Poisson structure of a periodic classical XYZ -chain

Classical variables ( -variables) are constructed for a periodic classical XYZ -chain (of the discrete Landau-Lifshitz equation). The connection of the quantum method of the inverse problem and the theory of finite-zone integration is discussed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 150, pp. 154–180, 1986.     

Disorder arising from the location of enantiomers in a twist-boat structure: 2,6-trans-2,4,6-tris(trichloromethyl)-1-oxa-3,5-dithian

Crystals of the title compound are orthorhombic, Pca2₁;a=27.586(4),b=10.509(3),c=11.080(2) Å,V=3212(1) ų,Z=8. The structure was solved by direct methods, from data collected at room temperature on an Enraf-Nonius CAD4 diffractometer, and refined by full-matrix least squares to a finalR value of 0.055 using 2043 reflections. One of the two independent molecules in the asymmetric unit is disordered. The disorder is manifested mainly between the oxygen atom and one sulfur atom and is caused by opposite enantiomers occupying corresponding positions in different unit cells. The endocyclic torsion angles in both independent molecules are very similar but the disposition of the heteroatoms on the twist-boat framework is different in the two molecules. Site occupancy of the two models on this framework in the disordered molecule is in the ratio 2179 with the smaller proportion being very similar to the ordered molecule and the remainder similar to that found in the normal molecule oftrans-4-chloro-2,4,6-tris(trichloromethyl)-1-oxa-3,5-dithian (Irving and Irving, 1988).     

Corrections for nonuniform sampling distortions in magnetic resonance imagery

A technique for estimating and correcting nonuniform sampling distortions in magnetic resonance imagery is presented. The technique consists of first estimating the sampling grid distortion using a parametric model, and then estimating the uniformly sampled data by interpolation on the nonuniform grid. Parameterized models for two particular sampling grid distortion are presented. Maximum likelihood and maximum a posteriori estimators are developed for these distortions. Using computer simulated data, these estimators are shown to perform well.     

Pharmacokinetics of anthracycline antibiotics deposited by polymers

An increase of doxorubicin concentration in different organs and tissues and its decrease in the peripheral blood were observed when studying pharmacokinetics of this drug administered in the 10% solution of polyvinylpyrrolidone. A prolonged and stable release of carminomycin from glue composition MK-10-0 "carminacryl" confirms an expediency of alpha-cyanoacrylate use for deposition of anthracycline antibiotics with the aim of loco-regional chemotherapy.     

Estimating the 3D skeletons and transverse areas of coronary arteries from biplane angiograms

A method for estimating the three-dimensional (3D) skeletons and transverse areas of the lumens of coronary arteries from digital X-ray angiograms is described. The method is based on the use of a 3D generalized cylinder (GC) consisting of a series of 3D elliptical disks transverse to and centered on a 3D skeleton (medial axis) of the coronary arteries. The estimates of the transverse areas are based on a nonlinear least-squares-error estimation technique described by D.W. Marquardt (1963). This method exploits densitometric profiles, boundary estimates, and the orientation of the arterial skeleton in 3-space and includes an automatic artery tracking procedure. It applies an adaptive window to the densitometric profile data that are used in the parameter estimation. Preliminary experimental tests of the procedure on angiograms of in vivo human coronaries and on synthetic images yield encouraging results.     

Fourier Transform Spectrometer for the 1 to 10mm region

A Fourier Transform Spectrometer using a 250 Watt Mercury lamp, a lamellar grating and a pumped He-cooled detector is applied to the millimeter wave spectral region. The pure rotation spectrum of CH₂F, the transmission of graphite particles in a cloud chamber, the interference on round copper dots and the absorption of iron whiskers have been observed.     

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.     

Invariant submanifolds and properCR foliations on a para-coKählerian manifold with concircular structure vector field

After recalling the basic properties of para-coKählerian manifolds \(\tilde M\) with concircular structure vector field ξ, the infinitesimal auto morphismsX of the structure 1-form \(\tilde \eta \) are considered. One of the results is that the Lie derivative of all powers of the structure 2-form \(\tilde \Omega ,\) i.e. \(\mathcal{L}x\tilde \Omega ^p ;p = 1,...,m,\) is exterior recurrent. Further two types of horizontal distributionsD _n which are normal to ξ. IfD _t (resp.D _n ) is involutive, the corresponding leafM _t (resp.M _n ) is a minimal submanifold of \(\tilde M\) . FurtherM _n is a symplectic submanifold and ξ is an umbilical normal section ofM _n . Finally proper immersion \(M \to \tilde M\) are discussed, whereM is aCR-sub-manifold whose horizontal distribution isD _t . It is shown that the vertical distribution is involutive, and the restriction of ξ toM is an symptotic direction. Some interesting special cases are treated.     

Forces of a fluid in a rotating straight pipe

The fluid flow through a rotating straight pipe is considered, the axis of rotation being perpendicular to the pipe axis. The flow of the fluid is taken as fully developed, i.e. the velocity field is assumed to be the same in all transverse cross sections of the pipe. The derivation presented applies to viscous and nonviscous incompressible fluids. For constant angular pipe velocity a simple and exact (Coriolis type) relationF=2Q(t) is derived between the forceF by which the fluid acts on the (unit length of the) pipe in the direction perpendicular to the two axes, the fluid mass flow rateQ(t) through the pipe, and the angular velocity. Variable angular velocities, i.e. , introduce an additional term into the expression for the inertial forceF, which depends only on and on known (constant) parameters; this term is known for given angular velocity(t). The flow configuration investigated here is an idealization of those appearing (over short space and time intervals) in the devices measuring mass flow rateQ(t) through the (Coriolis) forceF. Therefore the exact results derived here cast some light on the degree of precision one expects in these devices, where more complicated flow configurations are present than those looked at in this paper.     

On the contact dimensions of graphs

Every simple graphG=(V, E) can be represented by a family of equal nonoverlapping spheres {S _v :v V} in a Euclidean spaceR ⁿ in such a way thatuv E if and only ifS _u andS _v touch each other. The smallest dimensionn needed to representG in such a way is called the contact dimension ofG and it is denoted by cd(G). We prove that (1) cd(T)<(7.3) log |T| for every treeT, and (2)