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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.

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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.

Copyright of DIS - Dislessia, Discalculia & Disturbi di Attenzione is the property of Edizioni Centro Studi Erickson SpA and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of this paper is to address the question why the old Marx was interested in mathematics. While most interpreters argue that his interest was philosophical, it is maintained here that Marx tried to understand the developments of Economics and, particularly, of marginalism and that, in order to fully understand the new theoretical paradigma, he needed to study a particular branch of Mathematics, namely the derivatives. [ABSTRACT FROM AUTHOR]

I will examine in this paper the concept of process proposed by R. Ronchi in his book Canone minore (Feltrinelli 2016). I will retrace a certain relationship between this idea of process and two major languages which historically strived to elaborate an idea of process: the language of classical metaphysics, and the writing of modern and contemporary mathematics. On this basis I will investigate which status and which effects could have Ronchi's idea of process and the whole speculative itinerary proposed by Canone minore. A first hypothesis is formulated in the direction of what I could call a politics of knowledges and technologies. A second one in the direction of a mystic of knowledges and technologies. [ABSTRACT FROM AUTHOR]

Copyright of Ricerche di Pedagogia e Didattica is the property of Universita di Bologna, Dipartimento di Scienze dell'Educazione and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Ricerche di Pedagogia e Didattica is the property of Universita di Bologna, Dipartimento di Scienze dell'Educazione and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Form@re is the property of Firenze University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Archeologia dell'Architettura is the property of Edizioni all'Insegna del Giglio and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper proposes a reflection on mathematical beauty, considering the possibility of aesthetic qualities for formal language. Through a concise overview of the way this question is understood by some famous scientists and mathematicians, we turn our attention to Gian-Carlo Rota’s theoretical proposal: his reflections as a mathematician and philosopher offer a perspective, of phenomenological matrix, fruitful for looking at the question. Rota’s contribution allows us to focus on the role of competence, acquired through effort, sedimentation and habit of repetition, in cultivating the potential to recognise the aesthetic quality of formal language. Finally, we draw on some contributions from Gestalt theory, closely connected to twentieth-century phenomenology for chronological and conceptual reasons, applying the idea of gestalt wholeness to the mathematical product and proposing some reflections that may help to clarify some of the dynamics underlying the attribution of qualities of beauty to formulas or the detection of its lack.

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.

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.

The paper discusses the problem of infinity with a special reference to mathematical truth. The roots of this problem, in a sense, go back to early efforts to provide a rational account of the phenomena of change, and the phenomenon of motion in particular, and, in connection with this, to the attempt to cast light on the complex relationship between continuity and discreteness. If mathematics is to serve as a tool of a rational description of the world, is it possible to construct a mathematical model of phenomenal continuity? This question was raised already by Zeno when the Pythagorean hypothesis of the essential ‘granularity’ of the world began to crumble as a result of the discovery of incommensurable magnitudes. The discovery of incommensurable magnitudes, and along with it the discovery of irrational numbers, produced well-known paradoxes and gave rise to the question to what extent, if at all, mathematics can deliver a ‘metaphysical’ description of the world. In more recent times, the idea of infinity was built into the infinitesimal calculus which became the foundation of the mathematical description of nature, but the metaphysical questions have not gone away. The issues surrounding actual and potential infinity continue to be the subject of intense debates. Whereas some recognise only potential infinities, others, like Georg Cantor, accept actually existent infinities. This is directly connected with the question of mathematical truth, which, according to the Platonist tradition exists as objectively given. The paper argues that the Cantorian transfinite set theory cannot withstand criticism, and that rather than providing a (metaphysical) description of reality mathematics merely offers possible models in terms of which the world might be better or more conveniently interpreted. The so-called ‘mathematical truth’ reduces to the question of ‘correctness’, viz. whether a given mathematical proposition does or does not follow from given premises.

Racial laws, which for Italian Jews determined the loss of civil and political rights, and the complete banishment from scientific and academic circles, had a deep impact on Italian mathematics. Suddenly, it lost outstanding figures like T. Levi-Civita, V. Volterra, G. Castelnuovo and many others. Their discrimination triggered a series of institutional, epistemic and social transformations in high culture migration is one of them. After an brief overview of the diaspora of Jewish mathematicians from fascist Italy after 1938, the paper focuses on the experiences of some of them (such as G. Fubini, G. Fano, B. Segre, A. Terracini), who left to find a space for intellectual survival abroad and, eventually, succeeded in resuming their lives and scientific careers in the US, Great Britain, Switzerland and South America. [ABSTRACT FROM AUTHOR]

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.

The purpose of the paper is to study the uniqueness of meromorphic functions sharing a small function with finite weight. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [21]. We also solve an open problem as posed in the last section of [21].

In the last few decades quite a few articles have been published concerning Volterra's contributions to biomathematics. These articles are usually focused on the works of Volterra published after 1926, while they overlook Volterra's intense activity as scientific organizer in the field of oceanographic studies in the years that span from 1910 - the year of his celebrated dissertation about the applications of mathematics to social and biological sciences - to 1925, when he met his prospective son-in-law Umberto D'Ancona. In this article I shall try to fill this gap by telling the history of Volterra's scientific collaboration with Italian biologists (such as Giovan Battista Grassi, Luigi de Marchi and Gustavo Brunelli) in the decades before his meeting with Umberto D'Ancona. This story is worth telling because it helps to explain the stronger emphasis Volterra placed in his first biomathematical papers on the importance of the applications of mathematics to biology for practical matters (such as the prevention of epidemics and the enhancement of the fishing industry) rather than on more theoretical issues, which he tackled only in the last years of his life.

