On 4 January 2026, VNUHCM鈥揢niversity of Science (Nguyen Van Cu Campus) held an institutional-level doctoral defence for doctoral researcher Tr岷 Quang Minh. A member of the 2022 Mathematical Analysis cohort, Minh conducted his research under the supervision of Associate Professor L媒 Kim H脿. His thesis, entitled ‘Applications of Nonlinear Analysis to the Study of Certain Partial Differential Equations’, explores the Hadamard well-posedness of various classes of nonlinear partial differential equations (PDEs) and systems.

The research rigorously clarifies fundamental mathematical properties, including the existence, uniqueness, and continuous dependence of solutions on initial data, while offering a detailed analysis of solution behaviour.

To address complex mathematical problems, the candidate systematically employed advanced tools from modern nonlinear analysis, including fixed-point theorems, monotone operator theory, and compactness methods. The mathematical models examined in the thesis arise from a range of applied sciences鈥攕uch as physics, classical mechanics, and biology鈥攈ighlighting the close interaction between abstract mathematical theory and practical application.

The research outcomes are synthesised from one manuscript and three peer-reviewed articles published in leading international journals, including Journal of Differential Equations, Calculus of Variations and Partial Differential Equations, and Nonlinear Analysis: Real World Applications.

The thesis is structured around three principal strands. The first focuses on nonlinear pseudo-parabolic systems, investigating existence, uniqueness, global behaviour, decay estimates, and finite-time blow-up phenomena. The second concerns nonlinear Navier鈥揕am茅 systems, analysing Hadamard well-posedness and specific solution properties. The third examines fourth-order nonlinear dispersive wave equations, with particular emphasis on equations containing exponential growth terms.

Collectively, these results make a significant contribution to the theory of nonlinear partial differential equations and extend the scope of nonlinear analytical methods in contemporary mathematics.

Beyond its current achievements, the thesis proposes several advanced directions for future research, including the study of global compact attractors and their finite dimensionality, as well as the incorporation of stochastic terms into existing models. These directions hold strong potential for both theoretical development and applied relevance.

Following the defence, the Committee Representative announced the Resolution, confirming that the thesis meets the highest scientific standards. In recognition of its originality and scholarly quality, the Examination Committee unanimously recommended the conferment of the degree of Doctor of Mathematics upon Tr岷 Quang Minh.

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The core subject, PM2.5 fine dust, consists of ultrafine particles (鈮�2.5 micrometres in diameter) capable of penetrating deep into the lungs and circulatory system, posing severe health risks that include respiratory, cardiovascular diseases, and even cancer. Studies have highlighted that high PM2.5 concentrations also reduce visibility and negatively impact the wider environment.

In large urban areas such as HCMC, fine dust levels are a growing concern, often spiking during transitional seasons or periods of heavy industrial and traffic activity. Consequently, the ability to accurately forecast and issue early warnings for PM2.5 concentration is considered vital, empowering both citizens and city authorities to implement protective measures for health and the environment.

The study focused on applying a combination of machine learning and deep learning algorithms to simulate and predict PM2.5 concentration specifically within the central area of HCMC. The analysis revealed that several of the tested Artificial Intelligence (AI) models demonstrated superior forecasting efficacy compared to traditional methods. This superiority was observed in both simulating current conditions and generating short-term forecasts (1, 3, 5, and 7 days).

Based on these successful trials, the Research Student proceeded to develop a practical PM2.5 forecasting application featuring an intuitive, user-friendly interface. The application provides projected data for various time points, converts the dust concentration into the national Vietnam Air Quality Index (VN_AQI), and offers actionable health recommendations to the public.

This research contributes significantly by establishing and comparatively testing various forecasting models, thereby identifying the high-accuracy algorithms best suited to the urban context of HCMC. The findings suggest that AI models, particularly artificial neural networks, show substantial potential as supportive tools for air quality monitoring, especially in environments where observational data remains constrained.

Future work on this project will focus on two key areas: (i) expanding the monitoring network to encompass a greater number of locations across HCMC and adjacent regions to improve spatial coverage and better map PM2.5 distribution; and (ii) integrating further data streams, such as those related to traffic, population density, industrial emissions, and seasonality, to enhance the robustness of long-term forecasts, especially during severe pollution episodes.

