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We know from Zeckendorf's theorem that every positive integer n has unique representation of the form n = Σk=1 l akF(k), where ak ∊ {0, 1} and F(k) is a Fibonacci number such that the string a1a2a3. . . does not contain any consecutive 1's. In this paper we consider second order variant Fibonacci universal code from Gopala-Hemachandra sequence. Thereby, we describe the uses of this code in cryptography with an illustrative example. [ABSTRACT FROM AUTHOR]

The article presents information on a research paper on discrete mathematics which concludes that two fold systems hold good for all natural numbers. The authors construct a pairwise balanced design (PBD) for the order 6n+4 and two fold exit systems for the order 3n+2. It makes use of Steiner Triple System (STS), a type of block design in combinatorial mathematics, already existing for the order 6n+1 and 6n+3 and PBD for the order 6n+5.

In this paper we consider a problem of determining the optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand. Shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment. Any inventory system is periodic and repetitive in nature. We think that the periodicity of an inventory system is best taken care by a sinusoidal curve. Several inventory models have been developed so far to suit the real-time inventory systems. Sinusoidal inventory system in one such real-time model. The traditional EOQ ignores the time value of money .In this regard the present worth (PW) approach is used to justify EOQ w.r.t. the time value of money. Hence the sinusoidal inventory model is analyzed based on the present worth approach to determine the optimum period length and the economic order quantity. The necessary and sufficient conditions of the existence of the optimal solution are shown. The model is illustrated with a numerical example and sensitivity analysis has been performed. [ABSTRACT FROM AUTHOR]