Vibrational properties of noble gas endohedral fullerenes

Analysis of IR and Raman spectra of Ar@C(60) and Kr@C(60) shows that the incorporation of noble gas atoms causes a blue shift of low energy vibrations, which have radial character, and a red shift of higher energy ones which have a tangential character movement. The mechanism of these phenomena is explained on the basis of ab initio numerical experiments with DFT and MP2 procedures. Methodological discussions are advanced, altogether with a scheme for the estimation of the van der Waals interaction between fullerene and noble gas, based on the frequency shifts.     

Multiple gamma functions,multiple sine functions,and Appell’s <Emphasis Type="Italic">O</Emphasis>-functions

Kurokawa introduced q-multiple gamma functions and q-multiple sine functions. We show that the Appell’s O-function is expressed via the q-multiple gamma function. We also give some applications of this result. For example, we obtain a formula for the “Stirling modular form” and calculate special values of the q-multiple sine function. Moreover, we give some formulas of Eisenstein series and double cotangent functions and its generalization. Then the former gives an infinite product expression of the double sine function explicitly and a result of Kurokawa.     

Cost‐efficient monitoring of continuous‐time stochastic processes based on discrete observations

Planning a cost‐efficient monitoring policy of stochastic processes arises from many industrial problems. We formulate a simple discrete‐time monitoring problem of continuous‐time stochastic processes with its applications to several industrial problems. A key in our model is a doubling trick of the variables, with which we can construct an algorithm to solve the problem. The cost‐efficient monitoring policy balancing between the observation cost and information loss is governed by an optimality equation of a fixed point type, which is solvable with an iterative algorithm based on the Feynman‐Kac formula. This is a new linkage between monitoring problems and mathematical sciences. We show regularity results of the optimization problem and present a numerical algorithm for its approximation. A problem having model ambiguity is presented as well. The presented model is applied to problems of environment, ecology, and energy, having qualitatively different target stochastic processes with each other.     

Second Harmonic Generation in Bis Typed Organic Compounds

In systematic research on a series of new nonlinear organic materials, we found that Bis (4-nitrophenoxy) methane (BNPM) showed a large intensity of second harmonic light, which was 4.4 times as large as that of urea crystal by powder technique and easily crystallized from a solution. The crystal structure of BNPM, obtained by the X-ray diffraction method, was orthorhombic, space group P2₁2₁2 (point group 222), with unit-sell dimension a = 10.205 Å; b = 12.854 Å; c = 4.8822 Å. In addition, we found that the absorption edge of BNPM was 430 nm with a 0.9-mm-thick crystal, and we observed the second harmonic light with BNPM single crystal at the wavelength of 1064 nm and in the range from 906 nm to 990 nm.     

A simple method for counting the number of trapped ions in an ion trap

A technique is proposed for injection-seeding control of tunable lasers. It is based on a combination of successive external injection and intracavity self-injection of radiation when the active medium is pumped by dual-step pulses. The technique is tested both experimentally (in the case of Nd:YAG-laser-pumped pulsed dye lasers) and numerically, using a model developed by us. Full conversion of the broadband spectrum into the injected line is achieved for an output energy greater by a factor of about 50 than that managed by means of the traditional injection-seeding technique under identical conditions.     

Corelationship between local structure and water purifying ability of iron-containing waste glasses

A relationship between the structure and water purifying ability of waste glass prepared from household garbage and Fe₂O₃ was examined by ⁵⁷Fe-Mössbauer and induced coupled plasma (ICP) measurements. From the Debye temperature of waste glass, Fe^II proved to be loosely bound in the glass network as a network modifier. Dissolution amount of Fe^III into artificial drain can be controlled from 0.14 to 0.35 mg/l by changing the Fe₂O₃ content. It proved that chemical oxygen demand (COD) decreases in proportion to the content of Fe^III, indicating that iron causes decomposition of organic and phosphorus compounds.     

Synthesis of glycosaminoglycans via enzymatic polymerization

Hyaluronic acid and chondroitin were successfully synthesized as representative molecules of glucosaminoglycans and galactosaminoglycans found in a glycosaminoglycan family via enzymatic polymerization catalyzed by testicular hyaluronidases. A newly designed N-acetylhyalobiuronate oxazoline derivative with a β-D -glucuronyl-(1→3)-N-acetyl-D -glucosamine disaccharide structure served as a transition-state analogue substrate monomer for the enzyme, giving rise to artificial hyaluronic acid in 52% yields with a number-average molecular weight of 1.35 × 10⁴ through ring-opening polyaddition in a perfect regioselective and stereoselective manner. A novel N-acetylchondrosine oxazoline derivative with a β-D -glucuronyl-(1→3)-N-acetyl-D -galactosamine disaccharide structure also acted as a transition-state analogue substrate monomer for the enzyme, yielding artificial chondroitin in 35% yields with a number-average molecular weight of 2.5 × 10³. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3541–3548, 2003     

Measurement of Principal-Stress Directions from Photoelastic Experiment Using Generalized Phase-Shift Method

A generalized phase-shift method is developed for automatic measurement of principal-stress directions in the whole field of a model from photoelastic experiments. This method uses a set of light intensities obtained from the rotation of polaroids in dark-field plane polariscopes at each point. To investigate the accuracy of the measurement, time-series light intensity curves with different noise and different numbers of data which constitute the curves are used in computer simulation. The error of the measurement of the principal-stress directions obtained by the method is not greatly affected by noise when the number of data exceeds 50. This method is applied to a circular disk subjected to a concentrated load. The principal-stress directions obtained by the method are found to be in good agreement with the theory.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27–29, Saitama, Japan.