• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.96-104
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• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• Korean Journal of Food Science and Technology
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• v.34 no.6
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• pp.1062-1066
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• 2002

Low field NMR was employed to discriminate the geographical origin of sesame seeds from Sudan, China, and Korea. Sudan sesame seeds had the lowest contents of moisture and crude fat. Chemical components of Korean and Chinese sesame seeds were similar, whereas relaxation times $(T_1-IR,\;T_1-SR)$ measeured through spin-lattice relaxation pluse techniques using 20 MHz NMR showed significant difference (p0.05). Canonical discriminant analysis could be used to identify the habitat of sesame seeds with over 90% accuracy of NMR results. Non-destructive and fast NMR techniques can be applied to classify Korean sesame seeds from those of other origins.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.393-400
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• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)

• Journal of Microbiology and Biotechnology
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• v.17 no.10
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• pp.1645-1654
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• 2007

The total methylotrophic population associated with rice plants from different cultivars was enumerated at three different stages: vegetative, flowering, and harvesting. The bacterial population in the leaf, rhizosphere soil, endophytic in the stem and roots, and epiphytic in the florets and grains were determined from four rice cultivars, Il-mi, Nam-pyeoung, O-dae, and Dong-jin, sampled from three different field sites. The methylotrophic bacteria isolated on AMS media containing 0.5% methanol as the sole carbon source uniformly showed three distinct morphologies, which were recorded as separate groups and their distribution among the various samples was determined using the ecophysiological index. The growth stage at the time of sampling had a more significant effect on the methylotrophic population and their distribution than the field site or cultivar. A similar effect was also observed for the PPFMs, where their population in different plant parts increased from V10 to R4 and then decreased towards stage R9. A canonical discriminant analysis of the PPFM population from different parts of rice showed clear variations among the cultivars, sampled sites, and growth stages, although the variations were more prominent among the growth stages.

• Journal of Astronomy and Space Sciences
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• v.31 no.4
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• pp.285-294
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• 2014

The uneven mass distribution of the Moon highly perturbs the lunar spacecrafts. This uneven mass distribution leads to peculiar dynamical features of the lunar orbiters. The critical inclination is the value of inclination which keeps the deviation of the argument of pericentre from the initial values to be zero. Considerable investigations have been performed for critical inclination when the gravity field is assumed to be symmetric around the equator, namely for oblate gravity field to which Earth's satellites are most likely to be subjected. But in the case of a lunar orbiter, the gravity field of mass distribution is rather asymmetric, that is, sectorial, and tesseral, harmonic coefficients are big enough so they can't be neglected. In the present work, the effects of the first sectorial and tesseral harmonic coefficients in addition to the first zonal harmonic coefficients on the critical inclination of a lunar artificial satellite are investigated. The study is carried out using the Hamiltonian framework. The Hamiltonian of the problem is cconstructed and the short periodic terms are eliminated using Delaunay canonical variables. Considering the above perturbations, numerical simulations for a hypothetical lunar orbiter are presented. Finally, this study reveals that the critical inclination is quite different from the critical inclination of traditional sense and/or even has multiple solutions. Consequently, different families of critical inclination are obtained and analyzed.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.269-271
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• 2008

We prove that a full jack field does not exist on the sum of a trivial bundle and the canonical bundle on $G_{2,4}$, the Grassmanian of 2-planes in 4-space.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1097-1102
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• 2018

Let A and B be matrices which are polynomials in r pairwise commuting nilpotent matrices over a field. We give a sufficient condition for the null space of $A^i$ to equal that of $B^i$ for all i, in particular, for A and B to be similar.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.12
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• pp.24-30
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• 2010

The super-resolution near-field structure (super-RENS) disc system is the most promising one for next-generation optical data storage systems to succeed the Blu-ray disc (BD). In this paper, we apply the simplicial canonical piecewise-linear (SCPWL) model to modeling super-RENS read-out signals since reliable and accurate channel modeling is essential for performance analysis and development of equalizers for super-RENS systems. The validity of this model is verified using radio frequency (RF) signal samples obtained from a super-RENS disc, The experiment results on modeling indicate that the SCPWL model can be efficiently utilized for the nonlinear modeling of the super-RENS systems.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.653-658
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• 2001

In this paper, we find the necessary and sufficient conditions for the discrete time nonlinear system to be transformed into observable canonical form by state coordinates change. Unlike the continuous time case, our theorems give the desired state coordinates change without solving partial differential equations. Also, our approach is applicable to both autonomous systems and control systems by slight change of the definition of the vector field.