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Nguyen Van Thin

Publications and source records attributed to Nguyen Van Thin.

16 recordsLinked to original sources
arXiv2026

Normality Criteria for Differential Monomials and the Sharpness of Lappan-type Theorems

A fundamental result of Lappan [Comment. Math. Helv. \textbf{49} (1974), 492-495.] states that a meromorphic function $f$ in the unit disk $\mathbb{D}$ is normal if and only if its spherical derivative is bounded on a five-point subset $E \subset \mathbb{C}$. In this paper, we establish new normality criteria that bridge this classical result with contemporary trends in value distribution theory. We demonstrate that the cardinality of the set $E$ can be reduced from five to as few as three, provided that the spherical derivatives of the function and its successive derivatives $f, f', \dots, f^{(k-1)}$ are bounded on the pre-image of $E$. This shift reveals that analytic data from higher-order derivatives can effectively compensate for a reduction in geometric information from the target set. Furthermore, we extend the Pang-Zalcman theorem to a general class of differential monomials $M[f]$. We prove that if $(M[f])^{\#}$ is bounded on the set of $a$-points ($a \neq 0$), the family $\mathcal{F}$ is normal, provided the degree $d_M$ satisfies a specific sharp threshold relative to the weight $D_M$ and order $k$. These results offer a refined perspective on the natural boundaries of normality and generalize several established findings in the field.

math.CV↗
arXiv2024

Results on normal harmonic and $φ$-normal harmonic mappings

In this paper, we study the concepts of normal functions and $φ$-normal functions in the framework of planar harmonic mappings. We establish the harmonic mapping counterpart of the well-known Zalcman-Pang lemma and as a consequence, we prove that a harmonic mapping whose spherical derivative is bounded away from zero is normal. Furthermore, we introduce the concept of the extended spherical derivative for harmonic mappings and obtain several sufficient conditions for a harmonic mapping to be $φ$-normal.

math.CV↗
arXiv2024

Weighted Yosida Mappings of Several Complex Variables

Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let $φ: [0,\infty)\rightarrow (0,\infty)$ be positive function such that $$γ_r=\sup\limits_{r\leq a<b}\left|(φ(a)-φ(b))/(a-b)\right|\leq C,~r\in (0,\infty),$$ for some $C\in (0,1],$ and $\lim_{r\rightarrow\infty}γ_r=0.$ A holomorphic mapping $f:\mathbb{C}^{m}\rightarrow M$ is said to be a weighted Yosida mapping if for any $z,~ξ\in\mathbb{C}^{m}$ with $\|ξ\|=1,$ the quantity $φ(\|z\|)E_{M}(f(z), df(z)(ξ))$ remains bounded above, where $df(z)$ is the map from $T_z(\mathbb{C}^{m})$ to $T_{f(z)}(M)$ induced by $f.$ We present several criteria of holomorphic mappings belonging to the class of all weighted Yosida mappings.

math.CV↗
arXiv2024

SGD method for entropy error function with smoothing l0 regularization for neural networks

The entropy error function has been widely used in neural networks. Nevertheless, the network training based on this error function generally leads to a slow convergence rate, and can easily be trapped in a local minimum or even with the incorrect saturation problem in practice. In fact, there are many results based on entropy error function in neural network and its applications. However, the theory of such an algorithm and its convergence have not been fully studied so far. To tackle the issue, we propose a novel entropy function with smoothing l0 regularization for feed-forward neural networks. Using real-world datasets, we performed an empirical evaluation to demonstrate that the newly conceived algorithm allows us to substantially improve the prediction performance of the considered neural networks. More importantly, the experimental results also show that our proposed function brings in more precise classifications, compared to well-founded baselines. Our work is novel as it enables neural networks to learn effectively, producing more accurate predictions compared to state-of-the-art algorithms. In this respect, we expect that the algorithm will contribute to existing studies in the field, advancing research in Machine Learning and Deep Learning.

cs.LG↗
arXiv2023

On existence of multiple normalized solutions to a class of elliptic problems in whole $\mathbb{R}^N$ via penalization method

