A note on Besov regularity of layer potentials and solutions of elliptic PDE's

Let be a second order, (variable coefficient) elliptic differential operator and let , , 0$">, satisfy in the Lipschitz domain . We show that can exhibit more regularity on Besov scales for which smoothness is measured in with . Similar results are valid for functions representable in terms of layer potentials.

     

Characterization of Certain Holomorphic Geodesic Cycles on Quotients of Bounded Symmetric Domains in terms of Tangent Subspaces

Let be an irreducible bounded symmetric domain and Aut() be a torsion-free discrete group of automorphisms, X /. We study the problem of algebro-geometric and differential-geometric characterizations of certain compact holomorphic geodesic cycles S X. We treat special cases of the problem, pertaining to a situation in which S is a compact holomorphic curve, and to the case where is a classical domain dual to the hyperquadric. In both cases we consider algebro-geometric characterizations in terms of tangent subspaces. As a consequence we derive effective pinching theorems where certain complex submanifolds S X are proven to be totally geodesic whenever their scalar curvatures are pinched between certain computed universal constants, independent of the volume of the submanifold S, giving new examples of the gap phenomenon for the characterization of compact holomorphic geodesic cycles.Research funded by a CERG grant from Research Grants Council of Hong Kong.     

A mean value theorem on bounded symmetric domains

Let be a Cartan domain of rank and genus and , , the Berezin transform on ; the number can be interpreted as a certain invariant-mean-value of a function around . We show that a Lebesgue integrable function satisfying , , must be -harmonic. In a sense, this result is reminiscent of Delsarte's two-radius mean-value theorem for ordinary harmonic functions on the complex -space , but with the role of radius played by the quantity .

     

正线性算子对无穷区间上有界变差函数的点态逼近度

用ＢＶ［０，∞）表示在［０，∞）的每一有限子区间上为有界变差函数的函数构成的空间。用表示ＢＶ［０，∞）上的正线性算子，其中ｄｔＫｎ（ｘ，ｔ）是非负测度且，则有定理如果Ｌｎ（｜ｔ－ｘ｜β，ｘ）≤Ｃ（ｘ）／ｎｖ，，这里β＞０，ｖ≥１，Ｃ（ｘ）是一个与ｘ有关的常数，对ｆ∈ＢＶ［０，∞）和ｘ∈（０，∞）有这里作为应用，给出算子的逼近估计．     

e~(ax+bx~2)(a,b∈R)参数平面上的骚动区域

本文将参数（ａ，ｂ）平面分为七个区域，然后讨论在每一个区域中ｅａｘ＋ｂｘ２的不动点分布（§１）．在§２中，我们得到一个定理：在Ｄ∞１∪Ｄ∞Ｃ中ｅａｘ＋ｂｘ２是骚动的（在扩充意义下）．     

On Overspill Principles and Axiom Schemes for Bounded Formulas

We study the theories I?_n, L?_n and overspill principles for ?_n formulas. We show that IE_n ? L?_n ? I?_n, but we do not know if I?_n L?_n. We introduce a new scheme, the growth scheme Crγ, and we prove that L?_n ? Cr?_n? I?_n. Also, we analyse the utility of bounded collection axioms for the study of the above theories. Mathematics Subject Classification: 03F30, 03H15.     

Elimination of bounds in optimization problems by transforming variables

The problem of minimizing a nonlinear objective function ofn variables, with continuous first and second partial derivatives, subject to nonnegativity constraints or upper and lower bounds on the variables is studied. The advisability of solving such a constrained optimization problem by making a suitable transformation of its variables in order to change the problem into one of unconstrained minimization is considered. A set of conditions which guarantees that every local minimum of the new unconstrained problem also satisfies the first-order necessary (Kuhn—Tucker) conditions for a local minimum of the original constrained problem is developed. It is shown that there are certain conditions under which the transformed objective function will maintain the convexity of the original objective function in a neighborhood of the solution. A modification of the method of transformations which moves away from extraneous stationary points is introduced and conditions under which the method generates a sequence of points which converges to the solution at a superlinear rate are given.     

Membrane Organization and Dynamics of the G-Protein-Coupled Serotonin<Subscript>1A</Subscript> Receptor Monitored Using Fluorescence-Based Approaches

The G-protein-coupled receptor (GPCR) superfamily represents one of the largest classes of molecules involved in signal transduction across the plasma membrane. Fluorescence-based approaches have provided valuable insights into GPCR functions such as receptor–receptor and receptor–ligand interactions, real-time assessment of signal transduction, receptor dynamics on the plasma membrane, and intracellular trafficking of receptors. This has largely been possible with the use of fluorescent probes such as the green fluorescent protein (GFP) from the jellyfish Aequoria victoria and its variants. We discuss the potential of fluorescence-based approaches in providing novel information on the membrane organization and dynamics of the G-protein-coupled serotonin_1A receptor tagged to the enhanced yellow fluorescent protein (EYFP). These authors contributed equally to the work.     

Fundamental Domains for Finite Subgroups in <Emphasis Type="Italic">U</Emphasis>(2) and Configurations of Lagrangians

We show that every finite subgroup of U(2) is contained with index two in a group generated by involutions fixing Lagrangian planes. We describe fundamental domains for their action on related to the configuration of these Lagrangian planes.     

Enhanced biocompatibility in biostable poly(carbonate)urethane

In this work, we synthesized two MDI-based polyurethanes, including a poly(ether)urethane (PEU) and a poly(carbonate)urethane (PCU), by using different soft segments, poly(tetramethylene oxide) and poly(hexyl, ethyl)carbonate diol (M approximately 2,000). We demonstrated that, in addition to the enhanced biostability of PCU over PEU, the biological performances of PCU in vitro were also improved in general. These included, better cellular attachment and proliferation, less platelet activation, as well as reduced monocyte activation. The unusual wide-ranging enhancement in biocompatibility for PCU was believed to be related to the larger micro-phase separation in PCU (approximately 25 nm) that caused distinct protein adsorption on the surface. The total number of adherent monocytes (nonactivated and activated) on the bare sample surfaces, albumin pre-adsorbed sample surfaces, and fibrinogen pre-adsorbed sample surfaces.