• 한국공작기계학회논문집
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• 제12권2호
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• pp.71-78
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• 2003

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the variables are tightly coupled by the position, velocity, and acceleration level coordinates, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all variables, which are coupled by the constraints. The position velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The Perturbed constraint equations are then simultaneously solved for variations of all variables only in terms of the variations of the independent variables. Finally, the relationships between the variations of all variables and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent variables variations.

• 대한수학회논문집
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• 제13권2호
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• pp.377-384
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• 1998

Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

• 대한수학회논문집
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• 제18권2호
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• pp.375-383
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• 2003

Under some conditions on an array of rowwise independent random variables, Hu et at. (1998) obtained a complete convergence result for law of large numbers with rate {a$\_$n/, n $\geq$ 1} which is bounded away from zero. We investigate the general situation for rate {a$\_$n/, n $\geq$ 1) under similar conditions.

• 대한수학회보
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• 제37권2호
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• pp.255-263
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• 2000

Let ${X_{nk}}, u_n\; \leq \;k \leq \;u_n,\; n\; \geq\; 1}$ be an array of rowwise independent, but not necessarily identically distributed, random variables with $EX_{nk}$=0 for all k and n. In this paper, we povide a domination condition under which ${\sum^{u_n}}_=u_n\; S_{nk}/n^{1/p},\; 1\; \leq\; p\;<2$ converges completely to zero.

• 대한수학회보
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• 제60권3호
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• pp.687-703
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• 2023

In this paper, under some suitable conditions, we study the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables in upper expectation space. Some general results on necessary and sufficient conditions of the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables under sublinear expectations are established, which extend the corresponding ones in classic probability space to the case of sub-linear expectation space.

• 대한수학회보
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• 제35권4호
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• pp.769-775
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• 1998

In this paper, we obtain an analogue of law of the iterated logarithm for an array of independent, but not necessarily idetically distributed, random variables under some moment conditions of the array.

• 대한수학회보
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• 제34권4호
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• pp.617-626
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• 1997

This paper is concerned with the general strong law of large numbers for pairwise independent distributed random variables. Necessary and sufficient conditions for the SLLN are obtained.

• 대한가정학회지
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• 제25권1호
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• pp.105-119
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• 1987

The purpose of this study is to investigate the influences of demographic, personal and psychosocial variables on the wives' marital satisfaction in order to develop theories about the stablility of modern families. The data, collected from 490 mothers living in Seoul, is analyzed by statistical methods, such as Frequency Distribution, Pearson's Correlation, One-Way ANOVA, Scheffee-test and Multiple Regression Analysis. The major findings are as follows: 1) In my study, the Marital Satisfaction Scale consists of 7 dimensions; of which affective communication, problem-solving communication, and companionship are comparatively important variables. 2) Of demographic variables, wives' educational level is an influencing variable in 6 dimensions, and family monthly income, in general satisfaction. 3) Of personal variables, sex role attitude is a significantly influencing independent variable in satisfaction with children area and self actualization, variable in problem-solving communication area. 4) Of psychosocial variables, role enactment, role consensus, and role strain are proved to be influencing variables, but role salience is not. Also, role enactment is the most influencing independent variable in almost areas of marital satisfaction. 5) By given independent variables, variance is explained 30% of all. The implication that can be inferred from the above findings is that psychosocial variables are more important than demographic variables, and that personal variables such as androgyny, self-actualization should be encouraged to further research.

• 농촌지도와개발
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• 제8권2호
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• pp.201-208
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• 2001

The purpose of this study was to review the current studies on community attachment and its related variables to suggest directions for community attachment studies in Korea. Specific objectives of the study were to search the current studies on community attachment, to search for the significant variables related to community attachment, and to draw implications for community development in Korea. The major findings of the study were as follows; 1) Current studies on community attachment used individual characteristic variables such as length of residence in the community, age, size of population and density as major independent variables. 2) Studies on community attachment used community participation, social and cultural environment as major dependent variables, however, both independent variables and dependent variables were used interchangeably in many cases. 3) Recent studied on community attachment employed community economic and cultural variables, however, studies on community attachment in Korea was relatively limited in terms of quantity as well as quality. 4) Further research on community attachment should be conducted by utilizing various independent and dependent variables in various communities to increase the community attachment in rural and urban communities to further strengthen community development in Korea.

• 충청수학회지
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• 제22권1호
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• pp.1-5
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• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.