Parabolic Capacity and Soft Measures for Nonlinear Equations

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.     

Wavelets and adaptive grids for the discontinuous Galerkin method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method.     

Atomic varieties of sets with relative inverses

The generalization of the construction of the lattice of varieties for partial algebras is used for sets with relative inverses. There are many quantum structures representable by sets with relative inverses (orthomodular lattices, orthoalgebras, D-posets, test spaces,...). Varieties covering the trivial variety are investigated for the case of closed (strongest type) subalgebras and closed homomorphisms. Some similar results for weaker types are given. The context with set representation problems is considered for the set-theoretic difference operations.     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

Some aerodynamic and acoustic characteristicsof acute laryngitis

The purpose of the present study was to describe the effects ofacute laryngitis on some aerodynamic, acoustic, and perceptual measures. Eleven subjects with diagnosed acute laryngitis due to upper respiratory infection were recorded during a laryngitic episode and 1 week to 10 days after amelioration of the laryngitic condition. Fundamental frequency values, collapsed across the five vowels, were significantly reduced in the laryngitic compared with the normal speaking condition. The decrease in fundamental frequency associated with acute laryngitis suggests an increase in the mass of the vocal folds. In addition, aerodynamic values differed significantly for the laryngitic condition compared with the normal speaking condition, suggesting the presence of laryngeal hypofunction. Perceptual data indicated that speakers in the laryngitic condition were judged to have a hoarse voice when compared with the normal speaking condition.     

In‐situ synthesis of transparent and conductive carbon nanotube networks

A method for the production of transparent carbon nanotube networks (CNTNs) over transparent substrates was developed. In this method, CNTNs were grown directly in the target surface by applying the catalyst in specific zones of the substrate through lithographic techniques. The networks can be also transferred from the original substrate to other surfaces. The newly grown carbon nanotubes have a very high aspect ratio (>50000). Thus far, networks with an optical transmittance of 94% at 550 nm and a surface resistivity of 3.6 kΩ/sq have been produced. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Correlation of Plasma Sprayed Coating Deposition Efficiency with Volume Flux Measurements by Phase Doppler Anemometry (PDA)

The use of phase-Doppler anemometry (PDA) to characterize the detail in-flight plasma sprayed particle behavior has been demonstrated previously [Ma et al. Plasma Chem Plasma Process 24(1):85; 25(1):56] The present articles shows further that a direct relationship may exist between the PDA measured particle volume flux and the coating microstructure and deposition efficiency (DE). In the situation when the precise particle temperature information is not available, the PDA measured particle volume flux may provide an alternative to predict quantitatively the variation of the coating microstructure and the DE. By monitoring the in-flight particle volume flux variations, instead of the particle velocity, size and temperature individually and simultaneously, the optimal settings of the plasma spraying parameters may also be determined conveniently. However, it is noted that the effective applications of such approach depend largely on the particle surface morphology and the pre-determination of the particle size range.     

Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

Bayesian inference is considered for the seemingly unrelated regressions with an elliptically contoured error distribution. We show that the posterior distribution of the regression parameters and the predictive distribution of future observations under elliptical errors assumption are identical to those obtained under independently distributed normal errors when an improper prior is used. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution.     

A note on acyclic domination number in graphs of diameter two

A subset S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinality of an acyclic dominating set, denoted by γ_a(G), is called the acyclic domination number of G. Hedetniemi et al. [Acyclic domination, Discrete Math. 222 (2000) 151-165] introduced the concept of acyclic domination and posed the following open problem: if δ(G) is the minimum degree of G, is γ_a(G)?δ(G) for any graph whose diameter is two? In this paper, we provide a negative answer to this question by showing that for any positive k, there is a graph G with diameter two such that γ_a(G)-δ(G)?k.