On the Mean Absolute Geodesic Curvature of Closed Curves in 2-Dimensional Space Forms

In this paper,we establish some formulas on closed curves in 2-dimensional space forms.Mean absolute geodesic curvature is introduced to describe the average curving of a closed curve.Inthis sense,a closed curve could be compared with a geodesic circle that is the boundary of a convex geodesic circular disk containing the closed curve.The comparison can be used to show some properties of space forms only on themselves.     

On the isometric minimal immersion into a euclidean space

We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space. A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given. This work is partially supported by the National Science Foundation of China     

Two-point boundary value problems in relativistic dynamics

For gyro systems of relativistic type, we obtain solvability conditions for the two-point boundary value problem. We use the geodesic modeling method, in which the original problem is reduced to studying the existence of isotropic geodesic curves of the Kaluts-O. Klein Lorentz metric joining two fibers of a bundle over the configuration manifold of the system. As an example, we consider problems on the motion of charged test particles in an arbitrary electromagnetic field and in the outer Reissner-Nordstrem space-time in the field of a charged black hole and some external electromagnetic field.Translated fromMatematicheskie Zametki, Vol. 59, No. 3, pp. 437–449, March, 1996.This research was partially supported by the Russian Foundation for Basic Research under grant No. 94-01-00492a and by the International Science Foundation under grant No. NP4000.     

Deformations of balls in Schiffer’s conjecture for Riemannian symmetric spaces

It is proved that geodesic balls in a Riemannian symmetric space of rank one arestable solutions to a free-boundary problem for the Laplace-Beltrami operator with constant Dirichlet-Neumann boundary conditions. This result supports Schiffer's conjecture that balls are the only solutions to the problem. The main ingredient of the proof is a characterization of geodesic balls by the multiplicity of eigenvalues of the Laplace-Beltrami operator. Partially supported by a grant from the Academy of Sciences of Israel, no. 540/92-1 and by a grant from the US-Israel Science Foundation, no. 92-00246.     

Computing the geodesic center of a simple polygon

The geodesic center of a simple polygon is a point inside the polygon which minimizes the maximum internal distance to any point in the polygon. We present an algorithm which calculates the geodesic center of a simple polygon withn vertices in timeO(n logn).Work on this paper by the first author has been supported by National Science Foundation Grant No. DMS-8501947. Work on this paper by the second author has been supported by Office of Naval Research Grant No. N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation, and the IBM Corporation. Part of the work on this paper by the first two authors has been carried out at the Workshop on Movable Separability of Sets at the Bellairs Research Institute of McGill University, Barbados, February 1986. Work on this paper by the third author has been supported by the Fonds zur Förderung der wissenschaftlichen Forschung (FWF), Project S32/01.     

Reflections in submanifolds

This is a study of geodesic symmetries of a Riemannian manifold with respect to a submanifold. We analyze the significance of the property to be volume-preserving, isometric or preserving the mean curvature of the tubular neighborhoods.Work supported in part by the National Science Foundation and the Max-Planck-Institut für Mathematik, Bonn.     

Global superconvergence of finite element methods for parabolic inverse problems

In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators. This research was supported in part by the Shahid Beheshti University, the National Basic Research Program of China (2007CB814906), the National Natural Science Foundation of China (10471103 and 10771158), Social Science Foundation of the Ministry of Education of China (Numerical methods for convertible bonds, 06JA630047), Tianjin Natural Science Foundation (07JCYBJC14300).     

A new characterization of Suzuki-Ree group

It is proved that a Suzuki-Ree group can he characterized by the bet of its order components Project partially supported by the National Natural Science Foundation of China and Ph. D. Foundation of Southwest China Normal University.     

On IGMRES: An incomplete generalized minimal residual method for large unsymmetric linear systems

The truncated version of the generalized minimal residual method (GMRES), the incomplete generalized minimal residual method (IGMRES), is studied. It is based on an incomplete orthogonalization of the Krylov vectors in question, and gives an approximate or quasi-minimum residual solution over the Krylov subspace. A convergence analysis of this method is given, showing that in the non-restarted version IGMRES can behave like GMRES once the basis vectors of Krylov subspace generated by the incomplete orthogonalization are strongly linearly independent. Meanwhile, some relationships between the residual norms for IOM and IGMRES are established. Numerical experiments are reported to show convergence behavior of IGMRES and of its restarted version IGMRES(m). Project supported by the China State Key Basic Researches, the National Natural Science Foundation of China (Grant No. 19571014), the Doctoral Program (97014113), the Foundation of Returning Scholars of China and the Natural Science Foundation of Liaoning Province.     

