Operator trigonometry of preconditioning,domain decomposition,sparse approximate inverses,successive overrelaxation,minimum residual schemes

This paper extends the relationship between the author's operator trigonometry and convergence rates and other properties of important iterative methods. A new interesting trigonometric preconditioning lemma is given. The general relationship between domain decomposition methods and the operator trigonometry is established. A new basic conceptual link between sparse approximate inverse algorithms and the operator trigonometry is observed. A new underlying fundamental inherent trigonometry of the classical successive over‐relaxation scheme is exposed. Some improved trigonometric interpretations of minimum residual schemes are mentioned. Copyright © 2002 John Wiley & Sons, Ltd.     

Newton Trajectories in the Curvilinear Metric of Internal Coordinates

The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of the following of the reduced gradient (RGF) [see Quapp et al., Theoret. Chem. Acc. 100 (1998) 285], also named the Newton trajectory. All the important features of the potential energy surface are definable independently of the coordinate system. We demonstrate it for the Newton trajectory. We design a numerical scheme for the RGF method including the intrinsic curvilinear metric of internal coordinates. For the path following we extend the previous method to the use of a generalized singular value decomposition (SVD). An example of the HCN isomerization pathway is discussed.     

A～100区Tc同位素能级结构的研究

用投影壳模型对¹⁰¹Tc的受激正/负宇称转晕态结构进行了探讨, 为了从定量结果中抽取出物理内容也作出了正宇称转晕带的能带图. 此外, 各自起源于3/2^－[301], 5/2^－[303]和1/2⁺[431]尼尔逊态的3个带也在这个模型框架下进行了分析. 到目前为止, 在Z～42—44区关于N=52—54的中间核性质知之甚少, 为了解这些"过渡核", 以⁹⁵Tc为例, 对其能级结构也进行了研究.     

Soft Interference Cancellation for Random Coding in Massive Gaussian Multiple-Access

In 2017, Polyanskiy showed that the trade-off between power and bandwidth efficiency for massive Gaussian random access is governed by two fundamentally different regimes: low power and high power. For both regimes, tight performance bounds were found by Zadik et al., in 2019. This work utilizes recent results on the exact block error probability of Gaussian random codes in additive white Gaussian noise to propose practical methods based on iterative soft decoding to closely approach these bounds. In the low power regime, this work finds that orthogonal random codes can be applied directly. In the high power regime, a more sophisticated effort is needed. This work shows that power-profile optimization by means of linear programming, as pioneered by Caire et al. in 2001, is a promising strategy to apply. The proposed combination of orthogonal random coding and iterative soft decoding even outperforms the existence bounds of Zadik et al. in the low power regime and is very close to the non-existence bounds for message lengths around 100 and above. Finally, the approach of power optimization by linear programming proposed for the high power regime is found to benefit from power imbalances due to fading which makes it even more attractive for typical mobile radio channels.     

用DSPI方法和栅线投影法测量任意曲表面的三维变形

本文采用数字散斑干涉法和栅线投影法同时测量了任意曲表面的三维位移和三维形貌，并运用数字图像处理技术分析了曲表面的三维应变场，用实验方法获得了曲表面的主应变和主方向。     

单项式的控制序及逐次差分代换算法的终止性

We introduce a concept for the majorization order on monomials. With the help of this order, we derive a necessary condition on the positive termination of a general successive difference substitution algorithm(KSDS) for an input form f.     

求解非线性互补问题的逐次逼近拟牛顿法的收敛性分析

提出了求解非线性互补问题的一个逐次逼近拟牛顿算法。在适当的假设下,证明了该算法的全局收敛性和局部超线性收敛性。     

The magnetic field dependence of the deformation potential materials in the square well confinement potential

We study the optical Quantum Transition Line Shapes (QTLS) which show the absorption power and the Quantum Transition Line Widths (QTLW) of electron-deformation potential phonon interacting systems. In order to analyze the quantum transition, we compare the magnetic field dependencies of the QTLWand the QTLS on two transition processes, namely the intra-Landau level transition process and the inter-Landau level transition process. We apply the Quantum Transport theory (QTR) to the system in the confinement of electrons by square well confinement potential. We use the projected Liouville equation method with Equilibrium Average Projection Scheme (EAPS).      

Optimal quantum clocks based on wavepacket recurrences

We present the recurrence phenomena of an initially localized wavepacket as a foundation to the quantum clock. Various recurrence times in a multidimensional system serve as arms of the clock. The quantum clock so designed may provide the best precision and make the measurement of time possible to the smallest scale.