Synthesis,spectral, theoretical studies and in vitro antimicrobial activities of novel diphenyltin(IV) complexes of Schiff bases derived from phenacylamine

A series of new diphenyltin(IV) complexes of the type Ph₂SnL (L¹: N‐phenacyl‐5‐bromosalicylideneimine, Ph₂SnL¹; L²: N‐phenacyl‐3,5‐dichlorosalicylideneimine, Ph₂SnL²; L³: N–phenacyl‐4‐methoxysalicylideneimine, Ph₂SnL³) were synthesized and characterized by elemental analysis, IR, ¹H, ¹³C, ¹¹⁹Sn NMR spectroscopy and mass spectrometry techniques. The C―Sn―C angles in the complexes were calculated using equations with the ¹J(^117/119Sn―¹³C) values from ¹³C NMR spectra. The possible structures, NMR and electronic properties of the studied molecules were calculated through density functional theory and results compared with experimental data. All the complexes were found to be mildly active against several microorganisms and some fungi. Copyright © 2014 John Wiley & Sons, Ltd.     

Mathematical analysis and numerical simulations for the HSP70 synthesis model

The heat shock proteins (HSPs) protect the other proteins in the process of folding under stressful conditions such as oxygen deprivation, hypothermy or presence of alcohol. They have also an important role in tumour invasion. In this paper, the existence, uniqueness and permanence properties for the solution of the mathematical model which focuses on the synthesis of HSP70 is proved. Moreover the numerical simulations are performed by using FDM, namely a combination of backward and forward Euler methods, and the results confirm the expected behaviour of the solution.     

The Combination of Cross-Hyperconjugation and σ-Conjugation in 2,5-Oligosilanyl Substituted Siloles

Reaction of a 2,5-dilithiated silole with excess dichlorodimethylsilane gives the respective 2,5-bis(chlorodimethylsilyl) substituted silole. This compound can be converted to 2,5-bis(oligosilanyl) substituted siloles by addition of a suitable oligosilanide. In the UV spectra of the thus obtained compounds the lowest energy absorptions are bathochromically shifted compared to the absorptions of the two constituents, namely the 2,5-disilyl substituted silole and a trisilane. The bathochromic shift is interpreted as being caused by a mixed σ-conjugation/cross-hyperconjugation. This assumption is supported by TD-DFT calculations, which show a significant contribution from Si−Si bonds to the HOMO of the molecule.     

Computation of the 3-D Unsteady Flow Past Deforming Geometries

A 3-D incompressible unsteady flow solver based on simple finite elements with adaptive remeshing and grid movement for both moving and deforming surfaces is described. We demonstrate the combination of adaptive remeshing techniques with the incompressible flow solver with the computation of flow past an eel in 2-D and a blue-fin tuna in 3-D. The flow past a swimming tuna was computed for two extreme cases of the caudal fin frequency and swimming speed. A grid refinement study was performed and a grid converged solution for the force produced by the caudal fin was obtained.     

Oscillation analysis of neutral difference equations with delays

In this paper, we obtain some oscillation criteria for a class of neutral difference equations with time delays. We also investigate the behavior of the eventually positive solutions of these equations. To verify our results we give various numerical simulations by using the MATLAB programming.     

B-spline solution of non-linear singular boundary value problems arising in physiology

We use B-spline functions to develop a numerical method for computing approximations to the solution of non-linear singular boundary value problems associated with physiology science. The original differential equation is modified at singular point then the boundary value problem is treated by using B-spline approximation. The numerical method is tested for its efficiency by considering three model problems from physiology.     

There are 1,132,835,421,602,062,347 nonisomorphic one‐factorizations of K14

We establish by means of a computer search that a complete graph on 14 vertices has 98,758,655,816,833,727,741,338,583,040 distinct and 1,132,835,421,602,062,347 nonisomorphic one‐factorizations. The enumeration is constructive for the 10,305,262,573 isomorphism classes that admit a nontrivial automorphism. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 147–159, 2009     

On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms

We define a twisted two complex variables Rankin-Selberg convolution of Siegel cusp forms of degree 2. We find its group of functional equations and prove its analytic continuation to . As an application we obtain a non-vanishing result for special values of the Fourier Jacobi coefficients. We also prove the analytic properties for the characteristic twists of convolutions of Jacobi cusp forms. Research Supported by Fondecyt grants 1061147, 7060241.