Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

For the conventional translational shape-invariant potentials （TSIPs）, it has demonstrated that the phase contribution devoted by the scattered subwaves in the analytical transfer matrix quantization condition is integrable and independent of n. Based on this fact we propose a novel strategy to generate the whole set of conventional TSIPs and classify them into three types. The generating functions are given explicitly and the Morse potential is taken as an example to illustrate this strategy.

Hydrocarbon Generating Potential ofMineral-Bituminous Matrix in Source Rocks

Mineral-bituminous matrix (MBM) makes up a major part of source rocks, but itspotential in hydrocarbon generation is uncertain. Mineral and organic (maceral and kerogen)compositions, organic maturity and fluorescence of MBM are studied based on source rock samples from eastern Jiuquan (Jiudong) Basin. The results show that MBM is dominated by inorganic minerals and among the small percentage of organic components those of secondary originsare predominant over the primary species. This strongly indicates that the significance of MBMin hydrocarbon generation is limited.

The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method

We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.

Unravel the potential of zinc oxide nanoparticle-carbonized sawdust matrix for removal of lead(Ⅱ) ions from aqueous solution

Zinc oxide nanoparticles(ZnOnp) are molecular nanoparticles synthesized by a chemical precipitation method from zinc nitrate tetrahydrate and sodium hydroxide.Carbonized sawdust(CSD) was prepared from sawdust obtained from a local wood mill.The matrix of both provides a better material as an adsorbent.The present study applied the functionality of ZnOnp,CSD,and ZnOnp-CSD matrix as adsorbent materials for the removal of Pb(Ⅱ) ions from aqueous solution.The method of batch process was employed to investigate the potential of the adsorbents.The influence of pH,contact time,initial concentration of adsorbate,the dosage of adsorbents,and the temperature of adsorbate-adsorbent mixture on the adsorption capacity were revealed.The adsorption isotherm studies indicate that both Freundlich and Langmuir isotherms were suitable to express the experimental data obtained with theoretical maximum adsorption capacities(q_(m)) of 70.42,87.72,and 92.59 mg·g^(-1) for the adsorption of Pb(Ⅱ) ions onto ZnOnp,CSD,and ZnOnp-CSD matrix,respectively.The separation factors(R_(L)) calculated showed that the use of the adsorbents for the removal of Pb(Ⅱ) ions is a feasible process with R_(L) <1.The thermodynamic parameters obtained revealed that the processes are endothermic,feasible,and spontaneous in nature at 25-50℃.Evaluation of the kinetic model elected that the processes agreed better with pseudo-second order where the values of rate constant(k_2) obtained for the adsorption of Pb(Ⅱ) ions onto ZnOnp,CSD,and ZnOnp-CSD matrix are 0.00149,0.00188,and 0.00315 g·mg^(-1)·min^(-1),respectively.The reusability potential examined for four cycles indicated that the adsorbents have better potential and economic value of reuse and the ZnOnp-CSD matrix indicates improved adsorbent material to remove Pb(Ⅱ) ions from aqueous solution.

Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.

Ionization Potentials and Quantum Defects of 1s^2np^2p Rydberg States of Lithium Atom

In this work,ionization potentials and quantum effects of 1s^2 np ~2P Rydberg states of lithium are calculatedbased on the calibrated quantum defect function.Energy levels and quantum defects for 1s^2np^2P bound states andtheir adjacent continuum states are calculated with the R-matrix theory,and then the quantum defect function of the1s^2np (n7) channel is obtained,which varies smoothly with the energy based on the quantum defect theory.Theaccurate quantum defect of the 1s^2 7p^2P state derived from the experimental data is used to calibrate the originalquantum defect function.The new function is used to calculate ionization potentials and quantum effects of 1s^2np ~2P(n 7) Rydberg states.Present calculations are in agreement with recent experimental data in whole.

