Electron impact excitation of Ni-like gold studied by Dirac R-matrix method

We calculate the electron impact excitation of Ni-like gold by using the Dirac R-matrix theory, and the cor- responding collision strengths and effective collision strengths are obtained. In the calculations of the level energy, （1sZ2sZ2p6）3sZ3p63d10, 3s23p63d94/, 3s23p53d104/, and 3s3p63d104/（l = 0, 1,2,3） configurations are included and 107 fine-structure levels are generated. In the calculations of the collision strengths, only the first 59 levels are included. Com- parisons are made with the distorted wave （DW） results of Zeng et al. for both collision strengths and effective collision strengths. For the collision strengths, the two sets of calculations are in excellent agreement for most of the transitions. However, because of the inclusion of the resonances, our effective collision strengths are generally several times larger than those of Zeng et al.. The accuracy of our calculations is assessed.

Relativistic R-matrix calculations for L-shell photoionization cross sections of CⅡ

The photoionization cross section of the ground state 2s22p 2Po1/2 and the first excited state 2s22p2po1/2 of C II ions are systematically calculated using the fully relativistic R-matrix code DARC. The detailed resonances are presented and identified for the photon energy ranging from threshold （24.38 eV） up to 41.5 eV where the L-shell （2p, 2s） photoionization process is dominant. In the calculations, the relativistic effect and electronic correlation effect are well considered. It is found that the relativistic effect is very important for the light atomic system CII, which accounts for experimentally observed fine structure resonance peaks. A careful comparison is made between the present results and the experimental values, and also other theoretical data available in the literature, showing that good agreement is obtained for the resonance peaks.

Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra

Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.

r-Matrix Structure for a Restricted Flow with Bargmann Constraint

This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.

Relativistic RRR-matrix studies of photoionization processes of Ar^(5+)

The 3s–np photoionization processes of the ground state 2P1/2 and the metastable state 2P3/2 of Ar5＋ are investigated using our recently developed relativistic R-matrix code, where the interactions between the bound states and the continuum states are included. Both resonance positions and the oscillator strengths are in much better agreement with the absolute experimental measurements by Wang et al.[Wang J C, Lu M, Esteves D, Habibi M, Alna’washi G and Phaneuf R A 2007 Phys. Rev. A 75 062712] with a resolution of 80 meV than their theoretical results. The contributions of the two experimental unresolved transitions are distinguished in our calculations, which show that the transitions from the ground state also make significant contributions to some resonances. Our theoretical results are also in good agreement with the measurements for the first resonance with a higher resolution of 20 meV.

R-matrix for the 8-Dimensional Spin Representation of Uq(so7)

The purpose of the paper is to describe the solution to the quantum Yang-Baxter equation associated with the 8-dimensional spin representation Tsp of Uq(so7).The self-duality of Tsp and the symmetry of the corresponding braiding matrix are proved.Also,the minimal polynomial of the braiding R-matrix of Tsp is presented explicitly in an ingenious method by taking advantage of nice features of the spin representation Tsp.

Low-energy inelastic electron scattering from carbon monoxide:Excitation and de-excitation of the X^(1)Σ^(+),a^(3)Π,a'^(3)∑^(+),A^(1)Π,d^(3)Δ,e^(3)∑^(-),I^(1)∑^(-)and D^(1)Δelectronic states

Cross-sections for electronic excitation and de-excitation among the ground state and lowest-lying seven electronic excited states of carbon monoxide(CO)by low-energy electron impact are computed using the R-matrix method.The excitation cross-sections from the ground state to the electronic states a^(3)Π,a'^(3)Σ^(+)+and A^(1)Πagree with previous experimental and theoretical results.In addition,the cross-sections for the I^(1)Σ^(+)-and D^(1)Δstates of CO,which will cascade to CO a'^(3)Σ^(+)+and A^(1)Πstates,are calculated.Furthermore,in contrast to the typical increase in electronic excitation cross-sections with collision energy,the de-excitation cross-sections show a negative trend with increasing energy.

