A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invari...A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].展开更多
We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods...We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 （1）： 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m〉2k＋4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f^m（z）f^（k）（Z）=α→ ｜^f（k）（z）｜ ≤B or f^m（z）f^（k）（z）=α→｜f（z）｜ ≥, then F is normal in D.展开更多
We studied the normality criterion for families of meromorphic functions related to shared sets. Let F be a family of meromorphic functions on the unit disc △, a and b be distinct non-zero values, S={a,b}, and k be a...We studied the normality criterion for families of meromorphic functions related to shared sets. Let F be a family of meromorphic functions on the unit disc △, a and b be distinct non-zero values, S={a,b}, and k be a positive integer. If for every f∈ F, i） the zeros of f（z） have a multiplicity of at least k＋ 1, and ii） E^-f（k）（S） lohtain in E^-f（S）, then F is normal on .4. At the same time, the corresponding results of normal function are also proved.展开更多
The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R^3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is ...The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R^3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time p （the ratio of the sizes） and mass ratio τ=m^/m must be satisfied by some formulas. For any radius ratios ρ∈（0, 0.152996 918 2） or （0.715 223 148 7, 1.398 165 037）, there is only one central configuration. Otherwise, for any given mass ratio τ, there may exist more than one central configuration.展开更多
The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n...The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831].展开更多
A normal theorem concerning meromorphic functions sharing values was proved with the method of Zalcman- Pang.The theorem is as follows. If for each f in F, all zeros of f-a have multiplicity at least k (k≥2), f and i...A normal theorem concerning meromorphic functions sharing values was proved with the method of Zalcman- Pang.The theorem is as follows. If for each f in F, all zeros of f-a have multiplicity at least k (k≥2), f and its k-th derivative function share a, and if f=b whenever its k-th derivative equal b, then F is normal in D. This theorem improved the result of Chen and Fang [Chen HH, Fang ML, Shared values and normal families of meromorphic functions, Journal of Mathematical Analysis and Applications, 2001, 260: 124-132].展开更多
The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions [ and g which are not polynominals of degree ...The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions [ and g which are not polynominals of degree less than a positive integer k, if f^nf（k）and g^ng^（k） share （1,2）, where n is another positive integer not less than k＋10, then f^nf^（k） identically equals g^ng ^（k） or f^nf^（k）g^ng^（k） identically equals 1. Particularly for k =1, we improved the results of Yang [Yang CC, Hua XH, Uniqueness and value-sharing of meromorphic functions, Annales Academiae Scientiarum Fennicae Mathematica, 1997, 22： 395-406], and Fang [Fang ML, Hua XH, Entire function that share one value, Journal of Nanjing University, 1996, 13（1）： 44-48. （In Chinese）].展开更多
The uniqueness problem of entire functions sharing one small function was studied. By Picard＇s Theorem, we proved that for two transcendental entire functionsf（z） and g（z）, a positive integer n≥9, and a（z） （n...The uniqueness problem of entire functions sharing one small function was studied. By Picard＇s Theorem, we proved that for two transcendental entire functionsf（z） and g（z）, a positive integer n≥9, and a（z） （not identically eaqual to zero） being a common small function related to f（z） and g（z）, iffn（z）（f（z）-1）f＇（z） and gn（z）（g（z）-1）g＇（z） share a（z） ca, where CM is counting multiplicity, then g（z） ≡f（z）. This is an extended version of Fang and Hong＇s theorem [ Fang ML, Hong W, A unicity theorem for entire functions concerning differential polynomials, Journal of Indian Pure Applied Mathematics, 2001, 32 （9）： 1343-1348].展开更多
This paper presents an inequality, by use of which some results about the value distribution of f nf (k) are proved, where n and k are two positive integers.
The speed of a ship sailing in waves always slows down due to the decrease in efficiency of the propeller. So it is necessary and essential to analyze the unsteady hydrodynamic performance of propeller in waves. This ...The speed of a ship sailing in waves always slows down due to the decrease in efficiency of the propeller. So it is necessary and essential to analyze the unsteady hydrodynamic performance of propeller in waves. This paper is based on the numerical simulation and experimental research of hydrodynamics performance when the propeller is under wave conditions. Open-water propeller performance in calm water is calculated by commercial codes and the results are compared to experimental values to evaluate the accuracy of the numerical simulation method. The first-order Volume of Fluid(VOF) wave method in STAR CCM+ is utilized to simulate the three-dimensional numerical wave. According to the above prerequisite, the numerical calculation of hydrodynamic performance of the propeller under wave conditions is conducted, and the results reveal that both thrust and torque of the propeller under wave conditions reveal intense unsteady behavior. With the periodic variation of waves, ventilation, and even an effluent phenomenon appears on the propeller. Calculation results indicate, when ventilation or effluent appears, the numerical calculation model can capture the dynamic characteristics of the propeller accurately, thus providing a significant theory foundation forfurther studying the hydrodynamic performance of a propeller in waves.展开更多
文摘A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].
