HPU2 Journal of Science: Natural Sciences and Technology

On the spectral radius of bipartite graphs with bounded partite sets

Phi-Dung Hoang — Tue, 30 Dec 2025 00:00:00 +0700

This paper investigates the relationship between spectral graph theory and graph properties, specifically focusing on the spectral radius, which is the largest eigenvalue of the adjacency matrix of a graph. Our problem is finding sharp upper bounds for the spectral radius of bipartite graphs with given bounde vertex sets. We first review existing inequalities, noting and discuss their limitations, noting particularly that some, like Hong's inequality, are not always sharp for all graph types. Our primary contribution is an elementary and direct approach to solving an optimization problem: finding a bipartite graph with a bounded number of vertices that maximizes its spectral radius. We prove that for any bipartite graph with bounded vertex sets of \(n_1\) and \(n_2\), the spectral radius \(\rho(G)\) is bounded by \(\sqrt{n_1n_2}\). We demonstrate that this inequality is sharp, with equality holding exclusively for the complete bipartite graph \(K_{n_1,n_2}\).

A finiteness theorem for ends of weighted manifolds with a weighted Poincaré inequality

Tuan-Dung Ha — Tue, 30 Dec 2025 00:00:00 +0700

In this paper, we study complete weighted manifolds that satisfy a weighted Poincaré inequality, with the associated weight function assumed to be non-negative throughout the manifold. Our main focus is to study the geometric consequences of such an inequality on the global structure of the manifold, particularly at infinity. Specifically, we prove that such a manifold has only finitely many \(\phi\)-nonparabolic ends, provided that the Bakry-Émery Ricci curvature is bounded from below outside a compact subset with respect to the weight function. This result generalizes several existing theorems in the theory of Riemannian geometry and offers valuable insight into the interplay between curvature conditions and the topology of ends.

The synthesis of \(\text{TiO}_2\) nanosheets and their outperformance in the photocatalytic degradation of methylene blue

Tue, 30 Dec 2025 00:00:00 +0700

TiO₂ nanocrystals have been deployed as photocatalysts for the degradation of organic pollutants in wastewater due to their high chemical resistance and environmental friendliness. Because the reaction takes place on the catalyst surface, the crystal phase and the morphology of TiO₂ nanocrystals are important factors governing the catalytic activity. Herein, we prepared TiO₂ nanosheets by hydrothermal treatment of titanium (IV) butoxide in the presence of hydrofluoric acid. The crystallinity and the morphology of TiO₂ nanosheets were characterized by X-ray diffraction and scanning electron microscope (SEM), respectively. The photocatalytic activity of TiO₂ nanosheets was compared with that of commercially available TiO₂ nanoparticles (Degussa P25) using the degradation reaction of methylene blue (MB) in water under ultraviolet light at 365 nm. The X-ray diffraction and SEM characterizations indicated that anatase TiO₂ nanosheets with enriched {001} facets were successfully obtained. The MB degradation assay revealed that the decolorization of MB on TiO₂ nanosheets was 1.85 times faster than that on the TiO₂ nanoparticles counterpart. The synthesis and excellent photocatalytic activity of TiO₂ nanosheets demonstrated in this paper may promote the development of catalysts for removing organic pollutants in wastewater.

The sequential Cohen-Macaulayness of idealizations

Van-Loc Phan , Minh-Son Doan — Tue, 30 Dec 2025 00:00:00 +0700

Let (\(R\), m) be a Noetherian local ring and \(M\) a finitely generated \(R\)-module. The idealization \(R\ltimes M\), introduced by M. Nagata, has become a useful construction in commutative algebra. Recent work has characterized the approximate Cohen–Macaulayness of such idealizations via the length function associated with a good system of parameters. Motivated by these developments, we investigate via the sequential Cohen–Macaulayness of the idealization \(R\ltimes M\). We provide a characterization in terms of the length function with respect to a good system of parameters of the form \((x_1,0),\ldots,(x_r,0)\), where \(r=\dim R\). Furthermore, we provide equivalent conditions for \(R\ltimes M\) to be sequentially Cohen–Macaulay, expressed in terms of the length functions of both \(R\) and \(M\), and their respective dimension filtrations.

An identification problem governed by nonlinear fractional mobile-immobile equation, Part II: Stability and Regularity

Van-Tuan Tran, Thi-Thu Tran , Van-Dac Nguyen — Tue, 30 Dec 2025 00:00:00 +0700

This paper continues our recent work in [1], in which we investigated the existence and uniqueness of solutions for the inverse problem (IP): Seek the unknown term \(z\), along with the state \(u\) obeying the system

\[\nu_1{\partial_t}u+\nu_2\partial_t^\alpha u - \Delta u = z(x)h(t) + f(t,u), \text{ in }\Omega ,t \in (0,T], \,\tag{1}\]

\[u = 0\text{ on }\partial \Omega ,t \ge 0,\,\tag{2}\]

\[u(\cdot ,0)\text{ = }\xi \text{ in }\Omega ,\,\tag{3}\]

and the terminal measurement

\[u(x,T)=\varphi (u)(x), x \in \Omega . \,\tag{4}\]

In this setting, \(\Omega\subset\mathbb{R}^d\) with \(d \ge 1\) denotes a bounded domain whose boundary \(\partial\Omega\) is smooth. Motivated by considerations arising from numerical analysis, the primary aim of this work is to establish a set of sufficient conditions on the functions \(h\), \(f\), and \(\varphi\) that guarantee both the continuous dependence of solutions on the data and the regularity in time of the solution pair \((u,z)\) for the inverse problem (IP).

