• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.525-542
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• 2002

In this article, we prove a certain local-global principle for representation of binary forms by an infinite family of quinary positive integral quadratic forms.

• Journal of Ocean Engineering and Technology
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• v.27 no.2
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• pp.1-7
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• 2013

This paper aims at contributing to the field of ship design by introducing new systematic variation methods for ship hull forms. Hull form design is generally carried out in two stages. The first is the global variation considering the sectional area curve. Because the geometric properties of a sectional area curve have a decisive effect on the global hydrodynamic properties of ships, the design of a sectional area curve that satisfies various global design conditions, e.g., the displacement, longitudinal center of buoyancy, etc., is important in the initial hull form design stage. The second stage involves the local design of section forms. Section forms affect the local hydrodynamic properties, e.g., the local pressure in the fore- and aftbody. This paper deals with a new method for the systematic variation of sectional area curves. The longitudinal volume distribution of a ship depends on the sectional area curve, which can geometrically be controlled using parametric variation and a variation that uses the modification function. Based on these methods, we suggest a more generalized method in connection with the derivation of the lines for a new design compared to those for similar ships. This is the so-called the volumetric balanced variation (VOB) method for ship forms using a B-spline modification function and an optimization technique. In this paper the global geometric properties of hull forms are totally controlled by the form parameters. We describe the new method and some application examples in detail.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.729-737
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• 2006

We study Ribaucour transformations on nondegenerate local isometric immersions of Riemannian space forms into Lorentzian space forms with flat normal bundles. They can be explained by dressing actions on the solution space of Lorentzian Grassmannian systems.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1577-1590
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• 2008

We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.479-491
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• 2013

Let M be a smooth real hypersurface in complex space of dimension $n$, $n{\geq}3$, and assume that the Levi-form at $z_0$ on M has at least $(q+1)$-positive eigenvalues, $1{\leq}q{\leq}n-2$. We estimate solutions of the local $\bar{\partial}$-closed extension problem near $z_0$ for $(p,q)$-forms in Sobolev spaces. Using this result, we estimate the local solution of tangential Cauchy-Riemann equation near $z_0$ in Sobolev spaces.

• Journal of Ocean Engineering and Technology
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• v.30 no.4
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• pp.235-242
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• 2016

In general, ship hull form design is carried out in two stages. In the first stage, the longitudinal variation of the sectional area curves is adapted from a similar mother ship to determine the volume distribution in ships. At this design stage, the initial design conditions of displacement, longitudinal center of buoyancy, etc. are satisfied and the global hydrodynamic properties of the structure are optimized. The second stage includes the local designing of the sectional forms. Sectional forms are related to the local pressure resistance in the fore- and aft-body shapes, cargo boundaries, interaction between the hull and propeller, etc. These relationships indicate that the hull sections need to be optimized in order to minimize the local resistance. The volumetric balanced (VOB) variation of ship hull forms has been suggested by Kim (2013) as a generalized, systematic variation method for determining the sectional area curves in hull form design. This method is characterized by form parameters and is based on an optimization technique. This paper emphasizes on an extensional function of the VOB considering a geometrical wave profile. We select a container ship and an LNG carrier to demonstrate the applicability of the proposed technique. Through analysis, we confirm that the VOB method, considering the geometrical wave profile, can be used as an efficient tool in the hull form design for ships.

• Journal of Korean Society of Forest Science
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• v.79 no.2
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• pp.196-204
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• 1990

Pinus densiflora is not only widely distributed but also one of the most economically important timber species in Korea. In Korea, this species is classified into four local forms according to tree forms, as it has widely geographical variations. Trees of Ankang form are dwarfish nearly like shrubs, and those of Keumkang form are very tall and straight. Those of flatland and highland forms are exhibited in-between Ankang and Keumkang forms. This study was carried out to examine biomass, net production and production efficiency among four local forms of Pirzus densiflora forests growing in Korea. For the study, dimension analysis was used for trees and harvest method for shrubs and herbs in four 30-40 year-old stands showing the typical tree forms. Stand biomass of Ankang, flatland, highland and Keumkang forms were 29.87, 110.89, 133.53 and 205.42 t/ha, respectively. As going in order of Ankang, flatland, highland and Keumkang forms, the proportions of stem woods to total tree biomass increased while the proportions of stem barks, live branches, needles and roots showed a tendency to decrease. Stand net productions of Ankang, flatland, highland and Keumkang forms were 3.716, 10.796, 13.097 and 16.500 t/ha yr., respectively. As going in order of Ankang, flatland, highland and Keumkang forms, the proportions of stem woods and lire branches to total tree net production increased while the proportion of needles decreased. In case of live branches, the opposite trend of biomss and net production proportion may be resulted from the differences in the ratio of self-pruning. Net assimilation ratios of Ankang, flatland, highland and Keumkang forms were 1.406, 1.920, 1.487 and 1.677, respectively. Efficiency of needles to produce stems in those forms were 0.239, 0.714, 0.572 and 0.771, respectively. Considering the difference in measuring time, net assimilation ratio and efficiency of needles to produce stems may increase as going in order of Ankang, flatland, highland and Keumkang forms.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.149-156
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• 1991

The theory of the asymptotic behavior of Toeplitz forms is applicable to some problems concerning the local limit theorem.

• East Asian mathematical journal
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• v.37 no.5
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• pp.591-598
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• 2021

In this paper we study the Cauchy problem for the Chern-Simons gauged O(3) sigma model. We prove the local existence of solutions with low regularity initial data, observing null forms of the system and applying bilinear estimates for wave-Sobolev space H^{s, b}.

• Journal of Digital Convergence
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• v.12 no.9
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• pp.291-296
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• 2014

Most notices on local tax are perceived to be confusing, often leading to a negative feeling towards user due to the complex content and excessive information included in the tax forms. Several local governments have redesigned their notice forms in order to resolve these issues. Therefore I conducted an in-depth analysis of user experiences in regards to the issues posed by the design of the tax notice form so as to offer a basic set of data that can be used to improve the user experience and increase their understanding of the tax form.