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Thu Hien Nguyen

Publications and source records attributed to Thu Hien Nguyen.

9 recordsLinked to original sources
arXiv2024

Matrix-weighted estimates beyond Calderón-Zygmund theory

We investigate matrix-weighted bounds for the sublinear non-kernel operators considered by F. Bernicot, D. Frey, and S. Petermichl. We extend their result to sublinear operators acting upon vector-valued functions. First, we dominate these operators by bilinear convex body sparse forms, adapting a recent general principle due to T. Hytönen. Then we use this domination to derive matrix-weighted bounds, adapting arguments of F. Nazarov, S. Petermichl, S. Treil, and A. Volberg. Our requirements on the weight are formulated in terms of two-exponent matrix Muckenhoupt conditions, which surprisingly exhibit a rich structure that is absent in the scalar case. Consequently, we deduce that our matrix-weighted bounds improve the ones that were recently obtained by A. Laukkarinen. The methods we use are flexible, which allows us to complement our results with a limited range extrapolation theorem for matrix weights, extending the results of P. Auscher and J. M. Martell, as well as M. Bownik and D. Cruz-Uribe.

math.CA↗
arXiv2022

Hutchinson's intervals and entire functions from the Laguerre-Pólya class

We find the intervals $[α, β(α)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{a_{k-2}a_{k}} \in [α, β(α)]$ for all $k \geq 2,$ then $f$ belongs to the Laguerre--Pólya class. For instance, from J.I.~Hutchinson's theorem, one can observe that $f$ belongs to the Laguerre--Pólya class (has only real zeros) when $q_k(f) \in [4, + \infty).$ We are interested in finding those intervals which are not subsets of $[4, + \infty).$

math.CV↗
arXiv2021

On the number of real zeros of real entire functions with a non-decreasing sequence of the second quotients of Taylor coefficients

For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k,$ $a_k >0,$ we define the sequence of the second quotients of Taylor coefficients $Q := \left( \frac{a_k^2}{a_{k-1}a_{k+1}} \right)_{k=1}^\infty$. We find new necessary conditions for a function with a non-decreasing sequence $Q$ to belong to the Laguerre--Pólya class of type I. We also estimate the possible number of nonreal zeros for a function with a non-decreasing sequence $Q.$

math.CV↗
arXiv2021

On the entire functions from the Laguerre-Pólya I class with non-monotonic second quotients of Taylor coefficients

We study the entire functions $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ with non-monotonic second quotients of Taylor coefficients, namely, such that $\frac{a_{2m-1}^2}{a_{2m-2}a_{2m}} = a>1$ and $\frac{a_{2m}^2}{a_{2m-1}a_{2m+1}} = b>1$ for all $m \in \mathbb{N}.$ We obtain necessary and sufficient conditions under which such functions belong to the Laguerre-Pólya I class.

math.CV↗
arXiv2020

On the entire functions from the Laguerre-Pólya I class having the increasing second quotients of Taylor coefficients

We prove that if $f(x) = \sum_{k=0}^\infty a_k x^k,$ $a_k >0, $ is an entire function such that the sequence $Q := \left( \frac{a_k^2}{a_{k-1}a_{k+1}} \right)_{k=1}^\infty$ is non-decreasing and $\frac{a_1^2}{a_{0}a_{2}} \geq 2\sqrt[3]{2},$ then all but a finite number of zeros of $f$ are real and simple. We also present a criterion in terms of the closest to zero roots for such a function to have only real zeros (in other words, for belonging to the Laguerre--Pólya class of type I) under additional assumption on the sequence $Q.$

math.CV↗
arXiv2020

On the closest to zero roots and the second quotients of Taylor coefficients of entire functions from the Laguerre-Pólya I class

For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ we show that if $f$ belongs to the Laguerre-Pólya class, and the quotients $q_k := \frac{a_{k-1}^2}{a_{k-2}a_k}, k=2, 3, \ldots $ satisfy the condition $q_2 \leq q_3,$ then $f$ has at least one zero in the segment $[-\frac{a_1}{a_2},0].$ We also give necessary conditions and sufficient conditions of the existence of such a zero in terms of the quotients $q_k$ for $k=2,3, 4.$

math.CV↗
arXiv2019

VAIS Hate Speech Detection System: A Deep Learning based Approach for System Combination

Nowadays, Social network sites (SNSs) such as Facebook, Twitter are common places where people show their opinions, sentiments and share information with others. However, some people use SNSs to post abuse and harassment threats in order to prevent other SNSs users from expressing themselves as well as seeking different opinions. To deal with this problem, SNSs have to use a lot of resources including people to clean the aforementioned content. In this paper, we propose a supervised learning model based on the ensemble method to solve the problem of detecting hate content on SNSs in order to make conversations on SNSs more effective. Our proposed model got the first place for public dashboard with 0.730 F1 macro-score and the third place with 0.584 F1 macro-score for private dashboard at the sixth international workshop on Vietnamese Language and Speech Processing 2019.

cs.CL↗
arXiv2019

On the necessary condition for entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre-Pólya class

For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ we show that $f$ does not belong to the Laguerre-Pólya class if the quotients $\frac{a_{n-1}^2}{a_{n-2}a_n}$ are increasing in $n$, and $c:= \lim\limits_{n\to \infty} \frac{a_{n-1}^2}{a_{n-2}a_n}$ is smaller than an absolute constant $q_\infty$ $(q_\infty\approx 3{.}2336) .$

math.CV↗