On some universal sums of generalized polygonal numbers

For $m=3,4,\ldots$ those $p_m(x)=(m-2)x(x-1)/2+x$ with $x\in\mathbb Z$ are called generalized $m$-gonal numbers. Sun [13] studied for what values of positive integers $a,b,c$ the sum $ap_5+bp_5+cp_5$ is universal over $\mathbb Z$ (i.e., any $n\in\mathbb N=\{0,1,2,\ldots\}$ has the form $ap_5(x)+bp_5(y)+cp_5(z)$ with $x,y,z\in\mathbb Z$). We prove that $p_5+bp_5+3p_5\,(b=1,2,3,4,9)$ and $p_5+2p_5+6p_5$ are universal over $\mathbb Z$, as conjectured by Sun. Sun also conjectured that any $n\in\mathbb N$ can be written as $p_3(x)+p_5(y)+p_{11}(z)$ and $3p_3(x)+p_5(y)+p_7(z)$ with $x,y,z\in\mathbb N$; in contrast, we show that $p_3+p_5+p_{11}$ and $3p_3+p_5+p_7$ are universal over $\mathbb Z$. Our proofs are essentially elementary and hence suitable for general readers.Comment: Final published versio

China's urban unemployment challenge

Since the launching of its economic reform and opening up programs in 1979, China has experienced an unprecedented economic expansion, as its real GDP growing at an annual average rate of about 10%. Despite the robust performance, the pressure for employment creation has continued to persist and the situation of excess supply of labor, especially in the urban area, has been worsening. This paper explores the changing patterns of the urban labor market, and identifies the main characteristics of the urban unemployment. On that basis, some viable policy responses will be highlighted

Experimental investigation into amplitude-dependent modal properties of an eleven-span motorway bridge

The authors would like to thank their supporters. New Zealand Earthquake Commission (EQC) Research Foundation provided financial support for experimental work (Grant No. UNI/578). New Zealand Transport Agency (NZTA) provided access to the bridge. Piotr Omenzetter’s work within the LRF Centre for Safety and Reliability Engineering at the University of Aberdeen is supported by Lloyd’s Register Foundation. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research. Ge-Wei Chen’s doctoral study is supported by China Scholarship Council (CSC) (Grant No. 2011637065).Peer reviewe

Hybrid Satellite-Terrestrial Communication Networks for the Maritime Internet of Things: Key Technologies, Opportunities, and Challenges

With the rapid development of marine activities, there has been an increasing number of maritime mobile terminals, as well as a growing demand for high-speed and ultra-reliable maritime communications to keep them connected. Traditionally, the maritime Internet of Things (IoT) is enabled by maritime satellites. However, satellites are seriously restricted by their high latency and relatively low data rate. As an alternative, shore & island-based base stations (BSs) can be built to extend the coverage of terrestrial networks using fourth-generation (4G), fifth-generation (5G), and beyond 5G services. Unmanned aerial vehicles can also be exploited to serve as aerial maritime BSs. Despite of all these approaches, there are still open issues for an efficient maritime communication network (MCN). For example, due to the complicated electromagnetic propagation environment, the limited geometrically available BS sites, and rigorous service demands from mission-critical applications, conventional communication and networking theories and methods should be tailored for maritime scenarios. Towards this end, we provide a survey on the demand for maritime communications, the state-of-the-art MCNs, and key technologies for enhancing transmission efficiency, extending network coverage, and provisioning maritime-specific services. Future challenges in developing an environment-aware, service-driven, and integrated satellite-air-ground MCN to be smart enough to utilize external auxiliary information, e.g., sea state and atmosphere conditions, are also discussed