• Title, Summary, Keyword: Picard value

Search Result 3, Processing Time 0.025 seconds

PICARD VALUES AND NORMALITY CRITERION

  • Fang, Ming-Liang
    • Bulletin of the Korean Mathematical Society
    • /
    • v.38 no.2
    • /
    • pp.379-387
    • /
    • 2001
  • In this paper, we study the value distribution of meromorphic functions and prove the following theorem: Let f(z) be a transcendental meromorphic function. If f and f'have the same zeros, then f'(z) takes any non-zero value b infinitely many times.

  • PDF

UNIQUENESS THEOREMS OF MEROMORPHIC FUNCTIONS OF A CERTAIN FORM

  • Xu, Junfeng;Han, Qi;Zhang, Jilong
    • Bulletin of the Korean Mathematical Society
    • /
    • v.46 no.6
    • /
    • pp.1079-1089
    • /
    • 2009
  • In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

Neritic Paleocurrent Analysis of Pennsylvanian Tethyan Sea at Samcheog Coalfield, Korea (후기(後期) 석탄기(石炭紀) 테티스해내(海內) 한국 삼척탄전(三涉炭田)의 천해류(淺海流) 분석(分折))

  • Kim, Haang Mook
    • Economic and Environmental Geology
    • /
    • v.11 no.1
    • /
    • pp.21-37
    • /
    • 1978
  • The depositional environment of the Manhang and the Geumcheon Formation of the Pennsylvanian Gomog Croup is revealed to the shallow neritic marine milieu in this paper also as the results of Park (1963), Cheong(1975) and Kim (1976), through the analyses of stratigraphy, paleocurrent, properties of cross-beddings and sedimentational features. The formations contains some possible terrestrial sediments suggesting the paralic environment, which are however not recognized definitely within them. The paleocurrent analysis is made to the Manhang Formation only. The paleocurrent of the formation is known to belong to the shallow neritic longshore current. The paleocurrent analysis is based chiefly on the cross-bedding analysis, and subordinately on the texture of elastic coarse sediments. The paleocurrent mean is determined to $269^{\circ}$, that is, from east to west, of which direction is interpreted to the right angle to the slope of the basinal depository plane and also the parallel with die depositional strike, according to Klein (1960) and Selley's (1968) criteria. The variance value of paleocurrent directions of the Manhang Formation in the whole area studied is 6,374, and the values range from 3,394 to 6,957 according to the dirstricts. The paleocurreut pattern of the whole area shows polymodel, and the patterns in each district range from trimodel to quadrimodel. Those models approach to the shallow marine or paralic model of Tohill and Picard (1966), Picard and High (1968 a), Pisnak (1957) and Pettijohn (1962). The mean value of maximum inclinations of cross-beddings of the whole area is $19.9^{\circ}$ with the standard deviation of 8.4, and ranges from $15.6^{\circ}$ to $21.7^{\circ}$ in the districts. Comparing the histogram showing the frequency distribution of the maximum inclinations of cross-beddings of the Manhang Formation with the Pettijohn's (1962) histogram, it is found that the model approaches to his marine model. The Pennsylvanian Gomog Group of the coalfield is considered to have had been deposited in the pseudogeosynclinal zone on the plateau by the transgression of the Tethyan sea caused by the epirogenic movements during the Pennsylvanian Period.

  • PDF