vanish in general. As a main result among other properties, we show the non-vanishing of these numbers, apart from exceptional cases. We further derive an explicit product formula for their denominators, which follows from a von Staudt–Clausen type relation.

In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a comparison principle. We then illustrate our abstract statements for different concrete examples, where new results are achieved. In a preliminary step, we prove some well-posedness results for some nonlinear and nonautonomous evolution equations.

For any relatively prime integers r and s, let ar,s(n) denote the number of (r, s)- regular partitions of a positive integer of n into distinct parts. Prasad and Prasad (2018) proved many infinite families of congruences modulo 2 for a3,5(n). In this paper, we establish families of congruences modulo 2 and 4 for ar,s(n) with (r, s) ∈ {(2, 5), (2, 7), (4, 5), (4, 9)}. For example, we show that for all β ≥ 0 and n ≥ 0, we have a2,5 4 · 5 2β+1n + 37 · 5 2β − 1 6 ≡ 0 (mod 4) .

This paper is concerned with optimal temporal decay estimates for solutions of the Cauchy problem of a systems of multidimensional parabolic conservation laws. The results obtained in this paper supplement the results obtained in our previous paper.

For various applications (including: regularity study of free boundaries, and approximation in the mean of harmonic functions on unbounded domains by rapidly decreasing ones) it is desirable to have an estimate, valid for an arbitrary smooth function φ of compact support in IRn, bounding sup |φ| in the unit ball B in terms of sup |∆φ| on IR^n. Such an estimate cannot exist with no further assumptions on φ, but in the predecessor of this paper it was shown that if φ vanishes on a subset E of B with volume |E| > 0, such a bound holds , and uniformly with respect to all sets E with |E| not less than any prescribed positive constant. In the present paper an analogous estimate is obtained for φ which |φ(0)| ≤ 1, and grad(φ) vanishes on a subset E of B whose Newtonian capacity exceeds a positive constant. Various applications are given. The derivation of the basic estimate involves ideas which may have some independent interest, in particular “quasi-balayage”, the sweeping-out of a measure from its support to some other compact set such that the potentials of the two measures, while not equal on a neighborhood of infinity as required by (true) balayage, are asymptotically equal to some prescribed degree.

This paper is concerned with the application of the Kramer sampling theorem to Sturm-Liouville problems with coupled boundary conditions. In following the first paper with this title the analysis in this successor paper covers the case when the spectrum of the boundary value problem is allowed to be double, i.e. at least one eigenvalue is of multiplicity two. In all cases it is shown that Kramer analytic kernels can be defined, and that each kernel has an associated analytic interpolation function to give the Lagrange interpolation series.

In this paper we present four theorems on the convergence of first derivatives of certain Szasz-Mirakyan type operators for functions of one and two variables. Some approximation properties of these operators are given in some previous papers quoted in bibliography.

The paper concerns the Neumann problem for the equation uxy = c. By using the method of G. Fichera, introduced in paper [5] devoted to the Dirichlet problem, necessary and sufficient conditions for the existence of the solutions are found.

In a paper of 1982, D. Cioranescu and F. Murat considered the problem satisfied by the limit u of the sequence un solution of 0 −∆un = f in Ωn, un = 0 on ∂Ωn, where Ωn is a sequence of open sets which are contained in a fixed bounded open set Ω. In order to make this, they imposed several hypotheses about the sequence Ωn. Their results were later extended to the p-Laplacian operator by N. Labani and C. Picard. In the present paper, we prove that these hypotheses may be reduced to the following one: There exists a sequence zn ∈ W1,p(Ω) which is zero in Ω \ Ωn and which converges weakly to 1 in W1,p(Ω). Indeed, G. Dal Maso and U. Mosco have solved the above homogenization problem in the general case in which we do not make any hypothesis about Ωn using Γconvergence methods and recently, G. Dal Maso and A. Garroni have also solved this general problem by a method close to the one used by D. Cioranescu and F. Murat.

