Journal Articles - Mathematic and Statistic - 2021
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PublicationQuy luật " mâu thuẫn" của phép biện chứng duy vật trong dạy học Toán ở các Trường Đại học( 2021)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.
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PublicationApplying 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)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.
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PublicationNovel semi-empirical formula and examination for fission barriers of super-heavy nuclei with Z ≥ 100( 2021)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.
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PublicationDistribution Estimation of a Sum Random Variable from Noisy Samples( 2021)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.
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PublicationGlobal Well posedness for Fractional Sobolev Galpern Type Equations( 2021)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.