Journal Articles - Mathematic and Statistic - 2020

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  • Publication
    ACTIONS, PROCESSES, OBJECTS, SCHEMAS (APOS) IN MATHEMATICS EDUCATION: A CASE STUDY FOR MATRIX OPERATIONS
    ( 2020)
    Phan Anh Tài
    Matrix algebra forms a core part of the first year mathematics curriculum at the Vietnam universities and colleges and is applicable to many other areas besides pure mathematics. Besides, the transfer of knowledge from a primarily procedural or algorithmic school approach to formal presentation of concepts is a priority for conceptualization of matrix algebra concepts. The mastery of matrix operations was a necessary step for graduate students in higher education. On the other hand, they lack adequate knowledge of advanced linear algebra, such as matrix operations, which are fundamentals in quantitative research method learning and students often find the course difficult. However, the difficulty may not be solely because of the content but also because of the transition from elementary to advanced mathematics itself. This paper presents an application of APOS (Actions, Process, Object and Schema) theory to teach matrix operations at universities. APOS theory focuses on models of what might be going on in the mind of an individual when he or she is trying to learn a mathematical concept and uses these models to design instructional materials and/or to evaluate student successes and failures in dealing with mathematical problem situations
  • Publication
    An Efficient Method for Mining Top-K Closed Sequential Patterns
    ( 2020)
    Thi-Thiet Pham
    ;
    Tung Do
    ;
    Anh Nguyen
    ;
    Bay Vo
    ;
    Tzung-Pei Hong
    The problem of exploiting Closed Sequential Patterns (CSPs) is an essential task in data mining, with many different applications. It is used to resolve the situations of huge databases or low minimum support (minsup) thresholds in mining sequential patterns. However, it is challenging and needs a lot of time to customize the minsup values for generating appropriate numbers of CSPs desired by users. To conquer this issue, the TSP algorithm for mining top-k CSPs was previously proposed, with k being a given parameter. The algorithm would return the k CSPs which have the highest support values in a database. However, its execution time and memory usage were high. In this paper, an algorithm named TKCS (Top-K Closed Sequences) is proposed to mine the top-k CSPs ef ciently. To improve the execution time and memory usage, it uses a vertical bitmap database to represent data. Besides, it adopts some useful strategies in the process of exploiting the top-k CSPs such as: always choosing the sequential patterns with the greatest support values for generating candidate patterns and storing top-k CSPs in an ascending order of the support values to increase the minsup value more quickly. The empirical results show that TKCS has better performance than TSP for discovering the top-k CSPs in terms of both runtime and memory usage.
  • Publication
    Deconvolution of ℙ(X<Y) with unknown error distributions
    ( 2020)
    Cao Xuan Phuong
    ;
    Le Thi Hong Thuy
    This paper is devoted to a nonparametric estimation of the probability θ:=P(X
  • Publication
    Deconvolution of ℙ(X<Y) with unknown error distributions
    ( 2020)
    Cao Xuan Phuong
    ;
    Le Thi Hong Thuy
    This paper is devoted to a nonparametric estimation of the probability θ : = ℙ ( X < Y ) , where X, Y are continuous univariate random variables of interest and observed with additional random errors. We focus on the case where the distributions of the random errors are unknown but symmetric around zero and can be estimated from some additional samples. Using deconvolution techniques, we propose an estimator of θ which depends on a regularization parameter. We then establish upper and lower bounds on convergence rate of the estimator under mean squared error when error densities are assumed to be supersmooth.
  • Publication
    Một đồng nhất thức trên đa thức đối xứng
    ( 2020)
    Lê Văn Vĩnh
    Trong bài báo này, chúng tôi đưa ra và chứng minh một đồng nhất thức trên đa thức đối xứng. Để nhận được đồng nhất thức này, chúng tôi sử dụng lý thuyết nội suy, cụ thể là công thức nội suy Lagrange. Trong phần chứng minh đồng nhất thức, chúng tôi đưa ra hai cách chứng minh khác nhau. Cách chứng minh thứ hai sẽ là bước khởi đầu cho những nghiên cứu xa hơn của chúng tôi liên quan đến các đồng nhất thức trên đa thức đối xứng.
  • Publication
    Thuật toán "Tựa Newton" cho bài toán quy hoạch toàn phương lồi
    ( 2020)
    Đinh Tiến Liêm
    Bài báo này trình bày ngắn gọn những kiến thức cơ bản của quy hoạch phi tuyến, tập trung chủ yếu vào thuật toán “Tựa Newton”, và áp dụng thuật toán này để giải bài toán quy hoạch toàn phương lồi. Đây là thuật toán “khá tốt” để từ đó ta viết chương trình cho máy vi tính đi tìm nghiệm (xấp xỉ) của bài toán tối ưu toàn phương lồi. Với các ví dụ minh họa trình bày trong bài báo, chúng ta sẽ thấy được các nghiệm xấp xỉ cho từng bước giải, và hơn nữa ta sẽ thấy được điểm mạnh của thuật toán này.