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### A second-order upwinding finite difference scheme for the steady Navier-Stokes equations in primitive variables in a driven cavity with a multigrid solver

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### Definition and some Properties of Information Entropy

Formalized Mathematics

In this article we mainly define the information entropy [3], [11] and prove some its basic properties. First, we discuss some properties on four kinds of transformation functions between vector and matrix. The transformation functions are LineVec2Mx, ColVec2Mx, Vec2DiagMx and Mx2FinS. Mx2FinS is a horizontal concatenation operator for a given matrix, treating rows of the given matrix as finite sequences, yielding a new finite sequence by horizontally joining each row of the given matrix in order...

### The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements

Formalized Mathematics

In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.

### The Relevance of Measure and Probability, and Definition of Completeness of Probability

Formalized Mathematics

In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.

### Pseudo-Riemannian weakly symmetric manifolds of low dimension

Czechoslovak Mathematical Journal

We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions $2$ and $3$, based on the algebraic approach of such spaces through the notion of a pseudo-Riemannian weakly symmetric Lie algebra. We also study the general symmetry of reductive $3$-dimensional pseudo-Riemannian weakly symmetric spaces and particularly prove that a $3$-dimensional reductive $2$-fold symmetric pseudo-Riemannian manifold must be globally symmetric.

### Construction of Lyapunov functionals for linear Volterra integrodifferential equations and stability of delay systems.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

### Lyapunov functionals and periodicity in a system of nonlinear integral equations.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

### A Novel Capacity and Trust Based Service Selection Mechanism for Collaborative Decision Making in CPS

Computer Science and Information Systems

### Fixed points and controllability in delay systems.

Fixed Point Theory and Applications [electronic only]

### Positive periodic solutions of functional differential equations and population models.

Electronic Journal of Differential Equations (EJDE) [electronic only]

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