具有不耐烦顾客且修理工多重延误休假的两部件并联的可修排队系统

从具有不耐烦顾客和修理工多重延误休假的角度,利用马尔可夫过程理论、稳态平衡方程、母函数方程的方法,研究两部件（服务台）并联的可修排队系统,并求出稳态平均队长,从而检测该模型的可行性.     

Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems

Finite difference computations that involve spatial adaptation commonly employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This straightforward concept has proven to be extremely effective and practical. However, selections of core monitoring functions are often challenging and crucial to the computational success. This paper concerns six different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy singularities. While the first four monitoring strategies are within the so-called primitive regime, the rest belong to a later category of the modified type, which requires the priori knowledge of certain important quenching solution characteristics. Simulated examples are given to illustrate our study and conclusions.     

Weak Type Estimates for Intrinsic Square Functions on Weighted Morrey Spaces

In this paper, we will obtain the weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Morrey spaces $L^{1,\kappa}(w)$ for $0<\kappa<1$ and $w\in A_1$.     

Wigner function and the entanglement of quantized Bessel—Gaussian vortex state of quantized radiation field

A new kind of quantum non-Gaussian state with vortex structure, termed Bessel-Gaussian vortex state, is constructed, which is an eigenstate of sum of squared annihilation operators a² + b². The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality. It is also found that quantized vortex state is always in entanglement. And a scheme for generating such quantized vortex states is proposed.     

三种典型边界条件下受集中载荷梁大挠度弯曲精确解

利用Jacobi椭圆函数得到了自由端受集中载荷悬臂梁大挠度弯曲问题的显式精确解,不同于由传统椭圆积分公式得到的解,该显式精确解给出梁中任意点的转角,由此可方便的得到梁弯曲后各点的位移.研究表明:由该解出发,可得到任意位置受集中载荷悬臂梁问题的解;对称性分析表明该解可直接用于两端简支或两端固支梁中点受集中载荷的情况.最后分别给出了载荷取一系列值时以上三种边界条件下梁弯曲的挠度曲线.     

热机载荷作用下三维界面裂纹问题的权函数法分析

热机载荷共同作用下双材料和复合材料中的裂纹扩展往往发生在界面处,并且工程中实际遇到的裂纹大多数是三维裂纹.由于通用权函数仅仅与裂纹体的几何形状有关,与载荷、时间无关,因此在求解复杂冲击载荷下界面裂纹应力强度因子随时间的变化过程时,避免了反复的应力分析,计算效率得到提高.根据Betti互易原理,论文推导出三维界面裂纹问题通用权函数法的普遍表达式,并给出了热机载荷共同作用下三维界面Ⅰ型、Ⅱ型和Ⅲ型裂纹问题通用权函数法的有限元格式.通过与实例计算比较,表明此方法得到的结果可以达到满意的工程应用精度.     

TRPIV MEASUREMENT OF DRAG-REDUCTION IN THE TURBULENT BOUNDARY LAYER OVER RIBLETS PLATE

采用高时间分辨率粒子图像测速技术对沟槽壁面平板湍流边界层速度矢量场的时间序列及其统计量进行了实验测量,讨论了在同一来流速度下沟槽壁面对平均速度剖面﹑雷诺切应力及湍流强度的影响. 用流向速度分量的多尺度空间局部平均结构函数辨识壁湍流多尺度相干结构,用条件采样和相位平均技术提取壁湍流多尺度相干结构喷射和扫掠事件的脉动速度、展向涡量的二维空间拓扑形态. 结果表明,与同材料光滑壁面对比,沟槽壁面实现了10.73%的摩阻减小量;沟槽壁面湍流边界层湍流强度及雷诺切应力皆比光滑平板湍流边界层对应统计量小,说明沟槽壁面有效降低了湍流边界层内流体的脉动. 通过比较壁湍流相干结构猝发事件各脉动速度分量与展向涡量的空间分布特征,肯定了沟槽壁面的减阻效果,发现沟槽壁面通过抑制相干结构猝发事件实现减阻.     

STOCHASTIC P-BIFURCATION OF TRI-STABLE VAN DER POL-DUFFING OSCILLATOR

分析了乘性和加性噪声作用下三稳态Van der Pol-Duffing振子的随机P分岔. 首先用随机平均法得到系统的随机微分方程,求得系统响应幅值的稳态概率密度函数. 然后应用分岔分析的奇异性理论,求得随机P分岔发生的临界参数条件,得到多种定性不同的稳态概率密度曲线. 讨论了2种激励噪声强度和系统阻尼对响应稳态概率密度曲线峰的个数、各峰值相对大小的影响. 通过Monte-Carlo数值模拟对理论计算结果进行了验证.该方法可用于其他系统的随机P分岔分析.     

Radically distributed value and normal families of meromorphic functions

We establish several upper-bound estimates for the growth of meromorphic functions with radially distributed value. We also obtain a normality criterion for a class of meromorphic functions, where any two of whose differential polynomials share a non-zero value. Our theorems improve some previous results.     

Quasi-Periodic Solutions and Asymptotic Properties for the Isospectral BKP Equation

In this paper, based on a Riemann theta function and Hirota's bilinear form, a straightforward way is presented to explicitly construct Riemann theta functions periodic waves solutions of the isospectral BKP equation. Once the bilinear form of an equation obtained, its periodic wave solutions can be directly obtained by means of an unified theta function formula and the way of obtaining the bilinear form is given in this paper. Based on this, the Riemann theta function periodic wave solutions and soliton solutions are presented. The relations between the periodic wave solutions and soliton solutions are strictly established and asymptotic behaviors of the Riemann theta function periodic waves are analyzed by a limiting procedure. The N-soliton solutions of isospectral BKP equation are presented with its detailed proof.