Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Sign-changing solutions for a nonlinear degenerate elliptic system
No full textIn this article, we study the multiplicity of weak solutions to the non-linear degenerate elliptic system. The existence of sign-changing solutions is proved by the truncation method and the invariant sets of descending flow method
Controllability of non-autonomous measure driven integrodifferential evolution equations with nonlocal conditions
No full textThis research delves into the exact controllability of semilinear measure driven integrodifferential systems in nonlocal settings.We give enough controllability requirements using the measure of non-compactness and the Monch fixed point theorem without making any assumptions about how compact the evolution system is in relation to the linear part of the measure system. We find results here that both general- ize and improve upon many prior findings
Proudfoot-Speyer degenerations of scattering equations
Full text linkWe study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equationsWe study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equations
Cyclic polylopes through the lense of iterated integrals
Full text linkThe volume of a cyclic polytope can be obtained by forming an it-erated integral, known as the path signature, along a suitable piecewiselinear path running through its edges. Different choices of such a path arerelated by the action of a subgroup of the combinatorial automorphismsof the polytope. Motivated by this observation, we look for other polyno-mials in the vertices of a cyclic polytope that arise as path signatures andare invariant under the subgroup action. We prove that there are infinitelymany such invariants which are algebraically independent in the shufflealgebra
An explicit lower bound for large gaps between some consecutive primes
No full textThe main purpose of this paper is to clarify the numerical value of the constant cLG such that the above in- equality holds. We see that cLG is determined by several factors related to analytic number theory, for example, the ratio of integrals of functions in the multidimensional sieve of Maynard [14], the distribution of primes in arithmetic progressions to large moduli, and the coefficient of upper bound sieve of Selberg. We prove that the above inequality is valid at least for some cLG ≥ 2.0 × 10−17
Hyperplane arrangements in the grassmannian
Full text linkThe Euler characteristic of a smooth very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with d hyperplane sections removed. We provide a combinatorial formula, and explain how to compute this Euler characteristic in practice, both symbolically and numerically. Our particular focus is on generic hyperplane sections and on Schubert divisors. We also consider special Schubert arrangements relevant for physics. We study both the complex and the real case
On all-path convex, gated and Chebyshev sets in graphs
No full textWe present new characterizations for trees, block graphs, and geodetic graphs using all-path convex, gated and Chebyshev sets. Specifically, we prove that trees are exactly the graphs in which all-path convexity is a convex geometry. Block graphs are characterized as graphs in which all balls are all-path convex (equivalently, gated), and geodetic graphs are exactly those graphs where all balls (equivalently, closed neighborhoods) are Chebyshev. Additionally, we prove that almost all graphs have geodesically convex Chebyshev sets, provide a characterization of bipartite graphs with connected Chebyshev sets, and establish a criterion for graphs with trivial Chebyshev sets in the class of graph joins. Finally, we show that graphs of odd order with maximal number of edges under the Seidel switching operation always have trivial Chebyshev sets
On the radial solutions of a nonlinear Matukuma-type equation with double singular terms
No full textThis paper is concerned with the radial solutions of a Matukuma-type nonlinear equation with double singular terms,
∆pu+|x|m1 uδ1 +|x|m2 uδ2 = 0, x ∈ RN,
where p > 2, N ≥ 1, δ2 > δ1 ≥ 1, −p < m2 < m1 ≤ 0 and −N < m2 < m1 ≤ 0.
Our objective is to generalize a Matukuma-type equation since its importance in both geometry and physics. In this context, we prove the existence of global solutions, we give their classification and we present explicit behavior of positive solutions near the origin and infinity
Local and global solvability in attraction-repulsion chemotaxis systems with L2-initial data
No full textThis paper deals with the attraction-repulsion chemotaxis system under homogeneous Neumann initial-boundary conditions, where Ω ⊂ Rn (n ≤ 3) is a smoothly bounded domain and a,b,c,χ,ξ,α,β,γ,δ > 0 and τ ∈ {0, 1} are constants. The purpose of the present paper is to construct a local solution of this system for any L2-initial data without additional conditions on χ and ξ by using the theory for abstract evolution equations and to extend the local solution globally in the repulsion-dominant case by relying on a priori estimates
Bivariate exponential integrals and edge-bicolored graphs
Full text linkWe show that specific exponential bivariate integrals serve as generating functions of labeled edge-bicolored graphs. Based on this, we prove an asymptotic formula for the number of regular edge-bicolored graphs with arbitrary weights assigned to different vertex incidence structures. The asymptotic behavior is governed by the critical points of a polynomial. As an application, we discuss the Ising model on a random 4-regular graph and show how its phase transitions arise from our formula