In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.
New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function.
This paper contains a study of propagation of singular travelling waves u（x, t） for conservation laws ut ＋ [Ф（u）]x = ψ（u）, where Ф, ψ are entire functions taking real values on the real axis. Conditions for...This paper contains a study of propagation of singular travelling waves u（x, t） for conservation laws ut ＋ [Ф（u）]x = ψ（u）, where Ф, ψ are entire functions taking real values on the real axis. Conditions for the propagation of wave profiles β ＋ mδ and β ＋ mδt are presented （β is a real continuous function, m ≠ 0 is a real number and δ＇ is the derivative of the Dirac measure 5）. These results are obtained with a consistent concept of solution based on our theory of distributional products. Burgers equation ut ＋ （u2/2）x = 0, the iffusionless Burgers-Fischer equation ut ＋ a（u2/2）x = ru（1 - u/k） with a, r, k being positive numbers, Leveque and Yee equation ut ＋ ux = μx（1 - u）（u - u/k） with μ ≠ 0, and some other examples are studied within such a setting. A ＂tool box＂ survey of the distributional products is also included for the sake of completeness.展开更多
In this paper, we consider Markov branching processes with killing and resurrection. We first show that the Markov branching process with killing and stable resurrection is just the Feller minimum process which is hon...In this paper, we consider Markov branching processes with killing and resurrection. We first show that the Markov branching process with killing and stable resurrection is just the Feller minimum process which is honest and thus unique. We then further show that this honest Feller minimum process is not only positive recurrent but also strongly ergodic. The generating function of the important stationary distribution is explicitly expressed. For the interest of comparison and completeness, the results of the Markov branching processes with killing and instantaneous resurrection are also briefly stated. A new result regarding strong ergodicity of this difficult case is presented. The birth and death process with killing and resurrection together with another example is also analyzed.展开更多
文摘In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.
基金Project Supported in part by the University of Joensuu and the Satte Natural Fund of China.
文摘New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function.
基金supported by Fundac ao para a Ci encia e a Tecnologia,PEst OE/MAT/UI0209/2011
文摘This paper contains a study of propagation of singular travelling waves u（x, t） for conservation laws ut ＋ [Ф（u）]x = ψ（u）, where Ф, ψ are entire functions taking real values on the real axis. Conditions for the propagation of wave profiles β ＋ mδ and β ＋ mδt are presented （β is a real continuous function, m ≠ 0 is a real number and δ＇ is the derivative of the Dirac measure 5）. These results are obtained with a consistent concept of solution based on our theory of distributional products. Burgers equation ut ＋ （u2/2）x = 0, the iffusionless Burgers-Fischer equation ut ＋ a（u2/2）x = ru（1 - u/k） with a, r, k being positive numbers, Leveque and Yee equation ut ＋ ux = μx（1 - u）（u - u/k） with μ ≠ 0, and some other examples are studied within such a setting. A ＂tool box＂ survey of the distributional products is also included for the sake of completeness.
基金Xiangtan University New Staff Research Start-up Grant (Grant No. 08QDZ27)
文摘In this paper, we consider Markov branching processes with killing and resurrection. We first show that the Markov branching process with killing and stable resurrection is just the Feller minimum process which is honest and thus unique. We then further show that this honest Feller minimum process is not only positive recurrent but also strongly ergodic. The generating function of the important stationary distribution is explicitly expressed. For the interest of comparison and completeness, the results of the Markov branching processes with killing and instantaneous resurrection are also briefly stated. A new result regarding strong ergodicity of this difficult case is presented. The birth and death process with killing and resurrection together with another example is also analyzed.