面向轻量级新工具链:GNDS-JSON格式核数据的共振重建

为了验证基于GNDS-JSON格式处理评价核数据能否用于粒子输运模拟,构建了一个新的轻量级工具链。新工具链无须先将ENDF-6或GNDS格式的数据转换为自定义的内部数据结构,可以直接在读入的GNDS-JSON格式数据上进行处理。作为该轻量级工具链的第一步,成功实现了可分辨共振截面重建功能,并在ENDF/B-VIII.0数据库上与NJOY程序进行了比较。计算结果表明,除少数核素外,重建截面的最大相对偏差小于10^(-5),均方根相对偏差约为10^(-6),验证了基于GNDS-JSON打造轻量级新工具链的可行性。同时也发现了自研程序和Fudge程序在处理40 Ca的复杂R-Matrix形式共振参数时的错误。工具链的轻量化可为核数据处理工具的敏捷开发提供参考。

双探头梯形矩阵聚焦成像方法

R角是曲面变壁厚结构,传统超声检测方法难以对其轮廓和缺陷进行完整成像显示。针对此问题,首先,提出双探头全聚焦成像方法,实现R角区域的完整成像显示;其次,为了改善双探头全聚焦成像效率较低的问题,采用梯形矩阵聚焦成像算法,实现高效实时成像;最后,对典型变壁厚R角试件开展聚焦成像实验,验证了双探头梯形矩阵聚焦成像方法的有效性。结果表明,与传统单探头全聚焦成像方法相比,双探头梯形矩阵聚焦成像方法能够显示R角结构的完整内轮廓,并清楚显示和定位内部缺陷。

O_(q)(SO_(5)(C))经由U_(q)(so_(5)(C))的Jantzen途径实现

受Jantzen研究U_(q)(sl_(2)(C))和O_(q)(SL_(2)(C))方法的启发,利用U_(q)(so_(5)(C))自然表示理论中的R-矩阵,实现了B2型量子包络代数的对偶Hopf代数结构,即B2型仿射代数群的量子坐标环O_(q)(SO_(5)(C)).

Error propagation with R-matrix model fitting

The error propagation features with R-matrix model fitting 7Li, 11B and 17O systems have been researched systematically. Some laws of error propagation have been revealed, an experience formula for describing standard error propagation has been established, and the most possible error range for evaluated standard cross section of 6Li (n, α), 10B (n, α) and 10B (n, α1) has been determined.

A Few Integrable Dynamical Systems,Recurrence Operators,Expanding Integrable Models and Hamiltonian Structures by the r-Matrix Method

We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov-Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the （29-1）-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of （29-1）-dimensional expanding dynamical model of the （29-1）-dimensionaJ dynamical system is generated as well.

r-matrix and algebraic-geometric symplectic map

A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical(i. e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the explicit solution(here, the explicit solution means algebraic-geometric solution expressed by the Riemann-Theta function) of a soliton system or nonlinear evolution equation from Lax matrix, r-matrix, and the theory of nonlinearization through taking the Toda lattice as an example. The given algebraic-geometric solution of the Toda lattice is almost-periodic and includes the periodic and finite-band solution.

The r-matrix for constrained flows

The classical r-matrix and Poisson structure play an important role in our studying ofintegrable systems, since they contain underlying property of the system. Recently, inter-est has developed in the study of dynamical r-matrix structure, which depends also on thedynamical variables, and associated generalized Yang-Baxter equations. However,

CLASSICAL R-MATRIX APPROACH TO THE SYSTEM ASSOCIATED WITH THE THREE-WAVE INTERACTION EQUATIONS

The r-matrix is established for the system associated with the three-wave Interaction equations. Via the r-matrix, 3N functionally independent and involutive integrals of motion are obtained, which shows that the system is completely integrable in the Liouville sense.

