A new class of polynomials with applications

A New Class of q-Fibonacci Polynomials

the simple evaluation (3.2 ). This fact led me to a thorough study of this q-analogue via a combinatorial approach based on Morse code sequences. We show that these q-Fibonacci polynomials satisfy some other recurrences too, generalize some well-known facts for ordinary Fibonacci polynomials to this case, derive their generating function and study the special values Fn(1,−q ) and Fn(1,−1) which...

A new class of generalized Bernoulli polynomials and Euler polynomials

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava–Pintér addition theorem is obtained. We give new identities involving q-Bernstein polynomials.

DNA Barcoding: a new tool with wide array of applications

DNA barcoding is a new term introduced in to scientific literatures by Hebert and coworkers almost a decade ago. The concept of barcoding alone is well-known to the public: a series of black bars printed on many commercial products (Universal Product Code), which are used to distinguish different products. Advances made in molecular biology and molecular techniques late 20th century e.g. sequen...

A New Class of Banach Sequence Spaces

Optimization with Positive Trigonometric Polynomials: a Review and New Applications

This paper has a double purpose. Firstly, we review recent results regarding the characterization of positive multivariate trigonometric polynomials as functions of sumof-squares polynomials. Using the linear matrix inequality parameterization of sum-of-squares, we discuss several optimization applications, among which the design of 2D FIR filters with linear or nonlinear phase. Secondly, we pr...