The numerical solution of problems in calculus of variation using Chebyshev finite difference method

The Chebyshev finite difference method is used for finding the solution of the ordinary differential equations which arise from problems of calculus of variations. Our approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference scheme. Some numerical results are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and yields very accurate results.     

A numerical method for one‐dimensional nonlinear Sine‐Gordon equation using collocation and radial basis functions

In this article, we propose a numerical scheme to solve the one‐dimensional undamped Sine‐Gordon equation using collocation points and approximating the solution using Thin Plate Splines (TPS) radial basis function (RBF). The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Mechanisms of amphipathic helical peptide denaturation by guanidinium chloride and urea: a molecular dynamics simulation study

Urea and GdmCl are widely used to denature proteins at high concentrations. Here, we used MD simulations to study the denaturation mechanisms of helical peptide in different concentrations of GdmCl and urea. It was found that the helical structure of the peptide in water simulation is disappeared after 5 ns while the helicity of the peptide is disappeared after 70 ns in 2 M urea and 25 ns in 1 M GdmCl. Surprisingly, this result shows that the helical structure in low concentration of denaturants is remained more with respect to that solvated in water. The present work strongly suggests that urea interact more preferentially to non-polar and aromatic side chains in 2 M urea; therefore, hydrophobic residues are in more favorable environment in 2 M urea. Our results also reveal that the hydrogen bonds between urea and the backbone is the dominant mechanism by which the peptide is destabilized in high concentration of urea. In 1 M and 2 M GdmCl, GdmCl molecules tend to engage in transient stacking interactions with aromatics and hydrophobic planar side chains that lead to displacement of water from the hydration surface, providing more favorable environment for them. This shows that accumulation of GdmCl around hydrophobic surfaces in 1 M and 2 M GdmCl solutions prevents proper solvation of the peptide at the beginning. In high GdmCl concentrations, water solvate the peptide better than 1 M and 2 M GdmCl. Therefore, our results strongly suggest that hydrogen bonds between water and the peptide are important factors in the destabilization of peptide in GdmCl solutions.     

One‐Pot Four‐Component Synthesis of N2‐Alkyl‐N3‐[2‐(1,3,4‐oxadiazol‐2‐yl)aryl]benzofuran‐2,3‐diamines

A simple synthesis of N²‐alkyl‐N³‐[2‐(1,3,4‐oxadiazol‐2‐yl)aryl]benzofuran‐2,3‐diamines 5 via a one‐pot four‐component reaction is described (Scheme 1). A mixture of N‐(isocyanoimino)triphenylphosphorane ( 1 ), a 2‐aminobenzoic acid 2 , a 2‐hydroxybenzaldehyde 3 , and an isocyanide 4 in absolute EtOH at room temperature undergoes a smooth reaction to afford 5 in excellent yields (Table).     

Synthesis of the novel pyrimido[1,6-a]pyrimidine and imidazo[1,2-c]pyrimidine derivatives based on heterocyclic ketene aminals

A concise and efficient route for the synthesis of pyrimido[1,6-a]pyrimidines and imidazo[1,2-c]pyrimidines by simply refluxing a reaction mixture of different heterocyclic ketene aminals and N,N′-bis(arylmethylidene)arylmethane was developed. This protocol provides an alternative method for application in combinatorial and parallel synthesis in drug discovery.     

Uranyl sensor based on a N,N′-bis(salicylidene)-2-hydroxy-phenylmethanediamine and multiwall carbon nanotube electrode

The electrochemical determination of uranyl was investigated by using carbon paste electrode modified with a Schiff base namely N,N??-bis(salicylidene)-2-hydroxy-phenylmethanediamine (SHPMD/CPE) and also in the presence of carbon nanotube (SHPMD/CNT/CPE). The both modified electrodes displayed an irreversible peak at E _pa?=?0.798?V versus Ag/AgCl. The electrocatalytic reduction of uranyl has been studied on SHPMD/CNT/CPE, using cyclic and differential pulse voltammetry, chronocoulometry and linear sweep techniques. Electrochemical parameters including the diffusion coefficient (D), the electron transfer coefficient (??), the ionic exchange current (i) and the redox reaction rate constant (K) were determined for the reduction of uranyl on the surface of the modified electrodes. Linear range concentration is 0.002?C0.6???mol?L^?1 and the detection limit of uranyl is 0.206?nmol?L^?1. The proposed method was used to detect uranyl in natural waters and good recovery was achieved.     

Catalytic hydrogenation with frustrated Lewis pairs: selectivity achieved by size-exclusion design of Lewis acids

Catalytic hydrogenation that utilizes frustrated Lewis pair (FLP) catalysts is a subject of growing interest because such catalysts offer a unique opportunity for the development of transition-metal-free hydrogenations. The aim of our recent efforts is to further increase the functional-group tolerance and chemoselectivity of FLP catalysts by means of size-exclusion catalyst design. Given that hydrogen molecule is the smallest molecule, our modified Lewis acids feature a highly shielded boron center that still allows the cleavage of the hydrogen but avoids undesirable FLP reactivity by simple physical constraint. As a result, greater latitude in substrate scope can be achieved, as exemplified by the chemoselective reduction of α,β-unsaturated imines, ketones, and quinolines. In addition to synthetic aspects, detailed NMR spectroscopic, DFT, and (2)H isotopic labeling studies were performed to gain further mechanistic insight into FLP hydrogenation.     

Influence of the water molecules (n?=?1–6) on the interaction between Li+, Na+, K+ cations and indole molecule as tryptophan amino acid residue

Influence of the addition of water molecules (n = 1–6) on the interaction energy between Li⁺, Na⁺, K⁺ cations and indole molecule as tryptophan amino acid residue is considered at MP2(FULL)/6-311++G(d,p)//B3LYP/6-311++G(d,p) levels of theory. The calculations suggest that the size of cation and the number of water molecules are two important factors that affect the interaction energy between the hydrated metal cation and indole molecule. The strength of cation–π interactions get substantially reduced when the metal ion is solvated or the size of metal cation increases. Quantum theory of atoms in molecules analysis of cation–π interaction indicates that there is a correlation between the electron density (ρ(r)) in the cage critical points generated upon complexation and the distance between metal cation and centroid of phenyl ring in indole molecule.     

Vlasov-kinetic computer simulations of electrostatic waves in dusty plasmas: an overview of recent results

We have performed calculations for collisions between fully stripped ions, C⁶⁺ and N⁷⁺, and atomic hydrogen, in both its ground and first excited energy levels. We have employed the Classical Trajectory Monte Carlo method to obtain total ionization and charge exchange cross sections and state selective charge exchange cross sections in the 5–500 keV/amu energy range.