• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.65-79
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• 2007

An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson's rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.687-704
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• 2017

Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman transform of the convolution product can be expressed in terms of the product of the conditional FourierFeynman transforms of each function. Finally we establish change of scale formulas for the generalized analytic conditional Fourier-Feynman transform and the conditional convolution product. In this evaluation formulas and change of scale formulas we use multivariate normal distributions so that the orthonormalization process of projection vectors which are essential to establish the conditional expectations, can be removed in the existing conditional Fourier-Feynman transforms, conditional convolution products and change of scale formulas.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.437-456
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• 2003

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra $S(L^2_{a,b}[0,T])$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.793-809
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• 2008

The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the RK-eight stage seventh order limiting formulas. The parameters governing the arm model of a robot control problem have also been discussed through RK-eight stage seventh order limiting algorithm. The precised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. Based on the numerical results a thorough comparison is carried out between the numerical algorithms.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-672
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• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• Korean Journal of Agricultural Science
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• v.49 no.1
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• pp.77-91
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• 2022

North-South Korea economic integration is progressing slowly given the sensitive responses to changes in internal and external conditions. Nevertheless, advanced discussions focusing on North-South Korean economic cooperation should continue. Given this background, various studies of the economic effects of economic integration between North and South Korea have been conducted, but research on agricultural issues has been limited. The purpose of this study is to analyze the impact of the economic integration of South and North Korea on the agricultural market. In this study, a simultaneous equation model was constructed using a growth model. Solow's growth accounting approach is used to construct a model for estimating the macroeconomic effect of North-South economic integration. Also, the construction of growth accounting formulas subdivided into South and North Korea as well as agriculture and non-agricultural fields during the construction of the growth model is a major research achievement and differentiates it from previous studies. It is expected that the results of this study will serve as basic information for preparing policy measures to promote integration. However, there are many limitations when estimating the economic effects of North-South agricultural integration and obtaining policy implications given the insufficient available statistical data on agriculture in North Korea and the lack of related studies in the agricultural field. Therefore, it should be noted that there is an inherent problem in that the analysis results vary greatly depending on the assumptions set, as there is inevitably no choice but to rely on many and strong assumptions.

• 한국기계연구소 소보
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• s.18
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• pp.55-66
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• 1988

Many direct integration methods are used for numerical analyses of dynamic motion. In these methods, the governing equations of a dynamic system are integrated successively using a step-by-step numerical integration procedure. Time derivatives in the equations are generally approximated using difference formulas involving one or more increments of the time. Time increment has closely relationship with the accuracy of the motion analysis. In this paper, a 4th order Houbolt direct integration method is derived. For a spring-mass system, the motion of the system are analyzed from the 3rd order Houbolt and the 4th order Houbolt approaches respectively. Finally the paper proposes the optimal time-increment based on the accuracy of numerical analyses.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.409-420
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• 2001

In this paper we establish a Fubini theorem for various analytic Wiener and Feynman integrals. We then proceed to obtain several integration formulas as corollaries.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.591-601
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• 2023

In this note, we give a proof of the p-adic analogue of mild generalization of classical zeta functions by modifying Osipov's method. In addition, we obtain some identities for the p-adic integration, from which, some classical formulas for Euler numbers and polynomials have been deduced.

• Herbal Formula Science
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• v.30 no.3
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• pp.145-154
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• 2022

Objective : This study aims to study core herbs and formulas in Internal medicine on Spleen system, to enhance efficiency in teaching Internal medicine on Spleen system, Herbalogy, Formula science, and to increase integration of the courses. Methods : Frequency notion, which was generally used in previous studies, was used in this study along with network analysis. Results : Frequently used herbs, herbs with high centrality, frequently combined herbs and core formula were found in this study. The herb with the highest frequency and centrality was 'Citri Unshius Pericarpium', and 'Atractylodis Rhizoma Alba - Citri Unshius Pericarpium' was the most frequent herb combination. The results of network analysis showed a total of 5 herbal communities of combination. Conclusion : Core herbs were found based on the frequency notion, which is a traditional analysis method. Also, core herbs, herbal combinations, formulas that can that may be overlooked when using frequency notions were found by using network analysis. The results may lead to enhancing efficiency in the education of Internal medicine on Spleen system, Herbalogy, Formula science courses and the integration of courses.