Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation. This is applied to investigate homomorphisms between quasi-Banach algebras. The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300].     

Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs

In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first-order system and solved using existing Runge–Kutta method. The results clearly shown the advantage and the efficiency of the new method.     

A Positive Doubly Power Bounded Operator with a Nonpositive Inverse Exists on any Infinite-dimensional AL-Space

In this paper we construct a positive doubly power bounded operator with a nonpositive inverse on an AL-space.     

Spectroscopic studies of biologically active organotin(IV) derivatives of 2-[N-(2,4,6-tribromophenylamido]propanoic acid

Herein we describe the synthesis and characterization of compounds having the formulae R₂SnL₂ and R₃SnL, where R = Me, n-Bu, Ph and n-Oct and L = 2-[N-(2,4,6-tribromophenylamido]propanoic acid. All the complexes have been characterized by various spectroscopic methods (IR and ¹H, ¹³C, ¹¹⁹Sn NMR), elemental analysis, mass spectrometry and physical data. These compounds were also screened for their biological activity and found some encouraging results.     

1,1‐Organoboration of bis(trimethylstannyl)ethyne with trimethylsilyl‐ and dimethylsilyl‐dialkylboryl‐substituted alkenes: organometallic‐substituted allenes

The reactions of bis(trimethylstannyl)ethyne, Me₃Sn–C?C–SnMe₃ ( 4 ), with trimethylsilyl‐ or dimethylsilyl‐dialkylboryl‐substituted alkenes 1 – 3 afford organometallic‐substituted allenes 5 , 6 and 8 , 9 in high yield. In the case of (E)‐2‐trimethylsilyl‐3‐diethylboryl‐2‐pentene ( 1) , a butadiene derivative 7 could be detected as an intermediate prior to rearrangement into the allene. All reactions were monitored by ²⁹Si and ¹¹⁹Sn NMR, and the products were characterized by an extensive NMR data set (¹H, ¹¹B, ¹³C, ²⁹Si, ¹¹⁹Sn NMR). Copyright © 2003 John Wiley & Sons, Ltd.     

Group theory for tetraammineplatinum(II) withC 2v andC 4v point group in the non-rigid system

The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field of chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. We study the full non-rigid group (f-NRG) of tetraammineplatinum (II) with two separate symmetry groups C2v and C4v. We prove that they are groups of order 216 and 5184 with 27 and 45 conjugacy classes, respectively. Also, we will compute the character tables of these groups.     

Ca(NO3)2•4H2O-catalysed Biginelli Reaction: One-pot Synthesis of 1,2,3,4-Tetrahydropyrimidin-2-ones/pyrimidine-2-thiones under Solvent-free Conditions

The synthesis of 1,2,3,4-dihydropyrimidinone/thione derivatives was achieved in good to excellent yields using calcium(II) nitrate as catalyst to promote the Biginelli three-component condensation reaction from a diversity of aromatic aldehydes, β-keto compounds and urea or thiourea. The reaction was carried out under solvent-free conditions.