Rearrangement of 6,7-dithiabicyclo[3.1.1]heptane 6-oxides to a 7,8-dithia-6-oxabicyclo[3.2.1]octane catalyzed by montmorillonite K 10

Treatment of 2,2,4,4-tetramethyl-1,5-diphenyl-6,7-dithiabicyclo[3.1.1]heptane 6-endo-oxide ( 2 ) with Montmorillonitc K 10 in dichloromethane gave 2,2,-4,4-tetramethyl-1,5-diphenyl-7,8-dithia-6-oxabicyclo-[3.2.1]octane ( 6 ) (11%) with recovery of 2 (87%). Under similar reaction conditions, the 6-exo-oxide 7 and the sulfenate 6 gave a mixture of 6 (21%), 2 (67%), and 7 (9%) and a mixture of 2 (89%) and 6 (9%), respectively. These results indicate the relative thermodynamic stabilities of the three compounds to be 2 > 6 > 7 . PM3 calculations on these compounds showed the heats of formation (kcal/mol) to be in the following order: 6 (44.12783), 2 (57.46721), and 7 (59.37918). The driving force of this unusual 1,2-rearrangement of 2 and 7 to 6 would be the release of the ring strain of the bicyclo[3.1.1]heptane system of 2 and 7 by ring expansion.     

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.     

Conformal equations that are not Virasoro or Weyl invariant

Letters in Mathematical Physics - While the argument by Zamolodchikov and Polchinski suggests global conformal invariance implies Virasoro invariance in two-dimensional unitary conformal field...     

A new model for spectral sensitization of photoconduction in zinc oxide powder

Seven organic dyes were adsorbed on photoconductive zinc oxide powder and their sensitizing efficiencies were examined. The adsorption of dye induced a change in the dark conductivity, the magnitude of which appeared to represent the sensitizing power of the dye. The initial slope of sensitized photocurrent was found to be an exponential function of σ₀, the pre-exponential factor in the conductivity equation. A model is proposed, which is consistent with all the observations. In this model, the sensitized photoinjection of electrons is assumed to occur from surface states to the bulk, depending upon the population of the surface states. A critical surface level for the spectral sensitization is introduced to account for the observed temperature effect. Surface states located below the critical energy are assumed not to contribute for the sensitization.     

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)...