Thermal characterization of polyester-melamine coating matrices prepared under nonisothermal conditions

Thermal analysis methods (differential scanning calorimetry, thermogravimetric analysis, and dynamic mechanical thermal analysis) were used to characterize the nature of polyester-melamine coating matrices prepared under nonisothermal, high-temperature, rapid-cure conditions. The results were interpreted in terms of the formation of two interpenetrating networks with different glass-transition temperatures (a cocondensed polyester-melamine network and a self-condensed melamine-melamine network), a phenomenon not generally seen in chemically similar, isothermally cured matrices. The self-condensed network manifested at high melamine levels, but the relative concentrations of the two networks were critically dependent on the cure conditions. The optimal cure (defined in terms of the attainment of a peak metal temperature) was achieved at different oven temperatures and different oven dwell times, and so the actual energy absorbed varied over a wide range. Careful control of the energy absorption, by the selection of appropriate cure conditions, controlled the relative concentrations of the two networks and, therefore, the flexibility and hardness of the resultant coatings. (C) 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Cbem 41: 1603-1621, 2003.

On the completion of Latin rectangles to symmetric Latin squares

We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n - 1)-edge colouring of K-n (n even), and for an n-edge colouring of K-n (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Wurst: a protein threading server with a structural scoring function, sequence profiles and optimized substitution matrices

Wurst is a protein threading program with an emphasis on high quality sequence to structure alignments (http://www.zbh.uni-hamburg.de/wurst). Submitted sequences are aligned to each of about 3000 templates with a conventional dynamic programming algorithm, but using a score function with sophisticated structure and sequence terms. The structure terms are a log-odds probability of sequence to structure fragment compatibility, obtained from a Bayesian classification procedure. A simplex optimization was used to optimize the sequence-based terms for the goal of alignment and model quality and to balance the sequence and structural contributions against each other. Both sequence and structural terms operate with sequence profiles.

Recursive filtering of images with symmetric extension

Recursive filters are widely used in image analysis due to their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of symmetrically extended images for filters with symmetric denominator. We begin with an analysis of symmetric extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on symmetric domains as a linear but spatially varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system, along with a proof that this decomposition always exists. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring less computation than the standard recursive filtering. We give experimental evidence to verify these claims. (c) 2005 Elsevier B.V. All rights reserved.

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

A study of the effects of postcure treatments on polyester-melamine coating matrices

The effect of postcure high energy (gamma), ultraviolet (UV) and thermal treatment on the properties of polyester-melamine clearcoats of a range of compositions has been investigated. Two initial cure conditions were used, of which one was '' optimally '' cured and the other undercured. It was found that postcure treatments, particularly gamma and UV, led to coatings of similar mechanical and thermal properties irrespective of initial cure, although the change in properties on postcure treatment was greater for the under-cured samples. The results were interpreted in terms of the effect of the treatments on the structure of the crosslinked matrices. The study suggests the possibility of the development of a dual-cure process for polyester-melamines, whereby cure optimization and property improvement can be achieved. This could also be used to '' correct '' for small variations in thermal cure levels brought about by adventitious online fluctuations in cure oven conditions.

Hydrodynamic evaluation of kangaroo aortic valve matrices for tissue valve engineering

We evaluated the hydrodynamic performance of kangaroo aortic valve matrices (KMs) (19, 21, and 23 mm), as potential scaffolds in tissue valve engineering using a pulsatile left heart model at low and high cardiac outputs (COs) and heart rates (HRs) of 60 and 90 beats/min. Data were measured in two samples of each type, pooled in two CO levels (2.1 +/- 0.7 and 4.2 +/- 0.6 L/min; mean +/- standard errors on the mean), and analyzed using analysis of variance with CO level, HR, and valve type as fixed factors and compared to similar porcine matrices (PMs). Transvalvular pressure gradient (Delta P) was a function of HR (P < 0.001) and CO (P < 0.001) but not of valve type (P = 0.39). Delta P was consistently lower in KMs but not significantly different from PMs. The effective orifice area and performance index of kangaroo matrices was statistically larger for all sizes at both COs and HRs.

Drinfeld twists and algebraic bethe ansatz of the supersymmetric model associated with U-q(gl(m vertical bar n))

We construct the Drinfeld twists (or factorizing F-matrices) of the supersymmetric model associated with quantum superalgebra U-q(gl(m vertical bar n)), and obtain the completely symmetric representations of the creation operators of the model in the F-basis provided by the F-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the F-basis for the U-q(gl(2 vertical bar 1))-model (the quantum t-J model).

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

A scalarization technique for computing the power and exponential moments of gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C are appropriately dimensioned constant matrices. We solve the problems by a matrix product scalarization technique and interpret the solutions in system-theoretic terms. The results of the paper are applicable to Bayesian prediction in multivariate autoregressive time series and mean-reverting diffusion processes.