In this paper we study the problems of meromorphic functions sharing values in an angular domain and obtain some uniqueness results which are the improvement of the well-known five-value theorem and four-value theorem given by Nevanlinna.

In this paper we study the problem of normal families of meromorphic functions concerning shared values and prove that a family F of meromorphic functions in a domain D is normal if for each pair of functions f and g in F , f − af n and g − ag n share a value b in D where n is a positive integer and a, b are two finite constants such that n 4 and a = 0. This result is not true when n 3.

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The provirus DNA sequence of porcine endogenous retrovirus (PERV) distributed in the pig genome is the major obstacle that restricts the swine as the organ donors in xenotransplantation, and the copy number of PERV varies greatly among different breeds and individuals. In the experiment, 67 healthy, female Chinese Experimental Mini-Pigs (CEMPs) aged at 3-6 months were selected from the Animal Husbandry Station of China Agricultural University, the copy number of PERV and types of envelope protein gene (env) were then investigated by means of PCR analysis and Southern blotting. It is showed that the distribution of types of envelope protein gene in Landrace and CEMPs makes little difference, but the proportion of individuals carrying two types of envelope protein gene (env-A and env-B, which is denoted as env-AB) is much larger than those which carry only one type of envelope protein gene (env-A or env-B). Meanwhile, two endogenous retrovirus free pigs were found for the first time during our research, and the copy number of others is relatively low, which is about 10 to 20. All the results illuminate the genetic diversity of indigenous pig breeds in China and the potential of CEMPs to serve as organ donors in xenotransplantation.

In this paper we study the problem of meromorphic functions sharing three values with weight and obtain some theorems which improve the results given by Lahiri and others.