ON PROPERITIES OF A SERIAL SERVICE SYSTEM OF TWO SERVICE COUNTERS WITH FINITE WAITING SPACE

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Additivity of statistical moments in the exponentially modified Gaussian model of chromatography

A homologous series of saturated fatty acids ranging from C₁₀ to C₂₂ was separated by reversed-phase capillary liquid chromatography. The resultant zone profiles were found to be fit best by an exponentially modified Gaussian (EMG) function. To compare the EMG function and statistical moments for the analysis of the experimental zone profiles, a series of simulated profiles was generated by using fixed values for retention time and different values for the symmetrical (σ) and asymmetrical (τ) contributions to the variance. The simulated profiles were modified with respect to the integration limits, the number of points, and the signal-to-noise ratio. After modification, each profile was analyzed by using statistical moments and an iteratively fit EMG equation. These data indicate that the statistical moment method is much more susceptible to error when the degree of asymmetry is large, when the integration limits are inappropriately chosen, when the number of points is small, and when the signal-to-noise ratio is small. The experimental zone profiles were then analyzed by using the statistical moment and EMG methods. Although care was taken to minimize the sources of error discussed above, significant differences were found between the two methods. The differences in the second moment suggest that the symmetrical and asymmetrical contributions to broadening in the experimental zone profiles are not independent. As a consequence, the second moment is not equal to the sum of σ² and τ², as is commonly assumed. This observation has important implications for the elucidation of thermodynamic and kinetic information from chromatographic zone profiles.     

Matrix order indices in statistical mechanics

A new notion of matrix order indices which relates the matrix norm and its trace is introduced. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well as nonequilibrium, for which the indices present a quantitative measure of the level of ordering. They characterize not only the long-range order, but also mid-range order. In the latter case, when order parameters do not exist, the matrix indices are well defined, providing an explicit classification of various mid-range orders. The matrix order indices are suitable for describing phase transitions with both off-diagonal and diagonal orders. Contrary to order parameters whose correct definition requires the thermodynamic limit, the matrix indices do not necessarily need the latter. Because of this, such indices can distinguish between different phases of finite systems, thus, allowing for the classification of crossover phase transitions.     

The partition function of an interacting many body system

Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuations and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. Received 28 March 2002 Published online 17 September 2002     

Aspects of nucleation and drift processes in a one-dimensional model

We introduce a one-dimensional model involving the nucleation and the drift of many particles. The model originates from interacting kink systems and simulates time evolution in modulated systems. In this model the nucleation rate of a particle depends nonlocally on the density of preexisting particles and the drift of particles is due to a weak and repulsive interaction among them. We first study the statistics of this model in the case that the drift of particles is negligible, and then consider the effects of the drift of particles.     

The analysis of menstrual bleeding patterns: A review

Patterns of vaginal bleeding are an important factor in the acceptability of contraceptive methods. The analysis of data obtained from daily menstrual diary records is a major methodological problem to which no satisfactory solution exists. This review describes approaches to the analysis of bleeding patterns among contracepting and non-contracepting women and reviews the difficulties involved. The reference period method, introduced to avoid the arbitrary rules and definitions required for an analysis based on the concept of a menstrual cycle, is discussed and its limitations presented. The review draws on reports of meetings convened by the World Health Organization and the University of Exeter Family Planning Unit to discuss issues in the analysis. Previously unpublished methods are summarized and areas of controversy and topics for further research are identified.     

Overlap graph representation of B6 and B7

The virial coefficients B_n of the pressure of a thermodynamic system can be represented in terms of graphs. The recently defined overlap graphs are studied in detail. Furthermore, the overlap graph representation of the sixth and seventh virial coefficientsB ₆ andB ₇) is determined.     

介观物理系统的统计物理和持续电流

本文讨论介观系统的统计物理一些基本概念，在一般教科书和文献教很少有解释到的。我们讨论自平均效应，它在介观与宏观系统之不同，对杂质作系统平均后热力学量在介观与宏观系之不同。我们较详细引介用格林函数和图解法计算介观持续电流。同样，我们强调宏观系统和介观系统不同之处，对介观物理系统从计算热力学量的角度来看需要特别考虑因素。     

Vaginal bleeding patterns — the problem and an example data set

Data concerning the vaginal bleeding patterns of women using different forms of fertility regulation are presented. The data were collected in the form of diaries which were completed by the women themselves by recording the presence or absence of vaginal bleeding on a daily basis. The object of the paper is to invite suggestions for suitable methods of presentation and analysis of such data so that the results of studies on methods of fertility regulation can be better summarized and interpreted.     

Common Intersection Points of Bulk Modulus for Liquefied Natural Gas (LNG) Mixtures

During recent developments on the theories and experimental techniques of compressed liquids and liquid mixtures, it has been revealed that there exist some regularities. Among these, the regularity found by Huang and O'Connell is that the isotherms of reduced bulk modulus of compressed liquids as a function of molar volume intersect at a common point. This intersection is a useful tool for evaluating the reliability of an equation of state (EOS) for producing equilibrium properties of matter. This paper also deals with an extension of the above regularity to some liquefied natural gas (LNG) mixtures including: N₂+CH₄, N₂+C₂H₆, CH₄+C₂H₆, CH₄+C₃H₈, and CH₄+C₄H₁₀ at different temperatures. The present work gives a theoretical analysis for the common bulk modulus point in terms of a statistical‐mechanical equation of state for mixtures. In addition, we have calculated excess molar volume of N₂+CH₄ mixture in terms of temperature and compared it with experimental values.