RELATIONS BETWEEN PERFORMANCE POTENTIALS AND INFINITESIMAL REALIZATION FACTORS IN CLOSED QUEUEING NETWORKS

In this paper,the concept of the infinitesimal realization factor is extended to the parameter dependent performance functions in closed queueing networks.Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed.This provides a united framework for both IPA and non IPA approaches.Finally,another physical meaning of the service rate is given.

Energy Spectrum for a Short-Range 1/r Singular Potential with a Non-Orbital Barrier Using the Asymptotic Iteration Method

Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

有向量和在二和三种尺寸的库仑类型的分级的潜力的迪拉克方程用超级对称的量力学方法被解决。为如此的潜力的系统，为位置和动量操作符的矩阵元素的分析表达式被获得。

A Potential-Reduction Algorithm for Linear Complementarity Problems

Feasible-interior-point algorithms start from a strictly feasible interior point, but infeassible-interior-point algorithms just need to start from an arbitrary positive point, we give a potential reduction algorithm from an infeasible-starting-point for a class of non-monotone linear complementarity problem. Its polynomial complexity is analyzed. After finite iterations the algorithm produces an approximate solution of the problem or shows that there is no feasible optimal solution in a large region. Key words linear complementarity problems - infeasible-starting-point - P-matrix - potential function CLC number O 221 Foundation item: Supported by the National Natural Science Foundation of China (70371032) and the Doctoral Educational Foundation of China of the Ministry of Education (20020486035)Biography: Wang Yan-jin (1976-), male, Ph. D candidate, research direction: optimal theory and method.

北方沿海城市大气PM_(2.5)组分特征及来源分析:以青岛市为例

为探究北方沿海城市大气PM_(2.5)的化学组分特征及其关键来源,本文选择典型代表城市青岛市作为研究对象,在2021年3月−2022年2月采集大气PM_(2.5)样品,测定水溶性无机离子、碳组分及化学元素等组分,深入分析大气PM_(2.5)化学组分特征,采用正定矩阵因子分解(PMF)和潜在源贡献函数(PSCF)对青岛市PM_(2.5)的主要贡献源类和潜在源区进行分析研究.结果表明:①采样期间青岛市PM_(2.5)浓度平均值为42.2μg/m^(3),NO_(3)^(−)、NH_(4)^(+)、SO_(4)^(2−)、OC是PM_(2.5)的主导成分,浓度分别为11.77、5.76、5.20和6.67μg/m^(3),占比分别为27.88%、13.65%、12.32%和15.80%.②各组分浓度季节性变化与PM_(2.5)浓度变化基本一致,呈现冬季最高、夏季最低,春季、秋季相差较小的变化特征.③PMF模型解析结果表明,二次无机源是青岛市PM_(2.5)的主要来源,贡献率达42.8%;其次为二次有机源以及燃煤和生物质燃烧源,贡献率分别为18.1%、15.7%;机动车源贡献率为8.8%,海盐和船舶源贡献率为6.0%;而扬尘源和工艺过程源贡献率相对较低,分别为5.3%和3.3%.冬季燃煤和生物质燃烧源贡献率(24.4%)明显高于其他季节;春季和秋季扬尘源贡献率较高,分别为6.5%和9.8%;夏季二次有机源、海盐和船舶源以及机动车源的贡献率高于其他季节,贡献率分别达23.1%、12.4%和16.3%.④江苏省北部以及山东省中东部是青岛市各类源的主要潜在源区,江苏省东北部、长三角地区以及黄海海域是海盐和船舶源的主要潜在源区.研究显示,二次源是青岛市大气污染物的主要来源,燃煤源和生物质燃烧源、机动车源、海盐和船舶源的影响也不容忽视.二次源、机动车源以及海盐和船舶源可能是北方沿海城市PM_(2.5)的重点关注源类,在大气污染防治措施制定时需要加强对其的精细化管理.

