Invariance of the cone algebra without asymptotics

Let B be a manifold with conical singularities, and denote by the smooth bounded manifold with cylindrical ends obtained by blowing up near the singularities.B.-W. Schulze has developed a framework for a pseudodifferential calculus on B by defining various classes of distribution spaces and operator algebras, working in fixed coordinates on the manifold . I am showing here that the Mellin Sobolev spaces without asymptotics, the cone algebra without asymptotics, and its ideal of smoothing operators are independent of the choice of coordinates and therefore may be considered intrinsic objects for manifolds with conical singularities.     

On parallel asynchronous high-order solutions of parabolic PDEs

In achieving significant speed-up on parallel machines, a major obstacle is the overhead associated with synchronizing the concurrent processes. This paper presents high-orderparallel asynchronous schemes, which are schemes that are specifically designed to minimize the associated synchronization overhead of a parallel machine in solving parabolic PDEs. They are asynchronous in the sense that each processor is allowed to advance at its own speed. Thus, these schemes are suitable for single (or multi) user shared memory or (message passing) MIMD multiprocessors. Our approach is demonstrated for the solution of the multidimensional heat equation, of which we present a spatial second-order Parametric Asynchronous Finite-Difference (PAFD) scheme. The well-known synchronous schemes are obtained as its special cases. This is a generalization and expansion of the results in [5] and [7]. The consistency, stability and convergence of this scheme are investigated in detail. Numerical tests show that although PAFD provides the desired order of accuracy, its efficiency is inadequate when performed on each grid point.In an alternative approach that uses domain decomposition, the problem domain is divided among the processors. Each processor computes its subdomain mostly independently, while the PAFD scheme provides the solutions at the subdomains' boundaries. We use high-order finite-difference implicit scheme within each subdomain and determine the values at subdomains' boundaries by the PAFD scheme. Moreover, in order to allow larger time-step, we use remote neighbors' values rather than those of the immediate neighbors. Numerical tests show that this approach provides high efficiency and in the case which uses remote neighbors' values an almost linear speedup is achieved. Schemes similar to the PAFD can be developed for other types of equations [3].This research was supported by the fund for promotion of research at the Technion.     

大直径高能KrF激光束强度分布实验研究

 利用阵列探测器测出大直径（φ267mm）、高能量（400J）KrF激光束强度空间分布的均匀性和总能量。随着二极管电压的降低, 双向泵浦的束强度空间分布的均匀性变差,甚至成为马鞍型。二极管的最佳工作电压为550～600kV。     

一种改进型圆形球面虚共焦非稳腔数值模拟研究

 在分析具有均匀相位输出耦合器非稳腔优缺点的基础上,提出了一种改进型非稳腔。数值模拟结果表明这种非稳腔不仅克服了均匀相位输出耦合器非稳腔的缺点而且远场也有较好的聚焦能力。     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

高效的红外到可见上转换氟氧化物玻璃材料

本文报道了一种高效的Ｅｒ＾３＋掺杂红外到可见的上转换氟氧化物玻璃材料。材料的组份为６０ＴｅＯ２－８ＰｂＦ２－１０ＡｌＦ３－１０ＢａＦ２－１０ＮａＦ－２ＥｒＯ３／２,给出了样品的制血方法。测量了该材料在室温下的吸收光谱,在８０８和９７０ｎｍＬＤ激发下观察到了非常强的上转换荧光,测量了在不同激发波长激发下Ｅｒ＾３＋的绿色荧光,讨论了在８０８和９７０ｎｍ激发下上转换发光的机理。测量了上转换发射光谱,研     

超短脉冲强激光与团簇的相互作用

超短脉冲强激光与团簇的相互作用已被证明能够产生能量高达ＭｅＶ量级的高能离子和中子以及非常强的Ｘ射线辐射。广阔好原子团簇在超短脉冲强激光场的作用下的加热、电离和膨胀等机制,对这种相互作用的深入研究可能会对激光核聚变和Ｘ射线激光等应用领域产生重大影响。     

圆形球面虚共焦非稳腔的三维数值研究

 通过对1/2共焦腔和稳定腔的计算,考查了同三维菲涅耳积分方程相应的C 8程序的可靠性。对激光在三维圆形球面虚共焦非稳腔中的传输作了计算和分析。取相同的远场传输距离且放大率由大变小时，强度分布由近场的投影分布逐渐趋于远场的高斯、超高斯分布。     

Temporal coherent control induced by wave packet interferences in one and two photon atomic transitions

The interaction of a sequence of two identical ultrashort laser pulses with an atomic system results in quantum interferences as in Ramsey fringes experiments. These interferences allow achievement of temporal coherent control of the excitation probability. We present the results of a temporal coherent control experiment on two different atomic systems: one-photon absorption in K (4s-4p) and two-photon absorption in Cs (6s-7d). In K, the quantum interferences between the two excitation paths associated with the laser pulses are revealed through rapid oscillations of the excitation probability as a function of the time delay between the two pulses. These oscillations take place at the transition frequency (period T = 2.56 fs). The interferences are modulated by beats (at about 580 fs) resulting from the doublet structure of the excited state (4p (² P _1/2 , ² P _3/2 )). Three complementary interpretations of this experiment are presented: in terms of beats of quantum interferences, of variation in the spectrum intensity, and of wave packet interferences. Whenever the two laser pulses are temporally overlapped, optical interferences are superimposed on to the quantum interferences. The distinction between these two types of interference is clearly revealed in the two-photon excitation scheme performed on Cs (6s-7d (² D _3/2 , ² D _5/2 )) because quantum interferences occur at twice the frequency of the optical interferences. Received: 30 December 1997 / Revised: 28 February 1998 / Accepted: 4 March 1998     

Effect of the initial phase of the field in ionization by ultrashort laser pulses

We report on observable new features related to ionization of atoms by laser pulses of only few cycles and some intensity. We show that for particular photo-electron energies, the angular distribution becomes asymmetric and that this asymmetry is related to the initial phase of the field. Received: 4 November 1997/Revised: 21 January 1998/Accepted: 23 February 1998