The chromatic spectrum of 3-uniform bi-hypergraphs

Let $S=\{n_1,n_2,...,n_t\}$ be a finite set of positive integers with $\min(S)\geq 3$ and $t\geq 2$. For any positive integers $s_1,s_2,...,s_t$, we construct a family of 3-uniform bi-hypergraphs ${\cal H}$ with the feasible set $S$ and $r_{n_i}=s_i, i=1,2,...,t$, where each $r_{n_i}$ is the $n_i$th component of the chromatic spectrum of ${\cal H}$. As a result, we solve one open problem for 3-uniform bi-hypergraphs proposed by Bujt\'{a}s and Tuza in 2008. Moreover, we find a family of sub-hypergraphs with the same feasible set and the same chromatic spectrum as it's own. In particular, we obtain a small upper bound on the minimum number of vertices in 3-uniform bi-hypergraphs with any given feasible set

Evolutionary Game for Mining Pool Selection in Blockchain Networks

In blockchain networks adopting the proof-of-work schemes, the monetary incentive is introduced by the Nakamoto consensus protocol to guide the behaviors of the full nodes (i.e., block miners) in the process of maintaining the consensus about the blockchain state. The block miners have to devote their computation power measured in hash rate in a crypto-puzzle solving competition to win the reward of publishing (a.k.a., mining) new blocks. Due to the exponentially increasing difficulty of the crypto-puzzle, individual block miners tends to join mining pools, i.e., the coalitions of miners, in order to reduce the income variance and earn stable profits. In this paper, we study the dynamics of mining pool selection in a blockchain network, where mining pools may choose arbitrary block mining strategies. We identify the hash rate and the block propagation delay as two major factors determining the outcomes of mining competition, and then model the strategy evolution of the individual miners as an evolutionary game. We provide the theoretical analysis of the evolutionary stability for the pool selection dynamics in a case study of two mining pools. The numerical simulations provide the evidence to support our theoretical discoveries as well as demonstrating the stability in the evolution of miners' strategies in a general case.Comment: Submitted to IEEE Wireless Communication Letter

Consumer Behavior Research on Culture Identity of Traditional Chinese Costume

Since the Chinese Bourgeois Revolution in 1911, the old dress codes and etiquettes that were implemented for nearly three thousand years have been abandoned. Especially since the Reform and Opening up policy in 1979, western dress culture of fashion trends and fast fashion have had enormous influence on the younger generation of contemporary way of wearing. This paper\u27s main purpose was to study the present situation of culture identity of Chinese traditional clothing for contemporary Chinese consumers in dimensions of cognition, attitudes and buying behaviors. This study used quantitative and qualitative research methods and found that classical Chinese style had become the bottleneck of limiting its popularization and large-scale development to some extent for younger generations in modern China context and also found that the uniqueness of Chinese traditional style now become able to highlight the wearer\u27s status and hoped Chinese traditional clothing culture would bring more and more diversity and integrity to the modern fashion. The results of this study could provide decision-making references for enterprises in contemporary China and laid the foundation for further academic study

Preliminary Constitution of Luxury Brand Personality Dimensions

Twenty-first Century is an individualization century. More and more people purchase luxuries during the desire of self-expression become more expanding. Luxury brand build a deeply emotional communication with consumers through product style and brand character, which make consumers forming a sense of dependability and identification, then come into being consumption custom and become a loyalty one.But at the present stage, the system of brand personality dimension still has limitations when it explains the character of luxury brand. Luxury brand has especial meaning and value, reflects one\u27s social status and embodies product function and quality. On the other hand, luxury brand can easily build a strong relationship with consumers. In this paper, a new luxury brand character dimension scale is constituted in order to provide a scientific survey tools for study of luxury brand character, and provide method and evidence for the study of luxury brands