Development of a Simulation Model for Solid Objects Suspended in a Fluctuating Fluid

We introduce a new scheme for the future application of Real-coded Lattice Gas (RLG) to the numerical simulation of suspended solid objects in a fluctuating fluid environment. The reproduction of Brownian motion for a single solid object is verified through the Gaussian distribution of its displacements. The effectiveness of the solid–solid interaction model is also confirmed in an N-body simulation.     

Banach空间上有界可逆线性变换逆变换的结构

Fillmore在[1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Periodic Optical Pulses in Nonlinear Optical Fibers

We discuss the problem of transmitting polarized pulses along optical fibers with variable dispersion. The dissipation and mean dispersion are assumed to be zero, which allows using the model of the vector nonlinear Schrödinger equation. We consider an optical fiber consisting of arms of equal length, which is assumed to be large. We propose an asymptotic recursive procedure for calculating the amplitude and the phase of an optical pulse propagating along the optical cable with variable dispersion.     

Analysis of a 2D “liquid”plasma lattice

Adustyplasmacanbedefinedasacomplicatedplasmacontainingsmallsolidmattercalleddustgrainsordustparticles,whichareusuallychargednegatively,duetoelectronshighermobilitythanion,bycollectingelectronsandionsfromthebackgroundplasma.Theuniverseisfilledwithdustyplasmassuchasplanetaryrings,comettails,andnebulae.Also,inindustrialplasmaprocessing,particulatessuspendedinplasmaarethemajorcontaminationinsemiconductormanufacture.Studiesondustyplasmahavebeenextendedtofar-flungtopicssuchaswaves,instabilities,stro…     

A convenient strategy of dimerization by microwave heating and using 2,5-diketopiperazine as scaffold

A novel and convenient microwave-assisted dimerization of an active peptide compound using the DKPs as scaffold is described. The key reaction giving rise to the diketopiperazine scaffold is the intermolecular coupling. No epimerization was detected in the reactions used. Conventional and microwave heating of the reactions are compared. Synthesis by microwave irradiation gave the desired compounds in higher yields and in shorter reaction times than those obtained by conventional heating.     

Construction algorithms for polynomial lattice rules for multivariate integration

We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.

We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.

We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.

     

两部美国大学物理教材对我们教学改革的启示

介绍了美国两部大学物理教材的特点，分析了美国教材在教学内容、教学方法、教学手段现代化方面的特色，为我们的教学改革提供一些可供借鉴的经验。     

车前子中多糖含量的测定

采用蒽酮-硫酸法比色测定，用精制车前子多糖测得车前子多糖对葡萄糖的换算因子，对我国同属不同品种的车前子不同采集时间及炮制前后其多糖含量进行了比较研究。结果表明：此测定方法简便可行。供试液在8h内显色稳定，重现性较好，平均回收率为97．8％，RSD=1．41％(n=5)。江西吉安产大粒车前子生品多糖含量在9．15％～9．83％之间，炮制后其多糖含量在6．29％～6.81％之间；南昌新祺周车前GAP标准基地的大粒车前子生品多糖含量为7.85％～8．38％，炮制后其多糖含量为6．01％～6．64％；东北产的小粒车前子生品多糖含量为6．61％，炮制后其多糖含量为6．45％。     

A posteriori error estimates for a time discrete scheme for a phase-field system of Penrose-Fife type

A time discrete scheme is used to approximate the solution toa phase field system of Penrose–Fife type with a non-conservedorder parameter. An a posteriori error estimate is presentedthat allows the estimation of the difference between continuousand semidiscrete solutions by quantities that can be calculatedfrom the approximation and given data.