The present paper is meant as an introduction for the mathematically educated reader to problems of macroscopic limits of microscopic systems, and to the derivation of PDE's which describe the evolution of continuous media. The hydrodynamic, mean field and kinetic limits are considered for various models, which are chosen as simple as possible, the aim being of conveying the main ideas which led in recent years to the first steps in rigorous nonequilibrium statistical mechanics. The paper is self contained, as far as possible, in the sense that the mathematical notions that are needed are as a rule introduced in the text.

This paper is concerned with the connection between the Kramer sampling theorem and one form of the Lagrange interpolation formula. One particular interest of this connection is when the Kramer-type kernel has certain analytic properties since this leads to corresponding analyticity for the individual terms in the Lagrange interpolation series. Recent results have shown that one important and significant case of this connection is to be found in the generation of these Kramer-type kernels from self-adjoint boundary value problems, determined by symmetric ordinary linear differential expressions defined on intervals of the real line. In these cases the analyticity properties result from the presence of the spectral parameter of the corresponding selfadjoint differential operator. Results in this paper are restricted to consideration of the classic Sturm-Liouville differential expression of the second-order, but under the minimal (locally Lebesgue integrable) conditions on the coefficients; furthermore the expression is taken to be in the regular and/or limit-circle end-point classification. This approach follows earlier work of Weiss, Kramer, Campbell and others, and recent results of Butzer, Zayed and Schottler. The new methods adopted here should extend to other end-point classifications and to symmetric differential expressions of arbitrary order.

This paper is devoted to study the regular, Gorenstein, generically Gorenstein and non-regular Gorenstein local rings by means of delta invariant.

In this paper we prove the existence in W1(not in BV ) of a solution (in a very weak sense) for the boundary value problems.

Semilinear elliptic problems with solutions blowing up at the boundary are considered. The effect of a Hardy potential with a boundary singularity is discussed. Positive potentials reinforce the solution to blow up whereas negative prevent it. For the standard nonlinearities and sufficiently large potentials there exist solutions which are comparable to the blowing up solutions of the problem without Hardy potential. Near the boundary they depend only on the distance to the boundary, and the first order approximation is independent of the geometry. The precise estimates imply that those solutions are unique. The main tools used in this paper are the method of upper and lower solutions and boundary estimates for the blowup solutions without Hardy potential.

In this paper, we give some conditions to prove the existence of solutions for a nonlinear boundary value problem of fractional differential equations with higher order q, (n-1< q

Abstract. Let M be a compact complex manifold. In this paper we give a simple proof of the bimeromorphic invariance of the higher Todd genera of M, a result first proved implicitly in [7] using algebraic methods.

This paper dedicated to Umberto Mosco revisits a line of my research starting in the early 70's in the aim of identifying a path connecting different concepts which play a role in elliptic pde's, spectral theory and optimal control.

Half century ago, Umberto Mosco was the ``relatore di tesi (tesi about the Mosco- convergence) di laurea'' of the first author; a quart of century ago, the first author was the ``relatore di tesi di laurea'' of the second author. The roots of this paper are the Mosco-convergence of convex sets and the minimization of integral functionals of the Calculus of Variations. We consider integral functionals of the type J(v)=∫Ω j(x,Dv)-∫Ω f(x)v(x). We study the existence of T-minima (infinite energy minima) on convex sets of the Sobolev space W01,p(Ω) and the stability of the T-minima under the Mosco-convergence of the convex sets.

In this paper we construct, by means of a variational formulation, the solutions of a problem of elastodynamics which includes the effect of damage for the elastic material. The result is a wave equation with time dependent operators which represents the elastic coefficients of the material undergoing damage. The dynamics that we construct also satisfies a threshold condition with the same threshold value that characterizes the quasi-static evolution of damage (see [12]).

In this paper, the authors obtain an upper bound of second Hankel determinant for a new class of analytic functions defined through the Komatu integral operator. Our result extends the corresponding previously known results.

