Phytotesting as a Method of Determining the Degree of Eutrophication of Water Objects

We propose to evaluate the level of eutrophication of surface water in the middle reaches of the river Belaya in the vicinity of the town of Sterlitamak using "eutrophication factor", as the main indicator used by the average length of seedling cress in undiluted samples. We selected a few water samples in eight gauges above, below and within the city. We consider the seasonal dynamics of the level of eutrophication of the variability in different years (2011-2016). Statistical analysis of the data revealed positive and negative dependence. Studies show high nutrient content in this water body. Thus, our proposed method can be used to determine the level of eutrophication of different water bodies.

Single-machine stochastic scheduling with dependent processing times

A single machine is available to process a collection of stochastic jobs preemptively. Rewards are received at job completions. We seek policies for machine allocation which maximize the total reward. Application areas point to the need to study such models for resource allocation when job processing requirements are dependent. To this end, models are developed in which the nature of such dependence is derived from various notions of positive and negative dependence in common usage in reliability. Optimal policies for resource allocation of simple structure are obtained for a variety of such models.

Single-machine stochastic scheduling with dependent processing times

A single machine is available to process a collection of stochastic jobs preemptively. Rewards are received at job completions. We seek policies for machine allocation which maximize the total reward. Application areas point to the need to study such models for resource allocation when job processing requirements are dependent. To this end, models are developed in which the nature of such dependence is derived from various notions of positive and negative dependence in common usage in reliability. Optimal policies for resource allocation of simple structure are obtained for a variety of such models.

On the dependence structure of hitting times of multivariate processes

A direct approach to derive dependence properties among the hitting times of bivariate processes has been initiated by Ebrahimi (1987) and explored further by Ebrahimi and Ramallingam (1988). In this paper, new results are obtained for multivariate processes, which help us to identify positive and negative dependence structures among the hitting times of the processes. Applications of our theorems to reliability of systems are given.

On the dependence structure of hitting times of multivariate processes

A direct approach to derive dependence properties among the hitting times of bivariate processes has been initiated by Ebrahimi (1987) and explored further by Ebrahimi and Ramallingam (1988). In this paper, new results are obtained for multivariate processes, which help us to identify positive and negative dependence structures among the hitting times of the processes. Applications of our theorems to reliability of systems are given.

Bivariate processes with positive or negative dependent structures

In this paper various notions of positive and negative dependence for bivariate stochastic processes are introduced and their interrelationship is studied. Examples are given to illustrate these concepts.