We analyze gene coexpression network under the random matrix theory framework. The nearest-neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards. Eigenvector analysis of the network using inverse participation r...

In this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that permit the use of fast solvers. The main innovation is that the eigenvalues for two and three-dimensional domains can be calculated exactly by solving a set of one-dimensional e...

Fluid queueing models with finite capacity buffers are applied to analyze a wide range of real life systems. There are well established numerical procedures for the analysis of these queueing models when the load is lower or higher than the system capacity, but these numerical methods become unstable as the load gets close to the system capacity. One of the available numerical procedures is the...

the eigenvalues of a graph is the root of its characteristic polynomial. a fullerene f is a 3-connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n isthe number of vertices of f. in this paper we investigate the eigenvalues of a class of fullerenegraphs.

in this paper, the deformation of a thick-walled circular cylindrical shell of incompressible isotropic elastic material is considered. the shell, which is made of three-term strain energy function is subjected to the combined external and axial loading pressure. in order to obtain the relevant eigenvalues, which is the main objective of the work, the incremental equilibrium equations are so...

‎let $g$ be a graph with vertex set $v(g)$ and edge set $x(g)$ and consider the set $a={0,1}$‎. ‎a mapping $l:v(g)longrightarrow a$ is called binary vertex labeling of $g$ and $l(v)$ is called the label of the vertex $v$ under $l$‎. ‎in this paper we introduce a new kind of graph energy for the binary labeled graph‎, ‎the labeled graph energy $e_{l}(g)$‎. ‎it depends on the underlying graph $g$...

We revisit existence and stability of two-pulse solutions in the fifth-order Korteweg–de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of successive iterations for numerical (spectral) approximations of pulses and prove convergence of iterations in a neighborhood of two-pulse solutions. Second, we prove structural stability of embedded eigenvalues of negati...

We describe a general framework for avoiding spurious eigenvalues — unphysical unstable eigenvalues that often occur in hydrodynamic stability problems. In two example problems, we show that when system stability is analyzed numerically using descriptor notation, spurious eigenvalues are eliminated. Descriptor notation is a generalized eigenvalue formulation for differential-algebraic equations...

In this paper we consider the transmission eigenvalue problem corresponding to acoustic scattering by a bounded isotropic inhomogeneous object in two dimensions. This is a non self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concerned with theoretical error analysis of a finite element method for computing the eigenvalues and corresponding eigenfunctions...

Eigenvectors and eigenvalues are numbers and vectors associated to square matrices, and together they provide the eigen-decomposition of a matrix which analyzes the structure of this matrix. Even though the eigen-decomposition does not exist for all square matrices, it has a particularly simple expression for a class of matrices often used in multivariate analysis such as correlation, covarianc...