A physical space approach to wave equation bilinear estimates

Bilinear estimates for the wave equation in Minkowski space are normally proven using the Fourier transform and Plancherel’s theorem. However, such methods are difficult to carry over to non-flat situations (such as wave equations with rough metrics or connections with non-zero curvature). In this note, we describe an alternative physical space approach which relies on vector fields, energy estimates as well as tube localization, splitting into coarse and fine scales, and induction on scales (in the spirit of Wolff [29], [30]).     

Magnetic cellulosic materials based on TEMPO-oxidized viscose fibers

A simple method for preparation of magnetic cellulose fibers by coating (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO)-oxidized viscose with oleic-acid-coated or uncoated, freshly prepared magnetic nanoparticles (MNp) is presented. MNp attachment was facilitated by chemical activation of the cellulose fibers through introduction of negatively charged carboxylic groups using the well-established TEMPO-mediated oxidation protocol. The resulting composite materials preserved the intrinsic properties of the cellulose fibers, but gained notable specific features due to the presence of magnetic nanoparticles. The obtained composite materials were characterized using spectral (Fourier-transform infrared spectroscopy) and microscopic (scanning electron microscopy) methods. Thermogravimetric analyses were carried out to evaluate the thermal stability of the magnetic fibers. The magnetic properties were evaluated using vibrating-sample magnetometry.     

The resolution of the bounded L2 curvature conjecture in general relativity

This paper reports on the recent proof of the bounded L² curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the L²-norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.     

On the uniqueness of smooth,stationary black holes in vacuum

A fundamental conjecture in general relativity asserts that the domain of outer communication of a regular, stationary, four dimensional, vacuum black hole solution is isometrically diffeomorphic to the domain of outer communication of a Kerr black hole. So far the conjecture has been resolved, by combining results of Hawking [17], Carter [4] and Robinson [28], under the additional hypothesis of non-degenerate horizons and real analyticity of the space-time. We develop a new strategy to bypass analyticity based on a tensorial characterization of the Kerr solutions, due to Mars [24], and new geometric Carleman estimates. We prove, under a technical assumption (an identity relating the Ernst potential and the Killing scalar) on the bifurcate sphere of the event horizon, that the domain of outer communication of a smooth, regular, stationary Einstein vacuum spacetime of dimension 4 is locally isometric to the domain of outer communication of a Kerr spacetime.     

Equational spectrum of Hilbert varieties

We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.      

Structures and redox characteristics of electron-deficient vanadyl phthalocyanines

The first single-crystal X-ray structures of substituted vanadyl phthalocyanine materials reveal the high-valence vanadium ions (denoted as V(IV)), whose coordination by a highly electron-deficient ligand is facilitated by an axial oxo group. The metal center of the hydrophilic V═O core, encapsulated in F-rich hydrophobic pockets, reaches a coordination number of 6 by binding an additional H(2)O that, in turn, hydrogen-bonds with ketones, resulting in solvent-induced variable solid-state architectures. Fluoroalkyl (R(f)) ligand substituents hinder π-π stacking interactions and favor ordered long-range packing, as well as the facile formation of film materials that exhibit high thermal stability and oxidation resistance. Reversible redox chemistry and spectroscopic studies in both solution and the solid-state indicate single-site isolation in both phases and an R(f)-induced propensity for electron uptake and inhibition of electron loss. Repeated redox cycles reorganize the thin films to accommodate Li(+) ions and facilitate their migration. The facile reduction, combined with high stability and ease of sublimation imparted by the R(f) scaffold that suppresses oxidations, recommends the new materials for sensors, color displays, electronic materials, and redox catalysts, as well as other applications.     

Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions with regular rotating event horizon. For corresponding parameterizations, the metrics and connections define Finsler–Einstein geometries modeled on tangent bundles, or on nonholonomic (pseudo) Riemannian manifolds. In general, there are vacuum nonholonomic gravitational configurations which can not be generated in the limit of zero cosmological constant.     

Fractional nonholonomic Ricci flows

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman’s functionals and derived the corresponding fractional evolution (Hamilton’s) equations. We apply in fractional calculus the nonlinear connection formalism originally elaborated in Finsler geometry and generalizations and recently applied to classical and quantum gravity theories. There are also analyzed the fractional operators for the entropy and fundamental thermodynamic values.     

Energy dissipation characteristics of particle sloshing in a rotating cylinder

A study on the energy dissipation characteristics of granular materials flowing/sloshing in a rotating container is presented here. The objective is to develop a configuration for control of excessive structural oscillations, similar to those of tuned vibration absorbers and tuned sloshing absorbers. The effectiveness of energy dissipation through granular flow is primarily determined experimentally. A computational model is developed to understand the flow behavior and energy dissipation in this system. A promising kinematic match of the particle behavior is demonstrated between the numerical predictions and the experimental observations. The use of the granular flow in a rotating drum for vibration control is being investigated for the first time.     

A Model Predictive Control Algorithm Applied To Non-Linear Processes

Model predictive control (MPC) is an optimization-based approach that has been successfully applied to a wide variety of control problems. In most of nonlinear strategies, the controllers are based on linear models with fixed parameters so that the vast body of linear control theory can be applied. Other solutions include the use of a nonlinear analytical model, combinations of linear empirical models, etc. This paper presents an MPC algorithm which uses on-line simulation and rule-based control. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)