高技术产业创新活动对区域经济发展的驱动作用及其影响机制

厘清区域高技术产业如何赋能创新活动以助推地区经济发展,是提升区域发展整体效能、有效应对全球科技竞争的战略性问题。针对目前研发投资驱动的自主研发创新和外国直接投资驱动的跨国创新引入的作用机制及空间外溢的差异未明确,以及高技术产业技术市场化水平对不同创新活动经济效应的影响有待发掘的现状,将高技术产业科技密集度、技术市场化纳入创新驱动经济发展的研究框架,构建地理邻接矩阵和地理距离矩阵两种空间权重矩阵,以中国29个省份为研究对象,基于2011—2021年国家有关统计年鉴中的省级面板数据,运用动态空间杜宾模型实证分析自主研发创新、跨国创新引入对当地/邻近区域经济发展影响机制和空间外溢的差异性,探讨在高技术产业科技密集度及技术市场化水平的作用下,自主研发创新及跨国创新引入对经济发展的不同影响,并进一步分类对比分析高技术产业技术市场化水平、不同创新活动与区域经济发展的内在关系。结果表明:(1)区域创新活动水平与经济发展具有显著的空间依赖性,自主研发创新对经济发展的积极作用在长期内效果更明显,跨国创新引入对经济发展的积极作用在短期内效果更明显;(2)高技术产业科技密集度对当地的自主研发创新/跨国创新引入与经济发展之间的关系具有显著正向调节作用,且这一作用具有持久性;(3)随着高技术产业中技术市场化水平的提升,自主研发创新、跨国创新引入对区域经济发展的积极关系分别存在先下降后上升、先上升后下降的非线性变化,但这种正向作用整体力度呈现减弱趋势;(4)在科技密集区/欠密集区,随着高技术产业技术市场化水平的变化,不同创新活动对区域经济发展非线性影响的变化趋势虽然相同,但总体作用力度有所差异。最后从提高高技术产业的科技密集度和规范高新技术产业的技术市场化体系两方面提出相关对策建议。

An effective method to calculate the electron impact excitation cross sections of helium from ground state to a final channel in the whole energy region

The electron impact excitation(EIE) cross sections of an atom/ion in the whole energy region are needed in many research fields, such as astrophysics studies, inertial confinement fusion researches and so on. In the present work, an effective method to calculate the EIE cross sections of an atom/ion in the whole energy region is presented. We use the EIE cross sections of helium as an illustration example. The optical forbidden 1^(1)S–n^(1)S(n = 2–4) and optical allowed 1^(1)S–n^(1)P(n = 2–4) excitation cross sections are calculated in the whole energy region using the scheme that combines the partial wave R-matrix method and the first Born approximation. The calculated cross sections are in good agreement with the available experimental measurements. Based on these accurate cross sections of our calculation, we find that the ratios between the accurate cross sections and Born cross sections are nearly the same for different excitation final states in the same channel. According to this interesting property, a universal correction function is proposed and given to calculate the accurate EIE cross sections with the same computational efforts of the widely used Born cross sections,which should be very useful in the related application fields. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00142.

Weyl定理与(R)性质的判定

利用半Fredholm算子的扰动不变性,研究有界线性算子与上三角算子矩阵的Weyl型定理。首先,给出有界线性算子同时满足Browder定理和(R_(1))性质,或者同时满足Weyl定理和(R)性质的充要条件;然后,讨论上三角算子矩阵同时满足Weyl定理和(R)性质的条件。

基于SP-LSQR的综合孔径辐射成像方法

综合孔径微波辐射计是被动微波遥感领域中一种重要的探测器。综合孔径辐射计成像反演过程在数学上是病态的反问题,传统正则化方法虽然能够有效克服其病态性,但重构误差较大、对干扰噪声鲁棒性不强。与传统正则化方法相比,最小二乘Q-R矩阵(Least Square Q-R matrix,LSQR)分解算法具有计算精度高、数值稳定性好等优点,但收敛速度不够快。对此,文中提出利用子空间预处理LSQR(Subspace Preconditioned LSQR,SP-LSQR)算法进行综合孔径辐射计反演成像,提高收敛速度。仿真结果表明:与Tikhonov正则化和带限正则化相比,SP-LSQR方法不仅可以降低重构误差,而且对干扰噪声的鲁棒性更强。此外,与LSQR方法相比,SP-LSQR方法在不降低成像反演精度的情况下,有效提高了计算效率。

求解弱双四元数矩阵方程r-循环解的新方法

该文提出求解弱双四元数矩阵方程AX+XB=D的r-循环解及对称r-循环解的一种新方法.根据弱双四元数性质,利用vec算子把弱双四元数方程中变量X的位置统一变换到方程最后,然后根据弱双四元数的实表示方法将弱双四元数矩阵方程转化为实矩阵方程,再借助特殊矩阵的H-表示方法提取矩阵的独立元素参与运算,减少运算的复杂程度,通过数值试验检验了算法的有效性.最后将该文内容应用于采摘机器人手眼标定方法.