与年龄相关的半线性时变种群系统的最优捕获

本文讨论了如下的一类与年龄相关的半线性时变种群系统 : p t+ p r+μ( r,t) p +Φ( N ( t) ) p =-v( r,t) p,p( 0 ,t) =∫A0 m( r,t) p( r,t) dr,p( r,0 ) =p0 ( r) ,N ( t) =∫A0 p( r,t) dr,其中 p( r,t)为时刻 t年龄为 r的单种群年龄密度函数 ,v( r,t)为捕获策略 .主要利用泛函分析中的 Mazur定理和分离的思想 ,证明了状态方程解的存在唯一性 ,并论证了对于给定的目标泛函 ,在一定条件下最优捕获控制的存在性 .     

The smallest degree sum that yields potentially Kr,r-graphic sequences

We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r, n) such that every n-term graphic sequence π = (d1, d2,..., dn) with term sum σ(π) = d1 + d2 +…+ dn ≥σ(Kr,r, n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. πr has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined.     

一类非线性种群发展方程非局部柯西问题随机周期解的存在性

研究如下形式具有随机周期移民扰动的非线性种群发展方程的非局部柯西问题，{δp（r,t）/δt＋δp（r,t）/δr=-μ（r）p（r,t）＋f（t,p（r,t））,0＜r＜rm,t≥0,p（r,0）=p0（r）＋g（p（r,t0））,T＞t0＞0 p（0,t）=β（t）∫^r2 r1（k（r）h（r）p（r,t）dr这里，其他地区的种群迁入项厂以及非局部条件项g为紧算子，且厂是时间变量t的周期为T的周期函数．利用Shesfer不动点定理，可以证明上述柯西问题随机周期积分解的存在性．这篇论文的结果推广了前人的工作．     

围长为r的n阶本原有向图的点指数

研究本原有向图的顶点指数,运用图论与数论方法,得到了n阶围长为r的本原有向图的点指数expD（k）的上界：若rn,且r为素数,D∈Dn,r={D｜D为n阶本原有向图且围长为r},则expD（n,k）=rn-2r＋k（1≤k≤n）;若r｜n,且r为素数或素数的幂,D∈Dn,r,则expD（n,1）=rn-3r＋2.     

环Z/p\+kZ上m阶交错矩阵的计数定理及其应用

设W\-m(R)是有限局部环R=Z/p\+kZ上所有m阶交错矩阵所构成的集合（p是素数,k>1）. 该文通过确定R上任意m阶交错矩阵的标准形,计算出W\-m(R)在线性群GL\-m(R)作用下的轨道数及n(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)]),其中W（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])(∑[DD(]l[]i=1[DD)]s\-i=t)表示不变因子为（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])的所有m阶交错矩阵构成的集合,n(2r,2t,（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])表示其中的元素个数. 最后,作者利用有限局部环R上交错矩阵的标准形构作了一个Cartesian认证码,并计算出其全部参数.     

半群PO_(n,r)的秩

设POn为Xn上的保序部分变换半群.对任意的2≤r≤n一1,考虑半群PO_(n,r)={α∈PO_n:Im(α)■[r]}([r]={1,2,…,r}),证明了PO_(n,r)的秩为Σn-1k=r(nk)((k-1)(r-1))+r-1.     

一类矩阵迹不等式的推广

利用平均值不等式 ,得到关于矩阵迹的不等式 :如果 A1 ,A2 ,… ,Am 皆为 n阶 Hermite半正定矩阵 ,且乘法两两可交换 ,0 相似文献   

On Eckhoff's conjecture for Radon numbers; or how far the proof is still away

Eckhoff's conjecture for the Τ-Radon numbers r(Τ) of a convexity space. (X,C) says r(Τ) ≦ (r?1)(Τ?1)+1, with r = r(2). The main result of this note is that Eckhoff's conjecture is true in case ¦X¦ ≦ 2r and Τ = 3, i.e. each (2r?1)-set in a space with 2r?1 or 2r elements has a 3-Radon partition.     

单级零点较少的亚纯函数的一个界囿不等式

本文证明了:若.f(z)为复平面上的非线性亚纯函数,满足N1(r,1/f)=S(r,f),则对任何非零复数c,成立T(r,f)<11N(r,f)+11N(r,1/f'-c)+S(r,f).这里N1(r,1/f)表示f(z)的单级零点的计数函数.     

广义Grotzsch环函数的几个精确不等式

对$a\in(0,1/2]$和$r\in(0,1)$, Ramanujan广义模方程中的广义Gr\"otzsch环函数$\mu_a(r)$定义如下:$\mu_a(r)=[\pi\K'_a(r)]/[2\sin(\pi a)\K_a(r)]$. 该文通过研究$\mu_a(r)$和$\mu(r)$的关系,以及$\mu_a(r)$和一些初等函数的组合的单调性和凹凸性,获得了$\mu_a(r)$的几个精确不等式,从而把$\mu(r)$的一些熟知的性质推广到$\mu_a(r)$上.     

