Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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The generalized distance spectra of the M-join of graphs
Full text linkIn this paper, we obtain the generalized distance spectra of the graphs constructed by 19 unary and 21 binary graph operations of M-join type when the constituting graphs satisfy some conditions. Also, we deduce a result on the generalized distance spectrum of the double graph of a connected regular graph in the literature. As applications, we construct infinite families of generalized distance cospectral graphs. Also, we construct infinite families of distance (distance Laplacian, distance signless Laplacian) integral graphs
The information geometry of UMAP
Full text linkIn this note we highlight some connections of UMAP to the basic principles of Information Geometry. Originally, UMAP was derived from Category Theory observations. However, we posit that it also has a natural geometric interpretation
On discrete Hahn\u27s theorem
Full text linkWe give a discrete analogue of Hahn’s theorem and a discrete ex- tension for it; we show that an orthogonal polynomial sequence, whose m−th associated sequence of k−th ”discrete derivative” sequence is or- thogonal, is necessarily a D−ω -classical one, where Dω is the divided- difference operator
On the initial value problem with almost periodic linear part in a Banach space
Full text linkIn this article we present strong global solutions for the initial value problem in a reflexive Banach space, when the linear part of the corresponding differential evolution equation is Bohl-Bohr or Stepanov almost periodic function, and the displayed operator is infinitesimal generator of (C0)-semigrou
On the qualitative study of an abstract fractional functional differential equation via the Ψ-Hilfer derivative
Full text linkIn this article, we investigate the existence, uniqueness, and Ulam-Hyers stability of the equation:HD0α,β;Ψ(u(t)+g(t,u(t)))=Au(t) +f(t,u(t)), t ∈ [0,T], with initial condition I1−γ;Ψ0+ u(0)=u0,where HD0α,β;Ψ is the Ψ-Hilfer operator. We use the Banach fixed point principle and the Krasnoselskii\u27s fixed point theorem to achieve our results. We also investigate the stability of this equation. Our results generalize some recent ones on the subject
Construction of 3-helix systems of any index
Full text linkLet H(3) be a uniform of rank 3 hypergraph. A 3-helix S(3)(1,3) of \emph{centre} {c} is a 3-uniform hypergraph, with 3 hyperedges, all having in common exactly the centre {c}, with c of degree 3 and the remaining vertices of degree 1. In this paper we determine the spectrum of all S(3)(1,3)-designs, for every index λ
On diophantine singlefold specifications
Full text linkConsider an (m+1)-ary relation over the set N of natural numbers. Does there exist an arithmetical formula ⏀i(a0,...,am,x1,...,xk), not involving universal quantifiers, negation, or implication,such that representation and univocity conditions are met by each tuple in Nm+1 ?
Even if solely addition and multiplication operators (along with the equality relator and with positive integer constants) are adopted as primitive symbols of the arithmetical signature, the graph of any primitive recursive function is representable; but can representability be reconciled with univocity without calling into play one extra operation, namely ⟨b , n⟩ → bn ? As a preparatory step toward a hoped-for positive answer to this issue, one may consider replacing the exponentiation operator by any exponential-growth relation.
We discuss the said univocity, aka `singlefold-ness\u27, issue–first raised by Yuri Matiyasevich in 1974–, framing it in historical context. Moreover, we spotlight eight exponential-growth relation any of which, if Diophantine, could supersede exponentiation in our quest
On a system involving an integro-differential inclusion with subdifferential and caputo fractional derivative
Full text linkThe current work is concerned with a new system involving an integro-differential inclusion of subdifferential type and Caputo fractional derivative, in Hilbert spaces. We use a discretization approach to deal with the integro-differential inclusion. Then, we proceed by a fixed point theorem to handle the considered system
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 statedependent delay in Hilbert spaces. We obtain our significant findings using Grimmer’s resolvent operator theory and Schauder’s fixed point theorem. We give an example at the end to ensure the compatibility of the results
A two-function extension of a minimax theorem
Full text linkIn this note we extend a topological minimax theorem due to Ricceri [2] to the case of two functions