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.     

Stability of functions in Boolean models of gene regulatory networks

Boolean networks are used to model large nonlinear systems such as gene regulatory networks. We will present results that can be used to understand how the choice of functions affects the network dynamics. The so called bias-map and its fixed points depict much of the function's dynamical role in the network. We define the concept of stabilizing functions and show that many Post and canalizing functions are also stabilizing functions. Boolean networks constructed using the same type of stabilizing functions are always stable regardless of the average in-degree of network functions. We derive the number of all stabilizing functions and find it to be much larger than the number of Post and canalizing functions. We also discuss the implementation of functions and apply the presented results to biological data that give an approximation of the distribution of regulatory functions in eucaryotic cells. We find that the obtained theoretical results on the number of active genes are biologically plausible. Finally, based on the presented results, we discuss why canalizing and Post regulatory functions seem to be common in cells.     

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.     

Measuring non-Gaussian fluctuations through incoherent cooper-pair current

We study a Josephson junction (JJ) in the regime of incoherent Cooper-pair tunneling, capacitively coupled to a nonequilibrium noise source. The current-voltage (I-V) characteristics of the JJ are sensitive to the excess voltage fluctuations in the source, and can thus be used for wideband noise detection. Under weak driving, the odd part of the I-V can be related to the second cumulant of noise, whereas the even part is due to the third cumulant. After calibration, one can measure the Fano factors for the noise source, and get information about the frequency dependence of the noise.