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Abstract: We consider the problem of controlling the model of one-dimensional fluid flow through a soil packed tube in which a contaminant is initially distributed. A fluid is pumped through a tube to remove the contaminant. The control problem is to determine the optimal convective velocity due to the fluid being pumped by minimizing a given performance criterion. The performance criterion is chosen to be a combination of the total contaminant at the final time and the cost of the control. The set of orthogonal Fourier trigonometry series is used as a basis function of the Galerkin procedure to lump the distributed parameter system. A Legendre wavelet operational matrix of derivative is used to approximate the control and modal state variables. The main characteristics of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The effectiveness of the proposed approach is illustrated numerically and the results are quite satisfactory. [Copyright &y& Elsevier]

Abstract: In this paper, we study quasi-cyclic codes over the ring where . By exploring their structure, we determine the type of one generator quasi-cyclic codes over R and the size by giving a minimal spanning set. We also determine the rank and introduce a lower bound for the minimum distance of free quasi-cyclic codes over . We include some examples of quasi-cyclic codes of various lengths over . In particular, we obtain a family of 2-quasi-cyclic codes from cyclic codes over the ring . Finally, using the Gray map we obtain a family of optimal binary linear codes as the images of quasi-cyclic codes over R. [Copyright &y& Elsevier]

Abstract: We study the structure of cyclic DNA codes over the ring . We employ the deletion similarity distance on the set of codewords. A set of generators for this type of codes is found. We also study the -content of these type of codes and their deletion distance. Examples of cyclic DNA codes are constructed with their -content and their corresponding deletion distance. [Copyright &y& Elsevier]

Abstract: We study the structure of -constacyclic codes of an arbitrary length over the ring . We find a set of generators for each -constacyclic code and its dual. We study the rank of cyclic codes and find their minimal spanning sets. We prove that the Gray image of a -constacyclic code is a binary cyclic code of length . We conclude by giving examples of constacyclic codes and their Gray image binary codes. We give a direct construction of a [12,7,4] linear binary cyclic code that match the Hamming distance of the best binary code with length 12 and dimension 7. [Copyright &y& Elsevier]

Abstract: In this paper, we develop the theory for constructing linear and additive cyclic codes of odd length over that are suitable for DNA computing. We call this class of codes reversible complement cyclic codes. We use this theory to study all such codes of lengths , , 11 and . We list the codes that have the largest number of codewords for a given minimum Hamming distance. We show that some of these codes have more codewords than previously known codes with the same minimum Hamming distance. [Copyright &y& Elsevier]