Locally conformally Hermitian-flat manifolds

We introduce the notion of a locally conformally Hermitian-flat manifold and derive a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat. In addition, we construct a family of examples.     

<Emphasis Type="Italic">N</Emphasis>=1 supersymmetric conformal block recursion relations

We present explicit recursion relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 476–487, September, 2007.     

Berezin quantization of gauged WZW and coset models

Gauged WZW and coset models are known to be useful to prove holomorphic factorization of the partition function of WZW and coset models. In this note we show that these gauged models can be also important to quantize the theory in the context of the Berezin formalism. For gauged coset models Berezin quantization procedure also admits a further holomorphic factorization in the complex structure of the moduli space.This work is dedicated to Professor Michel Ryan on the occasion of his 60th birthday.     

任意多椭圆孔多裂纹无限大各向异性板应力强度因子求解的一种新方法

采用各向异性体平面弹性理论中的复势方法,应用保角变换技术,以F aber级数为工具,导出含任意多椭圆孔和裂纹群无限大各向异性板在远场载荷作用下其应力场和位移场的级数解,并在此基础上利用断裂力学方法确定裂纹尖端的应力强度因子,通过算例讨论了材料参数及裂纹、孔的尺寸等对应力强度因子的影响规律,得出了一些有益的结论。数值结果表明本文方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响。     

New algebraic structures from Hermitian one-matrix model

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra.     

Hom-Gel'fand–Dorfman Super-bialgebras and Hom-Lie Conformal Superalgebras

The aim of this paper is to introduce and study Hom-Gel'fand–Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing HomGel'fand–Dorfman super-bialgebras. Also, we obtain some infinite-dimensional Hom-Lie superalgebras from affinization of Hom-Gel'fand–Dorfman super-bialgebras. Finally, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish the equivalence between quadratic Hom-Lie conformal superalgebras and Hom-Gel'fand–Dorfman super-bialgebras.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.     

On the boundary layer/riblets interaction mechanisms and the prediction of turbulent drag reduction

Turbulent drag reduction experienced by ribletted surfaces is the result of both (1) the interaction between riblet peaks and the coherent structures that characterize turbulent near-wall flows, and (2) the laminar sublayer flow modifications caused by the riblet shape, which can balance, under appropriate conditions, the drag penalty due to the increased wetted surface. The latter “viscous” mechanism is investigated by means of an analytical model of the laminar sublayer, which removes geometrical restrictions and allows us to take into account “real” shapes of riblet contours, affected by manufacturing inaccuracies, and to compute even for such cases a parameter, called protrusion height, related to the longitudinal mean flow. By considering real geometries, riblet effectiveness is clearly shown to be related to the difference between the longitudinal and the transversal protrusion heights. A simple method for the prediction of the performances of ribletted surfaces is then devised. The predicted and measured drag reduction data, for different riblet geometries and flow characteristics, are in close agreement with each other. The soundness of the physical interpretation underlying this prediction method is consequently confirmed.     

Free percolation and seepage flows from watercourses

Free percolation and seepage flows from natural and artificial watercourses with curvilinear profiles are considered. The rigorous hydrodynamic solution of the problem of free percolation and seepage flow from a watercourse is obtained by representing the watercourse profiles in the plane of the Joukowski variable by means of the equation of a family of lemniscates and using the conformal mapping method. The calculated dependences for determining all the necessary parameters of the seepage flows and constructing the curvilinear watercourse profiles are given. In the case of a circular basis for the shape of the watercourse profile in the plane of the Joukowski variable these dependences coincide with the well-known exact dependences.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 94–99. Original Russian Text Copyright © 2004 by Anakhaev.