We show that the density μ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities μps of SNF over Z/p sZ with p a prime and s some positive integer. Our approach is to connect the SNF of a matrix with the greatest common divisors (gcds) of certain polynomials of matrix entries, and develop the theory of multi-gcd distribution of polynomial values at a...

Dynamical systems, such as electric circuits, mechanical systems, and chemical plants, can be modeled by mixed matrix pencils, i.e., matrix pencils having two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. Based on dimension analysis of dynamical systems, Murota (1985) introduced a physically ...

Besides the fact that – by definition – matrix-exponential processes (MEPs) are more general than Markovian arrival processes (MAPs), only very little is known about the precise relationship of these processes in matrix notation. For the first time, this paper proves the persistent conjecture that – in two dimensions – the respective sets, MAP(2) and MEP(2), are indeed identical with respect to...

This paper presents an improved algorithm for computing the Combinatorial Canonical Form (CCF) of a layered mixed matrix A = Q T , which consists of a numerical matrix Q and a generic matrix T . The CCF is the (combinatorially unique) nest block-triangular form obtained by the row operations on the Q-part, followed by permutations of rows and columns of the whole matrix. The main ingredient of ...

In this paper the necessary and sufficient conditions are given for the solution of a system of parameter varying linear inequalities of the form A (t)x ≥ b (t) for all t ∈ T , where T is an arbitrary set, x is the unknown vector, A (t) is a known triangular Toeplitz matrix and b (t) is a known vector. For every t ∈ T the corresponding inequality defines a polyhedron, in which the solution shou...

Reported here is a battery in the form of a cement-matrix composite, with cement paste as the matrix, the pore solution in cement as the electrolyte, zinc particles dispersed in the matrix as the anode, manganese dioxide particles dispersed in the matrix as the cathode, and carbon black dispersed in the matrix as the conductive additive in both anode and cathode regions. The electrolyte is cont...

We introduce a product-form approximation for tandem networks with Poisson arrivals and non-exponential service times. The proposed technique perturbs the model state space to match the sufficient conditions for product-form solution provided by the Reversed Compound Agent Theorem (RCAT). After characterizing the relationship between RCAT productforms and matrix geometric solutions, we develop ...

This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...

It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $X$-form. For instance, $e^{mathbf{A}t}$, $t^{mathbf{A}}$ and $a^{mathbf{A}t}$ will be evaluated by the new formulas in this par...