Estimates of ‖e itf‖ A(Γ), when Γ ⊂ ℝ n is a curve andf is a real-valued functionis a curve andf is a real-valued function

It is shown that there exists ann×n matrix all of whose eigenvalues and off-diagonal elements are prescribed. The number of such matrices is finite.     

Characteristics of the consistent ground state of the random phase approximation

Detailed considerations of the ground-state vector derived for the random phase approximation obtained earlier in a generator coordinate representation employing the unitary group parameter space reveal a particular correlated pair structure. The results of explicit calculations of ground-state averages are discussed.     

UV and IR absorption cross-sections of HCHO, HCDO, and DCDO

UV (240-370 nm) and IR (3200-1500 cm(-1)) absorption cross-sections of HCHO, HCDO, and DCDO in a bath gas of N(2) at atmospheric pressure and 296 K are reported from simultaneous measurements in the two spectral regions. Cross-sections were placed on an absolute scale through quantitative conversion of formaldehyde to CO and HCOOH by titration with Br atoms, also monitored by FTIR. The integrated UV absorption cross-sections of HCHO, HCDO, and DCDO are equal to within the experimental uncertainty.     

Detection of acetylene impurities in ethylene and polyethylene manufacturing processes using tunable diode laser spectroscopy in the 3-��m range

Using recently developed GaInAsSb/AlGaInAsSb DFB lasers, tunable diode laser spectroscopy (TDLS) has been extended into the 3-??m wavelength region for the detection of acetylene impurities in hydrocarbon compounds encountered in ethylene manufacturing. Measurements of acetylene in pure polymer grade ethylene and in a gas mixture of ethylene and ethane typical of the process stream around a hydrogenation reactor have been performed. Using a procedure incorporating subtraction of a hydrocarbon background spectrum a detection limit of 5?ppb?m was achieved under ordinary laboratory conditions. Under forced temperature cycling conditions, the detection limit deteriorated to 180 ppb?m, due to temperature drift caused by optical interferences generated by reflections in the laser TO8 can.     

Electron propagator theory and application

Summary The electron propagator theory is presented with somewhat of a historical perspective and the working equations are developed with the aim of taking advantage of molecular point group symmetry. A new electron propagator code, the vectorized electron propagator program (VEP), is introduced without full details about its structure and capabilities (such details are being published elsewhere). Applications to the (UV) photoelectron spectra of some donor-acceptor complexes of borane with carbon monoxide and water are presented at the level of second-order theory as an illustration of the theory and the VEP code.     

The influence of hyperfine structure and isotope shift on the detection of Rb by 2f-wavelength modulation diode laser absorption spectrometry-experimental verification of simulations

This work presents an experimental verification of a previously developed methodology for simulation of the 2f-wavelength modulation diode laser absorption spectrometry technique (2f-WM-DLAS) when the influence of hyperfine structure, isotope shift and collisional broadening and shift of an atomic transition is taken into account [J. Gustafsson, D. Rojas and O. Axner, Spectrochim. Acta, 52B, 1937–1953 (1997)]. The pilot element in the simulations was Rb, detected at the 780 nm 5s ²S_1/2−5p ²P_3/2 transition, in low-pressure cells and atmospheric-pressure reservoirs (e.g. graphite furnaces). This experimental investigation verifies that the simulations are able to predict, with good accuracy, experimental 2f-WM signals from Rb atoms under both low-pressure, room-temperature conditions and atmospheric-pressure, high-temperature conditions. This implies that the previously published simulation methodology can be used for predicting and optimizing 2f-WM signal strengths and shapes from Rb atoms (and thereby presumably also from other atoms) under a variety of pressure and temperature conditions.     

Studies on the Hydrolytic Behavior of Zirconium(IV)

The stability constants of zirconium(IV) hydrolysis species have been measured at 15, 25, and 35 °C [in 1.0 mol-dm^–3 (H,Na)ClO₄] using both potentiometry and solvent extraction. In addition, the solubility of [Zr(OH)₄(am)] has been investigated in a 1 mol-dm^–3 (Na,H)(ClO₄,OH) medium at 25 °C over a wide range of –log [H⁺] (0-15). The results indicate the presence of the monomeric species Zr(OH)³⁺, Zr(OH)₂ ²⁺, Zr(OH)₃ ⁺, and Zr(OH)₄ ⁰(aq) as well as the polymeric species Zr₄(OH)₈ ⁸⁺ and Zr₂(OH)₆ ²⁺. The solvent extraction measurements required the use of acetylacetone. As such, the stability constants of zirconium(IV) with acetylacetone were also measured using solvent extraction. All stability constants were found to be linear functions of the reciprocal of temperature (in kelvin) indicating that H ^o and S ^o are both independent of temperature (over the temperature range examined in the study). The results of the solubility experiments have shown four distinctly different solubility regions. In strongly acidic solutions, the solubility is controlled by the formation of polynuclear hydrolysis species in solution whereas in less acidic solution the formation of mononuclear hydrolysis species becomes dominant. The largest portion of the solubility curve is controlled by equilibrium with aqueous Zr(OH)₄ ⁰(aq) where the solubility is independent of the proton concentration. In alkaline solutions, the solubility increases due to formation of the zirconate ion. The middle region was used to determine the solubility constant (log *K _s10) of Zr(OH)₄(s). From the data in the alkaline region, a value of the stability of the zirconate ion has been determined. This is the first time that the possible evidence for the zirconate ion has been identified in aqueous solution that has previously been found only in the solid phase.     

Spectral analysis of multichannel MRS data

The use of phased-array receive coils is a well-known technique to improve the image quality in magnetic resonance imaging studies of, e.g., the human brain. It is common to incorporate proton (1H) magnetic resonance spectroscopy (MRS) experiments in these studies to quantify key metabolites in a region of interest. Detecting metabolites in vivo is often difficult, requiring extensive scans to achieve signal-to-noise ratios (SNR) that provide suitable diagnostic results. Combining the MR absorption spectra obtained from several receive coils is one possible approach to increase the SNR. Previous literature does not give a clear overview of the wide range of possible approaches that can be used to combine MRS data from multiple detector coils. In this paper, we consider the multicoil MRS approach and introduce several signal processing tools to address the problem from different nonparametric, semiparametric, and parametric perspectives, depending on the amount of available prior knowledge about the data. We present a numerical study of these tools using both simulated 1H MRS data and experimental MRS data acquired from a 3T MR scanner.