In this paper we study the existence of multiple normalized solutions to the following class of elliptic problems \begin{align*} \left\{ \begin{aligned} &-ε^2Δu+V(x)u=λu+f(u), \quad \quad \hbox{in }\mathbb{R}^N, &\int_{\mathbb{R}^{N}}|u|^{2}dx=a^{2}ε^N, \end{aligned} \right. \end{align*} where $a,ε>0$, $λ\in \mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier, $V:\mathbb{R}^N \to [0,\infty)$ is a continuous function, and $f$ is a continuous function with $L^2$-subcritical growth. It is proved that the number of normalized solutions is related to the topological richness of the set where the potential $V$ attains its minimum value. In the proof of our main result, we apply minimization techniques, Lusternik-Schnirelmann category and the penalization method due to del Pino and Felmer.

math.AP↗
arXiv2020

Normal family of meromorphic mappings and Big Picard's theorem

In this paper, we prove some results in normal family of meromorphic mappings intersecting with moving hypersurfaces. As some applications, we establish some results for normal mapping and extension of holomorphic mappings. A our result is strongly extended the Montel's normal criterion in the case several variables which is due to Tu in [Proc. Amer. Math. Soc. 127,1039-1049, 1999]. Our results are also strongly extended the results of Tu-Li in [Sci. China Ser. A. 48, 355-364, 2005] and [J. Math. Anal. Appl. 342, 629-638, 2006].

math.CV↗
arXiv2020

Schmidt's subspace theorem for moving hypersurface targets in subgeneral position with index in algebraic variety

Recently, Xie-Cao [15] obtained a Second Main Theorem for moving hypersurfaces located in subgeneral position with index which is extended the result of Ru [11]. By using some methods due to Son-Tan-Thin [13], Quang [9] and Xie-Cao [15], we shall give a Schmidt's Subspace Theorem for moving hypersurface targets in subgeneral position with index intersecting algebraic variety. Our result is a extension the Schmidt's Subspace Theorem due to Son-Tan-Thin [13] and Quang [9].

math.NT↗
arXiv2018

Difference analogue of second main theorems for meromorphic mapping into algebraic variety

In this paper, we prove some difference analogue of second main theorems of meromorphic mapping from Cm into an algebraic variety V intersecting a finite set of fixed hypersurfaces in subgeneral position. As an application, we prove a result on algebraically degenerate of holomorphic curves intersecting hypersurfaces and difference analogue of Picard's theorem on holomorphic curves. Furthermore, we obtain a second main theorem of meromorphic mappings intersecting hypersurfaces in N-subgeneral position for Veronese embedding in Pn(C) and a uniqueness theorem sharing hypersurfaces.

math.CV↗
arXiv2017

A second main theorem for holomorphic curve intersecting hypersurfaces

In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem for holomorphic curve of authors before.

math.CV↗
arXiv2017

Schmidt's subspace theorem for moving hypersurface targets

It was discovered that there is a formal analogy between Nevanlinna theory and Diophantine approximation. Via Vojta's dictionary, the Second Main Theorem in Nevanlinna theory corresponds to Schmidt's Subspace Theorem in Diophantine approximation. Recently, Cherry, Dethloff, and Tan (arXiv:1503.08801v2 [math.CV]) obtained a Second Main Theorem for moving hypersurfaces intersecting projective varieites. In this paper, we shall give the counterpart of their Second Main Theorem in Diophantine approximation.

math.NT↗
arXiv2017

On Nevanlinna - Cartan theory for holomorphic curves with Tsuji characteristics

In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex projective variety with the level of truncation. As applications of the second main theorems for an angle, we will discuss the uniqueness problem of holomorphic curves in an angle instead of the whole complex plane. Detail, we establish a result for uniqueness problem of holomorphic curve by inverse image of a hypersurface. In my knowledge, this is the first result for uniqueness problem of holomorphic curve by inverse image of hypersurface on angular domain. On complex plane, we obtain a uniqueness result for holomorphic curves, it is improvement of some results before [5, 10] in this trend.

math.CV↗
arXiv2017

A uniqueness problem for entire functions related to Bruck's conjecture

In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Bruck. The above uniqueness theorem is an improvement of a problem studied by L. Z. Yang et. al [14]. However, our method differs the method of L. Z. Yang et. al [14]. We mainly use normal family theory and combine it with Nevanlinna theory instead of using only the Nevanlinna theory as in [14].

math.CV↗