Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Moduli spaces in positive geometry
Full text linkThese are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M0,n of n distinct points on P1 as a positive geometry and a binary geometry. We develop mathematical formalism to study Cachazo-He-Yuan\u27s scattering equations and the associated scalar and Yang-Mills amplitudes. We discuss open superstring amplitudes and relations to tropical geometry
Multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales with impulsive effects
No full textIn this study, we explore the existence of multiple solutions for a dynamic Sturm-Liouville boundary value problem ontime scales that incorporate impulsive effects. Utilizing variational methods and applying certain critical point theorems from Riccerifor smooth functionals, we demonstrate the existence of at least three solutions to the problem. To illustrate the practical relevanceof our findings, we provide an example at the end
On semi-c-periodic functions of type I and applications
No full textIn this paper, we study the (newly introduced) class of functions called semi-c-periodic functions of type I in a Banach space. We first investigate their basic properties, including a convolution result. Using a suitable norm we prove that the set of such functions is a Banach space. We then study the existence and uniqueness of semi-c-periodic mild solutions for both autonomous and non-autonomous linear evolution equations. We achieve the existence results using the Banach fixed point theorem and the principle of reductio
Feasible sets for vertex colorings of P4-designs
Full text linkA P4-design of order v is a system Σ= (X,B) where X has v vertices and B is a set of copies of P4, called blocks, decomposing the complete graph Kv on X. A BP4-design is a P4-design Σ endowed with a coloring of the vertices of in such a way that in any block there are at least two vertices with the same color and two vertices with different colors. The feasible set Ω(Σ) of is the set of integers k for which Σ is k-colorable. The minimum and maximum of Ω(Σ) are, respectively, the lower and upper chromatic number of Σ. In this paper the study of BP4-designs is initiated, giving a lower and upper bound for feasible sets of BP4-designs and showing the existence, for any admissible integer v, of BP4-designs of order v with the largest possible feasible set. Some results are obtained for small values of v
An additive perturbation lemma for linear m-accretive operators in Hilbert spaces
Full text linkIn this paper, we give a new sufficient condition for the sum of a linear maximal accretive operator and an accretive one to be maximal accretive in Hilbert spaces setting. As an application, an extended result to the operator-norm error bound estimate for the exponential Trotter-Kato product formula is given
A study on k-coalescence of two graphs
Full text linkThe k-coalescence of two graphs is obtained by merging a k-clique of each graph. The Aα-matrix of a graph is the convex combination of its degree matrix and adjacency matrix. In this paper, we present some structural properties of a non-regular graph which is obtained from the k-coalescence of two graphs. Also, we derive the Aα-characteristic poly- nomial of k-coalescence of two graphs and then compute the Aα-spectra of k-coalescence of two complete graphs. In addition, we estimate the Aα-energy of k-coalescence of two complete graphs. Furthermore, we obtain some topological indices of vertex coalescence of two graphs, and as an application, we determine the Wiener, hyper-Wiener and Zagreb indices of Lollipop and Dumbbell graphs.
 
Structure of unital Q-Fréchet algebras A satisfying: Ax^2 = Ax, for every x ∈ A
Full text linkWe show that a unital Q-Fréchet algebra A satisfying Ax2 = Ax, for every x ∈ A, is isomorphic to Cn, n ∈ N*
An approach to Zaremba\u27s conjecture throughout Fibonacci sequences
Full text linkAccording to Zaremba\u27s conjecture, any integer is estimated to occur as the denominator of a finite continued fraction whose partial quotients are restricted by 5. This conjecture is proven true for infinity many integers, and we illustrate it for more additional ones that are related to Fibonacci sequences and its generalization
Local (2-Local) derivations and automorphisms and biderivations of complex ω-Lie algebras
No full textThe present paper is devoted to the description of local (2-local) deriva- tions and automorphisms and biderivations on some complex ω-Lie alge- bras. Given a three-dimensional complex ω-Lie algebras g, we prove that every local (2−local) derivation and automorphisms on g are derivations and automorphisms respectively if g is not C1. We give the matrix form of local derivations and automorphisms in the cases C1. Also, we give a de- scriptions of biderivations of three dimensional complex ω-Lie algebras
Regularity results for nonlinear anisotropic parabolic equations with measure data
Full text linkThis study focuses on a class of nonlinear anisotropic parabolic equations involving measurement data. We prove, under which condition on si(y), some existence and regularity results for solutions in anisotropic Sobolev spaces using compactness arguments and convergence results