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On 23 September, at VNUHCM鈥揢niversity of Science, doctoral researcher L锚 D瓢啤ng V瓢啤ng (cohort 2018) successfully defended his doctoral thesis in Microbiology entitled聽鈥淧roduction of TEV and HRV3C Proteases in Bacillus subtilis for Removing Fusion Tags in Recombinant Protein Purification鈥�,聽under the supervision of Assoc. Prof. Nguy峄卬 膼峄ヽ Ho脿ng and Assoc. Prof. Phan Th峄� Ph瓢峄g Trang.

Tobacco Etch Virus (TEV) protease and Human Rhinovirus 3C (HRV3C) protease are widely used tools for removing fusion tags during recombinant protein purification. However, most studies to date have focused on expression in聽Escherichia coli, a system that poses limitations due to endotoxin contamination, resulting in additional processing costs and time.

To address this issue, the thesis utilised聽Bacillus subtilis聽鈥� a safe expression host free of endotoxins 鈥� to generate and purify three proteases (His-TEV, His-HRV3C, His-GST-HRV3C). The study also developed GFP-based fusion protein substrates containing specific cleavage sites, enabling assessment of protease activity and kinetic parameters. Results confirmed the potential application of these proteases in recombinant protein purification, offering a more cost-effective and efficient production method.

The dissertation successfully cloned and purified the three proteases from聽B. subtilis, achieving activity levels comparable to commercial enzymes expressed in聽E. coli. In addition, expression plasmids for GFP-based substrates containing TEV/HRV3C cleavage sites were constructed, enabling precise activity and kinetic characterisation. The findings demonstrate that the proteases can be effectively applied to target recombinant protein purification.

These results open new directions for developing safe and cost-effective methods for recombinant protein purification, with potential applications in industry, agriculture, and medicine. In the future, optimising expression conditions in聽B. subtilis聽may improve yields, advancing towards large-scale production as an alternative to聽E. coli-based systems.

The thesis demonstrates not only the researcher鈥檚 capacity for independent research and critical scientific thinking, but also the quality of doctoral training at VNUHCM鈥揢niversity of Science. This successful defence lays the foundation for further studies on optimising聽Bacillus subtilis-expressed enzymes and contributes to the training of highly qualified human resources in biology and biotechnology.

For the full abstract of the thesis, please refer to the official page:聽

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The research focuses on the existence and uniqueness of weak solutions for Robin鈥揇irichlet boundary value problems in nonlinear Kirchhoff鈥揅arrier wave equations containing viscous-elastic and discrete nonlocal terms. The Kirchhoff鈥揅arrier equation serves as a key mathematical model for describing nonlinear waves in elastic materials or complex dynamical systems, while the discrete nonlocal term makes the solution at a point dependent on values at multiple locations, increasing analytical complexity. The concept of weak solutions allows the study of such problems in broader function spaces, suitable for addressing challenging nonlinear problems. In particular, when the discrete nonlocal terms are expressed as integral sums of Kirchhoff鈥揅arrier terms, the thesis demonstrates convergence of the solution sequence (P_n) to the weak solution of the limiting problem (P_鈭�), enabling approximate solutions to complex problems and facilitating theoretical validation and numerical implementation.

The thesis achieves key results across five Robin鈥揇irichlet problems, focusing on two main directions. Firstly, for single nonlinear Kirchhoff鈥揅arrier wave equations with discrete nonlocal terms, it proves the existence and uniqueness of weak solutions and, in many cases, the convergence of solution sequences to the weak solution of the limiting problem. Secondly, for systems of nonlinear Kirchhoff鈥揅arrier wave equations with discrete nonlocal terms, the thesis establishes the existence and uniqueness of weak solutions (uⁿ,vⁿ), confirms convergence to the weak solution of the limiting system, and develops a high-order iterative algorithm for computational simulation of complex physical systems. These results are of substantial theoretical significance in pure mathematics and have potential applications in nonlinear wave modelling, material mechanics, and engineering simulations.

