Fixed Points of Quasi (f,g)-Nonexpansive Multivalued Mapping

Fixed point theorems for hybrid pair of single valued and multivalued R-subweakly commuting maps are proved.     

On the Electrical and Optical Properties of Some Poly(Azomethine Sulfone)s in Thin Films

Poly(azomethine sulfone)s were synthesized by reacting 4,4′-sulfonyl bis(4-chlorophenyl) with 2,2-bis(4-hydroxyphenyl)propane and azomethine bisphenol in different molar ratios. Thin films were deposited from solution onto glass substrates. Study of the temperature dependences of the electrical conductivity, σ, and Seebeck coefficient, S, were performed in the temperature range 300 K–500 K. Thermal activation energies of electrical conduction, E_a , calculated from these dependences, ranged between 1.50 eV and 1.85 eV. The values of E_a were smaller for polymers with extended conjugation systems. The possibility to use the polymers in thermistor technology is discussed. The aspect of the temperature dependences of σ and S shows that a model based on the energy band-gap representation can be successfully used for explaining the electronic transport mechanism in the higher temperature range. In the lower temperature range, the mechanism of the electrical conduction is discussed in terms of the Mott variable range hopping conduction. The values of some optical parameters (absorption coefficient, optical band gap, etc.) were determined from transmission spectra.     

Preconcentration of trace amounts of formaldehyde from water, biological and food samples using an efficient nanosized solid phase, and its determination by a novel kinetic method

This work presents a sensitive method for the determination of formaldehyde. It is based on the use of modified alumina nanoparticles for its preconcentration, this followed by a new and simple catalytic kinetic method for its determination. Alumina nanoparticles were chemically modified by immobilization of 2,4-dinitrophenylhydrazine via sodium dodecyl sulfate as a surfactant. The formaldehyde retained on the modified adsorbent was then desorbed and determined via its catalytic effect on the oxidation of thionine by bromate ion. Factors affecting the preconcentration and determination of formaldehyde have been investigated. Formaldehyde can be detected in the range from 0.05 to 38.75 μg L^?1, and no serious interferences have been observed. The method has been successfully applied to the quantitation of formaldehyde in water, food, and certain biological samples.

Diastereoselective synthesis of 5-iminooxazolines and their subsequent transformation to α,α-disubstituted dipeptide esters: a formal [4+1] cycloaddition reaction of cyclohexyl isocyanide and Z-alkyl-α-benzoyl amino-acrylates

A novel atom economical diastereoselective synthesis of 5-iminooxazolines and their subsequent transformation to α,α-disubstituted dipeptide esters is described. Heating a mixture of cyclohexyl isocyanide and Z-α-benzoyl amino-acrylic acid alkyl esters under solvent-free conditions, afforded 5-iminooxazolines, which, upon specifications provided α,α-disubstituted dipeptide esters in good yield.     

A facile route to flavone and neoflavone backbones via a regioselective palladium catalyzed oxidative Heck reaction

A straightforward and atom-economical base-free palladium-catalyzed regioselective direct arylation of coumarins and chromenones is devised. This protocol is compatible with a wide variety of electron-donating and -withdrawing substituents and allows construction of various biologically important flavone and neoflavone backbones.     

(-)-Kunstleramide, a new antioxidant and cytotoxic dienamide from the bark of Beilschmiedia kunstleri gamble

A new dienamide, (2E,4E)-7-(3',4'-dimethoxyphenyl)-N-ethyl-6-(R)-hydroxyhepta- 2,4-dienamide, named (-)-kunstleramide (1), were isolated from the bark of Beilschmiedia kunstleri Gamble together with one neolignan: (+)-kunstlerone (2) and seven known alkaloids: (+)-nornuciferine (3), (-)-isocaryachine (4), (+)-cassythicine (5), (+)-laurotetanine (6), (+)-boldine (7), noratherosperminine (8), (+)-N-demethylphyllocaryptine (9). Their structures were established from spectroscopic techniques, most notably 1D- and 2D-NMR, UV, IR, OR, circular dichroism (CD) spectra and LCMS-IT-TOF. (-)-Kunstleramide (1) exhibited very poor dose-dependent inhibition of DPPH activity, with an IC?? value of 179.5 ± 4.4 μg/mL, but showed a moderate cytotoxic effect on MTT assays of A375, A549, HT-29, PC-3 and WRL-68 with EC?? values of 64.65, 44.74, 55.94, 73.87 and 70.95 μg/mL, respectively.     

Dual MRI-SPECT agent for pH-mapping

A new dual MRI/SPECT pH-responsive agent where the SPECT active moiety acts as reporter of the concentration making it possible to exploit the responsiveness of the MRI probe.     

Non-convex self-dual Lagrangians: New variational principles of symmetric boundary value problems

We study the concept and the calculus of Non-convex self-dual (Nc-SD) Lagrangians and their derived vector fields which are associated to many partial differential equations and evolution systems. They indeed provide new representations and formulations for the superposition of convex functions and symmetric operators. They yield new variational resolutions for large class of Hamiltonian partial differential equations with variety of linear and nonlinear boundary conditions including many of the standard ones. This approach seems to offer several useful advantages: It associates to a boundary value problem several potential functions which can often be used with relative ease compared to other methods such as the use of Euler-Lagrange functions. These potential functions are quite flexible, and can be adapted to easily deal with both nonlinear and homogeneous boundary value problems. Additionally, in most cases the solutions generated using this new method have greater regularity than the solutions obtained using the standard Euler-Lagrange function. Perhaps most remarkable, however, are the permanence properties of Nc-SD Lagrangians; their calculus is relatively manageable, and their applications are quite broad.     

Common fixed point results for two new classes of hybrid pairs in symmetric spaces

Some common fixed point theorems due to Abbas and Khan [M. Abbas, A.R. Khan, Common fixed points of generalized contractive hybrid pairs in symmetric spaces, Fixed Point Theor. Appl. 2009 (2009) 11, Article ID 869407, doi:10.1155/2009/869407], and Abbas and Rhoades [M. Abbas, B.E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings defined on symmetric spaces, Pan. Amer. Math. J. 18 (1) (2008) 55-62] are proved for two new classes of hybrid pair of mappings which contain occasionally weakly compatible hybrid pairs as a proper subclass. Consequently, some results proved by Hussain et al. [N. Hussain, M.A. Khamsi, A. Latif, Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal. 74 (2011) 2133-2140], Bhatt et al. [A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal. 73 (2010) 176-182] and many others are extended to hybrid pair of mappings. Examples are also presented to support the concepts defined in the paper.