arXiv subjects

Nguyen Thi Dung

Publications and source records attributed to Nguyen Thi Dung.

8 recordsLinked to original sources

arXiv2026

Degenerate four-wave mixing in a CPT-symmetric coupler with intermodal dispersion

Four-wave mixing provides a simple setting in which dispersion, nonlinearity, and non-Hermiticity compete to select resonant energy-transfer channels. We study degenerate four-wave mixing in a Kerr dual-core coupler with balanced gain and loss and frequency-dependent intercore coupling. The dispersive coupling changes the symmetry from conventional $\mathcal{PT}$ symmetry to a combined $\mathcal{CPT}$ symmetry and reshapes the two-branch linear spectrum. We determine the unbroken-$\mathcal{CPT}$ domain and classify the branch configurations that can satisfy the degenerate phase-matching condition. In the parameter ranges examined, three resonant channels persist over broad regions, whereas a same-branch channel appears only close to the symmetry-breaking threshold. In this near-threshold regime, a single pump can simultaneously satisfy two distinct nonzero sideband resonances. Direct pulse simulations confirm the predicted resonances and reveal secondary-wave generation and multifrequency cascades near eigenmode coalescence. A reduced three-wave model captures the initial dynamics away from the exceptional point but loses accuracy as the modal basis becomes ill-conditioned. These results show how dispersive coupling reorganizes resonances, group-velocity mismatch, and nonlinear energy exchange in a non-Hermitian wave system, and they identify the exceptional-point region as a regime where a few-mode description can break down.

physics.optics↗

arXiv2026

Stability and Interaction Dynamics of Solitons in Spatially Engineered High-Order Nonlinear Media

We study spatial solitons and their interaction dynamics in nonlinear optical media with spatially engineered refractive index and competing cubic-quintic (CQ) nonlinear profiles, using the variational approximation (VA), the hybrid variational approximation (HVA), and direct numerical simulations. The model was implemented in a symmetric step-index planar dielectric waveguide with a core exhibiting competing CQ nonlinearity and cladding layers possessing only a cubic nonlinear response. For stationary states, the Gaussian VA predicts two types of $N(μ)$ characteristic curves, where $N$ is soliton norm and $μ$ is propagation constant, separated by a boundary surface in parameter space, and numerical calculations reveal the same two types. Below this surface, the VA agrees with the numerical results mainly at low powers, while pronounced deviations in the profile and stability appear at high powers. Above the surface, the variational and numerical curves retain the same qualitative form, and a super-Gaussian ansatz accurately describes the high-power flat-top solitons. Soliton collisions produce four post-interaction regimes: Oscillation, Molecular, Splitting, and Breakup. The HVA reproduces the first three over a broad power range, including collisions involving flat-top solitons. Its main limitation arises in the Breakup regime, where strong radiation leaves the guiding region and cannot be represented by the adopted HVA ansatz. Nevertheless, for solitons associated with the second type of characteristic curves, the HVA still captures the breakup dynamics qualitatively. Thus, the HVA provides an efficient description of complex soliton interactions at a substantially lower computational cost than direct numerical simulations.

nlin.PS↗

arXiv2026

Frobenius Number Of Almost Symmetric Numerical Generalized Almost Arithmetic Semigroups

Let a, k, h, c be positive integers and d a non zero integer. Recall that a numerical generalized almost arithmetic semigroup S is a semigroup minimally generated by relatively prime positive integers a, ha + d, ha + 2d, . . . , ha + kd, c, that is its embedding dimension is k + 2. In a previous work, the authors described the Ap{é}ry set and a Gr{ö}bner basis of the ideal defining S under one technical assumption, the complete version will be published in a forthcoming paper. In this paper we continue with this assumption and we describe the Pseudo Frobenius set. As a consequence we give a complete description of S when it is symmetric or almost symmetric as well as generalize and extend the previous results of Ignacio Garc{í}a-Marco, J. L. Ram{í}rez Alfons{í}n and O. J. R{ø}dseth; we also find a quadratic formula for its Frobenius number that generalizes some results of J.C. Rosales, and P.A. Garc{í}a-S{á}nchez. Moreover, for given numbers a, d, k, h, c, a simple algorithm allows us to determine if S is almost symmetric or not and furthermore to find its type and Frobenius number.

