Constraints on operator ordering from third quantization

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.     

In situ X-ray observation of phase transformation in Fe2O3 at high pressures and high temperatures

A laser-heated sample in a diamond anvil cell and synchrotron X-ray radiation was used to carry out structural characterization of the phase transformation of Fe₂O₃ at high pressures (30-96 GPa) and high temperature. The Rh₂O₃(II) (or orthorhombic perovskite) structure transforms to a new phase, which exhibits X-ray diffraction data that are indicative of a CaIrO₃-type structure. The CaIrO₃-type structure exhibited an orthorhombic symmetry (space group: Cmcm) that was stable at temperatures of 1200-2800 K and pressure of 96 GPa (the highest pressure used). Unambiguous assignment of such a structure requires experimental evidence for the presence of two Fe species. Based on the equation of state of gold, the phase boundary of the CaIrO₃-type phase transformation was P (GPa)=59+0.0022×(T−1200) (K).     

Enhancement of sonochemical reaction of terephthalate ion by superposition of ultrasonic fields of various frequencies

The ultrasonic reactor with dual frequency was used and the effect of frequency on the fluorescence intensity of terephthalate ion was experimentally investigated in the frequency range from 176 to 635 kHz. The sonochemical reaction fields were visualized by using sonochemical luminescence of luminol solution. Compared with the fluorescence intensity of terephthalate ion for single frequency, the fluorescence intensity for dual frequency increased. The fluorescence intensity ratio of dual frequency to single frequency had maximum value when the frequency of transducer attached at the bottom wall was comparable in magnitude to that at the side wall. In the case of dual frequency, the sonochemical reaction fields became more extensive in the reactor and more intensive around the center of the reactor.     

Triallylstannyllithium-allyllithium as an initiator for the anionic reversible chain transfer polymerization of 1,3-butadiene

The anionic polymerization of 1,3-butadiene using a novel metalloidal anion initiator, triallylstannyllithium (TALi)-allyllithium (ALi), was studied. The TALi-ALi initiated anionic polymerization of 1,3-butadiene gave the star polymer along with the linear polybutadiene (PBD). The star polymer consisted of three PBD branches and a central tin atom. What is striking is a fact that the number-average molecular weights (M_n) and molecular weight distribution of three PBD branches and linear PBD were almost identical. A reversible chain transfer polymerization mechanism, which includes the equilibrium between tri(macroallyl)-stannyllithium and macroallylic anion, is proposed. © 1996 John Wiley & Sons, Inc.     

A new application of statistical moment theory to evaluate the swelling behavior of thermo-responsive gels

The loosely cross-linked poly(acryloyl-L -proline methyl ester) gel, which is known as one of the typical thermo-responsive gels, shows a volume transition around approximately 14°C in pure water. This volume transition is shifted to higher temperature by treatment in aqueous sodium dodecyl sulfate (SDS). The analysis of the swelling-temperature curve (frequency distribution) was performed according to a moment analysis, in which the area under the swelling-temperature curve (AUC), mean swelling transition temperature (MSTT) and variance of swelling transition temperature (VSTT) were calculated. It is shown that the apparent volume transition temperature can be estimated from MSTT and that VSTT can be used to characterize the shape of the corresponding curves.     

Simultaneous detection of ammonia and humidity using transmission surface plasmon resonance technique

Abstract

Gas sensing by using the transmission surface plasmon resonance (T-SPR) technique was demonstrated. Polyacrylic acid (PAA)/5-nm-thick gold/40-nm-thick silver/polycarbonate grating substrate structure (Sensor A) responded to ammonia; however, it exhibited a strong humidity dependence. Polyvinyl alcohol (PVA)/5-nm-thick gold/40-nm-thick silver/polycarbonate grating substrate structure (Sensor B) as the sensing material was also prepared and it mainly responded to humidity. The T-SPR properties of Sensors A and B were observed simultaneously by a stacking arrangement that enabled us to obtain the responses by using a single spectrophotometer. The ammonia concentration under various humidity conditions could be accurately obtained by simultaneous measurement of Sensors A and B.     

On the absolute Riesz summability of orthogonal series

- , [4]. , .     

Lattices of Intermediate Subfactors

LetNbe an irreducible subfactor of a typeII₁factorM. If the Jones index [M:N] is finite, then the set at(NM) of the intermediate subfactors for the inclusionNMforms afinitelattice. The commuting and co-commuting square conditions for intermediate subfactors are related to the modular identity in the lattice at(NN). In particular, simplicity of a finite groupGis characterized in terms of commuting square conditions of intermediate subfactors forNM=NG. We investigate the question of which finite lattices can be realized as intermediate subfactor lattices.     

The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to time

We discuss the local existance and uniqueness of solutions of certain nonstrictly hyperbolic systems, with Hölder continuous coefficients with respect to time variable. We reduce the nonstrictly hyperbolic systems to the parabolic ones, then we shall prove them by use of Tanabe-Sobolevski’s method.