Processes of flats induced by higher dimensional processes III

Stationary processes of k-flats in ^d can be thought of as point processes on the Grassmannian _k ^d of k-dimensional subspaces of ^d . If such a process is sampled by a (d–k+ j)-dimensional space F, it induces a process of j-flats in F. In this work we will investigate the possibility of determining the original k-process from knowledge of the intensity measures of the induced j-processes. We will see that this is impossible precisely when 1<k<d–1 and j=0,...,2[r/2]–1, where r is the rank of the manifold _k ^d . We will show how the problem is equivalent to the study of the kernel of various integral transforms, these will then be investigated using harmonic analysis on Grassmannian manifolds.The research of the first and third authors was supported in part by NSF grants DMS-9207019 and DMS-9304284. The research of the second author was supported in part by NFR contract number R-RA 4873-306 and the Swedish Academy of Sciences.     

Boundary and Lens Rigidity of Lorentzian Surfaces

Let be a Lorentzian metric on the plane that agrees with the standard metric outside a compact set and so that there are no conjugate points along any time-like geodesic of . Then and are isometric. Further, if and are two dimensional compact time oriented Lorentzian manifolds with space--like boundaries and so that all time-like geodesics of maximize the distances between their points and and are ``boundary isometric', then there is a conformal diffeomorphism between and and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

     

Carbon-13 and nitrogen-15 nuclear magnetic resonance of physostigmine (eserine)

The ¹⁵N and ¹³C nmr spectra of physostigmine are discussed along with complete assignment of the signals. This alkaloid ¹⁵ N nmr spectrum is notable because it contains nitrogens in three different environments.     

Proton-ionizable crown compounds. 4. New macrocyclic polyether ligands containing a triazole subcyclic unit

A series of macrocyclic polyether (crown) ligands containing the proton-ionizable s-triazole subcyclic unit were prepared by reacting the 1-THP blocked 3,5-bis(chloromethyl)-1H-1,2,4-triazole with various oligoethylene glycols. The starting bis(chloromethyl)triazole is a vessicant and must be used with caution. Triazolo-18-crown-6 ( 5 ) formed stable complexes with barium, strontium, copper and benzylammonium cations but not with potassium or lithium. The crystal structure of 5 showed the triazole proton to be on nitrogen 3 which is outside the macroring cavity.     

Formation and structure of self-assembled monolayers of alkanethiolates on palladium

The adsorption of n-alkanethiols onto polycrystalline thin films of palladium containing a strong (111) texture produces well-organized, self-assembled monolayers. The organization of the alkane chains in the monolayer and the nature of the bonding between the palladium and the thiol were studied by contact angle measurements, optical ellipsometry, reflection absorption infrared spectroscopy (RAIRS), and X-ray photoelectron spectroscopy (XPS). The XPS data reveals that a compound palladium-sulfide interphase is present at the surface of the palladium film. The RAIR spectra, ellipsometry data, and wetting properties show that the palladium-sulfide phase is terminated with an organized, methyl-terminated monolayer of alkanethiolates. The local molecular environment of the alkane chains transitions from a conformationally disordered, liquidlike state to a mostly all-trans, crystalline-like structure with increasing chain length (n = 8-26). The intensities and dichroism of the methylene and methyl stretching modes support a model for the average orientation of an ensemble of all-trans-conformer chains with a tilt angle of approximately 14-18 degrees with respect to the surface normal and a twist angle of the CCC plane relative to the tilt plane of approximately 45 degrees. The SAMs are stable in air, although the sulfur present at the surface oxidizes in air over a period of 2-5 days at room temperature. The differences in chain organization between SAMs formed by microcontact printing and by solution deposition are also examined by RAIRS and XPS.     

Quantitative Comparison Between Vacuum-Ultraviolet Irradiation and Remote Hydrogen Plasma Treatment of Hydrocarbon Polymers

The photon flux of vacuum ultraviolet (VUV) and ultraviolet (UV) radiation of a hydrogen plasma with and without a MgF₂window was recorded by fluorescence measurements of sodium salicylate layers. After the compensation of the MgF₂absorption by increasing the input power into the plasma source, a comparison between afterglow hydrogen plasma and VUV treatments was made. Polyethylene (PE), polypropylene (PP), and polystyrene (PS) were treated either with VUV radiation or with remote hydrogen plasma and mass loss and CH absorption loss were measured by a quartz crystal microbalance and by infrared reflection absorption spectroscopy, respectively. In the case of PE the effects of both treatments were found to be very similar white for PP slight differences were observed. For the actual set of experimental conditions, the radiation component is largely responsible for the efficiency of the plasma treatment. VUV and remote hydrogen plasma treatments of PS showed only a negligible loss of mass and CH absorption.     

Multi-residue method for the determination of chlorinated phenol metabolites in urine

Electron-capture-gas chromatographic (EC-GC) methods for the determination of chlorinated phenol metabolites of hexachlorobenzene (HCB) and pentachlorophenol (PCP) in urine are presented. After extraction the sample was reacted with diazomethane to produce the methyl ether of each metabolite prior to determination by EC-GC. An acid alumina column was used for cleanup and separation of methylated phenols into groups. Average recoveries of greater than 80% were obtained from urine fortified with known amounts of the phenol metabolites under investigation. A level of 1 ppb¹ was established as minimum detection limit for each phenol metabolite. Previously unreported urinary metabolites of HCB and PCP were found as a result of a rat feeding study. Levels of chlorinated phenol residues from (a) human general population and (b) a worker occupationally exposed to PCP are also included.     

Synthesis and binding affinities of novel SRIF-mimicking beta-D-glucosides satisfying the requirement for a pi-cloud at C1

[reaction: see text] The synthesis of four bioactive analogues of the somatostatin (SRIF-14) mimetic, beta-d-glucoside (+)-2, in which the C1 indole side chain is replaced with indole surrogates, has been achieved. These congeners, possessing the naphthyl, benzothiophene, benzyl, and benzofuran substituents, were predicted to satisfy the electrostatic requirements of the tryptophan binding pocket of SRIF. Unlike the previously described C4 picolyl and pyrazinyl congeners, these ligands bind the hSST4 receptor.     

Near-IR luminescence of monolayer-protected metal clusters

Visible-near-IR luminescence spectra of gold MPCs that are similar, irrespective of the number of core atoms (all <2 nm diameter) and different monolayers, are reported. The luminescence can be quantitatively invoked by introducing polar ligands into nonpolar MPC monolayers and by galvanic exchange of metal atoms on the MPC core surface with different metals. The observed emissions are believed to result from surface-localized states that depend on both the core metal of the nanoparticle and the ligands attached to the metal surface.