An ?-uniform hybrid scheme for singularly perturbed delay differential equations

In this paper, a singularly perturbed delay differential equation of first order has been considered. The problem is solved by using a hybrid scheme on a Shishkin mesh. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Truncation errors are obtained. Finally, numerical experiments are carried out on a test problem, confirming the effectiveness of the proposed technique.     

A theoretical study on structural, spectroscopic and energetic properties of acetamide clusters [CH3CONH2] (n=1-15)

Insights into the formation of hydrogen bonded clusters are of outstanding importance and quantum chemical calculations play a pivotal role in achieving this understanding. Structure and energetic comparison of linear, circular and standard forms of (acetamide)(n) clusters (n = 1-15) at the B3LYP/D95** level of theory including empirical dispersion correction reveals significant cooperativity of hydrogen bonding and size dependent structural preference. A substantial amount of impact of BSSE is observed in these calculations as the cluster size increases irrespective of the kind of arrangement. The interaction energy per monomer increases from dimer to 15mer by 90% in the case of the circular arrangement, by 76% in the case of the linear arrangement and by 34% in the case of the standard arrangement respectively. The cooperativity in hydrogen bonding is also manifested by a regular decrease in average OH and C-N bond distances, while average C=O and N-H bond lengths increase with increasing cluster size. Atoms-In-Molecules (AIM) analysis is used to characterize the nature of hydrogen bonding between the acetamide molecules in the cluster on the basis of electron density (ρ) values obtained at the bond critical point. An analysis of N-H bond stretching frequencies as a function of the cluster size shows a marked red shift as the cluster size increases from 1 to 15.     

Orlicz Figà – Talamanca Herz algebras and invariant means

The aim of this paper is to initiate a systematic study of the Orlicz Figà – Talamanca Herz algebras on locally compact groups. We also introduce and study invariant means on the dual of these algebras.     

Two-step single-colour photoionization spectroscopy of atomic uranium

The single-colour photoionization spectrum of atomic uranium is recorded in the spectral region from 366 to 371 nm. Most of the 43 observed resonances are found to be associated with the two-step photoionization process. Based on known energy levels seven new transitions have been proposed. Three of these transitions originate either from the ground state or the lowest metastable state at 620 cm^–1.     

Die konzentrisch gefÄrbten Ringe der Runkelrübe und das Liesegang-PhÄnomen

Ohne Zusammenfassung Deutsch von K. Popp (Leipzig).     

Study of levels in51Cr through51V (p,nγ) reaction

The low lying levels in⁵¹Cr have been populated by⁵¹V (p, ny)⁵¹Cr reaction. The angular distribution of the ground state electromagnetic transitions from 1165, 1353, 1479 and 1557 keV states have been measured. The results are compared with the Hauser-Feshbach model of the statistical theory of nuclear reactions. The spins for the levels at 1165, 1479 and 1557 keV are shown to be 9/2^?, 11/2^? and 5/2^? respectively.     

Triphenylmethyl hexafluoroarsinate-initiated polymerization of 1,2-butylene oxide

The polymerization of 1,2-butylene oxide initiated with triphenylmethyl hexafluoroarsinate in the ?20 to +25°C temperature range with 1,2-dichloroethane as solvent is characterized by a rapid nonstationary initial stage. This is followed by a second slower stage, during which the disappearance of monomer is first-order with respect to its concentration. The conversion of monomer at the end of the first stage is related to the initial catalyst concentration but not to the initial monomer concentration. Invoking the hypothesis of an instantaneous initiation reaction, the experimental results lead to the conclusion of the existence of a unimolecular termination step. Propagation-to-termination rate constant ratios yield a propagation–termination activation energy difference of 5.9 kcal/mole. The termination step proposed is thought to involve the formation of stable macrocyclic oxonium ions. These, in turn, can reactivate the polymerization by an intramolecular reaction leading to the formation of new active centers. An energy of activation of 8.7 kcal/mole was calculated for this reactivation. GPC analyses of the reaction products recovered at the end of the first stage revealed the presence of large proportions of oligomers. Based on kinetic data, the formation of oligomers is explained by a backbiting process similar to the reactivation reaction suggested for the initiation of the second stage.     

Static and time-dependent solutions of Einstein-Maxwell-Yukawa fields

An exact solution of Einstein-Maxwell-Yukawa field equations has been obtained in a space-time with a static metric. A critical analysis reveals that the results previously obtained by Patel [9], Singh [10], and Taub [11] are particular cases of our solution. The singular behavior of the solutions has also been discussed in this paper. Further, extending the technique developed by Janis et al. [12], for static fields, to the case of nonstatic fields, an exact time-dependent axially symmetric solution of EMY fields has been obtained. Our solution in the nonstatic case is nonsingular in the sense of Bonnor [15] and presents a generalization of the results obtained by Misra [7] to the case when a zero-mass scalar field coexists with a source free electromagnetic field.