• Journal of Astronomy and Space Sciences
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• v.9 no.1
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• pp.11-29
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• 1992

In 1963, Toomre built up classes of mass models for the highly flattened galaxies which have free parameters n, $a_n$ and $C_n$. In order to keep the universal dimension, we adopt parameters $b_n({C_n}^2={a_n}^{2n}+^2{b_n}^2/(n-1)!)$ insteal of $C_n$. Series of the normalized Toomre's mass models (G = $V_{max}$ =$R_{max}$ = 1, n = 1 to 7) are derived and the normalized parameters $a_n$ and $b_n$ are determined by the iteration method. Replacing parameters $a_n$ and $b_n$ to ${a_n}^l(=a_nr_{max})$ and ${b_n}^l(=b_n\cdotV_{max}/r_{max})$, we can get the generalization of Toomre's mass model.

• Structural Engineering and Mechanics
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• v.15 no.2
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• pp.249-267
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• 2003

In this study, circular plates subjected to general type of loads and supported on a two-parameter elastic foundation are analysed. The stiffness, elastic bedding and soil shear effect matrices of a fully compatible ring sector plate element, developed by Saygun (1974), are obtained numerically assuming variable thickness of the element. Ring sector soil finite element is also defined to determine the deflection of the soil surface outside the domain of the plate in order to establish the interaction between the plate and the soil. According to Vallabhan and Das (1991) the elastic bedding (C) and shear parameters ($C_T$) of the foundation are expressed depending on the elastic constants ($E_s$, $V_s$) and the thickness of compressible soil layer ($H_s$) and they are calculated with a suitable iterative procedure. Using ring sector elements presented in this paper, permits the generalization of the loading and the boundary conditions of the soil outside the plate.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.51-57
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• 2000

The aim of this research is to provide twenty five integrals involving hypergeometric function in the form of a single integral. Fifty two interesting integrals follow as special cases of our main findings. These results are obtained with the help of generalized Watson's theorem on the sum of a $_3$F$_2$ recently obtained by Lavoie, Grondin and Rathie. The integrals given in this paper are simple, interesting and easily established, and they may be useful.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.469-480
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• 2019

A generalized tiling is defined as a generalization of the properties of tiling a region of ${\mathbb{Z}}^2$ with dominoes, and comprises tiling with rhombus and any other tilings that admits height functions which can be ordered into a distributive lattice. By using properties of the distributive lattice, we prove that the Markov chain consisting of moving from one height function to the next by a flip is fast mixing and the mixing time ${\tau}({\epsilon})$ is given by ${\tau}({\epsilon}){\leq}(kmn)^3(mn\;{\ln}\;k+{\ln}\;{\epsilon}^{-1})$, where mn is the area of the grid ${\Gamma}$ that is a k-regular polycell. This result generalizes the result of the authors (T-tetromino tiling Markov chain is fast mixing, Theor. Comp. Sci. (2018)) and improves on the mixing time obtained by using coupling arguments by N. Destainville and by M. Luby, D. Randall, A. Sinclair.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.15-27
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• 2008

We present and discuss an algorithm for the numerical solution of initial value problems of the form $D_*^\alpha$y(t) = f(t, y(t)), y(0) = y0, where $D_*^\alpha$y is the derivative of y of order $\alpha$ in the sense of Caputo and 0<${\alpha}{\leq}1$. The algorithm is based on the fractional Euler's method which can be seen as a generalization of the classical Euler's method. Numerical examples are given and the results show that the present algorithm is very effective and convenient.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.12
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• pp.19-29
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• 1995

The basic technology for a production system represented by design, machining, assembly, and inspection, is machining technology such as CNC machine tools. etc. Direct Numerical Control, that effeciently manages NC programs is developing into Distributed Numerical Control that increases the utilization of the machining cell. It has the ability of monitoring and control, in real time, for CNC and periperial equipment. In this study, we develop a Distributed Numerical Control system that has real time and multitasking operation capability for the machining cell with various CNC's. With the consideration of economy, generalization and extension, the system is interfaced with CNC machine tools and periperial device using RS-485 network and RS-232C communication methods.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.559-581
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• 2013

