Behavior settings and eco-behavioral science: a new arena for mathematical social science permitting a richer and more coherent view of human activities in social systems,part II: Relationships to established disciplines,and needs for mathematical development

Part I of this paper presented the basic concepts of behavior settings and eco-behavioral science originated by the psychologist Roger Barker, showed how they could be linked with standard economic data systems, and suggested their use as a basis for time-allocation matrices and social system accounts. Part II discusses the relationships of behavior settings and eco-behavioral science to established disciplines, describes applications of mathematics to the new concepts by Fox and associates, and points out some major areas in need of mathematical and theoretical development. These areas include representation and measurement of patterns of relationships among roles within behavior settings, relationships among behavior settings within communities and organizations, and the evolution of large, heterogeneous populations of behavior settings over time. We hope some readers will be motivated to participate in this new scientific enterprise.     

Propagation of partially coherent Gaussian laser beams in graded-index fibres

Using statistical approach the author has solved the equations for the mutual coherence function of partially coherent Gaussian laser beams in graded-index fibres. The expressions for the complex degree of coherence and the intensity distribution have also been shown that the self-focusing length inside the fibre depends upon the degree of coherence. The result have been discussed for both conical and cylindrical guides.     

Morphology of Composite Nanoparticles of Immiscible Binary Systems Prepared by Gas-evaporation Technique and Subsequent Vapor Condensation

X–Y composite nanoparticles of four immiscible binary systems (Si–In, Ge–In, Al–In and Al–Pb) were prepared by the condensation of Y vapor onto X nanoparticles produced in advance by a gas-evaporation technique. The nanoparticles, which were observed by electron microscopy, were composed of two or more crystallites of the elements with different morphology. Their growth process is discussed with reference to the phase diagrams.     

A dynamic programming algorithm for dynamic lot size models with piecewise linear costs

We propose a new algorithm for dynamic lot size models (LSM) in which production and inventory cost functions are only assumed to be piecewise linear. In particular, there are no assumptions of convexity, concavity or monotonicity. Arbitrary capacities on both production and inventory may occur, and backlogging is allowed. Thus the algorithm addresses most variants of the LSM appearing in the literature. Computational experience shows it to be very effective on NP-hard versions of the problem. For example, 48 period capacitated problems with production costs defined by eight linear segments are solvable in less than 2.5 minutes of Vax 8600 cpu time.     

Optimal estimation in random coefficient regression models

In linear regression models with random coefficients, the score function usually involves unknown nuisance parameters in the form of weights. Conditioning with respect to the sufficient statistics for the nuisance parameter, when the parameter of interest is held fixed, eliminates the nuisance parameters and is expected to give reasonably good estimating functions. The present paper adopts this approach to the problem of estimation of average slope in random coefficient regression models. Four sampling situations are discussed. Some asymptotic results are also obtained for a model where neither the regressors nor the random regression coefficients replicate. Simulation studies for normal as well as non-normal models show that the performance of the suggested estimating functions is quite satisfactory.     

Elastic model for simulating ultrasonic inspection of smooth and rough defects

A model is presented for the scattering of ultrasonic waves from smooth and randomly rough defects. The model uses Kirchhoff theory and is elastic, such that mode-conversion between compressional and shear waves is included in the formulation. The model is designed to simulate ultrasonic non-destructive testing situations, by specifying the location and orientation of a defect within an isotropic material, together with transmitter and receiver locations on an inspection surface. Results are presented for the scattering of both monochromatic waves and of pulses. It is shown how small levels of roughness can affect echodynamic curves and how diffracted signals may become lost due to scatter from the rough faces of defects. It is also shown that the usual rules for coupling between waves of all three modes no longer hold when roughness is present. In particular, roughness leads to coupling between horizontally polarized shear (SH) waves and the other two wave modes. The model predictions are also compared with an earlier acoustic model, indicating the importance of mode-conversion effects when considering rough defects embedded within solids.     

井下水力活塞泵故障诊断的数学基础

依据水力活塞泵的工作原理，的故障诊断技术的数学模型，对其解的适定性作了完整的讨论，并且得到了该模型的级数型解。     

POPULATION AND HARVESTING THEORY FOR NONLINEAR SEX AND AGE-STRUCTURED RESOURCES

A sex-age-structured population model with density dependence in the conversion of reproductive potentials into zygotes and in first year survivorship is described. The model has two equilibria; the smallest is mathematically unstable, and the origin and the larger equilibrium are locally stable. The population can thus go extinct for certain initial states, or if the two equilibria coincide. The ratio between the two equilibria can be regarded as a measure of the risk of extinction, since it is related to the chance that detrimental environmental conditions will cause the population to enter the region of attraction of the origin. In simple monoecious models, recovery to former levels is only possible provided that the population is not driven to extinction before harvesting effort is reduced. Ratios between the two unexploited equilibria, and between the stable unexploited equilibrium and the recruitment level at which the two equilibria coincide are given solely in terms of the degree of density dependence in the model. I show that the harvesting strategy which maximizes the equilibrium yield has a four age form, involving harvesting of at most two male and two female age classes. Out of ten commercial Pacific groundfish species, knife-edge selectivity sustainable yields of eight are at least 90% of ultimate sustainable yield (USY). With no effort restrictions, the range of lengths at first capture which achieve more than 60% of USY is narrow. When one of the sexes is not harvested, sustainable yield is between 20% and 80% of USY, but lowest when females are not harvested.