The thesis has been recognised internationally through publications in reputable Scopus- and SCIE-indexed journals, including Results in Nonlinear Analysis (Q3), Nonlinear Functional Analysis and Applications (Q3), Mathematica Bohemica (Q3), Transactions of the National Academy of Sciences of Azerbaijan (Q3), and Mathematical Modelling and Analysis (Q2).

Building on these results, further research directions include investigating dynamic properties of solutions (finite-time blow-up, decay, stability) and developing computational examples to illustrate and verify theoretical findings.

For the full abstract of the thesis, please refer to the official page:

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The research addresses rip currents 鈥� hazardous offshore flows often found along beaches and a major cause of drowning incidents. The dissertation developed a mathematical model capable of simulating and forecasting rip currents in the Bai Dai area (Cam Ranh, Khanh Hoa). The model provides insights into rip current mechanisms, locations, and associated risks, with significant implications for coastal safety and management.

During the study, Mr Th峄媙h enhanced the HYDIST鈥揜C model by incorporating a time-varying wave radiation stress module. The improved model was applied to assess rip current occurrence and behaviour under the combined effects of waves and tides. Model outputs were validated against field measurements at Bai Dai, showing strong agreement and confirming the model鈥檚 reliability.

The thesis highlights the strong influence of oceanographic conditions on rip current formation. Results showed that stronger waves produce faster currents and a greater number of rip channels. Seasonal variation was evident: up to 12 rip currents were identified during the northeast monsoon compared with only three during the southwest monsoon. However, the southwest season overlaps with peak tourism, increasing risks to beachgoers. Tidal variation was also significant: during ebb tide, rip current velocity rose by 0.2鈥�0.4 m/s and rip length extended 5鈥�10 metres further offshore, heightening hazard levels. The study also mapped specific rip current locations, distinguishing them from longshore currents and eddies.

The dissertation makes an important contribution by developing a Vietnamese-designed mathematical model for rip current forecasting, reducing reliance on international commercial tools. Beyond rip current prediction, the HYDIST鈥揜C model can be coupled with seabed morphology modules to improve real-time forecasting accuracy. The outcomes provide both a scientific basis for coastal research and practical solutions for community safety, including recommendations for warning systems and lifeguard arrangements. The model offers potential for wider application across 水果派AV解说鈥檚 beaches, especially those with high tourist activity.

For the full abstract of the thesis, please refer to the official page:

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On 19 August 2025 at VNUHCM-University of Science, doctoral researcher L锚 Anh Qu峄慶 successfully defended a doctoral dissertation at institutional level with the topic 鈥淪tudy on the preparation of chitosan鈥揼lucosamine derivatives through Maillard reaction induced by Co-60 gamma irradiation and evaluation of selected biological activities鈥�, under the supervision of Prof. Nguy峄卬 Qu峄慶 Hi岷縩.

The dissertation investigated the preparation of chitosan鈥揼lucosamine derivatives through the Maillard reaction catalysed by Co-60 gamma irradiation, with the objective of enhancing the physical properties and biological activities of chitosan. Chitosan, a biopolymer of considerable potential in food science due to antibacterial, antioxidant, and non-toxic characteristics, has been constrained by poor solubility and sensitivity to environmental conditions.

The Maillard reaction between chitosan and glucosamine under Co-60 gamma irradiation was chosen as an environmentally friendly modification method, avoiding chemical catalysts and preventing the formation of harmful by-products such as 5-HMF. The study optimised reaction conditions, including reactant ratios and irradiation dose, achieving a yield of approximately 80 per cent. The Maillard reaction product (MRP CTS-GA) underwent comprehensive evaluation covering antibacterial and antioxidant performance, solubility, biosafety, and food preservation capacity.

The developed process for producing MRP CTS-GA achieved a yield of ~80 per cent without harmful by-products. Optimal conditions were established as a CTS:GA ratio of 1.6%:0.4% with an irradiation dose of 25 kGy. The resulting product displayed complete solubility in water, no cytotoxicity towards L929 cells, and no acute oral toxicity in experimental mice. Strong antibacterial activity, particularly against E. coli, was confirmed through mechanisms involving interaction and disruption of bacterial cell membranes (FESEM evidence).

