Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

The fMRI response of the LGN and V1 to cardinal red-green, blue-yellow, and achromatic visual stimuli

We compared the responsiveness of the LGN and the early retinotopic cortical areas to stimulation of the two cone-opponent systems (red - green and blue - yellow) and the achromatic system. This was done at two contrast levels to control for any effect of contrast. MR images were acquired on seven subjects with a 4T Bruker MedSpec scanner. The early visual cortical areas were localised by phase encoded retinotopic mapping with a volumetric analysis (Dumoulin et al, 2003 NeuroImage 18 576 - 587). We initially located the LGN in four subjects by using flickering stimuli in a separate scanning session, but subsequently identified it using the experimental stimuli. Experimental stimuli were sine-wave counterphasing rings (2 Hz, 0.5 cycle deg-1), cardinal for the selective activation of the L/M cone-opponent (RG), S cone-opponent (BY), and achromatic (Ach) systems. A region of interest analysis was performed. When presented at equivalent absolute contrasts (cone contrast = 5% - 6%), the BOLD response of the LGN is strongest to isoluminant red - green stimuli and weakest to blue - yellow stimuli, with the achromatic response falling in between. Area V1, on the other hand, responds best to both chromatic stimuli, with the achromatic response falling below. The key change from the LGN to V1 is a dramatic boost in the relative blue - yellow response, which occurred at both contrast levels used. This greatly enhanced cortical response to blue - yellow relative to the red - green and achromatic responses may be due to an increase in cell number and/or cell response between the LGN and V1. We speculate that the effect might reflect the operation of contrast constancy across colour mechanisms at the cortical level.

An investigation into the synthesis of polycarbazole squaraine derivatives

The polycondensation of squaric acid with 1,2-(9-Ethylcarbazol-3-yl)ethene and N-ethyliminostilbene in polyphosphoric acid yielded insoluble polymers which included substituted phosphate groups on the phenyl rings. The presence of phosphorus in these polymers was identified using solid-state P-31 NMR and EDAX techniques. Furthermore the phosphate groups were not ionic, hence no charge-balancing anions were present; Both polymers did not electrically conduct but exhibited dielectric breakdown values of 0.1 and 0.06 MV cm(-1) respectively.

Molecular motion in miscible polymer blends .1. Motion in blends of PEO and PVPh studied by solid-state C-13 T-1 rho measurements

Changes in molecular motion in blends of PEO-PVPh have been studied using measurements of C-13 T-1 rho relaxation times. C-13 T-1 rho relaxation has been confirmed as arising from spin-lattice interactions by observation of the variation in T-1 rho with rf field strength and temperature. In the pure homopolymers a minimum in T-1 rho is observed at ca. 50 K above the glass transition temperatures detected by DSC. After blending, the temperature of the minimum in T-1 rho for PEO increased, while that for PVPh decreased, however, the minima, which correspond to the temperatures where the average correlation times for reorientation are close to 3.1 mu s, are separated by 45 K (in a 45% PEO-PVPh blend). These phenomena are explained in terms of the local nature of T-1 rho measurements. The motions of the individual homopolymer chains are only partially coupled in the blend. A short T-1 rho has been observed for protonated aromatic carbons, and assigned to phenyl rings undergoing large-angle oscillatory motion, The effects of blending, and temperature, on the proportion of rings undergoing oscillatory motion are analyzed.

Self-organization with traveling waves: A case for a convective torus

A traveling wave of BaSO4 in the chlorite-thiourea reaction has shown concentric precipitation patterns upon being triggered by the autocatalyst HOCl. The precipitation patterns show circular rings of alternate null and full precipitation regions. This self-organization appears to be the result of the formation of a convective torus. The formation of the convective torus can be described as a Benard-Marangoni instability with lateral heating.

