基于区间灰数列的GM(1,1) 模型(GMBIGN(1,1))研究

GM(1,1)模型在灰系统的理论与应用研究中占有十分重要的地位,然而目前的GM(1,1)模型只能适用于对白化数表征的数列进行预测,而对于现实中存在的区间灰数表示的数列却无能为力.本文运用有关标准区间灰数的最新研究成果,构建了基于区间灰数表征的GM(1,1)模型GMBIGN(1,1)(GM(1,1)Based on Interval GreyNumber,GMBIGN(1,1)),并给出了其解析解.在此基础之上,本文以某地区某种能源价格区间变动情况这一现实经济问题为背景,建立了该地区某种能源价格区间变动的GMBIGN(1,1)模型,并对其进行了仿真与误差分析,效果良好.     

Alfred Kieser (Hg.)(2002): Organisationstheorien (5. Aufl.)

Ohne Zusammenfassung     

Notes on L(1,1) and L(2,1) labelings for n-cube

Suppose \(d\) is a positive integer. An \(L(d,1)\) -labeling of a simple graph \(G=(V,E)\) is a function \(f:V\rightarrow \mathbb{N }=\{0,1,2,{\ldots }\}\) such that \(|f(u)-f(v)|\ge d\) if \(d_G(u,v)=1\) ; and \(|f(u)-f(v)|\ge 1\) if \(d_G(u,v)=2\) . The span of an \(L(d,1)\) -labeling \(f\) is the absolute difference between the maximum and minimum labels. The \(L(d,1)\) -labeling number, \(\lambda _d(G)\) , is the minimum of span over all \(L(d,1)\) -labelings of \(G\) . Whittlesey et al. proved that \(\lambda _2(Q_n)\le 2^k+2^{k-q+1}-2,\) where \(n\le 2^k-q\) and \(1\le q\le k+1\) . As a consequence, \(\lambda _2(Q_n)\le 2n\) for \(n\ge 3\) . In particular, \(\lambda _2(Q_{2^k-k-1})\le 2^k-1\) . In this paper, we provide an elementary proof of this bound. Also, we study the \(L(1,1)\) -labeling number of \(Q_n\) . A lower bound on \(\lambda _1(Q_n)\) are provided and \(\lambda _1(Q_{2^k-1})\) are determined.     

ERP速成(上)

一天中午,丈夫在外给家里打电话:“亲爱的老婆,晚上我想带几个同事回家吃饭可以吗?”(订货意向) 妻子:“当然可以,来几个人,几点来,想吃什么菜?”丈夫:“6个人,我们7点左右回来,准备些酒、烤鸭、番茄     

中山大學嶺南(大學)學院

<正>中山大学岭南(大学)学院是一所国内一流、国际知名的经济管理学院,与成立于130多年前的岭南大学有着深厚的历史渊源。学院是全球同时获得AMBA、EQUIS和AACSB三大国际认证的为数不多的商学院之一,秉承"作育英才,服务社会"的岭南传统,致力于经济学、金融学、管理学的教学与研究,为中国乃至全球培养和输出具有人文精神、全球视野的经济管理人才。     

思絮(上)

<正> 能力与开发 一个人的智商无论高低,都有许多潜能,在一生之中,用过的潜能往往只有百分之一、千分之一、甚至万分之一。 当我们从商场买回一套西装,引起注意的是西装的款式;西装上的口袋有多少个,每个口袋有什么作用?这些问题很容易让人忽视。 同样道理,我们自身有哪些器官,每个器官有何功能,我们对这些器官司是否给予足够重视,开发利用得怎么样,这些问题一定会难住许我人。如果好好利用自己的双手,说不定会成为一名作家或画家;利用自己的嘴巴,认真练习演讲与口才,则很可能成为一名演讲家;努力锻炼自己的观察能     

中山大學嶺南(大學)學院

<正>作育英才·服务社会EDUCATION FOR SERVICE中山大学岭南(大学)学院是一所国内一流、国际知名的经济管理学院,与成立于130多年前的岭南大学有着深厚的历史渊源。学院是全球同时获得AMBA、EQUIS和AACSB三大国际认证的为数不多的商学院之一,秉承"作育英才,服务社会"的岭南传统,致力于经济学、金融学、管理学的教学与研究,为中国乃至全球培养和输出具有人文精神、全球视野的经济管理人才。     

