A new eco-friendly strategy for the preparation of linear and hyperbranched polycarbonates was developed. Our work referred to a one-pot condensation polymerization of various alcohols (diols and triols) with equivalent amounts of eco-friendly dimethyl carbonate (DMC) at 120
C, atmospheric pressure and in 1,4- dioxane solution using 4-dimethylaminopyridine (DMAP) or lithium acetylacetonate (LiAcac) as a catalyst. Polymer chains were built by pure transesterification of hydroxyl and methyl carbonate chain ends, and the single byproduct (methanol) was removed using a pressure-equalized addition funnel filled with 4 °A molecular sieves as the crucial equipment in this work. Using this strategy, hyperbranched polycarbonates with high molar masses (Mn up to 10 000 g mol1 and Mw up to 64 000 g mol1) and high hydroxyl end group contents (up to 94%) were successfully prepared using dimethyl carbonate instead of toxic phosgene or phosgene-based monomers for the first time. In addition, linear aliphatic polycarbonates of various diols were also synthesized with Mn up to 16 000 g mol1 and low molar mass distributions (ĐM 1.70). Another eco-friendly aspect of this work was the use of equimolar amounts of DMC to avoid waste and the disposal of excess DMC; in a classic 2-step polycondensation for polycarbonate synthesis excess DMC is a prerequisite in order to obtain high molar masses.

The main aim in this paper, we use the differential operators and matrix polynomial sets, generating matrix functions, integrals representation to derive the properties of Hermite matrix polynomials. Finally, we obtain an expansion of Hermite matrix polynomials in a series of Laguerre matrix polynomials and the Christoffel's formula of summation is established.

The main object of this paper is to consider the Bessel-Maitland matrix function in the following form: A different approach is adopted to study the radius of regularity, order and type of this function. Certain properties including integral representation and differential recurrence relations are also derived. Further, the composite Bessel- Maitland matrix function is introduced and its properties are discussed.

The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials also of two, three and several index are derived.

NULL

NULL

NULL

NULL

NULL

A sensitive and selective electrochemical method was developed for simultaneous determination of uric acid and xanthine using the nano boron doped ceria modified glassy carbon paste electrode (nano-B-CeO2/GCPE). The proposed sensor exhibited an excellent catalytic activity, high sensitivity and good selectivity toward the oxidation of uric acid and xanthine. The potential mutual interference of uric acid (UA), xanthine (XA), dopamine (DA) and ascorbic acid (AA) were examined indicting that their oxidation take place independently at the nano-B-CeO2/GCPE sensor. For simultaneous detection by synchronous change of the concentration of UA and XA, the linear ranges were 0.42–11.87 μM and 0.07–2.02 μM with detection limits of 5.39 × 10− 9 M and 2.36 × 10− 9 M, respectively. The proposed method was successfully applied to simultaneous determination of UA and XA in human urine and serum samples with satisfactory results.