Traveling waves are a near-ubiquitous phenomenon in mathematical biology, and have been studied in the context of embryonic development, cancer growth, wound healing, and epidemiology. Fisher's equation is the prototypical example of a problem that admits a traveling wave solution; it is a partial differential equation that was proposed to describe the spread of an advantageous gene. Although past investigators formulated and analyzed models for such translationally invariant systems at a macroscopic scale of interest, recent work has focused on analyzing and simulating traveling wave behavior in greater detail. This paper reviews the different scales and approaches by which researchers can model and simulate wave-like behavior, using the Fisher equation as a pedagogic example. We discuss different algorithms for simulating traveling waves, from traditional finite difference approaches to more recent hybrid multiscale algorithms.

The aim of this paper is to present an extensive overview of numerical simulations aimed at confirming and completing the theoretical results obtained in the analysis of some cerebrospinal fluid dynamics models which are treated from a purely mathematical view point. The present study is designed to support the first attempts in the approach to these physiological models from a more theoretical standpoint since their investigation in literature only concerns the modelization and the clinical feedback.

We investigate the internal observability of the wave equation with Dirichlet boundary conditions in tilings. The paper includes a general result relating internal observability problems in general domains to their tiles, and a discussion of the case in which the domain is the 30-60-90 triangle.

The aim of this paper is to study the existence of solutions for some quasilineare anisotropic elliptic problem associated with differential inclusion. We study the two cases of f∈ L∞(Ω) and f∈ L1(Ω). Moreover, we show the uniqueness of solution under some additional assumptions.

In this paper, we study the existence and uniqueness for nonlinear delay fractional differential equations with two orders of Caputo's fractional derivative using the Banach fixed point theorem. Also, we establish the Ulam stability of solutions. Finally, we give an example to illustrate the results.

Let X be a complex smooth projective variety of dimension n, and let E be an ample vector bundle on X. In this paper, we will introduce new invariants of generalized polarized manifolds (X,E), and we will study their properties. As an application, we study a lower bound for c_1(E)^n and the sectional genus g(X, c_1(E)) of (X, c_1(E)).

In this paper we extend the results proved in [7] about Feshbach resonances in a multichannel Hamiltonian H, proving a low energy expansion of the resolvent (H − k^2)^(−1) as k → 0 in the resonant case.

In this paper we study the evolution of vorticity in Navier-Stokes planar equations (with a small viscosity) and in Euler's axisymmetric tridimensional equations (with a large distance from the axis), when the initial vorticity is sharply concentrated around N points. We show that, in both cases, this evolution is close to the point-vortex dynamics for long times.

We describe an abstract version of the Theorem of Bogomolov-Tian-Todorov, whose underlying idea is already contained in various papers by Bandiera, Fiorenza, Iacono, Manetti. More explicitly, we prove an algebraic criterion for a differential graded Lie algebra to be homotopy abelian. Then, we collect together many examples and applications in deformation theory and other settings.

These lectures give a detailed and almost self-contained introduction to algebraic stacks. A great part of the paper is devoted to preliminary technical topics, both from category theory (like Grothendieck topologies, fibred categories and stacks) and algebraic geometry (like faithfully flat descent). All this machinery is finally used to present the definition and some basic properties first of algebraic spaces and then of algebraic stacks.

In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev polynomials of the first and second kind.

Reprint of the commemoration of Ruggiero Torelli, written by Guido Castelnuovo and published in Volume III (1918), pag. 16-20, of the Seminario Matematico della Facoltà di Scienze, i.e., Rendiconti di Matematica e delle sue applicazioni, serie I. This is the unique paper by Castelnuovo published in this journal.

In this paper we use Ekeland's ε-variational principle and we prove that, for some integral functionals, there exists a minimizing sequence compact in L∞.

Guido Castelnuovo (1865-1952) is one of the most outstanding personalities in the Italian school of Algebraic Geometry, he himself had contributed to found. His long life allowed him to be a testimony and a protagonist of the most significant events in Italy after its unification. Starting from the first years of the 20th century he oriented his mathematical interests towards Probability, Statistics, Actuarial Mathematics, Physics, History of Mathematics and Teaching. This paper goes through his life focusing on the aspects which seem to be particularly significant in understanding the evolution of his scientific interests.