• International Journal of Automotive Technology
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• v.6 no.4
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• pp.375-381
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• 2005

This paper presents linear algebraic equations in the form of recursive formula to compute elastokinematic characteristics of a suspension system. Conventional methods of elastokinematic analysis are based on nonlinear kinematic constrant equations and force equilibrium equations for constrained mechanical systems, which require complicated and time-consuming implicit computing methods to obtain the solution. The proposed linearized elastokinematic equations in the form of recursive formula are derived based on the assumption that the displacements of elastokinematic behavior of a constrained mechanical system under external forces are very small. The equations can be easily computerized in codes, and have the advantage of sharing the input data of existing general multi body dynamic analysis codes. The equations can be applied to any form of suspension once the type of kinematic joints and elastic components are identified. The validity of the method has been proved through the comparison of the results from established elastokinematic analysis software. Error estimation and analysis due to piecewise linear assumption are also discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.6
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• pp.1265-1272
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• 1988

Kinematic and dynamic equations of open-loop mechanical systems are derived using the velocity transformation. The velocities of a link are defined by the velocities of the previous link and relative velocities between the links. The velocities and angular velocities are expressed with joint velocities and 6*1 velocity transformation vector. Using the velocity relations, recursive formula are derived and compared to the previous results. The derived recursive formula are modified and applied to the dynamic simulation of a vehicle. The computational efficiency of the vehicle simulation with the derived recursive formula is much enhanced.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.363-370
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• 2002

We show that G(x) = $e^{(x}$(1-x))/ -1 is the exponential generating function for the labeled digraphs whose weak components are transitive tournaments and derive both a recursive formula and an explicit formula for the number of them on n vertices. Moreover, we investigate the asymptotic behavior for the coefficients of G(x) using Hayman's method.d.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.203-207
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• 2005

A loss system where two types of customers arrive in accordance with two independent Poisson processes is considered. An efficient recursive formula is developed for calculating the loss probability when the number of servers is large. Some practical examples regarding the performance evaluation of telecommunications networks are discussed.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.919-947
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• 2009

In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.1-15
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• 2017

Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.686-689
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• 2005

A numerical simulation method is developed to analyze the dynamic response of a cantilever switch, which is driven by electrostatic force and a basic component of electro-mechanical coupled system. First, point-charges model on conductor is proposed as a lumped parameter of electrical part. Then, this model is easily incorporated into a multi-body dynamics analysis algorithm, the generalized recursive dynamics formula previously developed by our research group. The resulting motion of a coupled overall system is formulated as a differential algebraic equation form including electrical and mechanical variables together. The equation is simultaneously solved in every time step. To implement this approach into the useful dynamics analysis tool, we used multibody dynamics software (RecurDyn) based on the generalized recursive formula using relative coordinate. The developed numerical simulation tool is evaluated by applying to many different driving condition and switch configuration. The final analysis model will be added to RecurDyn as a basic module for dynamics analysis of electro-mechanical coupled system.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.1
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• pp.101-111
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• 2001

Recursive formulas have been effective in solving the equations of motion for large scale constratined mechanical sys-tems. However, derivation of the formulas has been limited to individual terms in the equations of motion, such as veloci-ty, acceleration. and generalized forces. The recursive formulas are generalized in this paper. The velocity transformation method is employed to transform the equations of motion from Cartesian to the joint spaces. Computational structure of the equations of motion in the joint space is carefully examined to classify all necessary computational operations into sev-eral categories. The generalized recursive formula for each category is then developed and applied whenever such a cate-gory of computation is encountered. Since the velocity transformation method yields the equations of motion in a compact form and computational efficiency is achieved by generalized recursive formulas, the proposed method is not only easy to implement but is also efficient. A library of generalized recursive formulas is developed to implement a dynamic analysis algorithm using backward difference.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.397-397
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• 2000

There exists an increasing need of study for generalized consecutive k-out-of-n systems. This paper demonstrates that a recursive formula for multi-dimensional consecutive k-out-of-n systems can be systematically developed by means of conventional structure function analysis. By taking advantage of notational convenience, the formulae expressed in the same recursive fashion just as the one dimensional consecutive k-out-of-n system. With the aids of the recursive formulae, not only the exact reliability of the system, but also the optimal arrangement of components is obtainable in a straightforward way.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.665-674
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• 2015

Lack of a general matrix formula hampers implementation of the semi-partial correlation, also known as part correlation, to the higher-order coefficient. This is because the higher-order semi-partial correlation calculation using a recursive formula requires an enormous number of recursive calculations to obtain the correlation coefficients. To resolve this difficulty, we derive a general matrix formula of the semi-partial correlation for fast computation. The semi-partial correlations are then implemented on an R package ppcor along with the partial correlation. Owing to the general matrix formulas, users can readily calculate the coefficients of both partial and semi-partial correlations without computational burden. The package ppcor further provides users with the level of the statistical significance with its test statistic.