An embedded 3(2) pair of nonlinear methods for solving first order initial-value ordinary differential systems

In this paper, we present two families of second-order and third-order explicit methods for numerical integration of initial-value problems of ordinary differential equations. Firstly, a family of second-order methods with two free parameters is derived by considering a suitable rational approximation to the theoretical solution of the problem at some grid points. Imposing that the principal term of the local truncation error of this family vanishes, we obtain an expression for one of the parameters in terms of the other. With this approach, a new one-parameter family of third-order methods is obtained. By selecting any 3(2) pair of second and third order methods, they can be implemented as an embedded type method, thus leading to a variable step-size formulation. We have considered one 3(2) pair of second and third order methods and made a comparison of numerical results with several ode solvers which are currently used in practice. The comparison of numerical results shows that the embedded 3(2) pair outperforms the methods considered for comparison.     

New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations

We present a three-step two-parameter family of derivative free methods with seventh-order of convergence for solving systems of nonlinear equations numerically. The proposed methods require evaluation of two central divided differences and inversion of only one matrix per iteration. As a result, the proposed family is more efficient as compared with the existing methods of same order. Numerical examples show that the proposed methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations.     

Concise and Practical Asymmetric Synthesis of a Challenging Atropisomeric HIV Integrase Inhibitor

A practical and efficient synthesis of a complex chiral atropisomeric HIV integrase inhibitor has been accomplished. The combination of a copper‐catalyzed acylation along with the implementation of the BI‐DIME ligands for a ligand‐controlled Suzuki cross‐coupling and an unprecedented bis(trifluoromethane)sulfonamide‐catalyzed tert‐butylation renders the synthesis of this complex molecule robust, safe, and economical. Furthermore, the overall synthesis was conducted in an asymmetric and diastereoselective fashion with respect to the imbedded atropisomer.     

3D nanogap interdigitated electrode array biosensors

Three-dimensional interdigitated electrodes (IDEs) have been investigated as sensing elements for biosensors. Electric field and current density were simulated in the vicinity of these electrodes as a function of the electrode width, gap, and height to determine the optimum geometry. Both the height and the gap between the electrodes were found to have significant effect on the magnitude and distribution of the electric field and current density near the electrode surface, while the width of the electrodes was found to have a smaller effect on field strength and current density. IDEs were fabricated based on these simulations and their performance tested by detecting C-reactive protein (CRP), a stress-related protein and an important biomarker for inflammation, cardiovascular disease risk indicator, and postsurgical recuperation. CRP-specific antibodies were immobilized on the electrode surface and the formation of an immunocomplex (IC) with CRP was monitored. Electrochemical impedance spectroscopy (EIS) was employed as the detection technique. EIS data at various concentrations (1 pg/mL to 10 μg/mL) of CRP spiked in buffer or diluted human serum was collected and fitted into an equivalent electrical circuit model. Change in resistance was found to be the parameter most sensitive to change in CRP concentration. The sensor response was linear from 0.1 ng/mL to 1 μg/mL in both buffer and 5% human serum samples. The CRP samples were validated using a commercially available ELISA for CRP detection. Hence, the viability of IDEs and EIS for the detection of serum biomarkers was established without using labeled or probe molecules.     

The Antimicrobial efficacy of Elaeis guineensis: characterization, in vitro and in vivo studies

The urgent need to treat multi-drug resistant pathogenic microorganisms in chronically infected patients has given rise to the development of new antimicrobials from natural resources. We have tested Elaeis guineensis Jacq (Arecaceae) methanol extract against a variety of bacterial, fungal and yeast strains associated with infections. Our studies have demonstrated that E. guineensis exhibits excellent antimicrobial activity in vitro and in vivo against the bacterial and fungal strains tested. A marked inhibitory effect of the E. guineensis extracts was observed against C. albicans whereby E. guineensis extract at ?, 1, or 2 times the MIC significantly inhibited C. albicans growth with a noticeable drop in optical density (OD) of the bacterial culture. This finding confirmed the anticandidal activity of the extract on C. albicans. Imaging using scanning (SEM) and transmission (TEM) electron microscopy was done to determine the major alterations in the microstructure of the extract-treated C. albicans. The main abnormalities noted via SEM and TEM studies were the alteration in morphology of the yeast cells. In vivo antimicrobial activity was studies in mice that had been inoculated with C. albicans and exhibited good anticandidal activity. The authors conclude that the extract may be used as a candidate for the development of anticandidal agent.     

