On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem

Analytical solutions for the Cahn-Hilliard initial value problem are obtained through an application of the homotopy analysis method. While there exist numerical results in the literature for the Cahn-Hilliard equation, a nonlinear partial differential equation, the present results are completely analytical. In order to obtain accurate approximate analytical solutions, we consider multiple auxiliary linear operators, in order to find the best operator which permits accuracy after relatively few terms are calculated. We also select the convergence control parameter optimally, through the construction of an optimal control problem for the minimization of the accumulated L ²-norm of the residual errors. In this way, we obtain optimal homotopy analysis solutions for this complicated nonlinear initial value problem. A variety of initial conditions are selected, in order to fully demonstrate the range of solutions possible.     

Performance of columns packed with the new shell particles,Kinetex-C18

The performance of the new Kinetex-C₁₈ column was investigated. Packed with a new brand of porous shell particles, this column has an outstanding efficiency. Once corrected for the contribution of the instrument extra column volume, the minimum values of the reduced plate heights for a number of low molecular weight compounds (e.g., anthracene and naphtho[2,3-a]pyrene) were between 1.0 and 1.3, breaking the legendary record set 3 years ago by Halo-C₁₈ packed columns. The liquid-solid mass transfer of proteins (e.g., insulin and lyzozyme) is exceptionally fast on Kinetex-C₁₈ much faster than on the Halo-C₁₈ column. The different contributions of dispersion and mass transfer resistances to the column efficiency were determined and discussed. The possible reasons for this extremely high column efficiency are discussed.     

Application of a process friendly morpholine synthesis to (S,S)-Reboxetine

We report our results on the construction of a morpholine ring system from the corresponding epoxide and amino alcohol. From this study, we were able to convert a previous four-step synthesis into a more efficient two-step process.     

Synthesis of alkylpyrroles by use of a vinamidinium salt

The synthesis of alkyl-substituted 2-pyrrolecarboxylate esters has been accomplished by the condensation reaction of a symmetrical vinamidinium salt and glycine ester derivatives.     

Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: <Emphasis Type="Italic">SU</Emphasis>(3)

We complete the computation of spectral measures for SU(3) nimrep graphs arising in subfactor theory, namely the SU(3) ADE{SU(3) \mathcal{ADE}} graphs associated with SU(3) modular invariants and the McKay graphs of finite subgroups of SU(3). For the SU(2) graphs the spectral measures distill onto very special subsets of the semicircle/circle, whilst for the SU(3) graphs the spectral measures distill onto very special subsets of the discoid/torus. The theory of nimreps allows us to compute these measures precisely. We have previously determined spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with all SU(2) modular invariants, all subgroups of SU(2), the torus \mathbbT², SU(3){\mathbb{T}^2,\,SU(3)}, and some SU(3) graphs.     

Numerical study of vortex effects in superconducting microstrip lines

A high transition temperature superconducting microstrip structure is modeled using the theoretical approach developed by Coffey and Clem for elucidating the vortex effects in propagation. Impedance type Green’s functions are derived for the electric field around the strip and the propagation characteristics are computed for a wide range of applied field, reduced temperature and superconducting strip thickness in a Galerkin procedure. The increase of static field and temperature result in increased vortex motion, which in turn, causes a corresponding change in the propagation characteristics of the transmission line. Numerical results are presented for propagation parameters and quality factor.     

Solution of Some Structural Analysis Problems by Orthogonal Collocation

Abstract

Application of the method of orthogonal collocation to boundary value problems in structural and applied mechanics is investigated. Typical boundary value problems, such as the torsion of rectangular bars and the bending of plates, are employed as illustrative examples. Simplicity in application and good accuracy of orthogonal collocation are demonstrated by the solution of such complex problems as the large deflection analysis of rectangular isotropic, orthotropic, and sandwich plates. Results are compared wherever possible with existing solutions based on much more laborious and lengthy methods of computation. Excellent agreements are obtained.     

Copper(II) tetrafluroborate-promoted Meinwald rearrangement reactions of epoxides

Epoxides undergo a highly efficient Meinwald rearrangement in the presence of catalytic quantities of copper(II) tetrafluoroborate to give carbonyl compounds in high yields and with excellent selectivity. The low toxicity and ease of handling of this reagent make it an attractive alternative to the more corrosive or costly Lewis acids frequently employed.     

Photolysis of benzoyl esters of 2,2′-dinitrodiphenylcarbinols in neutral and basic media

The photolysis of 2,2′-dinitrodiphenylmethylbenzoates (1a–1d) in 2-propanol gives dibenzo-[c, f]-[1,2]diazepin-11-one-oxides (5a–5d) as the major product. Dibenzo[c, f]-[1,2]diazepin-11-ones (2a–2d), 2,2′-dinitrobenzophenones (3a–3d), 2-amino-2′-nitrobenzophenones (4a–4d) and N-hydroxyacridones (6a–6d) are also formed in the reaction. When the irradiation is carried out in benzene, 3-(2′-nitrophenyl)-2,1-benzisoxazoles (7a–7d) are also obtained together with the above products.     

Die Bestimmung von Cumarin und Melilots?ure

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