Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

Dimensional Properties of Fractional Brownian Motion

Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.     

Degeneracy in NLP and the development of results motivated by its presence

We study notions of nondegeneracy and several levels of increasing degeneracy from the perspective of the local behavior of a local solution of a nonlinear program when problem parameters are slightly perturbed. Ideal nondegeneracy at a local minimizer is taken to mean satisfaction of second order sufficient conditions, linear independence and strict complimentary slackness. Following a brief exploration of the relationship of these conditions with the classical definition of nondegeneracy in linear programming, we recall a number of optimality and regularity conditions used to attempt to resolve degeneracy and survey results of Fiacco, McCormick, Robinson, Kojima, Gauvin and Janin, Shapiro, Kyparisis and Liu. This overview may be viewed as a structured survey of sensitivity and stability results: the focus is on progressive levels of degeneracy. We note connections of nondegeneracy with the convergence of algorithms and observe the striking parallel between the effects of nondegeneracy and degeneracy on optimality conditions, stability analysis and algorithmic convergence behavior. Although our orientation here is primarily interpretive and noncritical, we conclude that more effort is needed to unify optimality, stability and convergence theory and more results are needed in all three areas for radically degenerate problems.Research supported by National Science Foundation Grant ECS 90-00560 and Grant N00014-89-J-1537 Office of Naval Research     

LIGHT-SCATTERING STUDY OF POLYELECTROLYTE HOLLOW CAPSULES

Silver halide (AgX) microcrystal was used as template to synthesize hollow polyelectrolyte capsules. These hollow capsules were characterized by laser light scattering (LLS) used to measure the size of the capsules in solution. The ratio of hydrodynamic radius (Rh) from dynamic LLS to the radius of gyration (Rg) from static LLS is almost unity, revealing that the entities are hollow in solution. The results suggest that the LLS method can be regarded as a good complement to the confocal laser scanning microscopy (CLSM) method for the characterization of small hollow capsules, and it possesses the advantage of not needing fluorescence labeling.     

不同交联度的杜仲胶的红外光谱研究

研究了不同交联度的杜仲胶在室温及加热后红外光谱的变化规律．发现在室温下测定的样品红外光谱在低波数内对应链段变形振动的几个特征峰、加热后会消失或弥散，而交联度的改变对其影响不大，即使材料中结晶完全消失而变成高弹态．因此，推测这些特微峰的存在，应该和杜仲胶弹性网络中交联点间链段存在着明显的构象规整性有关．     

Quality assurance system for a decomposition method as demonstrated for the Wickbold combustion technique

 A five-step model for a quality assurance system is developed for an internal quality control check. It includes the quality control of the decomposition method and the detection method as steps belonging together. The Wickbold combustion technique as decomposition method in combination with atomic absorption spectrometry was chosen. The vaporization of the elements mercury, arsenic, lead, antimony and selenium is based on combustion in an oxyhydrogen flame. To check the efficiency of the analytical system, the uncertainty of results was calculated on the basis of the "Guide to the Expression of Uncertainty in Measurement". Received: 13 January 1997 · Accepted: 29 March 1997     

SYNTHESIS AND PROPERTIES OF POLYSTYRENE／LAPONITE NANOCOMPOSITES

Exfoliated polystyrene (PS)/laponite nanocomposites were prepared successfully. The characteristic doo1 diffraction peak of organo-laponite disappeared in the XRD patterns of nanocomposites, indicating that the laponite layers were exfoliated and the ordered crystal structure of laponite was destroyed because of the styrene polymerization. TEM observations showed that the exfoliated laponite primary particles were dispersed randomly in the PS matrix with lateral dimensions from 1 nm to 10 rim. SEM results showed that the PS/laponite nanocomposite particles were almost monodispersed spheres with the size of about 120 rim. Because of the interaction between PS and laponite nanolayers, the nanocomposites exhibited higher thermal stability and glass transition temperature when compared to pure PS.     

Regularity of Viscosity Solutions of the Biased Infinity Laplacian Equation

In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc.     

Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity

Consider the variational integral where Ω⊂ℝ ⁿ andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that . We approximateJ by a sequence of regularized functionalsJ _δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ _δ-minimizers.     

Wiener's test for space-time random walks and its applications

This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.