In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not pre...In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.展开更多
The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have o...The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1]展开更多
Inertial fusion energy （IFE） has been considered a promising, nearly inexhaustible source of sustainable carbon-free power for the world＇s energy future. It has long been recognized that the control of hydrodynamic...Inertial fusion energy （IFE） has been considered a promising, nearly inexhaustible source of sustainable carbon-free power for the world＇s energy future. It has long been recognized that the control of hydrodynamic instabilities is of critical importance for ignition and high-gain in the inertial-confinement fusion （ICF） hot-spot ignition scheme. In this mini-review, we summarize the progress of theoretical and simulation research of hydrodynamic instabilities in the ICF central hot-spot implosion in our group over the past decade. In order to obtain sufficient understanding of the growth of hydrodynamic instabilities in ICF, we first decompose the problem into different stages according to the implosion physics processes. The decomposed essential physics pro- cesses that are associated with ICF implosions, such as Rayleigh-Taylor instability （RTI）, Richtmyer-Meshkov instability （RMI）, Kelvin-Helmholtz instability （KHI）, convergent geometry effects, as well as perturbation feed-through are reviewed. Analyti- cal models in planar, cylindrical, and spherical geometries have been established to study different physical aspects, including density-gradient, interface-coupling, geometry, and convergent effects. The influence of ablation in the presence of preheating on the RTI has been extensively studied by numerical simulations. The KHI considering the ablation effect has been discussed in detail for the first time. A series of single-mode ablative RTI experiments has been performed on the Shenguang-II laser facility. The theoretical and simulation research provides us the physical insights of linear and weakly nonlinear growths, and nonlinear evolutions of the hydrodynamic instabilities in ICF implosions, which has directly supported the research of ICF ignition target design. The ICF hot-spot ignition implosion design that uses several controlling features, based on our current understanding of hydrodynamic instabilities, to address shell implosion stability, has been briefly described, several of which are novel.展开更多
The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B^n in C^n is modified....The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B^n in C^n is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ_(G,γ)(f)](z) preserves the properties of S_Ω~*(A, B), as well as strong and almost spirallikeness of type β and order α on B^n. Thus, the mappings in S_Ω~*(A, B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.展开更多
文摘In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.
文摘The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1]
基金supported by the National Natural Science Foundation of China(Grant Nos.11275031,11675026,11475032,11475034,11575033,and 11274026)the Foundation of President of Chinese Academy of Engineering Physics(Grant No.2014-1-040)the National Basic Research Program of China(Grant No.2013CB834100)
文摘Inertial fusion energy （IFE） has been considered a promising, nearly inexhaustible source of sustainable carbon-free power for the world＇s energy future. It has long been recognized that the control of hydrodynamic instabilities is of critical importance for ignition and high-gain in the inertial-confinement fusion （ICF） hot-spot ignition scheme. In this mini-review, we summarize the progress of theoretical and simulation research of hydrodynamic instabilities in the ICF central hot-spot implosion in our group over the past decade. In order to obtain sufficient understanding of the growth of hydrodynamic instabilities in ICF, we first decompose the problem into different stages according to the implosion physics processes. The decomposed essential physics pro- cesses that are associated with ICF implosions, such as Rayleigh-Taylor instability （RTI）, Richtmyer-Meshkov instability （RMI）, Kelvin-Helmholtz instability （KHI）, convergent geometry effects, as well as perturbation feed-through are reviewed. Analyti- cal models in planar, cylindrical, and spherical geometries have been established to study different physical aspects, including density-gradient, interface-coupling, geometry, and convergent effects. The influence of ablation in the presence of preheating on the RTI has been extensively studied by numerical simulations. The KHI considering the ablation effect has been discussed in detail for the first time. A series of single-mode ablative RTI experiments has been performed on the Shenguang-II laser facility. The theoretical and simulation research provides us the physical insights of linear and weakly nonlinear growths, and nonlinear evolutions of the hydrodynamic instabilities in ICF implosions, which has directly supported the research of ICF ignition target design. The ICF hot-spot ignition implosion design that uses several controlling features, based on our current understanding of hydrodynamic instabilities, to address shell implosion stability, has been briefly described, several of which are novel.
基金supported by the National Natural Science Foundation of China(Nos.11271359,11471098)the Joint Funds of the National Natural Science Foundation of China(No.U1204618)the Science and Technology Research Projects of Henan Provincial Education Department(Nos.14B110015,14B110016)
文摘The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B^n in C^n is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ_(G,γ)(f)](z) preserves the properties of S_Ω~*(A, B), as well as strong and almost spirallikeness of type β and order α on B^n. Thus, the mappings in S_Ω~*(A, B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.
