An Investigation of the Effect of the Canonical Transformation on the Lagrangian

The transformation of the Euler-Lagrange derivative under the point transformation is explicitly stated, and from this view point, the canonical transformation is reinvestigated. In our arguments, the canonical transformations are discussed strictly separately from the canonical equations. A proof is given that the Lagrangian can be restored after any infinitesimal canonical transformation. Some identities are obtained giving relations between canonically transformed and untransformed Lagrangians. Using the identities, the relation between the Noether charge and the generator of the canonical transformation is investigated. The chiral gauge, Galilei and scale transformations are considered as applications to field theory.     

Raman and infrared spectra of the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers of β-carotene: Key bands distinguishing stretched or terminal-bent configurations form central-bent configurations

Raman and infrared spectra in the region of 1800-150 cm⁻¹ were recorded for a set of cis-trans isomers of d̃-carotene, i.e. the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers. Spectral comparison revealed Raman and infrared key bands which (1) distinguish stretched or terminal-bent configurations (all-trans, 7-cis and 9-cis) from central-bent configurations (13-cis and 15-cis), and (2) distinguish unmethylated 7-cis and 15-cis configuratios. Keybands (1) include Raman bands at 1160 and 1140 cm⁻¹ and infrared bands at 825 and 775 cm⁻¹ (the intensity varies with the position of the cis-bend) Key bands (2) include Raman bands at 1274 and 962 cm⁻¹ and an infrared band at 741 cm⁻¹ (characteristic of the 7-cis configuration), and also a Raman band at 1247 cm⁻¹ and an infrared band at 775 cm⁻¹ (characteristic of the 15-cis configuration). The normal modes for the key bands were determined by a set of normal coordinate calculations for the isomeric configurations of a simplified model of d̃-carotene. The key bands were mainly related to the C H in-plane bendings, coupled with the CC or C C stretching, or to the C H out-of-plane wagging vibrations, some of which coupled with the CC torsion.     

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.     

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)...     

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     

Guerbet reaction of primary alcohols leading to beta-alkylated dimer alcohols catalyzed by iridium complexes

[IrCl(cod)]2 and [Cp*IrCl2]2 complexes catalyzed efficiently the Guerbet reaction of primary alcohols to beta-alkylated dimer alcohols in good yields. For instance, the reaction of 1-butanol in the presence of [Cp*IrCl2]2 (1 mol %), t-BuOK (40 mol %), and 1,7-octadiene (10 mol %) produced 2-ethyl-1-hexanol in 93% yield. Various primary alcohols undergo the Guerbet reaction under the influence of Ir complexes to give the corresponding dimer alcohols in good yields. This method provides an alternative direct route to beta-alkylated primary alcohols which are prepared by aldol condensation of aldehydes followed by hydrogenation.     

Direction control of chemical wave propagation in self-oscillating gel array

A chemomechanical actuator utilizing a reaction-diffusion wave across gap junction was constructed toward a novel mircoconveyer by micropatterned self-oscillating gel array. Unidirectional propagation of the chemical wave of the Belousov-Zhabotinsky (BZ) reaction was induced on gel arrays. In the case of using a triangle-shaped gel as an element of the array, the chemical wave propagated from the corner side of the triangle gel to the plane side of the other gel (C-to-P) across the gap junction, whereas it propagated from the plane side to the corner side (P-to-C) in the case of the pentagonal gel array. Numerical analysis based on the Keener-Tyson model was done for understanding the mechanism of unidirectional propagation in triangle and pentagonal gel arrays. The swelling and deswelling changes of the gels followed the unidirectional propagation of the chemical wave.     

One-electron photooxidation and site-selective strand cleavage at 5-methylcytosine in DNA by sensitization with 2-methyl-1,4-naphthoquinone-tethered oligonucleotides

Photosensitized one-electron oxidation was applied to discriminate a specific base site of 5-methylcytosine (mC) generated in DNA possessing a partial sequence of naturally occurring p53 gene, using a sensitizing 2-methyl-1,4-naphthoquinone (NQ) chromophore tethered to an interior of oligodeoxynucleotide (ODN) strands. Photoirradiation and subsequent hot piperidine treatment of the duplex consisting of mC-containing DNA and NQ-tethered complementary ODN led to oxidative strand cleavage selectively at the mC site, when the NQ chromophore was arranged so as to be in close contact with the target mC. The target mC is most likely to be one-electron oxidized into the radical cation intermediate by the sensitization of NQ. The resulting mC radical cation may undergo rapid deprotonation and subsequent addition of molecular oxygen, thereby leading to its degradation followed by strand cleavage at the target mC site. In contrast to mC-containing ODN, ODN analogs with replacement of normal cytosine, thymine, adenine, or guanine at the mC site underwent less amount of such an oxidative strand cleavage at the target base site, presumably due to occurrence of charge transfer and charge recombination processes between the base radical cation and the NQ radical anion. Furthermore, well designed incorporation of the NQ chromophore into an interior of ODN could suppress a competitive strand cleavage at consecutive guanines, which occurred as a result of positive charge transfer. Thus, photosensitization by an NQ-tethered ODN led to one-electron oxidative strand cleavage exclusively at the target mC site, providing a convenient method of discriminating mC in naturally occurring DNA such as human p53 gene as a positive band on a sequencing gel.