In this paper I reflect on the nature of mathematical beauty, and examine the connections between mathematics and the arts. I employ Plutarch’s distinction between the intelligible and the sensible, to compare the beauty of mathematics with the beauties of music, poetry and painting. While the beauty of mathematics is almost exclusively intelligible, and the beauties of these arts primarily sensible, it is pointed out that the latter share with mathematics a certain kind of intelligible beauty. The paper also contains reflections on the formal beauty and timelessness of mathematics, beauty as richness flowing from simplicity, form and content in mathematics, and mathematics and fiction. It concludes with some remarks on the question of why mathematical beauty is so little appreciated by non-mathematicians.

In this paper, we investigate the relationship between dual (Weak) Subtraction algebras, Heyting algebras and BE-algebras. In fact, the purpose of this paper is to show that BE-algebra is a generalization of Heyting algebra and dual (Weak) Subtraction algebras. Also, we show that a bounded commutative self distributive BE-algebra is equivalent to the Heyting algebra.

In this paper the authors introduced a new generalized differintegral operator for meromorphic univalent functions in U* = {z : z ∈ C, 0 < |z| < 1}. The objective of this paper is to establish certain results concerning the Hadamard product of functions in the classes ∑^{∗,m}_{μ,λ} (α, β , γ, k) and ∑^h_{μ,λ} (α, β , γ, k).

In this paper, we prove various existence results of a mild solution for a fractional nonlocal functional semilinear differential inclusion involving Caputo derivative in Banach spaces. We consider the case when the values of the orient field are convex as well as nonconvex. Moreover, we study the topological structure of solution sets. Our results extend or generalize results proved in recent papers.

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.

This paper deals with the study of two-dimensional Saigo-Maeda operators of Weyl type associated with Aleph function defined in this paper. Two theorems on these defined operators are established. Some interesting results associated with the H-functions and generalized Mittag-Leffler functions are deduced from the derived results. One dimensional analog of the derived results is also obtained.

The paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interval. The paper also investigates a few properties concerning the convergence of powerseries, Taylor's expansion around a point and the order of a zero.

Any mathematical description of structures should start from a precisely stated definition of the concept of "structure". Unfortunately no universally accepted definition of this type exists. All that can be said is that the concept of "structure" is changing together with the modern physico-mathematical thought, so that different 'points of view' on the problem of the mathematical description of structures can be distinguished. The aim of this paper is to compare the explicative and predictive power of these different 'viewpoints' without entering into historical detail, in order to critically examine the limits and powers of the mathematical tools available today.

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.

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) .

In this paper, we investigate the transportation problem with fractional objective function when the demand and supply quantities are varying. A set of mathematical programs is obtained to determine the objective value. Due to varying economic policies in the global world, it is hard to specify the supply and demand quantities for transportation problem. A transportation problem with fractional objective function is based on a network structure consisting of a finite number of nodes and arcs attached to them. After the derivation, we obtained the result in range, where the total transportation cost would appear. In addition to allowing for simultaneous changes in supply and demand values, the total cost bounds are calculated directly. This methodology would be very beneficial in the decision making. A numerical example has given in this paper for the support of theory.

In a paper in 2008, Herzog, Hibi and Ohsugi introduced and studied the semigroup ring associated to the set of minimal vertex covers of an unmixed bipartite graph. In this paper we relate the dimension of this semigroup ring to the rank of the Boolean lattice associated to the graph.

A famous conjecture by R. Stanley relates the depth of a module, an algebraic invariant, with the so-called Stanley depth, a geometric one. We describe two related geometric notions, the cover depth and the greedy depth, and we study their relations with the Stanley depth for Stanley-Reisner rings of simplicial complexes. This leads to a quest for the existence of extremely non-partitionable simplicial complexes. We include several open problems and questions.This paper is a report about a research project suggested by J. Herzog at the summer school P.R.A.G.MAT.I.C. 2008 at the University of Catania. In particular, the paper describes a direction where we expect that possible counterexamples can be found at least for a weaker version of Stanley’s conjecture.

O objetivo deste artigo é analisar, a partir dos textos de Platão e de comentadores, a apresentação de argumentos a favor da utilização da matemática e da geometria como propedêutica à aprendizagem da filosofia, bem como investigar as reverberações da ontologia e da epistemologia platônicas nesse programa pedagógico. Pretende-se, ainda, apontar comparativamente similaridades entre crises nos fundamentos da matemática e seu impacto na concepção de racionalidade, tanto no universo grego antigo como na contemporaneidade.The aim of this paper is to analyze, based on Plato's and commentators' texts, the presentation of arguments for the use of mathematics and geometry as propaedeutics to philosophy learning, as well as to investigate the reverberations of platonic ontology and epistemology in this pedagogical program. The paper will also consider similarities between crises in the foundations of mathematics and the impact of these crises on the conception of rationality, both in ancient Greek universe and in contemporary world.

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.

Using the results in papers [2] and [3] in this paper we prove the existence of the interpolating spline-function by the null space dimension of operators A and T.

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.

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.