Carbamazepine oxidation catalyzed by iron and manganese porphyrins supported on aminofunctionalized matrices

This work describes the catalytic activity of manganese and iron porphyrins, Mn and Fe(TFPP)Cl, covalently immobilized on the aminofunctionalized supports montmorillonite K-10 (MontX) and silica (SilX), where X= 1 or 2 represents the length of the organic chain (""arms"") binding the metalloporphyrin to the support. These systems were characterized by UV-vis and Electronic Paramagnetic Resonance (EPR), and they were used as catalysts in the oxidation of carbamazepine (CBZ) by the oxidants iodosylbenzene (PhIO) and hydrogen peroxide. The manganese porphyrin (MnP) catalysts proved to be efficient and selective for the epoxide, the main CBZ metabolite in natural systems. MnMont1 was an excellent catalyst when PhIO was used as oxidant, even better than the same MnP in homogeneous system. Supports bearing short ""arms"" led to the best yields. Although H2O2 is an environmentally friendly oxidant, low product yields were obtained when it was employed in CBZ oxidation. Fe(TFPP)CI immobilized on aminofunctionalized supports was not an efficient catalyst, probably due to the presence of Fe(H) species in the matrix, which led to the less reactive intermediate PFe(IV)(O). (c) 2007 Elsevier B.V. All rights reserved.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

The requirement of zinc and calcium ions for functional MMP activity in demineralized dentin matrices

The progressive degradation of resin-dentin bonds is due, in part, to the slow degradation of collagen fibrils in the hybrid layer by endogenous matrix metalloproteinases (MMPs) of the dentin matrix. In in vitro durability studies, the storage medium composition might be important because the optimum activity of MMPs requires both zinc and calcium. Objective. This study evaluated the effect of different storage media on changes in matrix stiffness, loss of dry weight or solubilization of collagen from demineralized dentin beams incubated in vitro for up to 60 days. Methods. Dentin beams (1 mm x 2 mm x 6 mm) were completely demineralized in 10% phosphoric acid. After baseline measurements of dry mass and elastic modulus (E) (3-point bending, 15% strain) the beams were divided into 5 groups (n = 11/group) and incubated at 37 degrees C in either media containing both zinc and calcium designated as complete medium (CM), calcium-free medium, zinc-free medium, a doubled-zinc medium or water. Beams were retested at 3, 7, 14, 30, and 60 days of incubation. The incubation media was hydrolyzed with HCl for the quantitation of hydroxyproline (HOP) as an index of solubilization of collagen by MMPs. Data were analyzed using repeated measures of ANOVA. Results. Both the storage medium and the storage time showed significant effects on E, mass loss and HOP release (p < 0.05). The incubation in CM resulted in relatively rapid and significant (p < 0.05) decreases in stiffness, and increasing amounts of mass loss. The HOP content of the experimental media also increased with incubation time but was significantly lower (p < 0.05) than in the control CM medium, the recommended storage medium. Conclusions. The storage solutions used to age resin-dentin bonds should be buffered solutions that contain both calcium and zinc. The common use of water as an aging medium may underestimate the hydrolytic activity of endogenous dentin MMPs. (c) 2010 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be 'guessed' from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics II. Application to reflection and refraction at a dielectric interface

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.

Reorganization of structural proteins in vascular smooth muscle cells grown in collagen gel and basement membrane matrices (Matrigel): A comparison with their in situ counterparts