文摘We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 （1）： 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m〉2k＋4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f^m（z）f^（k）（Z）=α→ ｜^f（k）（z）｜ ≤B or f^m（z）f^（k）（z）=α→｜f（z）｜ ≥, then F is normal in D.
文摘We studied the normality criterion for families of meromorphic functions related to shared sets. Let F be a family of meromorphic functions on the unit disc △, a and b be distinct non-zero values, S={a,b}, and k be a positive integer. If for every f∈ F, i） the zeros of f（z） have a multiplicity of at least k＋ 1, and ii） E^-f（k）（S） lohtain in E^-f（S）, then F is normal on .4. At the same time, the corresponding results of normal function are also proved.
基金Funded by Natural Science Foundation of China (No. 10231010)KJ of Chongqing Educational Committee (No.KJ071105)and Chongqing Three Gorges University (No. SXXYYB07004).
文摘The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R^3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time p （the ratio of the sizes） and mass ratio τ=m^/m must be satisfied by some formulas. For any radius ratios ρ∈（0, 0.152996 918 2） or （0.715 223 148 7, 1.398 165 037）, there is only one central configuration. Otherwise, for any given mass ratio τ, there may exist more than one central configuration.
文摘The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831].
文摘A normal theorem concerning meromorphic functions sharing values was proved with the method of Zalcman- Pang.The theorem is as follows. If for each f in F, all zeros of f-a have multiplicity at least k (k≥2), f and its k-th derivative function share a, and if f=b whenever its k-th derivative equal b, then F is normal in D. This theorem improved the result of Chen and Fang [Chen HH, Fang ML, Shared values and normal families of meromorphic functions, Journal of Mathematical Analysis and Applications, 2001, 260: 124-132].
文摘The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions [ and g which are not polynominals of degree less than a positive integer k, if f^nf（k）and g^ng^（k） share （1,2）, where n is another positive integer not less than k＋10, then f^nf^（k） identically equals g^ng ^（k） or f^nf^（k）g^ng^（k） identically equals 1. Particularly for k =1, we improved the results of Yang [Yang CC, Hua XH, Uniqueness and value-sharing of meromorphic functions, Annales Academiae Scientiarum Fennicae Mathematica, 1997, 22： 395-406], and Fang [Fang ML, Hua XH, Entire function that share one value, Journal of Nanjing University, 1996, 13（1）： 44-48. （In Chinese）].
基金Funded by The National Natural Science Foundation of China under Grant No. 10671067.
文摘The uniqueness problem of entire functions sharing one small function was studied. By Picard＇s Theorem, we proved that for two transcendental entire functionsf（z） and g（z）, a positive integer n≥9, and a（z） （not identically eaqual to zero） being a common small function related to f（z） and g（z）, iffn（z）（f（z）-1）f＇（z） and gn（z）（g（z）-1）g＇（z） share a（z） ca, where CM is counting multiplicity, then g（z） ≡f（z）. This is an extended version of Fang and Hong＇s theorem [ Fang ML, Hong W, A unicity theorem for entire functions concerning differential polynomials, Journal of Indian Pure Applied Mathematics, 2001, 32 （9）： 1343-1348].
文摘This paper presents an inequality, by use of which some results about the value distribution of f nf (k) are proved, where n and k are two positive integers.
基金Supported by the National Natural Science Foundation of China （51379043, 41176074, 51209048, 51409063）, High Tech Ship Research Project of Ministry of Industry and Technology （G014613002）, and the Support Plan for Youth Backbone Teachers of Harbin Engineering University （HEUCFQ 1408）
文摘The speed of a ship sailing in waves always slows down due to the decrease in efficiency of the propeller. So it is necessary and essential to analyze the unsteady hydrodynamic performance of propeller in waves. This paper is based on the numerical simulation and experimental research of hydrodynamics performance when the propeller is under wave conditions. Open-water propeller performance in calm water is calculated by commercial codes and the results are compared to experimental values to evaluate the accuracy of the numerical simulation method. The first-order Volume of Fluid(VOF) wave method in STAR CCM+ is utilized to simulate the three-dimensional numerical wave. According to the above prerequisite, the numerical calculation of hydrodynamic performance of the propeller under wave conditions is conducted, and the results reveal that both thrust and torque of the propeller under wave conditions reveal intense unsteady behavior. With the periodic variation of waves, ventilation, and even an effluent phenomenon appears on the propeller. Calculation results indicate, when ventilation or effluent appears, the numerical calculation model can capture the dynamic characteristics of the propeller accurately, thus providing a significant theory foundation forfurther studying the hydrodynamic performance of a propeller in waves.
