We report in this paper the ground-state energy 2s^(2)^(1)S and total energies of doubly excited states 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I of the Helium isoelectronic sequence from H-to Ca^(18+).Calculations are perf...We report in this paper the ground-state energy 2s^(2)^(1)S and total energies of doubly excited states 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I of the Helium isoelectronic sequence from H-to Ca^(18+).Calculations are performed using the Modified Atomic Orbital Theory(MAOT)in the framework of a variational procedure.The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function[1]combining with Hylleraas-type wave function[2].The study leads to analytical expressions which are carried out under special MAXIMA computational program.This first proposed MAOT variational procedure,leads to accurate results in good agreement as well as with available other theoretical results than experimental data.In the present work,a new correlated wave function is presented to express analytically the total energies for the 2s21S ground state and each doubly 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the(nI^(2))systems.展开更多
In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary condit...In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.展开更多
In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are applied to the proble...In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are applied to the problem. The effectiveness of the each modified is verified by several examples.展开更多
A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium w...A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.展开更多
In this paper,we investigate the fifth-order modified Korteweg-de Vries(mKdV)equation on the half-line via the Fokas unified transformation approach.We show that the solution u(x,t)of the fifth-order mKdV equation can...In this paper,we investigate the fifth-order modified Korteweg-de Vries(mKdV)equation on the half-line via the Fokas unified transformation approach.We show that the solution u(x,t)of the fifth-order mKdV equation can be represented by the solution of the matrix Riemann-Hilbert problem constructed on the plane of complex spectral parameter θ.The jump matrix L(x,t,θ)has an explicit representation dependent on x,t and it can be represented exactly by the two pairs of spectral functions y(θ),z(θ)(obtained from the initial value u0(x))and Y(θ),Z(θ)(obtained from the boundary conditions v0(t),{vk(t)}_(1)^(4)).Furthermore,the two pairs of spectral functions y(θ),z(θ)and Y(θ),Z(θ)are not independent of each other,but are related to the compatibility condition,the so-called global relation.展开更多
We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robus...We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist.展开更多
Two spodumene samples for helium isotope standard were prepared. According to the preparation criterion on first grade national standard materials, homogeneity tests of helium contents and isotope compositions of two ...Two spodumene samples for helium isotope standard were prepared. According to the preparation criterion on first grade national standard materials, homogeneity tests of helium contents and isotope compositions of two samples were carried out using the heat melt method. The homogeneity tests and certification analysis show that 4He contents and 3He/4He ratios of two reference material samples are homogeneous. Afterward two standard samples were distributed to four laboratories for cooperative fixed values. All data of various laboratories submit to normal distribution and not abnormity values. The average values of each laboratory are recommended as values of two spodumene samples for helium isotope standard.展开更多
目的探讨早期改良ROX(mROX)指数对间质性肺病急性加重(AE-ILD)患者短期预后的临床预测价值。方法回顾性分析2022年1月—2024年12月于徐州医科大学附属医院住院的149例AE-ILD患者的临床资料。根据患者28 d存活情况,将患者分为死亡组(65例...目的探讨早期改良ROX(mROX)指数对间质性肺病急性加重(AE-ILD)患者短期预后的临床预测价值。方法回顾性分析2022年1月—2024年12月于徐州医科大学附属医院住院的149例AE-ILD患者的临床资料。根据患者28 d存活情况,将患者分为死亡组(65例)和存活组(84例)。收集患者的一般资料与基线数据,记录患者入院时及入院24 h mROX指数。采用单因素Cox回归分析筛选潜在影响因素,建立多因素Cox比例风险模型确定AE-ILD患者住院死亡的独立预测因子;限制性立方样条(RCS)确定mROX指数与AE-ILD患者28 d死亡的关系;绘制受试者工作特征(ROC)曲线,探究mROX指数对AE-ILD患者28 d死亡的预测价值并计算最佳截断值;采用Kaplan-Meier法绘制不同24 h mROX指数水平患者的生存曲线。结果死亡组入院时mROX指数(6.8±3.6)及24 h mROX指数[5.2(3.8,6.5)]均低于存活组(P<0.05),多因素Cox比例风险回归分析结果显示,入院时mROX指数(HR=0.76,95%CI:0.71~0.81,P<0.05)及24 h mROX指数(HR=0.42,95%CI:0.34~0.52,P<0.05)是AE-ILD患者28 d死亡的影响因素。24 h mROX指数预测AE-ILD患者28 d死亡的ROC曲线下面积为0.940(95%CI:0.921~0.957,P<0.05),最佳截断值为8.89。RCS显示24 h mROX指数与AE-ILD患者住院死亡风险呈非线性正相关关系(P<0.05)。当24 h mROX>8.89时,死亡风险随指数升高呈显著下降趋势(非线性检验P<0.001)。结论24 h mROX指数的降低与AE-ILD患者的28 d死亡率增加有关,24 h mROX指数对AE-ILD患者28 d死亡具有良好的预测能力。展开更多
文摘We report in this paper the ground-state energy 2s^(2)^(1)S and total energies of doubly excited states 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I of the Helium isoelectronic sequence from H-to Ca^(18+).Calculations are performed using the Modified Atomic Orbital Theory(MAOT)in the framework of a variational procedure.The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function[1]combining with Hylleraas-type wave function[2].The study leads to analytical expressions which are carried out under special MAXIMA computational program.This first proposed MAOT variational procedure,leads to accurate results in good agreement as well as with available other theoretical results than experimental data.In the present work,a new correlated wave function is presented to express analytically the total energies for the 2s21S ground state and each doubly 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the(nI^(2))systems.
