PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.

Stability, causality, and quasinormal modes of cosmic strings and cylinders

In this work we consider the evolution of a massive scalar field in cylindrically symmetric space-times. Quasinormal modes have been calculated for static and rotating cosmic cylinders. We found unstable modes in some cases. Rotating as well as static cosmic strings, i.e., without regular interior solutions, do not display quasinormal oscillation modes. We conclude that rotating cosmic cylinder space-times that present closed timelike curves are unstable against scalar perturbations.

Phase transitions and regions of stability in Reissner-Nordstrom holographic superconductors

The phase transition of Reissner-Nordstrom AdS(4) interacting with a massive charged scalar field has been further revisited. We found exactly one stable and one unstable quasinormal mode region for the scalar field. The two of them are separated by the first marginally stable solution.

Gravitational stability of simply rotating Myers-Perry black holes: Tensorial perturbations

We study the stability of D >= 7 asymptotically flat black holes rotating in a single two-plane against tensor-type gravitational perturbations. The extensive search of quasinormal modes for these black holes did not indicate any presence of growing modes, implying the stability of simply rotating Myers-Perry black holes against tensor-type perturbations.

Stability of higher dimensional Reissner-Nordstrom-anti-de Sitter black holes

We investigate stability of the D-dimensional Reissner-Nordstrom-anti-de Sitter metrics as solutions of the Einstein-Maxwell equations. We have shown that asymptotically anti-de Sitter (AdS) black holes are dynamically stable for all values of charge and anti-de Sitter radius in D=5,6...11 dimensional space-times. This does not contradict dynamical instability of RNAdS black holes found by Gubser in N=8 gauged supergravity, because the latter instability comes from the tachyon mode of the scalar field, coupled to the system. Asymptotically AdS black holes are known to be thermodynamically unstable for some region of parameters, yet, as we have shown here, they are stable against gravitational perturbations.

(In)stability of D-dimensional black holes in Gauss-Bonnet theory

We make an extensive study of evolution of gravitational perturbations of D-dimensional black holes in Gauss-Bonnet theory. There is an instability at higher multipoles l and large Gauss-Bonnet coupling alpha for D = 5, 6, which is stabilized at higher D. Although a small negative gap of the effective potential for the scalar type of gravitational perturbations exists for higher D and whatever alpha, it does not lead to any instability.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Structure, stability, depolarized light scattering, and vibrational spectra of fullerenols from all-electron density-functional-theory calculations

We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C(60)(OH)(n)] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke's three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C(60)(OH)(36). Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1, 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C(60)(OH)(24) isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4, 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.

Stability of biomass-derived black carbon in soils

Black carbon (BC) may play ail important role in the global C budget, due to its potential to act as a significant sink of atmospheric CO(2). In order to fully evaluate the influence of BC oil the global C cycle, in understanding of the stability of BC is required. The biochemical stability of BC was assessed in a chronosequence of high-BC-containing Anthrosols from the central Amazon, Brazil, using a range of spectroscopic and biological methods. Results revealed that the Anthrosols had 61-80% lower (P < 0.05) CO(2) evolution per unit C over 532 days compared to their respective adjacent soils with low BC contents. No significant (P > 0.05) difference in CO(2) respiration per unit C was observed between Anthrosols with contrasting ages of BC (600-8700 years BP) Lind soil textures (0.3-36% clay). Similarly, the molecular composition of the core regions of micrometer-sized BC particles quantified by synchrotron-based Near-Edge X-ray Fine Structure (NEXAFS) spectroscopy coupled to Scanning Transmission X-ray Microscopy (STXM) remained similar regardless of their ages and closely resembled the spectral characteristics or fresh BC. BC decomposed extremely slowly to ail extent that it was not possible to detect chemical changes between Youngest and oldest samples, as also confirmed by X-ray Photoelectron Spectroscopy (XPS). Deconvolution of NEXAFS spectra revealed greater oxidation oil the surfaces of BC particles with little penetration into the core of the particles. The similar C mineralization between different BC-rich soils regardless of soil texture underpins the importance of chemical recalcitrance for the stability of BC, in contrast to adjacent soils which showed the highest mineralization in the sandiest soil. However, the BC-rich Anthrosols had higher proportions (72-90%) of C in the more stable organo-mineral fraction than BC-poor adjacent soils (2-70%), Suggesting some degree of physical stabilization. (c) 2008 Elsevier Ltd. All rights reserved.

