Minimizing Lp-norm among the Functions of Bounded Second Derivatives.
The existence of nonminimal regular harmonic maps from to
An energy estimate of an exterior problem and a Liouville theorem for harmonic maps
A note on ultrametric matrices
It is proved in this paper that special generalized ultrametric and special matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and matrices, respectively. Moreover, we present a new class of inverse -matrices which generalizes the class of matrices.
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
The first Dirichlet eigenvalue of bicyclic graphs
In this paper, we have investigated some properties of the first Dirichlet eigenvalue of a bicyclic graph with boundary condition. These results can be used to characterize the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicyclic graphs with a given graphic bicyclic degree sequence with minor conditions. Moreover, the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicycle graphs with fixed interior vertices of degree...
Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
A sharp upper bound for the spectral radius of a nonnegative matrix and applications
We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results.
The P-Laplacian spectral radius of weighted trees with a degree sequence and a weight set.
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