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Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation
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作者 Yolanda Silvia Santiago Ayala 《Journal of Applied Mathematics and Physics》 2023年第4期1061-1076,共16页
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r... In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study. 展开更多
关键词 Semigroups Theory Weakly Continuous Operators Existence of Solution generalized schrödinger equation Distributional Problem Periodic Distributional Space
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Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass 被引量:1
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作者 Altug Arda Ramazan Sever 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第7期51-54,共4页
The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. T... The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before. 展开更多
关键词 position dependent mass schr5dinger equation generalized morse potential Nikiforov-Uvarovmethod energy eigenvalues EIGENFUNCTIONS
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Generalized Harmonic Oscillator and the Schrdinger Equation with Position-Dependent Mass
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作者 JU Guo-Xing CAI Chang-Ying REN Zhong-Zhou 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第5期797-802,共6页
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue a... We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator. 展开更多
关键词 generalized harmonic oscillator schr6dinger equation position-dependent mass coherent state
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A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schrödinger Equations
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作者 Hongjuan Zhang Boying Wu Xiong Meng 《Communications on Applied Mathematics and Computation》 2022年第1期84-107,共24页
In this paper,we consider the local discontinuous Galerkin method with generalized alter-nating numerical fluxes for two-dimensional nonlinear Schrödinger equations on Carte-sian meshes.The generalized fluxes not... In this paper,we consider the local discontinuous Galerkin method with generalized alter-nating numerical fluxes for two-dimensional nonlinear Schrödinger equations on Carte-sian meshes.The generalized fluxes not only lead to a smaller magnitude of the errors,but can guarantee an energy conservative property that is useful for long time simulations in resolving waves.By virtue of generalized skew-symmetry property of the discontinuous Galerkin spatial operators,two energy equations are established and stability results con-taining energy conservation of the prime variable as well as auxiliary variables are shown.To derive optimal error estimates for nonlinear Schrödinger equations,an additional energy equation is constructed and two a priori error assumptions are used.This,together with properties of some generalized Gauss-Radau projections and a suitable numerical initial condition,implies optimal order of k+1.Numerical experiments are given to demonstrate the theoretical results. 展开更多
关键词 Local discontinuous Galerkin method Two-dimensional nonlinear schrödinger equation generalized alternating fluxes Optimal error estimates
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Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model
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作者 Yolanda Silvia Santiago Ayala 《Journal of Applied Mathematics and Physics》 2023年第4期919-932,共14页
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends ... In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study. 展开更多
关键词 Groups Theory Weakly Continuous Operators Existence of Solution generalized schrödinger Type equation Homogeneous equation Periodic Distributional Space
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On examining the predictive capabilities of two variants of the PINN in validating localized wave solutions in the generalized nonlinear Schr?dinger equation
