Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

Two-dimensional angular optical scattering patterns of microdroplets in the mid infrared with strong and weak absorption

Two-dimensional angular optical scattering (TAOS) patterns of droplets composed of a mixture of H2O and D2O are detected in the mid infrared. First, a lens is used in the Abbé sine condition to collect a small solid angle of light, where the scattering pattern matches well numerical simulations based on Mie theory. Next, TAOS patterns from droplets spanning a large (approximately 27pi sr) solid angle are captured simultaneously at two wavelengths. The effects of absorption are evident in the patterns and are discernible without the need for curve matching by Mie theory.     

Calculation of optical matrix elements in Gallium Arsenide

Results are presented for optical matrix elements calculated numerically for a 2 × 2 lattice of delta-function impurity potentials in Gallium Arsenide. The calculations show clearly the change in the character of the state with increasing binding energy and particularly the increase in importance of the higher minima over the absolute conduction band minimum at г. Comparison with some experimental work is made from which good qualitative agreement is clear.     

Observation of the optoacoustic effect in an optical fibre

The rediationless absorption of light propagating in optical fibres induces both stress waves and thermal waves in the fibre medium. Detection of such waves is termed the optoacoustic effect. Successful detection in optical fibres is easily obscured by scattered light impinging on the detector. We have obtained a signal of 2 mV on a piezoceramic transducer attached to a commercial step-index optical fibre after passage of a 1 J ruby laser light pulse along the fibre axis. No signal was, however, produced when the transducer was not in contact with the fibre. Similar results were obtained using chopped cw laser radiation but then more care had to be taken since the transducers used had a measureable sensitivity to the low frequency chopped radiation emitted perpendicular to the optical fibre axis.     

Designed iron carbonyls as carbon monoxide (CO) releasing molecules: rapid CO release and delivery to myoglobin in aqueous buffer, and vasorelaxation of mouse aorta

The physiological roles of CO in neurotransmission, vasorelaxation, and cytoprotective activities have raised interest in the design and syntheses of CO-releasing materials (CORMs) that could be employed to modulate such biological pathways. Three iron-based CORMs, namely, [(PaPy(3))Fe(CO)](ClO(4)) (1), [(SBPy(3))Fe(CO)](BF(4))(2) (2), and [(Tpmen)Fe(CO)](ClO(4))(2) (3), derived from designed polypyridyl ligands have been synthesized and characterized by spectroscopy and X-ray crystallography. In these three Fe(II) carbonyls, the CO is trans to a carboxamido-N (in 1), an imine-N (in 2), and a tertiary amine-N (in 3), respectively. This structural feature has been correlated to the strength of the Fe-CO bond. The CO-releasing properties of all three carbonyls have been studied in various solvents under different experimental conditions. Rapid release of CO is observed with 2 and 3 upon dissolution in both aqueous and nonaqueous media in the presence and absence of dioxygen. With 1, CO release is observed only under aerobic conditions, and the final product is an oxo-bridged diiron species while with 2 and 3, the solvent bound [(L)Fe(CO)](2+) (where L = SBPy(3) or Tpmen) results upon loss of CO under both aerobic and anaerobic conditions. The apparent rates of CO loss by these CORMs are comparable to other CORMs such as [Ru(glycine)(CO)(3)Cl] reported recently. Facile delivery of CO to reduced myoglobin has been observed with both 2 and 3. In tissue bath experiments, 2 and 3 exhibit rapid vasorelaxation of mouse aorta muscle rings. Although the relaxation effect is not inhibited by the soluble guanylate cyclase inhibitor ODQ, significant inhibition is observed with the BK(Ca) channel blocker iberiotoxin.     

Lattice-induced frequency shifts in Sr optical lattice clocks at the 10(-17) level

We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching 5×10(-17) after a 1 h integration time. We put the first experimental upper bound on the multipolar M1 and E2 interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the 10(-17) level, even for lattices as deep as 150 recoil energies.