Journal Articles - Mathematic and Statistic - 2021

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Browsing Journal Articles - Mathematic and Statistic - 2021 by Title

  • Publication
    An automatic clustering for interval data using the genetic algorithm
    ( 2020)
    Tai Vovan
    ;
    Dinh Phamtoan
    ;
    Le Hoang Tuan
    ;
    Thao Nguyentrang
    This paper proposes an Automatic Clustering algorithm for Interval data using the Genetic algorithm (ACIG). In this algorithm, the overlapped distance between intervals is applied to determining the suitable number of clusters. Moreover, to optimize in clustering, we modify the Davies & Bouldin index, and to improve the crossover, mutation, and selection operators of the original genetic algorithm. The convergence of ACIG is theoretically proved and illustrated by the numerical examples. ACIG can be implemented effectively by the established Matlab procedure. Through the experiments on data sets with different characteristics, the proposed algorithm has shown the outstanding advantages in comparison to the existing ones. Recognizing the images by the proposed algorithm gives the potential in real applications of this research.
  • Publication
    Applying ARCH, GARCH, GARCH MLR Models to Forecast Volatility of Transportation Sector through Its Three Subscribe Modes Like Road, Water, Seas Ways: Empirical Case of Ho Chi Minh, Vietnam
    ( 2021)
    Vu Thi Kim Hanh
    The paper aims to empirically apply ARCH, GARCH (a,b) model to weight the average of the variance in historical data. (a,b) is order of model which this paper applies a = 1 and b = 1 in which b is order of GARCH, and a is order of ARCH which is square residual of the previous day. The objective of empirical Application is to forecast the volatility of GDP of Transportation Logistics (TL) through GDP of its three sub-sectors which are Road Transportation (RT), Inland Water Transportation (IWT), and Seas Transportation (ST). The author then has proposal models are MLR, ARCH MIR and GARCH (a,b) MLR to assess the dependence GDP of TL on GDP of its three sub-sectors which are RT, IWT, and ST. The first finding of study is ARCH and GARCH (a,b) which a = 1 and b = 1 can be empirically applied to predict the volatility of GDP of TL through GDP of RT, IWT, and ST. The second finding is that after tested MLR, ARCH MLR, and MLR GARCH (1,1), the output results show that almost values are not statistical significance, that means we cannot use MLR, ARCH MLR, and GARCH (1,1) MLR to assess the dependence of GDP of TL on GDP of its three sub-sectors which are RT, IWT, and ST.
  • Publication
    Convergence rate of a gradient projection method for solving variational inequalities
    ( 2021)
    Under the error bound assumption, we establish the linear convergence rate of a gradient projection method for solving co-coercive variational inequalities. Using this result, we unify and improve several results in variational inequalities, fixed point problems, and convex feasible problems. Numerical experiments are conducted to illustrate the theoretical results
  • Publication
    Distribution Estimation of a Sum Random Variable from Noisy Samples
    ( 2021)
    Cao Xuan Phuong
    ;
    Le Thi Hong Thuy
    Let X, Y be independent continuous univariate random variables with unknown distributions. Suppose we observe two independent random samples X′1,…,X′n and Y′1,…,Y′m from the distributions of X′=X+ζ and Y′=Y+η, respectively. Here ζ, η are random noises and have known distributions. This paper is devoted to an estimation for unknown cumulative distribution function (cdf) FX+Y of the sum X+Y on the basis of the samples. We suggest a nonparametric estimator of FX+Y and demonstrate its consistency with respect to the root mean squared error. Some upper and minimax lower bounds on convergence rate are derived when the cdf’s of X, Y belong to Sobolev classes and when the noises are Fourier-oscillating, supersmooth and ordinary smooth, respectively. Particularly, if the cdf’s of X, Y have the same smoothness degrees and n=m, our estimator is minimax optimal in order when the noises are Fourier-oscillating as well as supersmooth. A numerical example is also given to illustrate our method.
  • Publication
    Global Well posedness for Fractional Sobolev Galpern Type Equations
    ( 2021)
    Huy Tuan Nguyen
    ;
    Nguyen Anh Tuan
    ;
    Chao Yang
    This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to reveal the influence of the degree of the source nonlinearity on the well-posedness of the solution. By considering four different types of nonlinearities, we derive the global well-posedness of mild solutions to the problem corresponding to the four cases of the nonlinear source terms. For the advection source function case, we apply a nontrivial limit technique for singular integral and some appropriate choices of weighted Banach space to prove the global existence result. For the gradient nonlinearity as a local Lipschitzian, we use the Cauchy sequence technique to show that the solution either exists globally in time or blows up at finite time. For the polynomial form nonlinearity, by assuming the smallness of the initial data we derive the global well-posed results. And for the case of exponential nonlinearity in two-dimensional space, we derive the global well-posedness by additionally use of Orlicz space.
