吉吉岛冒险

易飞不想就这么空手而归,他在城堡四周四处走动,希望能发现一些进入城堡的线索.经过一番仔细的搜索,易飞终于在城堡的角落处发现了一个亮着的显示屏.显示屏上滚动播放着提示语:1～16在每个图形中都只能使用一次.每一横排之和为34,每一纵列之和为34,每条对角线上四个数之和为34,中心的四个数之和为34,四个角上的四个数之和为...     

马氏环境中马氏链的一个概率不等式及其应用

本文研究了马氏环境中马氏链构成的随机变量之和的概率不等式问题.利用了结尾的方法,获得了马氏环境中马氏链构成的随机变量之和的尾部概率不等式,作为结果的应用,给出了将过程限制在(S,S∩F,PS)上的强大数定律.文中提出的方法和结果对研究独立的随机变量之和的大样本性质是十分有用的.     

拟fine环和2-fine环（英文）

称环R是fine环,如果R中每个非零元素均可以表示为一个可逆元与一个幂零元之和.Fine环的概念由Cǎlugǎreanu和Lam在[J.Algebr Appl.,2016,15(9):1650173,18 pp.]中给出,fine环和单环密切相关.本文研究如下两类环:每个非幂零元素均可表示为一个可逆元与一个幂等元之和的环以及每个元素均可表示为一个可逆元与两个幂零元之和的环.     

随机多个随机变量之和的期望公式的一种新证法

用随机变量之和的分布的卷积公式直接给出随机多个随机变量之和的期望公式的证明 ,避免了原有的证明过程需引入条件期望和全期望公式的麻烦 .     

平行四边形法求网格中的图形的面积

<正>《中学生数学学》2016年第3期(初中刊)课外练习题栏目刊登的初一年级第3题为:图中的正三角形用虚线划分成36个全等的小正三角形,问图中阴影三角形的面积是多少个小正三角形面积之和?给出的答案为:图中小正三角形有36个,而非阴影部分的面积之和为25个小正三角形的面积之和.所以阴影三角形的面积为36-25=11个小正三角形面积之和.     

一个填数概率问题的探讨

我们来讨论如下一道概率问题:将1,2,3,4,5,6填入如图1所示的三角形的6个圈中,每个数恰在三角形中出现一次,求填数后三角形3边上的数字之和相等的概率.显然,将1,2,3,4,5,6填入图1的三角形中的填法共有6!种,下面我们讨论三边上的数字之和相等的填法种数.设每条边上的3数之和均为s     

高二年级同步测试题

<正>一、选择题1.设(5x-(x^1/2))ⁿ的展开式的各项系数之和为M.二项式系数之和为N,若M-N=240.则展开式中x³的系数为（ ）.     

带有拒绝的单机和同型机排序问题

研究了带有拒绝的单机和同型机排序问题. 对于单机情形, 工件的惩罚费用是对应加工时间的\alpha倍.如果工件有到达时间, 目标为最小化时间表长与惩罚费用之和, 证明了这个问题是可解的.如果所有工件在零时刻到达, 目标为最小化总完工时间与惩罚费用之和, 也证明了该问题是可解的.对于同型机排序问题, 研究了工件分两批在线实时到达的情形, 目标为最小化时间表长与惩罚费用之和.针对机器台数2和m, 分别给出了竞争比为2和4-2/m的在线算法.     

平移、齐次化在圆锥曲线高考题中的应用

圆锥曲线是历年高考命题中的重点也是难点,经常涉及到斜率之和、斜率之积等问题,对学生分析问题及运算能力有较高要求.很多学生在知道思路的情况下,往往因为计算复杂而无果而终.2021年高考乙卷第21大题及近三年高考题中多次出现可以转化为斜率之积或之和的问题,以及涉及直线过定点的问题,等等.有没有一种方法能避开复杂计算来解决有关斜率之和、斜率之积的问题呢?本文中从2021年全国高考乙卷第21大题说起.     

Goodman公式的推广

1959年,Goodman发现了任一p阶图中k₃与k₃的个数之和,即f₃,仅是顶点的度d_i的函数之和（1≤i≤p）.人们总企图求得k₄的个数与k₄个数之和的公式f₄.首先,证明f₄并不仅是d_i的函数之和（1≤i≤p）;然后,求了f₄的公式,但它们还依赖一个自同构图c₁₁.     

Rates of Ideal Convergence for Approximation Operators

In this paper, we study a general Korovkin-type approximation theory by using the notion of ideal convergence which includes many convergence methods, such as, the usual convergence, statistical convergence, A-statistical convergence, etc. We mainly compute the rate of ideal convergence of sequences of positive linear operators.     

拓扑半群上概率测度的条件组合收敛与SHIFT组合收敛

本文用部分群化的方法,研究拓扑半群上概率测度的条件组合收敛性与SHIFT组合收敛性,得到了一些充分条件,并推广了一些组合收敛性结果.     

Further arguments for slice convergence in nonreflexive spaces

It is shown that no notion of set convergence at least as strong as Wijsman convergence but not as strong as slice convergence can be preserved in superspaces. We also show that such intermediate notions of convergence do not always admit representations analogous to those given by Attouch and Beer for slice convergence, and provide a valid reformulation. Some connections between bornologies and the relationships between certain gap convergences for nonconvex sets are also observed.Research supported in part by an NSERC research grant and by the Shrum endowment.NSERC postdoctoral fellow.     

Lacunary equi-statistical convergence of positive linear operators

In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical convergence by the help of modulus of continuity of positive linear operators are studied.      

Gähler’s neighbourhood condition for convergence approach spaces

We characterize convergence approach spaces that are approach spaces by generalizing a neighbourhood condition from the category of convergence spaces to the category of convergence approach spaces. We also study this condition in the categories of limit tower spaces and probabilistic convergence spaces.     

Globally convergent methods for semi-infinite programming

Recently developed methods for nonlinear semi-infinite programming problems have only local convergence properties. In this paper, we show how the convergence can be globalized by the use of an exact penalty function. Both convergence and rate of convergence results are established.     

HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD

A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper.For every convergence theorem,a convergence ball is respectively introduced,where the hypothesis conditions of the corresponding theorem can be satisfied.Since all of these convergence balls have the same center x~*,they can be viewed as a homocentric ball. Convergence theorems are sorted by the different sizes of various radii of this homocentric ball, and the sorted sequence represents the degree of weakness on the conditions of convergence theorems.     

Convergence of Polynomial Level Sets

In this paper we give a characterization of pointwise and uniform convergence of sequences of homogeneous polynomials on a Banach space by means of the convergence of their level sets. Results are obtained both in the real and the complex cases, as well as some generalizations to the nonhomogeneous case and to holomorphic functions in the complex case. Kuratowski convergence of closed sets is used in order to characterize pointwise convergence. We require uniform convergence of the distance function to get uniform convergence of the sequence of polynomials.

     

含有lnn的正项级数敛散性的若干个判定方法

研究了含有lnn的正项级数的敛散性判定的常见六种方法.首先探讨研究此类级数敛散性的意义,然后通过举例说明判定含有lnn的正项级数的常见的六种方法,重点探讨利用比较法判定级数的敛散性.     

Convergence of the Nelder-Mead method

We develop a matrix form of the Nelder-Mead simplex method and show that its convergence is related to the convergence of infinite matrix products. We then characterize the spectra of the involved matrices necessary for the study of convergence. Using these results, we discuss several examples of possible convergence or failure modes. Then, we prove a general convergence theorem for the simplex sequences generated by the method. The key assumption of the convergence theorem is proved in low-dimensional spaces up to 8 dimensions.