Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions

In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions lying in planes at integer distances 2, 3, 4, …  to the origin. The faces are considered up to the action of the group of integer-linear transformations.     

Fabrication of bamboo-shaped GaN nanorods

Bamboo-shaped GaN nanorods were formed through a simple sublimation method. They were characterized by means of X-ray powder diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and selected-area electron diffraction (SAED). The TEM image showed that the nanorods were bamboo-like. XRD, HRTEM and SAED patterns indicated that the nanorods were single-crystal wurtzite GaN. Received: 8 January 2001 / Accepted: 28 April 2001 / Published online: 20 December 2001     

Exponential decay rate of survival probability in a disastrous random environment

Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf; ^d in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0. Received: 21 May 1996 / In revised form: 2 February 1997     

Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems

Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular, the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners which constitute popular preconditioning strategies for such problems. Received May 3, 1996     

Cr^4＋：YAG可饱和吸收特性测量

测量了Cr4+:YAG材料的可饱和吸收特性,用多种数据分析方法处理了实验结果,Cr4+:YAG的基态吸收截面σgs=11×10-19cm2,激发态吸收截面σes=1.2×10-19cm2。     

Characteristic of a broadband Ti:LiNbO3 optical modulator with buried electrodes and etched grooves in the buffer layer

Traveling wave Ti:LiNbO₃ Mach-Zehnder optical modulators with buried electrodes and etched grooves in the SiO₂ buffer layer are analyzed by the finite element method. The tradeoff between the bandwidth BW and the half-wave voltage Vπ is discussed. The value of BW/Vπ is used to weight the total performance of the modulator. Taking a thick buffer layer and etching deep grooves in the buffer layer are demonstrated as two effective methods to improve the performance of the modulator. A 3-dB optical bandwidth of 18 GHz with half-wave voltage 5V at a wavelength of 1.55 pm could be obtained even though the electrode is not very thick. When the requirement of half-wave voltage is not very critical, a bandwidth of more than 100 GHz can be obtained.     

Non-linearity of the interactions between bottom-up and top-down signals in multistable visual perception

Summary Both bottom-up sensory information and top-down influences contribute to the perception processes. We studied the perceptual alternations of a multistable ambiguous pattern. We observed that it is possible to interfere on the process of the perception alternance by means of subliminal visual stimuli, which either contrast or second the previous perception. We investigated also the effect of the top-down volitional factor on the perceptual alternation. By using a combination of such top-down factor and bottom-up stimulation, we ascertained that a non-linear type of interaction occurs between the two above factors. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

The Existence of Periodic Orbits for Higher Dimensional Autonomous Systemswith Small Perturbations

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