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作者 K Thulasidharan N Sinthuja +1 位作者 N Vishnu Priya M Senthilvelan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2024年第11期161-174,共14页
We introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equat... We introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equation.This equation comprises four physically significant nonlinear evolution equations,namely,the NLS,Hirota,Lakshmanan-Porsezian-Daniel and fifth-order NLS equations.The generalized NLS equation demonstrates nonlinear effects up to quintic order,indicating rich and complex dynamics in various fields of physics.By combining concepts from the physics-informed neural network and theory-guided neural network(TgNN)models,the SCTgNN aims to enhance our understanding of complex phenomena,particularly within nonlinear systems that defy conventional patterns.To begin,we employ the TgNN method to predict the behaviour of localized waves,including solitons,rogue waves and breathers,within the generalized NLS equation.We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions.Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations. 展开更多
关键词 generalized nonlinear schr?dinger equation SOLITON rogue waves BREATHERS SCTgNN TgNN
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Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics
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作者 徐涛 陈勇 林机 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第12期80-93,共14页
We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger (CCQNLS) equations through the generalized Darboux transformation (DT). A special vector sol... We investigate some novel localized waves on the plane wave background in the coupled cubic-quintic nonlinear Schrdinger (CCQNLS) equations through the generalized Darboux transformation (DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higher-order localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions; (ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons; (iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α. These results further uncover some striking dynamic structures in the CCQNLS system. 展开更多
关键词 generalized Darboux transformation localized waves SOLITON rogue wave BREATHER coupled cubic-quintic nonlinear schr dinger equations
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应用全新G'/(G+G')展开方法求解广义非线性Schrdinger方程和耦合非线性Schrdinger方程组 被引量:13
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作者 石兰芳 聂子文 《应用数学和力学》 CSCD 北大核心 2017年第5期539-552,共14页
研究了一种全新的G'/(G+G')展开方法,并应用这种方法讨论了广义非线性Schrdinger方程和一类耦合非线性Schrdinger方程组新形式的精确解,包括双曲余切函数解、余切函数解和有理函数解.全新G'/(G+G')展开方法不但直... 研究了一种全新的G'/(G+G')展开方法,并应用这种方法讨论了广义非线性Schrdinger方程和一类耦合非线性Schrdinger方程组新形式的精确解,包括双曲余切函数解、余切函数解和有理函数解.全新G'/(G+G')展开方法不但直接而有效地求出方程的新精确解,而且扩大了解的范围,这种新方法对于研究偏微分方程具有广泛的应用意义. 展开更多
关键词 全新G'/(G+G')展开方法 广义非线性schrodinger方程 耦合非线性schrodinger方程组 精确解
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广义非线性Schrdinger方程的多辛格式与模方守恒律 被引量:7
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作者 黄浪扬 《计算物理》 CSCD 北大核心 2009年第5期693-698,共6页
通过正则变换,构造出广义非线性Schrdinger方程的多辛方程组.对此多辛方程组,导出了一个新的模方守恒多辛格式.数值实验结果表明,多辛格式具有长时间的数值行为,且在保持模方守恒律方面优于蛙跳格式和辛欧拉中点格式.
关键词 广义非线性schrdinger方程 多辛方程组 守恒律 多辛格式 数值实验
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广义非线性Schrdinger方程的Lie-Bcklund对称
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作者 管习文 熊庄 +1 位作者 刘玉斌 周焕强 《四川师范大学学报(自然科学版)》 CAS CSCD 1992年第3期74-77,共4页
本文证明,由Kundu引入的广义非线性Schrōdinger方程具有无穷多个彼此对易的Lie-Bācklund对称.此外,还建立了无穷小Lie-Bācklund 对称和定域运动常数之间的一一对应关系.
关键词 广义非线性schrōdinger方程 定域运动常数 Lie-Bācklund对称
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广义非线性分数阶Schrdinger方程组周期边值问题整体解的存在唯一性
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作者 张娜 辛杰 葛焕敏 《鲁东大学学报(自然科学版)》 2016年第1期1-10,共10页
本文研究了广义非线性分数阶Schrdinger方程组的周期初边值问题,运用一致先验估计和Galёrkin方法证明了其周期边值问题整体光滑解的存在性和唯一性.
