Overlapping Schwarz waveform relaxation method for the solution of the forward–backward heat equation

In this article we analyzed the convergence of the Schwarz waveform relaxation method for solving the forward–backward heat equation. Numerical results are presented for a specific type of model problem.     

Magnetic resonances of Fe and Ni nanoparticles in films of silicon suboxide produced by ion irradiation of triethoxysilane gels containing Fe or Ni solute atoms

The structure and magnetic properties of composite films obtained by ion irradiation or thermal treatment of triethoxysilane gels containing iron or nickel in solution are investigated by means of X-ray diffraction, electron microscopy and electron spin resonance. Ion irradiated gels are converted into silica glasses containing metallic nanoparticles with a narrow range of sizes. These particles exhibit a magnetic resonance with a preferential alignment of magnetic moments perpendicular to the surface. This unusual out of plane anisotropy seem to be ascribed to an interaction of the moments with radiation defects. The magnetization in irradiated film is comparable to that in films of same materials submitted to a thermal conversion at 1000 °C in vacuum. But the latter films are porous and contain particles of metal and silicide or silicate with a wider range of sizes.     

拟圆周与交比

设(z_1,z_2,z_3,z_4)=((z_1-z_3)(z_2-z_4))/((z_1-z_4)(z_2-z_3))表示扩充复平面■~2上互不相同有序四点z_1,z_2,z_3,z_4的交比,利用交比刻画了圆周与拟圆周的几何性质,得到(1)■~2上的Jordan曲线Γ是圆周(或直线)当且仅当Γ上任意互不相同的有序四点z_1,z_2,z_3,z_4,满足|(z_1,z_4,z_2,z_3)| |(z_1,z_2,z_4,z_3)|=1; (2)■~2上的Jordan曲线Γ是拟圆周当且仅当存在常数c≥1,对Γ上任意互不相同的有序四点z_1,z_2,z_3,z_4,满足|(z_1,z_4,z_2,z_3)| |(z_1,z_2,z_4,z_3)|≤c．     

A note on the Selberg class (degrees 0 and 1)

We give a classification of the Dirichlet polynomials in the Selberg class as entire quotients of Dirichlet series with periodic coefficients and the Riemann zeta-function. Received: 2 November 2001     

Cayley-Bacharach and evaluation codes on complete intersections

Hansen (Appl. Algebra Eng. Comm. Comput. 14 (2003) 175) uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in P². In this paper, we generalize Hansen's results from P² to P^m; we also show that the hypotheses of Hansen (2003) may be weakened. The proof is succinct and follows by combining the Cayley-Bacharach Theorem and the bounds on evaluation codes obtained in Hansen (Zero-Dimensional Schemes (Ravello, 1992), de Gruyter, Berlin, 1994, pp. 205-211).     

James-Stein estimators for time series regression models

The least squares (LS) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences.     

退压式La_3Ga_5SiO_(14)晶体电光调QNd∶YAG激光器激光性能研究

通过对硅酸镓镧(LGS)晶体旋光性与电光效应的交互作用的理论研究,推导出晶体旋光性和电光效应共同作用下的光强表示式I=1-4B2(Asin 2ω-Ccos 2ω)2。利用此表示式设计计算了旋光晶体LGS尺寸为8 mm×8 mm×25 mm电光Q开关在1064 nm波长使用时的开关电压和偏振角分别为4995 V和27.3°。将理论研究得到的结论应用于LGS晶体电光调Q的Nd∶YAG晶体激光器的实验研究中,实验结果与理论计算结果基本一致。得到输出能量为361 mJ,脉冲宽度为7.8 ns的脉冲激光输出。     

Simple tangential family germs and perestroikas of their envelopes

A tangential family is a 1-parameter system of regular curves emanating tangentially from another regular curve. We classify simple tangential family germs up to A-equivalence. We describe perestroikas of envelopes of simple tangential family germs of small codimension under small deformations of the germ among tangential families.     

A direct approach to sojourn times in a busy period of an M/M/1 queue

In this paper we present a direct approach to obtaining joint distributions of various quantities of interest in a busy period in an M/M/1 queue. These quantities are: the sojourn times and waiting times of all the customers in the busy period, the busy period length and the number of customers served in a busy period. Since the evolution of the total workload process between two successive customer arrivals is deterministic, this work gives statistic of the complete evolution of the workload process within a busy period. This work was done when the author was post doctoral fellow with the MAESTRO group at INRIA, Sophia Antipolis, France, and was supported by project no. 2900-IT-1 from the Centre Franco-Indien pour la Promotion de la Recherche Avancee (CEFIPRA).