The product also demonstrated protective effects on lipids, proteins, and DNA in pork muscle cells against hydroxyl free radicals. Practical trials showed that a 1000 mg/L MRP CTS-GA solution extended the shelf-life of pork tenderloin by 6 hours at 28 掳C under aerobic conditions, 8 days at 5 掳C under aerobic conditions, and 14 days at 5 掳C under anaerobic conditions. These findings confirmed strong potential for application in the preservation of fresh food.

The dissertation highlights significant promise in food technology while advancing a sustainable research direction through the use of Co-60 gamma irradiation as a substitute for chemical agents, thereby enabling future industrial-scale application. This approach reflects contemporary trends in food industry development and contributes to reducing health risks for consumers. The defence proceeded in a serious academic atmosphere, with doctoral researcher L锚 Anh Qu峄慶 presenting the research clearly, addressing questions from reviewers convincingly, and receiving high recognition from the Examination Committee.

The Examination Committee engaging in discussion and academic review with doctoral researcher L锚 Anh Qu峄慶 during the defence session.

Kh谩nh T. _ Translated by PMN

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The dissertation focused on developing a gamma transmission (GT) measurement system using a ^137Cs radioactive source and an NaI(Tl) detector for determining the thickness of homogeneous material plates. To calibrate the system and optimise measurement accuracy, the candidate employed the Monte Carlo simulation programme MCNP version 6.1 to generate a comprehensive database covering various materials and thickness ranges.

A notable contribution of the dissertation was the proposed method of low-energy photon beam scanning to determine critical detector parameters, including crystal diameter and length, distance from the entrance window to the crystal, and the mass density of the reflective layer. These parameters enabled the simulation configuration to achieve high accuracy, with the full-energy peak efficiency simulation error remaining below 3.5% across the energy range from 31 keV to 1408 keV.

From the simulation data, a library of gamma transmission spectra was established for numerous materials (effective atomic numbers from 3 to 83) and sample thicknesses from 0.1 mm to 70 mm. The candidate defined the ratio R 鈥� the area ratio between the spectrum with a sample and without a sample 鈥� to determine material thickness by interpolating ln(R) values into a calibration curve derived from simulation analysis.

The method was verified through 162 practical measurements on four materials: graphite, aluminium, C45 steel, and copper. Results demonstrated an average relative deviation of only 0.52% between the measured and actual thickness values, with a maximum deviation of 2.17%. These figures confirm the reliability of the proposed measurement system and analytical model.

Beyond enhancing the measurement method, the dissertation introduced a model to estimate the measurable thickness range (RMT) corresponding to the desired accuracy (DA) within the GT technique. This tool serves as valuable support for users in selecting appropriate measurement parameters, reducing measurement time, and ensuring accurate results in non-destructive testing applications.

In terms of application potential, the measurement system and analytical tools developed in the study can be implemented directly in industrial production lines where material quality inspection is required. To broaden applicability, the candidate also identified future research directions, including thickness measurement for multilayer materials and calibration for complex geometries such as round tubes, curved surfaces, or inclined surfaces, which are common in manufacturing processes.

Building on these directions for further study, the doctoral defence brought the research to a successful conclusion. In a rigorous academic atmosphere, doctoral researcher Hu峄硁h 膼矛nh Ch瓢啤ng presented the work with clarity, addressed all review questions with well-founded responses, and received high commendation from the academic committee for the scientific contribution and practical relevance of the dissertation.

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Doctoral researcher Tr岷 Thanh H霉ng (cohort 2017) has successfully defended the doctoral thesis at the institution level in Biotechnology at VNUHCM-University of Science. The thesis, titled 鈥淎ntibacterial Activity and Biological Effects of Litsea cubeba Fruit Essential Oil and Constituents Against Helicobacter pylori,鈥� was supervised by Dr Tr岷 Trung Hi岷縰 and Dr L瓢啤ng Th峄� M峄� Ng芒n.

