An iterative procedure for determining an unknown spacewise-dependent coefficient in a parabolic equation

An inverse problem for the determination of an unknown spacewise-dependent coefficient in a parabolic equation is considered. The problem is reformulated as a nonclassical parabolic equation along with the initial and boundary conditions. The iterative fixed point projection method is applied to solve the reformulated problem. The comparison analysis of proposed method with a least square method and some numerical examples are presented.     

Asymptotic analysis of interactions between highly conducting cylinders

We consider the conduction of heat or electricity between a pair of equal, touching cylinders embedded in a matrix. We solve exactly a problem in which each cylinder contains a heat source, and analyse the solution asymptotically for the case in which the conductivity of the fibres is much greater than that of the matrix. Using this analysis, we assess the accuracy of approximate schemes for calculating the interactions between the fibres of a composite material. We conclude that the approximate solutions are better at predicting global quantities, such as total flux, than they are at predicting pointwise quantities such as the temperature field.     

Preparation and properties of a new solid state borate ion selective electrode and its application

A new borate ion selective electrode using solid salts of Ag₃BO₃, Ag₂S and Cu₂S has been developed. Detailed information is provided concerning the composition, working pH and conditioning of the electrode. An analytically useful potential change occurred from 1 × 10⁻⁶ to 1 × 10⁻¹ M borate ion. The slope of the linear portion was 31 ± 2 mV/10-fold changes in borate concentration. The measurements were made at constant ionic strength (0.1 M NaNO₃) and at room temperature. The effect of Cl⁻, Br⁻, NO₃⁻, SO⁼₄, H₂PO₄⁻ anions and K⁺, Na⁺, Cu²⁺, Ag⁺, Ca²⁺ cations on borate response is evaluated and it was found that only Ag⁺ had a small interference effect. The lifetime of the electrode was more than two years, when used at least 4-5 times a day, and the response time was about 20-30 s. Borate content in waste water of borax factory, tap water of a town situated near to the borax factory and city tap water far from these mines were also determined. The validation was made with differential pulse polarography for the same water sample, and high consistency was obtained.     

Butylene linked palladium N-heterocyclic carbene complexes: Synthesis and catalytic properties

New bis(NHC)-Pd complexes were synthesized and characterized by elemental analysis, ¹H NMR, ¹³C NMR, and IR spectroscopy. The reaction of Pd(OAc)₂ and bis(benzimidazolium) salts in DMSO gave the monomeric palladium complex in which the N-heterocyclic carbene was bound to the metal centre. The crystal and molecular structure of the cis-dibromo{1,1′-di[2,3,4,5,6-pentamethylbenzyl]-3,3′-butylenedibenzimidazol-2,2′-diylidene}-palladium(II) complex was determined by single-crystal X-ray diffraction. The activity of the Pd(II) complexes in the direct arylation of benzothiazole with arylbromides was investigated. A preliminary catalytic study showed that these bis(NHC)-Pd complexes were highly active in the direct arylation of benzothiazole with arylbromides.     

Use of bis(benzimidazolium)–palladium system as a convenient catalyst for Heck and Suzuki coupling reactions of aryl bromides and chlorides

Six new, sterically demanding bis(benzimidazolium) salts (2a–f) as NHC precursors have been synthesized and characterized. These salts, in combination with palladium acetate, provide active catalysts for the cross‐coupling of aryl chlorides and bromides under mild conditions in aqueous media. Copyright © 2006 John Wiley & Sons, Ltd.     

A Long Wavelength Excitable Fluorophore; Chloro Phenyl Imino Propenyl Aniline (CPIPA) for Selective Sensing of Hg (II)

In this study, a very sensitive and highly selective irreversible optical chemical sensor (optode) for mercury ions was described. The sensing scheme was based on the interaction of Hg (II) with a newly synthesized fluoroionophore; chloro phenyl imino propenyl aniline (CPIPA) in plasticized PVC membrane. The sensor membranes were tested for the determination of mercury ion in aqueous solutions by batch and flow-through methods. The optodes allow determination of Hg (II) in the working range of 1.0 × 10⁻⁹–1.0 × 10⁻⁵ M with a detection limit of 4.3 ppb. The sensor exhibited excellent selectivity for Hg (II) with respect to several common alkali, alkaline earth and transition metal ions. The association constant of the 1:1 complex formation for Hg (II) was found to be K_a = 1.86 × 10⁵ M⁻¹. The CPIPA exhibited high fluorescence quantum yield, long excitation and emission wavelength and high Stokes’ shift values in the solid matrix which makes it compatible with solid state optics.     

Ionic conductivity of PVdF-co-HFP/LiClO4 in terms of free volume defects probed by positron annihilation lifetime spectroscopy

ABSTRACT

Polymers based on ionic conducting materials have important interest because of their potential applications in polymer electrolytes and membranes for fuel cell application. PVdF-co-HFP poly(viniliden-co-hexafluoropropylene) was chosen as a polymer matrix because of its high ionic conductivity and better mechanical properties. Polymer matrix composites were prepared with various amounts of LiClO₄ salt by a solution casting method. The sample-ionic conductivity measurements were recorded by AC impedance analyzer at different frequencies from 0.1?Hz to 20?MHz and at different temperatures from 273 to 373?K.

The changes of nanoscopic free volume and free volume fraction in these materials were investigated in terms of temperature from 273 to 373?K using Positron Annihilation Lifetime Spectroscopy (PALS) and Simha-Somcynsky (SS) Hole Theory. The free volume had a bump at about 3% in weight percentage of the salt and there is a slight increase after 10%. The effects of weight percentages of LiClO₄ and temperature were investigated. The mechanism of the ac ionic conductivity was presented in terms of the free volume models, however thermo-occupancy function justifies the best accurate representation of the data.     

On Complex Fibonacci Quaternions

Horadam defined the Fibonacci quaternions and established a few relations for the Fibonacci quaternions. In this paper, we investigate the complex Fibonacci quaternions and give the generating function and Binet formula for these quaternions. Moreover, we also give the matrix representations of them.     

Bilevel programming for generating discrete representations in multiobjective optimization

Mathematical Programming - The solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade-off information. The ultimate goal is to identify...     

Sterically hindered N-aryl/benzyl substituted piperidoimidazolin-2-ylidene palladium complexes and their catalytic activities

A series of N-aryl (2a,b) or benzyl (2c,d) substituted piperidoimidazolinium salts and their palladium complexes (3a-d) were prepared and characterized by ¹H, ¹³C NMR, IR spectroscopy and elemental analysis. The crystal structures of 3a and 3c have been determined by X-ray crystallography. Thermogravimetric analysis (TGA) was applied to complexes (3a–d). The palladium complexes have been employed as catalyst for Suzuki-Miyaura cross coupling. The N-aryl substituted complex 3b was a highly efficient precatalyst and successfully employed in Suzuki-Miyaura cross coupling reactions of (hetero)aryl chlorides with arylboronic acids in air. In addition, the oxidative addition step of the reaction mechanism involving chlorobenzene and the catalysts 3a, 3b, 3c and 3d were computationally investigated by the DFT-$\omega$-B97X-D method and complete agreement were obtained with the catalytic results. To measure σ-donating and π-acceptor properties of the new ligands, the rhodium carbonyl complexes were also prepared.