In 1907, Oskar Perron showed that a positive square matrix has a unique largest positive eigenvalue with a positive eigenvector. This result was extended to irreducible nonnegative matrices by Geog Frobenius in 1912, and to irreducible nonnegative tensors and weakly irreducible nonnegative tensors recently. This result is a fundamental result in matrix theory and has found wide applications in ...

We consider solutions of a system of refinement equations written in the form φ = ∑ α∈Z a(α)φ(2 · −α), where the vector of functions φ = (φ1, . . . , φr)T is in (Lp(R)) and a is a finitely supported sequence of r × r matrices called the refinement mask. Associated with the mask a is a linear operator Qa defined on (Lp(R)) by Qaf := ∑ α∈Z a(α)f(2 · −α). This paper is concerned with the convergen...

The paper focuses on finding out several physical quantities to exert an influence on the spatial parameters of complex-octonion curved space, including the metric coefficient, connection coefficient, and curvature tensor. In the flat space described with the complex octonions, the radius vector is combined with the integrating function of field potential to become a composite radius vector. An...

We consider solutions of a system of reenement equations written in the form as = X 2Z a()(2 ?) where the vector of functions = (1 ; : : : ; r) T is in (L p (R)) r and a is a nitely supported sequence of rr matrices called the reenement mask. Associated with the mask a is a linear operator Q a deened on (L p (R)) r by Q a f := P 2Z a()f(2 ?). This paper is concerned with the convergence of the ...

This study presents a comparison of recognition performance between feature extraction on the T-Zone face area and Radius based block on the critical point. A T-Zone face image is first divided into small regions where Local Binary Pattern (LBP) histograms are extracted and then concatenated into a single feature vector. This feature vector will further reduce the dimensionality scope by using ...

Using nonparaxial vector diffraction theory derived using the Hertz vector formalism, integral expressions for the electric and magnetic field components of light within and beyond an apertured plane are obtained for an incident plane wave. For linearly polarized light incident on a circular aperture, the integrals for the field components and for the Poynting vector are numerically evaluated. ...

The new method proposed in this work not only measures the particle size distribution and the average molar mass accurately using the static light scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid for dilute poly-disperse homogenous spherical particles in dispersion, but also enables us to have insight into the theoretical analysis of the dimensionless shape paramet...

Nomenclature CR,CI = empirical constants C = speed of sound, m/s D = Van-Driest damping function E = specific total energy f = frequency, Hz G = level-set variable hf,i = heat of formation of species i at reference condition k = turbulent kinetic energy lF = laminar flame thickness, m l = inner-layer flame thickness, m n = unit vector normal to flame front p = pressure Pr = Prandtl number q = r...

In this paper we consider a vector integer programming problem with the linear partial criteria. Numerical evaluations of two types of stability of the Pareto set have been found. Usually the stability (quasistability) of a vector optimization problem (see [1-10]) is understood as the property of nonappearance of new optimal solutions (preservation of initial) under small perturbations of the p...