On June 13, 2025, the AARG research group of the Faculty of Mathematics and Statistics organized a regular scientific seminar. This is a regular activity of the group, and this time, the seminar dedicated space to student groups being guided by members of the AARG group. The student groups presented and shared research results in the fields of Numerical Analysis, Partial Differential Equations, Probability and Statistics, AI, etc. With the comments and sharing from the lecturers, the student groups had more opportunities to study, practice and open up many new research directions in the future. In addition, the seminar also expanded the scale of academic cooperation by welcoming the participation of students from Ho Chi Minh City University of Education, contributing to improving the academic quality and the spirit of exchange and cooperation between universities. Lecturers attending the seminar include: Mr. Chu Duc Khanh, Mr. Nguyen Thanh Nhan, Mr. Nguyen Huu Can, Ms. Tran Minh Phuong, Ms. Che Ngoc Ha, Mr. Le Truong Nhat, Mr. Nguyen Le Toan Nhat Linh, Mr. Tran Ngoc Thach, Mr. Nguyen Duc Tho, Ms. Tran Thi Son Thao.
* Typical topics presented:
1. Multistep methods for solving some real-life models
- Reporters: Huynh Nhut Truong, Dao Nhat Gia An
- Supervisors: Assoc. Prof. Dr. Tran Minh Phuong, Dr. Nguyen Huu Can
- Summary: Study of multi-step methods such as Adams–Bashforth and Adams–Moulton to solve the initial value problem for ordinary differential equations. Numerical simulations on the application are written in Python language applied on real models from physics, finance, medicine, military, ... to evaluate the effectiveness and application of the methods.
2. Gradient evaluation for logarithmic two-phase problems
- Reporter: Nguyen Tan Phuc
- Supervisors: Assoc. Prof. Dr. Tran Minh Phuong, Assoc. Prof. Dr. Nguyen Thanh Nhan
- Summary: Study on the regularity of weak solutions in generalized weighted Lorentz spaces through the gradient evaluation method. The results contribute to understanding the influence of input data and expanding applications in practical two-phase models.
3. Estimation of the CDF of a Sum of IID Random Variables
- Presenters: Lai Ngoc Bao Tram, Duong Thanh Tuyen, Nguyen Thi Thanh Hoa
- Supervisor: Assoc. Prof. Dr. Cao Xuan Phuong
- Summary: Propose a non-parametric method to estimate the cumulative distribution function of the sum of random variables with the same distribution. The technique is based on the inverse characteristic function and truncation of the integral domain, giving good convergence results and illustrated through simulation examples and the central limit theorem.
4. Convergence analysis of iterative models with optimal error bounds
- Presenter: Huynh Trung Hieu
- Supervisor: Assoc. Prof. Dr. Tran Minh Phuong, Assoc. Prof. Dr. Nguyen Thanh Nhan
- Summary: Analyze the convergence of two-step iterative methods in Banach space with the tool of Optimal Error Bounds (OEBs). The results provide necessary and sufficient conditions for convergence and allow for effective comparison between different iterative schemes.
5. Regularity for solutions to non-uniformly elliptic equations in generalized function spaces
- Presenter: Khuu Tan Dat
- Supervisor: Assoc. Prof. Dr. Tran Minh Phuong
- Summary: Construct global estimates for the solutions of elliptic equations based on the maximum operator technique and generalized function spaces such as Lorentz, Orlicz and Morrey extensions. The results make important contributions to the problem of heterogeneous materials.
6. Interval-valued time series prediction for Vietnam stock indicators using Ensemble LSTM networks
- Presenter: Phan Vu Hoang Giang
- Supervisor: Master. Che Ngoc Ha
- Summary: Applying LSTM networks combined with deep learning to predict interval time series for financial indices such as VN-Index. The model consists of two stages: processing simulated data and training LSTM to predict the central value and variability.
7, On the stability in the fractional order of space-time fractional reaction-diffusion equations
- Reporters: Ngo Viet Lam, Tran Quoc Cong, Tran Minh Hai
- Supervisor: Dr. Tran Ngoc Thach
- Summary: Studying the anomalous diffusion equation in a heterogeneous environment. The topic proves the continuity of the solution in the order of non-integer derivatives and proves the stability of the solution under appropriate assumptions. This is a modern approach in physical and biological modeling.
The academic atmosphere at the seminar was extremely exciting with many in-depth questions, suggesting new research directions. The students not only had the opportunity to rub shoulders with a real research environment but also demonstrated their confidence, analytical thinking and scientific presentation skills.
The Faculty of Mathematics - Statistics believes that academic forums like this will fuel the passion for research for students, opening up opportunities to develop into future scientists - dynamic, creative and integrated.
Here are some pictures of the report:
