The Existence and Uniqueness of Solutions of a Class of Evolution Equations

In this paper, a class of evolution equations which have special boundary conditions is discussed. The spectrum properties of an operator which is associated with this class of equations arc provided, and the existence and uniqueness of solutions of this class of equations is proved by the theory of pertu rbation of C_0-semigroups. In the last part of this paper, a condition which ensures the solutions to be non-negative is given. Some results of the time-independent population systems in [1-5] are our examples.     

一种时间分辨激光诱导击穿光谱的测量方法

激光诱导击穿光谱(LIBS)是一种动态光谱。时间分辨LIBS光谱测量是研究激光诱导等离子体演化和谱线自吸收的重要技术。结合激光诱导击穿光谱测量的时序特性,提出一种利用常规性能光谱探测设备获得微秒级时间分辨LIBS光谱的测量方法。通过控制毫秒级光谱探测设备的积分延迟时间,获得不同延时下的LIBS光谱信号,对所得光谱进行处理得到相应特征谱线拟合强度,将所测的特征谱线强度按照一定的时间间隔进行差分,得到差值即为差分间隔时间内特征谱线的积分强度。采用差分时间间隔应大于系统最差时序精度,同时优选无重叠干扰和背底连续的谱线信号进行分析。以等离子体产生后持续时间为横坐标,计算所得谱线差值强度为纵坐标,即可获得特征谱线的强度演化曲线。通过实验验证,使用积分时间为毫秒量级光谱仪和时序精度为0.021微秒控制系统,该方法可以实现微秒量级时间分辨LIBS光谱测量,可用于表征LIBS光谱特征谱线演化过程,降低了LIBS光谱时间分辨测量系统成本。     

Hutton一致结构的点式处理

从点一集映射出发给出通常一致结构的等价刻画,以此为基础在Ｆｕｘｘｙ格上引入一种（拟）一致结构,它是Ｈｕｔｔｏｎ（拟）一致结构的相应简化。     

Asymptotics of dissipative nonlinear evolution equations with ellipticity: different end states

In this paper, we consider the global existence and asymptotic behaviors of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects:

(E)     

Mild solutions of non-autonomous second order problems with nonlocal initial conditions

In this paper we establish the existence of mild solutions for a non-autonomous abstract semi-linear second order differential equation submitted to nonlocal initial conditions. Our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the Hausdorff measure of non-compactness.     

Investigating particle and volatile evolution during pulverized coal combustion using high-speed digital in-line holography

Devolatilization is an important process in pulverized coal combustion because it affects the ignition, volatile combustion, and subsequent char burning and ash formation. In this study, high-speed digital in-line holography is employed to visualize and quantify the particle and volatile evolution during pulverized coal combustion. China Shanxi bituminous coal particles sieved in the range of 105–154 µm are entrained into a flat flame burner through a central tube for the study. Time-resolved observations show the volatile ejection, accumulation, and detachment in the early stage of coal combustion. Three-dimensional imaging and automatic particle extraction algorithm allow for the size and velocity statistics of the particle and stringy volatile tail. The results demonstrate the smaller particle generation and coal particle swelling in the devolatilization. It is found that the coal particles and volatiles accelerate due to the thermal buoyancy and the volatiles move faster than the coal particles. On average, smaller particles move faster than the larger ones while some can move much slower possibly because of the fragmentation.     

Non-Autonomous Evolution Equations on Nonsmooth Domair

The solution of a stationary boundary value problem on a domain with conical points has singularities near these points. Here we first consider existence results in appropriate weighted Sobolev spaces in order to incorporate the singularities. We secondly use these results to prove existence, uniqueness and regularity of solutions of non-autonomous second order evolution equations on such domains.     

Influence of the variance of degree distributions on the evolution of cooperation in complex networks

We study how initial network structure affects the evolution of cooperation in a spatial prisoner’s dilemma game. The network structure is characterized by various statistical properties. Among those properties, we focus on the variance of the degree distribution, and inquire how it affects the evolution of cooperation by three methods of imitation. For every method, it was found that a scale-free network does not always promote the evolution of cooperation, and that there exists an appropriate value of the variance, at which cooperation is optimal.     

Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations

This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form , where A generates a strongly continuous semigroup in a Banach space , F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e ^{2π iℳ(f)}⊂e ^{2π iℳ(u)}. If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given.