When smooth muscle cells are enzyme-dispersed from tissues they lose their original filament architecture and extracellular matrix surrounds. They then reorganize their structural proteins to accommodate a 2-D growth environment when seeded onto culture dishes. The aim of the present study was to determine the expression and reorganization of the structural proteins in rabbit aortic smooth muscle cells seeded into 3-D collagen gel and Matrigel (a basement membrane matrix). It was shown that smooth muscle cells seeded in both gels gradually reorganize their structural proteins into an architecture similar to that of their in vivo counterparts. At the same time, a gradual decrease in levels of smooth muscle-specific contractile proteins (mainly smooth muscle myosin heavy chain-2) and an increase in p-nonmuscle actin occur, independent of both cell growth and extracellular matrix components. Thus, smooth muscle cells in 3-D extracellular matrix culture and in vivo have a similar filament architecture in which the contractile proteins such as actin, myosin, and alpha -actinin are organized into longitudinally arranged myofibrils and the vimentin-containing intermediate filaments form a meshed cytoskeletal network, However, the myofibrils reorganized in vitro contain less smooth muscle-specific and more nonmuscle contractile proteins. (C) 2001 Academic Press.

The design of hazard risk assessment matrices for ranking occupational health risks and their application in mining and minerals processing

Two hazard risk assessment matrices for the ranking of occupational health risks are described. The qualitative matrix uses qualitative measures of probability and consequence to determine risk assessment codes for hazard-disease combinations. A walk-through survey of an underground metalliferous mine and concentrator is used to demonstrate how the qualitative matrix can be applied to determine priorities for the control of occupational health hazards. The semi-quantitative matrix uses attributable risk as a quantitative measure of probability and uses qualitative measures of consequence. A practical application of this matrix is the determination of occupational health priorities using existing epidemiological studies. Calculated attributable risks from epidemiological studies of hazard-disease combinations in mining and minerals processing are used as examples. These historic response data do not reflect the risks associated with current exposures. A method using current exposure data, known exposure-response relationships and the semi-quantitative matrix is proposed for more accurate and current risk rankings.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Capacidad de enraizamiento de plantas matrices promisorias de Myrciaria dubia (Kunth) Mc Vaugh en cámaras de subirrigación¹

Camu camu es una fruta nativa de la Amazonía, que llama la atención por el alto contenido de vitamina C (6,116 mg/ 100 g de pulpa), está en proceso de domesticación, por lo cual se está investigando un método de propagación vegetativa que permita avanzar en el proceso de mejoramiento genético. El objetivo de este trabajo fue evaluar la capacidad rizogénica de plantas matrices promisorias de camu camu "Myrciaria dubia (Kunth) McVaugh" según el aumento del número de hojas, mediante la técnica de estacas herbáceas en cámaras de subirrigación. El ensayo fue conducido mediante un Diseño de Bloques Completamente al Azar (DBCA) con arreglo factorial 9Ax3B, con 3 repeticiones y 15 estacas por unidad experimental. El factor A, estuvo constituido por nueve plantas matrices y el factor B: pares de hojas con 3 niveles: 1; 2 y 3 pares. El enraizamiento fue evaluado después de 90 días. Se observó que existió interacción estadística significativa para las variables: porcentaje de enraizamiento, longitud y número de raíces. Para las variables porcentaje de callo y porcentaje de mortalidad se encontró efecto de la planta matriz y pares de hojas. Los resultados muestran que el porcentaje de enraizamiento estuvo influenciado por efectos intrínsecos adherentes a la variabilidad genotípica de las plantas matrices, presentando un alto grado de dispersión, que osciló entre 91,11 % y 0,00 %, mostrando una alta variabilidad y marcada influencia de la planta matriz sobre el proceso de rizogénesis, influyendo de manera altamente significativa en el enraizamiento. Con respecto al área foliar, estacas con 2 y 3 pares de hojas, independiente de la planta matriz, presentaron mayor capacidad de enraizamiento. Con base en estos resultados se concluye que el efecto de la variabilidad genotípica y el área foliar influyen de manera altamente significativa en el proceso de rizogénesis de estacas herbáceas de camu camu.

Completion problems for real matrices, II

Thirty years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [C-ij], i,j is an element of {1, 2}, where C-1,C-1 and C-2,C-2 are square submatrices, when some of the blocks C-ij are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks C-1,C-1, C-2,C-2 are fixed and the others vary.