The Jump of the Laplacian on a Submanifold

Assume that a submanifold M ? ?ⁿ of an arbitrary codimension k ? {1, …, n} is closed in some open set O→?ⁿ. With a given function u ? C²(O\M) we may associate its trivial extension u: O→? such that u|_O\M=u and u|m ≡ 0. The jump of the Laplacian of the function u on the submanifold M is defined by the distribution Δu — Δu. By applying some general version of the Fubini theorem to the nonlinear projection onto M we obtain the formula for the jump of the Laplacian (Theorem 2.2).     

High-spin structure in 169W and 170W

High-spin states in ^{169, 170}W have been populated in ${}^{154}\text{Gd}\text{(}{}^{20}\text{Ne}\text{, x}\text{n}\text{)}$ reactions. In-beam γ-ray spectroscopic techniques with multi-detector set-ups, multiplicity filters and an anti-Compton shield have been used. Levels up to about spin 30 (tentatively up to 36) in ¹⁷⁰W and up to $\text{57}\text{2}$ (tentatively up to $\text{61}\text{2}$) in ¹⁶⁹W have been identified. The data are interpreted within the framework of a pairing-selfconsistent cranking model. The nuclear shape evolution with increasing spin is studied theoretically within a configuration-controlled shell correction approach and also pairing effects are studied. The behaviour of the yrast states around 28⁺ in ¹⁷⁰W can be related in a model-dependent way to a reduction of the neutron-pairing correlations.     

The effect of DNA phase structure on DNA walks

We have performed several kinds of DNA walks which often are the first steps for further analysis of DNA structure and long range correlations. The DNA walks analysing frequency of G+C versus A+T cannot indicate the coding strand while purine versus pyrimidine DNA walks or two-dimensional (A-T,G-C) DNA walks in some instances can indicate the coding strand but cannot resolve the coding frame. The modified two-dimensional (A-T,G-C) DNA walks respecting the three-nucleotide codon structure show very high correlation in nucleotide composition of DNA coding sequences. They can distinguish between coding and non-coding sequences and indicate the strand and the phase in which DNA is coding. Received: 8 January 1998 / Received in final form and Accepted: 28 January 1998     

High-nuclearity close-packed palladium-nickel carbonyl phosphine clusters: heteropalladium

[Pd(16)Ni(4)(CO)(22)(PPh(3))(4)](2)(-) (1) and [Pd(33)Ni(9)(CO)(41)(PPh(3))(6)](4)(-) (2) were obtained as the two major products from the reduction of PdCl(2)(PPh(3))(2) with [Ni(6)(CO)(12)](2)(-). Their crystal structures as [PPh(4)](+) salts were unambiguously determined from CCD X-ray crystallographic analyses; the resulting stoichiometries were ascertained from elemental analyses. Infrared, multinuclear (1)H, (31)P[(1)H] NMR, UV-vis, CV, variable-temperature magnetic susceptibility, and ESI FT/ICR mass spectrometric measurements were performed. The Pd(16)Ni(4) core of 1 ideally conforms to a ccp nu(3) tetrahedron of pseudo-T(d)() (4 3m) symmetry. Its geometry normal to each tetrahedral Pd(7)Ni(3) face (i.e., along each of the four 3-fold axes) may be viewed as a four-layer stacking of 20 metal atoms in a ccp [a(Ni(1)) b(Pd(3)) c(Pd(6)) a(Pd(7)Ni(3))] sequence. A comparative analysis of the different ligand connectivities about the analogous metal-core geometries in 1 and the previously reported [Os(20)(CO)(40)](2)(-) has stereochemical implications pertaining to the different possible modes of carbon monoxide attachment to ccp metal(111) surfaces. The unique geometry of the Pd(33)Ni(9) core of 2, which has pseudo-D(3)(h)() (6 2m) symmetry, consists of five equilateral triangular layers that are stacked in a hcp [a(Pd(7)Ni(3)) b(Pd(6)) a(Pd(7)Ni(3)) b(Pd(6)) a(Pd(7)Ni(3))] sequence. Variable-temperature magnetic susceptibility measurements indicated both 1 and 2 to be diamagnetic over the entire temperature range from 5.0 to 300 K. Neutral Pd(12)(CO)(12)(PPh(3))(6) (3) and [Pd(29)(CO)(28)(PPh(3))(7)](2)(-) (4) as the [PPh(4)](+) salt were obtained as minor decomposition products from protonation reactions of 1 and 2, respectively, with acetic acid. Compound 3 of pseudo-D(3)(d)() (3 2/m) symmetry represents the second highly deformed hexacapped octahedral member of the previously established homopalladium family of clusters containing uncapped, monocapped, bicapped, and tetracapped Pd(6) octahedra. The unprecedented centered 28-atom polyhedron for the Pd(29) core of 4 of pseudo-C(3)(v)() (3m) symmetry may be described as a four-layer stacking of 29 metal atoms in a mixed hcp/ccp [a(Pd(1)) b(Pd(3)) a(Pd(10)) c(Pd(15))] sequence.     

Pillared montmorillonites modified with silver

Alumina, zirconia and titania pillared montmorillonites additionally modified with silver were tested as catalysts of NO reduction with NH₃ or C₂H₄. Ammonia was much more effective reducer of NO than ethylene. The silver containing TiO₂-pillared clay has been found to be the most active catalyst for NO reduction both with NH₃ or C₂H₄. Oxidation of the reducing agents by oxygen limited the NO conversion in the high temperature region. The ammonia and nitric oxide adsorption sites were studied by the temperature programmed desorption methods (TPD). This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthesis and characterization of a discotic uranium-containing liquid crystal

The synthesis of several UO(2)-alaskaphyrin derivatives functionalized with aliphatic chains is described. These compounds are found to be liquid-crystalline and form columnar mesophases, as judged from polarizing optical microscopy studies, and represent the first uranium-containing discotic mesogens.     

Structure of the reaction product of chloral hydrate and isocyanic acid

In a recent article describing the reactions of isocyanic acid with carbonyl compounds, Hoover, Stevenson, and Rothrock (1) observed that chloral reacted slowly with free isocyanic acid at 0° to give CCl₃CH(OH)NCO, m.p. 25°. On stirring with water, this was converted to a solid, m.p. 190-200°, assigned structure A. This latter substance was also produced by reaction of isocyanic acid directly with chloral hydrate.