Oscillator strengths of the 4s4p~^{{\mathsf{1,3}}}P1↦ 4snd~^{\mathsf {1,3}}D2 transitions of neutral calcium

A detailed study has been performed for estimating the orbital energies, positions and shifts of the Lyman lines of C⁵⁺, Al¹²⁺ and Ar¹⁷⁺ under strongly coupled plasma with a view to understand such line positions and shifts obtained in laser produced plasma experiments. The effect of strongly coupled plasma has been treated within the Ion Sphere (IS) model. Both non-relativistic and relativistic methods have been used for estimating the spectral properties. Theoretical estimates with IS model of the plasma are in conformity with the results of laser plasma experiments on these highly stripped ions. The experimental data for the systems have also been compared with the theoretical estimates using Debye screening model of the plasma with spatial confinements which gives additional restrictions to the wave functions at finite boundaries.     

On the quasi-exact solvability of a singular potential inD-dimensions: confined and unconfined

TheD-dimensional quasi-exact solutions for the singular even-power anharmonic potentialV(q)=aq ²+bq ⁻⁴+cq ⁻⁶ are reported. We show that whilst Dong and Ma’s [J. Phys. A, Vol. 31 (1998) 9855] quasi-exact ground-state solution (inD=2) is beyond doubt, their solution for the first excited state is exotic. Quasi-exact solutions for the ground and first excited states are also given for the above potential confined to an impenetrable cylindrical (D=2) or spherical (D=3) wall.     

Light-cone Yang-Mills mechanics: <Emphasis Type="Italic">SU</Emphasis>(2) vs. <Emphasis Type="Italic">SU</Emphasis>(3)

We investigate the light-cone SU(n) Yang-Mills mechanics formulated as the leading order of the long-wavelength approximation to the light-front SU(n) Yang-Mills theory. In the framework of the Dirac formalism for degenerate Hamiltonian systems, for models with the structure groups SU(2) and SU(3), we determine the complete set of constraints and classify them. We show that the light-cone mechanics has an extended invariance: in addition to the local SU(n) gauge rotations, there is a new local two-parameter Abelian transformation, not related to the isotopic group, that leaves the Lagrangian system unchanged. This extended invariance has one profound consequence. It turns out that the light-cone SU(2) Yang-Mills mechanics, in contrast to the well-known instant-time SU(2) Yang-Mills mechanics, represents a classically integrable system. For calculations, we use the technique of Gröbner bases in the theory of polynomial ideals.     

Miniaturized TEG with thermal generation of free carriers

The rising interest in low temperature heat energy conversion encourages the application of thermoelectric devices. However, conventional thermoelectric devices used in the Seebeck mode as thermoelectric generators have several shortcomings and thus are inefficient when used as a generator. Additionally, the high cost–power ratio of these modules anticipates the commercial success on a broad basis. One way to achieve better suited products is provided by miniaturization of thermoelectric devices in order to enable the use of mass production methods. But in small devices the contact effects become dominant and reduce the efficiency and power density considerably. We show that using pn‐junctions with thermal generation of free carriers offers the possibility to achieve better contact properties and thus higher efficiencies and power densities.

     

Structure of Gröbner bases with respect to block orders

In this paper we study the structure of Gröbner bases with respect to block orders. We extend Lazard's theorem and the Gianni-Kalkbrenner theorem to the case of a zero-dimensional ideal whose trace in the ring generated by the first block of variables is radical. We then show that they do not hold for general zero-dimensional ideals.

     

General Jacobi Identity Revisited Again

Synthetic differential geometry occupies a unique position in topos-theoretic physics. Nevertheless it has appeared somewhat too conceptual to physicists in general, partly because it has appeared to lack computational aspects. Its computational facets are really concerned with computation of the quasi-colimit of a finite diagram of infinitesimal spaces, or equivalently, with computation of the limit of a finite diagram of Weil algebras. Indeed we have been forced to do a highly involved computation of the above kind by hand in our previous papers (Nishimura, H. in Int. J. Theor. Phys. 36:1099–1131, 1997 and Nishimura, H. in Int. J. Theor. Phys. 38:2163–2174, 1999). The principal objective in this paper is to show that Grö bner bases techniques provide us with means that relegate such computations to computers.     

多元分次Lagrange插值

对多元多项式分次插值适定结点组的构造理论进行了深入的研究与探讨.在沿无重复分量代数曲线进行Lagrange插值的基础上,给出了沿无重复分量分次代数曲线进行分次Lagrane插值的方法,并利用这一结果进一步给出了在R~2上构造分次Lagrange插值适定结点组的基本方法.另外,利用弱Gr(o|¨)bner基这一新的数学概念,以及构造平面代数曲线上插值适定结点组的理论,进一步给出了构造平面分次代数曲线上分次插值适定结点组的方法,从而基本上弄清了多元分次Lagrange插值适定结点组的几何结构和基本特征.     

Thermodynamic properties of two-dimensional Yukawa systems

The simple analytical approximation for the energy densities in two-dimensional Yukawa systems is proposed for the wide range of parameters of non-ideal fluids. The use of this approach allows determining all thermodynamic functions and characteristics on the base of general thermodynamic relationships. The comparisons of obtained results with the numerical study of thermodynamic properties are presented. Simulations were performed for parameters typical for the laboratory dusty plasma experiments.     

等离子体屏蔽对He2+与H原子碰撞电离微分截面的影响

应用经典径迹Monte Carlo（CTMC）方法研究了He²⁺与H原子在等离子体环境下的碰撞电离过程,计算了在5—400 keV/u的能区随等离子体屏蔽作用变化的碰撞电离总截面和一阶微分截面.等离子体中带电粒子之间的相互作用采用Debye-Hückel模型来描述.由于等离子体屏蔽效应的存在,靶中束缚态电子能级及其经典微正则分布以及入射离子与靶电子的相互作用都发生了变化,而这些变化会直接影响碰撞电离过程.研究发现,碰撞电离总截面随等离子屏蔽的增加而增大,特别是在10 keV/u以下的低能区电离截面有量级的增加.对随能量变化的一阶微分截面,在低能碰撞过程中,屏蔽作用增加,微分截面呈量级增加,高能碰撞微分截面呈倍数增加.同时,屏蔽作用导致电离电子向高能方向移动,随着碰撞能量的增加两体碰撞机制的贡献越来越大,并在较高的出射电子能量出现了一个新的峰.对无屏蔽的自由原子碰撞过程,CTMC方法计算出的电离总截面在碰撞能量大于70 keV/u的较高能区在实验误差内与实验测量结果符合很好,而在较低的能区比实验值小30%—50%. 关键词： 重粒子碰撞电离 等离子体屏蔽效应 经典径迹Monte Carlo方法 Debye-Hückel模型     

布尔环上的分支Gr(o)bner基算法

众所周知Gr\"obner基在很多领域都有着十分重要的应用.近些年来Gr\"obner基算法有了很大的改进,其中最著名的是Faug\`ere提出的F4和F5算法. 这两个算法具有很高的效率但通常需要消耗大量的内存.鉴于此,将给出一个布尔环上基于zdd数据结构的分支Gr\"obner基算法,该算法不仅可以大大降低对内存的消耗,还能有效的控制矩阵规模,从而提高算法的整体效率.详细阐述并证明了算法的基本理论,介绍该分支算法的数据结构及分支策略.最后通过实验数据可以发现,在很多例子中此算法都要优于Magma中的F4算法.