Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

Influence of Artificial Accelerated Aging on Dimensional Stability of Acrylic Resins Submitted to Different Storage Protocols

Purpose: The aim of this study was to evaluate the influence of artificial accelerated aging on dimensional stability of two types of acrylic resins (thermally and chemically activated) submitted to different protocols of storage. Materials and Methods: One hundred specimens were made using a Teflon matrix (1.5cmx0.5mm) with four imprint marks, following the lost-wax casting method. The specimens were divided into ten groups, according to the type of acrylic resin, aging procedure, and storage protocol (30 days). GI: acrylic resins thermally activated, aging, storage in artificial saliva for 16 hours, distilled water for 8 hours; GII: thermal, aging, artificial saliva for 16 hours, dry for 8 hours; GIII: thermal, no aging, artificial saliva for 16 hours, distilled water for 8 hours, GIV: thermal, no aging, artificial saliva for 16 hours, dry for 8 hours; GV: acrylic resins chemically activated, aging, artificial saliva for 16 hours, distilled water for 8 hours; GVI: chemical, aging, artificial saliva for 16 hours, dry for 8 hours; GVII: chemical, no aging, artificial saliva for 16 hours, distilled water for 8 hours; GVIII: chemical, no aging, artificial saliva for 16 hours, dry for 8 hours GIX: thermal, dry for 24 hours; and GX: chemical, dry for 24 hours. All specimens were photographed before and after treatment, and the images were evaluated by software (UTHSCSA-Image Tool) that made distance measurements between the marks in the specimens (mm), calculating the dimensional stability. Data were submitted to statistical analysis (two-way ANOVA, Tukey test, p = 0.05). Results: Statistical analysis showed that the specimens submitted to storage in water presented the largest distance between both axes (major and minor), statistically different (p < 0.05) from control groups. Conclusions: All acrylic resins presented dimensional changes, and the artificial accelerated aging and storage period influenced these alterations.

Color stability of silorane-based composites submitted to accelerated artificial ageing-An in situ study

Objectives: To assess the in situ color stability, surface and the tooth/restoration interface degradation of a silorane-based composite (P90, 3M ESPE) after accelerated artificial ageing (AAA), in comparison with other dimethacrylate monomer-based composites (Z250/Z350, 3M ESPE and Esthet-X, Dentsply). Methods: Class V cavities (25 mm(2) x 2 mmdeep) were prepared in 48 bovine incisors, which were randomly allocated into 4 groups of 12 specimens each, according to the type of restorative material used. After polishing, 10 specimens were submitted to initial color readings (Easyshade, Vita) and 2 to analysis by scanning electronic microscopy (SEM). Afterwards, the teeth were submitted to AAA for 384 h, which corresponds to 1 year of clinical use, after which new color readings and microscopic images were obtained. The values obtained for the color analysis were submitted to statistical analysis (1-way ANOVA, Tukey, p < 0.05). Results: With regard to color stability, it was verified that all the composites showed color alteration above the clinically acceptable levels (Delta E >= 3.3), and that the silorane-based composite showed higher Delta E (18.6), with a statistically significant difference in comparison with the other composites (p < 0.05). The SEM images showed small alterations for the dimethacrylate-based composites after AAA and extensive degradation for the silorane-based composite with a rupture at the interface between the matrix/particle. Conclusion: It may be concluded that the silorane-based composite underwent greater alteration with regard to color stability and greater surface and tooth/restoration interface degradation after AAA. (C) 2011 Elsevier Ltd. All rights reserved.

The Effect of Polymerization Cycles on Color Stability of Microwave-Processed Denture Base Resin

Purpose: This study evaluated the effect of different microwave polymerization cycles on the color changes of a microwave-processed denture base resin after accelerated aging and immersion in beverages. Materials and Methods: Specimens of light pink acrylic resin were divided into three groups according to polymerization cycle: (A) 500 W for 3 minutes, (B) 90 W for 13 minutes + 500 W for 90 seconds, and (C) 320 W for 3 minutes + 0 W for 4 minutes + 720 W for 3 minutes. Control groups were a heat-processed acrylic resin (T) and a chemically activated denture repair resin (Q). Eight specimens per group were aged in an artificial aging chamber and evaluated at 20, 192, and 384 hours. Another series of 40 specimens per group were immersed in water, coffee, tea, cola, or red wine and evaluated at 1, 12, and 36 days. Color was measured by a spectrophotometer before and after aging or immersion. Color changes (Delta E) were analyzed by ANOVA/Bonferroni t-test (alpha = 0.05). Results: Mean Delta E (+/- SD) after 384 hours of accelerated aging were (A) 2.51 +/- 0.50; (B) 3.16 +/- 1.09; (C) 2.89 +/- 1.06; (T) 2.64 +/- 0.34; and (Q) 9.03 +/- 0.40. Group Q had a significantly higher Delta E than the other groups. Color changes of immersed specimens were significantly influenced by solutions and time, but the five groups showed similar values. Mean Delta E at 36 days were (water) 1.4 +/- 0.8; (coffee) 1.3 +/- 0.6; (tea) 1.7 +/- 0.5; (cola) 1.4 +/- 0.7; and (red wine) 10.2 +/- 2.7. Results were similar among the five test groups. Conclusions: Color changes of the microwave-polymerized denture base resin tested were not affected by different polymerization cycles after accelerated aging or immersion in beverages. These changes were similar to the conventional heat-polymerized acrylic resin test, but lower than the repair resin after accelerated aging.