舟山近岸海域沉积物中重金属分布与生态风险评估

为进一步摸清舟山近岸海域表层沉积物重金属的分布特征及污染来源基础情况,2018年8月对舟山近岸海域29个表层沉积物中7种重金属(Cu、Zn、Pb、Cd、Cr、Hg、As)分布特征进行了调查,采用正定因子矩阵(PMF)探究舟山表层沉积物重金属污染来源,并基于潜在生态风险指数法评价了重金属的污染水平及潜在生态风险程度。结果表明:(1)各重金属含量的均值大小排列为Zn>Cr>Cu>Pb>As>Cd>Hg,分布大致由西往东含量逐渐降低,但部分区域存在高值区。各重金属的空间波动程度依次为Pb>Cu>Cd>Cr>Zn>As>Hg。(2) PMF来源解析模型分析出3种主要污染源,分别为交通运输活动、工业生产活动、农业生产活动。(3)各重金属的潜在生态风险系数大小排列为Cd>Hg>Cu>Pb>As>Cr>Zn,其中Cd和Hg为舟山近岸海域的主要潜在生态风险因子。舟山近岸海域沉积物重金属分布受人类活动影响显著,需要开展更全面的风险评价以保护海洋环境和生态健康。

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method

A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.

Energy eigenvalues from an analytical transfer matrix method

A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.

An Upper Bound on the Higgs Self-Coupling and Higgs Boson Mass from the Positivity Condition of the Mass Matrix

The actual value of Higgs boson mass is difficult to determine theoretically due to lack of knowledge on the exact value of Higgs self coupling constant l. The purpose of this paper is to obtain an upper bound on the Higgs mass in the Standard Model on the basis of one-loop effective potential in the ’t Hooft-Landau gauge and MS scheme. The condition of positivity of mass matrix at ф?= ф0 (where ф0 is the absolute minimum of the effective potential) of the scalar field gives an upper bound on the Higgs self coupling as l ≤ 0.881. This condition yields an upper bound on the Higgs mass as mH ≤ 229.48 GeV.

基于修正四元半偏减法集对势的区域农业旱灾脆弱性评估

为增强旱灾脆弱性评估结果的可靠性和合理性,从微观层次挖掘联系数系统结构中各分量之间的迁移运动信息,根据半偏联系数思想构建了四元联系数的迁移率矩阵,以此实现了联系数系统内相邻、相隔分量的转化,将修正后的联系数分量代入四元半偏减法集对势中,得到修正后的四元半偏减法集对势,并将其应用于蚌埠市农业旱灾脆弱性评估中。结果表明:修正前后的四元半偏减法集对势值对蚌埠市农业旱灾脆弱性及其子系统的评估结果是一致的;修正后的四元半偏减法集对势值变化范围更小、敏感度更高,结果更为稳健,对脆弱性评估集对系统变化趋势的反映更加准确可靠,具有推广应用前景。

Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD

Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.

潜水矿化度对毛细水上升高度的制约特征研究

为了探究不同土壤类型矿化度对毛细水上升高度的制约特征,文章选取不同粒径砂性土与砂质壤土开展不同矿化度影响下的土壤毛细水室内柱试验研究,定量刻画了粒径与矿化度对毛细水上升高度的差异,建立了对数函数拟合模型。试验结果表明,矿化度通过改变土壤水的重力势、基质势来制约毛细水的上升高度。矿化度为0.8、15.0、50.0g/L时,72 h中砂最大毛细水上升高度h_(max)分别为32.5、31.3、30.2 cm,细砂h_(max)分别为50.4、48.6、48.7 cm,粉砂h_(max)分别为72.3、76.4、76.0 cm,砂质壤土h_(max)分别为59.0、60.2、58.6 cm;粉砂和砂质壤土的毛细水上升速率变化波动较大,全试验周期内毛细水上升高度h与时间t可用三参数对数函数刻画。该研究结果揭示了矿化度对毛细水上升高度的制约特征,深化了毛细水上升高度的机理研究,可为土壤盐渍化治理、确定地下水生态水位提供技术支撑。