The Application of Asymmetric Entangled States in Quantum Game

In the present letter, we propose a more general entangling operator to the quantization of Cournot economic model, in which players can access to a continuous set of strategies. By analyzing the relation between the von Neumann entropy of the entangled state and the total profit of two players precisely, we find that the total profit at the Nash equilibrium always achieves its maximal value as long as the entropy tends to infinity. Moreover, since the asymmetry is introduced in the entangled state, the quantum model shows some kind of "encouraging" and "suppressing" effect in profit functions of different players.Comment: 6 pages, 5 figure

Solvability of a higher-order multi-point boundary value problem at resonance

summary:Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance \displaylines { x^{(n)}(t)=f(t, x(t), x'(t),\cdots , x^{(n-1)}(t)),\quad t\in (0,1),\cr x(0)=\sum _{i=1}^{m}\alpha _{i}x(\xi _{i}),\quad x'(0)=\cdots =x^{(n-2)}(0)=0,\quad x^{(n-1)}(1)=\sum _{j=1}^{l}\beta _{j}x^{(n-1)}(\eta _{j}),\cr } where $f\colon [0, 1]\times \mathbb R^n\rightarrow \mathbb R$ is a Carathéodory function, $0<\xi _{1}<\xi _{2}<\cdots <\xi _{m}<1$, $\alpha _{i}\in \mathbb R$, $i=1,2,\cdots , m$, $m\geq 2$ and $0<\eta _{1}<\cdots <\eta _{l}<1$, $\beta _{j}\in \mathbb R$, $j=1,\cdots , l$, $l\geq 1$. In this paper, two of the boundary value conditions are responsible for resonance

An underground air-route temperature prediction model for ultra-deep coal mines

Due to modern mining methods deployed in recent years, production of coal mines has been expanded significantly compared to thirty years ago. As a consequence, the mining depth of coal mines is becoming ever deeper. A common world-wide problem that underground coal mines are currently experiencing is the hazard caused by the underground hot environment, which also promotes a great need of reliable mitigation measures to assist mine operators controlling the heat stress for miners as well as maintaining the normal operation of the mine. In this paper, a model for underground air-route temperature prediction in ultra-deep mines based on previous findings was developed. In developing this model, the idea of heat balance was used to establish the temperature calculation equation. Various underground heat sources (air compress, wall oxidation, underground heat, machinery, etc.) are covered in the model to improve the prediction accuracy. In addition, a PC-based numerical tool was also developed to aid users using such a mathematical model. Finally, a few temperature measurements for an ultra-deep underground coal mine were performed to demonstrate the applicability of the proposed mathematical prediction model