Subdirect sums of doubly diagonally dominant matrices.
On symmetric matrices with exactly one positive eigenvalue.
Inequalities for the minimum eigenvalue of -matrices.
A note on estimates for the spectral radius of a nonnegative matrix.
A weak regular splitting for singular linear systems.
Bounds for the (Laplacian) spectral radius of graphs with parameter
Let be a simple connected graph of order with degree sequence . Denote , and , where is a real number. Denote by and the spectral radius of the adjacency matrix and the Laplacian matrix of , respectively. In this paper, we present some upper and lower bounds of and in terms of , and . Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results.
Regions containing eigenvalues of a matrix.
Preconditioned diagonally dominant property for linear systems with -matrices.
Some new results on determinantal inequalities and applications.
A note on generalized Perron complements of -matrices.
Some bounds for the spectral radius of the Hadamard product of matrices.
Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels
Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials and the...
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