Chain spaces via Clifford algebras

In this note we show that the chain space belonging to a quadric can be embedded into the chain geometry over a Clifford algebra via a generalized stereographic projection.     

Studies on basicity of alkali metal catron exchanged β and X zeolites by pyrrole-IR spectroscopy

The strength of basic sites has been measured by pyrrole-IR on alkali metal cation exchanged β and X zeolites, as well as NaOH loaded Naβ. The influence of cation type and the structure of zeolites on their basicity has been studied. The acidic and basic properties of the samples were investigated by NH3-TPD and isopropanol reaction. It was shown that the strength of basic sites on samples could be characterized by the shift of vNH band in the pyrrole-IR spectra. The framework oxygen charges were calculated from the Sanderson electronegativity. The changes in basic properties with various alkali metal cation are consistent with the changes of local oxygen charges of the zeolite framework.     

An investigation of the Al2O3-CdSe interface in accumulation

The Al₂O₃−CdSe interface of a thin-film transistor is investigated in the frequency range 30 Hz-30 kHz under weak depletion and accumulation. The surface states are, most likely, located in the insulator Al₂O₃ with a concentration varying from 4·10¹⁸ to 10¹⁹ cm⁻³ eV⁻¹. The surface states have a negligible influence on the thin-film transistor operation.     

An algebraic characterization ofB-convergent Runge-Kutta methods

Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung     

Point approximation of a space-homogeneous transport equation

Summary We present an approximation method of a space-homogeneous transport equation which we prove is convergent. The method is very promising for numerical computation. Comparison of a numerical computation with an exact solution is given for the Master equation.     

Optimal tristance anticodes in certain graphs

For z₁,z₂,z₃∈Zⁿ, the tristance d₃(z₁,z₂,z₃) is a generalization of the L₁-distance on Zⁿ to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticodeA_d of diameter d is a subset of Zⁿ with the property that d₃(z₁,z₂,z₃)?d for all z₁,z₂,z₃∈A_d. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determine the cardinality and completely classify the optimal tristance anticodes in Z² for all diameters d?1. We then generalize this result to two related distance models: a different distance structure on Z² where d(z₁,z₂)=1 if z₁,z₂ are adjacent either horizontally, vertically, or diagonally, and the distance structure obtained when Z² is replaced by the hexagonal lattice A₂. We also investigate optimal tristance anticodes in Z³ and optimal quadristance anticodes in Z², and provide bounds on their cardinality. We conclude with a brief discussion of the applications of our results to multi-dimensional interleaving schemes and to connectivity loci in the game of Go.     

镧系金属一氢化物有效芯势研究

采用Cundari和Stevens等推导的有效芯势对镧系金属一氢化物进行了理论计算，以探讨镧系金属元素与氢的相互作用。结果表明所有镧系金属一氢化物基态时理论上是稳定的，最稳定的是SmH,最不稳定的是DyH;键长计算结果显示，基态时镧系金属一招兵买马花物有独立王国 收缩现象发生；红外振动频率理论计算值与实验结果一致；成键轨道中，金属原子轨道的贡献主要是s轨道和d轨道：从CeH至ErH(GdH)例外）随着外层电子的增加s轨道成分逐渐增大d轨道成分逐渐减小；从TmH和LuH（包括GdH)，成键轨道中金属原子轨道的贡献主要是d轨道，约为90％；约大多数镧系金属一氧化物的成键轨道中金属原子轨道f成分小于1％。     

理论研究C8H80-（H2O）n（n=1～5）团簇

应用密度泛函B3LYP／6—31＋G（d，p）方法对C8H80-（H2O）n（n=1～5）团簇这种弱相互作用体系进行垒自由度能量梯度优化，得到该系列团簇的稳定蛄构．计算结果表明。在该系列二元团簇中，一方面水分子数目的多少对苯基丙酮分子的结构影响很小，另一方面由于苯基丙酮分子的存在，破坏了团簇中水分子的对称性结构，在团簇内部极力形成O—H—O这样弯曲的有方向性的氢键．对苯基丙酮-水这样结构复杂的团簇，指认光谱的难度非常大，本文只讨论了与C=O有关的振动峰和水分子的对称伸缩振动的最强峰．     

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions. The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged.