On the loss of regularity for a class of weakly hyperbolic operators

In this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators. (C) 2009 Elsevier Inc. All rights reserved.

Tagging Giant Otters (Pteronura brasiliensis) (Carnivora, Mustelidae) for radio-telemetry studies

Memphis Zoo, U.S. Forest Service, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico CNPq, Earthwatch Institute

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

Radio frequency plasma-induced hydrogen bonding on kaolinite

The radio frequency (RF) plasma-modified surfaces of kaolinite were investigated by diffuse reflectance infrared Fourier transform spectroscopy (DRIFT) and deuteration techniques to determine the nature of RF plasma-induced surface functional groups, the altered sites in the lattice, and interaction mechanism between RF plasma and the surface of the kaolinite. It has been concluded that the RF plasma-induced infrared (IR) vibration absorption bands at 2805, 3010, and 3100 cm(-1) are attributable to the stretching vibration of hydrogen-bonded hydroxyl groups, and the band at 1407 cm(-1) is attributable to the bending vibration of (HO-)Al-O or (HO-)Si-O groupings with hydrogen-bonded hydroxyl groups. Structural alteration occurred on both the surface and subsurface region of the kaolinite during RF plasma treatment. Further structural alteration or adjustment was also observed on well-modified and well-deuterated kaolinite. There are two types of OD bands visible in the DRIFT spectra of this kaolinite, one type which decreased rapidly as a function of time in moist air, and the other which remained unchanged during the measurement. Furthermore, the appearance of broad IR bands at 3500-3100 cm(-1) as a result of deuteration is evidence of structural disturbance by RF plasma treatment lattice deuteration. An RF plasma-induced hydrogen bonding model on the surface of the kaolinite is proposed.