无穷大的比较及应用

利用无穷大的比较,讨论了无穷大的比较在比较函数大小、计算极限、确定方程的根及判断正项级数收敛性上的应用。

Effect of an Arbitrary Dust Size Distribution Dust Particles for Vortex-Like Ion Distribution Dusty Plasma

In order to investigate the effect of an arbitrary dust size distribution for vortex-like ion distributiondusty plasma,we use a reasonable polynomial-expressed function to represent an arbitrary dust size distribution.Thenumerical results of linear dispersion relation,nonlinear solitary wave amplitude,width and velocity for polynomialexpressed dust size distribution dusty plasma with vortex-like ion distribution have been studied.

A robust new metric of phenotypic distance to estimate and compare multiple trait differences among populations

Whereas a rich literature exists for estimating population genetic divergence, metrics of phenotypic trait divergence are lacking, particularly for comparing multiple traits among three or more populations. Here, we review and analyze via simula- tion Hedges＇ g, a widely used parametric estimate of effect size. Our analyses indicate that g is sensitive to a combination of unequal trait variances and unequal sample sizes among populations and to changes in the scale of measurement. We then go on to derive and explain a new, non-parametric distance measure, ＇Aft＇, which is caiculated based upon a joint cumulative distribution function （CDF） from all populations under study. More precisely, distances are measured in terms of the percentiles in this CDF at which each population＇s median lies. Ap combines many desirable features of other distance metrics into a single metric; namely, compared to other metrics, p is relatively insensitive to unequal variances and sample sizes among the populations sam- pied. Furthermore, a key feature of Ap--and our main motivation for developing it--is that it easily accommodates simultaneous comparisons of any number of traits across any number of populations. To exemplify its utility, we employ Ap to address a ques- tion related to the role of sexual selection in speciation： are sexual signals more divergent than ecological traits in closely related taxa？ Using traits of known function in closely related populations, we show that traits predictive of reproductive performance are indeed, more divergent and more sexually dimorphic than traits related to ecological adaptation [Current Zoology 58 （3）： 426-439 2012].

Dynamic bivariate normal copula

Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.

Nonsmooth Semi-Infinite Minmax Programming Involving Generalized(Φ, ρ)-Invexity

This paper introduces some new generalizations of the concept of （~, p）-invexity for non- differentiable locally Lipschitz functions using the tools of Clarke subdifferential. These functions are used to derive the necessary and sufficient optimality conditions for a class of nonsmooth semi-infinite minmax programming problems, where set of restrictions are indexed in a compact set. Utilizing the sufficient optimality conditions, the authors formulate three types of dual models and establish weak and strong duality results. The results of the paper extend and unify naturally some earlier results from the literature.