Matrix and vector models in the strong coupling limit

We consider matrix and vector models in the large-N limit: we study N × N matrices and vectors with N² components. In the case of a zero-dimensional model (D = 0), we prove that in the strong coupling limit (g → ∞), the partition functions of the two models coincide up to a coefficient. This also holds for D = 1. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 236–243, May, 2008.     

Hermitian lattices without a basis of minimal vectors

It is shown that over infinitely many imaginary quadratic fields there exists a Hermitian lattice in all even ranks which is generated by its minimal vectors but which is not generated by minimal vectors.

     

AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

The author proves that if f : C→Cn is a transcendental vector valued meromorphic function of finite order and assume Σa∈Cn ∪{∞}δ(a) = 2, then,where .This result extends the related results for meromorphic function by Singh and Kulkarni.     

空气中PM2.5的动态扩散及宏观预测

以PM2.5扩散、衰减模式为研究对象,分析探究了PM2.5的扩散规律、危机治理及其后5年的治理问题.首先通过主成分分析法,建立了PM2.5与其它污染物之间的多元非线性对数模型.同时引入相对湿度的影响因素对模型进行再度优化,提高了模型的拟合优度.运用统计学原理,得出采集点之间的PM2.5具有较高的协同性.另外分析了静态下PM2.5污染物颗粒的受力和漂移模式和从点源、面源两方面分析了PM2.5动态扩散模式,建立了PM2.5的扩散偏微分方程模型.根据建立的扩散模型,对突变的污染物浓度确定安全区域的范围.最后建立综合费用和专项费用的多目标优化模型,利用贝叶斯支持向量机方法对PM2.5进行宏观预测,并运用系统动力学理论对目标值进一步优化,并对不同治理模式进行对比分析.     

Projective vector fields on Finsler manifolds

In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.     

The existence of light‐like homogeneous geodesics in homogeneous Lorentzian manifolds

In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo‐Riemannian manifold admits a homogeneous geodesic through arbitrary point. In the present paper this affine method is refined and adapted to the pseudo‐Riemannian case. Using this method and elementary topology it is proved that any homogeneous Lorentzian manifold of even dimension admits a light‐like homogeneous geodesic. The method is illustrated in detail with an example of the Lie group of dimension 3 with an invariant metric, which does not admit any light‐like homogeneous geodesic.     

The contribution of K.-H. Elster to generalized conjugation theory and nonconvex duality

This article surveys the main contributions of K.-H. Elster to the theory of generalized conjugate functions and its applications to duality in nonconvex optimization.     

一般Hopf曲面上向量丛的结构

得到了非主Hopf曲面上连续复向量丛全纯结构的存在性及可滤性问题的充要条件.