materials and methods phe degrading bacteria were isolated from surface sediments. isolated strains were then identified by biochemical and molecular (16s rdna gene sequence) analysis. rsm was employed to evaluate the optimum biodegradation of phe by the most effective isolated strain. the investigated parameters included the temperature, inoculum sizes, ph, nh4cl concentration, and salinity. o...

For α, β, γ, δ ∈ Z and ν = (α, β, γ, δ), the q-Fibonacci numbers are given by F ν 0 (q) = 0, F ν 1 (q) = 1 and F ν n+1(q) = q αn−βF ν n (q) + q γn−δF ν n−1(q) for n > 1. And define the q-Lucas number Ln(q) = F ν n+1(q)+ q γ−δF ν∗ n−1(q), where ν∗ = (α, β− α, γ, δ − γ). Suppose that α = 0 and γ is prime to n, or α = γ is prime to n. We prove that Ln(q) ≡ (−1) (mod Φn(q)) for n > 3, where Φn(q) i...

Using orthogonal polynomials, we give a different approach to some recent results on tridi-agonal matrices. 1. Introduction and preliminaries. Most of the results on tridiagonal matrices can be seen in the context of orthogonal polynomials. Here, we will see two examples. The aim of this note is to give simplified proofs of some recent results on tridiagonal matrices , using arguments from the ...

We study polynomial identities of algebras with involution nonassociative over a field characteristic zero. prove that the growth sequence ⁎-codimensions finite-dimensional algebra is exponentially bounded. construct series fractional ⁎-PI-exponent. also family infinite-dimensional Cα such exp⁎(Cα) does not exist.

A sequence of rational functions in a variable q is q-holonomic if it satisfies a linear recursion with coefficients polynomials in q and qn. In the paper, we assign a tropical curve to every q-holonomic sequence, which is closely related to the degree of the sequence with respect to q. In particular, we assign a tropical curve to every knot which is determined by the Jones polynomial of the kn...

We show that every real polynomial f nonnegative on [−1, 1]n can be approximated in the l1-norm of coefficients, by a sequence of polynomials {fεr} that are sums of squares. This complements the existence of s.o.s. approximations in the denseness result of Berg, Christensen and Ressel, as we provide a very simple and explicit approximation sequence. Then we show that if the moment problem holds...

This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of this problem obtained by first lifting the original problem into the space of measures with continuous densities and then restricting these den...

We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure preserving $\mathbb{Z}^d$-actions with multivariable integer polynomial iterates is the sum of a nilsequence and null sequence, extending recent result second author. To this end, we develop new seminorm bound estimate for multiple averages improving results in previous work fir...

Abstract Automatic sequences are not suitable for cryptographic applications since both their subword complexity and expansion small, correlation measure of order 2 is large. These highly predictable despite having a large maximum complexity. However, recent results show that polynomial subsequences automatic sequences, such as the Thue–Morse sequence, better candidates pseudorandom sequences. ...

Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of → and ↑ steps determine the solution of the recursion formula. If the recursion can be solved by a polynomial sequence, we apply ...