Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.     

A filtering method for the interval eigenvalue problem

We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer approximation (superset) of the real eigenvalue set of an interval matrix, we propose a filtering method that iteratively improves the approximation. Even though our method is based on a sufficient regularity condition, it is very efficient in practice and our experimental results suggest that it improves, in general, significantly the initial outer approximation. The proposed method works for general, as well as for symmetric interval matrices.     

T1 THEOREM FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

Suppose μ is a Radon measure on Rd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co ＞ 0 such that for all x ∈ supp(μ) and r ＞ 0,μ(B(x,r)) ≤ Corn, where 0 ＜ n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa's results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

A Note on Pad ′e Approximants Pairs as Limits of Algebraic Polynomials Pairs of Weighted Best Approximation in Orlicz Spaces

In this short note, we show the behavior in Orlicz spaces of best approxima-tions by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.     

Pulsed electrodeposition of monocrystalline Ni nanowire array and its magnetic properties

By means of a porous template without removing the aluminium substrate, a technique of pulsed electrodeposition with an intermittent symmetric square pulse has successfully been applied to fabricate Ni nanowire array. The as-obtained nanowires have a diameter of about 60 nm and exhibit high aspect ratio of more than 50. The electron diffraction pattern investigation demonstrates that the nanowires are single crystal. Moreover, a highly preferential orientation [2 2 0] of the as-obtained Ni nanowires with high purity decided by XRD has been obtained, and the preferred orientation is weakened remarkably by an annealing process. Furthermore, the investigation of magnetic properties by VSM indicates that the as-obtained Ni nanowire array has an obvious magnetic anisotropy and exhibits a good thermal stability.     

Quantic Superpositions and the Geometry of Complex Hilbert Spaces

The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. An in-depth analysis of superpositions is proposed, in which states are represented by one-dimensional subspaces, not by unit vectors as in Dirac’s notation. Superpositions must be considered when one cannot distinguish between possible paths, i.e., histories, leading to the current state of the system. In such a case the resulting state is some compound of the states that result from each of the possible paths. States can be compounded, i.e., superposed in such a way only if they are not orthogonal. Since different classical states are orthogonal, the claim implies no non-trivial superpositions can be observed in classical systems. The parameter that defines such compounds is a proportion defining the mix of the different states entering the compound. Two quantities, p and θ, both geometrical in nature, relate one-dimensional subspaces in complex Hilbert spaces: the first one is a measure of proximity relating two rays, the second one is an angle relating three rays. The properties of superpositions with respect to those two quantities are studied. The algebraic properties of the operation of superposition are very different from those that govern linear combination of vectors. This work was partially supported by the Jean and Helene Alfassa fund for research in Artificial Intelligence, by the Israel Science Foundation grant 183/03 on “Quantum and other cumulative logics” and by EPSRC Visiting Fellowship GR/T 24562 on “Quantum Logic”.     

Symmetric Gauss-Seidel multigrid solution of the Euler equations on structured and unstructured grids

The efficient symmetric Gauss-Seidel (SGS) algorithm for solving the Euler equations of inviscid, compressible flow on structured grids, developed in collaboration with Jameson of Stanford University, is extended to unstructured grids. The algorithm uses a nonlinear formulation of an SGS solver, implemented within the framework of multigrid. The earlier form of the algorithm used the natural (lexicographic) ordering of the mesh cells available on structured grids for the SGS sweeps, but a number of features of the method that are believed to contribute to its success can also be implemented for computations on unstructured grids. The present paper reviews, the features of the SGS multigrid solver for structured gr0ids, including its nonlinear implementation, its use of “absolute” Jacobian matrix preconditioning, and its incorporation of multigrid, and then describes the incorporation of these features into an algorithm suitable for computations on unstructured grids. The implementation on unstructured grids is based on the agglomerated multigrid method developed by Sørensen, which uses an explicit Runge-Kutta smoothing algorithm. Results of computations for steady, transonic flows past two-dimensional airfoils are presented, and the efficiency of the method is evaluated for computations on both structured and unstructured meshes.     

Instability investigation for rotating thin spherical membrane

A fluid-filled truncated spherical membrane fixed along its truncated edge to a horizontal, rigid and frictionless plane and spinning around a center axis was investigated. A two-parameter Mooney–Rivlin model was used to describe the material of the membrane. The truncated sphere was modeled in 3D using finite element meshes with different symmetry properties. A quadratic function was used for interpolating hydro-static pressure, giving a symmetric tangent stiffness matrix, thereby reproducing the conservative problem. Various problem settings were considered, related to the spinning, and different instability behaviors were observed. Multi-parametric problems were defined, generalized paths including primary and secondary paths were followed. Stability of the multi-parametric problem was evaluated using generalized eigenvalue analysis based on the total differential matrix for the constrained problem. Numerical results showed that mesh symmetry affected the simulated stability behavior. Fold line evaluations showed the parametric effects on critical solutions.     

Singular integrals with mixed homogeneity in Triebel-Lizorkin spaces

In this paper, we study the singular integral

     

Products of weighted composition and differentiation operators into weighted Zygmund and Bloch spaces

We characterize boundedness and compactness of products of differentiation operators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.