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.     

民俗与人情——论沈从文《萧萧》

沈从文的作品构筑了湘西的民俗风情画及人性善美面所展现的乡土人情,以此而言,的确和老舍、赵树理等出身于民间的作家一样有着描绘民间文化自由自在精神的本质。这些作家都善于运用民俗承载民间充满着清新刚健的生命情趣与活力;然而民俗并非全然正面,人情也未必美善。《萧萧》一文内容述及封建社会对女性带来极大精神创伤的“童养媳”习俗及民间以私法惩罚情感出轨者的陋习。沈从文综合了风土描写、人道主义与知识分子的批判,从“山山水水和人物风俗”的美善视角书写出《萧萧》中的悖反与颠覆。因成长环境使然,他善于将民俗风土运用于创作中,再加上受到来自周作人“人学”的影响,对社会上有违人道的事件有所反映。《萧萧》在沈从文“追求美善人性”的思考下,综合了看似矛盾的陋俗与乡土中的良善人情。     

Integer-magic spectra of sun graphs

Let A be a non-trivial Abelian group. A graph G=(V,E) is A-magic if there exists a labeling f:E→A∖{0} such that the induced vertex set labeling f ⁺:V→A, defined by f ⁺(v)=∑f(uv) where the sum is over all uv∈E, is a constant map. The integer-magic spectrum of a graph G is the set IM(G)={k∈ℕ∣G is ℤ _k -magic}. A sun graph is obtained from an n-cycle, by attaching paths to each pair of adjacent vertices in the cycle. In this paper, we investigate the integer-magic spectra of some sun graphs. Dedicated to Prof. Frank K. Hwang, on the occasion of his 65th birthday. Supported by Faculty Research Grant, Hong Kong Baptist University.     

Power in consensus: Legitimacy,global value chains and inequality in telecommunications standard-setting

Power is central to GVC research, but the concept is usually restricted to ‘direct’ market power that generates rents. This paper examines ‘diffuse’ conceptualizations of power in GVCs that focus on social construction, arguing that they exist along a continuum from ‘fractured’ to ‘encompassing’. Then, empirically, it shows how different types of power intermix in telecommunications standard-setting from 1999 to 2021, using a comprehensive dataset of every finalized work item in 3GPP. Given powerful network effects in telecommunications, the industry is ripe for monopolistic rents and unequal value capture on a global scale. However, these are attenuated by a layering of power relations, and particularly, an intermediary form of social construction – legitimacy – which is the primary driver of telecommunications standard-setting, and a new type of constitutive power in GVCs, alongside governmentality and hegemony. This is illustrated by focusing on two major shifts in legitimacy in 3GPP – the rise of Huawei and network operators. The paper shows how power becomes layered with collective forms of power partially neutralizing inter-firm forms of dyadic power, which attenuates monopolistic value capture.     

Mental health in vietnam and the move to incorporate social work: A mixed methods study of staff perceptions and expectations

In 2010, Vietnam established social work as a profession. As part of their strategic plan, the government aims to incorporate social work into existing hospitals and health care facilities in the country, including psychiatric hospitals and mental health care centers. This paper, based upon survey and focus group data from 194 people working in three major mental health facilities in Hanoi, explores direct care staffs’ perceptions of this historic incorporation of social work, with a particular eye to the benefits and challenges of the transition. Results show most staff members thought social workers would provide great support to the many unmet needs of their largely underserved and impoverished patients. They also viewed social workers as a potential resource to the treatment team by reducing work overload. Existing staff, however, were less attuned to the clinical functions of social workers in mental health settings, often equating social work with community development and social movements. Some were concerned about social workers taking on their tasks; others about new social workers being hindered by the professional hierarchy in which doctors were placed at the top. Successful integration of social workers will hinge on strong support from policy-makers and leaders of mental health systems.     

