Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.     

Correction to: convergence rates for Kaczmarz-type algorithms

Numerical Algorithms - We will refer to the paper “Convergence rates for Kaczmarz-type algorithms”, published in Numerical Algorithms, 79(1)(2018), 1-17. It was observed by Dr. Mokhtar...     

Almost summing and multiple almost summing multilinear operators on l p spaces

We use the Maurey–Rosenthal factorization theorem to give a characterization of almost summing and multiple almost summing multilinear operators on a cartesian product of l _p spaces. As applications we give the necessary and sufficient conditions for the multiplication operator on l _p spaces be almost summing and multiple almost summing.     

New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials

This paper reports a new numerical approach for numerically solving types of fractional variational problems. In our approach, we use the fractional integrals operational matrix, described in the sense of Riemann–Liouville, with the help of the Lagrange multiplier technique for converting the fractional variational problem into an easier problem that consisting of solving an algebraic equations system in the unknown coefficients. Several numerical examples are introduced, combined with their approximate solutions and comparisons with other numerical approaches, for confirming the accuracy and applicability of the proposed approach.     

Synthesis of Mixed Alkylphosphites and Alkylphosphates

Some mixed phosphites having two different alkyl chain were obtained as forerunners for mixed phosphates Mixed dialkyl phosphates were obtained in good yields (40-80%) by phase transfer catalysis in liquid-liquid sistem, starting from different dialkyl phosphites and aliphatic alcohols. The reaction conditions were optimized in order to obtain good yields in phosphites and phosphates respectively. Compounds were analyzed by IR, P 31 -NMR.     

The Preparation,Characterization and Properties of Catalase Immobilized on Crosslinked Gellan

In the present paper, the reaction of chemical immobilization of catalase on a crosslinked macromolecular carrier of a polysaccharide structure (gellan) is studied. The influence of some reaction parameters (enzyme/carrier, activator/carrier ratios, duration) on the activity of enzymatic products is analyzed. The kinetics of the biocatalytic process, stability under different pH and temperature conditions, and the inhibitors effect were studied for the immobilized enzymes.     

Novel Supports Based on Polysaccharides for Sustained‐Release of Isosorbide Dinitrate

Novel supports based on carboxymethylcellulose (CMC), crosslinked with epichlorohydrin (EPC), and microparticles based on acetylphthalylcellulose (APC), for sustained‐release of isosorbide dinitrate (Isoket, Ik), were obtained. The drug has been included into CMC hydrogels through diffusion from ethanol‐water solution. Studies about the ethanol–water ratio influence on including the drug have shown an increased amount of included drug at higher content of water in the alcohol‐water mixture. Isoket–ACP microparticles have been obtained by drug and polymer co‐precipitation from emulsified aqueous solution.

The kinetics for “in vitro” release of Ik from polymeric materials, in simulated conditions for intestinal tract medium, where the drug is preferentially absorbed, has been analyzed. The experimental data have shown a “zero” order kinetic for drug release, which is characteristic for systems controlled by diffusion.     

Crosslinked Networks Based on Polysaccharides and Collagen for Pilocarpine Sustained Release

The paper presents the experimental studies regarding synthesis and characterization of hydrogels based on gellan (Gel)/chitosan (CS) and collagen (Col), obtained by crosslinking with glutaraldehyde (GLA). The influence of the polysaccharide content and GLA ratio on the final composition and swelling characteristics was evaluated. Hydrogels swelling analysis, in distilled water and phosphate buffer (PBS, pH 7.2) has shown higher swelling degrees at increased concentration of polysaccharide into hydrogels. In vitro release of pilocarpine has demonstrated the possibility to use gellan-collagen and chitosan-collagen hydrogels as ophthalmic drug delivery matrix.