Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Exact colorations of graphs and digraphs

A coloration is an exact regular coloration if whenever two vertices are colored the same they have identically colored neighborhoods. For example, if one of the two vertices that are colored the same is connected to three yellow vertices, two white and red, then the other vertex is as well. Exact regular colorations have been discussed informally in the social network literature. However they have been part of the mathematical literature for some time, though in a different format. We explore this concept in terms of social networks and illustrate some important results taken from the mathematical literature. In addition we show how the concept can be extended to ecological and perfect colorations, and discuss how the CATREGE algorithm can be extended to find the maximal exact regular coloration of a graph.

Development and release mechanism of diltiazem HCl prolonged release matrix tablets

A coated matrix tablet formulation has been used to develop controlled release diltiazem HCl (DIL) tablets. The developed drug delivery system provided prolonged drug release rates over a defined period of time. DIL tablets prepared using dry mixing and direct compression and the core consisted of hydrophilic and hydrophobic polymers such as hydroxypropylmethylcellulose (HPMC), Eudragits RLPO/RSPO, microcrystalline cellulose, and lactose. Tablets were coated with Eudragit NE 30D, and the influence of varying the inert hydrophobic polymers and the amount of the coating polymer were investigated. The release profile of the developed formulation was described by the Higuchi model. Stability trials up to 6 months displayed excellent reproducibility.