The chemistry of novolac resins .3. C-13 and N-15 nmr studies of curing with hexamethylenetetramine

The reactions between novolac resins and hexamethylenetetramine (HMTA) which occur on curing have been studied by C-13 and N-15 high-resolution n.m.r. in both solution and the solid state. Strong evidence for the existence of many curing intermediates is obtained. New curing intermediates are reported along with experimental data to support previously postulated intermediates. The initial curing reactions between novolac and HMTA produce various substituted benzoxazines and benzylamines. Thermal decomposition/oxidation and further reactions of these initial intermediates generate methylene linkages between phenolic rings for chain extension and cross-linking. Among the three kinds of methylene linkages, the para-para methylene linkages are formed at relatively lower temperatures. Various imine, amide and imide side-products also concurrently appear during the process. The initial amount of HMTA plays a critical role in the curing reactivity and chemical structures of the cured resins. The lower the amount of HMTA, the lower the temperature at which curing occurs, and the lower the amount of the nitrogen-containing side-products in the finally cured resins. The ortho-linked intermediates are relatively stable, and can remain in the cured resins up to higher temperatures. The study provides an extensive description of the curing reactions of novolac resins. (C) 1997 Elsevier Science Ltd.

Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

Embryonic development of the nervous system of the temnocephalid flatworm Craspedella pedum

The nervous system of temnocephalid flatworms consists of the brain and three pairs of longitudinal connectives extending into the trunk and tail. The connectives are crosslinked by an invariant number of regularly spaced commissures. Branches of the connectives innervate the tentacles of the head and the sucker organ in the tail. A set of nerve rings encircling the pharynx and connected to the brain and connectives constitute the pharyngeal nervous system. The nervous system is formed during early embryogenesis when the embryo represents a multilayered mesenchymal mass of cells. Gastrulation and the formation of separate epithelial germ layers that characterize most other animal groups are absent. The brain arises as a bilaterally symmetric condensation of postmitotic cells in the deep layers of the anterior region of the embryonic mesenchyme. The pattern of axon outgrowth, visualized by labeling with anti-acetylated tubulin (acTub) antibody, shows marked differences from the pattern observed in other flatworm taxa. in regard to the number of neurons that express the acTub epitope. Acetylated tubulin is only expressed in neurons that form long axon tracts. In other flatworm species, such as the typhloplanoid Mesostoma and the polyclad Imogine, which were investigated by us with the acTub antibody (Hartenstein and Ehlers [2000] Dev. Genes Evol. 210:399-415; Younossi-Hartenstein and Hartenstein [2000] Dev. Genes Evol. 210:383-398), only a small number of pioneer neurons become acTub positive during the embryonic period. By contrast, in temnocephalids, most, if not all, neurons express acTub and form long, large-diameter axons. Initially, the brain commissure, pharyngeal nerve ring, and the connectives are laid down. Commissural tracts and tentacle nerves branching off the connectives appear later. We speculate that the precocious differentiation of the nervous system may be related to the fact that temnocephalids move by muscle action, and possess a massive and complex muscular system when they hatch. In addition, they have muscular specializations such as the anterior tentacles and the posterior sucker that are used as soon as they hatch. By contrast, juveniles of Mesostoma and larvae of polyclads move predominantly by ciliary action that may not require a complex neural circuitry for coordination. (C) 2001 Wiley-Liss, Inc.

A comparative study of the radiation resistance of four optically transparent polyimides

A comparative study of the high energy radiation resistance to formation of radicals in two pairs of polymers is reported. In one pair of polymers the phenyl groups containing the imide rings are separated by an ether linkage and in the other pair they are separated by an hexafluoroisopropylidine group. Two of the polymers contained aromatic amine units linked through an ether linkage and the other two polymers contained a trifluoromethyl biphenyl diamine. The polymers were shown to retain a high level of transparency in the visible region following radiolysis to doses as high as 8 Gy. ESR studies of the resistance to radical formation on radiolysis. at 77 K revealed that the polymers containing ether linkages were more stable than their fluorinated analogues, but all were less stable than Kapton (R). (C) 2001 Elsevier Science Ltd. All rights reserved.