λKm,n的Ck—因子分解

本给出多重完全二部图λKm,n存在Ck-因子分解的充分必要条件：（1）k=0(mod2),k≥4;(2)2m=2n≡(modk);(3)λm=λn≡0(mod2)，其中当λ=1时m=n=k=6例外。     

对称的完全二部有向图的Ck^→—因子分解

给出对称的完全二部多重有向图λK^*m,n。存在Ck^→-因子分解的充分必要条件：(1)k≡0(mod2)，k≥4；(2)2m=2n≡0(mod k)。     

关于2003年全国高中数学联赛加试第二题

题目　设三角形三边长分别是整数l、m、n ,且l>m >n .已知　3l1 0 4 =3m1 0 4 =3n1 0 4 ,其中 {x}=x - [x],而 [x]表示不超过x的最大整数 .求这种三角形周长的最小值 .1　试题的另解解 :由已知得3l≡3m ≡3n(mod 1 0 4 ) .①式① 3l≡3m≡3n(mod 2 4 ) ,3l≡3m≡3n(mod 54 ) 3l-n≡3m -n≡1 (mod 2 4 ) ,3l-n≡3m -n≡1 (mod 54 ) .因为 ( 3,2 4 ) =( 3,54 ) =1 ,根据欧拉定理得 3φ( 2 4) ≡1 (mod 2 4 ) ,3φ( 54) ≡1 (mod 54 ) ,其中φ(2 4 ) =2 4 1- 12 =8,φ(5 4) =5 41- 15 =5 0 0 .设k1、k2 是分别使 3k≡1 (mod 2 4 ) ,3k≡1 (mod …     

确定n^（n^n）末位数的一个简易数表

以n′、n″分别表示n的末 1和末 2位数码 ,N′表示nnn的末位数 ,则有定理　设n′≠ 0 .(1 )若n≡ 1 (mod 4) ,则n′=N′;(2 )若n≡ 3 (mod 4) ,则N′≡ (n′) 3(mod 1 0 ) ;(3 )若n≡ 0或 2 (mod 4) ,则N′ =6.引理 1 [1] 　n4 q r的末位数与nr 同 .引理 2　n′为非零偶数 ,则n4 q末位为 6.证明 :n′=2 ,4,6,8和n4 ≡ (n′) 4≡ 6(mod 1 0 ) .故n4q=(n4 ) q≡ 6q≡ 6(mod 1 0 ) .定理的证明 :(1 )有n =4k 1 ,由引理 ,nn 末位 =(4k 1 ) 1的末位≡ 1 (mod 4) ,故nn=4q 1 .再用引理 ,nnn=n4q 1≡n≡n′(mod 1 0 ) ,即N′ =n′ .(2 )当n≡ …     

λK_(n,n)的P_(2k+1)-因子分解

给出了当d=gcd(λ,4k)≠1时,平衡完全二部多重图λKn,n存在P2k+1-因子分解的充分必要条件为n=0(mod 4k(2k+1)/d)。     

关于愉快图的Bodendick猜想(Ⅰ)

在文献[1]一文中,我们证明了下述定理定理一.对于正整数n,k,若适合下列条件之一,则C_n(2k)是愉快图。(1)n≡0(mod 4),1≤k≤[(n-4)/2];(2)n≡2(mod 4),1≤k≤[(n-4)/2],k≠2;(3)n≡1(mod 4),1≤k≤n/3,k≠[(n+3)/4],k≠2;(4)n≡3(mod 4),1≤k≤n/3,k≠[(n+1)/4].     

λKn,n的P2k+1——因子分解

给出了当d=gcd(λ,4k)≠1时，平衡完全二部多重图λKn,n存在P2k 1-因子分解的充分必要条件为n≡0(mod4k(2k 1)／d)。     

图C_nUP_4的优美性

证实了图C_nUP_4当n=12k 1(k≥5),n=12k 3(k≡0,1,5(mod6),且k≥5),n=12k 5(k≡1,2(mod 4),且k≥5)时的优美性。     

一组三角函数有限和公式及推导

本文对三角函数有限和式sum from k=1 to n(sec~m)(2k)/(2n+1)π进行了化简计算,得到了结果sum from k=1 to n(sec~m)(2k)/(2n+1)π=2~(m-1)(2n+1)A_1_0(m,n)-2~(m-1)(n+1)~m其中m≥2,41_0≡-m(mod2n+1),A_1_0(m,n)是与m,n有关的式子。为简便起见,本文中将使用如下记号:     

对称的完全二部有向图的(P|→)_(2k)-因子分解

给出了对称的完全二部有向图K*m,n存在(P|→)2k-因子分解的充分必要条件为m=n≡0(mod k (2k-1))。     

竞赛图传递性的充要条件

研究了二部竞赛图和竞赛图的传递性，给出了它的充分必要条件．     

An efficient parallel algorithm for shortest paths in planar layered digraphs

INTRODUCTION Computing shortest paths in directed graphs isa fundamental optimization problem with applica-tions to many areas of computer sciences and op-eration research (Bellman, 1958; Coremen, 1990;Cohen, 1993). Given a digraph G with non-negativeweights on its edges and two vertices s and t of G,the single-pair shortest path problem consists ofdetermining a directed path from s to t with mini-mum total weight. Among the well-known sequential algorithmsfor this problem is the classic…     

An efficient parallel algorithm for shortest paths in planar layered digraphs

This paper presents an efficient parallel algorithm for the shortest path problem in planar layered digraphs that runs in O(log3n) time with n processors. The algorithms uses a divide and conquer approach and is based on the novel idea of a one-way separator, which has the property that any directed path can be crossed only once.     

Visual and orthographic information in learning to read and the influence of phonics instruction

In the Jackson and Coltheart theory of acquisition of word reading it is claimed that, near the beginning of the partial alphabetic phase of development, children have full use of abstract letter units (ALUs). This claim and less exclusive alternatives were examined. In Experiment 1, normal progress children with on average 9 months of school reading instruction, either with or without explicit phonics, read with moderate accuracy (orthographically) familiar words in upper-case letters (e.g., AND) that are visually dissimilar from their lower-case forms. Lower-case forms were read with greater accuracy but only for familiar words, there being no letter-case effect for less familiar words. Children with explicit phonics showed less impairment in reading accuracy when words were presented in upper-case form than children without such phonics. Children with on average 22 months of instruction, in Experiment 2, read relatively unfamiliar words that required some phonological mediation. Those without explicit phonics instruction read words with digraphs in unfamiliar upper case less accurately than in lower case, while those with explicit phonics showed no such letter-case difference. The results supported the view that children do not have full use of ALUs in early alphabetic reading, both children with and without explicit phonics to some extent using letter identities specific to lower case for representation of familiar words.     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

Western and Eastern culture differences in commercial field

The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity.     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.