Synthesis and two-electron redox behavior of diazuleno[2,1-a:1,2-c]naphthalenes

The Diels-Alder reaction of di-2-azulenylacetylene with tetraphenylcyclopentadienone afforded 7,8,9,10-tetraphenyldiazuleno[2,1-a:1,2-c]naphthalene in one pot via autoxidation of the presumed 1,2-di-2-azulenylbenzene derivative. In contrast, a similar reaction of bis(1-methoxycarbonyl-2-azulenyl)acetylene with tetraphenylcyclopentadienone gave the 1,2-di-2-azulenylbenzene derivative. The following cyclodehydrogenation reaction of the benzene derivative with iron(III) chloride afforded diazuleno[2,1-a:1,2-c]naphthalene 6,11-bismethoxycarbonyl derivative. The redox behavior of these novel diazuleno[2,1-a:1,2-c]naphthalenes was examined by cyclic voltammetry (CV). These compounds exhibited two-step oxidation waves at +0.22 to +0.71 V upon CV, which revealed the formation of a radical cation and dication stabilized by the fused two azulene rings under the electrochemical oxidation conditions. Since the 1,2-di-2-azulenylbenzene derivative was oxidized at higher oxidation potentials (+0.83 and +1.86 V), the fusion of the two azulene rings to naphthalene increased electron-donating properties because of the formation of a closed-shell dicationic structure. Formation of the radical cation was characterized by UV-vis spectroscopy under the electrochemical oxidation conditions, although no evidence was obtained for the presumed dication under the conditions of the UV-vis spectroscopy measurement.     

Soluble polymer-supported catalysts containing pendant quaternary onium salts for the addition reaction of oxiranes with carbon dioxide

The addition reaction of oxiranes ( 15a-d ) with carbon dioxide (CO₂) was carried out using 1 mol % of soluble polymer-supported quaternary onium salts as catalysts under atmospheric pressure. The reaction of 15a-d with CO₂ proceeded very smoothly to give the corresponding five-membered cyclic carbonates ( 16a-d ) in high yields at 90-100°C. The catalytic activity of the soluble polymer-supported quaternary onium salts was strongly affected by the following factors: kind of reaction solvent, degree of introduction of the pendant onium salt residues in the polymer chain, and type of alkyl group on the onium salts due to the balance between lipophilicity and steric hindrance of the onium salt residue. Furthermore, these soluble polymer-supported quaternary onium salts were found ordinarily to have higher catalytic activity than low molecular weight quaternary onium salts under the same reaction conditions. It was also found that the rate of reaction was proportional both to catalyst concentration and to oxirane concentration. © 1995 John Wiley & Sons, Inc.     

Limit theorems for trimmed sums

This paper studies the heavily trimmed sums (*) _{[ns] + 1} ^[nt] X _j ⁽ⁿ⁾ , where {X _j ⁽ⁿ⁾ } _{j = 1} ⁿ are the order statistics from independent random variables {X ₁,...,X _n } having a common distributionF. The main theorem gives the limiting process of (*) as a process oft. More smoothly trimmed sums like _{j = 1} ^[nt] J(j/n)X _j ⁽ⁿ⁾ are also discussed.     

Cyclization from Higher Excited States of Diarylethenes Having a Substituted Azulene Ring

The cyclization reaction of diarylethenes having an azulene ring occurs only via higher excited states. Novel diarylethenes having an azulene ring with a strong donor or acceptor were synthesized and examined in these reactions. A derivative having an electron-donating 1,3-benzodithiol-2-ylidenemethyl group at the 1-position of the azulene ring showed photochromism, whereas neither a derivative having a π-conjugated electron-donating group at the 3-position of the azulene ring nor derivatives having a π-conjugated electron-withdrawing group at the 1- or 3-position of the azulene ring showed any photochromism. The photoreactivities of these compounds were explained by calculating forces and bond orders on the excited states using density functional theory (DFT) and time-dependent (TD)-DFT.     

In vivo estimation of optical properties of rat liver using single-reflectance fiber probe during ischemia and reperfusion

Optical Review - To quantify the changes in optical properties of in vivo rat liver tissue, we applied diffuse reflectance spectroscopy (DRS) system using single-reflectance fiber probe during...     

The Effects of Comprehensive Exercise Program on the Adjustments of Standing Balance in Community-Dwelling Elderly Persons

The objective of this study was to assess the effect of comprehensive exercise program widely accepted as a community-based physical intervention for the prevention of falling in the elderly persons on their controlling standing balance. Twenty-six community-dwelling elderly persons (13 males and females; 69.8 ± 2.8 years old) participated in this study. Daily exercise was comprised of walking for more than 30 min, stretching, muscle strengthening and balance exercise without exercise equipments. The intervention was continued for three months. Indicators of standing balance related to static balance, dynamic balance and postural response were measured before and after the intervention. As an effect of the intervention on static balance, the sway of center of pressure (COP) in the static stance significantly increased. In the dynamic balance, significant improvements were observed in one leg standing time, the 10-m gait time, functional reach. Additionally, the maximal movable length of COP which subjects can move voluntarily to right and left significantly increased. In the postural response, the integrated electromyography (IEMG) induced by postural response for sudden postural perturbation significantly decreased in the lower leg muscles. Since less muscular activities were sufficient to maintain posture, it was suggested that postural response was elicited more efficiently following the intervention. This study suggested that the comprehensive exercise program, which has been widely introduced as community-based interventions for the prevention of falling, have extensive effects on the control of standing balance covering static balance, dynamic balance and postural response in the elderly persons.     

Certain Probabilistic Aspects of Semistable Laws

We study the extent to which the property of semistability of a random vector in ^d is determined by semistability of its marginals, and the place of semistable laws within the family of type G and sub-stable laws. Similarities and differences between stable and semistable laws are discussed.     

The Dichotomy of Recurrence and Transience of Semi-Lévy Processes

A semi-Lévy process is an additive process with periodically stationary increments. In particular, it is a generalization of a Lévy process. The dichotomy of recurrence and transience of Lévy processes is well known, but this is not necessarily true for general additive processes. In this paper, we prove the recurrence and transience dichotomy of semi-Lévy processes. For the proof, we introduce a concept of semi-random walk and discuss its recurrence and transience properties. An example of semi-Lévy process constructed from two independent Lévy processes is investigated. Finally, we prove the laws of large numbers for semi-Lévy processes.     

Trimmed sums of i.i.d. Banach space valued random variables

Limit laws for trimmed sums of triangular arrays of i.i.d. Banach space valued random variables are studied. It is shown that if the array belongs to the domain of attraction of an infinitely divisible law without Gaussian component on a separable Banach space of type 2, then the trimmed sum converges weakly to a nondegenerate Banach space valued random variable.