The Order of Best Approximation in Some Classes of Functions

Starting from the equivalence between the Ditzian–Totik modulus and , where , in this article large classes of functions are introduced for which the modulus can be easily calculated. As a consequence, very good estimates for the bestapproximation are obtained. The attempts to estimate or calculate themodulus can be a very intricateproblem.     

Geometric phase for degenerate states of spin-1 and spin-1/2 pair

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model.      

Nonbinary quantum error-correcting codes from algebraic curves

We give a new exposition and proof of a generalized CSS construction for nonbinary quantum error-correcting codes. Using this we construct nonbinary quantum stabilizer codes with various lengths, dimensions, and minimum distances from algebraic curves. We also give asymptotically good nonbinary quantum codes from a Garcia–Stichtenoth tower of function fields which are constructible in polynomial time.     

On convexity of a planar domain with a pair of concave tomography projections

We describe simple sufficient conditions on tomography-type measurements of a planar set which imply convexity of this set. The cases of partial convexity and higher-dimensional sets are considered as well.     

Selective localization of organoclay and effects on the morphology and mechanical properties of LDPE/PA11 blends with distributed and co‐continuous morphology

A study was made on the effect of small amounts of organically modified clay on the morphology and mechanical properties of blends of low‐density polyethylene and polyamide 11 at different compositions. The influence of the filler on the blend morphology was investigated using wide angle X‐ray diffractometry, scanning and transmission electron microscopy and selective extraction experiments. The filler was found to locate predominantly in the more hydrophilic polyamide phase. Although such uneven distribution does not have a significant effect on the onset of phase co‐continuity of the polymer components, it brings about a drastic refinement of the microstructure for the blends both with droplets/matrix and co‐continuous morphologies. In addition to the expected reinforcing action of the filler, the resulting fine microstructure plays an important role in enhancing the mechanical properties of the blends. This is essentially because of a good quality of stress transfer across the interface between the constituents, which also seems to benefit for a good interfacial adhesion promoted by the filler. Our results provide the experimental evidence for the capabilities of nanoparticles added to multiphase polymer systems to act selectively as a reinforcing agent for specific domains of the material and as a medium able to assist the refinement of the polymer phases during mixing. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 600–609, 2010     

Continuity properties of the integrated density of states on manifolds

We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous “periodic” IDS which is regularized by a random perturbation.     

On States of Total Weighted Occupation Times of a Class of Infinitely Divisible Superprocesses on a Bounded Domain

In this paper, general conditions of state classification for the total weighted occupation times of a class of infinitely divisible superprocesses on a bounded domain D in ℝ ^d are given. As an application, some sufficient and necessary conditions are found for the total weighted occupation times of some special superprocesses on D to be absolutely continuous or singular with respect to the Lebesgue measure on D. The research of Yan-Xia Ren is supported by NNSF of China (Grant No. 10471003) and Foundation for Authors Awarded Excellent Ph.D. Dissertation.     

Convergence analysis of a family of Steffensen-type methods for generalized equations

A class of Steffensen-type algorithms for solving generalized equations on Banach spaces is proposed. Using well-known fixed point theorem for set-valued maps [A.L. Dontchev, W.W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc. 121 (1994) 481-489] and some conditions on the first-order divided difference, we provide a local convergence analysis. We also study the perturbed problem and we present a new regula-falsi-type method for set-valued mapping. This study follows the works on the Secant-type method presented in [S. Hilout, A uniparametric Secant-type methods for nonsmooth generalized equations, Positivity (2007), submitted for publication; S. Hilout, A. Piétrus, A semilocal convergence of a Secant-type method for solving generalized equations, Positivity 10 (2006) 673-700] and extends the results related to the resolution of nonlinear equations [M.A. Hernández, M.J. Rubio, The Secant method and divided differences Hölder continuous, Appl. Math. Comput. 124 (2001) 139-149; M.A. Hernández, M.J. Rubio, Semilocal convergence of the Secant method under mild convergence conditions of differentiability, Comput. Math. Appl. 44 (2002) 277-285; M.A. Hernández, M.J. Rubio, ω-Conditioned divided differences to solve nonlinear equations, in: Monogr. Semin. Mat. García Galdeano, vol. 27, 2003, pp. 323-330; M.A. Hernández, M.J. Rubio, A modification of Newton's method for nondifferentiable equations, J. Comput. Appl. Math. 164/165 (2004) 323-330].