Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Stability results for impulsive functional differential equations with infinite delay

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Watershed scale temporal stability of soil water content

The recognition of temporally stable locations with respect to soil water content is of importance for soil water management decisions, especially in sloping land of watersheds. Neutron probe soil water content (0 to 0.8 m), evaluated at 20 dates during a year in the Loess Plateau of China, in a 20 ha watershed dominated by Ust-Sandiic Entisols and Aeolian sandy soils, were used to define their temporal stability through two indices: the standard deviation of relative difference (SDRD) and the mean absolute bias error (MABE). Specific concerns were (a) the relationship of temporal stability with soil depth, (b) the effects of soil texture and land use on temporal stability, and (c) the spatial pattern of the temporal stability. Results showed that temporal stability of soil water content at 0.2 m was significantly weaker than those at the soil depths of 0.6 and 0.8 m. Soil texture can significantly (P<0.05) affect the stability of soil water content except for the existence of an insignificant difference between sandy loam and silt loam textures, while temporal stability of areas covered by bunge needlegrass land was not significantly different from those covered by korshinsk peashrub. Geostatistical analysis showed that the temporal stability was spatially variable in an organized way as inferred by the degree of spatial dependence index. With increasing soil depth, the range of both temporal stability indices showed an increasing trend, being 65.8-120.5 m for SDRD and 148.8-214.1 m for MABE, respectively. This study provides a valuable support for soil water content measurements for soil water management and hydrological applications on sloping land areas. (C) 2010 Elsevier B.V. All rights reserved.

Quercetin in lyotropic liquid crystalline formulations: Physical, chemical and functional stability

The purpose of this study was to develop a lyotropic liquid crystalline formulation using the emulsifier vitamin E TPGS and evaluate its behavior after incorporation of a flavonoid, quercetin. The physical (macro and microscopic), chemical (determination of quercetin content by the HPLC method) and functional (determination of quercetin antioxidant activity by DPPH center dot assay) stability of the lamellar liquid crystalline formulation containing flavonoid was evaluated when stored at 4+/-2 degrees C; 30+/-2 degrees C/70+/-5% RH (relative humidity) and 40+/-2 degrees C/70+/-5% RH during 12 months. The lamellar liquid crystalline structure of the formulation was maintained during the experiment, however chemical and functional stability results showed a great influence of the storage period in all conditions tested. A significant decrease in quercetin content (approximately 40%) was detected during the first month of storage and a similar significant loss in antioxidant activity was detected after 6 months. The remaining flavonoid content was unchanged during the final 6 months of the experimental period. The results suggest possible interactions between quercetin and the liquid crystalline formulation, which could inhibit or reduce the quercetin activity incorporated in the system. In conclusion, the present study demonstrated that incorporation of quercetin (1%) did not affect the liquid crystalline structure composed of vitamin E TPGS/IPM/PG-H2O (1:1) at 63.75/21.25/15 (w/w/w). Nevertheless, of the total quercetin incorporated in the system only 60% was free to act as an antioxidant.

Effect of Oven Heating Time of Asphaltic Concrete on Marshall Stability, MLR-82-02, 1982

It has been observed in the Laboratory that an increase in oven heating time of relatively short duration between mixing and compaction of asphaltic concrete hot mixes can have an effect on the Marshall stability results obtained. The purpose of this short investigation is to determine the effect of oven heating time on the density and stability of hot mixes.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Analysis of void volumes in proteins and application to stability of the p53 tumour suppressor protein

We have developed a new method for the analysis of voids in proteins (defined as empty cavities not accessible to solvent). This method combines analysis of individual discrete voids with analysis of packing quality. While these are different aspects of the same effect, they have traditionally been analysed using different approaches. The method has been applied to the calculation of total void volume and maximum void size in a non-redundant set of protein domains and has been used to examine correlations between thermal stability and void size. The tumour-suppressor protein p53 has then been compared with the non-redundant data set to determine whether its low thermal stability results from poor packing. We found that p53 has average packing, but the detrimental effects of some previously unexplained mutations to p53 observed in cancer can be explained by the creation of unusually large voids. (C) 2004 Elsevier Ltd. All rights reserved.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

STABILITY FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations are obtained by means of the correspondence of this class of equations with GODEs.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

Postsurgical stability of counterclockwise maxillomandibular advancement surgery: Affect of articular disc repositioning

Purpose: This study evaluated the affect of disc displacement and articular disc repositioning on stability after surgical counterclockwise rotation and advancement of the maxillomandibular complex.Patients and Methods: A total of 72 patients (59 females, 13 males), with an average age of 30 years (range, 15 to 60 years) were evaluated. The patients were divided into 3 groups. Group 1 (G1; n = 21), with healthy temporomandibular joints (TMJs), underwent double jaw surgery only. Group 2 (G2; n = 35), with articular disc dislocation, underwent articular disc repositioning using the Mitek anchor (Mitek Surgical Products, Westwood, MA) technique concomitantly with orthognathic surgery. Group 3 (G3; n = 16), with articular disc dislocation, underwent orthognathic surgery only. Average postsurgical follow-up was 31 months. Each patient's lateral cephalograms were traced, digitized twice, and averaged to estimate surgical changes and postsurgical stability.Results: After surgery, the occlusal plane angle was decreased significantly in all 3 groups: by -6.3 +/- -15.0 degrees in G1, by -9.6 +/- 4.8 degrees in G2, and by -7.1 +/- 4.8 degrees in G3. The maxillomandibular complex was advanced and rotated counterclockwise similarly in all 3 groups, with advancement at the menton of 12.4 +/- 5.5 mm in G1, 13.5 +/- 4.3 mm in G2, and 13.6 +/- 5.0 mm in G3; advancement at the B point of 9.5 +/- 4.9 mm in G1, 10.2 +/- 3.7 mm in G2, and 10.8 +/- 3.7 mm in G3; and advancement at the lower incisor edge of 7.1 +/- 4.6 mm in G1, 6.6 +/- 3.2 mm in G2, and 7.9 +/- 3.0 mm in G3. Postsurgery, the occlusal plane angle increased in G3 (2.6 +/- 3.8 degrees; 37% relapse rate) but remained stable in G1 and G2. Postsurgical mandibular changes in the horizontal direction demonstrated a significant relapse in G3 at the menton (-3.8 +/- 4.1 mm; 28%), the B point (-3.0 +/- 3.4 mm; 28%), and the lower incisor edge (-2.3 +/- 2.1 mm; 34%) but remained stable in G1 and G2.Conclusions: Maxillomandibular advancement with counterclockwise rotation of the occlusal plane is a stable procedure for patients with healthy TMJs and for patients undergoing simultaneous TMJ disc repositioning using the Mitek anchor technique. Those patients with preoperative TMJ articular disc displacement who underwent double-jaw surgery and no TMJ intervention experienced significant relapse. (C) 2008 American Association of Oral and Maxillofacial Surgeons.

Improving the stability conditions of TS fuzzy systems with fuzzy Lyapunov functions

In this paper, the fuzzy Lyapunov function approach is considered for stabilizing continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing a slack LMI variable into the problem formulation. The stability results are thus used in the state feedback design which is also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilizing conditions presented. © 2011 IFAC.

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.