In this paper, a new structure for image encryption using Recursive cellular automata is presented. The image encryption contains three Recursive cellular automata in three steps, individually. At the first step, the image is blocked and the pixels are substituted by reversible cellular automata. In the next step, pixels are scrambled by the second cellular automata and at the last step, the blocks are attached together and the pixels are substituted by the third cellular automata. Due to reversibility of cellular automata, the decryption of the image is possible by doing the steps reversely. The experimental results show that encrypted image is not understandable visually, also this algorithm has satisfactory performance of quantitative assessment from some other schemes.

In this paper, we aim to encode the set of all positive integers so that the codewords not only be uniquely decodable but also be an instantaneous set of binary sequences. Elias introduces three Recursive algorithms for universal coding of positive integers where each codeword contains binary representation of the integer plus an attachment portion that gives some information about the first part [1]. On the other hand, Fibonacci coding which is based on Fibonacci numbers is also introduced by Apostolico and Fraenkel for coding of integers [2]. In this paper, we propose a new lossless Recursive algorithm for universal coding of positive integers based on both Recursive algorithms and Fibonacci coding scheme without using any knowledge about the source statistics [3]. The coding schemes which don’t use the source statistics is called universal coding, in these universal coding schemes we should use a universal decoding scheme in the receiver side of communication system. All of these encoding and decoding schemes assign binary streams to positive integers and conversely, without any need of use to probability masses over positive integers. We show that if we use Fibonacci coding in the first part of each codeword we can achieve shorter expected codeword length than Elias Omega code. In addition, our proposed algorithm has low complexity of encoding and decoding procedures.

The rate of time preference plays an important role in discounting instantaneous utility in economic growth models and also in calculating social discount rate in cost-benefit analysis. In empirical researchers, this rate is assumed to be constant. However, the rate of time preference might vary over time. This paper develops a new algorithm to estimate this rate as a varied coefficient for the Iranian economy over the period 1965-2010. In our algorithm, we use a Recursive method to estimate the initial values for the rate of time preference as a function of consumption. Given the effect of the rate of time preference on saving, and knowing their initial values, we use a filtering method to estimate these rates as a function of life expectancy. The average value of time preference rate over the period under consideration is 2.38 percent. This rate is found to be higher during the period of economic uncertainties such as Iran-Iraq imposed war. However, the rate is decreasing after the end of war.

In this article, we present a Recursive algorithm to obtain a series of refinements of the classical Young inequality. These inequalities conduce to equalities whenever the number of the iteration in the Recursive algorithm tends to infinity. Also these refinements applied to establish some improved reverse Young and matrix Young inequalities with Hilbert-Schmidt norm.

Digital image has special cryptography algorithms for its specific properties. A mathematics sequence in most image cryptography has been used for image scrambling. The used mathematics sequence has a Recursive equation which it has some coefficients that changes of these coefficients can generate different sequences. Performance of this sequence in image cryptography is evaluated with different standard criteria. Due to complexity of system and no direct relation between the coefficient and evaluation criteria, selection of the suitable coefficient is not easily possible. In this article, by considering a general form of Recursive equation and define a fitness function, the proper coefficients are calculated by genetic algorithm that satisfies the evaluation criteria. The experimental results show that Recursive equation that is computed by the genetic algorithm has satisfactory performance from some schemes.

We propose a novel algorithm called RCA_MC, in which we use the breadth first search method (BFS) in conjunction with edge contraction and connectivity properties of a given undirected graph to enumerate and scan all its minimal edge cutsets. It is known that the problem of enumerating all minimal edge cutsets of a given graph is #P-complete. In addition, we introduce the concepts of pivot vertex and absorbable clusters, and use them to develop our enhanced Recursive contraction for scanning all mimimal edge cutsets, called ERCA_MC, of a given graph. Simulation results provide empirical evidence that the complexity of the ERCA_MC algorithm is linear per cutset.

Redundancy Allocation Problem (RAP) is one of the most important problems in the field of reliability. This problem aims to increase system reliability, under constraints such as cost, weight, etc. In this paper, we work on a system with series-parallel configuration and multi-state components. To draw the problem nearer to real condition, we merge this problem with discount levels in purchasing components. For calculating sub-systems reliability, we used Recursive algorithm. Because RAP belongs to Np. Hard problems, for optimizing the presented model a new Genetic algorithm (GA) was used. The algorithm parameters tuned using Response surface methodology (RSM) and for validation of GA an enumeration method was used.

Our main objective is to study some qualitative behavior of the solutions of the difference equation xn+1 = gxn−k + (axn + bxn−k) / (cxn − dxn−k), n = 0, 1, 2, ..., where the initial conditions x−k,..., x−1, x0 are arbitrary positive real numbers and the coefficients, a, b, c and d are positive constants, while k is a positive integer number.