Determine the source term of a two-dimensional heat equation

Let $\Omega$ be a two-dimensional heat conduction body. We consider the problem of determining the heat source $F(x,t)=\varphi(t)f(x,y)$ with $\varphi$ be given inexactly and $f$ be unknown. The problem is nonlinear and ill-posed. By a specific form of Fourier transforms, we shall show that the heat source is determined uniquely by the minimum boundary condition and the temperature distribution in $\Omega$ at the initial time $t=0$ and at the final time $t=1$. Using the methods of Tikhonov's regularization and truncated integration, we construct the regularized solutions. Numerical part is given.Comment: 18 page

Determination of the body force of a two-dimensional isotropic elastic body

Let $\Omega$ represent a two$-$dimensional isotropic elastic body. We consider the problem of determining the body force $F$ whose form $\phi(t)(f_1(x),f_2(x))$ with $\phi$ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov's regularization and truncated integration, we construct a regularized solution from the data given inexactly and derive the explicitly error estimate. Numerical part is givenComment: 23 page

Determine the spacial term of a two-dimensional heat source

We consider the problem of determining a pair of functions $(u,f)$ satisfying the heat equation $u_t -\Delta u =\varphi(t)f (x,y)$, where $(x,y)\in \Omega=(0,1)\times (0,1)$ and the function $\varphi$ is given. The problem is ill-posed. Under a slight condition on $\varphi$, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term $f$ from non-smooth data. The error estimate and numerical experiments are given.Comment: 18 page

ViCGCN: Graph Convolutional Network with Contextualized Language Models for Social Media Mining in Vietnamese

Social media processing is a fundamental task in natural language processing with numerous applications. As Vietnamese social media and information science have grown rapidly, the necessity of information-based mining on Vietnamese social media has become crucial. However, state-of-the-art research faces several significant drawbacks, including imbalanced data and noisy data on social media platforms. Imbalanced and noisy are two essential issues that need to be addressed in Vietnamese social media texts. Graph Convolutional Networks can address the problems of imbalanced and noisy data in text classification on social media by taking advantage of the graph structure of the data. This study presents a novel approach based on contextualized language model (PhoBERT) and graph-based method (Graph Convolutional Networks). In particular, the proposed approach, ViCGCN, jointly trained the power of Contextualized embeddings with the ability of Graph Convolutional Networks, GCN, to capture more syntactic and semantic dependencies to address those drawbacks. Extensive experiments on various Vietnamese benchmark datasets were conducted to verify our approach. The observation shows that applying GCN to BERTology models as the final layer significantly improves performance. Moreover, the experiments demonstrate that ViCGCN outperforms 13 powerful baseline models, including BERTology models, fusion BERTology and GCN models, other baselines, and SOTA on three benchmark social media datasets. Our proposed ViCGCN approach demonstrates a significant improvement of up to 6.21%, 4.61%, and 2.63% over the best Contextualized Language Models, including multilingual and monolingual, on three benchmark datasets, UIT-VSMEC, UIT-ViCTSD, and UIT-VSFC, respectively. Additionally, our integrated model ViCGCN achieves the best performance compared to other BERTology integrated with GCN models

The process of developing professional capacity for teachers

The primary aim of Vietnam's new educational program is to enhance students' knowledge and skills through practical learning experiences, enabling them to tackle academic and real-world challenges. However, teachers in Dong Thap province face limitations in their professional competencies. Thus, this study aims to address these issues by examining different models for developing teachers' professional competencies. 1,116 participants participated in this study (258 managers and 868 teachers from high schools and preschools) who completed two questionnaires assessing their professional competence and the perceived importance of professional development. The findings reveal that teachers lack subject knowledge, interdisciplinary understanding   and skills in teaching design and assessment. Both school managers and teachers recognize the necessity of professional competence development. A three-step process for enhancing teachers' professional competence is proposed for implementing professional development activities based on these findings

Developing the professional capacity of preschool teachers through pedagogical training activities

The primary purpose of educational programs is to enhance students’ knowledge and skills through pedagogical training activities. However, preschool teachers in Vietnam face limitations in their professional capacity. Thus, this study aimed to address issues by evaluating the level of implementation of pedagogical training activities for preschool education students. The study used a scale for students' pedagogical practice activities to gather quantitative data from 629 participants (managers, lecturers and preschool teachers) in Dong Thap province in Vietnam to assess the extent of implementation of pedagogical training activities for preschool education students. The results showed that preschool teachers may not possess the essential knowledge of pedagogical practices. Pedagogical training uses conventional work-and-activity techniques despite the fact that it prioritizes innovation. Moreover, all school managers, teachers and students recognized the necessity of developing the professional capacity of preschool teachers. These findings illustrate the critical need for revitalizing educational approaches that are consistent with Vietnam's developing preschool teacher professional development context. The present study proposes some measures to innovate pedagogical practice activities in order to meet the requirements for developing the professional capacity of preschool teachers in Vietnam. Such initiatives hold promise for reshaping the educational landscape and fostering a culture of continuous improvement within the primary education sector of Vietnam

Ice formation in the Arctic during summer: false-bottoms

The only source of ice formation in the Arctic during summer is a layer of ice called false-bottoms between an under-ice melt pond and the underlying ocean. Of interest is to give a mathematical model in order to determine the simultaneous growth and ablation of false-bottoms, which is governed by both of heat fluxes and salt fluxes. In one dimension, this problem may be considered mathematically as a two-phase Stefan problem with two free boundaries. Our main result is to prove the existence and uniqueness of the solution from the initial condition.Comment: 22 page

Some preliminary results of paleo-tsunami study in the coastal region of the Nghe An province, Vietnam

In the coastal region of the Nghe An province, the geomorphology is characterized by appearances of fields of arca granosa with placura placenta and hills of placura placenta with arca granosa, namely: The hills of placura placenta with the arca granosa shells in the Quynh Van and Nghi Tien communes; the fields of arca granosa with the placura placenta: deep-seated in the Quynh Nghia, Dien Chau and along the Nghi Yen coast  which have age of 4,500 - 4,300 yrs.; The appearance of the placura placenta-arca granosa shell’s fields and hills which do not originate from either marine transgression in the Holocene epoch, tectonic movement or artificiality; Our results suggest that there were three tsunami events occurring in the past during the periods of 4,500 - 4,300; 4,100 - 3,900 and 900 - 600 yrs., respectively in the region

Applied bioinformatics tools for analysis of Microrna-214 expression and prediction of its potential targets genes in Nasopharyngeal carcinoma

miRNA (microRNA) are short RNA molecules in length from 20 to 24 nucleotides that have been shown to play an important role in regulating gene expression in many different types of human cancer. Meanwhile, miRNA-214 is one of the known miRNAs involved in the formation of nasopharyngeal carcinoma (NPC) through overexpression that promotes proliferation and development of cancer cells. However, in Vietnam, the study of miR-214 related to NPC has not been conducted yet. With the aims to develop the further studies of miR-214 on NPC in Vietnamese patients, in this initial study, we conducted the analysis of miR-214 expression in previous publications, as well as the prediction of miR-214 potential target genes, which involved in many cellular pathways. Here we applied bioinformatics tools to predict miRNAs and their targets, and discuss the role of miR-214 in the context of human cancers. As the results, miR-214 acted as the oncogenic roles in NPC, relevanted to many pathways, such as cell proliferation, apoptosis, metastasis and invasion through the its target genes LTF, Bim, Bax, LINC0086, etc. In conclusion, the use of computional approaches facilitate the further experimental validation of miRNAs in general, particularly miR-214, in Vietnamese NPC patients