The Average Widths of Sobolev-Wiener Classes and Besov-Wiener Classes

This paper concerns the problem of average σ-width of Sobolev-Wiener classes W^rpq(R^d),W^rpq(M,R^d),and Besov-Wiener classes S^rpqθb(R^d).S^rpqθB(R^d),S^rpqθb(M,R^d),S^rpqθB(R^d)in the metric Lq(R^d) for 1≤q≤p≤∞.The weak asymptotic results concerning the average linear widths,the average Bernstein widths and the infinite-dimensional Gel‘fand widths are obtained,respectively.     

Solutions for the prescribing mean curvature equation

By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^＋ under certain assumptions. We also obtain the asymptotic behaviors of the solutions.     

N-Widths and Average Widths of Besov Classes in Sobolev Spaces

In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.     

Global weakly discontinuous solutions to quasilinear hyperbolic systems of conservation laws with damping with a kind of non-smooth initial data

For the Cauchy problem with a kind of non-smooth initial data for weakly linearly degenerate hyperbolic systems of conservation laws with the linear damping term, we prove the existence and uniqueness of global weakly discontinuous solution u = u(t, x) containing only n weak discontinuities with small amplitude on t ≥ 0, and this solution possesses a global structure similar to that of the similarity solution of the corresponding homogeneous Riemann problem. As an application of our result, we obtain the existence and uniqueness of global weakly discontinuous solution, continuous and piecewise C ¹ solution with discontinuous first order derivatives, of the flow equations of a model class of fluids with viscosity induced by fading memory. De-Xing Kong: Supported by the National Science Foundation of China(Grant 10371073), the Special Funds for Major State Basic Research Projects of China (Grant 2000077306), the Qi Ming Xing programme of Shanghai Government, and the Project sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the Ministry of Education of China.     

Convergence Rate of the L-N Estimator in Poisson-Gamma Models

We focus on in this paper the convergence rate of the L-N estimators for the fixed effect β in Poisson-Gamma models which are typical hierarchical generalised linear models（HGLMs）. Under the proper assumptions on response variables and some smoothing conditions, we obtain the strong consistency and the convergence rate of the L-N estimator based on the combination of L-N and quasi-likelihood.     

An operator Arzelà-Ascoli theorem

The author generalizes the Arzela-Ascoli theorem to the setting of matrix order unit spaces, extending the work of Antonescu-Christensen on unital C^＊-algebras. This gives an affirmative answer to a question of Antonescu and Christensen.     

Decay parameter and related properties of 2-type branching processes

We consider the decay parameter, invariant measures/vectors and quasi-stationary dis- tributions for 2-type Markov branching processes. Investigating such properties is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for 2-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Z+2 \ 0. It is shown that this λC can be directly ...     

A Null Space Approach for Solving Nonlinear Complementarity Problems

In this work, null space techniques are employed to tackle nonlinear complementarity problems （NCPs）. NCP conditions are transform into a nonlinear programming problem, which is handled by null space algorithms, The NCP conditions are divided into two groups, Some equalities and inequalities in an NCP are treated as constraints, While other equalities and inequalities in an NCP are to be regarded as objective function. Two groups are all updated in every step. Null space approaches are extended to nonlinear complementarity problems. Two different solvers are employed for all NCP in an algorithm.     

The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming

We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold . The research of Defeng Sun is partly supported by the Academic Research Fund from the National University of Singapore. The research of Jie Sun and Liwei Zhang is partly supported by Singapore–MIT Alliance and by Grants RP314000-042/057-112 of the National University of Singapore. The research of Liwei Zhang is also supported by the National Natural Science Foundation of China under project grant no. 10471015 and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China.     

On Pairs of Linear Equations in Three Prime Variables

In this paper, we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.     

Convergence of the Augmented Lagrangian Method for Nonlinear Optimization Problems over Second-Order Cones

The paper analyzes the rate of local convergence of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under the constraint nondegeneracy condition and the strong second order sufficient condition, we demonstrate that the sequence of iterate points generated by the augmented Lagrangian method locally converges to a local minimizer at a linear rate, whose ratio constant is proportional to 1/τ with penalty parameter τ not less than a threshold . Importantly and interestingly enough, the analysis does not require the strict complementarity condition. Supported by the National Natural Science Foundation of China under Project 10771026 and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.     

