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.     

Nitrostyrene Derivatives of Adenosine 5′-Glutarates Modified with an Alkyl Spacer and their inhibitory activity on epidermal growth factor receptor protein tyrosine kinase

β-Nitrostyrene derivatives of adenosine 5′-glutarates are potent and selective bisubstrate-type inhibitors of the epidermal growth factor receptor protein tyrosine kinase (EGF-R PTK). In an attempt to improve the inhibitory activity, this type of compounds was modified with alkyl spacers of varying length between the nitrostyrene and the glutaryl units. The spacers consisted of 1, 3, 4, and 5 atoms to give compounds of the benzyl, oxyethyl, oxypropyl, and oxybutyl series, respectively (Schemes 1 and 2). Adenosine 5′-esters were prepared in the benzyl and oxypropyl series only. Compared to the compounds in the parent series without spacer (IC₅₀ = 0.7–12 μM ), most of the modified compounds inhibited the EGF-R PTK only marginally or were inactive (IC₅₀ ≥ 100 μM ). The only exceptions were the free acids 19 and 20 with IC₅₀ values of ca. 5 μM . It is noteworthy that esterification of these two hydrogen glutarates with either MeOH or adenosine yielded inactive compounds, which is in contrast to the corresponding substances without spacers.