Ines Ben Chobba, Ahmed Bekir, Riadh Ben Mansour, Noureddine Drira, Néji Gharsallah and Adel Kadri Laboratoire de Biotechnologies Végétales Appliquées à l’Amélioration des Cultures, Faculté des Sciences de Sfax, B.P. 1171, 3000 Sfax, University of Sfax, Tunisia. Département de Génie des procédés, ISET Sfax, Km 2,5 Rte de Mahdia, 3099 Sfax, University of Sfax, Tunisia. Unité de recherche Biotechn...

Christopher Banerji, 2 Toufik Mansour, and Simone Severini Department of Computer Science, and Centre of Mathematics & Physics in the Life Sciences and Experimental Biology, University College London, London WC1E 6BT, United Kingdom Statistical Cancer Genomics, Paul O’Gorman Building, UCL Cancer Institute, University College London, London WC1E 6BT, United Kingdom Department of Mathematics, Uni...

Based on weighted noncrossing partitions of type B, we obtain type B analogues of Coker’s identities on the Narayana polynomials. A parity reversing involution is given for the alternating sum of Narayana numbers of type B. Moreover, we find type B analogues of the refinements of Coker’s identities due to Chen, Deutsch and Elizalde. By combinatorial constructions, we provide type B analogues of...

The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schrödinger equation in non-commutative space. It is shown that the experimental data for Helium atom puts an upper bound on the magnitude of the parameter of non-commutativity, θ...

A hardware-efficient algorithm and architecture for computing Zadoff–Chu (ZC) sequence elements on-line using the CORDIC algorithm are proposed. Zadoff–Chu sequences possess good correlation properties that are essential in a variety of engineering applications, such as establishing timing synchronization between a mobile terminal and a base station in the emerging 3GPP long-term evolution (LTE...

In this thesis, we study blockciphers, meaning that the encryption (and decryption)sends a block of n bits on a block of n bits. There is essentially two main structures usedfor a blockcipher: the Feistel structure (used for DES) and the SPN structure (used forAES). The study of the security of these structures and schemes has led to many practicaland theoretical advances. We pr...

In [BabStein] Babson and Steingŕımsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. In [Kit1] Kitaev considered simultaneous avoidance (multi-avoidance) of two or more 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous subwords in a permutation. There eithe...

We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe’s identity. It is well-known that the number of ways of choosing k points, no two consecutive, from a collection of n points arranged on a cycle is n n−k ( n−k k ) (see [11, Lemma 2.3.4]). A generalization of this result was obtained by Kaplansky [5], who proved that the number of k-subsets {x1, . . . , xk} of ...