Optimized mean based second derivative-free families of Chebyshev–Halley type methods

In this paper, we present new interesting fourth-order optimal families of Chebyshev–Halley type methods free from second-order derivative. In terms of computational cost, eachmember of the families requires two functions and one first-order derivative evaluation per iteration, so that their efficiency indices are 1.587. It is found by way of illustration that the proposed methods are useful in high-precision computing environment. Moreover, it is also observed that larger basins of attraction belong to ourmethods although the othersmethods are slow and have darker basins while some of the methods are too sensitive upon the choice of the initial guess.     

Graft Copolymerizations of Polysaccharides. II. Acrylamide Grafting to Yellow Dextrin

Graft copolymers of acrylamide and yellow dextrin were prepared using cerium(IV) as initiator. The yellow dextrin had a very broad molecular weight distribution but was fractionated utilizing dialysis and ultrafiltration membranes. Initiator efficiencies were determined using size exclusion chromatography and were found to be between 2.4 and 34%. Initiator efficiency increased with acrylamide concentration at constant cerium (IV) and yellow dextrin concentrations, and decreased with increasing cerium(IV) concentration at constant acrylamide and yellow dextrin concentrations. Plots of acrylamide conversion and intrinsic viscosity vs initial acrylamide concentration at constant yellow dextrin and ceric ion concentrations showed a maximum at about 2.0 M.     

Organometallic Polymers. XXVII. Radical-Initiated Polymerization and Copolymerization of π-(2, 4-Hexadien-1-yl Acrylate) tricarbonyliron

The novel monomer, π-(2, 4-hexadiene- l-yl acrylate) tricarbonyliron (HATI), has been prepared by two routes. It was homopolymerized and copolymerized with acrylonitrile, vinyl acetate, styrene, and methyl acrylate in benzene solutions. In all cases azobisisobutyronitrile was the initiator. The relative reactivity ratios, where HATI is defined as M₁, were determined: r₁ = 0.34, r₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = vinyl acetate; r₁ = 0.26, r₂ = 1.81, M₂ = styrene; and r₁ = 0.30, r₂ = 0.74, M₂ = methyl acrylate. The homo-and copolymers had high values of T_g. When polymerizations are carried out at high concentrations, a very high molecular weight tail is observed in HATI hompolymerizations and in HATI-methyl acrylate copolymerizations. The polymers were characterized by IR, gel permeation chromatography, viscosity, and differential scanning calorimetry studies. Finally, thermal decompositions carried out in air resulted in decomposition of the Fe(CO)₃ group, producing Fe₂O₃ as a fine powder. Thermal decomposition under nitrogen (in solution and on solids ground into KBr pellets) resulted in slow destruction of the Fe(CO)₃ groups but the resulting polymer mass was insoluble, and the question of what form the iron exists in (Fe metal, oxides, carbides, etc.) has not been answered.     

Polymerization of Methane and Olefin Mixtures over Fluosulfonic Acid and Antimony Pentafluoride

Mixtures of methane and olefins (ethylene, propylene, butenes, butadiene, and styrene) have been polymerized over HSO₃ F-SbF₃ to yield an oily oligomer with a molecular weight ranging from 100 to 700. The NMR spectra of each polymer showed a sharp peak at or near 1.25 &, suggesting the presence of block methylene in the polymer. The formation of block methylene is surprising considering the fact that the polymerization reaction is carbonium ion in nature. A primary cation has been invoked to explain the results. The formation of this primary cation must involve some extraordinary stabilization by some component in the acid.     

Nonsingular Semiperfect Cs-Rings II

In this paper we obtain the precise structure of right nonsingularsemiperfect right CS-rings. It is shown that such rings aredirect sums of certain specific block matrix rings. 1991 MathematicsSubject Classification 16L30, 16D70.