Role of Prehistories in the Initial Value Problems of Fractional Viscoelastic Equations

The fractional viscoelastic equation (FVE), which is a second-order differential equation with fractional derivatives describing the dynamical behavior of a single-degree-of-freedom viscoelastic oscillator, is considered. Some viscoelastic damped mechanical systems may be described by FVEs. However, FVEs with conventional nonzero initial values cannot generally be solved. In this paper, the prehistories of the unknown functions before the initial times, referred to as the initial functions, are taken into account to solve FVEs. Mathematically, appropriate initial functions are essential for unique solutions of FVEs. Physically, the initial functions reflect the processes of giving the initial values. FVEs are solved for some initial functions both by analytical and numerical methods. The initial functions affect the solutions of FVEs. It is discussed how the solutions depend on the initial functions. Implication of the solutions to viscoelastic materials will be discussed.     

Precipitation of Zinc Sulfide Particles from Homogeneous Solutions

Zinc sulfide particles were homogeneously precipitated by thermal decomposition of thioacetamide in acidic aqueous solutions in a one-step process. The influence of the operating conditions (initial concentration of zinc ion and TAA) on the nucleation time and number concentration of the generated particles was investigated. The experimental results show that the model of homogeneous nucleation previously developed and successfully tested for silver particle generation by a chemical reduction method can also be applied to the formation of zinc sulfide particles by homogeneous precipitation. Furthermore, in the particle formation method in which the nucleation time t* can be measured, the particle number concentration n* can be predicted by the simple relation n*=1/(4pir*Dt*) (r* is the critical nucleus radius, and D the monomer diffusion coefficient). Thus the particle number concentration can be easily predicted even if the rate expression and the critical supersaturation concentration are unknown. Copyright 2000 Academic Press.     

Network structure of fine silica particles

The network structure of silica aerogels heated at 300, 400 and 500°C in dried air have been determined by neutron total scattering measurements using a pulsed spallation neutron source. SANS experiments were also performed to obtain the particle size of the silica constituting aerogel. The elementary particle size obtained is about 13Å in diameter. The distances of the Si-O and O-O interactions in such fine silica particles are 1.61 and 2.64 Å, respectively, which are the same as those of fused silica. The coordination numbers of these pairs are found to be less evident than those of fused silica. In addition, the distances of the Si-Si pairs in the aerogels are slightly longer than that of fused silica. According to the heat treatment temperature, the coordination numbers of the Si-O and O-O interactions increase and the distance of the Si-Si pair decreases. These results indicate that although the network structure of fine silica particles treated at lower temperature is loose and imperfect, such structure can be changed by heating at relatively low temperature. The Raman spectra and the skeletal density measurements of the aerogels support also these results.     

A Method of Orthogonal Oligosaccharide Synthesis Leading to a Combinatorial Library Based on Stationary Solid‐Phase Reaction

A new, efficient synthesis of oligosaccharides, which involves solid‐phase reactions without mixing in combination with an orthogonal‐glycosylation strategy, is described. Despite a great deal of biological interest, the combinatorial chemistry of oligosaccharides is an extremely difficult subject. The problems include 1) lengthy synthetic protocols required for the synthesis and 2) the variety of glycosylation conditions necessary for individual reactions. These issues were addressed and solved by using the orthogonal‐coupling protocol and the application of a temperature gradient to provide appropriate conditions for individual reactions. Furthermore, we succeeded in carrying out solid‐phase reactions with neither mechanical mixing nor flow. In this report, the synthesis of a series of trisaccharides, namely, α/β‐L ‐Fuc‐(1→6)‐α/β‐D ‐Gal‐(1→2/3/4/6)‐α/β‐D ‐Glc‐octyl, is reported to demonstrate the eligibility of the synthetic method in combinatorial chemistry.     

Reversible and stable redox behavior of a Pt(II) bis(dithiobenzoate)-type complex attributed to rotaxane-based stabilization

A three-dimensionally insulated Pt(II) bis(dithiobenzoate) complex with a [1]rotaxane structure was synthesized using permethylated cyclodextrins. We have confirmed macrocyclic insulation is necessary to yield the Pt(II) bis(dithiobenzoate) complex with high selectivity. Furthermore, the formed Pt(II) complex showed highly stable and reversible two-step redox behavior in cyclic voltammetry due to the three-dimensional insulation.     

Einen Saugfiltrierapparat

Ohne Zusammenfassung     

Exponents of 2-multiarrangements and multiplicity lattices

We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.