In this paper we show that all totally real superconformal minimal tori in CP 2 correspond with doubly-periodic finite gap solutions of the Tzitzéica equation ωzz̄ = e −2ω − eω. Using the results on the Tzitzéica equation in integrable system theory, we describe explicitly all these tori by Prym-theta functions. Introduction Over the past few years the integrable system approach played an import...

As is known, the Schur complements of diagonally dominant matrices are diagonally dominant; the same is true of doubly diagonally dominant matrices. The purpose of this paper is to extend the results to the generalized doubly diagonally dominant matrices (a proper subset of H -matrices); that is, we show that the Schur complement of a generalized doubly diagonally dominant matrix is a generaliz...

let (m,g ) be a compact immersed hypersurface of (rn+1,) , λ1 the first nonzeroeigenvalue, α the mean curvature, ρ the support function, a the shape operator, vol (m ) the volume of m,and s the scalar curvature of m. in this paper, we established some eigenvalue inequalities and proved theabove.1) 1 2 2 2 2m ma dv dvn∫ ρ ≥ ∫ α ρ ,2)( )2 2 1 2m 1 mdv s dvn nα ρ ≥ ρ∫ − ∫ ,3) if the scalar curvatu...

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discu...

abstract limitations of traditional (conventional) soil surveys and improvement of information technology have lead soil surveyors to invent new methods which are generally called digital soil mapping (dsm). the aim of these methods is the prediction of soil classes or soil properties based on easily-available or measuring environmental variables. the objective of this investigation is to study...