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.

Physical Properties of an Acrylic Resin after Incorporation of an Antimicrobial Monomer

Purpose: This study evaluated the effect of the incorporation of the antimicrobial monomer methacryloyloxyundecylpyridinium bromide (MUPB) on the hardness, roughness, flexural strength, and color stability of a denture base material. Materials and Methods: Ninety-six disk-shaped (14-mm diameter x 4-mm thick) and 30 rectangular (65 x 10 x 3.3 mm(3)) heat-polymerized acrylic resin specimens were divided into three groups according to the concentration of MUPB (w/w): (A) 0%, (B) 0.3%, (C) 0.6%. Hardness was assessed by a hardness tester equipped with a Vickers diamond penetrator. Flexural strength and surface roughness were tested on a universal testing machine and a surface roughness tester, respectively. Color alterations (Delta E) were measured by a portable spectrophotometer after 12 and 36 days of immersion in water, coffee, or wine. Variables were analyzed by ANOVA/Tukey HSD test (alpha = 0.05). Results: The following mean results (+/-SD) were obtained for hardness (A: 15.6 +/- 0.6, B: 14.6 +/- 1.7, C: 14.8 +/- 0.8 VHN; ANOVA: p = 0.061), flexural strength (A: 111 +/- 17, B: 105 +/- 12, C: 88 +/- 12 MPa; ANOVA: p = 0.008), and roughness (A: 0.20 +/- 0.11, B: 0.20 +/- 0.11, C: 0.24 +/- 0.08 mu m; ANOVA: p = 0.829). Color changes of immersed specimens were significantly influenced by solutions and time (A: 9.1 +/- 3.1, B: 14.8 +/- 7.5, C: 13.3 +/- 6.1 Delta E; ANOVA: p < 0.05). Conclusions: The incorporation of MUPB affects the mechanical properties of a denture base acrylic resin; however, the only significant change was observed for flexural strength and may not be critical. Color changes were slightly higher when resin containing MUPB was immersed in wine for a prolonged time; however, the difference has debatable clinical relevance.

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.

Step size control for efficient discrete element simulation

The step size determines the accuracy of a discrete element simulation. The position and velocity updating calculation uses a pre-calculated table and hence the control of step size can not use the integration formulas for step size control. A step size control scheme for use with the table driven velocity and position calculation uses the difference between the calculation result from one big step and that from two small steps. This variable time step size method chooses the suitable time step size for each particle at each step automatically according to the conditions. Simulation using fixed time step method is compared with that of using variable time step method. The difference in computation time for the same accuracy using a variable step size (compared to the fixed step) depends on the particular problem. For a simple test case the times are roughly similar. However, the variable step size gives the required accuracy on the first run. A fixed step size may require several runs to check the simulation accuracy or a conservative step size that results in longer run times. (C) 2001 Elsevier Science Ltd. All rights reserved.

Translabial color Doppler urodynamics

Color Doppler ultrasound is a new method for documenting fluid leakage in the setting of video-urodynamic testing. In order to compare color Doppler ultrasound with traditional fluoroscopic imaging we performed a prospective blinded comparative clinical study. Fifty-two consecutive patients undergoing urodynamic investigations for symptoms of incontinence or prolapse were examined using fluoroscopy and translabial color Doppler ultrasound to document stress leakage. The investigators were blinded to each other's results. Both tests were performed at maximum bladder capacity and with an indwelling 5 Fr microtransducer catheter, in both the supine and the erect positions. Equivalent results for both methods were obtained in 48 out of 52 patients (Cohen's kappa = 0.82). It was therefore concluded that translabial color Doppler ultrasound imaging can reliably demonstrate leakage through the female urethra on Valsalva maneuver or coughing.

