This article discusses some diculties in the implementation of combinatorial algorithms associated with the choice of all elements with certain properties among the elements of a set with great cardinality.The problem has been resolved by using multidimensional arrays. Illustration of the method is a solution of the problem of obtaining one representative from each equivalence class with respect to the described in the article equivalence relation in the set of all m ∼ n binary matrices. This equivalence relation has an application in the mathematical modeling in the textile industry.

The maximum likelihood method in view of future data (i.e., the maximization of expected loglikelihood) enables estimates of geometric distribution parameter. This estimator is de ned as an estimator in which n (number of data) in the maximum likelihood estimator is replaced with (n + a_{0}); a_{0} takes a value such as -1 or -0:5. The value of a_{0} re ects knowledge about the range where the parameter is to be found. Therefore, when we know that the true parameter of a population lie in a particular range, this method gives a larger expected log-likelihood than the maximum likelihood estimator. Simple simulations show that this new estimator gives anticipated results. The characteristic of the estimator with (n + a_{0}) is similar to that for the mean squared error (MSE), that is, the expectation of the sum of the squared di erence between the true parameter and its estimate. This new methodology in which estimators are modi ed using some constants for yielding better estimators in terms of prediction will contribute to various elds where the number of data is not very large.

The operation of substitution consists of replacing a vertex of a graph by another graph. This new graph is characterized through a function (of substitution) that can be self-definable. The purpose of this work is to construct evolution operators for orbit {w^{k}(G)}, where each element of {w^{k}(G)} is obtained by substituting each vertex of the previous element by a graph. Here, both the initial graph G as the family of graphs of substitution, are known. In this paper, simple and finite graphs will be used, framed in the graphs theory’s area.

This paper study the two unit warm stand by system in which the demand of items increases arbitrarily for some random amount of duration. Whenever demands of items to which the machines are producing is heavy the standby unit also starts operation and when the demand becomes Normal, the standby unit which is in operation comes into standby mode. Failure of the standby unit remains undetected therefore the standby unit is inspected at random intervals of time. The failure can also be detected at the time of need of standby unit to become operative. If the standby unit is found to be failed in the inspection then it is sent for repair immediately. Failure time distribution for both operative and standby units are assumed to be negative exponential. Regenerative point techniques with markov renewal process is used to obtain various reliability characteristics of system. Repair time distribution of units failed during operation and standby position are same and assumed to be general.

Feedback Shift Register (FSR) is generally the basic element of pseudo random generators used to generate cryptographic channel or set of sequences for encryption keys. This type of generator is widely used in stream cipher and communication systems such as C.D.M.A (Code Division Multiple Access), mobile communication systems, ranging and navigating systems, spread spectrum communication systems.

The objective of the present paper is to propose a method for determining linear recurring sequences generating linear feedback shift register (LFSR) from primitive polynomials (and vice-versa). The linear recurring sequences facilitate the construction of maximum length LFSR. It also insists, in the last part, on the cryptographic security of LFSR and indicates some open problems in the area of nonlinear feedback shift registers (NLFSR) based pseudo random generators.

In the present paper we establish a coupled xed point result in partially ordered fuzzy metric spaces by utilizing the control function. We obtain our results for Hadžić type t-norm. We also establish two lemmas and deduce a corollary. By an application of the xed point theorem in fuzzy metric spaces, a corresponding result is obtained in metric spaces. Our work extends some existing results [1, 2, 3].

Krylov subspace methods have been considered to solve singular linear systems Ax = b. One of these methods is the DGMRES method. DGMRES is an algorithm to solve the Drazin{ inverse solution of the large scale and sparse consistent or inconsistent singular linear systems with with arbitrary index. In this paper, we present an improved version of this algorithm. Numerical experiments show that computation time is signi cantly less than that of computation time obtained by the DGMRES algorithm.