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ON PARTIAL VALUE SHARING RESULTS OF MEROMORPHIC FUNCTIONS WITH THEIR SHIFTS AND ITS APPLICATIONS
Noulorvang, Vangty,Pham, Duc Thoan Korean Mathematical Society 2020 대한수학회보 Vol.57 No.5
In this paper, we give some uniqueness theorems of nonconstant meromorphic functions of hyper-order less than one sharing partially three or four small periodic functions with their shifts. As an application, some sufficient conditions for periodicity of meromorphic functions are given. Our results improve and extend previous results of W. Lin, X. Lin and A. Wu [11].
On vanishing theorems for locally conformally flat Riemannian manifolds
Dang Tuyen Nguyen,Duc Thoan Pham 대한수학회 2022 대한수학회보 Vol.59 No.2
In this paper, we obtain some vanishing theorems for $p$-harmonic 1-forms on locally conformally flat Riemannian manifolds which admit an integral pinching condition on the curvature operators.
On the uniqueness of meromorphic function and its shift sharing values with truncated multiplicities
Hai Nam Nguyen,Vangty Noulorvang,Duc Thoan Pham 대한수학회 2019 대한수학회보 Vol.56 No.3
In this paper, we deal with unicity of a nonconstant zero-order meromorphic function $f(z)$ and its shift $f(qz)$ when they share four distinct values $IM$ or share three distinct values with multiplicities truncated to level 4 in the extended complex plane, where $q\in\mathbb C\setminus\{0\}$. We also give an uniqueness result for $f(z)$ sharing sets with its shift.
ON THE UNIQUENESS OF MEROMORPHIC FUNCTION AND ITS SHIFT SHARING VALUES WITH TRUNCATED MULTIPLICITIES
Nguyen, Hai Nam,Noulorvang, Vangty,Pham, Duc Thoan Korean Mathematical Society 2019 대한수학회보 Vol.56 No.3
In this paper, we deal with unicity of a nonconstant zero-order meromorphic function f(z) and its shift f(qz) when they share four distinct values IM or share three distinct values with multiplicities truncated to level 4 in the extended complex plane, where $q{\in}\mathbb{C}{\setminus}\{0\}$. We also give an uniqueness result for f(z) sharing sets with its shift.
Thi Tuyet Luong,Dang Tuyen Nguyen,Duc Thoan Pham 대한수학회 2018 대한수학회보 Vol.55 No.1
In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the $p$-Casorati determinant with $p\in\mathbb C^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition ``order=0". The results obtained include $p$-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.
Thu Thuy Hoang,Hong Nhat Nguyen,Duc Thoan Pham 대한수학회 2023 대한수학회보 Vol.60 No.2
Let $f$ be a nonconstant meromorphic function of hyper-order strictly less than 1, and let $c\in\mathbb C\setminus\{0\}$ such that $f(z + c) \not\equiv f(z)$. We prove that if $f$ and its exact difference $\Delta_cf(z) = f(z + c) - f(z)$ share partially $0, \infty$ CM and share 1 IM, then $\Delta_cf = f$, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.
Luong, Thi Tuyet,Nguyen, Dang Tuyen,Pham, Duc Thoan Korean Mathematical Society 2018 대한수학회보 Vol.55 No.1
In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.