Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...

In this paper a two-state Markovian maintenance process where the true state is unknown will be considered. The operating cost per period is a continuous random variable which depends on the state of the process. If investigation cost is incurred at the beginning of any period, the system wit I be returned to the "in-control" state instantaneously. This problem is solved using the average crite...

This paper investigates the powerplay in one-day cricket. The rules concerning the powerplay have been tinkered with over the years, and therefore the primary motivation of the paper is the assessment of the impact of the powerplay with respect to scoring. The form of the analysis takes a “what if” approach where powerplay outcomes are substituted with what might have happened had there been no...

In this work the authors develop a mathematical model for the dynamics of a major helminth parasite of man, schistosomiasis. The model is a system of coupled non-linear equations. Numerical experimentations with the model reveal the remarkable stability of the dynamics of schistosomiasis. The steady state is invariably reached within 10-15 years of the start of the infection. A numerical soluti...

In this paper, we studied and formulated the relapsed SIR model of a constant size population with standard incidence rate. Also, the optimal control problem with treatment and vaccination as controls, subject to the model is formulated. The analysis carried out on the model, clearly showed that the infection free steady state is globally asymptotically stable if the bas...

among state`s duties are constructing roads, water pipelines and the likes. in order to do these the state sometimes has to utilize private owners` lands. this research, we seek to investigate this questions that is there any possibility of liability for usurpation for state if these formalities are not be observed? some researchers have questioned the possibility of this liability. in this res...

using analytical method of usul al-fiqh, the present essay deals with opinions of shiite usulis on this question whether continuity of the previous state can be used with regard to time, temporal affairs, and affairs conditioned upon time. as for the first, we investigate opinions of usulis in this connection first, answer the problem of lack of doubt as to subsistence and that of lack of unity...