The independence of initial vectors in the subdivision schemes

Starting with an initial vector λ = (λ(κ))κ∈z ∈ ep(Z), the subdivision scheme generates asequence (Snaλ)∞n=1 of vectors by the subdivision operator Saλ(κ) = ∑λ(j)a(k - 2j), k ∈ Z. j∈zSubdivision schemes play an important role in computer graphics and wavelet analysis. It is very interesting tounderstand under what conditions the sequence (Snaλ)∞n=1 converges to an Lp-function in an appropriate sense.This problem has been studied extensively. In this paper we show that the subdivision scheme converges forany initial vector in ep(Z) provided that it does for one nonzero vector in that space. Moreover, if the integertranslates of the refinable function are stable, the smoothness of the limit function corresponding to the vectorλ is also independent of λ.     

Finite Group Schemes over Bases with Low Ramification

Let A be a complete characteristic (0,p) discrete valuation ring with absolute ramification degree e and a perfect residue field. We are interested in studying the category FF _A' of finite flat commutative group schemes over A withp-power order. When e= 1, Fontaine formulated the purely linear algebra notion of a finite Honda system over A and constructed an anti-equivalence of categories betweenineFF _A'> and the category of finite Honda systems over A when p> 2. We generalize this theory to the case e – 1.     

The Osher scheme for non-equilibrium reacting flows

An extension of the Osher upwind scheme to non-equilibrium reacting flows is presented, Owing to the presence of source terms, the Riemann problem is no longer self-similar and therefore its approximate solution becomes tedious. With simplicity in mind, a linearized approach which avoids an iterative solution is used to define the intermediate states and sonic points. The source terms are treated explicitly. Numerical computations are presented to demonstrate the feasibility, efficiency and accuracy of the proposed method. The test problems include a ZND (Zeldovich-Neumann-Doring) detonation problem for which spurious numerical solutions which propagate at mesh speed have been observed on coarse grids. With the present method, a change of limiter causes the solution to change from the physically correct CJ detonation solution to the spurious weak detonation solution.     

Si团簇的结构特性研究

采用由 M.Menon等人的非正交紧束缚模型,结合遗传算法和分子动力学方法,对n=2～20的中小尺寸Si团簇的结构进行了优化,计算了束缚能Eb、平均配位数CN,团簇的裂化能Efrag,总能的二阶差分Δ2E,最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能隙Eg, 结合Mullikon集居数分析研究了电子特性,得出了随着团簇尺寸的增加,团簇的构型发生了近球形-长椭球形-近球形的转变、n=4,7,10等团簇具有较强稳定性、团簇中原子之间共价键性结合占支配地位等主要结论.所得的主要结论与已有的从头计算和实验结果相一致.     

SYMPLECTIC SCHEMES FOR NONAUTONOMOUS HAMILTONIAN SYSTEM

ＳＹＭＰＬＥＣＴＩＣＳＣＨＥＭＥＳＦＯＲＮＯＮＡＵＴＯＮＯＭＯＵＳ　ＨＡＭＩＬＴＯＮＩＡＮ　ＳＹＳＴＥＭＱＩＮＭＥＮＧＺＨＡＯ（秦孟兆）（ＩｎｓｔｉｔａｔｅｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓａｎｄＳｃｉｅｎｔｉｆｉｃ－Ｅｎｇｉｎｅｅ...     

实现水窗波段X射线激光的途径

研究了类氢、类氦、类锂和类钠离子等四种实现复合机制Ｘ射线激光的方案，对可能实现水窗波段Ｘ射线激光的几种方案比较，分析了其各种的优缺点，并讨论了可能的具体实验方法。     

On the Existence of Auslander–Reiten Sequences of Group Representations II

This is the second part of our study of the existence ofAuslander–Reiten sequences of group representations. In Part I weconsidered representations of group schemes in characteristic 0; in thispart we consider representations of group schemes in characteristicp; and in Part III we give applications to representations ofabstract groups and Lie algebras.     

Stability conditions for a pipeline polling scheme in satellite communications

This paper considers the unknown stability conditions of a pipeline polling scheme proposed for satellite communications. This scheme is modelled as a cyclic-service system with limited service and reservation. The walk times and the maximum number of services to be performed during each polling are dependent on the queue lengths of the stations. The main result is the derivation of the necessary and sufficient stability conditions of the system. Our approach is to map the multi-dimensional stability problem into many 1-dimensional stability problems through the concept of the least stable queue. The least stable queue is one that will become unstablefirst when the system load increases in some parameter region. The stability of the least stable queue thus implies stability of the system. The stability region for the whole system is then the union of the queue stability regions of all the least stable queues that are obtained through dominant systems and Loynes' theorem. We also propose a computable sufficient condition that is tighter than the existing result and present some numerical results.     

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

~~Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation1. Feynman, R., There's plenty of room at the bottom, Journal of Microelectromechanical Systems, 1992, 1: 60 -66. 2. Piekos, E. S., Breuer, K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, Transactions of the ASME, Journal of Fluids Engineering, 1996, 118: 464-469. 3. Beskok, A., Karniadakis, G. E., Trimmer, W., Rarefaction and …     

New Simple Method for Obtaining Integrable Hierarchies of Soliton Equations with Multicomponent Potential Functions

A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra is constructed, whose commutation operation is clear as that in loop algebra . Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra of the loop algebra is constructed. Taking advantage of above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out.