On (s,t)-relaxed L(2,1)-labeling of graphs

We initiate the study of relaxed \(L(2,1)\)-labelings of graphs. Suppose \(G\) is a graph. Let \(u\) be a vertex of \(G\). A vertex \(v\) is called an \(i\)-neighbor of \(u\) if \(d_G(u,v)=i\). A \(1\)-neighbor of \(u\) is simply called a neighbor of \(u\). Let \(s\) and \(t\) be two nonnegative integers. Suppose \(f\) is an assignment of nonnegative integers to the vertices of \(G\). If the following three conditions are satisfied, then \(f\) is called an \((s,t)\)-relaxed \(L(2,1)\)-labeling of \(G\): (1) for any two adjacent vertices \(u\) and \(v\) of \(G, f(u)\not =f(v)\); (2) for any vertex \(u\) of \(G\), there are at most \(s\) neighbors of \(u\) receiving labels from \(\{f(u)-1,f(u)+1\}\); (3) for any vertex \(u\) of \(G\), the number of \(2\)-neighbors of \(u\) assigned the label \(f(u)\) is at most \(t\). The minimum span of \((s,t)\)-relaxed \(L(2,1)\)-labelings of \(G\) is called the \((s,t)\)-relaxed \(L(2,1)\)-labeling number of \(G\), denoted by \(\lambda ^{s,t}_{2,1}(G)\). It is clear that \(\lambda ^{0,0}_{2,1}(G)\) is the so called \(L(2,1)\)-labeling number of \(G\). \(\lambda ^{1,0}_{2,1}(G)\) is simply written as \(\widetilde{\lambda }(G)\). This paper discusses basic properties of \((s,t)\)-relaxed \(L(2,1)\)-labeling numbers of graphs. For any two nonnegative integers \(s\) and \(t\), the exact values of \((s,t)\)-relaxed \(L(2,1)\)-labeling numbers of paths, cycles and complete graphs are determined. Tight upper and lower bounds for \((s,t)\)-relaxed \(L(2,1)\)-labeling numbers of complete multipartite graphs and trees are given. The upper bounds for \((s,1)\)-relaxed \(L(2,1)\)-labeling number of general graphs are also investigated. We introduce a new graph parameter called the breaking path covering number of a graph. A breaking path \(P\) is a vertex sequence \(v_1,v_2,\ldots ,v_k\) in which each \(v_i\) is adjacent to at least one vertex of \(v_{i-1}\) and \(v_{i+1}\) for \(i=2,3,\ldots ,k-1\). A breaking path covering of \(G\) is a set of disjoint such vertex sequences that cover all vertices of \(G\). The breaking path covering number of \(G\), denoted by \(bpc(G)\), is the minimum number of breaking paths in a breaking path covering of \(G\). In this paper, it is proved that \(\widetilde{\lambda }(G)= n+bpc(G^{c})-2\) if \(bpc(G^{c})\ge 2\) and \(\widetilde{\lambda }(G)\le n-1\) if and only if \(bpc(G^{c})=1\). The breaking path covering number of a graph is proved to be computable in polynomial time. Thus, if a graph \(G\) is of diameter two, then \(\widetilde{\lambda }(G)\) can be determined in polynomial time. Several conjectures and problems on relaxed \(L(2,1)\)-labelings are also proposed.     

思絮(下)

<正> 苦与甜 杨斌小时候是一个苦孩子,5岁时父亲去世,由奶奶养活,奶奶靠卖一分钱一杯的茶水维持生活,家里很穷,从小到大很少吃肉。 有一次杨斌看见邻居吃橘子直吞口水,奶奶告诉杨斌: “咱们穷,你只有争气,才能有未来”。杨斌每天下午4点钟以后才和奶奶去菜市场买菜,这时的菜便宜,都是人家买剩的。 读初二时,杨斌坚持每天早晨4点钟到南京的马路边读英语,一直坚持到上大学。后来,杨斌成为欧亚集团董事长,被中国财经界誉为中国财富的“黑马”,在2001年《福布斯》公布的大陆首富排行榜中位居第二。     

ERP速成(下)

鸡蛋又不够了,打电话叫小贩送来。(紧急采购) 6:30,一切准备就绪,可烤鸭还没送来,急忙打电话询问:“我是李太太,怎么订的烤鸭还没送来。”(采购委外单跟催) “不好意思,送货的人已经走了,可能是堵车吧,马