Determining the complete molecular composition of petroleum and its refined products is not feasible with current analytical techniques because of the astronomical number of molecular components. Modeling the composition and behavior of such complex mixtures in refinery processes has accordingly evolved along a simplifying concept called lumping. Lumping reduces the complexity of the problem to...

In this survey, we provide the most important computational methods to find the PageRank. This is a new comprehensive review of all major issues which are associated with PageRank problem, covering the basic topics, the iterative methods, lumping of nodes, the modification of lumping the nodes, rank-one perturbation, rank-r perturbation, advanced numerical linear algebra methods, conditioning, ...

Unlike synchronic linguists, who can ask their consultants for additional data and examples, historical linguists are, for the most part, stuck with the data we have. Only rarely are we able to add to the corpus of available texts, or find additional examples of a rare combination of phonemes. The problems of historical linguistics are thus inherently probabilistic: we must constantly decide wh...

Simulation accuracy of a methodology for composable modeling of microelectromechanical systems (MEMS) is assessed by comparing against analytic equations and finite element simulations. Several MEMS canonical problems are composed hierarchically as networks of simple elements with models written in an analog hardware description language. Schematics built from this model library, called NODAS (...

First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreduci...

a nonstandard finite difference (nsfd) scheme has been constructed and analyzed for a mathematical model that describes lotka–volterra food web model. this new discrete system has the same stability properties as the continuous model and,on the whole, it preservesthe same local asymptotic stability properties. linearized stability theory and schur–cohn criteria are used for local asymptoticstab...

Conservation agencies need information to guide planning activities and allocation of limited mitigation resources at regional scales. Utilization hydrological modeling tools sub-watershed scales can adequately represent existing conditions, but on a few discrete uncoordinated efforts cannot be scaled up the entire region. Conversely, large scale studies suffer from overgeneralization caused by...