math.AC↗

arXiv2025

In silico study on the cytotoxicity against Hela cancer cells of xanthones bioactive compounds from Garcinia cowa: QSAR based on Graph Deep Learning, Network Pharmacology, and Molecular Docking

Cancer is recognized as a complex group of diseases, contributing to the highest global mortality rates, with increasing prevalence and a trend toward affecting younger populations. It is characterized by uncontrolled proliferation of abnormal cells, invasion of adjacent tissues, and metastasis to distant organs. Garcinia cowa, a traditional medicinal plant widely used in Southeast Asia, including Vietnam, is employed to treat fever, cough, indigestion, as a laxative, and for parasitic diseases. Numerous xanthone compounds isolated from this species exhibit a broad spectrum of biological activities, with some showing promise as anti cancer and antimalarial agents. Network pharmacology analysis successfully identified key bioactive compounds Rubraxanthone, Garcinone D, Norcowanin, Cowanol, and Cowaxanthone alongside their primary protein targets (TNF, CTNNB1, SRC, NFKB1, and MTOR), providing critical insights into the molecular mechanisms underlying their anti-cancer effects. The Graph Attention Network algorithm demonstrated superior predictive performance, achieving an R2 of 0.98 and an RMSE of 0.02 after data augmentation, highlighting its accuracy in predicting pIC50 values for xanthone based compounds. Additionally, molecular docking revealed MTOR as a potential target for inducing cytotoxicity in HeLa cancer cells from Garcinia cowa.

q-bio.MN↗

arXiv2024

Factor-critical graphs and dstab, astab for an edge ideal

Let $G$ be a simple, connected non bipartite graph and let $I_G$ be the edge idealof $G$. In our previous work we showed that L. Lovász's theorem on ear decompositions offactor-critical graphs and the canonical decomposition of a graph given by Edmonds and Gallai are basic tools for the irreducible decomposition of $I^{k}_G$. In this paper we use some tools from graph theory, mainly Withney's theorem on ear decompositions of 2-edge connected graphs in order to introduce a new method to make a graph factor-critical. We can describe the set $\cup_ {k=1}^{\infty}{\rm Ass} (I^{k}_G)$ in terms of some subsets of $G$. We give explicit formulas for the numbers astab$(I_G)$ and dstab$(I_G)$, which are, respectively, the smallest number $k$ such that ${\rm Ass} (I^{k}_G)= {\rm Ass} (I^{k+i}_G)$ for all $i\geq 0$ and the smallest number $k$ such that the maximal ideal belongs to ${\rm Ass}(I^{k}_G)$. We also give very simple upper bounds for astab$(I_G)$ and dstab$(I_G)$.

math.AC↗

arXiv2015

Sequentially Cohen-Macaulay Rees algebras

This paper studies the question of when the Rees algebras associated to arbitrary filtration of ideals are sequentially Cohen-Macaulay. Although this problem has been already investigated by N. T. Cuong, S. Goto and H. L. Truong, their situation is quite a bit of restricted, so we are eager to try the generalization of their results.

math.AC↗

arXiv2015

Topics on sequentially Cohen-Macaulay modules

In this paper, we study the two different topics related to sequentially Cohen-Macaulay modules. The questions are when the sequentially Cohen-Macaulay property preserve the localization and the module-finite extension of rings.

math.AC↗

arXiv2007

Top local cohomology and the catenaricity of the unmixed support of a finitely generated module

Let $(R,\m)$ be a Noetherian local ring and $M$ a finitely generated $R-$module with $\dim M=d.$ This paper is concerned with the following property for the top local cohomology module $H^d_\m(M)$: $$\Ann (0:_{H^d_\m(M)}\p)=\p\ \text{for all prime ideals} \p\supseteq\Ann H^d_\m(M).$$ In this paper we will show that this property is equivalent to the catenaricity of the unmixed support $\Usupp M$ of $M$ which is defined by $\Usupp M=\Supp M/U_M(0)$, where $U_M(0)$ is the largest submodule of $M$ of dimension less than $d.$ Some characterizations of this property in terms of system of parameters as well as the relation between the unmixed supports of $M$ and of the $\m$-adic completion $\hat M$ are given.

math.AC↗