Conformational stability of peanut agglutinin using small angle X-ray scattering

In this work, quaternary conformational studies of peanut agglutinin (PNA) have been carried out using small-angle X-ray scattering (SAXS). PNA was submitted to three different conditions: pH variation (2.5, 4.0, 7.4 and 9.0), guanidine hydrochloride presence (0.5-2 M) at each pH value, and temperature ranging from 25 to 60 degrees C. All experiments were performed in the absence and presence of T-antigen to evaluate its influence on the lectin stability. At room temperature and pH 4.0,7.4 and 9.0, the SAXS curves are consistent with the PNA scattering in its crystallographic native homotetrameric structure, with monomers in a jelly roll fold, associated by non-covalent bonds resulting in an open structure. At pH 2.5, the results indicate that PNA tends to dissociate into smaller sub-units, as dimers and monomers, followed by a self-assembling into larger aggregates. Furthermore, the conformational stability under thermal denaturation follows the pH sequence 7.4 > 9.0 > 4.0 > 2.5. Such results are consistent with the conformational behavior found upon GndHCl influence. The presence of T-antigen does not affect the protein quaternary structure in all studied systems within the SAXS resolution. (C) 2010 Elsevier B.V. All rights reserved.

Validity and reliability of the Portuguese version of the Epilepsy Medication Treatment Complexity Index for Brazil

We evaluated the reliability and validity of a Brazilian-Portuguese version of the Epilepsy Medication Treatment Complexity Index (EMTCI). Interrater reliability was evaluated with the intraclass correlation coefficient (ICC), and validity was evaluated by correlation of mean EMTCI scores with the following variables: number of antiepileptic drugs (AEDs), seizure control, patients` perception of seizure control, and adherence to the therapeutic regimen as measured with the Morisky scale. We studied patients with epilepsy followed in a tertiary university-based hospital outpatient clinic setting, aged 18 years or older, independent in daily living activities, and without cognitive impairment or active psychiatric disease. ICCs ranged from 0.721 to 0.999. Mean EMTCI scores were significantly correlated with the variables assessed. Higher EMTCI scores were associated with an increasing number of AEDs, uncontrolled seizures, patients` perception of lack of seizure control, and poorer adherence to the therapeutic regimen. The results indicate that the Brazilian-Portuguese EMTCI is reliable and valid to be applied clinically in the country. The Brazilian-Portuguese EMTCI version may be a useful tool in developing strategies to minimize treatment complexity, possibly improving seizure control and quality of life in people with epilepsy in our milieu. (C) 2011 Elsevier Inc. All rights reserved.

Leg preference and interlateral asymmetry of balance stability in soccer players

To examine the effect of long lasting practice on pedal behavior in sport, we compared experienced adult soccer players and nonsoccer players on leg preference in motor tasks requiring general mobilization, soccer related mobilization, and body balance stabilization. We also evaluated performance asymmetry between the right and left legs in static and dynamic unipedal body balance based on center of pressure displacement, and correlated that with kg preference in balance stabilization tasks. Results revealed (a) a distinct leg preference between mobilization and stabilization tasks, which were significantly different between Mayers and nonplayers, (b) similar balance stability between the right and left legs, (c) greater stability of experienced players compared with nonplayers in static and dynamic balance, and (d) absence of a significant kg preference correlation with interlateral balance asymmetry. These results suggest an effect of extensive soccer skill practice on establishing leg preference for specific mobilization tasks and overall balance control.

Performance of body fat and body mass index cutoffs in elevated blood pressure screening among male children and adolescents

For percentage of body fat (%BF), there are no internationally accepted cutoffs. The primary function of body fat cutoffs should be to identify not only excessive body fatness, but also the increased risk of unhealthy outcomes, such as hypertension. The purpose of this study was to analyze the accuracy of different %BF and body mass index (BMI) cutoffs as screening measures for EBP in pediatric populations. It was a cross-sectional study with a sample of 358 male subjects from 8 to 18 years old. BP was measured by the oscilometric method, and body composition was measured by dual-energy X-ray absorptiometry (DXA). The accuracy of three reference tables used for body fat cutoffs was assessed. The three body fat reference tables were highly specific, but insensitive, for elevated BP screening. For elevated BP screening, all body fat cutoffs presented similar sensitivity (range=48.3-53.7%) and specificity (range=79.2-84.1%). The body fat cutoffs performed no better than BMI in screening of children and adolescents at risk of elevated BP (EBP). BMI seems a more attractive tool for this function, as it performed similarly and can be applied in large surveys and with lower costs. Hypertension Research (2011) 34, 963-967; doi:10.1038/hr.2011.61; published online 26 May 2011