How to Express a Parallel Sum of k Matrices

We present an alternative expression for the parallel sum of k Hermitian nonnegative definite matrices by using the Moore-Penrose inverse of a block matrix.     

赋权矩阵及其性质

本文给出了以S为行权和向量的权矩阵类T_＋(S)中每个权矩阵都可逆的一个充要条件．     

Density Correlations in the Two-Dimensional Coulomb Gas

We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory of an equivalent sine-Gordon model is used to determine the density correlation length. At the surface of a rectilinear plain wall, the universality of the asymptotic behavior of the density correlations is suggested. A scaling analysis implies a local form of the compressibility sum rule near a hard wall. A symmetry of the Coulomb system with respect to the Möbius conformal transformation, which induces a gravitational source acting on the particle density, is established. Among the consequences, a universal term of the finite-size expansion of the grand potential is derived exactly for a disk geometry of the confining domain.     

带风险指数的金融均衡的存在性定理及其结构特征(下)

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、虚资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Duffie，D＆W．Shfer（1985）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下会随机风险因素的情形，也适用于商品空间为无限维的情形，除此之外，还给出了怎样判别资产结构是否属于T类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均市分配不确定性的反却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

运用反例基于识别的手写数字串分割

采用基于识别的分割方法进行手写数字串分割.在识别的过程中,运用反例样本估计分类器参数,实验数据表明,这种运用反例样本训练的分类器与没有经过反例样本训练的分类器相比,将提高拒识率到19%左右,从而保证了较高的识别率,验证了只有经过反例训练的分类器的输出结果才是可信赖的.     

正负系数中立型差分方程的正解的存在性

In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature     

Hyperbolic spaces are of strictly negative type

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.

     

Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

SECOND BEST TAXES AND QUOTAS IN NITROGEN REGULATION

This paper investigates second best policies to regulate nitrogen leaching. When the policy maker controls the total nitrogen use, an overall tax is superior to an action equivalent overall quota. When the goal is to regulate the expected level of nitrogen leaching, expected profit of a risk neutral farmer is greater under an overall tax than under an overall quota under a reasonable condition. The welfare ranking of action equivalent taxes and quotas for a risk averse farmer is generally ambiguous. In the numerical analyses, overall taxes turned out to be superior to overall quotas with both targets, despite a very high value of absolute risk aversion, 0.01. These results suggest that an overall tax is probably a superior policy to an overall quota to regulate expected total nitrogen use or expected nitrogen leaching for risk neutral and most of risk averse farmers.     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.