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...

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 ...

A Raptor code is a concatenation of a fixed rate precode and a Luby-Transform (LT) code that can be used as a rateless error-correcting code over communication channels. By definition, Raptor codes are characterized by irregularity features such as dynamic rate, check-degree variability, and joint coding, which make the design of hardware-efficient decoders a challenging task. In this paper, se...