Normal families and uniqueness theorems for entire functions

There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S,f)=E(S,f′), then f≡f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.     

The skew elliptical distributions and their quadratic forms

In this paper, a family of the skew elliptical distributions is defined and investigated. Some basic properties, such as stochastic representation, marginal and conditional distributions, distribution under linear transformations, moments and moment generating function are derived. The joint distribution of several quadratic forms is obtained. An example is given to show that the distributions of some statistics as the functions of the quadratic forms can be derived for various applications.     

A spectroscopic investigation of turbulence in magnetized plasmas

We present a spectroscopic investigation of turbulence in the Tore-Supra edge plasma, where deuterium spectral lines are found to exhibit a power-law behavior in their wings. Such a feature is not predicted by the equilibrium line broadening theory in the conditions of the edge plasma, where the thermal Stark effect is negligible. Therefore, the possible role of turbulence is investigated along two separate paths. Indeed, both the Stark and the Doppler profiles may differ significantly from the equilibrium profiles.     

On the Nonrepresentability of Functions of Several Variables by Quadratures

The paper completes the construction of a multidimensional topological version of differential Galois theory. We construct a rich class of germs of functions of several variables which is closed under superpositions and other natural operations. The main theorem describes the behavior of the monodromy groups of such germs under the natural operations. As a result, we obtain topological obstructions to the representability of functions by quadratures, which give the strongest known statements about unsolvability of equations in closed form.     

Large Deviations of Empirical Measures Under Symmetric Interaction

We prove the large deviation principle for the joint empirical measure of pairs of random variables which are coupled by a totally symmetric interaction. The rate function is given by an explicit bilinear expression, which is finite only on product measures and hence is non-convex.     

级数小于1的亚纯函数的Borel例外值

证明了当超越亚纯函数的级小于1时，其Norel例外值最多只有一个．由于存在任何级的整函数，因此一个例外值总可达到，故所得结果不能再改进。     

Clifford分析中的多周期和准多周期Riemann边值问题

本文考虑了R^n 1空间中椭圆函数和准椭圆函数的一些性质，然后分别讨论了周期和准周期Riemann边值问题，给出了解的表达式和可解条件。     

平面动力问题的理论求解

通过对平面动力问题控制方程的分析,研究了相应的应力函数，得出了关于应力函数的基本方程。     

Pairwise Correlations in a Multicomponent Anisotropic Liquid

We investigate a multicomponent anisotropic liquid system. The first spatial moment of the direct correlation function is taken into account to obtain asymptotic expressions for the pairwise correlation functions. In this approximation, we obtain the pairwise correlation functions that describe the system behavior not only in the critical-state neighborhood but also in the noncritical domain. We show that the critical parameters for the anisotropic system differ from those for the isotropic system.     

Asymptotic Expansion of the Distribution Density Function for the Sum of Random Variables in the Series Scheme in Large Deviation Zones

The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in the Cramer zone and Linnik power zones for the distribution density function of sums of independent random variables in a triangular array scheme. The result was obtained using general Lemma 6.1 of Saulis and Statuleviius in Limit Theorems for Large Deviations (Kluwer, 1991) and joining the methods of characteristic functions and cumulants. The work extends the theory of sums of random variables and in a special case, improves S. A.Book's results on sums of random variables with weights.