The acquisition of movement skills: Practice enhances the dynamic stability of bimanual coordination

During bimanual movements, two relatively stable inherent patterns of coordination (in-phase and anti-phase) are displayed (e.g., Kelso, Am. J. Physiol. 246 (1984) R1000). Recent research has shown that new patterns of coordination can be learned. For example, following practice a 90 degrees out-of-phase pattern can emerge as an additional, relatively stable, state (e.g., Zanone & Kelso, J. Exp. Psychol.: Human Performance and Perception 18 (1992) 403). On this basis, it has been concluded that practice leads to the evolution and stabilisation of the newly learned pattern and that this process of learning changes the entire attractor layout of the dynamic system. A general feature of such research has been to observe the changes of the targeted pattern's stability characteristics during training at a single movement frequency. The present study was designed to examine how practice affects the maintenance of a coordinated pattern as the movement frequency is scaled. Eleven volunteers were asked to perform a bimanual forearm pronation-supination task. Time to transition onset was used as an index of the subjects' ability to maintain two symmetrically opposite coordinated patterns (target task - 90 degrees out-of-phase - transfer task - 270 degrees out-of-phase). Their ability to maintain the target task and the transfer task were examined again after five practice sessions each consisting of 15 trials of only the 90 degrees out-of-phase pattern. Concurrent performance feedback (a Lissajous figure) was available to the participants during each practice trial. A comparison of the time to transition onset showed that the target task was more stable after practice (p = 0.025). These changes were still observed one week (p = 0.05) and two months (p = 0.075) after the practice period. Changes in the stability of the transfer task were not observed until two months after practice (p = 0.025). Notably, following practice, transitions from the 90 degrees pattern were generally to the anti-phase (180 degrees) pattern, whereas, transitions from the 270 degrees pattern were to the 90 degrees pattern. These results suggest that practice does improve the stability of a 90 degrees pattern, and that such improvements are transferable to the performance of the unpractised 270 degrees pattern. In addition, the anti-phase pattern remained more stable than the practised 90 degrees pattern throughout. (C) 2001 Elsevier Science B.V. All rights reserved.

Let your feet do the walking: constraints on the stability of bipedal coordination

In this paper we consider whether the behaviour of the neural circuitry that controls lower limb movements in humans is shaped primarily by the spatiotemporal characteristics of bipedal gait patterns, or by selective pressures that are sensitive to considerations of balance and energetics. During the course of normal locomotion, the full dynamics of the neural circuitry are masked by the inertial properties of the limbs. In the present study, participants executed bipedal movements in conditions in which their feet were either unloaded or subject to additional inertial loads. Two patterns of rhythmic coordination were examined. In the in-phase mode, participants were required to flex their ankles and extend their ankles in synchrony. In the out-of-phase mode, the participants flexed one ankle while extending the other and vice versa. The frequency of movement was increased systematically throughout each experimental trial. All participants were able to maintain both the in-phase and the out-of-phase mode of coordination, to the point at which they could no longer increase their frequency of movement. Transitions between the two modes were not observed, and the stability of the out-of-phase and in-phase modes of coordination was equivalent at all movement frequencies. These findings indicate that, in humans, the behaviour of the neural circuitry underlying coordinated movements of the lower limbs is not constrained strongly by the spatiotemporal symmetries of bipedal gait patterns.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Techniques to determine ignition, flame stability and burnout of blended coals in p.f. power station boilers

The blending of coals has become popular to improve the performance of coals, to meet specifications of power plants and, to reduce the cost of coals, This article reviews the results and provides new information on ignition, flame stability, and carbon burnout studies of blended coals. The reviewed studies were conducted in laboratory-, pilot-, and full-scale facilities. The new information was taken in pilot-scale studies. The results generally show that blending a high-volatile coal with a low-volatile coal or anthracite can improve the ignition, flame stability and burnout of the blends. This paper discusses two general methods to predict the performance of blended coals: (1) experiment; and (2) indices. Laboratory- and pilot-scale tests, at least, provide a relative ranking of the combustion performance of coal/blends in power station boilers. Several indices, volatile matter content, heating value and a maceral index, can be used to predict the relative ranking of ignitability and flame stability of coals and blends. The maceral index, fuel ratio, and vitrinite reflectance can also be used to predict the absolute carbon burnout of coal and blends within limits. (C) 2000 Elsevier Science Ltd. All rights reserved.