正则预解算子族的乘积扰动

设K∈C（R＋）和B是一个有界线性算子．作者证明如果犃生成一个指数有界的A正则预解算子族，那么BA，AB或A（I＋B），（I＋B）A也生成一个指数有界的k-正则预解算子族．此外，作者也给出了k正则预解算子族的加法扰动的相应结果．     

双连续C正则预解算子族的生成定理

基于C正则预解算子族和双连续C_0半群引入了双连续C正则预解算子族的概念,考察了双连续C正则预解算子族生成元与预解式之间的关系,给出了双连续C正则预解算子族Hille-Yosida型生成定理,从而对Bananch空间强连续半群的生成定理进行了推广.     

Hilbert空间上依范连续的α-次预解算子族

主要运用Laplace-Stieltjes的方法,讨论Hilbert空间上α-次预解算子族的依范连续性与其预解式的关系,得到一个主要结果：Hilbert空间上α-次预解算子族的依范连续性与其预解式在当｜τ｜→∞时,‖（ω＋iτ）~（α-1）R（（ω＋iτ）~α,A）‖→0等价.     

C-正则预解算子族的遍历性

本文研究了C-正则预解算子族的Abel遍历性和Cesaro遍历性.给出了两种遍历性的 相互关系及其基本性质.     

非预解形式线性微分方程的解

通过几个实例给出解非预解形式线性微分方程的一般方法,并讨论了预解形式的线性微分方程与非预解形式的线性微分方程解集的差别.     

预解算子控制的无穷时滞分数阶微分方程解的存在性

本文研究了一类预解算子控制的具有无穷时滞的分数阶泛函微分方程.利用解析预解算子理论和不动点定理,得到了具有无穷时滞分数阶微分方程适度解的存在性,推广和改进了一些已知的结果.     

无单位元环A=sZ_(st)的同调不变量Tor_m~(Z,Z)的计算

设A=sZst,A~=A Z,本文作者给出了A~-模Z的自由预解,并以此为基础计算了T orAm(Z,Z).     

无单位元环A=sZst的同调不变量Tor(A~)m(Z,Z)的计算

设A=sZst,(A~)=A( )Z,本文作者给出了(A~)-模Z的自由预解,并以此为基础计算了TorAm(Z,Z).     

BKP方程族的Pfaffian解

本文从约化的角度考虑BKP方程族的Pfaffian形式的解.证明了通过施加适当的微分约束,KP方程族的格拉姆行列式的解很自然的约化为BKP方程族的解.     

BKP方程族的Pfaffian解

本文从约化的角度考虑BKP方程族的Pfaffian形式的解.证明了通过施加适当的微分约束,KP方程族的格拉姆行列式的解很自然的约化为BKP方程族的解.     

Graph family operations

In previous papers, Catlin introduced four functions, denoted , , , and , between sets of finite graphs. These functions proved to be very useful in establishing properties of several classes of graphs, including supereulerian graphs and graphs with nowhere zero k-flows for a fixed integer k3. Unfortunately, a subtle error caused several theorems previously published in Catlin (Discrete Math. 160 (1996) 67–80) to be incorrect. In this paper we correct those errors and further explore the relations between these functions, showing that there is a sort of duality between them and that they act as inverses of one another on certain sets of graphs.     

A classification of the structures of some Sperner families and superimposed codes

In this paper we will give a new proof by using group action to prove the uniqueness of maximal Sperner families of [n]. We will also prove the uniqueness of Sperner families F of [n] with by using a combinatorial approach. Furthermore, by using the uniqueness of Sperner family, we will classify all the structures of (1,2) superimposed codes of size 9×10 and 9×11.     

Fitting Quantiles: Doubling,HR, HQ,and HHH Distributions

Abstract

This article introduces a family of distributional shapes which is flexible in the sense that it contains skewed and symmetric laws as well as heavy-tailed and light-tailed laws. The proposed family is also practically convenient because it is easy to fit to a table of quantiles from any distribution. Inversely, for each of the distributional shapes it is trivial to compute quantiles for any desired probability, and it is possible to compute the corresponding densities.     

Chain Intersecting Families

Let be a family of subsets of an n-element set. is called (p,q)-chain intersecting if it does not contain chains and with . The maximum size of these families is determined in this paper. Similarly to the p = q = 1 special case (intersecting families) this depends on the notion of r-complementing-chain-pair-free families, where r = p + q − 1. A family is called r-complementing-chain-pair-free if there is no chain of length r such that the complement of every set in also belongs to . The maximum size of such families is also determined here and optimal constructions are characterized. The first author is a member of the Egerváry Research Group (EGRES). Research is supported by OTKA grants T 037547 and TS 049788, by European MCRTN Adonet, Contract Grant No. 504438 and by the Egerváry Research Group of the Hungarian Academy of Sciences. The work of the second author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant numbers T037846 and NK62321.     

贪婪t－相交有限序列族

设Ｆ为有限序列族，对ａ＝（ａ１，ａ２，…，ａｎ）∈Ｆ，ａｉ为整数且０≤ａｉ≤ｓｉ（整数），记ｓ（ａ）＝｛ｊ｜１≤ｊ≤ｎ，ａｊ＞０｝，ｓ（Ｆ）＝｛ｓ（ａ）｜ａ∈Ｆ｝，及Ａ｛１，２，…，ｎ｝时Ｗ（Ａ）＝Пｉ∈Ａｓｉ．称Ｆ为贪婪ｔ－相交，如对任何ａ，ｂ∈Ｆ，至少有ｔ个ａｉ，ｂｉ＞０，且Ｗ（Ａ）≥Ｗ（（｛１，２，…，ｎ｝－Ａ）＋Ｂ）对任何Ａ∈Ｓ（Ｆ）及ＢＡ（｜Ｂ｜＝ｔ－１）成立．本文得到当ｓ１＞ｓ２＞…＞ｓｎ时的最大贪婪ｔ－相交有限序列族．     

Admissible values of one parameter for maximal Sperner families of subsets of the type (<Emphasis Type="Italic">k,k</Emphasis> + 1)

In this paper we generalize one assertion (obtained by us earlier) on admissible values of a certain parameter for partial maximal Sperner families (m. S. f.) of subsets of a finite set of the type (k, k + 1). We also prove that the minimal value of the parameter under consideration for all m. S. f. of the type (k, k + 1), except for two families, is less than \(\left( {_k^{n - 1} } \right)\) ? 1.     

A Katona-type proof of an Erd?s-Ko-Rado-type theorem

Let p?1/2 and let μ_p be the product measure on {0,1}ⁿ, where μ_p(x)=p^∑x_i(1-p)^n-∑x_i. Let A⊂{0,1}ⁿ be an intersecting family, i.e. for every x,y∈A there exists 1?i?n such that x_i=y_i=1. Then μ_p(A)?p. Our proof uses a probabilistic trick first applied by Katona to prove the Erd?s-Ko-Rado theorem.