Stability of anisotropic self-gravitating fluids

The aim of this paper is to study the stability as well as the existence of self-gravitating anisotropic fluids in [Formula: see text]-dominated era. Taking a cylindrically symmetric and static spacetime, we computed the corresponding equations of motion in the background of anisotropic fluid distributions. The realistic formulation of energy momentum tensor as well as theoretical model of the scale factors are considered in order to describe some physical properties of the anisotropic fluids. To find the stability of the compact star, we have used Herrera’s technique which is based on finding the radial and the transverse components of the speed of sound. Moreover, the behaviors of other physical quantities are also discussed like anisotropy, matching conditions of interior metric and exterior metric and compactness of the compact structures are also discussed.

A comment on Xie and Xu: ‘Mapping quantitative trait loci in tetraploid species’

Xie & Xu (2000) present a model for mapping quantitative trait loci in an autotetraploid population. However, one aspect of their model, namely gamete formation, does not properly represent the biological process in autotetraploid species. This paper gives a more realistic formulation for this part of the model, and discusses the consequences for multipoint mapping.

Optimal Clustering

Cluster analysis can be performed with several models. One method is to seek those clusters for which the total flow between all within-cluster members is a maximum. This model has, until now, been viewed as mathematically difficult because of the presence of products of integer variables in the objective function. In another optimization model of cluster analysis, the p-median, a central member is found for each cluster, so that relationships of cluster members with the various central members are maximized (or minimized). This problem, although mathematically tractable, is a less realistic formulation of the general clustering problem. The formulation of the maximum interflow problem is here transformed in stages into a linear analogue which is economically solvable. Computation experience with the several transformed stages is reported and a practical example of the analysis demonstrated.

Generalizing the secretary problem

The secretary problem refers to a certain class of optimal stopping problems based on relative ranks. To allow a more realistic formulation of the problem, this paper considers an arbitrary loss function. A finite and an infinite problem are defined and the optimal solutions are obtained. The solution for the infinite problem is given by a differential equation while the finite problem is given by a difference equation. Under general conditions, the finite problem tends to the infinite problem. An example involving the secretary problem with interview cost is considered and illustrates the usefulness of the present paper.