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.     

Self-chemical ionization of diethylzinc

The self-chemical ionization of diethylzinc is examined by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry and semiempirical molecular orbital calculations. Electron impact of diethylzinc neutral produces the radical cation, C(4)H(15)Zn(+) (m/z x 122), which reacts further with the neutral (C(2)H(5))(2)Zn to give the following product ions: Zn(+) (m/z x 64), C(2)H(5)Zn(+) (m/z x 93), C(4)H(9)Zn(+) (m/z x 121), C(4)H(11)Zn(2)(+) (m/z x 187), and C(6)H(15)Zn(2)(+) (m/z x 215). To determine the structure and pathways for production of these ions, monoisotopic (12)C(4)H(15)(64)Zn(+), (64)Zn(+) and (12)C(2)H(5)(64)Zn(+) were individually isolated and reacted with the neutral background. We also performed semiempirical molecular orbital calculations (ZINDO/1). The molecular orbital calculations and experimental data are consistent in predicting that the ethyl group on the diethylzinc cation carries the positive charge. Copyright 1999 John Wiley & Sons, Ltd.     

The photophysics of the 2,6 dialkoxy anthracenes: Evidence for excited state side-chain conformational relaxation

Three 2,6 dialkoxyanthracenes with varying ether sidechain lengths (methyl, n-propyl and n-hexyl) are synthesized and characterized. When compared to unsubstituted anthracene, the spectroscopic properties of the alkoxy-anthracenes are significantly different. The oscillator strength appears to be evenly distributed between the L_a and L_b states, rather than concentrated in the low-energy L_a state, and the transition dipole moments are rotated by ～30° in the molecular frame. More importantly, all three derivatives undergo an intramolecular conformational change in the excited state that gives rise to a reshaping of the fluorescence spectrum on the nanosecond timescale. This process has an activation energy of 8±1 kJ/mol. By ～150 K the fluorescence spectrum reflects only the high energy conformer, whose emission lineshape is similar to that of the unsubstituted anthracene. The temperature-dependent changes in the monomeric fluorescence spectra of these compounds will have to be taken into account in future studies of their solid-state spectroscopy.     

Thermal and complex impedance analysis of amorphous and crystalline lithium salt mixtures

Amorphous electrolytes consisting of the lithium salts, Li[R-NSO₂CF₃] were prepared and the attendant low ionic conductivities of the lithium salt mixtures (1×10⁻⁶ S cm⁻¹ at room temperature) are attributed to high glass transition temperatures. An example is the novel amorphous salt, Li[18-C-6NSO₂CF₃] which produces an amorphous salt mixture with Li[N(SO₂CF₃)₂] (LiTFSI).     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

The 31P NMR spectra and structure of some compounds containing phosphonium ions in 25-oleum solution

25-oleum has proved to be an extremely useful solvent for recording the ³¹P NMR spectra of a variety of compounds containing phosphonium ions. Not only have data in very good agreement with previous solid state and solution results been obtained, but the structures of some solids containing mixtures of phosphorus (V) species have been ascertained for the first time.     

The 35Cl NQR spectra and structure of pentafluorophenyltetrachlorophosphorane C6F5PCl4

The low temperature structure of C₆F₅PCl₄ was confirmed by ³⁵Cl NQR measurements as ψ-trigonal bipyramidal, with the C₆F₅ group axial. Discrepancies were found with previously reported data, possible causes of these are discussed.     

LIGHT DAMAGE IN THE RAT RETINA: EFFECT OF A RADIOPROTECTIVE AGENT (WR-77913) ON ACUTE ROD OUTER SEGMENT DISK DISRUPTIONS

Primary events in the course of light induced retinal lesions are still not fully elucidated. Under chronic conditions, lipid peroxidation in the retina and death of photoreceptor cells are observed. The radioprotective agent WR-77913 scavenges singlet oxygen, hydrated electrons and free radicals. WR-77913 was used to protect against acute light induced photoreceptor outer segment membrane disruptions in the rat retina. There was a partial but not complete protection at higher illuminance levels (800 lx for 30 min), whereas threshold lesions (400 lx for 30 min) were almost completely prevented. These observations indicate an involvement of photodynamic reactions in causing acute photoreceptor lesions.     

Transmission spectra of light to the mammalian retina

A simple method has been developed to determine the optical properties of the anterior segment of the intact eye. This consists of a probe that is inserted into the posterior sclera and detects light passing through the anterior segment. The probe is connected to a charge-coupled device spectrophotometer via a fiber optic bundle. It was determined that the young rat anterior segment transmits light down to 300 nm, whereas calf and rabbit eyes transmit no UVB and only part of the UVA to the posterior segment. The absorbing species in these animals is most likely NAD(P)H, which has an absorption maximum at approximately 345 nm and is associated with zeta-crystallin. A young primate anterior segment transmits almost no UV with a steep increase in transmission at CA 400 nm. Because some experiments employed a light tube that is used to illuminate the retina during vitrectomies, this method can be used to determine the transmission spectra of the anterior segment of humans in vivo.