Existence of Z-cyclic 3PDTWh(<Emphasis Type="Italic">p</Emphasis>) for Prime <Emphasis Type="Italic">p</Emphasis> ≡ 1 (mod 4)

A directed triplewhist tournament on p players over Z _p is said to have the three-person property if no two games in the tournament have three common players. We briefly denote such a design as a 3PDTWh(p). In this paper, we investigate the existence of a Z-cyclic 3PDTWh(p) for any prime p ≡ 1 (mod 4) and show that such a design exists whenever p ≡ 5, 9, 13 (mod 16) and p ≥ 29. This result is obtained by applying Weil’s theorem. In addition, we also prove that a Z-cyclic 3PDTWh(p) exists whenever p ≡ 1 (mod 16) and p < 10, 000 except possibly for p = 257, 769. Gennian Ge’s Research was supported by National Natural Science Foundation of China under Grant No. 10471127, Zhejiang Provincial Natural Science Foundation of China under Grant No. R604001, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.     

The Characterization of Finite Simple Groups, L3（3^2m-1）（m≥2）, by Their Element Orders

In this paper the following theorem is proved： Every group L3（q） for q = 3^（2m-1）（m≥2） is characterized by its set of element orders.     

The Kakeya maximal operator with a special base

LetM _ℛ f be the Kakeya maximal function in d-dimensional Euclidean space with some base ℛ, consisting of cylinders of eccentricity N. The inequality ∥M _ℛ f∥ _d ⩽c(logN)^ε∥ is shown for a base ℛ satisfying a direction condition, where ε and c are constants depending only on d. to the memory of Professor Ruilin Long The author is partly supported by the Grants-in-Aid for Scientific Research, The Ministry of Education, Science and Culture, Japan.     

Modified High-order Upwing Method for Convection Diffusion Equation

Abstract   In this paper, we study the high-order upwind finite difference method for steady convection-diffusion problems. Based on the conservative convection-diffusion equation, a high-order upwind finite difference scheme on nonuniform rectangular partition for convection-diffusion equation is proposed. The proposed scheme is in conversation form, satisfies maximum value principle and has second-order error estimates in discrete H ¹ norm. To illustrate our conclusion, several numerical examples are given. Supported by the Research Fund for Doctoral Program of High Education of China State Education Commission.     

Stochastic comparison and preservation of positive correlations for Lévy-type processes

The stochastic comparison and preservation of positive correlations for Levy-type processes on R^d are studied under the condition that Levy measure v satisfies f{0〈｜z｜≤1）｜z｜｜v（x, dz） - v（x, d（-z））｜ 〈 ∞, x∈ R^d, while the sufficient conditions and necessary ones for them are obtained. In some cases the conditions for stochastic comparison are not only sufficient but also necessary.     

Asymptotic bound on binary self-orthogonal codes

We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R = 1/2, by our constructive lower bound, the relative minimum distance δ ≈ 0.0595 (for GV bound, δ ≈ 0.110). Moreover, we have proved that the binary self-orthogonal codes asymptotically achieve the Gilbert-Varshamov bound. This work was supported by the China Scholarship Council, National Natural Science Foundation of China (Grant No.10571026), the Cultivation Fund of the Key Scientific and Technical Innovation Project of Ministry of Education of China, and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060286006)     

A probabilistic approach to the first Dirichlet eigenvalue on non-compact Riemannian manifold

By using diffusion process with absorbing boundary, some lower bounds are obtained for the first Dirichlet eigenvalue of operator Δ+∇h on a non-compact complete Riemannian manifold. The resulting estimates contain McKean's estimate for ∇h=0. Moreover, the first Dirichlet eigenvalue for elliptic operators onR ^d and the first mixed eigenvalue are also studied. Some examples show that our estimates can be sharp even for ∇h≠0. Research supported in part by NFSC and the State Education Commission of China     

Circular neighbor-balanced designs universally optimal for total effects

In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.     

Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RBMO(μ) functions of Tolsa with non-doubling measures is obtained, provided that‖μ‖=∞and multilinear singular integrals are bounded from L1(μ)×L1(μ)to L1/2,∞(μ).