On the left regular representation of a separable locally compact group

For an arbitrary separable locally compact group G we exhibit a canonical Borel subset $\text{G}\text{?}{}_{\mathrm{\Delta }}$ of the quasi-dual $\text{G}\text{?}\text{of}\text{G}$ (with the Mackey Borel structure), such that $\text{G}\text{?}{}_{\mathrm{\Delta }}$ is a standard Borel space in the induced Borel structure, and such that the canonical measure for the left regular representation λ_Gof G is concentrated on $\text{G}\text{?}{}_{\mathrm{\Delta }}$. On the basis of this we discuss the (non-unimodular) “Plancherel theorem.”     

The microwave spectrum of MnO3F

The microwave spectrum of MnO₃F has been remeasured and several corrections and new results have been obtained: B₀ = 4129.141 MHz, D_J = 1.12 kHz, D_JK = 1.87 kHz; $\text{α}{}_3{}^{\mathrm{B}}\text{= 8.622}$, $\text{α}{}_5{}^{\mathrm{B}}\text{= ? 11.994}$, $\text{α}{}_6{}^{\mathrm{B}}\text{= 6.042}$, |q₅| = 16.005, and |q₆| = 8.456 MHz.     

A theoretical study of malonate and formate calcium binding by ab initio techniques

Ab initio calculations at the STO—3G level have been performed on the binding of CA(II) ion to malonate and formate with and without d orbitals in the basis set for the CA(II) ion. The malonate and formate binding results with CA(II) are similar. The addition of d orbitals to CA(II) has little effect on the conformational minimum. The results are qualitatively similar to those from our previous calculations on the Mg²⁺—malonate interaction: a single carboxyl interaction with the metal ion appears to be preferred over a conformation in which two carboxyl groups bind to Ca(II). Moreover, the single carboxyl group interaction with CA(II) appears to be favored over the binding of CA(II) to a single oxygen of a carboxyl group.     

Intravenous administration of Gd-DTPA prior to DWI does not affect the apparent diffusion constant

MRI measurements of water diffusion and blood perfusion are increasingly used for the evaluation of organ functionality and tissue viability (e.g., in tumors). While diffusion-weighted imaging is performed without contrast agents, measurement of blood perfusion is normally performed based on the administration of paramagnetic substances such as gadolinium diethylenetriamine pentaacetic acid (Gd-DTPA). Simultaneous measurements of these two parameters are often preferred. However, it may be argued that Gd-DTPA causes constriction of small blood vessels or alters hemodynamic parameters such as blood viscosity, thereby corrupting subsequent measurements of the apparent diffusion constant (ADC). The objective of the current study was to investigate the possible changes in the ADC in tumors following intravenous administration of 0.2 and 0.4 mmol/kg of Gd-DTPA in mice. The study was conducted with C3H mouse mammary carcinomas inoculated in the right foot of the animal subjects. The results were compared with findings in a sham group, demonstrating that Gd-DTPA had no significant impact on the ADC as measured in a 7-T animal system.     

Optical biosensor with dispersion compensation

Dispersion limits performance in many optical systems. In surface plasmon resonance (SPR) biosensors, the sensing area is an optical element in which the dispersion depends on the effective refractive index of the biochemical compounds to be measured. We report a method of compensating for wavelength dispersion in SPR biosensors employing two integrated diffractive optical coupling elements in a polymer substrate. The dispersion compensation is achieved over the whole dynamic measurement range and provides a biosensor more robust to wavelength fluctuations than prism-coupler SPR systems. The concept can readily be employed in other types of sensor measuring refractive-index changes.     

Peak-type and dip-type metal-clad waveguide sensing

Two types of operation for metal-clad waveguide sensors, peak-type and dip-type operation, are described. The newly discovered peak-type operation [Sens. Actuators B 94, 304 (2003)] can be achieved by use of a few-nanometers-thick cladding of a metal with a large imaginary permittivity, whereas conventional dip-type operation is obtained with a metal cladding with small imaginary permittivity some tens of nanometers thick. Both types of operation are described, and the main differences are illustrated.     

High-resolution dissociative recombination of cold H3+and first evidence for nuclear spin effects

The energy-resolved rate coefficient for the dissociative recombination (DR) of H(3)(+) with slow electrons has been measured by the storage-ring method using an ion beam produced from a radiofrequency multipole ion trap, employing buffer-gas cooling at 13 K. The electron energy spread of the merged-beams measurement is reduced to 500 microeV by using a cryogenic GaAs photocathode. This and a previous cold- measurement jointly confirm the capability of ion storage rings, with suitable ion sources, to store and investigate H(3)(+) in the two lowest, (J,G) = (1,1) and (1,0) rotational states prevailing also in cold interstellar matter. The use of para-H(2) in the ion source, expected to enhance para-H(3)(+) in the stored ion beam, is found to increase the DR rate coefficient at meV electron energies.     

4-metalated condensed pyrimidines: their preparation and reaction with aldehydes under Barbier-type conditions

[reaction: see text] The organometallic intermediate obtained from halogen-metal exchanges of 4-iodo-6-phenylthieno[2,3-d]pyrimidine under Barbier-type conditions was reacted with aldehydes to form the corresponding alcohols in moderate yields. The reaction involving an organolithium intermediate proceeded only at low temperature, whereas the reaction involving a magnesium ate intermediate also proceeded at room temperature. A crystal structure confirms that the expected constitutional alcohol isomer is formed, where no migration has taken place. The conditions were also suitable for 9-benzyl-6-iodopurine.     

The dual spectral set conjecture

Suppose that where are real numbers such that and The union is not assumed to be disjoint. It is shown that the translates , , tile the real line for some bounded measurable set if and only if the exponentials , , form an orthogonal basis for some bounded measurable set