东阳有奇肴

在上海的一个公园茶室喝茶写作，结识一位陈姓历史老师，原籍东阳。我是到过东阳的，参观过卢氏大宅，买过当地名茶“东白”。也寻觅过当地的一些小吃。我知道该地读书风气极盛。据说分布在海内外教授级的文人学者多达千余人，严济慈先生就是东阳人．因而我对东阳人刮目相看，同时对那位老师也根尊重。

趣·味·奇·得——数学快乐教学的四大“法宝”

在小学阶段开展快乐学习,有利于减轻学生的学习负担,使得学生德、智、体全面发展,同时也有利于学生生动、活泼、健康地成长。那么,在数学教学中,如何推行快乐教学呢？笔者认为,在教学时教师应做到“四有”,即有“趣”、有“味”、有“奇”、有“得”。

庭中有奇树

承玺莫名的熟悉感令暮衍稍觉困惑。他确定从未见过这位公主。但许多事总是无从解释。她见过他，或许是在某次热闹的宴会上．抑或是她的香车与他的骏马错身的一瞬。她笃信他与过去相关，如同抓住黑暗中漏下的一缕光，想寻着这线索，拼凑出记忆的缺失。

箱鲀防身有奇招

如果一条鱼想保护自己不受伤言，它会怎么做？在你给出答案之前．不妨先来和箱鲀打个招呼。在这方面．它绝对算是高手！

EFFICIENT NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FLEXIBLE ROD HIT BY RIGID BALL

Impact dynamics of flexible solids is important in engineering practice. Obtaining its dynamic response is a challenging task and usually achieved by numerical methods. The objectives of the study are twofold. Firstly, the discrete singular convolution （DSC） is used for the first time to analyze the impact dynamics. Secondly, the efficiency of various numerical methods for dynamic analysis is explored via an example of a flexible rod hit by a rigid ball. Three numerical methods, including the conventional finite element （FE） method, the DSC algorithm, and the spectral finite element （SFE） method, and one proposed modeling strategy, the improved spectral finite element （ISFE） method, are involved. Numerical results are compared with the known analytical solutions to show their efficiency. It is demonstrated that the proposed ISFE modeling strategy with a proper length of con- ventional FE yields the most accurate contact stress among the four investigated models. It is also found that the DSC algorithm is an alternative method for collision problems.

A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on α priori （sequentially） adapted meshes and study its convergence. The scheme on α priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find α priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in χ, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for improving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical solution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N^-1 = o （ε^v）, where N denotes the number of nodes in the spatial mesh, and the value v = v（K） can be chosen arbitrarily small for suitable K.

Properties of Strange Matter in a Model with Effective lagrangian

The strange hadronic matter with nucleons, -hyperons and -hyperons is studied by using an effective nuclear model in a mean-field approximation. The density and strangeness fraction dependence of the effective baryon masses as well as the saturation properties and stabilities of the strange hadronic matter are discussed.

Carter subgroups of singular classical groups over finite fields

Let F q be a finite field with qelements where q=p~α. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (n+t,n)(F q), singular unitary group U (n+t,n)(F (q^2)) and singular orthogonal group O (n+t,n)(F q)(n is even) over finite fields F q.

Analytic and Experimental Studies of the Errors in Numerical Methods for the Valuation of Options

The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There are two parameters in the coefficients of the resulting linear parabolic partial differential equation.For a range of values of these parameters,the solution of the problem has a boundary or an initial layer.The initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior layer.We construct analytically the asymptotic solution of the equation in a finite domain.Based on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the boundary.Also,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are studied.We present numerical computations,which determine experimentally the parameter-uniform rates of convergence.We note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.

Finite-Difference Methods for a Class of Strongly Nonlinear Singular Perturbation Problems

The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the boundary layers.The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed.For the central scheme,error estimates are derived in a discrete L^1 norm.They are of second order and decrease together with the perturbation parameterε.The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically.Numerical results showε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.

Boundedness of a Kind of Oscillatory Singular Integral Operators

In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygmund kernel, which had been studied by Ricci and Stein in [6], and extend their result. We get that T is bounded on L^P（R^n）（1〈p〈∞） when -1〈u〈 αd（1/2-｜1/p-1/2）.

Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid

Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.

Chinese Carmaker Chery＇s Exports Quadruple in First Half Year

Chinese carmaker Chery Automobile said its exports quadrupled in the first half of the year, with overseas sales likely to top 100,000 vehicles for the whole year.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

Minimum Coverings of Complete Directed Graphs with Odd Size Circuits

Let DKv denote the symmetric complete directed graph with v vertices, the covering number C(v,m) is a minimum number of covering DKv by m-circuits. In this paper, C(v,m) is determined for any fixed odd positive integer m and positive integer v, m ≤ v ≤ m + 6.

Embeddings of weighted Sobolev spaces and degenerate elliptic problems

New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div(a(x)?u)=b(x)f(x,u)in?,u=0 on??,where?is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.

Tetravalent edge-transitive graphs of order p^2q

A graph is called edge-transitive if its full automorphism group acts transitively on its edge set.In this paper,by using classification of finite simple groups,we classify tetravalent edge-transitive graphs of order p2q with p,q distinct odd primes.The result generalizes certain previous results.In particular,it shows that such graphs are normal Cayley graphs with only a few exceptions of small orders.

On the control of fusion in the local category for the p-block with a minimal nonabelian defect group

If B is a p-block of a finite group G with a minimal nonabelian defect group D (p is an odd prime number) and (D, b D ) is a Sylow B-subpair of G, then N G (D, b D ) controls B-fusion of G in most cases. This result is of great importance, because we can use it to obtain a complete set of representatives of G-conjugate classes of B-subsections and to calculate the number of ordinary irreducible characters in B. This result is key to the calculation of the structure invariants of the block with a minimal nonablian defect group. On the other hand, we improve Brauer's famous formula k(B) =Σ (ω,b ω ) l(b ω ),where (ω, b ω ) ∈ [(G : sp(B))]. Let p be any prime number, B be a p-block of a finite group G and (D, b D ) be a Sylow B-subpair of G. H is a subgroup of N G (D, b D ) satisfying N G (R, b R ) = N H (R, b R )C G (R), (R, b R ) ∈ A 0 (D, b D ), N G ( w , b w' ) = N H ( w , b w' )C G (w' ), (w' , b w' ) ∈ (D, b D ). If w 1 , . . . , w l is a complete set of representatives of H-conjugate classes of D, then (w 1 , b w 1 ), . . . , (w l , b w l ) is a complete set of representatives of G-conjugate classes of B-subsections in G. In particular, we have k(B) =Σ l j=1 l(b w j ).

Two-dimensional numerical manifold method with multilayer covers

In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform meshes.This is believed to be one of the most important open issues in NMM.In this study multilayer covers are proposed to solve this issue.In addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong singularities.The global cover and the local covers have their own partition of unity,and they all participate in the approximation to the solution.Being advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements.With no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly facilitated.Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.

SINGULAR LIMIT SOLUTIONS FOR TWO-DIMENSIONAL ELLIPTIC PROBLEMS WITH EXPONENTIALLY DOMINATED NONLINEARITY

The authors consider the existence of singular limit solutions for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Dirichlet boundary condition and generalize the results of [3].