Delivering a comprehensive presentation to the assessment committee, the researcher outlined the study conducted on 25 essential oils extracted from 24 medicinal plants commonly used in traditional Vietnamese medicine. Among these, Litsea cubeba essential oil (听L. cubeba) demonstrated the strongest potential in inhibiting Helicobacter pylori 鈥� a bacterial strain widely recognised as a leading cause of peptic ulcers. Both the 聽L. cubeba and six key constituents (citronellol, citral, citronellal, linalool, 1,8-cineole, and limonene) exhibited strong antibacterial effects against H. pylori strain ATCC 43504 and five antibiotic-resistant clinical strains.

The research clarified several mechanisms of action through which the聽L. cubeba and these constituents affect H. pylori. These included inhibition of urease 鈥� a crucial enzyme enabling bacterial survival in the acidic gastric environment; prevention of biofilm formation; increased membrane permeability; morphological alterations; disruption of outer membrane integrity; and DNA fragmentation. Notably, 聽L. cubeba completely inhibited the adhesion of H. pylori to gastric mucosa (as tested on mice). These findings highlight promising potential for application in preventing H. pylori infection.

Among the tested constituents, citral displayed effectiveness comparable to the L. cubeba in inhibiting urease activity and biofilm formation, whereas citronellol demonstrated greater capacity to disrupt membrane integrity and damage DNA. Other compounds 鈥� including limonene, citronellal, linalool, and 1,8-cineole 鈥� also produced notable biological effects, although levels of activity varied depending on the specific mechanism examined.

With these results, the research provides a scientific foundation for applying L. cubeba in the prevention and supportive treatment of gastric ulcers associated with H. pylori. In addition, the findings may guide future investigations seeking natural substances capable of complementing or replacing antibiotics in the management of gastric conditions, particularly in light of growing antibiotic resistance.

_{锔� Detailed information on the dissertation has been published on of VNUHCM-University of Science.}

PMN_Photo credit: Doctoral researcher Tr岷 Thanh H霉ng

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Doctoral researcher 膼岷璾 Th峄� Hu岷� (class 2018) has successfully defended a doctoral thesis at the university level in the field of Algebra and Number Theory at VNUHCM-University of Science. The dissertation, entitled 鈥淪ymmetric Sets of Subgroups in Division Rings with Involution鈥�, was supervised by Prof. B霉i Xu芒n H岷, former Vice Dean of the Faculty of Mathematics and Computer Science.

This thesis represents an in-depth contribution to the field of pure mathematics, specifically in ring theory and group theory 鈥� two foundational branches of modern algebra. The research investigates 鈥渟ymmetric sets鈥� within specialised algebraic structures known as division rings with involution.

These structures can be understood as mathematical systems that possess not only the basic operations of addition and multiplication, but also a distinctive 鈥渞eflection鈥� operation 鈥� known as involution 鈥� that introduces internal symmetry into the structure.

The thesis offers new insights into the classification and internal structure of algebraic systems with involution. A noteworthy result is the generalisation of a classical theorem concerning the decomposition of algebraic structures, providing conditions under which a subgroup can reflect the global structure of the ring.

In particular, the thesis clarifies the criteria under which an algebraic system can be described by a quaternion ring 鈥� a four-dimensional algebra over a base field, widely applied in theoretical physics, computer graphics, and quantum mechanics.聽[*]

Another significant contribution is the establishment of a relationship between the symmetry of subgroups and the global structure of the ring. This holistic approach demonstrates that satisfying certain specific subgroup-level conditions may lead to defining characteristics of the entire system.

The research outcomes not only advance the theory of involution and division rings, but also open new directions for further investigation in abstract algebra. In the concluding chapter, the thesis proposes future research pathways, such as exploring other types of involution (e.g. second-type involution) and extending the analysis to less-studied classes of rings beyond the classical framework.

The successful defence marks a significant milestone in the academic journey of doctoral researcher 膼岷璾 Th峄� Hu岷� at VNUHCM-University of Science. Warmest congratulations on this achievement.

[*] Note: Applications of quaternion rings in physics, computer graphics, and related fields are general mathematical applications and are not direct contents of this dissertation.

_{锔� Detailed information on the dissertation has been published on of VNUHCM-University of Science.}

PMN_Photo credit: Prof. B霉i Xu芒n H岷

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