Director reorientation and order reconstruction: competing mechanisms in a nematic cell

We propose a model to explore the competition between two mechanisms possibly at work in a nematic liquid crystal confined within a flat cell with strong uniaxial planar conditions on the bounding plates and subject to an external field. To obtain an electric field perpendicular to the plates, a voltage is imposed across the cell; no further assumption is made on the electric potential within the cell, which is therefore calculated together with the nematic texture. The Landau-de Gennes theory of liquid crystals is used to derive the equilibrium nematic order tensor Q. When the voltage applied is low enough, the equilibrium texture is nearly homogeneous. Above a critical voltage, there exist two different possibilities for adjusting the order tensor to the applied field within the cell: plain director reorientation, i.e., the classical Freedericksz transition, and order reconstruction. The former mechanism entails the rotation of the eigenvectors of Q and can be described essentially by the orientation of the ordinary uniaxial nematic director, whilst the latter mechanism implies a significant variation of the eigenvalues of Q within the cell, virtually without any rotation of its eigenvectors, but with the intervention of a wealth of biaxial states. Either mechanism can actually occur, which yields different nematic textures, depending on material parameters, temperature, cell thickness and the applied potential. The equilibrium phase diagram illustrating the prevailing mechanism is constructed for a significant set of parameters.      

A Monotonicity of Moments Concerned with Order Restricted Statistical Inference

In the order restricted statistical inference problem, moments of the distance between a true parameter and the least square estimate are non-decreasing when the true parameter moves along a half line from an initial point in the null space. This follows from stochastically larger property of the distance.     

亚纯函数的因子分解

该文研究复合意义下的亚纯函数的因子分解,完善文献[1]中定理1的证明,得出判断某些函数为拟素的或 E -拟素的必要条件     

Sikkema-Bernstein算子对只有第一类间断点的有界函数的逼近

本文研究了在［０，１］上只有第一类间断点的有界函数，用Ｓｉｋｋｅｍａ－Ｂｅｒｎｓｔｅｉｎ算子逼近，给出３点态逼近阶，得到的结果是本文中的定理     

广义Hadamard乘积

本文讨论了整函数f(Z)和g(z)的阶与型及其特殊的广义Hadamard乘积的阶与型之间的关系.并推广了文献[2]的结果.     

二阶椭圆方程的混合有限元分析

本文给出二阶椭圆方程的一种新的混合框架,并给出两种混合有限元法.     

SOME OSCILLATION THEOREMS OF HIGHER ORDER NON－HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH TRANSCENDENTAL MEROMORPIC COEFFICIENTS

ＳＯＭＥＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＯＦＨＩＧＨＥＲＯＲＤＥＲＮＯＮ－ＨＯＭＯＧＥＮＥＯＵＳＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＴＲＡＮＳＣＥＮＤＥＮＴＡＬＭＥＲＯＭＯＲＰＩＣＣＯＥＦＦＩＣＩＥＮＴＳ￥ＣｈｅｎＺｏ...     

张弛振子中加周期序列标度常数的映象阶数不依赖性

在最简单的张弛振子中,通过实验研究了当描述振子的映象阶数不同时加周期序列标度常数的变化。实验表明:当映象阶数为3阶时,沿临界线或沿超临界区某条线的加周期序列标度常数都分别为β～2.0和7～3.0;当映象阶数理论上为无穷阶,实践上高于3阶时,在误差范围内,β和γ的值与3阶时相同。这就证实加周期序列标度常数只反映法瑞树的性质,与映象的性质无关。     

REDCAT: a residual dipolar coupling analysis tool

Recent advancements in the utilization of residual dipolar couplings (RDCs) as a means of structure validation and elucidation have demonstrated the need for, not only a more user friendly, but also a more powerful RDC analysis tool. In this paper, we introduce a software package named REsidual Dipolar Coupling Analysis Tool (REDCAT) designed to address the above issues. REDCAT is a user-friendly program with its graphical-user-interface developed in Tcl/Tk, which is highly portable. Furthermore, the computational engine behind this GUI is written in C/C++ and its computational performance is therefore excellent. The modular implementation of REDCAT's algorithms, with separation of the computational engine from the graphical engine allows for flexible and easy command line interaction. This feature can be utilized for the design of automated data analysis sessions. Furthermore, this software package is portable to Linux clusters for high throughput applications. In addition to basic utilities to solve for order tensors and back calculate couplings from a given order tensor and proposed structure, a number of improved algorithms have been incorporated. These include the proper sampling of the Null-space (when the system of linear equations is under-determined), more sophisticated filters for invalid order-tensor identification, error analysis for the identification of the problematic measurements and simulation of the effects of dynamic averaging processes.     

Simple random order methods to share costs

A simple random order method (SROM) is an extension of Webers random order values (ROVs), which allows the convex weights on orderings of agents to depend on the set of agents with strictly positive demands. Thus, a SROM permits different coalitions of agents adopting exogenously different ROVs to take into account the differences in, for example, bargaining abilities, rights or status of the agents in a cost sharing problem. Within the family of additive methods satisfying the dummy axiom, we characterize SROMs by Measurement Invariance in the discrete cost sharing model where demands are indivisible, and Ordinality in the continuous model where demands are divisible, respectively.I am indebted to Yves Sprumont for initiating and providing the starting point of this paper, and for his great help in this work. I thank Hervé Moulin, Ahmet Alkan, Anirban Kar, an associate editor, and a referee whose comments greatly improved the paper. I gratefully acknowledge the support from Sabanci University Research Fund.