We provide three new polynomial generalizations for the Pell sequence an, also, new formulas for this sequence. An interesting relation, in terms of partitions, between the Pell and the Fibonacci sequences is given, Finally two combinatorial interpretations for the Fibonacci numbers are given by making use of the Rogers-Ramanujan identities.

  We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibili...

In the first part of the paper we prove that the Zeckendorf sum-ofdigits function sZ(n) and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the q-ary expansions of integers are asymptotically independent.

Recently, motivated by the study of vectorized stream cipher systems, the joint linear complexity and joint minimal polynomial of multisequences have been investigated. Let S be a linear recurring sequence over finite field Fqm with minimal polynomial h(x) over Fqm. Since Fqm and F m q are isomorphic vector spaces over the finite field Fq, S is identified with an m-fold multisequence S over the...

We introduce concepts of “recursive polynomial remainder sequence (PRS)” and “recursive subresultant,” along with investigation of their properties. A recursive PRS is defined as, if there exists the GCD (greatest common divisor) of initial polynomials, a sequence of PRSs calculated “recursively” for the GCD and its derivative until a constant is derived, and recursive subresultants are defined...

The software package developed in the thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user–defined expected sequence factors of the input coefficients. We present a specialized hybrid approach to finding exact representations for polynomial sequences that is motivated by the need for an automated procedures to discover the precise forms...

Prediction of image sequences is widely used inimage processing and transmission schemes such as Differential Pulse Code Modulation (DPCM).Traditional linear prediction employs linear predictors for simplicity. The nonlinear Volterra predictor can be used as an alternative to linear predictor to account for the nonlinear components in the image signals. The proposed quadratic predictor is more ...

We introduce concepts of “recursive polynomial remainder sequence (PRS)” and “recursive subresultant,” and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we calculate “recursively” with new PRS for the GCD and its derivative, until a constant is derived. We call such a PRS a recursive PRS. We define recursive subresult...