Adaptive methods for periodic initial value problems of second order differential equations

In this paper numerical methods involving higher order derivatives for the solution of periodic initial value problems of second order differential equations are derived. The methods depend upon a parameter p > 0 and reduce to their classical counter parts as p → 0. The methods are periodically stable when the parameter p is chosen as the square of the frequency of the linear homogeneous equation. The numerical methods involving derivatives of order up to 2q are of polynomial order 2q and trigonometric order one. Numerical results are presented for both the linear and nonlinear problems. The applicability of implicit adaptive methods to linear systems is illustrated.     

Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations

The authors investigated the asymptotic joint distributions of certain functions of the eigenvalues of the sample covariance matrix, correlation matrix, and canonical correlation matrix in nonnull situations when the population eigenvalues have multiplicities. These results are derived without assuming that the underlying distribution is multivariate normal. In obtaining these expressions, Edgeworth type expansions were used.     

P-stable methods for periodic initial value problems of second order differential equations

A class ofP-stable finite difference methods is discussed for solving initial value problems of second order differential equations which have periodic solutions. The methods depend upon a parameterp>0, and reduce to the classical Störmer-Cowell methods forp=0. It is shown that whenp is chosen for linear problems as the square of the frequency of the periodic solution, the methods areP-stable and for some suitable choice ofp, they have extended finite interval of periodicity.     

A remarkably simple N-formylation of anilines using polyethylene glycol

N-Formylation of anilines has efficiently been carried out at room temperature in excellent yields by treatment with formic acid in polyethylene glycol (PEG-400). No additional solvent and catalyst are required.     

Wacker-type oxidative functionalization of β-substituted unsaturated sulfoxides

The Wacker-type oxidation is an important procedure catalyzed by palladium complexes. A mild and general method for the preparation of β-substituted-δ-oxosulfoxides from the corresponding β-substituted-γ,δ-unsaturated sulfoxides is described. The products are versatile synthetic intermediates for the preparation of syn- and anti-1,3-diol and 1,3-aminoalcohol derivatives.     

Improved Nafion-based amperometric sensor for hydrogen in argon

An improved polymer electrolyte membrane fuel cell-based amperometric hydrogen sensor has been developed. The sensor operates at room temperature, and the electrolyte used in the sensor is Nafion which is a proton-conducting solid polymer electrolyte. Platinum black is used as both anode and cathode. The sensor functions as a fuel cell, H₂/Pt//Nafion//Pt/O₂, and a mechanical barrier limits the supply of hydrogen to the sensing side electrode. The limiting current is found to be linearly related to the hydrogen concentration. The sensor can be used to measure hydrogen in argon in parts per million and percentage levels. The basic principle, details of assembly, and response behavior of the sensor are discussed.     

Base-Catalyzed Synthesis of Spiropyrazoloaminonitriles with Arylidene Pyrazolone and Vinylogous Malononitriles through a Cascade Michael Addition and Cyclization

Synthesis of title compounds were accomplished by a reaction of vinyl malononitriles and arylidene pyrazolones catalyzed by base. This protocol proceeds via Michael addition followed by intramolecular cyclization leading to the formation of two new C−C bonds. Further the same reaction was also conducted with α,α-dicyano olefins and vinyl malononitriles to furnish 1,6-dihydro biphenyl compounds. Simple reaction conditions, high yields and compatibility are the advantages of this protocol.     

A simple one pot synthesis of novel tricyclic quinazolinones

Synthesis of a series of tricyclic quinazolinones have been accomplished starting from anthranilamide and 1,3-cyclic dione promoted by TsOH·H₂O The protocol presented herein based on retro-Dieckmann type reaction, leading to incorporation of dione as an acyclic unit into the product. Simple reaction conditions, broad scope, excellent yields are the advantages of this protocol. Further, this methodology is extended to the synthesis of pyridopyrimidinones and benzimidazopyridines.     

One‐Pot Three‐Component Synthesis of Pyrazolyl‐thiadiazinyl‐2H‐chromen‐2‐one Derivatives

An efficient novel one‐pot synthesis of pyrazolyl‐thiadiazinyl‐2H‐chromen‐2‐ones. In this process, an equimolar mixture of substituted 3‐(2‐bromoacetyl)‐2H‐chromen‐2‐ones, thiocarbohydrazide and pentane‐2,4‐dione were taken in absolute ethanol. All these synthesized compounds were characterized by their analytical and spectral data.