Nanomolar Determination of Methyldopa in the Presence of Large Amounts of Hydrochlorothiazide Using a Carbon Paste Electrode Modified with Graphene Oxide Nanosheets and 3‐(4′‐Amino‐3′‐hydroxy‐biphenyl‐4‐yl)‐acrylic Acid

A novel electrochemical sensor for sensitive detection of methyldopa at physiological pH was developed by the bulk modification of carbon paste electrode (CPE) with graphene oxide nanosheets and 3‐(4′‐amino‐3′‐hydroxy‐biphenyl‐4‐yl)‐acrylic acid (3,′AA). Applying square wave voltammetry (SWV), in phosphate buffer solution (PBS) of pH 7.0, the oxidation current increased linearly with two concentration intervals of methyldopa, one is 1.0×10^?8–1.0×10^?6 M and the other is 1.0×10^?6–4.5×10^?5 M. The detection limit (3σ) obtained by SWV was 9.0 nM. The modified electrode was successfully applied for simultaneous determination of methyldopa and hydrochlorothiazide. Finally, the proposed method was applied to the determination of methyldopa and hydrochlorothiazide in some real samples.     

Construction of a Novel Carbon Paste Clarithromycin Sensor for Low Level Concentration Measurement,Applications to Pharmaceutical and Biological Analysis

A potentiometric carbon paste sensor was fabricated for determination of clarithromycin based on incorporation of the ion association complex of the clarithromycin‐phosphotungstate. The proposed sensor exhibited a Nernstian slope of 59.2±0.3 mV per decade for clarithromycin over a wide concentration range of 7.4×10^?7 to 1.5×10^?3 M, with a low detection limit of 5.0×10^?7 M. The proposed sensor manifested advantages of very fast response, long life time and, most importantly, excellent selectivity for clarithromycin relative to a wide variety of common foreign inorganic cation, and also biological species. The sensor was successfully applied to determine clarithromycin in clarithromycin tablet, blood serum and urine samples. The inclusion complex formation between β‐cyclodextrin and clarithromycin was studied by the proposed sensor. The influence of the temperature on the response of the sensor was investigated and the temperature coefficient of the sensor was calculated.     

Molecular Architecture Manipulation in Free Radical Copolymerization: An Advanced Monte Carlo Approach to Screening Copolymer Chains with Various Comonomer Sequence Arrangements

A Kinetic Monte Carlo (KMC) simulation approach has been adopted in this study to capture evolutionary events in the course of free radical copolymerization, through which batch and starved‐feed semibatch processes are compared. The implementation of the KMC code deve­loped in this work: (i) enables satisfactory control of the molecular weight of the copolymer by tracking the profiles of concentrations of macroradicals, monomers, and polymer as well as degree of polymerization, polydispersity, and chain length distribution; (ii) captures the bivariate distribution of chain length and copolymer composition; (iii) comprehensively tracks and analyzes detailed information on the molecular architecture of the growing chains, thus distinguishing between sequence length and polydispersity of chains produced in batch and starved‐feed semibatch operations; (iv) makes possible the screening of products, based on such details as the number and weight fractions of products having different comonomer units located at various positions along the copolymer chains. The aforementioned characteristics are achieved by stochastic calculations through code developed in‐house. This KMC simulator becomes a very useful tool for the development of tailored copolymers through free radical polymerization, with blocks separated with single units of a different type.

     

Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces

In this article, we study the property of norm retrievability of spanning vectors in a finite dimensional complex Hilbert space ?. Using the set of zero trace operators on ? and two sets of self-adjoint operators on ? denoted by 𝒮^1,0 and 𝒮^1,1, we present some equivalent conditions to the norm retrievable frames in ?. We will also show that the property of norm retrievability for n-dimensional complex Hilbert space ? with n≠2 is stable under enough small perturbation of the frame set only for phase retrievable frames.     

