scholarly journals Normalized Laplace operators for hypergraphs with real coefficients

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas
Keyword(s):  
Real Coefficient ◽  
Laplace Operators ◽  
Spectrum Of The Laplacian

Abstract Chemical hypergraphs and their associated normalized Laplace operators are generalized and studied in the case where each vertex–hyperedge incidence has a real coefficient. We systematically study the effect of symmetries of a hypergraph on the spectrum of the Laplacian.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

On eigenvalue problem of the Laplace operators for ellipsoidal areas

2018 ◽  
Vol 2018 (1) ◽  
pp. 146-154
Author(s):  
D.G. Rakhimov ◽  
◽  
Sh.M. Suyarov ◽  
Keyword(s):  
Eigenvalue Problem ◽  
Laplace Operators

The Spectrum of the Laplacian on the Pentagasket

2003 ◽  
pp. 1-24 ◽  
Author(s):  
Bryant Adams ◽  
S. Alex Smith ◽  
Robert S. Strichartz ◽  
Alexander Teplyaev
Keyword(s):  
Spectrum Of The Laplacian

scholarly journals An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Ying Wang ◽  
Baodong Zheng ◽  
Chunrui Zhang
Keyword(s):  
Dynamic Systems ◽  
Real Coefficient ◽  
Coupled Systems ◽  
Decomposition Technique ◽  
Exponential Polynomials ◽  
Basic Theorem ◽  
Algebraic Criterion ◽  
The Stability

We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.

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