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    International Transactions in Mathematical Sciences and Computer (ITMSC)




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    1 Cost-Benefit Analysis of A Two Unit Standby System With Preventive Maintenance of Priority Unit

    Author: Pradeep Chaudhary* and Lavi Tyagi,(Pages: 1-19)
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    Abstract:

    The paper deals with a system model comprises of two non-identical units (unit-1 and unit-2). Unit-1 gets priority in operation as well as in repair over the unit-2 and is known as priority unit. The priority unit goes for preventive maintenance (P.M.) after working for a random period of time and after getting preventive maintenance, it again becomes operative. During the preventive maintenance of priority unit the other unit starts operation. A single repairman is always available with the system to repair a failed unit and P.M. of unit-1. The priority is also given to the P.M. of unit-1 over the repair of unit-2. The failure time distributions of both the units and time to P.M. of unit-1 are taken to be exponential with different parameters whereas the repair time distributions of both the unit and P.M. time of unit-1are taken as general with different c.d.fs. Each repaired unit always works as good as new.

    Keyword:

    Transition probability, regenerative point, reliability, MTSF, preventive maintenance, availability

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    3 ON THE NAGELL TYPE DIOPHANTINE EQUATION p^n= x^2+N

    Author: Surya Prakash Gautam, Hari Kishan, Satish Kumar,(Pages: 21-25)
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    Abstract:

    In this paper, the Diophantine equation p^n= x^2+N has been discussed, where n, N, x are positive integers and p is an odd prime. This Diophantine equation has some solutions if N=N_1×N_2 (N_1>N_2 )and 〖(N〗_1+N_2),〖(N〗_1-N_2) both are divisible by 2 and (〖(N〗_1+N_2))/2 of the form p^z, where z is any natural number.

    Keyword:

    Diophantine equation, Exponent Diophantine equation, Factor method

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