Critical behavior of a metallic diffuse-fringe film percolation system

Preparation of a metallic diffuse-fringe film system and its electrical properties are reported. The anomalousR-I characteristics, third-harmonic coefficient and critical behavior are observed in the film system. Analysis shows that this behavior is caused by the location-dependent tunneling and hopping effects, which result from. the continuous variation of the diffuse fringe structure of the film due to the increase of the current. Project supported by the National Natural Science Foundation of China and Zhejiang Provincial Natural Science Foundation of China.     

DIMENSION AND DIFFERENTIABILITY OFA CLASS OF FRACTAL INTERPOLATION FUNCTIONS

Abstract. In this paper, a new iterated function system consisting of non-linear affine maps is constructed. We investigate the fractal interpolation functions generated by such a system and get its differentiabillty, its box dimension, its packing dimension,and a lower bound of its Hausdorff dimension.     

A Zoll Counterexample to a Geodesic Length Conjecture

We construct a counterexample to a conjectured inequality L ≤ 2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin’s theorem concerning the existence of Zoll surfaces integrating an arbitrary infinitesimal odd deformation of the round metric. Thus the round metric is not optimal for the ratio L/D. F.B. supported by the Swiss National Science Foundation. C.C. supported by NSF grants DMS 02-02536 and DMS 07-04145. M.K. supported by the Israel Science Foundation (grants 84/03 and 1294/06)     

General A-P iterative algorithm in shift-invariant spaces

A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.     

The Existence of a Positive Solution of D α[x(t) − x(0)] = x(t)f(t,x t )

This paper is devoted to the problem of existence of positive solution for a delay differential equation with fractional order. Some sufficient conditions for its existence of positive solution are given. This work was supported in part by the Key Project of the National Nature Science Foundation of China (No. 60534020), the National Nature Science Foundation of China (No. 60474037), and Program for New Century Excellent Talents in University (No. NCET-04-415).     

On pole assignment of distributed parameter systems with unbounded input elements

In this paper, the pole assignment problem is considered for a class of distributed parameter systems with unbounded input element and with multiple spectral structure. A formula on the spectrum of the closed loop operator is proved and a formula of pole assignment is obtained. Finally, an example concerning a beam vibration is given. This work is supported by the National Natural Sciences Foundation of China and the National Key Project of China, and partly by the Post Doctoral Science Foundation of China and the Youth Science Foundation of Shanxi.     

Trapping quasiminimizing submanifolds in spaces of negative curvature

LetM be a Hadamard manifold with all sectional curvatures bounded above by some negative constant. A well-known lemma essentially due to M. Morse states that every quasigeodesic segment inM lies within an a priori bounded distance from the geodesic arc connecting its endpoints. In this paper we establish an analogue of this fact for quasiminimizing surfaces in all dimensions and codimensions; the only additional requirement is that the sectional curvatures ofM be bounded from below as well. We apply this estimate to obtain new solutions to the asymptotic Plateau problem in various settings. The second author was supported by the Swiss National Science Foundation and enjoyed the hospitality of the University of Bonn. The collaboration between the authors was facilitated by the program GADGET II.     

A superlinearly and quadratically convergent SQP type feasible method for constrained optimization

A new SQP type feasible method for inequality constrained optimization is presented, it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations. The directions of the master algorithm are generated by only one quadratic programming, and its step-size is always one, the directions of the auxiliary algorithm are new “secondorder“ feasible descent. Under suitable assumptions, the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence.     

‖A −1‖∞ and equidiagonal-dominance

In this paper, the matrix of equidiagonal-dominance is defined and several theorems about ‖A ⁻¹‖_∞ and its evaluation are established. Many interesting numerical examples are given. This work is supported by the National Natural Science Foundation of China and the Science Foundation of Academy of Engineering Physics of China     

Non-constant stationary solutions to a prey-predator model with diffusion

In this paper, a nonlinear predator reproduction and prey competition model with diffusion is discussed. Some existence and non-existence results concerning non-constant positive steady-states are presented using topological degree argument and the energy method, respectively. The first author was supported by the National Natural Science Foundation of China (No. 10771032) and the Natural Science Foundation of Jiangsu province BK2006088, and the second author was supported by National Natural Science Foundation of China (No. 10601011).     

Almost Chebyshev set with respect to bounded subsets

The uniqueness and existence of restricted Chebyshev center with respect to arbitrary subset are investigated. The concept of almost Chebyshev sets with respect to bounded subsets is introduced. It is proved that each closed subset in a reflexive locally uniformly convex (uniformly convex, respectively) Banach space is an almost Chebyshev subset with respect to compact convex subsets (bounded convex subsets and bounded subsets, respectively). Project supported by the National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province, and the State Major Key Project for Basic Researchers of China.