Article
Mathematics
Michal Tichy
Summary: In this paper, it is demonstrated that the geometric deformation of shearing can improve the decay rate of the heat semigroup associated with the Dirichlet Laplacian in an unbounded strip. The proof is based on the Hardy inequality resulting from shearing as established in [2] and the method of self-similar variables and weighted Sobolev spaces for the heat equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Shiping Cao, Hua Qiu, Haoran Tian, Lijian Yang
Summary: We introduce a graph-directed pair of planar self-similar sets that have fully symmetric Laplacians. We discuss the spectral decimation properties of these two fractals and provide a comprehensive description of their Dirichlet and Neumann eigenvalues and eigenfunctions.
SCIENCE CHINA-MATHEMATICS
(2022)
Article
Mathematics, Applied
Alessandra A. Verri
Summary: This paper investigates the essential spectrum and discrete spectrum in a sheared waveguide, and discusses the possibility of discrete spectrum under certain conditions. It also demonstrates that the number of discrete eigenvalues can be arbitrarily large when the waveguide is thin enough.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Physics, Mathematical
F. L. Bakharev, S. G. Matveenko
Summary: The asymptotic behavior of eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in a narrow two-dimensional domain (a thin Kirchhoff plate with rigidly clamped edges) as its width tends to zero is studied, revealing the localization effect of eigenfunctions which exhibit exponential decay as they move away from the widest plate region.
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
B. R. Rakshith, Kinkar Chandra Das
Summary: This paper investigates the problem of determining a graph by its distance Laplacian spectrum. It is proven that the distance Laplacian spectrum of a complete k-partite graph is unique. Furthermore, the distance Laplacian spectral determination of a complete k-partite graph with edge addition is studied, and it is shown that graphs whose complements are disconnected and determined by their Laplacian spectra also have distance Laplacian spectral determination.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Veronica Felli, Benedetta Noris, Roberto Ognibene
Summary: This work investigates the homogeneous Neumann eigenvalue problem for the Laplacian on a bounded Lipschitz domain and a singular perturbation of it. The study reveals that the sharp asymptotic behavior of the perturbed eigenvalue is influenced by the Sobolev capacity of the subset where the perturbed eigenfunction vanishes when converging to a simple eigenvalue of the limit Neumann problem. Additionally, a focus is placed on the case of Dirichlet boundary conditions imposed on a subset scaling to a point, and the vanishing order of the Sobolev capacity of such shrinking Dirichlet boundary portion is determined through blow-up analysis for the capacitary potentials.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Multidisciplinary Sciences
Hilal A. A. Ganie, Yilun Shang
Summary: The paper introduces the definitions of Laplacian and signless Laplacian matrices of a digraph D, and derives their combinatorial representations and applications. The paper concludes with digraph examples to demonstrate detailed calculations.
Article
Mathematics
Huyuan Chen, Mousomi Bhakta, Hichem Hajaiej
Summary: The purpose of this paper is to study the eigenvalues of the Dirichlet problem and prove the existence of a sequence of eigenvalues and their upper and lower bounds. The results of this study are of great significance for a better understanding of this problem.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Cesar R. De Oliveira, Alex F. Rossini
Summary: In this paper, we study the Laplacian in thin curved domains in the plane and space, with specific types of Robin boundary conditions and cross-sections. We derive nontrivial effective Schrodinger operators on the reference curve when the diameters of the cross sections tend to zero, using norm resolvent convergences. One novelty is that the changing sign in the Robin parameter does not require renormalization, and another novelty is that the torsion has no effect on the effective operators.
COMMUNICATIONS IN ANALYSIS AND GEOMETRY
(2022)
Article
Mathematics, Applied
Zalman Balanov, Edward Hooton, Wieslaw Krawcewicz, Dmitrii Rachinskii
Summary: In this paper, non-radial solutions to the problem -Delta u = f(z, u), u|(delta D) = 0 on the unit disc were proven to exist, with an investigation into the symmetric properties of these solutions and a numerical example with S-4-symmetry presented.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
Ali H. Alkhaldi, Meraj Ali Khan, Shyamal Kumar Hui, Pradip Mandal
Summary: The objective of this paper is to study the inequality for Ricci curvature of a semi-slant warped product submanifold and discuss the equality case. Physical applications of these inequalities are provided, and the relationship between the base manifold and a sphere with constant sectional curvature is also discussed.
Article
Mathematics, Applied
Hilal A. Ganie, S. Pirzada, Vilmar Trevisan
Summary: In this study, upper bounds for the sum of k largest Laplacian eigenvalues of two large families of graphs were obtained. As a consequence, Brouwer's Conjecture was proven for a large number of graphs belonging to these families.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Tingzeng Wu, Tian Zhou, Huazhong Lu
Summary: This article studies the star degree of graphs, provides a formula for computing the star degree of a graph, derives the star degree set of n-vertex graphs, and determines the graphs with extremal star degree. Furthermore, it is shown that some graphs with given star degree can be determined by their signless Laplacian permanental spectra.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics
Rafael T. Amorim, Alessandra A. Verri
Summary: We investigate the spectrum of the Dirichlet Laplacian operator on twisted strips in any space dimension. It is demonstrated that suitable twisting effects can generate discrete eigenvalues for the operator. Specifically, we examine the scenario where the twisting effect increases infinitely as the strip's width approaches zero, and find an asymptotic behavior for the eigenvalues.
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Huyuan Chen, Laurent Veron
Summary: This paper provides bounds for the sequence of eigenvalues in the Dirichlet problem, and shows that the sum of the eigenvalues is independent of the volume of the domain. The paper also discusses the lower and upper bounds of the principal eigenvalue, as well as the asymptotic behavior of the eigenvalues.
ADVANCES IN CALCULUS OF VARIATIONS
(2023)
