Fixed Point Theorems in Cone Symmetric Spaces

In this paper, some common fixed point theorems for general occasionally weakly compatible selfmaps and non-selfmaps on cone symmetric spaces were proved. The interesting point of this paper is that we do not assume that the cone is solid. Our results generalize and complete the corresponding results in [9-15].

Strong Approximation by Riesz Means on Compact Symmetric Spaces

The rates of strong approximation by Riesz means on compact symmetric spaces are established.

VARIATIONAL PROPERTIES OF THE INTEGRATED MEAN CURVATURES OF TUBES IN SYMMETRIC SPACES

Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.

Ricci Symmetries of Static Space-Times with Maximal Symmetric Transverse Spaces

In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V with all non-zero components and the static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor det R ≠0. It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. It also covers our previous results as a spacial case. Some new metrics admitting proper Ricci collineations are also investigated.

Ricci Collineations of Static Space Times with Maximal Symmetric Transverse Spaces

A complete classification of static space times with maximal symmetric transverse spaces is provided, according to their Ricci collineations. The classification is made when one component of Ricci collineation vector field V is non-zero （cases 1 - 4）, two components of V are non-zero （cases 5 - 10）, and three components of V are non-zero （cases 11 - 14）, respectlvily. Both non-degenerate （detRab ≠ 0） as well as the degenerate （det Rab = 0） cases are discussed and some new metrics are found.

Curvature Estimates for Irreducible Symmetric Spaces

By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, and thus get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of compact type. As an application, this paper verifies Sampson＇s conjecture in most cases for irreducible Riemannian symmetric spaces of noncompact type.

Orbits of Real Semisimple Lie Groups on Real Loci of Complex Symmetric Spaces

Let G be a complex semisimple algebraic group and X be a complex symmetric homogeneous G-variety. Assume that both G, X as well as the G-action on X are defined over real numbers.Then G（R） acts on X（R） with finitely many orbits. We describe these orbits in combinatorial terms using Galois cohomology, thus providing a patch to a result of Borel and Ji.

Homogeneous Einstein-like metrics on symmetric spaces

In this paper, we study homogeneous Einstein-like metrics on the compact irreducible symmetric space M, which is not isometric to a compact Lie group and has rank greater than 1. Whenever there exists a closed proper subgroup G′ of G = Isom_0(M) acting transitively on M, we find all the G′-invariant A-metrics and B-metrics on M. More precisely, we prove that G′-invariant metrics on M must be A-metrics, and G′-invariant B-metrics on M are always Einstein.

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.

On the Mean Exit Time for Compact Symmetric Spaces

Given a compact symmetric space, M, we obtain the mean exit time function from a principal orbit, for a Brownian particle starting and moving in a generalized ball whose boundary is the principal orbit. We also obtain the mean exit time flmction of a tube of radius r around special totally geodesic submanifolds P of M. Finally we give a comparison result for the mean exit time function of tubes around submanifolds in Riemannian manifolds, using these totally geodesic submanifolds in compact symmetric spaces as a model.

EQUIFOCAL HYPERSURFACESIN SYMMETRIC SPACESEQUIFOCAL HYPERSURFACESIN SYMMETRIC SPACES

This note investigates the multiplicity problem of principal curvatures of equifocal hypersurfaces in simply connected rank 1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces in the symmetric spaces.

Vanishing Theorem for Irreducible Symmetric Spaces of Noncompact Type

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.

The Partial Positivity of the Curvature in Riemannian Symmetric Spaces

In this paper, the partial positivity （resp., negativity） of the curvature of all irreducible Riemannian symmetric spaces is determined. From the classifications of abstract root systems and maximal subsystems, the author gives the calculations for symmetric spaces both in classical types and in exceptional types.

OUTER OPERATORS FOR THE NONCOMMUTATIVE SYMMETRIC HARDY SPACES ASSOCIATED WITH FINITE SUBDIAGONAL ALGEBRA

In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.

Complete Spacelike Hypersurfaces with Constant Scalar Curvature in Locally Symmetric Lorentz Spaces

The complete space-like hypersurfaces with constant normal saclar curvature is discussed in a locally symmetric Lorentz space. A classified theorem is obtained by the operator L1 introduced by S Y Cheng and S T Yau [3].

COMPLETE SPACE-LIKE SUBMANIFOLDS IN LOCALLY SYMMETRIC SEMI-DEFINITE SPACES

The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.

ORLICZ-LORENTZ SEQUENCE SPACES EQUIPPED WITH THE ORLICZ NORM In memory of Henryk Hudzik,a great man,our teacher and colleague

In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,research on such a general case is conducted for the first time.After showing that the Orlicz norm is equal to the Amemiya norm in general and giving some important properties of this norm,we study the problem of existence of order isomorphically isometric copies of l∞in the space(λ_(φ,ω),‖·‖_(φ,ω)^(O))and we find criteria for order continuity and monotonicity properties of this space.We also find criteria for monotonicity properties of n-dimensional subspaces λ_(φ,ω)^(n)(n≥2)and the subspace(λ_(φ,ω))_(a) of order continuous elements of λ_(φ,ω).Finally,as an immediate consequence of the criteria considered in this article,the properties of Orlicz sequence spaces equipped with the Orlicz norm are deduced.

ON SOME GENERALIZED DIFFERENCE PARANORMED SEQUENCE SPACES ASSOCIATED WITH MULTIPLIER SEQUENCE DEFINED BY MODULUS FUNCTION

In this article we introduce the paranormed sequence spaces （f,A, Am,p）, c0（f,A,Am,p） and L00（f,A, Am,p）, associated with the multiplier sequence ∧ = （hk）, defined by a modulus function f. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS

In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.