A new approach to obtain the non-Condon factors in closed form for two one-dimensional harmonic oscillators

A simple algebraic approach to calculate general Franck-Condon overlaps is extended to evaluate non-Condon factors for two one-dimensional harmonic oscillators. The method is based on the use of eigenstates of the harmonic oscillator annihilation operator which allows to obtain in terms of a multi-dimensional Hermite polynomial the overlap of harmonic oscillator functions associated with different Born-Oppenheimer potentials. The presented approach is self-contained, only basic concepts of quantum mechanics associated with the harmonic oscillator system are needed. The obtained expression for the Franck-Condon overlaps is similar to the Ansbacher’s formula and equivalent to the one calculated by Malkin and Man’ko. However our final expression has the advantages that only real numbers are involved and it is straightforward to get the limit case of equal frequencies. Concerning the non-Condon factors two approaches leading to different formulas are considered, both of which reduce to triple sums of products of three Hermite polynomials.     

Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory

Multi-dimensional asymptotically quasi-Toeplitz Markov chains with discrete and continuous time are introduced. Ergodicity and non-ergodicity conditions are proven. Numerically stable algorithm to calculate the stationary distribution is presented. An application of such chains in retrial queueing models with Batch Markovian Arrival Process is briefly illustrated. AMS Subject Classifications Primary 60K25 · 60K20     

Compehensive two-dimensional gas chromatography (GC×GC) and its applicability to the characterization of complex (petrochemical) mixtures

In general, petrochemical products contain only a limited number of chemical classes of compounds (sample dimensionality). The enormous number of individual components within these classes, however, soon puts limitations upon a single chromatographic technique when it comes to adequate characterization of these products. Comprehensive two-dimensional gas chromatography (GC×GC) clearly opens the possibility of estimating the composition of hydrocarbon mixtures in a far more detailed fashion than hitherto possible. Although the emphasis of papers of GCxGC thus far almost exclusively applies to the unsurpassed peak-capacity, in the oil industry there is a need for characterization, rather than for analyzing all the individual compounds. In principle a GCxGC system can provide an almost perfect match between its intrinsic properties and the dimensionality of oil samples. To establish the applicability of GCxGC towards petrochemical analytical challenges, a commercially aavailable prototype instrument was subjected to an exhaustive characterization of a typical hydrocarbon precess stream and a fast characterization of a light gas oil. Although there are no fundamental limitations towards the quantitative aspects of a GCxGC system, this paper confines itself to qualitative results only. Quantitative aspects of GCxGC will be published in a forthcoming paper.     

On reconstruction of objects from measurements of the diffracted field (*)

The aim of this paper is the shape restoration of a plane object from measurements of its diffracted field at a discrete and finite set of points. The plane sampling lattice is supposed: i) rectangular; ii)periodic.

The problem is approached as an interpolation one. A numerical algorithm for practical reconstructions is presented. A-priori limitations on the perimeter of the object and conditions on the samples lead to a-priori bounds able to estimate the precision of the reconstruction.     

超滤、高效液相色谱和毛细管电泳的多维组合用于胎脑垂体组织培养液的分离分析

采用超滤、高效液相色谱和毛细管电泳的多维组合分离分析了胎脑垂体组织培养液的成分，比较了各种工具的不同组合产生的分离效果，考察了获取最多信息量或达到最佳分离的条件，获得了满意结果。     

On the Multi-Dimensional Duality Principle of Sawyer Type

A multi-dimensional version of the duality principle of Sawyer type [1] is obtained whenever the corresponding weight satisfies some doubling property. Received June 27, 2000, Accepted September 14, 2000     

Review of the role and methodology of high resolution approaches in aroma analysis

Analysis of the odour complexity in food and beverage products demands high resolution approaches for distinguishing individual aroma-impact compound(s), and for assessing their contribution to the global aroma of a sample. This paper aims to review current applications incorporating different advanced separation methodologies, and their roles in achieving high resolution aroma analysis. This includes prior low resolution gas chromatography–olfactometry (GC–O) with fractionation procedures using chemical manipulation, adsorption chromatography and ion exchange separation. Innovative multidimensional gas chromatography (MDGC) arrangements that are appropriately designed with olfactometry are of specific focus here. The revelation of resolved components using these integrated approaches provides significantly improved knowledge of aroma composition in samples.     

An optimization approach to adaptive multi-dimensional capital management

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cramér–Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model.     

分位点随机配序抽样

该文针对统计计算中的某些随机模拟问题提出了分位点随机配序抽样法.该方法是由抽样分布的分位点和伪随机序复合构成的,适用于固定区域上多重积分的计算及随机变量的抽样.该文通过几个典型实例说明该方法在具体问题中的应用,并验证了该方法的计算精度.     

"稀溶液的依数性"多维互动教学模式的探索

Colligative properties of dilute solutions are the basic contents for chemistry, chemical engineering and biomedicine majors. The teaching model of multidimensional interact takes teachers as the leader and students as the main body. Through the multi-dimensional interaction among teachers and students, students and groups, students' interest in learning, strong sense of cooperation and independent learning ability can be cultivated. This paper introduces the implementation process of the multi-dimensional interactive teaching mode of "colligative properties of dilute solutions", which includes clarifying the purpose of interaction, constructing learning groups, raising interactive questions, launching interactive activities and implementing interactive evaluation, etc. Multi-dimensional teaching goals can be achieved through group explorations, group presentations and group discussions.