C 1 Quintic Splines on Type-4 Tetrahedral Partitions

Starting with a partition of a rectangular box into subboxes, it is shown how to construct a natural tetrahedral (type-4) partition and associated trivariate C ¹ quintic polynomial spline spaces with a variety of useful properties, including stable local bases and full approximation power. It is also shown how the spaces can be used to solve certain Hermite and Lagrange interpolation problems.     

The fixed point property in ordered sets of width two

We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.     

Four modes competition and chaos in a shell

Steady-state chaotic vibrations of a shallow shell as a system with a nonsymmetrical restoring force and one equilibrium state are considered. Mode interaction and its effect on a chaotic behavior of the shell is studied. The terms "natural" and "imposed" chaos are introduced for the response of resonant and nonresonant modes. It is shown that such a qualitative difference is important for better understanding of chaos in systems with distributed parameters, and may be very useful for numerical investigations. Some qualitative comparisons with previous papers on chaos in distributed mechanical systems are also made. (c) 1994 American Institute of Physics.     

Hopanoids of methylotropic acetobacteria

Squalene, 35-methoxyho-6-ene-32R,33R,34S-triol, hop-22(29)-ene, and hopan-22-ol have been isolated fromAcetobacter sp. VSB 917. The structures of the substances isolated and of the 35-methoxyhop-6-ene-32R,33R,34S-triol triacetate obtained have been established by IR, mass, and¹H and¹³C NMR spectroscopies.Vitaminy Scientific-Production Association, Moscow. Translated from Khimiya Prirodnykh Soedinenii, Nos. 3,4, pp. 367–372, May–August, 1992.     

Assignments of carbon NMR resonances for microcrystalline ubiquitin

Solid-state NMR 2D spectroscopy was used to correlate carbon backbone and side-chain chemical shifts for uniformly (13)C,(15)N-enriched microcrystalline ubiquitin. High applied field strengths, 800 MHz for protons, moderate proton decoupling fields, 80-100 kHz, and high magic angle sample spinning frequencies, 20 kHz, were used to narrow the most of the carbon line widths to 0.5-0.8 ppm. Homonuclear magnetization transfer was effected by matching the proton RF field to the spinning frequency, the so-called dipolar-assisted rotational resonance (DARR) (Takegoshi, K.; Nakamura, S.; Terao, T. Chem. Phys. Lett. 2001, 344, 631-637), and a mixing time of 20 ms was used to maximize the intensity of one-bond transfers between carbon atoms. This polarization transfer sequence resulted in roughly 14% transfer efficiencies for directly bonded carbon pairs and 4% transfer efficiencies for carbons separated by a third carbon. With this simple procedure, the majority of the one-bond correlations was observed with moderate transfer efficiencies, and many two-bond correlations were also observed with weaker intensities. Spin systems could be identified for more than half of the amino acid side chains, and site-specific assignments were readily possible via comparison with 400 MHz (15)N-(13)C-(13)C correlation spectroscopy (described separately).     

Study of the inversion of 4-benzamido-3-hydroxythiophane

Inversion during the acid hydrolysis of trans-4-benzamido-3-hydroxythiophane is accomplished through the intermediate formation of cis-2-phenyltetrahydrothieno[3,4-d]oxazoline. The latter has cis ring fusion, and the oxazoline ring is planar. Opening of the oxazoline ring is not accompanied by inversion and leads to cis-3,4-substituted thiophanes. Migration of the acyl group from the nitrogen to the oxygen atom was detected in substituted thiophanes.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No.10, pp. 1339–1344, October, 1971.     

Sepaconitine — A new alkaloid from Aconitum septentrionale

The structure of a new alkaloid sepaconitine isolated from the epigeal part ofAconitum septentrionale has been established on the basis of spectral characteristics.     

Syntheses of di- and tetrahydropyrroles

The constants and thermodynamic parameters of the ring-chain tautomeric equilibrium of p-substituted (benzene ring) 2,3,3-trimethyl-1-aryl-2-hydroxy-5-pyrrolidones in aqueous pyridine solution were determined by PMR spectroscopy. Conversion of the ring tautomer to the open form is accompanied by an increase in the enthalpy and entropy. The AH value decreases by a factor of 2.8 kcal/mole on passing from electron-donor substituents to electron-acceptor substituants, whereas the AS value remains approximately constant and decreases by 2–4 eu only for strong electron acceptors (COOCH₃, CN, and NO₂). The correlation between the free energies and the a substituent constants in the benzene ring is discussed.See [1] for communication XII.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 634–638, May, 1977.