Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Asymptotic behavior of solutions for parabolic problems of fractional type and sign-changing measure data
Full text linkWe prove a new asymptotic behavior result (with respect to the time variable t) of entropy solutions for fractional parabolic problems, with Dirichlet boundary at infinity, whose model is
where (−∆)spu is the fractional (s, p)-Laplace operator (with ps < N, 0<s<1 and p>2− s), u0 ∈L1 (RN) and μ is a bounded, compactly supported Radon measure whose support is compactly contained in Q := (0, ∞) × RN , N ≥ 2 (not depending on time) which does not charge the sets of the fractional (s, p)-capacity
Almost automorphic solutions for Lotka-Volterra systems with diffusion and time-dependent parameters
Full text linkIn this work we study the response for a class of Lotka-Volterra prey- predator systems with diffusion and time-dependent parameters to a large class of oscillatory type functions, namely the pseudo almost automorphic type oscillations. To this end, using the exponential dichotomy approach and a fixed point argument, we propose to analyze a class of nonau- tonomous semilinear abstract evolution equation of the form (⋆)z′(h) = A(h)z(h) + g(h, z(h)), h ∈ R, where A(h), h ∈ R is a family of closed linear operators acting in a Banach space T, the nonlinear term g is μ- pseudo-almost automorphic in a weak sense (Stepanov sense) with re- spect to h and Lipschitzian in T with respect to the second variable. Therefore, according to the results obtained for equation (⋆) we establish the existence and uniqueness of μ-pseudo-almost automorphic solutions in the strong sense (Bohr sense) to a nonautonomous system of reaction- diffusion equations describing a Lotka-Volterra prey-predator model with diffusion and time-dependent parameters in a generalized almost auto- morphic environment
An agent framework to explore pathfinding strategies in maze navigation problem
Full text linkThe planning of paths in complex, interconnected, and unknown structures, such as mazes, is a crucial topic in various fields, including artificial intelligence and robotics. Agents capable of making independent decisions require efficient navigation through mazes, and their performance can be influenced by various dynamics and features. Understanding these factors is essential not only for developing more efficient and robust navigation algorithms but also for gaining deeper insights into which attributes to prioritize in the design and implementation of autonomous agents. In this article, we analyze different multi-agent systems, focusing particularly on the analysis of various navigation strategies based on the concepts of memory and visibility. Our goal is to identify the parameters that impact the agents\u27 performance the most and how variations on these key parameters influence agents efficiency on complex maze-solving
Lie product and fixed points preservers
Full text linkLet B(X) be the algebra of all bounded linear operators on a complex Banach space X . In this paper, it is determined the form of surjective maps φ : B(X ) → B(X ) that satisfy F (φ (A)φ (B) − φ (B)φ (A)) = F (AB − BA) for every A,B ∈ B(X), where F(A) denotes the set of all fixed points of an operator A ∈ B(X)
Uncertainty inequality and approximate inversion formulas for r-weighted Fock spaces
Full text linkWe introduce r-weighted Fock space Fr,β which generalizes some previously known Hilbert spaces, and study the multiplication operator Mr and its adjoint. A general uncertainty inequality of Heisenberg type is obtained. We also consider the extremal functions for the r-difference operator Dr on the space and obtain approximate inversion formulas
Weakly Arf property for amalgamation of semigroups and rings
Full text linkWe provide a characterization of the weakly Arf property for the amalgamation of numerical semigroups and for amalgamation algebra
Algebraic surfaces with nonhyperelliptic linear pencil of genus 4 and irregularity one
Full text linkWe construct algebraic surfaces with nonhyperelliptic linear pencil of genus 4 and of rank 3 whose slope is equal to 4 and with irregularity one. Furthermore, we consider the converse. Namely, we obtain the structure of the surfaces with the above properties.
 
Existence of homoclinic solutions for two classes of differential systems with p-Laplacian
Full text linkIn this paper, we are concerned with a class of periodic differential systems with p-Laplacian when the potential is with superquadratic or asymptotically quadratic growth at infinity in the second variable. Using the monotonicity tric of Jeanjean and the concentration compactness principle, we prove the existence of homoclinic solution. Some recent results in the literature are generalized and significantly improved
Line idempotent graph of some commutative rings
Full text linkLet X be a finite commutative ring with unity and Id(X) be the set of idempotent elements of X. The idempotent graph G_Id(X) of X is a simple undirected graph with all elements of X as vertices and two distinct vertices x, y are adjacent if and only if x + y ∈ Id(X). In this paper, we have considered the idempotent graph of some commutative rings and investigated those graph and their complement for being line graphs