文摘In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.
文摘In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are applied to the problem. The effectiveness of the each modified is verified by several examples.
基金Project supported by the Major State Basic Research Program of China (No. 19990328)the National Tackling Key Problems Program (No. 20050200069)+4 种基金the National Natural Science Foundation of China (Nos. 10771124, 10372052, 11101244, and 11271231)the Doctorate Foundation of the Ministry of Education of China (No. 20030422047)the Shandong Province Natural Science Foundation (No. ZR2009AQ012)the Independent Innovation Foundation of Shandong University(No. 2010TS031)the Scientific Research Award Fund for Excellent Middle-Aged and Young Scientists of Shandong Province (No. BS2009NJ003)
文摘A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.
基金supported by the National Natural Science Foundation of China under Grant Nos.12147115 and 11835011the Natural Science Foundation of Anhui Province under Grant No.2108085QA09+3 种基金the University Natural Science Research Project of Anhui Province under Grant No.KJ2021A1094China Postdoctoral Science Foundation under Grant No.2022M712833the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No.22HASTIT019the Natural Science Foundation of Henan Province under Grant No.202300410524
文摘In this paper,we investigate the fifth-order modified Korteweg-de Vries(mKdV)equation on the half-line via the Fokas unified transformation approach.We show that the solution u(x,t)of the fifth-order mKdV equation can be represented by the solution of the matrix Riemann-Hilbert problem constructed on the plane of complex spectral parameter θ.The jump matrix L(x,t,θ)has an explicit representation dependent on x,t and it can be represented exactly by the two pairs of spectral functions y(θ),z(θ)(obtained from the initial value u0(x))and Y(θ),Z(θ)(obtained from the boundary conditions v0(t),{vk(t)}_(1)^(4)).Furthermore,the two pairs of spectral functions y(θ),z(θ)and Y(θ),Z(θ)are not independent of each other,but are related to the compatibility condition,the so-called global relation.
文摘We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Padé approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist.
文摘Two spodumene samples for helium isotope standard were prepared. According to the preparation criterion on first grade national standard materials, homogeneity tests of helium contents and isotope compositions of two samples were carried out using the heat melt method. The homogeneity tests and certification analysis show that 4He contents and 3He/4He ratios of two reference material samples are homogeneous. Afterward two standard samples were distributed to four laboratories for cooperative fixed values. All data of various laboratories submit to normal distribution and not abnormity values. The average values of each laboratory are recommended as values of two spodumene samples for helium isotope standard.
文摘目的探讨早期改良ROX(mROX)指数对间质性肺病急性加重(AE-ILD)患者短期预后的临床预测价值。方法回顾性分析2022年1月—2024年12月于徐州医科大学附属医院住院的149例AE-ILD患者的临床资料。根据患者28 d存活情况,将患者分为死亡组(65例)和存活组(84例)。收集患者的一般资料与基线数据,记录患者入院时及入院24 h mROX指数。采用单因素Cox回归分析筛选潜在影响因素,建立多因素Cox比例风险模型确定AE-ILD患者住院死亡的独立预测因子;限制性立方样条(RCS)确定mROX指数与AE-ILD患者28 d死亡的关系;绘制受试者工作特征(ROC)曲线,探究mROX指数对AE-ILD患者28 d死亡的预测价值并计算最佳截断值;采用Kaplan-Meier法绘制不同24 h mROX指数水平患者的生存曲线。结果死亡组入院时mROX指数(6.8±3.6)及24 h mROX指数[5.2(3.8,6.5)]均低于存活组(P<0.05),多因素Cox比例风险回归分析结果显示,入院时mROX指数(HR=0.76,95%CI:0.71~0.81,P<0.05)及24 h mROX指数(HR=0.42,95%CI:0.34~0.52,P<0.05)是AE-ILD患者28 d死亡的影响因素。24 h mROX指数预测AE-ILD患者28 d死亡的ROC曲线下面积为0.940(95%CI:0.921~0.957,P<0.05),最佳截断值为8.89。RCS显示24 h mROX指数与AE-ILD患者住院死亡风险呈非线性正相关关系(P<0.05)。当24 h mROX>8.89时,死亡风险随指数升高呈显著下降趋势(非线性检验P<0.001)。结论24 h mROX指数的降低与AE-ILD患者的28 d死亡率增加有关,24 h mROX指数对AE-ILD患者28 d死亡具有良好的预测能力。
