A Spinorization of a Constrained Vector System and a Spinor Reconstruction Theorem

An elementary method of conctructing a spinor from vectors satisfying constraint conditions is proposed. We consider orthonormal triad and tetrad as an orientable physical object and introduce parameter representations of them, in terms of the Euler angles and the pseudo-Euler angles. Having determined the transformation property of the parameters, we set up the spinor determining equation. This equation is solved. The solution (spinor) contains four arbitrary complex constants, in 3 + 1 dimensional space. Using the proposed method, we prove the spinor reconstruction theorem, i.e. the original Dirac spinor can be reconstructed from seven of the sixteen hermitian bilinear forms, except the overall phase factor (the gauge freedom of the 1st kind). The energy density of the spinor field is written in terms of currents and their space derivatives.     

Operating principles of the cerebral cortex as a six-layered network in primates: beyond the classic canonical circuit model

The cerebral cortex performs its computations with many six-layered fundamental units, collectively spreading along the cortical sheet. What is the local network structure and the operating dynamics of such a fundamental unit? Previous investigations of primary sensory areas revealed a classic “canonical” circuit model, leading to an expectation of similar circuit organization and dynamics throughout the cortex. This review clarifies the different circuit dynamics at play in the higher association cortex of primates that implements computation for high-level cognition such as memory and attention. Instead of feedforward processing of response selectivity through Layers 4 to 2/3 that the classic canonical circuit stipulates, memory recall in primates occurs in Layer 5/6 with local backward projection to Layer 2/3, after which the retrieved information is sent back from Layer 6 to lower-level cortical areas for further retrieval of nested associations of target attributes. In this review, a novel “dynamic multimode module (D3M)” in the primate association cortex is proposed, as a new “canonical” circuit model performing this operation.     

Measurement Accuracy in Phase-Shifting Point Diffraction Interferometer with Two Optical Fibers

A phase-shifting point diffraction interferometer (PS/PDI) with point sources of two single mode optical fibers has been developed, which will be appropriate for the surface figure measurement of large aperture optics on a sub-nanometer scale. To reduce the measurement error factors, a fiber optic plate (FOP) is used as a projection plane for interference pattern. Errors caused by imperfection of optical alignment, such as position of point sources and tilt of FOP, are minimized by analyzing the measured phase data with an original method. Measurement accuracy in the PS/ PDI is estimated with the interference pattern produced by the two optical fiber sources. If inhomogeneity of the FOP and a systematic error of the PS/PDI are eliminated, the measurement accuracy of the present system is estimated to be less than 4nm P-V and 0.7nm rms, respectively, at a measurement wavelength of 632.8 nm.     

On p-class groups of relative cyclic p-extensions

Archiv der Mathematik - We prove a general stability theorem for p-class groups of number fields along relative cyclic extensions of degree $$p^2$$ , which is a generalization of a finite-extension...     

Temperature sensitivity of Ge-B-SiO(2) waveguide Bragg gratings on a crystallized glass substrate

Waveguide Bragg gratings were fabricated by plasma-enhanced chemical-vapor deposition followed by irradiation with KrF excimer laser light through a phase mask. The period of the Bragg grating was 0.53 mum, and the Bragg wavelength was ~1.53 mum . The temperature dependence of the Bragg wavelength was 11 pm/ degrees C for a 10GeO(2) -90SiO(2)(mol.%) core waveguide on a Si substrate, and the Bragg wavelength shift was successfully reduced to 5.0pm/ degrees C by use of a 14GeO(2)-12B(2)O(3)-74SiO(2) (mol.%) core and a crystallized glass substrate with a thermal-expansion coefficient of -2.0x10(-6)(/ degrees C) .     

Numerical computation of the nonlinear Schrödinger equation with higher order group velocity dispersion and frequency-dependent gain using the differential method

Optical Review - The response of light in a nonlinear dispersive medium is governed by the nonlinear Schrödinger equation (NLSE). In general, for higher order group velocity dispersion (GVD)...     

Reaction dynamics of excited 2-(3-benzoylphenyl)propionic acid (ketoprofen) with histidine

Photoreaction dynamics of 2-(3-benzoylphenyl)propionic acid (ketoprofen, KP), one of nonsteroidal anti-inflammatory drugs, with histidine in a phosphate buffer solution (pH 7.4) was investigated with the laser flash photolysis. The deprotonated form of KP (KP(-)) was decarboxylated via UV laser excitation to form a carbanion. It was found that histidine accelerates the protonation reaction of the carbanion to 3-ethylbenzophenone ketyl biradical (3-EBPH) for the first time. The experimental results of the photoreaction of KP with alanine as well as the photoreaction of KP with 4-methylimidazole (a part of the side chain of histidine) in methanol, clearly showed that the protonated form of histidine is a key species for the protonation reaction of the carbanion. These series of the initial reactions should result in the occurrence of photosensitization in vivo. The reaction mechanism was discussed in detail.     

Generation and detection of the radical cation and the dication derived from 4,9‐diethyl[1,4]dihydrodithiino[5,6‐f]benzotrithiole and its 5‐oxide

4,9‐Diethyl[1,4]dihydrodithiino[5,6‐f]benzotrithiole (DTBT) gave a radical cation, DTBT(•+), and a dication, DTBT(2+), on treatment with a single‐electron oxidizing reagent. Both compounds showed an ESR signal, whereas the dication, generated by this procedure, was silent for ¹H NMR. Hydrolysis of DTBT(2+) gave DTBT 1‐oxide (DTBT 1‐O) and 2‐oxide (DTBT 2‐O) together with DTBT and a mixture of several dioxides. A singlet‐state dication, DTBT(2+)‐S, which was generated upon treatment of DTBT 5‐oxide (DTBT 5‐O) with concentrated D₂SO₄, was detected by ¹H and ¹³C NMR. After 20 h, the NMR signals disappeared while the solution was active for ESR. The results suggest that (i) a species generated from DTBT by oxidation with the single‐electron oxidizing reagent is a triplet‐state dication, DTBT(2+)‐T, and (ii) DTBT(2+)‐S, initially generated, gradually isomerizes to DTBT(2+)‐T in the solution, and DTBT(2+)‐T forms a partial spin pair. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:394–401, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20445