关键词 广义非线性分数阶schrdinger方程组 Gagliardo-Nirenberg不等式 Galёrkin方法
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Boundary Conditions for Sturm-Liouville Equation with Transition Regions and Barriers or Wells 被引量:1
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作者 Alfred Wünsche 《Advances in Pure Mathematics》 2021年第4期254-295,共42页
By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or we... By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or wells between two asymptotic potentials for which the solutions are supposed as known. We call such expansions “moment series” because the coefficients are determined by moments of the function. An infinite system of boundary conditions is obtained and it is shown how by truncation it can be reduced to approximations of a different order (explicitly made up to third order). Reflection and refraction problems are considered with such approximations and also discrete bound states possible in nonsymmetric and symmetric potential wells are dealt with. This is applicable for large wavelengths compared with characteristic lengths of potential changes. In Appendices we represent the corresponding foundations of Generalized functions and apply them to barriers and wells and to transition functions. The Sturm-Liouville equation is not only interesting because some important second-order differential equations can be reduced to it but also because it is easier to demonstrates some details of the derivations for this one-dimensional equation than for the full three-dimensional vectorial equations of electrodynamics of media. The article continues a paper that was made long ago. 展开更多
关键词 schrödinger equation Drude Approximation Transition Layer Potential Barrier Potential Well Reflection REFRACTION Moment Series generalized Functions Delta Function and Its Derivatives Discrete or Bound Eigenstates
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On the Riemann–Hilbert problem of a generalized derivative nonlinear Schrödinger equation
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作者 Bei-Bei Hu Ling Zhang Tie-Cheng Xia 《Communications in Theoretical Physics》 SCIE CAS CSCD 2021年第1期6-17,共12页
In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert pr... In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 in the inverse problem,the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed.Moreover,we also obtain that the spectral functions f(η),s(η),F(η),S(η)are not independent of each other,but meet an important global relation.As applications,the generalized DNLS equation can be reduced to the Kaup-Newell equation and Chen-Lee-Liu equation on the half-line. 展开更多
关键词 Riemann-Hilbert problem generalized derivative nonlinear schrödinger equation initial-boundary value problems unified transformation method
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Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrodinger dynamical model and its applications
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作者 Xiaoyong Qian Dianchen Lu +1 位作者 Muhammad Arshad Khurrem Shehzad 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第2期154-163,共10页
We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),sol... We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),solitary waves,periodic and other wave solutions of the perturbed Kaup-Newell Schrodinger equation in mathematical physics are achieved by utilizing two mathematical techniques,namely,the extended F-expansion technique and the proposed exp(-φ(ξ))-expansion technique.This dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrodinger equation.In engineering and applied physics,these wave results have key applications.Graphically,the structures of some solutions are presented by giving specific values to parameters.By using modulation instability analysis,the stability of the model is tested,which shows that the model is stable and the solutions are exact.These techniques can be fruitfully employed to further sculpt models that arise in mathematical physics. 展开更多
关键词 extended F-expansion method generalized exp(-φ(ξ))-expansion technique perturbed Kaup-Newell schr?dinger equation traveling wave solutions
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New sub-equation method to construct solitons and other solutions for perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in optical fiber materials 被引量:1
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作者 Elsayed M.E.Zayed Abdul-Ghani Al-Nowehy Reham M.A.Shohib 《Journal of Ocean Engineering and Science》 SCIE 2019年第1期14-23,共10页
In a previous work,Zayed and Al-Nowehy have applied the Riccati equation mapping method combined with the generalized extended(G/G)-expansion method and found new exact solutions of the nonlinear KPP equation.In the ... In a previous work,Zayed and Al-Nowehy have applied the Riccati equation mapping method combined with the generalized extended(G/G)-expansion method and found new exact solutions of the nonlinear KPP equation.In the present article,we propose a different method,namely,a new sub-equation method consists of the Riccati equation mapping method and the(G/G,1/G)-expansion method to find new exact solutions of the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in optical fiber materials.This proposed method is not found elsewhere.Hyperbolic,trigonometric and rational function solutions are given.New solutions of the generalized Riccati equation are presented for the first time which are not reported previously.The solutions of the given nonlinear equation can be applied in ocean engineering for calculating the height of tides in the ocean. 展开更多
关键词 New sub-equation method (G/G 1/G)-expansion method generalized Riccati equation mapping method Perturbed nonlinear schrödinger equation Exact solutions.
