A new efficient DQ algorithm for the solution of elliptic problems in higher dimensions

Two new efficient algorithms are developed to approximate the derivatives of sufficiently smooth functions. The new techniques are based on differential quadrature method with quartic B-spline bases as test functions. To obtain the weighting coefficients of differential quadrature method (DQM), we use the midpoints of a uniform partition mixed with near-boundary grid points. This enables us to obtain the weighting coefficients without adding the new extra relations. By obtaining the error bounds, it is proved that the method in its classic form is non-optimal. Then, some new weighting coefficients are constructed to obtain higher accuracy. By obtaining the error bounds, it is proved that the new algorithm is superconvergent. Afterwards, by defining some new symbols, we find a way to approximate the partial derivatives of multivariate functions. Also, some approximations are constructed to the mixed derivatives of multivariate functions. Finally, the applicability of the methods is examined by solving some well-known problems of partial differential equations. Some examples of 2D and 3D biharmonic, Poisson, and convection-diffusion equations are solved and compared to the existing methods to show the efficiency of the proposed algorithms.     

Spectrophotometric determination of acidity constants of some anthraquinones and anthrones in methanol-water mixtures

The acidity constants of some synthetic derivatives of 9,10-anthraquinone and 9-anthrone in methanol-water mixtures at 25 degrees have been determined spectrophotometrically. A linear reverse relationship is observed between pK(a1) of all acids and the mole fraction of methanol. The influence of substituents in the molecular structure on the ionization constants is discussed.     

<Emphasis Type="Italic">Ferula gummosa</Emphasis> Fruits: An Aromatic Antimicrobial Agent

Ferula gummosa Boiss. (Apiaceae) fruit volatile oil was analyzed by GC/MS. Seventy-three components (96.89%) were identified, and the major components were β-pinene (43.78%), α-pinene (27.27%), and myrcene (3.37%). The antimicrobial activity of the oil was tested on three strains of Gram positive bacteria (Staphylococcus aureus, S. epidermis, and Bacillus subtilis), three strains of Gram negative bacteria (Escherichia coli, Salmonella typhi, and Pseudomonas aeruginosa), and two strains of fungi (Candida albicans and C. kefyr). The essential oil remarkably inhibited the growth of the tested microorganisms. The results indicate that the fruits have potential for use as an aromatic antimicrobial agent.__________Published in Khimiya Prirodnykh Soedinenii, No. 3, pp. 252–254, May–June, 2005.     

Simultaneous kinetic-spectrophotometric determination of sulfide and sulfite and genetic algorithim variable selection using partial least squares calibration

Simultaneous multicomponent analysis is usually carried out using multivariate calibration models, such as the partial least squares (PLS) one, that utilize the full spectrum. It has been shown by both experimental and theoretical considerations that better results can by obtained by proper selection of the spectral range to be included in calculations. A genetic algorithm (GA) is one of the most popular methods for selecting variables for PLS calibration of mixtures with almost identical spectra without loss of predictive capability. In this work, a simple and precise method for rapid and accurate simultaneous determination of sulfide and sulfite ions based on the addition reaction of these ions with new fuchsin at pH 8 and 25°C using PLS regression and GA for variable selection is proposed. The concentrations of sulfide ions varied between 0.05–2.50 and 0.15–2.00 μg/mL, respectively. A series of model solutions containing different concentrations of sulfide and sulfite were used to check the predictive ability of GA-PLS models. The root mean square error of prediction with PLS on the whole data set was 0.19 μg/mL for sulfide and 0.09 μg/mL for sulfite. After the application of GA, these values reduced to 0.04 and 0.03 μg/mL, respectively. The text was submitted by the authors in English.     

Cubic spline solution of singularly perturbed boundary value problems with significant first derivatives

We develop a numerical technique for a class of singularly perturbed two-point singular boundary value problems on an uniform mesh using polynomial cubic spline. The scheme derived in this paper is second-order accurate. The resulting linear system of equations has been solved by using a tri-diagonal solver. Numerical results are provided to illustrate the proposed method and to compared with the methods in [R.K. Mohanty, Urvashi Arora, A family of non-uniform mesh tension spline methods for singularly perturbed two-point singular boundary value problems with significant first derivatives, Appl. Math. Comput., 172 (2006) 531–544; M.K. Kadalbajoo, V.K. Aggarwal, Fitted mesh B-spline method for solving a class of singular singularly perturbed boundary value problems, Int. J. Comput. Math. 82 (2005) 67–76].     

Regeneration of stochastic processes: an inverse method

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.     

Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure

This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.     

Biaryl formation via Suzuki and Stille coupling reactions using palladium nanoparticle/polymeric N‐heterocyclic carbene grafted silica as recyclable and efficient catalyst

Palladium nanoparticles supported on polymeric N‐heterocyclic carbene grafted silica as an efficient organic–inorganic hybrid catalyst is introduced. Pd⁰ nanoparticle formation, which is stabilized by the polymeric N‐heterocyclic carbene ligands and ionic liquid units, was confirmed using X‐ray photoelectron spectroscopy. Scanning electron microscopy images showed microparticles of modified silica while transmission electron microscopy images displayed a fine distribution of Pd nanoparticles. The modified structure was applied successfully in biaryl formation via Suzuki and Stille coupling reactions. Various biaryls were generated through the reaction of phenylboronic acid or tetraphenyltin with a variety of haloarenes via cross‐coupling reactions. This catalyst showed promising activity after being recycled several times. Copyright © 2016 John Wiley & Sons, Ltd.     

Real and Imaginary Parts of Magnetic Susceptibility of Fine Dispersed Nanoparticles Synthesized by Reverse Micelle: From Superparamagnetic Trend to Ferrimagnetic State

Ni_0.6Zn_0.4Fe_2?xCr_xO₄ (x = 0–0.5) ferrite nanoparticles were prepared using reverse micelle process. X-ray diffraction patterns demonstrated that single phase of spinel ferrites are obtained. TEM micrographs demonstrate the formation of well dispersed nanoparticle with almost spherical morphologies. The EDS analysis proved that the chemical composition has almost uniform distribution in the whole series of samples. Magnetic dynamics of the samples was studied by the measurement of AC magnetic susceptibility versus temperature at different frequencies. The phenomenological Néel–Brown and Vogel–Fulcher models were employed to distinguish between the interacting or non-interacting system. Results exhibited that there is strong interaction between fine particles. The results obtained from vibrating sample magnetometer confirmed that with an increase in chromium content, the saturation magnetization increases. SQUID results at 2 K displayed the ferromagnetic state in nanoparticle and it was found that with an increase in substitution contents, the coercivity decreased.