L~1空间中L-R型迁移方程的解对边界参数的连续依赖性

在L~1空间研究种群细胞增生中一类具扰动项的积分边界条件的迁移方程.证明了迁移算子是预解正算子,得到了微分算子的共轭算子,并证明其定义域的正锥在共轭空间的正锥中共尾,得到迁移算子的增长界等于其谱界.最后利用主算子对边界参数的连续依赖证明了迁移方程的解对边界参数连续依赖.     

L~1空间中具有周期边界条件的迁移方程的性质

在L~1空间研究板几何中具有周期边界条件的迁移方程.证明了迁移算子是预解正算子,得到了微分算子的共轭算子及共轭算子的定义域.证明了迁移算子的共轭算子定义域的正锥在共轭空间的正锥中共尾.最后证明了迁移算子的增长界等于其谱界.     

具积分边值条件的迁移方程的性质

在L~1空间上研究了一类增生的细菌群体中具积分边界条件的迁移方程.得出迁移算子是预解正算子,微分算子的共轭算子及共轭算子的定义域.证明了迁移算子的共轭算子定义域的正锥在共轭空间的正锥中共尾.最后证明了迁移算子的增长界等于其谱界.     

具有广义边界条件的迁移方程的性质

研究迁移理论中一类具有广义周期边界条件,非均匀介质板几何的定态迁移方程,证明了迁移算子是预解正算子,得到了微分算子的共轭算子及共轭算子的定义域.证明了迁移算子的共轭算子定义域的正锥在共轭空间的正锥中共尾.最后证明了迁移算子的增长界等于其谱界.     

平板几何中迁移方程的谱界和增长界的一个注记

本文在L~1空间研究平板几何中具有零边界的迁移方程,通过证明具有反射边界条件的迁移算子的预解式的范数对反射系数连续依赖,得到了反射边界迁移算子的预解式一致收敛于零边界迁移算子的预解式,进而得到零边界下谱界和增长界相等.     

L~1空间中具有不完全反射边界条件的迁移方程的性质

在L~1空间研究平板几何中具有不完全反射边界条件的迁移方程,证明了迁移方程中的微分算子和积分算子是预解正算子,得到了微分算子的共轭算子及其定义域,最后证明了微分算子共尾.     

两不同型部件并联可修系统主算子的性质

研究了两不同型部件并联可修系统.通过选取空间及定义算子A和B,将模型方程转化成了Banach空间中的抽象Cauchy问题.通过分析系统主算子A的谱分布,求出A的谱上界.利用预解正算子及共尾理论,证明了A的谱上界和增长界相等.     

电站两辅助设备冷贮备系统主算子的性质

研究了由两个同型部件、一个转换开关和一个修理工组成的电站单元机组辅助设备的冷贮备系统.通过选取空间及定义算子,将模型方程转化成了Banach空间中的抽象Cauchy问题.通过分析系统主算子的谱分布,求出主算子的谱上界.利用预解正算子及共尾理论,证明了主算子的谱上界和增长界相等.     

复合结构可修复系统口香糖算子的性质

研究了有15个部件串并联工作的多状态口香糖生产可修复系统.运用C_0半群的理论,证明了系统算子是稠定的预解正算子,得出了系统算子的共轭算子及其定义域,并证明了系统算子的增长界为0.最后运用了预解正算子中共尾的概念及相关理论,证明了系统算子的谱上界也是0.     

Banach空间一类非线性算子方程的迭代求解及应用

在不假定锥正规、再生和算子连续的条件下,利用锥理论和单调迭代方法证明了一类非线性算子方程x=A(x,x)解的存在性定理,并应用于Banach空间一阶微分方程的终值问题.     

最小距离固定且优于Gilbert—Varshamov界的码

本文构造了一类GF(q)上的码,其中GF(q)为q个元素的有限域.这些码的冗余取到渐进界r(q,n,7) 4 m,此界优于Gilbert-Varshamov存在界r(q,n,7) 5m.     

Improving probability bounds by optimization over subsets

The simple device of maximization over subsets of events can provide substantial improvement over the Dawson-Sankoff degree two lower bound on the probability of a union of events and can also exceed a sharper bound that uses individual and pairwise joint event probabilities developed by Kuai, Alajaji, and Takahara. In each of their examples, the maximized bound achieves the exact probability of the union using a subset of events containing no redundant events of the original set of events.     

Multilinear enumerative techniques

When S is a finite set and G a finite group acting on S, we consider the problem of rejecting isomorphs in a G-stable subset of S. In previous work we developed a linear algebraic context for this problem by constructing the finite dimensional vector spaceF ^s whereF is a field of characteristic zero. When S is a finite function space, or a finite direct product of finite function spacesF ^s acquires a multilinear structure By various specializations ofG and S and by applications of results which have appeared elsewhere, identities of Sheehan, deBruijn and P61ya are obtained. Furthermore, these same techniques are applied to examples which do not have a clear resolution using the more common formulas     

Bounds for the sum of distances of spherical sets of small size

We derive upper and lower bounds on the sum of distances of a spherical code of size N in n dimensions when $N=\mathrm{\Theta }(n^{\alpha }),0<\alpha ?2$. The bounds are derived by specializing recent general, universal bounds on energy of spherical sets. We discuss asymptotic behavior of our bounds along with several examples of codes whose sum of distances closely follows the upper bound.     

凸集值映射的整体误差界

考虑了凸集值映射的整体误差界，推广Li和Singer(1998)的主要定理到无界情形并肯定地回答了该文的猜想．作为应用，给出了线性Hoffman误差界定理一个简单的新证明．     

Bhattacharyya bound of variances of unbiased estimators in nonregular cases

Summary Bhattachayya bound is generalized to nonregular cases when the support of the density depends on the parameter, while it is differentiable several times with respect to the parameter within the support. Some example is discussed, where it is shown that the bound is sharp. Research supported by NSF Grant MCS-8301409.     

Nonlinear codes with asymptotic parameters better than the Gilbert-Varshamov and the Xing Bounds

In this paper, we show that the Gilbert-Varshamov and the Xing bounds can be improved significantly around two points where these two bounds intersect by nonlinear codes from algebraic curves over finite fields.     

The New Minimum Distance Bounds of Goppa Codes and Their Decoding

A couple of new lower bounds of the minimum distance of Goppa codes is derived, using an extended field code for a Goppa code which contains the Goppa code as its subfield-subcode. Also presented are procedures for both error-only and error-and-erasure decoding for Goppa codes up to the new lower bounds, based on the Berlekamp-Massey algorithm and the Feng-Tzeng multisequence shift-register synthesis algorithms which have been used for decoding cyclic codes up to the BCH and HT(Hartmann-Tzeng) bounds.