Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type

A new approach to soliton equations, based on τ functions (or Hirota's dependent variables), vertex operators and the Clifford algebra of free fermions, is applied to study a new hierarchy of Kadomtsev-Petviashvili type equations (the BKP hierarchy). The infinite-dimensional orthogonal group acts on the space of BKP τ-functions. The Sawada-Kotera equation is obtained as a reduction of BKP. Its infinitesimal transformations constitute the Euclidean Lie Algebra A₂⁽²⁾.     

Monodromy preserving deformation of linear ordinary differential equations with rational coefficients: I. General theory and τ-function

A general theory of monodromy preserving deformation is developed for a system of linear ordinary differential equations $\text{d}\text{Y}\text{d}\text{x}\text{=A(x)Y}$, where A(x) is a rational matrix. The non-linear deformation equations are derived and their complete integrability is proved. An explicit formula is found for a 1-form ω, expressed rationally in terms of the coefficients of A(x), that has the property dω=0 for each solution of the deformation equations. Examples corresponding to the “soliton” and “rational” solutions are discussed.     

The reciprocity relation of the Selberg function

The reciprocity relation of the Beta function is reformulated, and that of the Selberg function is presented.     

Electrochemical monitoring of glutamate release at multiple positions in a rat hippocampal slice.

The continuous monitoring of the distribution of glutamate (Glu), a neurotransmitter released at synaptic terminals, is important in terms of understanding the signal transfer mechanism in the brain. In this study, we monitored the concentration of Glu released at multiple positions in a hippocampal slice continuously, and obtained an approximate Glu distribution by using our electrochemical glutamate sensor array. After confirming our sensor's high sensitivity to Glu, we placed a slice on the array, and measured the currents at selected electrodes in the array. When we stimulated a specific position in the slice electrically, the glutamate concentration increased in different areas after several tens of seconds. The presence of glutamate receptor blockers suppressed these increases. This suggests that the electrical signal was transferred along with neurons through synapses and stimulated the Glu release. Our multichannel glutamate sensor should be a powerful tool to determining the distribution of real-time glutamate non-invasively for the studies using biological samples.     

Mechanical property and molecular weight distribution changes with photo- and chemical-degradation on LDPE films

In order to clarify the effect of photo- and chemical-degradation on the structure of polyethylene materials, the change in molecular weight distribution and mechanical properties of photo- and chemical-degraded LDPE films were investigated. The molecular weight distribution was significantly changed with photo-exposing times, and the drastic change appeared especially for 8 days-exposed samples where the molecular weight of the high molecular weight fraction increased. However, the molecular weight of the lower molecular weight fraction was almost the same for all the photo-exposed films, irrespective of irradiation time, and also for chemical-degraded films. It is suggested that the molecular chains with a certain length, which consist of a crystal lamellae in spherulites, cannot be broken by photo-irradiation. Consequently, there would be threshold for the molecular weight in terms of photo-degradation process, and almost the same threshold can be observed for the chemical-etching films. Stress-strain curves were measured for photo-degraded films and their “quenched films after remolding” and “annealed films after remolding”, and chemical-degraded films.     

Automatic microdistillation flow-injection system for the spectrophotometric determination of fluoride

An automatic flow-injection (FI) system including on-line separation by microdistillation and spectrophotometric detection has been developed for the determination of trace amounts of fluoride. This ion was separated from sample matrix by distillation in the presence of sulfuric and phosphoric acids, and was subsequently determined with spectrophotometry based on the mixed-ligand complex of lanthanum(III)-fluoride-alizarin complexone. The proposed FI system has high sampling frequency (20 samples h⁻¹), small sample size (600 μl) and the dynamic range of 0.05-15 mg l⁻¹ with relative standard deviations of below 1.2%. Interfering ions such as aluminum(III) and iron(III) was effectively eliminated. The method was successfully applied to the determination of fluoride in industrial drainage after water treatment.     