Extramarital Sex Among Vietnamese Married Men: Results of a Survey in Urban and Rural Areas of Northern and Southern Vietnam

Research on extramarital sex (EMS) is commonly conducted from a perspective that implicitly understands this behavior as a violation of the marital relationship. In contrast, Vietnamese cultural norms have, at some points in history, condoned if not outright encouraged EMS in the name of preserving family lineage. Yet little is known about the prevalence of EMS among contemporary Vietnamese men and its association with marriage quality. This is a notable gap, given the enormous sociocultural and ideological shifts the country has experienced over the past several decades. Drawing upon a sample of 126 married men (Mean age = 45.56; SD = 10.52) surveyed in urban (Hanoi and Ho Chi Minh City) and rural areas (Ha Tay and Can Tho) in Vietnam, we examined the relationship between EMS and geographic region, demographic characteristics, sexual values, quality of marriage, and sexual satisfaction within marriage. Our results show that geographic location had a strong impact on EMS, while most marital relationship quality variables did not impact the odds of EMS for married men in Vietnam.     

Estimation and Model Selection for Left-truncated and Right-censored Lifetime Data with Application to Electric Power Transformers Analysis

In lifetime analysis of electric transformers, the maximum likelihood estimation has been proposed with the EM algorithm. However, it is not clear whether the EM algorithm offers a better solution compared to the simpler Newton-Raphson (NR) algorithm. In this article, the first objective is a systematic comparison of the EM algorithm with the NR algorithm in terms of convergence performance. The second objective is to examine the performance of Akaike's information criterion (AIC) for selecting a suitable distribution among candidate models via simulations. These methods are illustrated through the electric power transformer dataset.     

The determinants of price in online auctions: more evidence from unbalanced panel data

This study provides an alternative approach that takes account of the unobserved effects of each seller under a sample selection framework while using online auction data. We use data collected from Yahoo! Kimo Auction (Taiwan) to demonstrate that earlier empirical results of online auction studies may be biased due to violating the assumption of independence of the error terms between sample observations. Empirical findings show that seller reputation is no longer as the most important factor for buyers to bid on items, while the sample data confirm the unobserved heterogeneity of sellers and sample selection problem.     

The Moderating Effects of National Age Stereotyping on the Relationships between Job Satisfaction and its Determinants: A Study of Older Workers across 26 Countries

This research explores how national age stereotypes impact older workers' job‐related perceptions by examining probability based samples across 26 countries taken from the European Social Survey. Multilevel data analysis was undertaken. Results show that, at the individual level, both extrinsic rewards and intrinsic rewards directly impact older workers' job satisfaction. At the country level, significant variations are found in the relationships between job satisfaction and related rewards for older workers across the 26 countries. Society's stereotypical views towards older people explained some of these cross‐country variations. This study contributes to extant literature by explicating the process by which society's age stereotypes and the meta‐stereotypes held by older workers affect how these workers make sense and take meaning out of their job‐related circumstances leading to enhanced or diminished job satisfaction. Implications highlight the need for management to be vigilant in identifying and dealing with age stereotypes in the workplace. Furthermore, managers need to be more aware of the potential harmful consequences arising from negative meta‐stereotypes and should implement strategies to tackle workplace stereotypes that would lead to negative meta‐stereotypes held by older workers.     

Circular L(j,k)-labeling number of direct product of path and cycle

Let j, k and m be positive numbers, a circular m-L(j,k)-labeling of a graph G is a function f:V(G)→[0,m) such that |f(u)?f(v)| _m ≥j if u and v are adjacent, and |f(u)?f(v)| _m ≥k if u and v are at distance two, where |a?b| _m =min{|a?b|,m?|a?b|}. The minimum m such that there exist a circular m-L(j,k)-labeling of G is called the circular L(j,k)-labeling number of G and is denoted by σ _j,k (G). In this paper, for any two positive numbers j and k with j≤k, we give some results about the circular L(j,k)-labeling number of direct product of path and cycle.