Hybrid Materials Based on Conducting Polymers for Nitrite Sensing: A Mini Review

Well-known as a hazardous compound, nitrite constitute a real threat to the public health. So, there is a pressing need to detect and quantify them in different matrix. Even though conventional analytical methods can be used to address this issue, electrochemistry allows a fast, sensitive, and efficient analysis. Conducting polymers continue to raise great interest among scientific communities due to their properties. Moreover, their combination with carbon nanomaterials, or metallic nanoparticles improves their properties, and provides great results. In this paper, we will focus on some revealing works devoted to the electrochemical detection of nitrite using this kind of materials.     

Electrochemical determination of traces lead ions using a new nanocomposite of polypyrrole/carbon nanofibers

Journal of Solid State Electrochemistry - In this paper, a new nanocomposite of polypyrrole (PPy) and carbon nanofibers (CNFs)-modified carbon paste electrode (CPE) has been reported for the...     

Divided-difference equation and three-term recurrence relations of some systems of bivariate q-orthogonal polynomials

Partial divided-difference equations and three-term recurrence relations satisfied by the bivariate Askey–Wilson and the bivariate q-Racah polynomials are computed in this work. By using limiting processes, partial divided (or q)-difference equations and three-term recurrence relations are also provided for each of the following families of orthogonal polynomials: the bivariate continuous dual q-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous q-Hahn, the bivariate q-Hahn, the bivariate dual q-Hahn, the bivariate q-Krawtchouk, the bivariate q-Meixner, and the bivariate q-Charlier polynomials.     

Characterization of semi-classical orthogonal polynomials on nonuniform lattices

We state and prove characterization theorem for semi-classical orthogonal polynomials on nonuniform lattices (quadratic lattices of a discrete or q-discrete variable). This theorem proves the equivalence between the four characterization properties, namely, the Pearson type equation for the linear functional, the strictly quasi-orthogonality of the derivatives, the structure relation, and the Riccati equation for the formal Stieltjes function. We give the classification of the semi-classical linear functional of class one on nonuniform lattice. Using the definition and the properties of the associated orthogonal polynomials, we prove that semi-classical orthogonal polynomials satisfy the second-order divided difference equation on nonuniform lattices.     

On Fourth-order Difference Equations for Orthogonal Polynomials of a Discrete Variable: Derivation,Factorization and Solutions

We derive and factorize the fourth-order difference equations satisfied by orthogonal polynomials obtained from some modifications of the recurrence coefficients of classical discrete orthogonal polynomials such as: the associated, the general co-recursive, co-recursive associated, co-dilated and the general co-modified classical orthogonal polynomials. Moreover, we find four linearly independent solutions of these fourth-order difference equations, and show how the results obtained for modified classical discrete orthogonal polynomials can be extended to modified semi-classical discrete orthogonal polynomials. Finally, we extend the validity of the results obtained for the associated classical discrete orthogonal polynomials with integer order of association from integers to reals.     

Divided-difference equation,inversion, connection,multiplication and linearization formulae of the continuous Hahn and the Meixner–Pollaczek polynomials

From the study of various properties of some difference operators, we prove in the first part of this work that the continuous Hahn and the Meixner–Pollaczek polynomials are solutions of a second-order divided-difference equation of hypergeometric- type. Next, using some algorithmic tools, we solve the inversion, connection, multiplication and linearization problems for the continuous Hahn and the Meixner–Pollaczek polynomials.     

Determination of mercury(II) by invertase enzyme inhibition coupled with batch injection analysis

The determination of mercury(II) ions at the trace level by inhibition of the invertase enzyme-catalysed hydrolysis of sucrose into glucose and fructose coupled to electrochemical batch injection analysis was investigated using two approaches. In the first, the glucose produced was detected by injection of 100 microliters samples into the batch injection cell containing a platinum electrode modified by immobilised glucose oxidase. In the second, the glucose and fructose present in injected samples were oxidised directly at a copper-modified glassy carbon electrode. The experimental parameters were optimised and the degree of enzyme inhibition by mercury(II) ions under both conditions was measured. Mercury concentrations in the ng ml-1 range were determined by these two techniques with low sample and reagent consumption. Comparison is made between the two methods and perspectives as a screening test for field application are indicated.     

Characterization of the D w -Laguerre-Hahn Functionals

We give some characterization theorems for the D w -Laguerre-Hahn linear functionals and we extend the concept of the class of the usual Laguerre-Hahn functionals to the D w -Laguerre-Hahn functionals, recovering the classic results when w tends to zero. Moreover, we show that some transformations carried out on the D w -Laguerre-Hahn linear functionals lead to new D w -Laguerre-Hahn linear functionals. Finally, we analyze the class of the resulting functionals and we give some applications relative to the first associated Charlier, Meixner, Krawtchouk and Hahn orthogonal polynomials.