Search

Copyright of Reti Medievali 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 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.)

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).

Physical activity provides numerous benefits to physical and mental health, even affecting learning. Despite this, one of the main modern problems is represented by sedentariness. Children and adolescents spend most of their time at school. Therefore, a valid teaching methodology to benefit from the positive effects of physical activity and reduce sedentary moments could be interdisciplinary learning, which integrates physical education into various curricular subjects. Specifically, this paper proposes a systematic literature review of some protocols (n = 11) to investigate whether an elementary school’s integrated physical education and mathematics curriculum can improve learning in the logic-cognitive domain. From all the studies reviewed, the strong importance of interdisciplinary teaching, linking mathematics to physical education, was confirmed to reduce sedentary moments and enable a better attitude toward this discipline, breaking down the many stereotypes that often paint it as a complex and abstract subject.

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.

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.

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.

This article tackles a thorny issue within the reception of Badiou’s philosophy, i.e., the question of the role of the “social” within the ontological framework it outlines. Acknowledging that the question of the social is underdeveloped in Badiou’s system, the paper argues that there are resources in it to develop a social ontology, and attempos to flesh it out through an original and sustained reading of Badiou’s key formula on the distinction between democratic materialism and materialist dialectic: “there are only bodies and languages, except that there are truths”.

This paper explores the recent updating of Badiou's general philosophical proposal in the specific approach of a "speculative strategy" in his recent book The Immanence of Truths. I hypothesize that the idea of a "speculative strategy" is a third stage in Badiou's project called "philosophy of the event", which fulfills and radicalizes the previous stages of "platonism of the multiple" and "communism of Idea", development whose continuity rests on the internal unity of his project flinking his ontological and meta-ontological wager as a necessarily systematic philosophy. First, I will show the general elements of Badiou's philosophy, explaining its stages and the emergence of what I will call "philosophy of the event and multiple being". Secondly, I will delve specifically into the convergence of the ontological thesis and the meta-ontological one, to characterize the author's enterprise as a systematic project detached from ontotheology thanks to the speculative recourse to mathematics to think infinity. Finally, I will argue that the "strategy" of the author's recent work implies a specification of the role of mathematics within his speculative ontology.

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) .