Abstract:
In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover shows a new method of cutting graph. Around this model, there are six algorithms in this paper including exact graph traversal, Algebra calculation of natural number, graph partition and graph coloring.

Abstract:
This paper will contribute to a practical problem, Urban Traffic. We will investigate those features, try to simplify the complexity and formulize this dynamic system. These contents mainly contain how to analyze a decision problem with combinatorial method and graph theory algorithms; how to optimize our strategy to gain a feasible solution through employing other principles of Computer Science.

Abstract:
One of the early failures of coating is blister. Here two different coatings were applied on various materials and microstructures. The formation of the blister, and its microstructural and material dependencies were evaluated. It is concluded that general organic coating forms more severe blisters than that of the metallic effect coating. General organic coating protects the samples by insulation film while metallic coating protects by acting as galvanic protection. Therefore, the failure modes are also different, namely blister and filiform corrosion. The dependencies on the microstructures and on material types also follow the insulation film concept and galvanic protection concept.

Abstract:
The pore structure and strength of carbon membrane are controlled by introducing different additives into raw materials. It is indicated that sesbania powder has an obvious effect on the pore structure of carbon membrane, and the obtained pores have the maximum diameter of 0.723 μm, average diameter of 0.319 μm and minimum diameter of 0.241 μm, respectively; whereas, medium temperature pitch has an obvious effect on the strength of carbon membrane, and increases the linear pressure and flexural strength to 13.68 N/mm and 19.80 MPa, respectively.

Abstract:
This paper studies the capacity of hybrid wireless networks with opportunistic routing (OR). We first extend the opportunistic routing algorithm to exploit high-speed data transmissions in infrastructure network through base stations. We then develop linear programming models to calculate the end-to-end throughput bounds from multiple source nodes to single as well as multiple destination nodes. The developed models are applied to study several hybrid wireless network examples. Through case studies, we investigate several factors that have significant impacts on the hybrid wireless network capacity under opportunistic routing, such as node transmission range, density and distribution pattern of base stations (BTs), and number of wireless channels on wireless nodes and base stations. Our numerical results demonstrate that opportunistic routing could achieve much higher throughput on both ad hoc and hybrid networks than traditional unicast routing (UR). Moreover, opportunistic routing can efficiently utilize base stations and achieve significantly higher throughput gains in hybrid wireless networks than in pure ad hoc networks especially with multiple-channel base stations.

Abstract:
This paper studies the capacity of hybrid wireless networks with opportunistic routing (OR). We first extend the opportunistic routing algorithm to exploit high-speed data transmissions in infrastructure network through base stations. We then develop linear programming models to calculate the end-to-end throughput bounds from multiple source nodes to single as well as multiple destination nodes. The developed models are applied to study several hybrid wireless network examples. Through case studies, we investigate several factors that have significant impacts on the hybrid wireless network capacity under opportunistic routing, such as node transmission range, density and distribution pattern of base stations (BTs), and number of wireless channels on wireless nodes and base stations. Our numerical results demonstrate that opportunistic routing could achieve much higher throughput on both ad hoc and hybrid networks than traditional unicast routing (UR). Moreover, opportunistic routing can efficiently utilize base stations and achieve significantly higher throughput gains in hybrid wireless networks than in pure ad hoc networks especially with multiple-channel base stations.

Abstract:
Based on the model of symmetric and asymmetric duopoly option game, this paper discusses the present value of profit flows and the sunk investment costs for the trapezoidal fuzzy number. It constructs the fuzzy expressions of the investment value and investment threshold of followers and leaders under fuzzy environment and conducts numerical analysis. This offers a kind of explanation to the investment strategies under fuzzy environment. 1. Introduction Under the condition of uncertain symmetric duopoly game model, the model was firstly proposed by Smets [1]. For the research of asymmetric enterprises, Huisman [2] considered the initial investment cost and two asymmetry enterprise option-game models. Technology investment extends the already existing real option models by the introduction of the game theory. Under the environment of imperfect competition, the original idea of decision-making model of investment cost asymmetry investment came from the Grenadier’s [3] duopoly model. Kong and Kwok [4] studied the real options problem of strategic investment game between two asymmetry enterprises. Pawlina and Kort [5] studied the influence to the investment decision caused by the difference of the enterprise and discussed the relationship of the value of enterprises and the different investment cost. Zme？kal [6] used the European call option of fuzzy random variables to assess the value of the enterprise. Yoshida [7] constructed symmetric triangular fuzzy numbers with the assumption that the stock price was fuzzy and stochastic; the fuzzy objective definition was introduced with fuzzy expectation with the assumption that the fuzzy degree and stock price were in proportion. It gave rise to the pricing formula of the European option and the fuzzy hedge strategy. Hui and Yong [8] studied the influence of the enterprise investment strategy given by the investment cost’s variance and the time required by the success of technical innovation strategy. Carlsson et al. [9] considered the rates’ fuzzy option formula of fuzzy relation and used the optimization theory to build R & D project’s investment decision model. Liu [10] applied the fuzzy theory to build the model of currency option pricing, which converts the risk-free interest rate. The volatility and the original asset price to the fuzzy number under fuzzy environment, based on the model of equivalent martingale measuring and Black-Scholes. The Problem of Trapezoidal Fuzzy Number The concept of fuzzy set was initiated by Zadeh [11]. From the definition of Carlsson and Fullér [12], a fuzzy set is a fuzzy set

Abstract:
We first construct the global unique solution by assuming that the initial data is small in the $H^3$ norm but the higher order derivatives could be large. If further the initial data belongs to $\Dot{H}^{-s}$ ($0\le s<3/2$) or $\dot{B}_{2,\infty}^{-s}$ ($0< s\le3/2$), we obtain the various decay rates of the solution and its higher order derivatives. In particular, the decay rates of the density and temperature of electron could reach to $(1+t)^{-13/4}$ in $L^2$ norm.

Abstract:
We first construct the global unique solution by assuming that the initial data is small in the H^3 norm but its higher order derivatives could be large. If further the initial data belongs to \Dot{H}^{-s} (0\le s<3/2) or \dot{B}_{2,\infty}^{-s} (0< s\le3/2), we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the L^p-L^2 (1\le p\le 2) type of the decay rates follow without requiring the smallness for L^p norm of initial data. In particular, the decay rate for the difference of densities could reach to (1+t)^{-13/4} in L^2 norm.

Abstract:
This collaborative action research involving a supervisor and a student
teacher aims to assist 23 Form Four (16 years old) students to overcome their
misconceptions on the topic of forces in
equilibrium state. This study adopts the action research cycle: Identify-Plan-Act-Reflect.
The pre-test results showed that students had problems in recognizing the
forces. Consequently, a teaching intervention was planned and carried out to
improve students’ ability to identify and recognize the forces that exist for an
object in the equilibrium state. The teaching intervention emphasizes on the
basic characteristics of the force arrow namely the direction, magnitude, labeling
and starting point of force. The post test results showed that students’
ability to draw the force arrows correctly had improved, with the exception of
identifying the starting point of force. The action research study managed to
guide the student teacher to identify and help to overcome misconceptions of
her students.