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THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES EQUATIONS IN THE WHOLE DOMAIN
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作者 邹委员 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期887-908,共22页
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k... We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data. 展开更多
关键词 thermomechanical Cucker-Smale model Stokes equations strong solutions global existence
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THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME
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作者 Lin ZHENG Shu WANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1877-1885,共9页
This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ3.Under the smallness assumption on both the external potential and the initial perturbation... This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ3.Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces,the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method. 展开更多
关键词 fluid-particle flowing regime global existence
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The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms
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作者 WANG Ji-nan SUN Da-wei 《Chinese Quarterly Journal of Mathematics》 2024年第3期315-323,共9页
We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min... We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough. 展开更多
关键词 Kirchhoff-type equation The existence Positive solution Variational method
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Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition
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作者 Mohamed Karimou Gazibo Duni Yegbonoma Frédéric Zongo 《Applied Mathematics》 2024年第7期455-463,共9页
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
关键词 Lebesgue and Sobolev Spaces with Variable Exponent Weak Solution Entropy Solution Degenerate Parabolic-Hyperbolic Equation Conservation Law Leray Lions Type Operator Neumann Boundary Condition existence Result
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Existence of Solutions of a Convolution Integral Equation
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作者 Henry Otoo Benjamin Dadzie Mensah Lewis Brew 《Journal of Applied Mathematics and Physics》 2024年第5期1835-1847,共13页
In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined... In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball B<sub>r</sub> belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation. 展开更多
关键词 VOLTERRA Integral Equation CONVOLUTION Fixed Point existence Noncompactness
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Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source
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作者 Xiaoxin Yang 《Journal of Applied Mathematics and Physics》 2024年第1期181-193,共13页
This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz... This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay. 展开更多
关键词 Nonlocal Parabolic Equation Singular Potential Logarithmic Nonlocal Source Global existence DECAY
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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 Fourth-Order Three-Point Boundary Value Problem Sign-Changing Green’s Function Fixed Point Index Iterative Technique Monotone Positive Solution existence
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Global Existence of the Solution for a Reduced Model of the Vectorial Quantum Zakharov System
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作者 Guiyu Yang 《Journal of Applied Mathematics and Physics》 2024年第2期533-542,共10页
In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the glob... In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data. 展开更多
关键词 Quantum Zakharov System Global existence Logarithmic Sobolev Inequality
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SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS
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作者 张学梅 阚士坤 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1175-1194,共20页
Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro... Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered. 展开更多
关键词 singular p-Laplacian equation boundary blow-up sub-supersolution method existence nonexistence and estimates sufficient and necessary conditions
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THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM
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作者 高承华 何兴玥 王晶晶 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2615-2628,共14页
In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are cont... In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained. 展开更多
关键词 system of k-Hessian equations k-convex solutions existence MULTIPLICITY fixed-point theorem
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THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS
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作者 Hakho HONG 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期469-491,共23页
The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals ga... The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals gas.Under the small initial perturbation,the proof of the global existence is based on an elementary energy method using the continuation argument of local solution.Moreover,the uniqueness of global solutions and large time behavior of the density are given.It is one of the main difficulties that the pressure p is not the increasing function of the densityρ. 展开更多
关键词 Navier-Stokes-Korteweg system van der Waals gas existence UNIQUENESS
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Effect of existence state of asphaltenes on the asphaltenes-wax interaction in wax deposition
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作者 Yun Lei Han Wang +5 位作者 Shuang-Shuang Li Xue-Qian Liu Hao-Ran Zhu Yu-Ming Gao Hao-Ping Peng Peng-Fei Yu 《Petroleum Science》 SCIE EI CAS CSCD 2023年第1期507-514,共8页
Asphaltenes are the most elusive substances in waxy crude oil,especially the complex structures,which leads to significant precipitation and aggregation characteristics of asphaltenes,and affects the asphaltenes-wax i... Asphaltenes are the most elusive substances in waxy crude oil,especially the complex structures,which leads to significant precipitation and aggregation characteristics of asphaltenes,and affects the asphaltenes-wax interaction.In this study,the concept of the existence state of asphaltenes was introduced to semi-quantitatively investigate the precipitation and aggregation characteristics of asphaltenes.On this basis,the influence of the existence state of asphaltenes on wax deposition was studied by coldfinger device and high-temperature gas chromatography,and the composition and properties of the deposits were analyzed.Four main findings were made:(1)As the asphaltene concentration increases,the existence state of asphaltenes gradually transitions from dispersed state to aggregated state,and the asphaltene concentration of 0.30 wt%in this study is the starting point of the transition.(2)The existence state of asphaltenes in crude oil does affect the process of wax deposition,as shown in the fact that the dispersed asphaltenes promote the occurrence of wax deposition,while the aggregated asphaltenes can inhibit wax deposition.(3)In the presence of the aggregated asphaltenes,that is,when the asphaltene concentration is higher than 0.30 wt%,the shedding phenomenon of deposit layer was observed,and with the increase of aggregated asphaltenes,the deposit layer fell off earlier.(4)With the increase of the dispersed asphaltenes,the wax appearance temperature(WAT)and wax content of the deposits all showed an increasing trend,while with the appearance of the aggregated asphaltenes,the above situation was reversed.The findings of this study can help for better understanding of the interaction between the asphaltenes and wax in wax deposition. 展开更多