Study on content of hydrophilic silica from rice husk in reinforced deproteinized natural rubber materials

Tue, 30 Dec 2025 00:00:00 +0700

The environment is an area of global concern that the whole world is concerned about, especially issues such as global warming and the depletion of natural resources. Scientists have made efforts to overcome these negative impacts. Not out of this trend, the polymer material science is one of the major fields that emits a lot of greenhouse gases. In this study, we focus on improving the mechanical properties, include: Hardness, tensile strength, elongation.... There are two components: first, the matrix part is made from rubber. The disadvantage of synthetic rubber is that it is difficult to biodegrade, but natural rubber is available. In addition, the filler mainly used is carbon black, a product derived from petroleum. This filler is mainly derived from petroleum, it is not a finite resource to be used sustainably, so an alternative filler is needed. In this study, we use deproteinized natural rubber (DPNR) instead of synthetic rubber for the purpose of being environmentally friendly and increasing the service life and silica filler, which is thermally inert and derived from the ash after combustion of rice husk. The current research is called hydrophilic silica from rice husk (Hi-Silica). The Hi-Silica ratio was examined from about 0 to 70 parts per hundred rubber (phr). The results showed that Hi-Silica at 40 phr of rubber gave the best durability through mechanical property tests and has stability at high temperatures.

The efficient and mild synthesis of phenacyl bromide via bromination using N-bromosuccinimide catalyzed by brønsted acidic ionic liquid under ultrasound irradiation

Cong-Thang Duong, Minh-Duong Ho, Que-Tran Tran Thi, Xuan-Thi Luu Thi — Tue, 30 Dec 2025 00:00:00 +0700

Phenacyl bromide is an important substrate for the synthesis of various biologically active heterocyclic compounds and industrial chemicals. Synthesis of phenacyl bromide via the bromination of the alpha carbon in acetophenone by using N-bromosuccinimide has been carried out in the presence of 1-(4-sulfobutyl)-3-methylimidazolium hydrogen sulfate (BAIL). Under the ultrasound irradiation, the yield of phenacyl bromide and 2,2-dibromo-2-phenylethanone has been achieved at 84% and 11%, respectively, in a very short time, ten minutes. Additionally, 1-(4-sulfobutyl)-3-methylimidazolium hydrogen sulfate was recovered and reused five times, without significantly reducing the yield of phenacyl bromide. This work has developed an approach that not only improves reaction time and product selectivity but also aligns with 'green chemistry' principles by employing a recoverable and reusable catalyst.

Genetic diversity of Shan tea (Camellia sinensis var. assamica) from Cao Son Commune, Lao Cai province using RAPD-PCR

Tue, 30 Dec 2025 00:00:00 +0700

Shan tea (Camellia sinensis var. assamica) represents a valuable indigenous genetic resource predominantly distributed in the mountainous regions of Northwest Vietnam, especially in Lao Cai province. To assess the genetic diversity of these tea populations, this study employed the Random Amplified Polymorphic DNA (RAPD)-PCR technique using six specific primers to analyze 16 leaf samples collected from Muong Khuong district. A total of 38 DNA bands were amplified, of which 32 were polymorphic, demonstrating the high effectiveness of the RAPD primer. The genetic similarity coefficient ranged from 0.62 to 0.92, suggesting a relatively wide genetic variability among the Shan tea individuals. Cluster analysis grouped the samples into four major genotypic clusters. These findings provide important molecular data to support broader conservation planning and guide selective breeding programs aimed at improving tea quality and climate resilience in indigenous Shan tea populations.

Quadratic programming and quadratically constrained quadratic programming: theory, algorithms, and applications

Kim-Thuy Dinh Thi — Tue, 30 Dec 2025 00:00:00 +0700

This survey provides a systematic review of quadratic programming (QP) and quadratically constrained quadratic programming (QCQP) problems. The paper reviews mathematical formulations and problem taxonomies based on convexity properties, surveys optimality conditions through Lagrangian theory and KKT conditions, and examines foundational work by Markowitz, Wolfe, and Frank-Wolfe and key algorithmic developments. Four major algorithmic paradigms are examined: (1) active-set methods with finite convergence properties, (2) polynomial-time interior-point methods, (3) modern operator-splitting approaches including OSQP and ADMM, and (4) semidefinite programming relaxations for non-convex cases, with review of their theoretical properties and convergence guarantees. The methodology is illustrated through case studies in facility location optimization and production planning that demonstrate the application of KKT conditions and Lagrange multiplier theory, while examples from portfolio optimization to model predictive control illustrate broader applicability. This work connects classical optimization theory with contemporary algorithmic approaches, providing insights for researchers and guidance for practitioners in operations research, engineering, and applied mathematics.

Phase transitions and thermodynamic properties of the reissner-nordström black hole in (n + 1) dimensional spacetime

Van-Quyet Hoang, Khanh-Linh Nguyen, Thi-Trang Nguyen — Tue, 30 Dec 2025 00:00:00 +0700

This study investigates the thermodynamic properties and phase transitions of charged Reissner-Nordström Anti-de Sitter black holes in (n + 1) -dimensional spacetime. The analysis is conducted within the framework of extended phase space thermodynamics, where the cosmological constant is treated as a dynamic pressure. We first derived analytical expressions for key thermodynamic quantities, then performed numerical calculations to explore the phase structure. Our analysis confirms a critical point and a first-order, liquid-gas-like phase transition analogous to the van der Waals system. A key finding is that the spatial dimension n significantly influences the critical parameters; black holes in higher dimensions exhibit higher temperatures and pressures in corresponding states. This work extends the well-known four-dimensional analogy to arbitrary dimensions, offering a more generalized perspective on black hole thermodynamics that is crucial for testing the universality of these phenomena and for higher-dimensional models in fundamental physics.