Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.     

Complex homogeneous splines on the torus

We construct functions M_α which are piecewise homogeneous polynomials on the (d+1)-dimensional torus U^d+1. These functions possess complete symmetry with respect to the independent variables. The symmetry and homogeneous relations for these functions are exploited to obtain a recurrence relation and explicit representations. Furthermore, we show that , where ω=e^12x/k, 0≤j_t≤k−1, are linearly independent. By restricting M_α to U^d, we obtain the complex analogue of polynomial box splines on a (d+1)-direction mesh on U^d, which is a multivariate analogue of B-splines on the circle studied by I.J. Schoenberg^[8].     

A modified Tolman mass-energy formula

A modified Tolman mass (energy) formula is derived for spherically symmetric, time-independent systems. In the absence of surfaces of discontinuity, the modified formula has, in contradistinction to the original formula, the following desirable properties: (i) it always gives the correct mass of the system as a whole; (ii) it always gives the correct mass of any portion of the system which is surrounded by vacuum; and (iii) it remains invariant under a rescaling of the time coordinate of the formt Ct, C=constant. In the presence of surfaces of discontinuity the Tolman mass formula is further modified by the addition of the Israel mass associated with each surface. The resulting formula also has the above three properties. A new exact solution of Einstein's equations which is well behaved everywhere and is, in a sense, a generalization of Florides' new interior Schwarzschild solution is also presented.This result explains why, takingT ₁ ¹ =[C] in Section 2, we were able to obtain a solution free of surfaces of discontinuity.     

Index formulas for generalized Wiener-Hopf operators and boson-fermion correspondence in 2N dimensions

The kernels of operators associated with special chiral gauge transformations (kinks) in the 2N-dimensional Dirac theory are explicitly determined. The result is used to obtain index formulas for Fredholm operators corresponding to continuous chiral gauge transformations. Moreover, the Fock space quadratic forms corresponding to the kinks are proved to converge to the Dirac field as the kink size goes to zero. It is also shown that forN 1, 2(mod 4) the Majorana field can be reached in a similar fashion.Work supported by the Netherlands Organisation for the Advancement of Research (NWO)     

Inherent limitations in ectomography

Ectomography, a general tomographic method currently being implemented in nuclear medicine, is described. The object is viewed from different directions from the same projection angle, and the reconstruction process can be described as a two-dimensional filtered back-projection technique. One limitation of this limited-angle approach is that a three-dimensional Fourier representation of the acquired projections has a cone where data are missing. This empty cone can cause distortions in the tomogram by insufficient elimination of details outside the reconstructed tomographic section and by distortion of details in the section. The degree of distortion is dependent on the extension of the object in all directions and on the projection angle. Despite these limitations ectomography can be superior to single-photon-emission computed tomography for imaging sections that are close and parallel to the surface of the object, as in imaging of the hip joint or the heart.     

Crystal and molecular structure of 1R,3S,5S,7R,10R-3,6,6,10,14-Pentamethyltricyclo[10.3.0.05,7]pentadeca-11,14-diene-1, 10-dihydroxy-2,13-dione (Japodagrol), C20H28O4

A new cytotoxic macrocyclic diterpenoid named Japodagrol, C₂₀H₂₈O₄, has been isolated from the ornamental plantJatropha podagrica, family Euphorbiaceae, grown in Nigeria. The structure of the title compound, C₂₀H₂₈O₄, was solved by X-ray analysis.M _r =332.44, monoclinic space groupC2,a=23.285(4),b=6.5105(12),c=12.505(3) Å,=98.504(17),V=1874.8 ų,Z=4,D _c =1.178 Mg/m³. CuK radiation (graphite crystal monochromator, =1.54184 A), (CuK)=6.13 cm^–1,F(000)=720,T=290 K. Final conventionalR factor=0.035,R _w =0.038 for 3349 observed reflections. The structure was solved with the programDirdif. The 5-membered ring is closed to a half-chair form. The compound contains inter- and intramolecular hydrogen bonds.     

Slowly relaxing tunneling states in neutron-irradiated quartz: A study of the internal friction at audio-frequencies

The internal friction of two neutron-irradiated quartz samples was measured at audio-frequency as a function of temperature. This is an extension of acoustic measurements to much lower frequencies and thus to much longer time scales. A temperature independent behaviour has been observed and is discussed in the framework of the tunnelling model. One of the major assumptions of this model regarding the tunnelling states with long relaxation time could be verified for neutron-irradiated quartz.     

Formation of patchy surface overlayers alkali adsorption and alkali carbon monoxide and oxygen coadsorption on Ru (0001) and Ru(10\overline 1 0)

The retarding-potential and LEED methods are used for obtaining information about the structure and uniformity of alkali (K and CS) and alkali-coadsorbate (CO and O) layers on Ru(0001) and Ru surfaces at 300 K. It was established that for alkali layers on the anisotropic Ru surface and for mixed coadsorbate layer the shape of the retarding potential curves, used for the work function measurements, becomes anomalous which indicates coexistence of patches of different work function on the surface. LEED data on these patchy surfaces showed the formation of a variety of ordered structures depending on the coadsorbate coverages. On the basis of the existing theory a simple mathematical simulation was performed in an attempt to interpret the observed changes in the retarding potential curves. The possible changes of this curves, induced by the formation of patches with varying contribution to the total retarding potential signal and the advantage of the retarding field method for determination the uniformity of surface overlayers are discussed.     

Characterization of reaction products formed during thin-layer chromatographic detection of thiocarbamate herbicides

The reaction between thiocarbamate herbicides and 2,6-dichlorobenzoquinone-N-chloroimine or 2,6-dibromobenzoquinone-N-chloroimine is suitable for the detection of these herbicides on thin-layer plates with high sensitivity. The reactions were followed by infrared, nuclear magnetic resonance and mass spectrometry. We have established the formation of 2,6-dichlorobenzoquinone-S-alkyl sulphenylimines. In the case of the bromo-derivative, halogen exchange and substitution on the quinone ring took place simultaneously leading to the formation of mixed halogenated 2,6-dihalo- and, in addition, 2,3,6-trihalobenzoquinone-S-alkyl sulphenylimines. The final product of the detection reaction, i.e. 2,6-dichlorobenzoquinone-S-alkyl sulphenylimine was reacted with 2,6-dibromobenzoquinone-N-chloroimine where 2,6-dichloro-3-bromobenzoquinone-S-alkyl sulphenylimine formed as a consequence of the looser bromine-carbon linkage on the 2 and 6 positions of the quinone ring.     

Pseudo-cross-conjugated mesomeric betaines. 1. Synthesis of pseudo-cross-conjugated mesomeric betaines from quinoxaline derivatives

A new method for the synthesis of pseudo-cross-conjugated mesomeric betainic heterocyclic compounds with an angular nitrogen atom has been developed consisting in the reaction of 1,4-dielectrophile — -carbethoxy-2-(3-chloro)quinoxalylacetonitrile with azoles. Experimental regularities have been studied and a reaction mechanism has been proposed including the stage of formation of an ylide from a quaternary azolium salt. A pseudo-crossconjugated mesomeric betainic heterocyclic compound containing a thiazole ring compound has been synthesized for the first time.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1528–1533, November, 1992.