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.     

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     

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。     

SWAPCO Nuclear Corporation (SWAPCO)

SWAPCO is a nuclear fuel brokerage company which has managed to survive in a highly competitive niche market for fourteen years. The market is currently declining and the company must develop a strategy for survival and future growth. The case is designed to enable students to think about the effects of a rapidly changing market on a company's business and the effect of changes in the external environment on the company. It leads to discussion of market strategies, the role of government in business, the effects of competition and other external factors in the survival and growth of a business. This revised version was published online in July 2006 with corrections to the Cover Date.     

Poor (Wo)man's Bootstrap

The bootstrap is a convenient tool for calculating standard errors of the parameter estimates of complicated econometric models. Unfortunately, the fact that these models are complicated often makes the bootstrap extremely slow or even practically infeasible. This paper proposes an alternative to the bootstrap that relies only on the estimation of one‐dimensional parameters. We introduce the idea in the context of M and GMM estimators. A modification of the approach can be used to estimate the variance of two‐step estimators.     

(Re) Defining Emerging Risks

The concept of emergence in risk management can be seen as a revealing symptom of the increasing need for organizations to update their portfolio of risks and opportunities in a rapidly changing and highly competitive environment. Accordingly, the concept of emerging risks has been widely discussed in both scientific and business communities, with, however, a lack of agreement as to whether we should distinguish these risks from others and, if so, what should be the adopted approach for their governance. After reviewing a large set of definitions and conceptions of emerging risks, this article aims at exploring the existence of distinctive features allowing the characterization of a risk as emerging or not. First, we will demonstrate that the features used in the various definitions are ineffective to achieve this distinction. Furthermore, we will argue that all events and consequences associated with risks are or have been states of nature that emerged from complex interactions involving combinations of hazardous activities and stakes. Accordingly, emerging risks are no longer a specific category of risks; they are rather an early step in every risk life cycle that deserves specific governance approaches.     

Outbound Foreign Direct Investment (FDI) Motivation and Domestic Employment by Multinational Enterprises (MNEs)

This study investigates whether and how outbound foreign direct investment (FDI) boosts or reduces domestic employment by multinational enterprises (MNEs). Based on analyses of a firm-level sample of 18,252 subsidiary-year cases of Japanese MNEs in 59 countries from 1996 to 2010, the findings indicate that outbound FDI motivated by (1) market seeking for scale and scope expansion, (2) natural resource seeking, or (3) strategic asset seeking tends to serve as a “strategic complement” that enhances domestic employment by MNEs. However, outbound FDI motivated by (4) market seeking associated with declines in domestic demand or (5) labor resource seeking tends to act as a “strategic substitute” that reduces domestic employment by MNEs. The implications for theory, practice, and policymaking are discussed.     

整合系统方法论（ISM）对复杂决策范式（CDP）形成的关系研究

分析了决策的系统性问题,指出系统方法论(SM)和决策研究范式(DP)的内在关系.进一步,分析了整合系统方法论(ISM)对复杂决策范式(CDP)形成的关系.     

Diffusing (let it happen) or disseminating (make it happen) innovations in health care

Management has different options for spreading new products. Our study empirically assessed the integral effects of both diffusion and dissemination on innovation adoption. Data on diffusion (as measured by social network density) and on dissemination (as measured by formulating objectives and executing focused activities) was gathered using a questionnaire given to 356 medical specialists, nested in 38 teams. We found both separate and integral effects for diffusion and dissemination. This shows the potential for both engaging the social network structures (diffusion) and adding process measures (dissemination) in order to optimize the innovation spreading process.     

Decentralized WIP-oriented manufacturing control (DEWIP)

DEWIP is a manufacturing control system for job shop environments aiming at achieving short and reliable lead times by establishing WIP control loops between the manufacturing work centres. The paper describes the mode of function, the setting of parameters and simulation results of the new manufacturing control system. The setting of parameters is done with the aid of the funnel model and the theory of logistic operating curves, both developed at the Institute of Production Systems at the University of Hanover. The simulation is conducted using industrial data and makes it possible to assess DEWIP with regard to lead times, WIP level, performance and schedule reliability. DEWIP is compared both with an uncontrolled process and with the manufacturing control systems Load oriented order release (LOOR), Conwip and Polca. The results suggest that DEWIP and the models employed for the setting of parameters are suitable for job shop production and therefore offer a valuable alternative to prevailing centralized manufacturing control systems.