On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

限进介质固相萃取及其应用

系统地介绍了限进介质固相萃取的原理、特点、发展现状及其发展趋势,并对该技术在生物和环境样品前处理中的应用作了较详细的综述。引用文献58篇。     

Infrared and Raman spectra, conformational stability, ab initio calculations, and vibrational assignments for methylaminothiophosphoryl difluoride

Infrared spectra (4000–50 cm⁻¹) of the vapor, amorphous and crystalline solids and Raman spectra (3600–10 cm⁻¹) of the liquid with qualitative depolarization data as well as the amorphous and crystalline solids of methylaminothiophosphoryl difluoride, CH₃N(H)P(=S)F₂, and three deuterated species, CD₃N(H)P(=S)F₂, CH₃N(D)P(=S)F₂, and CD₃N(D)P(=S)F₂, have been recorded. The spectra indicate that in the vapor, liquid and amorphous solid a small amount of a second conformer is present, whereas only one conformer remains in the low temperature crystalline phase. The near-infrared spectra of the vapor confirms the existence of two conformers in the gas phase. Asymmetric top contour simulation of the vapor shows that the trans conformer is the predominant vapor phase conformer. From a temperature study of the Raman spectrum of the liquid the enthalpy difference between the trans and near-cis conformers was determined to be 368±15 cm⁻¹ (4.41±0.2 kJ/mol), with the trans conformer being thermodynamically preferred. Ab Initio calculations with structure optimization using the 6-31G(d) and 6-311+G(d,p) basis sets at the restricted Hartree–Fock (RHF) and/or with full electron correlation by the perturbation method to second order (MP2) support the occurrence of near-trans (5° from trans) and near-cis (20° from cis) conformers. From the RHF/6-31G(d) calculation the near-trans conformer is predicted to be the more stable form by 451 cm⁻¹ (5.35 kJ/mol) and from the MP2/6-311+G(d,p) calculation by 387 cm⁻¹ (4.63 kJ/mol). All of the normal modes of the near-trans rotamer have been assigned based on infrared band contours, depolarization values and group frequencies and the assignment is supported by the normal coordinate calculation utilizing harmonic force constants from the MP2/6-31G(d) ab initio calculations.     

Finding transition states using reduced potential-energy surfaces

 We propose a method to locate saddle points that is based on the interplay between the driving coordinate and the restricted quasi-Newton algorithm. The method locates the transition state using a reduced potential-energy surface. The reduced potential-energy surface is characterized by the set of driving coordinates. The proposed algorithm starts at a point on the surface that is slightly perturbed from either reactant or product and, in principle, converges to the transition state. Finally we give a special type of update Hessian matrix formula that should be applied in optimizations carried out on reduced potential-energy surfaces. Received: 29 September 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

一般线性李超代数及其超群的无穷小子群的表示

在索特征代数闭域上考虑一般线性李超代数gl(m |n)的限制表示与超群GL(m | n)的有理表示以及它们的关系.主要结果为: (1)对gl(m | n)的不可约限制表示进行分类,其中某些单模恰是Kac-模.类似于复数域情形,给出了Kac-模不可约的充要条件; (2)当m≠n(mod p)以及p≥2h-2(h=max{m,n})时,gl(m | n)的限制投射模可以被提升为有理GL(m | n)-模,并且证明了不可约表示的投射覆盖具有Z-滤过,即滤过中的每个子商同构于"baby Vlerma模";(3)得到了一般线性超群G=GL(m | n)的r阶nobenius核的反转公式,它反映了单Gγ-模的投射覆盖的Z-滤过重数与广义baby Verma模的合成因子效之间的关系.     

Analyticity of the sine family with L p -maximal regularity for second order Cauchy problems

If the second order problem u（t） ＋ Bu（t） ＋ Au（t） = f（t）, u（0） =u（0） = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ（λ^2 ＋ λB ＋ A）^-1‖ and ‖B（λ^2 ＋ λB ＋ A）^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0.     

A stochastic system with MMPP input and an access function

In classical studies of loss systems with restricted availability, the utilization was suggested of a probabilistic loss function, defining the conditional probability of an incoming call being rejected, as a function of the number of occupations in the destination group of servers. This paper gives an exact analysis of stochastic processes of practical relevance, associated with a system with MMPP (Markov Modulated Poisson Process) input, finite queueing capacity and a general loss function, assuming exponential service times. In addition to the process defining the state of the system at any instant, the analysis of the overflow point process (associated with the rejected arriving customers), the accepted point process (associated with the accepted arriving customers), and of the departure process will be presented. Together with the exact analysis of this system, based on the matrix analytical methodology of Neuts, (1981), we will derive expressions for calculating some key-parameters of pertinent associated processes, which may also be used for their approximate modelling. Also, examples of applications and of blocking probability calculations in specific models of this class will be presented.     

On the Ulam stability of mixed type mappings on restricted domains

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982-1998 we established the Hyers-Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1983 F. Skof was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 S.M. Jung investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by S.M. Jung, in 1998. Besides we establish the Ulam stability of mixed type mappings on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.     

Frobenius problem for semigroups \mathsf{S}(d_{1},d_{2},d_{3})

We find the matrix representation of the set Δ(d ³), where d ³=(d ₁,d ₂,d ₃), of integers that are unrepresentable by d ₁,d ₂,d ₃ and develop a diagrammatic procedure for calculating the generating function Φ(d ³;z) for the set Δ(d ³). We find the Frobenius number F(d ³), the genus G(d ³), and the Hilbert series H(d ³;z) of a graded subring for nonsymmetric and symmetric semigroups and enhance the lower bounds of F(d ³) for symmetric and nonsymmetric semigroups.