  • Publication
    Global Well posedness for Fractional Sobolev Galpern Type Equations
    ( 2021)
    Huy Tuan Nguyen
    ;
    Nguyen Anh Tuan
    ;
    Chao Yang
    This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to reveal the influence of the degree of the source nonlinearity on the well-posedness of the solution. By considering four different types of nonlinearities, we derive the global well-posedness of mild solutions to the problem corresponding to the four cases of the nonlinear source terms. For the advection source function case, we apply a nontrivial limit technique for singular integral and some appropriate choices of weighted Banach space to prove the global existence result. For the gradient nonlinearity as a local Lipschitzian, we use the Cauchy sequence technique to show that the solution either exists globally in time or blows up at finite time. For the polynomial form nonlinearity, by assuming the smallness of the initial data we derive the global well-posed results. And for the case of exponential nonlinearity in two-dimensional space, we derive the global well-posedness by additionally use of Orlicz space.
  • Publication
    Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors
    ( 2021)
    Cao Xuan Phuong
    ;
    Le Thi Hong Thuy
    ;
    Vo Nguyen Tuyet Doan
    Let X, Y, W, δ and ε be continuous univariate random variables defined on a probability space such that Y=X+ε and W=X+δ. Herein X, δ and ε are assumed to be mutually independent. The variables ε and δ are called classical and Berkson errors, respectively. Their distributions are known exactly. Suppose we only observe a random sample Y1,…,Yn from the distribution of Y. This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function FW of W based on the observations as well as on the distributions of ε, δ. An estimator for FW depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, δ and ε, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results.
  • Publication
    Novel semi-empirical formula and examination for fission barriers of super-heavy nuclei with Z ≥ 100
    ( 2021)
    N D Ly
    ;
    N N Duy
    ;
    K Y Chae
    ;
    N T T Quyen
    In this study, we developed a semi-empirical formula for predicting fission barriers of super-heavy nuclei (SHN), which have fissilities χ > 48.5428, based on a former formula proposed by Myers and Swiatecki [1999 Phys. Rev. C 60, 014 606]. We calculated fission barriers for isotopes with Z = 100–135 using our formula and the Lublin-Strasbourg Drop model. It was found that the macroscopic component of the fission barrier is less than 0.2 MeV, which is large enough to be considered with microscopic part for many SHN. These results were compared to each other and to those estimated using other approaches. Through evaluations of theoretical fission barriers, we found that there is a significant difference, up to a few MeV, between the results obtained from different models. In other words, recent fission barrier predictions are very uncertain. Finally, the results of this study are useful for estimating the spontaneous-fission lifetime and production cross sections of unknown super-heavy nuclei.
  • Publication
    Performance of Equilibrium Optimizer for the Traveling Salesman Problem
    ( 2021)
    Quyen Nguyen
    ;
    Minh-Phung Bui
    This paper presents a new method based on Equilibrium Optimizer (EO) algorithm that is inspired from the mass balance of a control volume for traveling salesman problem (TSP). For enhancing the efficiency of EO, the 2- opt movement algorithm is used to update the solution generated by EO. The efficiency of the proposed EO for the TSP problem has been compared with Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) on different instances consisting of the 14-city, 30-city, 48-city and 52-city. The calculated results show that for the large scale instances such as 48-city and 52-city, EO has found the better tour than PSO. In comparison with GA, EO has ability finding the best tour with the smaller mean and standard deviation. The comparisons with previous methods in literature have also demonstrated that EO has ability to search the better tour than other methods. Thus, the proposed EO can be a potential method for the TSP problem.
  • Publication
    Quy luật " mâu thuẫn" của phép biện chứng duy vật trong dạy học Toán ở các Trường Đại học
    ( 2021)
    Nguyễn Văn Lộc
    Bài báo phân tích quy luật “mâu thuẫn” của phép biện chứng duy vật trong dạy học Toán cho sinh viên các trường đại học. Nội dung quy luật "mâu thuẫn": Khái niệm mặt đối lập và khái niệm mâu thuẫn; Quá trình vận động của mâu thuẫn. Vận dụng quy luật "mẫu thuẫn trong dạy học toán: Quy luật "mâu thuẫn" trong dạy học biến đổi các hình thái thể hiện các đối tượng toán học; Quy luật "mâu thuẫn" trong chứng minh đẳng thức toán học; quy luật "mâu thuẫn" trong ánh xạ đẳng cấu của toán học...và quy luật "mâu thuẫn" và sự phát hiện chướng ngại trong giải toán.