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 .

     

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）．     

关于具有恢复消息功能的认证方案的一点注记

简述了基本的Nyberg-Rueppel认证方案和HMP认证方案,指出了LC认证方案是HMP认证方案的一个特例。     

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.     

多圆柱上的完全准凸映射

在C~n中有界凸Reinhardt域上讨论了一类介于凸映射类与星形映射类之间的“完全准凸映射类”.特别地,在C~n中的多圆柱上给出了完全准凸映射的分解定理,得到了多圆柱上判别凸映射的一个改进的充分条件.     

Finite element approximation of spectral problems with Neumann boundary conditions on curved domains

This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain . Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain in the framework of the abstract spectral approximation theory.

     

Analytic models for commuting operator tuples on bounded symmetric domains

For a domain in and a Hilbert space of analytic functions on which satisfies certain conditions, we characterize the commuting -tuples of operators on a separable Hilbert space  such that is unitarily equivalent to the restriction of to an invariant subspace, where is the operator -tuple on the Hilbert space tensor product  . For the unit disc and the Hardy space , this reduces to a well-known theorem of Sz.-Nagy and Foias; for a reproducing kernel Hilbert space on such that the reciprocal of its reproducing kernel is a polynomial in and  , this is a recent result of Ambrozie, Müller and the second author. In this paper, we extend the latter result by treating spaces for which ceases to be a polynomial, or even has a pole: namely, the standard weighted Bergman spaces (or, rather, their analytic continuation) on a Cartan domain corresponding to the parameter in the continuous Wallach set, and reproducing kernel Hilbert spaces for which is a rational function. Further, we treat also the more general problem when the operator is replaced by ,  being a certain generalization of a unitary operator tuple. For the case of the spaces on Cartan domains, our results are based on an analysis of the homogeneous multiplication operators on , which seems to be of an independent interest.

     

Extremal Solutions for Quasilinear Elliptic Inclusions in All of ℝN with State-Dependent Subdifferentials

This paper deals with quasilinear elliptic differential inclusions defined in all of ^N and governed in general by a nonpotential quasilinear elliptic operator of the Leray–Lions type and a multivalued term in form of a (nonmonotone) state-dependent subdifferential. We prove the existence of entire extremal solutions within a sector of an ordered pair of appropriately defined upper and lower solutions without imposing any condition at infinity. Therefore, standard variational methods cannot be applied here. Furthermore, due to the unboundedness of the domain and due to lack of monotonicity of the operators involved, no comparison results are available such that the problem under consideration becomes even more difficult.