This paper is motivated by a 2001 paper of Choie and Kim and a 2006 paper of Bump and Choie. The paper of Choie and Kim extends an earlier result of Bol for elliptic modular forms to the setting of Siegel and Jacobi forms. The paper of Bump and Choie provides a representation theoretic interpretation of the phenomenon, and shows how a natural generalization of Choie and Kim's result on Siegel modular forms follows from a natural conjecture regarding ($g$, K)-modules. In this paper, it is shown that the conjecture of Bump and Choie follows from work of Boe. A second proof which is along the lines of the proof given by Bump and Choie in the genus 2 case is also included, as is a similar treatment of the result of Choie and Kim on Jacobi forms.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.203-219
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• 2018

This paper is devoted to the study of strongly ${\alpha}-semicommutative$ rings, a generalization of strongly semicommutative and ${\alpha}-rigid$ rings. Although the n-by-n upper triangular matrix ring over any ring with identity is not strongly ${\bar{\alpha}}-semicommutative$ for $n{\geq}2$, we show that a special subring of the upper triangular matrix ring over a reduced ring is strongly ${\bar{\alpha}}-semicommutative$ under some additional conditions. Moreover, it is shown that if R is strongly ${\alpha}-semicommutative$ with ${\alpha}(1)=1$ and S is a domain, then the Dorroh extension D of R by S is strongly ${\bar{\alpha}}-semicommutative$.

• The Journal of Korean Society for School & Community Health Education
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• v.7
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• pp.59-74
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• 2006

Objectives: The purpose of this research is to find out the relations among children‘s perceived competences, expressive disposition of interpersonal relations, and parents’ social support, which influence their self image. Methods: The samples to achieve the purpose of this research are composed of 294 students in G elementary school, OO city, Kyounggido, the number of male students in the fifth year being 71, female 77, and male students in the sixth year being 73, female 73. After having excluded the data of 9 students among them due to their insincere reply, this research analyzed the data of 285 students by using SPSS WIN Ver. 13.0. Results: First, after having observed the average difference stemming from each method, this research found that there is no sexual difference in parents‘ social support. (p<.05). In children's perceived competences, female students is higher only in active aspect than male students, but there is no meaningful difference in other aspects. In expressive disposition of interpersonal relations, the showing-off and narcissistic expressive tendency of female students is higher than that of male students, but there is no meaningful difference in other aspects. Second, this research found out the meaningful static correlation among parents' social support, children's perceived competences, and expressive disposition of interpersonal relations. Parents' emotional, appreciative, and informative support has the static correlation with all the other aspects of children's perceived competences, and material support has the static correlation with children's academic, active, and general self-esteeming sense (p<.05, p<.01). Third, this research observed, of all the aspects of parents' social support and expressive disposition of interpersonal relations, what variable is affecting children's perceived competences, and found that parents' appreciative support, showing-off and narcissistic expressive tendency, material support, and informative support, each in order, has meaningful influence (p<.05, p<.01). This fact shows that the further the children recognize these supports of their parents', the more affirmatively they recognize their competences, and the further the children of showing-off and narcissistic expressive disposion recognize their competences. Conclusions: First, sampling was conducted of the fifth and sixth male and female students of OO elementary school, and so the result of this research has the applicative limitation in the generalization for all the elementary school students. Therefore this research suggests further researches by broad sampling for the more advanced generalization. Second, this research only observed the differnce of perception deriving from gender and school year, but the parents' social support levels perceived by children reveal many differnces according to children's characters or their families' variables. Therefore this research suggests subsequent researches on various variables.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.831-845
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• 2014

In this paper, we obtain new generating functions involving families of pairs of inverse functions by using a generalization of the Srivastava's theorem [H. M. Srivastava, Some generalizations of Carlitz's theorem, Pacific J. Math. 85 (1979), 471-477] obtained by Tremblay and Fug$\grave{e}$ere [Generating functions related to pairs of inverse functions, Transform methods and special functions, Varna '96, Bulgarian Acad. Sci., Sofia (1998), 484-495]. Special cases are given. These can be seen as generalizations of the generalized Bernoulli polynomials and the generalized degenerate Bernoulli polynomials.