TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II

We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier-free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.     

The solution of the neutron transport equation in a slab with anisotropic scattering

The neutron transport equation for a slab geometry with the extremely anisotropic scattering kernel is considered. The albedo and transmission factors are calculated using the variation method. The effect of the extremely anisotropic parameter on the variation of the slab albedo and transmission factor is calculated. The obtained results are compared with the published data.     

柱几何Rayleigh-Taylor不稳定性的数值模拟

给出了柱几何中流体力学方程组及其在数值模拟中采用的计算方法。对二维柱几何Rayleigh-Taylor不稳定性进行数值模拟,在线性阶段与线性理论符合得很好;不稳定性增长进入非线性区域的阈值依赖于界面的位置,并且明显不同于平面情况。     

组合几何蒙特卡罗粒子输运支撑软件框架JCOGIN介绍

介绍了JCOGIN支撑软件框架层次式、模块化的体系结构及其核心数据结构。这些使得JCOGIN软件框架能够支撑大规模复杂几何的蒙特卡罗（MC）粒子输运并行计算。同时介绍了在JCOGIN支撑软件框架下研发的JMCT程序,并进行了性能测试,在2万处理器核上模拟20亿粒子,并行效率达到70%。     

Protective measurement and quantum reality

It is shown that from the expectation values of obervables, which can be measured for a single system using protective measurements, the linear structure, inner product, and observables in the Hilbert space can be reconstructed. A universal method of measuring the wave function of a single particle using its gravitational field is given. Protective measurement is generalized to the measurement of a degenerate state and to many particle systems. The question of whether the wave function is real is examined, and an argument of Einstein in favor of the ensemble interpretation of quantum theory is refuted.     

Effect of initial-state target polarization on single ionization of helium by 1-keV electron impact

We report new results of triple differential cross sections for the single ionization of helium by 1-KeV electron impact at the ejection energy of 10 eV. Investigations have been made for both the perpendicular plane and the plane perpendicular to the momentum transfer geometries. The present calculation is based on the three-Coulomb wave function. Here we have also incorporated the effect of target polarization in the initial state. A comparison is made between the present calculation with the results of other theoretical methods and a recent experiment [D黵r M, Dimopoulou C, Najjari B, Dorn A, Bartschat K, Bray I, Fursa D V, Chen Z, Madison D H and Ullrich J 2008 Phys. Rev. A 77 032717]. At an impact energy of 1 KeV, the target polarization is found to induce a substantial change of the cross section for the ionization process. We observe that the effect of target polarization plays a dominant role in deciding the shape of triple differential cross sections.     

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.     

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。     

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.     

Spectral flow invariants and twisted cyclic theory for the Haar state on

In [A.L. Carey, J. Phillips, A. Rennie, Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras. arXiv:0801.4605], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SU_q(2) and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of the modular group of the Haar state. In contrast to the Cuntz algebras studied in [A.L. Carey, J. Phillips, A. Rennie, Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras. arXiv:0801.4605], the computations are considerably more complex and interesting, because there are non-trivial ‘eta’ contributions to this index.