Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data

Lin and Zhang (J. Roy. Statist. Soc. Ser. B 61 (1999) 381) proposed the generalized additive mixed model (GAMM) as a framework for analysis of correlated data, where normally distributed random effects are used to account for correlation in the data, and proposed to use double penalized quasi-likelihood (DPQL) to estimate the nonparametric functions in the model and marginal likelihood to estimate the smoothing parameters and variance components simultaneously. However, the normal distributional assumption for the random effects may not be realistic in many applications, and it is unclear how violation of this assumption affects ensuing inferences for GAMMs. For a particular class of GAMMs, we propose a conditional estimation procedure built on a conditional likelihood for the response given a sufficient statistic for the random effect, treating the random effect as a nuisance parameter, which thus should be robust to its distribution. In extensive simulation studies, we assess performance of this estimator under a range of conditions and use it as a basis for comparison to DPQL to evaluate the impact of violation of the normality assumption. The procedure is illustrated with application to data from the Multicenter AIDS Cohort Study (MACS).     

Depth profile analysis of polyimide film treated by potassium hydroxide

The structural change in the depth direction of a polyimide (UPILEX‐S) film treated in alkaline solution, which was a representative surface treatment used to form a seed layer for plating and to improve the adhesive strength, was analyzed by means of micro Fourier transform infrared attenuated total reflection (FTIR‐ATR) line analysis with gradient shaving preparation. The polyimide film was treated with KOH. The imide ring opened through the alkaline treatment, and the amide structure and carboxylic acid salt were formed. The attainment depth of this structural change was almost proportional to the treatment time, and it reached about 8 μm after a 30‐min treatment. The degree of structural change through the alkaline treatment was almost constant after it reached a considerably degraded stage, and the chemically changed region penetrated into the inner part of the film from the surface. An intermediate layer before the final degraded stage appeared in the treated layer, and its thickness increased with the treatment time. The region that was changed chemically by the alkaline treatment progressed to the inner part simultaneously and continuously as the treatment time increased. The combined use of gradient shaving preparation and micro FTIR‐ATR line analysis was found to be extremely effective for the depth profiling of organic materials. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2071–2078, 2003     

Dynamic mechanical thermal analysis transitions of partially and fully substituted cellulose fatty esters

The main transitions of cellulose fatty esters with different degrees of substitution (DSs) were investigated with dynamic mechanical thermal analysis. Two distinct main relaxations were observed in partially substituted cellulose esters (PSCEs). They were attributed to the glass‐transition temperature and to the chain local motion of the aliphatic substituents. The temperatures of both transitions decreased when DS or the number of carbon atoms (n) of the acyl substituent increased. Conversely, all the transitions of fully substituted cellulose esters occurred within a narrow temperature range, and they did not vary significantly with n. This phenomenon was explained by the formation of a crystalline phase of the fatty substituents. The presence of few residual OH groups in PSCEs was responsible for a large increase in the storage bending modulus, and it eliminated the effect of n on damping. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 281–288, 2003     

Concerning seven and eight mutually orthogonal Latin squares

In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 419. © 2003 Wiley Periodicals, Inc.     

Memory and a priori best strategy in complex adaptive systems

We employ an agent‐based model to show that memory and the absence of an a priori best strategy are sufficient for self‐segregation and clustering to emerge in a complex adaptive system with discrete agents that do not compete over a limited resource nor contend in a winner‐take‐all scenario. An agent starts from a corner of a two‐dimensional lattice and aims to reach a randomly selected site in the opposite side within the shortest possible time. The agent is isolated during the course of its journey and does not interact with other agents. Time‐bound obstacles appear at random lattice locations and the agent must decide whether to challenge or evade any obstacle blocking its path. The agent is capable of adapting a strategy in dealing with an obstacle. We analyze the dependence of strategy‐retention time with strategy for both memory‐based and memory‐less agents. We derive the equality spectrum to establish the environmental conditions that favor the existence of an a priori best strategy. We found that memory‐less agents do not polarize into two opposite strategy‐retention time distributions nor cluster toward a center distribution. © 2004 Wiley Periodicals, Inc. Complexity 9: 41–46, 2004     

Characterization of host-lattice emission and energy transfer in BaMgAl10O17:Eu

Host-lattice emission, energy transfer and degradation processes are characterized in undoped and Eu-doped BaMgAl₁₀O₁₇. Undoped BaMgAl₁₀O₁₇ exhibits a broad emission centered at 265 nm when excited at wavelengths shorter than 190 nm. This emission is assigned to exciton recombination at Ba-O groups in the cation layer of the lattice. The emission exhibits excellent overlap with the excitation band of Eu²⁺ in this host, providing a means of host-to-activator energy transfer in the doped phosphor. The exciton emission is relatively stable to thermal damage, but undergoes a peak shift and significant decrease in intensity after exposure to VUV radiation. Heating of VUV-damaged materials in air leads to some repair of the spectral properties.     

Gravitational Collapse of Self-Similar Perfect Fluid in 2 + 1 Gravity

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity.     

Does the beam width affect the generalized M factor of hard-edged diffracted beams?

A detailed study of the generalized M² factor of hard-edged diffracted beams based on the truncated second-order moments method, asymptotic analysis and self-convergent beam width approach is performed. The dependence of the generalized M² factor on the parameters characterizing the spatial profile, and beam truncation, etc. is analyzed.