Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Survey on balanced graph and hypergraph designs
No full textIn this paper we recall some results on balanced type conditions for graph and hypergraph designs. The usual definition of balanced graph design (see [23]) is the following: a G-design is balanced if the number of blocks containing any vertex is constant. Later, other balanced type conditions have been introduced for graph designs and extended to hypergraph designs. In the latter case the new notion of edge balanced has been introduced, being related to the number of times that a pair is contained in an edge of a block
Approximate controllability of impulsive integrodifferential equations with state-dependent delay
Full text linkThis paper considers the approximate controllability of mild solutions for impulsive semilinear integrodifferential equations with state-dependent delay in Hilbert spaces. We obtain our significant findings using Grimmer\u27s resolvent operator theory and Schauder\u27s fixed point theorem. We give an example at the end to ensure the compatibility of the results
Line cozero-divisor graphs
Full text linkLet R be a commutative ring. The cozero-divisor graph of R denoted by Γ′(R) is a graph with the vertex set W∗(R), where W∗(R) is the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if x ∈/ Ry and y ∈/ Rx. In this paper, we investigate when the cozero-divisor graph is a line graph. We completely present all commutative rings which their cozero-divisor graphs are line graphs. Also, we study when the cozero-divisor graph is the complement of a line graph
Approximate controllability for some integrodifferential measure driven system with nonlocal conditions
Full text linkIn this work, we focus on a specific category of nonlocal integrodifferential equations. The development of a few new sufficient postulates that guarantee solvability and approxi- mative controllability is described here. We apply the theory of the resolvent operator in the sense of Grimmer, as well as the fixed point strategy and the theory of the Lebesgue-Stieljes integral, in the context of the space of regulated functions. In light of this, the prevalence of our findings is greater than that which is found in the literature. At last, and example is comprised that exhibits the significance of developed theory
Herz-type Sobolev spaces on domains
Full text linkWe introduce Herz-type Sobolev spaces on domains, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces. Some remarks on CaffarelliKohnNirenberg inequality are given
On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists
Full text linkSegal constructed a derived equivalence for an interesting 5-fold flop that was provided by Abuaf. The aim of this article is to add some results for the derived equivalence for Abuaf\u27s flop. Concretely, we study the equivalence for Abuaf\u27s flop by using Toda-Uehara\u27s tilting bundles and Iyama-Wemyss\u27s mutation functors. In addition, we observe a ``flop-flop=twist" result and a ``multi-mutation=twist" result for Abuaf\u27s flop
Stability of constant equilibria in a Keller--Segel system with gradient dependent chemotactic sensitivity
Full text linkThis paper deals with the Keller–Segel system with gradient depen- dent chemotactic sensitivity,
where Ω ⊂ Rn (n ∈ N) is a bounded domain with smooth boundary, and χ > 0, p ∈ (1, ∞) are constants. The purpose of this paper is to establish stability of constant equilibria under some smallness conditions for the initial data
Addendum to the paper: Fixed points for non-expansive set-valued mappings
Full text linkThe aim of this paper is to improve or simplify some theorems which have been published in the paper ``Fixed points for non-expansive set-valued mappings" in this journal after a stay of the author at the University of Catania. In particular in the previous paper the main results were that in general the known properties of the set of fixed points for contractive set-valued mappings fail as soon as one replaces ``contractive\u27\u27 by ``non-expansive\u27\u27. In fact, as we shall prove in this addendum, some of them hold true when the surrounding space is finite-dimensional, or the domain is compact. Some results of the previous paper are reproved here with a simpler proof for making this addendum more self-contained
Entropy methods and application in the field of collective behaviour
No full textThese notes summarize a series of lectures given by Claudia Negulescu at the Institut supérieur de l\u27aéronautique et de l’espace (ISAE-SUPAERO) during the years 2019-2022. They are devoted to an elementary and self-consistent approach of the mathematical theory emerging in the modelling of the collective behaviour of certain natural phenomena. The notion of entropy plays here a crucial role, in particular entropy dissipative techniques are the basis for the investigation of the qualitiative behaviour of nonlinear PDEs. The lectures are based on published works, which were specifically chosen to illustrate different techniques in the field of collective behaviour
Some results on a graph associated with a non-quasi-local atomic domain
Full text linkLet R be an atomic domain which admits at least two maximal ideals. Let Irr(R) denote the set of all irreducible elements of R and let A(R) = {Rπ | π ∈ Irr(R)}. Let I(R) denote the subset of A(R) consisting of all Rπ ∈ A(R) such that π does not belong to the Jacobson radical of R. With R, we associate an undirected graph denoted by G(R) whose vertex set is I(R) and distinct vertices Rπ1 and Rπ2 are adjacent if and only if Rπ1 ∩ Rπ2 = Rπ1π2. The aim of this article is to discuss some results on the connectedness of G(R) and on the girth of G(R)