Towards a definition of "difference" in osteoarthritis

To assess existing information regarding detectable differences in osteoarthritis (OA), a systematic literature search was conducted up to December 1999. Thirty-three articles were considered methodologically relevant to the definition and categorization of detectable differences in OA. It was determined that the musculoskeletal literature contains a wealth of information that relates to observed changes, much of which is derived from the clinical trials literature, but there have been relatively few methodological studies that have systematically evaluated the nature, categorization, and relevance of the change. Furthermore, most of those that have been published take the perspective of an individual or groups of experts other than that of the patient. This summary of the current literature reveals that the diverse sources of information go part way towards developing an understanding of detectable differences and their importance in the area of OA research and clinical practice. Stakeholders' interests as well as factors that modulate perceptions of importance need to be taken under consideration. In particular, the patient's perspective of the importance of change at an individual level requires further evaluation. This area of clinical research is relatively underdeveloped, but there is considerable opportunity for progress.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Color constancy and the functional significance of McCollough effects

A central problem in visual perception concerns how humans perceive stable and uniform object colors despite variable lighting conditions (i.e. color constancy). One solution is to 'discount' variations in lighting across object surfaces by encoding color contrasts, and utilize this information to 'fill in' properties of the entire object surface. Implicit in this solution is the caveat that the color contrasts defining object boundaries must be distinguished from the spurious color fringes that occur naturally along luminance-defined edges in the retinal image (i.e. optical chromatic aberration). In the present paper, we propose that the neural machinery underlying color constancy is complemented by an 'error-correction' procedure which compensates for chromatic aberration, and suggest that error-correction may be linked functionally to the experimentally induced illusory colored aftereffects known as McCollough effects (MEs). To test these proposals, we develop a neural network model which incorporates many of the receptive-field (RF) profiles of neurons in primate color vision. The model is composed of two parallel processing streams which encode complementary sets of stimulus features: one stream encodes color contrasts to facilitate filling-in and color constancy; the other stream selectively encodes (spurious) color fringes at luminance boundaries, and learns to inhibit the filling-in of these colors within the first stream. Computer simulations of the model illustrate how complementary color-spatial interactions between error-correction and filling-in operations (a) facilitate color constancy, (b) reveal functional links between color constancy and the ME, and (c) reconcile previously reported anomalies in the local (edge) and global (spreading) properties of the ME. We discuss the broader implications of these findings by considering the complementary functional roles performed by RFs mediating color-spatial interactions in the primate visual system. (C) 2002 Elsevier Science Ltd. All rights reserved.

Diversity and change in Australia's rangelands: a post-productivist transition with a difference?

Australia's rangelands are experiencing a post-productivist transition at a tempo comparable to Western Europe's, but in contexts that ensure marked divergence in impulses, actors, processes and outcomes. In Australia's most marginal lands, a flimsy mode of pastoral occupance is being displaced by renewed indigenous occupance, conservation and tourism, with significant changes in land ownership, property rights, investment sources and power relations, but also with structural problems arising from fugitive income streams. The sharp delineation between structurally coherent commodity-oriented regions and emerging amenity-oriented regions can provisionally be mapped at a national scale. A comparison of Australia with Western Europe indicates that three distinct but interconnected driving forces are propelling the rural transition, namely: agricultural overcapacity; the emergence of amenity-oriented uses; and changing societal values.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

"Owned by...". Country of origin's new cue

This study identifies and explores a new country of origin (COO) cue, “owned by….” The importance of three extrinsic cues “owned by …,” “made in …” and price was examined using conjoint analysis. Data were collected from a sample of 268 undergraduate students familiar with color televisions. Segments were formed using cluster analysis and analyzed using multiple discriminant analysis. “Owned by …” was found to be important and distinct from the “made in …” cue. Segments based on the two COO cues were identified using importance weights and individual utilities. When segments were formed using individual utilities the individual difference construct, economic nationalism, provided discriminatory power while consumer ethnocentrism did not, supporting the hypothesis that economic nationalism and consumer ethnocentrism differ. Practitioners can now use “owned by …” knowing that it forms an important and distinct marketing tool. Limitations and future research are discussed.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.