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啁啾激光调控谐波截止能量及强度的研究 被引量:8
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作者 刘航 李义 +1 位作者 姚震 冯立强 《激光技术》 CAS CSCD 北大核心 2017年第5期708-711,共4页
为了调控谐波辐射过程,采用数值求解3维薛定谔方程的方法,进行了啁啾激光对调控谐波辐射截止能量及强度的理论分析。通过分析激光包络图、电子电离几率、谐波辐射时频分析图,给出了谐波截止能量延伸以及谐波强度增强的原因。结果表明,... 为了调控谐波辐射过程,采用数值求解3维薛定谔方程的方法,进行了啁啾激光对调控谐波辐射截止能量及强度的理论分析。通过分析激光包络图、电子电离几率、谐波辐射时频分析图,给出了谐波截止能量延伸以及谐波强度增强的原因。结果表明,在负向啁啾场下,谐波截止能量附近的强度与无啁啾参量相比增强了1个数量级;当引入半周期调控激光场后,谐波截止能量得到有效延伸;适当叠加谐波谱上的谐波,可获得一个46as的脉冲;该脉冲强度比无啁啾参量下获得的脉冲强1个数量级。该研究对调控谐波的辐射过程及阿秒脉冲的输出是有帮助的。 展开更多
关键词 激光光学 3维薛定谔方程 高次谐波 半周期激光场 阿秒脉冲
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红外激光与远紫外激光场驱动H_2^+辐射谐波 被引量:2
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作者 刘航 李义 冯立强 《激光技术》 CAS CSCD 北大核心 2018年第2期145-150,共6页
为了了解H_2^+谐波辐射的过程,采用数值求解非玻恩-奥本海默近似薛定谔方程的方法,理论研究了H_2^+在10fs/800nm红外激光与6fs/30nm远紫外激光驱动下谐波辐射的特点。结果表明,谐波辐射的贡献主要来源于拉比振荡、多光子共振电离、电荷... 为了了解H_2^+谐波辐射的过程,采用数值求解非玻恩-奥本海默近似薛定谔方程的方法,理论研究了H_2^+在10fs/800nm红外激光与6fs/30nm远紫外激光驱动下谐波辐射的特点。结果表明,谐波辐射的贡献主要来源于拉比振荡、多光子共振电离、电荷共振增强电离以及离解态电离;随着远紫外光的加入,谐波光谱呈现能量间隔为远紫外光子能量的多重谐波截止结构;当远紫外光与红外激光的延迟时间大于零或小于零时,谐波光谱呈现红移和蓝移的现象。该研究对理解分子谐波辐射过程是有帮助的。 展开更多
关键词 激光光学 薛定谔方程 高次谐波 多重谐波截止能量 谐波调频
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飞秒孤子在色散渐增光纤中谱压缩的数值分析 被引量:1
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作者 梁锐 周晓军 +3 位作者 张旨遥 秦祖军 李和平 刘永 《光子学报》 EI CAS CSCD 北大核心 2010年第5期811-814,共4页
通过数值求解修正了的广义非线性薛定谔方程,研究了孤子在色散渐增光纤中的谱压缩进程.详细分析了入射脉冲峰值功率对输出脉冲的谱宽和中心波长的影响,并描述了脉冲的脉宽、谱宽及啁啾在光纤中的演化过程.计算结果表明,脉宽200fs、中心... 通过数值求解修正了的广义非线性薛定谔方程,研究了孤子在色散渐增光纤中的谱压缩进程.详细分析了入射脉冲峰值功率对输出脉冲的谱宽和中心波长的影响,并描述了脉冲的脉宽、谱宽及啁啾在光纤中的演化过程.计算结果表明,脉宽200fs、中心波长1550nm的基孤子在群速度色散从-1ps2/km至-11ps2/km线性变化的长100m的色散渐增光纤中传输时,脉冲谱宽由12.6nm压缩至5.2nm,即可获得最大压缩比为2.42. 展开更多
关键词 光纤光学 谱压缩 色散渐增光纤 基孤子 非线性薛定谔方程
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广义振子势的精确束缚态解(英文) 被引量:3
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作者 陈刚 袁奇英 《原子与分子物理学报》 CAS CSCD 北大核心 2004年第1期143-148,共6页
本文求解了广义振子势在r ,θ ,φ方向上的Schr dinger方程 ,得到了它的能级和相应的归一化角向、径向波函数。利用广义拉盖尔多项式的积分公式得到了广义振子势的径向矩阵元的通向表达式。
关键词 广义振子势 schrOEdinger方程 束缚态 精确解 径向矩阵元
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