https://science.thanglong.edu.vn/index.php/volc <p>About Mathematics and Mathematical Sciences (Vol. C), published in English language.</p> Thang Long University en-US Thang Long Journal of Science: Mathematics and Mathematical Sciences 3030-4911 https://science.thanglong.edu.vn/index.php/volc/article/view/219 In this survey paper we give an overview on some aspects of singularities of algebraic plane curves over an algebraically closed field of arbitrary characteristic. We review, in particular, classical results and recent developments on invariants of plane curve singularities. Hong Duc Nguyen Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2025-03-12 2025-03-12 4 1 https://science.thanglong.edu.vn/index.php/volc/article/view/222 In this paper, we investigate shared value problems related to a meromorphic function of hyper order less than one and its linear differencedifferential polynomial. In general, under certain conditions of sharing values of the meromorphic functions and their difference-differential polynomial, a given meromorphic function must satisfy a difference-differential equation. Furthermore, we also study the order of meromorphic solutions of some classes of difference-differential equations. Thin Van Nguyen Assoc Phương Hà Trần Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2025-03-02 2025-03-02 4 1 https://science.thanglong.edu.vn/index.php/volc/article/view/227 In this paper, we introduce a new algorithm for solving strongly monotone variational inequality problem, where the constraint set is the solution set of the split variational inequality and fixed point problem. Our method uses dynamic step sizes selected based on information of the previous step, which gives strong convergence result without the prior knowledge of the given bounded linear operator’s norm. In addition, using our method, we do not require any information of the Lipschitz and strongly monotone constants of the mappings. Several corollaries of our main result are also presented. Finally, a numerical example has been given to illustrate the effectiveness of our proposed algorithm. Việt Anh Trần Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2025-04-02 2025-04-02 4 1 https://science.thanglong.edu.vn/index.php/volc/article/view/231 In this paper, we prove that a non-autonomous stochastic differential equation generates a continuous random dynamical system. The flow then possesses a random pullback attractor under thedissipativity condition(s) of the drift and smallness of diffusion part. Doctor Hong Phan Thanh Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Sciences 2025-05-25 2025-05-25 4 1 https://science.thanglong.edu.vn/index.php/volc/article/view/235 This article is an attempt to investigate the possibility to be injective of the Singer transfer TrM s : F2 ⊗GLs P(H∗Vs ⊗ M∗) → Exts A (Σ-sM, F2) for M being the A -modules F2 = Hå∗S0 or Hå∗RP∞. The existence of a positive stem critical element of Exts,t A (Hå∗RP∞, F2) in the image of the transfer TrRP∞ s is equivalent to the existence of a positive stem critical element of Exts+1,t+1 A (F2, F2) in the image of the transfer Trs+1. If the existences happen, then TrRP∞ s and Trs+1 are not injective. We show that the critical element P h ä2 is not in the image of the fourth transfer, TrRP∞ 4 : F2 ⊗GL4 P(H∗V4 ⊗ Hå∗RP∞)t-4 → Ext4 A,t(Hå∗RP∞, F2). Singer’s conjecture is still open, as we have not known any critical element, which is in the image of the transfer. Prof Huu Viet Hung Nguyen Copyright (c) 2025 2025-05-12 2025-05-12 4 1 https://science.thanglong.edu.vn/index.php/volc/article/view/228 Accurate credit risk assessment is crucial for the stability and growth of peer-to-peer (P2P) lending platforms. This study investigates the effectiveness of machine learning models in predicting loan defaults using historical Lending Club data. We evaluate logistic regression, decision tree, and random forest, employing feature engineering techniques like one-hot and weight of evidence encoding. Model performance is assessed using K-fold cross-validation and metrics such as accuracy and AUC. To enhance model interpretability, we utilize explainable AI techniques like LIME and SHAP, enabling lenders and borrowers to understand the factors driving loan defaults. Our findings demonstrate that while complex models offer higher predictive accuracy, simpler models like logistic regression with WoE encoding provide a suitable balance between accuracy and interpretability, fostering trust and responsible lending within the P2P lending ecosystem. Thuy Tien Dinh Thi Tra My Nguyen Copyright (c) 2025 Thang Long Journal of Science: Mathematics and Mathematical Sciences 4 1