LF拓扑空间中r连通性的讨论

研究了LF拓扑空间中r连通性的拓扑不变性质和樊畿定理型刻画,在提出了r序同态和r连通性的基础上讨论了二者的基本性质,证明了r连通性是r拓扑性质;得到了r连通性的樊畿定理;为讨论r连通性的其他性质奠定了基础.     

EXISTENCE PROBLEMS OF ADDITIVE SELECTION MAPS FOR ANOTHER TYPE SUBADDITIVE SET-VALUED MAP

In this paper,we consider the following subadditive set-valued map F:X → P 0 (Y):F r ∑ i=1 x i + s ∑ j=1 x r+ j rF r ∑ i=1 x i r + sF s ∑ j=1 x r+ j s, x i ∈ X,i=1,2,,r + s,where r and s are two natural numbers.And we discuss the existence and unique problem of additive selection maps for the above set-valued map.     

Converse theorems for multidimensional Kantorovich operators

L _p [0, l]. . . - .

---

---

Supported by National Science Foundation, Zhejiang Provincial Science Foundation of China, and Alexander von Humboldt Foundation of Germany.     

分支问题开折的强（r|s）稳定性与弱（r|s）稳定性

该文讨论了分支问题开折的强（r,s）稳定性及弱（r,s）稳定性,并给出了（r,s）无穷小稳定性、强（r,s）稳定性及弱（r,s）稳定性的等价性．     

Puiseux expansion for space curves

For any ideal I in a convergent power series ring {X₁,..,X_n} (n2) with one dimensional zero set X (ⁿ, 0) we give a method of computing a parametrization of each irreducible component of the reduction of X. This generalizes the well-known method of the Newton polygon or the so called Puiseux expansion for plane curves (see [N], [P], and [B]). The slope of a side of the Newton polygon is generalized to what we calltropism of the ideal. It may be visualized as the direction of a hyperplane touching the Newton polyhedron of every element of the ideal at least along an edge.The author is grateful to the SFB 40 Theoretische Mathematik, Bonn, where this work was prepared.     

Estimation of the Coefficient of Multiple Determination

Assume that we have iid observations on the random vector X = (X ,...,X ) following a multivariate normal distribution N (,) where both R and (p.d.) are unknown. Let denote the multiple correlation coefficient between X and (X ,...,X ). The parameter = , called the multiple coefficient of determination, indicates the proportion of variability in X explained by its best linear fit based on (X ,..., X ). In this paper we consider the point estimation of under the ordinary squared error loss function. The usual estimators (MLE, UMVUE) have complicated risk expressions and hence it is quite difficult to get exact decision-theoretic results. We therefore follow the asymptotic decision theoretic approach (as done by Ghosh and Sinha (1981, Ann. Statist., 9, 1334-1338)) and study Second Order Admissibility of various estimators including the usual ones.     

函数F(α)=(A~rB~αA~r)~((p+2r)/(α+2r))的最优单调区间

设p>0且A,B是Hilbert空间上两个正算子,Furuta给出若A>B>0,那么对任意r>0,F(α)=(ArBαAr)p+2r/α+2r 是关于α>P单调递减的,但是他指出这个结果在0<α0的条件下并不一定成立.本文给出: (1)如果-1/2-2r,那么F(α)在(-∞,-P-4r]及[p,+∞)上单调递增,并且这两个区间不能扩大; (3)如果r>0,P>0,那么[p,+∞)也是F(α)的最佳单调区间.     

Diophantine方程组a~2+b~2=c~r和a~x+b~y=c~z的一点注记

设r是大于1的正奇数,m是正偶数,V(r)+U(r)(-1)~(1/2)=(m+(-1)~(1/2))~r.本文证明了:当a=|V(r)|,b=|U(r)|,c=m~2+1时,如果r≡5(mod8),m>r~2且r<11500或者m>2r/π且r>11500,则方程a~x+b~y=c~z仅有正整数解(x,y,z)=(2,2,r).     

OI_n的理想K(n,r)的极大逆子半群

Xn为n元有限集,OIn为Xn上的一切保序严格部分一一变换半群.记K(n,r)={α∈OIn∶|Tmα|≤r}(0≤r≤n-1)则K(n,r)(0≤r≤n-1)是OIn的理想.我们刻划了K(n,r)(1≤r≤n-1)的极大逆子半群.     

Threshold theorems for a stochastic model of an epidemic with natural immunization

A stochastic model of an epidemic is investigated, taking account of the removal of ill members of the population (by death, by recovery with immunization, by isolation) and natural immunization. Limiting distributions are found for the size of the epidemic, the number immunized ₁, and their sum, under the assumption that the original number of susceptible individuals n and the number of ill individuals m , while n 1,n ₀< , where and are the coefficients for the contraction of the disease and of immunization respectively.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 385–392, September, 1970.