Homogeneous Liquid–Liquid Microextraction for Determination of Organochlorine Pesticides in Water and Fruit Samples

A fast and effective preconcentration method for extraction of organochlorine pesticides (OCPs) was developed using a homogeneous liquid–liquid extraction based on phase separation phenomenon in a ternary solvent (water/methanol/chloroform) system. The phase separation phenomenon occurred by salt addition. After centrifugation, the extraction solvent was sedimented in the bottom of the conical test tube. The OCPs were transferred into the sedimented phase during the phase separation step. The extracted OCPs were determined using gas chromatography–electron capture detector. Several factors influencing the extraction efficiency were investigated and optimized. Optimal results were obtained at the following conditions: volume of the consolute solvent (methanol), 1.0 mL; volume of the extraction solvent (chloroform), 55 μL; volume of the sample, 5 mL; and concentration of NaCl, 5 % (w/v). Under optimal conditions, the preconcentration factors in the range of 486–1,090, the dynamic linear range of 0.01–100 μg L^?1, and the limits of detection of 0.001–0.03 μg L^?1 were obtained for the OCPs. Using internal standard, the relative standard deviations for 1 μg L^?1 of the OCPs in the water samples were obtained in the range of 4.9–8.6 % (n = 5). Finally, the proposed method was successfully applied for extraction and determination of the OCPs in water and fruit samples.     

Application of Sulfonic Acid Functionalized SBA‐15 as a New Nanoporous Acid Catalyst in the Green One‐Pot Synthesis of Spirooxindole‐4H‐pyrans

Sulfonic acid functionalized SBA‐15 (SBA‐Pr‐SO₃H) as a new nanoporous solid acid catalyst was applied in the green one‐pot synthesis of spirooxindole‐4H‐pyrans via condensation of isatins, malononitrile or methyl cyanoacetate or ethyl cyanoacetate, and 4‐hydroxycoumarin in water solvent. SBA‐Pr‐SO₃H was proved to be an efficient heterogeneous nanoporous solid acid catalyst with a pore size of 6 nm that could be easily handled and removed from the reaction mixture by simple filtration and can be recovered and reused for several times without any loss of activity. The significant merits of present methodology are its simplicity, short reaction time, good yields, and environmentally benign mild reaction condition as water was used as a green solvent.     

On the fractional derivatives of radial basis functions: Theories and applications

The paper provides the fractional integrals and derivatives of the Riemann‐Liouville and Caputo type for the five kinds of radial basis functions, including the Powers, Gaussian, Multiquadric, Matérn, and Thin‐plate splines, in one dimension. It allows to use high‐order numerical methods for solving fractional differential equations. The results are tested by solving two test problems. The first test case focuses on the discretization of the fractional differential operator while the second considers the solution of a fractional order differential equation.     

On the Schröder–Bernstein property for modules

The well known Schröder–Bernstein Theorem states that any two sets with one to one maps into each other are isomorphic. The question of whether any two (subisomorphic or) direct summand subisomorphic algebraic structures are isomorphic, has long been of interest. Kaplansky asked whether direct summands subisomorphic abelian groups are always isomorphic? The question generated a great deal of interest. The study of this question for the general class of modules has been somewhat limited. We extend the study of this question for modules in this paper. We say that a module Msatisfies the Schröder–Bernstein property (S-B property) if any two direct summands of M which are subisomorphic to direct summands of each other, are isomorphic. We show that a large number of classes of modules satisfy the S-B property. These include the classes of quasi-continuous, directly finite, quasi-discrete and modules with ACC on direct summands. It is also shown that over a Noetherian ring R, every extending module satisfies the S-B property. Among applications, it is proved that the class of rings R for which every R-module satisfies the S-B property is precisely that of pure-semisimple rings. We show that over a commutative domain R, any two quasi-continuous subisomorphic R-modules are isomorphic if and only if R is a PID. We study other conditions related to the S-B property and obtain characterizations of certain classes of rings via those conditions. Examples which delimit and illustrate our results are provided.