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NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH MULTIPLE VALUES
Li, Yuntong,Liu, Zhixiu Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
In this paper, we consider some normality criteria concerning multiple values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain D. Let k be a positive integer and ${\psi}(z){\not\equiv}0$, ${\infty}$ be a meromorphic function in D. If, for each $f{\in}\mathcal{F}$ and $z{\in}D$, (1) $f(z){\neq}0$, and all of whose poles are multiple; (2) all zeros of $f^{(k)}(z)-{\psi}(z)$ have multiplicities at least k + 3 in D; (3) all poles of ${\psi}(z)$ have multiplicities at most k in D, then $\mathcal{F}$ is normal in D.
Normal families of meromorphic functions with multiple values
Yuntong Li,Zhixiu Liu 대한수학회 2017 대한수학회보 Vol.54 No.2
In this paper, we consider some normality criteria concerning multiple values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $D$. Let $k$ be a positive integer and $\psi(z) \not \equiv 0,\infty$ be a meromorphic function in $D$. If, for each $f\in \mathcal{F}$ and $z\in D$, (1) $f(z)\neq 0$, and all of whose poles are multiple; (2) all zeros of $f^{(k)}(z)-\psi(z)$ have multiplicities at least $k+3$ in $D$; (3) all poles of $\psi(z)$ have multiplicities at most $k$ in $D$, then $\mathcal{F}$ is normal in $D$.
NORMALITY CRITERIA FOR A FAMILY OF MEROMORPHIC FUNCTIONS WITH MULTIPLE ZEROS
Datt, Gopal,Li, Yuntong,Rani, Poonam Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some of the results of Fang and Zalcman [4] and Chen et al. [2] to a great extent.
Yiting Xu,Jiamei Huang,Yuntong Li,Meijie Wang,Ying Cao,Conghui Yuan,Birong Zeng,Lizong Dai 한국고분자학회 2017 Macromolecular Research Vol.25 No.8
A novel zwitterionic hybrid amphiphilic copolymer containing polyhedral oligomericsilsesquioxane (POSS), and poly(methacrylate isobutyl POSS)-b-poly (3-dimethyl(methacryloyloxyethyl) ammonium propane sulfonaten-co-2-(diethylamino) ethyl methacrylate-co-styrene) (PMAiBuPOSS-b-P(DMAPS-co-DMAEMAco- St)), was prepared by the ring open reaction of 1, 3-propane sultone with tertiary amine on the precursor polymer. This hybrid copolymer could self-assemble into spherical micelle with a relatively narrow size distribution. The micelle size exhibited a great dependence on pH, as the size of the micelles was of evidently decreases with the increase of the pH value. Controllable release of pyrene from the micelles was investigated by fluorescent emission spectra. Micelles with more zwitterionic units would lead to less pyrene release and longer equilibrium time. The protein adsorption resistance of the micelles was tested by mixing them with fetal bovine serum. The antifouling ability was improved by increasing the number of zwitterionic units as well as decreasing the number of DMAEMA units. This novel hybrid amphiphilic random copolymer with the pH-responsive and anti-protein-fouling ability, can be potentially used for drug carriers for controlled release.