Linear colorings of subcubic graphs

A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induce a union of disjoint paths. In this paper, we prove that for every connected graph with maximum degree at most three and every assignment of lists of size four to the vertices of the graph, there exists a linear coloring such that the color of each vertex belongs to the list assigned to that vertex and the neighbors of every degree-two vertex receive different colors, unless the graph is $C_5$ or $K_{3,3}$. This confirms a conjecture raised by Esperet, Montassier, and Raspaud. Our proof is constructive and yields a linear-time algorithm to find such a coloring

Bid for an international meeting: A guide for Taiwanese associations

The meeting and exhibition industry is commonly referred to the MICE industry because it pertains to meetings, incentives, conventions, and exhibitions. Ancient eastern and medieval European countries were familiar with the practice of conducting meetings centuries ago. However, those meetings were most commonly designed to address the aftermath of war. During the seventeenth century, the Peace of Westphalia, a series of treaties, concluded the Thirty Years War and created a precedent that through large-scale meeting; significantly international problems among countries could be resolved. Until the early nineteenth century, international meetings between countries were popular. The scopes and topics of discussion also expanded. Eventually, such meetings became a normal component of international relations (Dai, 2007)

U(1)U(1) gauge vector field on a codimension-2 brane

In this paper, we obtain a gauge invariant effective action for a bulk massless $U(1)$ gauge vector field on a brane with codimension two by using a general Kaluza-Klein (KK) decomposition for the field. It suggests that there exist two types of scalar KK modes to keep the gauge invariance of the action for the massive vector KK modes. Both the vector and scalar KK modes can be massive. The masses of the vector KK modes $m^{(n)}$ contain two parts, $m_{1}^{(n)}$ and $m_{2}^{(n)}$, due to the existence of the two extra dimensions. The masses of the two types of scalar KK modes $m_{\phi}^{(n)}$ and $m_{\varphi}^{(n)}$ are related to the vector ones, i.e., $m_{\phi}^{(n)}=m_{1}^{(n)}$ and $m_{\varphi}^{(n)}=m_{2}^{(n)}$. Moreover, we derive two Schr\"{o}dinger-like equations for the vector KK modes, for which the effective potentials are just the functions of the warp factor.Comment: 15 pages,no figures, accepted by JHE

RF Energy Harvesting for Implantable ICs with On-chip Antenna

Nowadays, as aging population increasing yearly, the health care technologies for elder people who commonly have high blood pressure or Glaucoma issues have attracted much attention. In order to care of those people, implantable integrated circuits (ICs) in human body are the direct solution to have 24/7 days monitoring with real-time data for diagnosis by patients themselves or doctors. However, due to the small size requirement for the implanted ICs located in human organs, it\u27s quite challenging to integrate with transmitting and receiving antenna in a single chip, especially operating in 5.8-GHz ISM band. This research proposes a new idea to solve the issue of integrating an on-chip antenna with implanted ICs. By adding an additional dielectric substrate upon the layer of silicon oxide in CMOS technology, utilizing the metal-6, it can form an extremely compact 3D-structure on-chip antenna which is able to be placed in human eye, heart or even in a few mm-diameter vessels. The proposed 3D on-chip antenna is only 1x1x2.8 mm3 with -10 dB gain and 10% efficiency, which has capability to communicate at least within 5 cm distance. The entire implanted battery-less wireless system has also been developed in this research. A designed 30% efficiency Native NMOS rectifier could generate 1 V and 1 mA to supply the designed low power transmitter including voltage-controlled oscillator (VCO) and power amplifier (PA). The entire system performance is well evaluated by link budget analysis and the simulation result demonstrates the possibility and feasibility of future on-demand easy-to-design implantable SoC