关键词 ASPHALTENES Precipitation/aggregation existence state of asphaltenes Deposition
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The existence of radial k-admissible solutions for n-dimension system of k-Hessian equations
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作者 HE Xing-yue WANG Jing-jing GAO Cheng-hua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期310-316,共7页
In this paper,we focus on a general n-dimension system of k-Hessian equations.By introducing some new suitable growth conditions,the existence results of radial k-admissible solutions of the k-Hessian system are obtai... In this paper,we focus on a general n-dimension system of k-Hessian equations.By introducing some new suitable growth conditions,the existence results of radial k-admissible solutions of the k-Hessian system are obtained.Our approach is largely based on the well-known fixed-point theorem. 展开更多
关键词 k-Hessian equations radial k-admissible solutions existence xed-point theorem
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THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS
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作者 崔磊磊 郭佳星 李工宝 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1131-1160,共30页
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri... In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0. 展开更多
关键词 Kirchhoff type equations potential functions having non-degenerate critical points the Lyapunov-Schmidt reduction method multi-peak solutions existence and local uniqueness
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THE EXISTENCE OF WEAK SOLUTIONS AND PROPAGATION REGULARITY FOR A GENERALIZED KDV SYSTEM
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作者 郭柏灵 肖亚敏 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期942-958,共17页
This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial da... This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3). 展开更多
关键词 global existence propagation regularity KdV system
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Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem
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作者 Xiaoming Liu Yongxiang Li 《Advances in Pure Mathematics》 2023年第8期495-503,共14页
The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have stud... The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained. 展开更多
关键词 Fully Third-Order BVP SOLUTION Positive Solution existence and Uniqueness Inequality Conditions
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The Three Aspects of “Human Existence” from the Human Rights Perspective
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作者 刘志强 闫乃鑫 QIAN Chuijun(Translated) 《The Journal of Human Rights》 2023年第6期1198-1223,共26页
At present,the West overrides the east in international human rights discourse.In order to break through the shackles,it is imperative to provide legal support for China’s human rights discourse.taking the concept of... At present,the West overrides the east in international human rights discourse.In order to break through the shackles,it is imperative to provide legal support for China’s human rights discourse.taking the concept of“human existence”as the fulcrum and comparing it with nature,otherness,and community as the reference,the human being showcases triple facets:“individual person”,“person in relations”,and“person with rights”,which correspond to the three personal perspectives and progressively deduce the subjectivity of human beings,the world history of human rights,and the comprehensive and free development of human rights discourse.the concept of“individual person”is the starting point of human rights,and the harmonious,moral concept of subjectivity provides an orderly basis for the importance of the“right to subsistence and right to development”.“person in relations”represents the externality of human rights,and the world-historical view of time and space has laid the value foundation for the unity of“universality and particularity of human rights”.“person with rights”is the goal of human rights,and the concept of cooperation for the well-rounded and free development of human rights paves the conceptual way for the realization of people’s well-being. 展开更多
关键词 human existence human rights human rights discourse
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Existence and Stability of Solutions for a Class of Fractional Impulsive Differential Equations with Atangana-Baleanu-Caputo Derivative
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作者 Xuefan Lin Weimin Hu +1 位作者 Youhui Su Yongzhen Yun 《Journal of Applied Mathematics and Physics》 2023年第12期3914-3927,共14页
In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differen... In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results. 展开更多
关键词 Fractional Differential Equation Fixed Point Theorem existence of Solutions
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Unity is the Vital Cornerstone of Human Existence
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作者 《国际人才交流》 2023年第4期4-5,共2页
Any journalist would consider it a career highlight to cover a major historical event or witness a ground-breaking breakthrough.I am thankful that the milestone 20th National Congress of the Communist Party of China (... Any journalist would consider it a career highlight to cover a major historical event or witness a ground-breaking breakthrough.I am thankful that the milestone 20th National Congress of the Communist Party of China (CPC) came as a fortuitous stroke of serendipity in my professional life. 展开更多
关键词 existence BREAKTHROUGH BREAKING
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Construction of Legal System of China's Farmland Protection under the Coexistence of Multiple Objectives:Historical Logic,Practical Problems and Optimization Paths
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作者 Shengnan MA Jiaxin ZHOU Yongfang YANG 《Asian Agricultural Research》 2023年第2期26-34,38,共10页
[Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's r... [Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's reform and opening up,reveal the problems and deep-seated reasons of its legislation,clarify the direction of farmland protection in the new period,and solve the"non-agricultural""non-grain"and ecological problems of farmland.[Methods]Literature analysis and inductive deduction methods were used.[Results]The evolution of the farmland protection legal system has gone through the process of"national consciousness-policy guidelines-institutional system",the change from"single subject to multiple subjects";change from the use of"one-way administrative means to coordinated use of administrative,economic and technical means".The practical problems of the farmland protection legal system are mainly due to the insufficient systematization of the farmland protection legal system itself,the generalization of quantity protection,the transformation of quality protection,and the absence of ecological protection.[Conclusions]It is recommended to improve the existing farmland protection legal system from the establishment of the Farmland Protection Law,the improvement of the farmland protection public participation mechanism and supervision mechanism,the establishment of the farmland quality construction and improvement system,the differentiated farmland occupation and supplementation balance system,and the ecological restoration system. 展开更多
关键词 Farmland protection Legal system construction Policy evolution Existing problems Optimization path
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