Riemannian manifolds in noncommutative geometry

We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c${}^c$ manifolds; and conversely, in the presence of a spin^c${}^c$ structure. We also show how to obtain an analogue of Kasparov’s fundamental class for a Riemannian manifold, and the associated notion of Poincaré duality. Along the way we clarify the bimodule and first-order conditions for spectral triples.     

从机械能守恒的角度推导单摆简谐振动的周期

本文给出了利用基本的物理原理结合高等数学公式的方法推导单摆做简谐运动的周期公式,可以简明扼要地理解单摆简谐运动的过程.     

用于诊断纳秒脉冲电流的微分环现场标定技术

分析了用于纳秒脉冲电流测量的微分环标定难点,提出微分环现场标定方法。通过脉冲形成线脉冲充电以解决微分环标定中信噪比较低、可信度较差等问题;分析了脉冲形成线充电时间、充电电压及脉冲形成开关击穿电压等回路参数对标定结果的影响。基于闪光二号加速器,对测量二极管电流的微分环进行了现场标定,前级隔离开关平均击穿电压为25 kV时,微分环标定回路电流达到1.3 kA,微分环灵敏度为9.311010,方差为0.151010。     

不同应用条件下最佳绝缘子构型

绝缘子的沿面闪络制约着脉冲功率系统向高电压、大电流方向发展,总结了几种实际应用条件下的最佳绝缘子构型,并对不同角度下绝缘子表面的带电情况进行了分析。结果表明,表面电荷对不同绝缘子构型的性能起着至关重要的作用,需要根据不同的应用条件来开展实验研究以确定最佳的绝缘子构型。     

Approximate Solutions of Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equations Using an Enhanced Algorithm of the Generalized Two-Dimensional Differential Transform Method

By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.     

One-loop renormalizability of noncommutative U(1) gaugetheory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propagators in noncommutative U(1) gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to θ²-order, but for a massive scalar field they are renormalizable only to θ-order.     

A lattice Boltzmann model with an amending function forsimulating nonlinear partial differential equations

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form $u_t+\alpha uu_{xx}+\beta u^n u_x+\gamma u_{xxx}+\xi u_{xxxx}=0$. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman--Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.     

Relative position determination of a lunar rover using high-accuracy multi-frequency same-beam VLBI

Multi-frequency same-beam VLBI means that two explorers with a small separation angle are simultaneously observed with the main beam of receiving antennas. In the same-beam VLBI, the differential phase delay between two explorers and two receiving telescopes can be obtained with a small error of several picoseconds. The differential phase delay, as the observable of the same-beam VLBI, gives the separation angular information of the two explorers in the celestial sphere. The two-dimensional relative position on the plane-of-sky can thus be precisely determined with an error of less than 1 m for a distance of 3.8×105 km far away from the earth, by using the differential phase delay obtained with the four Chinese VLBI stations. The relative position of a lunar rover on the lunar surface can be determined with an error of 10 m by using the differential phase delay data and the range data for the lander when the lunar topography near the rover and the lander can be determined with an error of 10 m.     

厄米多项式的定义及其他

分析了关于厄米多项式的争论.介绍了厄米多项式的两种定义.