Organometallic chemistry : V. Protonation of acylferrocenes under stable ion conditions in fso3h-so2c1f solution

Protonation of acylferrocenes (FeCOR) in FSO₃H-SO₂CIF(SO₂) solution was studied by PMR spectroscopy. The site of protonation is found to be at the carbonyl oxygen atom. Temperature dependent PMR spectra of protonated acylferrocenes FeCROH⁺ (R = CH₃, C₂H₅, C₆H₅, OCH₃) were observed indicating intermolecular hydrogen exchange with the acid solvent system. In addition the PMR spectra of acylferrocenes in FSO₃ H-SO₂ CIF(SO₂) were found to be dependent upon the acid concentration.     

A model for the complex permittivity of water at frequencies below 1 THz

Experimental permittivity data of liquid water, compiled from the open literature, were selectively applied to support a modeling strategy. Frequencies up to 1 THz and atmospheric temperatures are covered with an expression made up by two relaxation (Debye) terms. The double-Debye model reduces to one term when the high frequency limit is set at 100 GHz, and the model can be extended to 30 THz by adding two resonance (Lorentzian) terms. The scheme was carried out by employing nonlinear least-squares fitting routines to data we considered reliable.     

Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Criticality and phase transitions in ionic fluids

Recent experimental investigations of criticality and phase separation in ionic fluids have revealed behavior of great theoretical interest. In seeking to understand the experiments, some of which appear to exhibit argonlike criticality and some of which exhibit classical (mean-field) criticality, a convenient starting point is the restricted primitive model (RPM) of symmetrically charged hard spheres, all of equal diameter , each sphere bearing a positive or negative charge of magnitudeq. There is overall charge neutrality, so that the expected number densities of the anions and cations are equal, ₊= _-. Studies of RPM charge-charge and density-density correlation functions indicate that the fluctuation-suppressing mechanism that yields mean-field critical behavior in nonionic systems with long-range interparticle potentials is not operative in the RPM. On the basis of plausible assumptions, Ising-like behavior is instead expected. The above work is summarized. New work of Zhang and the author is outlined, showing that when one loses the RPM symmetry (through, e.g., different valence, diameter, or dipole moment of anions and cations) a strong coupling between charge-charge and density-density correlation ensues. The way in which this can be expected to give rise to mean-field or mean-field-like behavior is noted. Other new observations concern the mean-field analogy found by Høye and the author between the parameter 2/(d–2) (d is the dimensionality) in that model and the monomer number in high polymers, with respect to the coexistence-curve shape dependence on those parameters.     

Relativistic quarks bound with a one-body tensor potential

A dipole fit to electromagnetic form factors is used to determine a quark density in the nucleon. A radial tensor potential is used to bind the quarks into states of goodJ, J _z, and parity. The tensor potential radial component is taken to satisfy the equationT = T ₀, whereT ₀ is a parameter of the model. This linear divergence equation can be simultaneously solved with the Dirac equation for the bound quark wave functions. A self-consistent solution is possible where the mass density used as the source for the binding potential is the same as that determined from the solution for the quark wave functions.     

Chaos in thermal pulse combustion

An experimental thermal pulse combustor and a differential equation model of this device are shown to exhibit chaotic behavior under certain conditions. Chaos arises in the model by means of a progression of period-doubling bifurcations that occur when operating parameters such as combustor wall temperature or air/fuel flow are adjusted to push the system toward flameout. Bifurcation sequences have not yet been reproduced experimentally, but similarities are demonstrated between the dynamic features of pressure fluctuations in the model and experiment. Correlation dimension, Kolmogorov entropy, and projections of reconstructed attractors using chaotic time series analysis are demonstrated to be useful in classifying dynamical behavior of the experimental combustor and for comparison of test data to the model results. Ways to improve the model are suggested. (c) 1995 American Institute of Physics.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :

The CO fundamental-band laser as secondary frequency standard at 5 µm

We present a very high-resolution heterodyne spectrometer based on a CO laser which operates down to fundamental-band transitions of the molecule. This allows us to detect saturated absorption signals on these transitions at very low pressure (0.4 Pa) and laser intensity (< 1 mW/cm²), yielding a linewidth of about 250 kHz. With the CO fundamental-band laser stabilized to these saturation signals we have measured the transition frequencies of the fundamental bands of three isotopic species to an accuracy of typically 20 kHz (v/v 3 × 10^–10), referenced to the CO₂ frequency standard. Together with additional frequency measurements of the first hot bands, these provide the first heterodyne frequency data of sub-Doppler accuracy for transitions in low lying bands of CO. They now represent the most accurate secondary frequency standard in the spectral region around 5 µm (60 THz).