A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

Summary Consider the solution of one-dimensional linear initial-boundary value problems by a finite element method of lines using a piecewiseP ^th -degree polynomial basis. A posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep+1 that vanish at element ends. Error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error. Computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are, furthermore, applicable in situations that are not supported by the analysis.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 90-0194; by the U.S. Army Research Office under Contract Number DAAL03-91-G-0215; and by the National Science Foundation under Institutional Infrastructure Grant Number CDA-8805910     

A new approach to the synthesis of 16-heteroprostanoids via isoxazole intermediates

Translated from Khimiya Geterotsiklicheskikh Soedinenii. Vol. 30. No. 3, pp. 424–425, March, 1994.     

Rearragnement of 1-allyloxy-2-allylthio-4-methyl-benzene TO 2,4-dimethyl-6-allyl-7 hydroxy-2,3-dihydrobenzothiophene

1-Allyloxy-2-allylthio-4-methylbenzene rearranges in NN-diethylaniline at 215°C with migration of allyloxy and allylthio groups to form 2,4-dimethyl-6-allyl-7-hydroxy-2,3dihydrobenzothiophene.M. V. Lomonosov State University, Moscow 119899. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 480–482, 1994. Original article submitted March 5, 1994.     

Aziridinylketones and their cyclic anils. 12

We have measured the PMR spectra of 5, 7-diaryl-1, 4-diazabicyclo[4. ].O]hept-4-enes. We have studied the structure of the 5-(4-nitrophenyl)-7-phenyl derivative by x-ray diffraction. We show that the six-membered heterocycle has the half-chair form. The 6-H and 7-H protons of the aziridine ring are trans, while the 7-aryl is exo relative to the six-membered ring. Introduction of substituents into the aromatic ring has practically no effect on the geometry of the bicycle.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1117–1124, August, 1994.For Communication 11, see [1].     

Hydroxyl-containing mesogens. Synthesis and liquid-crystalline properties of 2-o-hydroxyarylpyrimidines

We have synthesized 5-alkyl(alkoxy)-2-(o-lzydroxy-p-alkoxyphenyl)pyrimidines and considered the effect of the OH group on the inesomorphism. We have found that in binuclear o-hydroxyarylpyrimidines, an ortho OH group forming an intramolecular hydrogen bond increases T_mp, inhibits the appearance of nematic properties, and promotes the appearance of a smectic A.Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 30, No. 1, pp. 90–92, January, 1994.     

Reversed phase behaviour of high molecular mass polystyrenes in ethyl acetate solvent mixtures

Chromatographia - The reversed phase behaviour of high molecular mass polystyrenes was investigated on C18 bonded phase columns with ethyl acetate-methanol and ethyl acetateacetonitrile mobile...     

Separation of 23 dansylated amino acids by micellar electrokinetic chromatography at low temperature

Summary The baseline separation of 23 dansylated amino acids (including 3 didansylated species) is reported. Lowering of the analysis temperature and fine control of the surfactant concentration were essential in obtaining this result. Calibration graphs with good linearity were obtained.     

Theory of relaxed density matrices: Application to second-order response properties

The evaluation of second derivatives of the electronic energy for nonvariational wave functions using an energy functional is discussed. It is shown that, in certain cases, the formation of the first-order relaxed density matrix leads to an efficient algorithm for the calculation of second-order response properties. Detailed formulas are given for second-order Møller–Plesset perturbation theory. © 1994 John Wiley & Sons, Inc.