About the Notion of Semiring of Sets

We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved.     

Iterative Algebras without Projections

We deal with iterative algebras of functions of -valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of -valued logic, for , without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of -valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is.     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.     

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

On the nonexistence of finite time bubble trees in symmetric harmonic map heat flows from the disk to the 2-sphere

Let and be the unit disk and the unit sphere, and let be a radially symmetric harmonic map heat flow, whose singularities coincide with downward energy jumps. Then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time.     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

激光二极管泵浦单频连续工作的Nd：YAG激光器

在国内首次报道了激光二极管泵浦单频连续工作的Ｎｄ：ＹＡＧ激光器，采用扭摆模腔技术方法，在８０８ｎｍ激光二极管连续泵浦下，取得１０６４ｎｍ连续单频工作，输出功率５５ｍＷ的结果，泵浦阈值２７６ｍＷ，斜率效率２３％，线宽小于２５ＭＨｚ（受仪器测量精度限制）。     

系列柱形薄壁腔靶制备工艺研究

为了从实验上深入研究超热电子产生规律，从而减少或抑制超热电子对惯性约束聚变（ＩＣＦ）的危害，我们制备了一系列薄壁腔靶，以供实验研究。本文详细地描述了柱形薄壁腔靶的制备工艺。利用ＮＧ－１０４型精密单向纵切车床，采用金刚石刀具车削，提高心轴质量，表表粗糙度可达０．１μｍ。采用电镀和磁控溅射二种方法镀膜，为了使腔靶壁厚均匀，在镀膜时，必须使心轴匀速旋转。利用磁控溅射在腔靶外表面再涂上１μｍ左右厚的二氧化硅，以提高超薄壁腔靶的强度和自立能力。在腐蚀心轴时，必须仔细控制酸的浓度，防止在腐蚀时因产生气泡太多，太快而使腔靶破裂。用Ｘ射线照相法和扫描电子显微镜测量腔靶的几何参数。制备系列柱形薄壁腔靶达到指标为：壁厚范围２～３０μｍ，壁厚均匀性小于１０％，表面粗糙度０．２～０．３μｍ。最后介绍了在“神光Ⅰ”上打靶结果。结果表明，实验值与理论值符合较好。