利用微扰法分析两个相互耦合的参量四波混频过程

利用微扰法在旋转波近似下分析了铷原子中两个独立的参量四波混频过程和一个耦合的参量四波混频过程.当用超短激光脉冲相干激发这两个参量四波混频过程时,两个过程就会同时出现并且存在相互耦合作用.微扰分析表明,耦合的参量四波混频信号中可以观察到量子拍,量子拍幅度的大小不仅取决于超短脉冲的特性,而且依赖于两个耦合的参量四波混频过程中的相位匹配.     

Algorithms for flows with parametric capacities

We consider the problem of finding maximal flows with respect to capacities which are linear functions of a parametert [0,T]. Since this problem is a special case of a parametric linear program the classichorizontal approach can be applied in which optimal solutions are computed for successive subintervals of [0,T]. We discuss an alternative algorithm which approximates in each iteration the optimal solution for allt [0,T]. Thisvertical algorithm is a labeling type algorithm where the flow variables are piecewise linear functions. Flow augmentations are done alongconditional flow augmenting paths which can be found by modified path algorithms. The vertical algorithm can be used to solve the parametric flow problem optimally as well as to compute a good approximation for allt if the computation of the optimal solution turns out to be too time consuming.Partially supported by NSF Grants ECS-8412926 and INT-8521433, and NATO Grant RG 85/0240.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

Parametric decomposition of powers of ideals versus regularity of sequences

Let be an ideal in a Noetherian local ring . Then the sequence is -regular if every is a non-zerodivisor in and if for all integers , where runs over the elements of the set .

     

Selecting distances in arrangements of hyperplanes spanned by points

In this paper we consider a problem of distance selection in the arrangement of hyperplanes induced by n given points. Given a set of n points in d-dimensional space and a number k, , determine the hyperplane that is spanned by d points and at distance ranked by k from the origin. For the planar case we present an O(nlog²n) runtime algorithm using parametric search partly different from the usual approach [N. Megiddo, J. ACM 30 (1983) 852]. We establish a connection between this problem in 3-d and the well-known 3SUM problem using an auxiliary problem of counting the number of vertices in the arrangement of n planes that lie between two sheets of a hyperboloid. We show that the 3-d problem is almost 3SUM-hard and solve it by an O(n²log²n) runtime algorithm. We generalize these results to the d-dimensional (d4) space and consider also a problem of enumerating distances.     

参数Kleene系统中的广义重言式

引入新的一组带对数ｐ（ｐ∈「０,１」的ｔ－范∧ｐ,ｔ－余范∨ｐ和蕴涵θｐ,讨论它们的基本性质。在此基础上参数Ｋｌｅｅｎｅ系统Ｋｐ与三值Ｋｌｅｅｎｅ系统Ｋ３,三值Ｌｕｋａｓｉｅｗｉｃｚ系统Ｌ３和经典二值系统Ｂ２关于（广义）重言式的相互关系,指出系统Ｋｐ对广义重言式而言是可判定的。     

Generation and amplification of dual-color femtosecond pulses by a noncollinear optical parametric up-conversion process

Noncollinear optical parametric up-conversion generation and amplification are realized in a thick β-barium borate (BBO) crystal, and a couple of visible femtosecond up-conversion laser pulses can be achieved by a femtosecond pulse at 800 nm as the pump sources. The theoretical and experimental results indicate that there exist phase-matching conditions for dual-color noncollinear parametric up-conversion generation and amplification, and their wavelengths can be tuned by rotating the BBO crystal. This parametric up-conversion generation and amplification can be attributed to three and five-wave mixing in a thick BBO crystal, and it shows the potential application on optical parametric chirped pulse amplification (OPCPA) to generate multi-color ultraviolet or visible femtosecond laser pulses pumped directly by femtosecond fundamental laser pulses without frequency-doubling or tripling.     

Parametric model of the BAW resonator phase-noise

Excepted for the very short terms the frequency stability of ultra-stable oscillators is mainly limited by the resonator noise. In this work we proposed a parametric model of the bulk acoustic wave (BAW) resonator phase noise based on an equivalent circuit. This model explains phase noise generated by a BAW crystal from a point of view of parametric fluctuations and proves the f⁻¹ dependences of the crystal noise. The model performance is verified with simulation. Simulation results are compared to experimental data and discussed. Comparison of three existing models is made.     

Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

Let B be the unit ball in Cn with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e−tf(z,t)−z has a zero of order k+1 at z=0. In this paper, we obtain growth and covering theorems for . Moreover, we consider coefficient bounds and examples of mappings in .     

参数法和非参数法估计组合样中被测组分含量的置信区间

本文以散装生铁块的随机样本分析结果为基础,应用Ｍｏｎｔｅ Ｃａｒｌｏ模拟法考察了组合样本中Ｓｉ、Ｍｎ,Ｃ,Ｓ,Ｐ含量（或份样平均值）的分布情况,研究了组分含量的置信区间,对参数法和非参数法的结果进行了比较。结果表明,对近似符合正态分布的原始总体或当组合样中的份样数目较多时,两种方法所估计的置信区间相近。但对偏离正态分布（或ｔ－分布）的总体且组合样中的份样数目较少时,非参数法较参数法的结果更符合实际