MOCVD growth of high-quality AlGaAs on Si substrates for high-efficiency solar cells

The crystallinity and solar cell efficiency of Al_0.22Ga_0.78As layers grown on Si substrates have been studied by varying the thermal cycle annealing (TCA) temperature. The optimum TCA temperature to obtain an Al_0.22Ga_0.78As layer with long minority carrier lifetime and high conversion efficiency has been presented. The active-area conversion efficiency of an Al_0.22Ga_0.78As solar cell on a Si substrate as high as 10.2% has been obtained under AM0 and 1 sun conditions.     

Optimization of pairings and detection conditions for measurement of FRET between cyan and yellow fluorescent proteins.

Detection of F?rster resonance energy transfer (FRET) between cyan and yellow fluorescent proteins is a key method for quantifying dynamic processes inside living cells. To compare the different cyan and yellow fluorescent proteins, FRET efficiencies were measured for a set of the possible donor:acceptor pairs. FRET between monomeric Cerulean and Venus is more efficient than the ECFP:EYFP pair and has a 10% greater F?rster distance. We also compared several live cell microscopy methods for measuring FRET. The greatest contrast for changes in intramolecular FRET is obtained using a combination of ratiometric and spectral imaging. However, this method is not appropriate for establishing the presence of FRET without extra controls. Accurate FRET efficiencies are obtained by fluorescence lifetime imaging microscopy, but these measurements are difficult to collect and analyze. Acceptor photobleaching is a common and simple method for measuring FRET efficiencies. However, when applied to cyan to yellow fluorescent protein FRET, this method becomes prone to an artifact that leads to overestimation of FRET efficiency and false positive signals. FRET was also detected by measuring the acceptor fluorescence anisotropy. Although difficult to quantify, this method is exceptional for screening purposes, because it provides high contrast for discriminating FRET.     

Asymmetric cyclopropanation of 2,5-dimethyl-2,4-hexadiene by copper catalysts bearing new bisoxazoline ligands

Some new bisoxazoline ligands with an aryl group at the 4-position and gem-dimethyl groups at the 5-position on the oxazoline ring were prepared from arylglycines. Remarkable enhancement of the trans-selectivity (trans/cis = 87/13) and the enantioselectivity (96% ee for the trans product) was demonstrated for the asymmetric cyclopropanation of 2,5-dimethyl-2,4-hexadiene with tert-butyl diazoacetate catalyzed by the new copper-bisoxazoline complex.     

Effects of T-tubules on dielectric spectra of skeletal muscle simulated by boundary element method with two-dimensional models

In order to investigate the origin of large intensity the alpha-relaxation in skeletal muscles observed in dielectric measurements with extracellular electrode methods, effects of the interfacial polarization in the T-tubules on dielectric spectra were evaluated with the boundary-element method using two-dimensional models in which the structure of the T-tubules were represented explicitly. Each model consisted of a circular inclusion surrounded by a thin shell corresponding to the sarcolemma. The T-tubules were represented by simplified two types of invagination of the shell: straight invagination along the radial directions, and branched one. Each of the models was subjected to two kinds of calculations relevant to experiments with the extracellular and the intracellular electrode methods. Electrical interactions between the cells were omitted in the calculations. Both calculations showed that the dielectric spectra of the models contained two relaxation terms. The low-frequency relaxation term assigned to the alpha-relaxation depended on the structure of the T-tubules. Values of the relaxation frequency of the alpha-relaxation obtained from the two types of calculations agreed with each other. At the low-frequency limit, the permittivity obtained from the extracellular-electrode-type calculations varied in proportion to the capacitance obtained from the intracellular-electrode-type ones. These results were consistent with conventional lumped and distributed circuit models for the T-tubules. This confirms that the interfacial polarization in the T-tubules in a single muscle cell is not sufficient to explain the experimental results in which the intensity of the alpha-relaxation in the extracellular-electrode-type experiments exceeded the intensity expected from the results of the intracellular-electrode-type experiments. The high-frequency relaxation term that was assigned to the beta-relaxation was also affected by the T-tubule structure in the calculations relevant to the extracellular-electrode-type experiments.