Robust adaptive efficient estimation for semi-Markov nonparametric regression models

Statistical Inference for Stochastic Processes - We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model...     

Nonlinear maximum principles for dissipative linear nonlocal operators and applications

We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations.     

The Effect of a Substrate on the Current-vs-Voltage Characteristics of Thin-Film Sandwich Structures Based on Buckminsterfullerene

We analyze the current-vs-voltage (J-V) characteristics of ITO/C₆₀/Al sandwich cells, where ITO is the double indium tin oxide, C₆₀ is the buckminsterfullerene and Al is the thermally evaporated top aluminum electrode. These cells were obtained on either glass/ITO or polyethyleneterephthalate/ITO substrates (or, optionally, on glass/ZnO substrates) in a parallel process under identical conditions. However, the J-V dependences in each series behave very differently. The results are discussed in terms of the migration of admixtures from a bulk substrate material toward the top metallic electrode, thus modifying the photovoltaic properties of cells.     

Crystal and molecular structure of 11,12-dihydroxydrim-8(9)-en-7-one

The crystal structure of 11,12-dihydroxydrim-8(9)-en-7-one was determined by X-ray diffraction. The unit cell parameters are a = 7.534(3), b = 12.192(5), c = 8.067(4) Å, β = 98.01(3) Å, space group P2₁, and Z = 2 for C₁₅H₂₄O_3. The structure was solved by direct methods and refined in the anisotropic approximation to R = 0.051 and R _w = 0.113. The intramolecular O-H?O hydrogen bond [2.892(6) Å] between the hydroxy groups closes an additional seven-membered H-ring in the molecule. In the crystal, the intermolecular O-H?O hydrogen bond [2.857(4) Å] between the hydroxyl group and the carbonyl oxygen atom links the molecules related by the translation along the c-axis to form infinite chains.     

Almost Global Existence for the Prandtl Boundary Layer Equations

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H¹ space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within \({\varepsilon}\) of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time \({T_{\varepsilon} \geqq {\rm exp}(\varepsilon^{-1} / {\rm log}(\varepsilon^{-1}))}\).     

Analyticity and Gevrey-Class Regularity for the Second-Grade Fluid Equations

We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of the solutions that does not vanish as t → ∞, and which is independent of the Rivlin–Ericksen material parameter α. Applications to the damped incompressible Euler equations are also given.     

Nonlinear Instability for the Critically Dissipative Quasi-Geostrophic Equation

We prove that linear instability implies non-linear instability in the energy norm for the critically dissipative quasi-geostrophic equation.     

On Some Electroconvection Models

We consider a model of electroconvection motivated by studies of the motion of a two-dimensional annular suspended smectic film under the influence of an electric potential maintained at the boundary by two electrodes. We prove that this electroconvection model has global in time unique smooth solutions.