• East Asian mathematical journal
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• v.28 no.1
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• pp.101-107
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• 2012

For each dimension exceeds 1, determining the number of multi-dimensional partitions of a positive integer is an open question in combinatorial number theory. For n ${\leq}$ 14 and d ${\geq}$ 1 we derive a formula for the function ${\wp}_d(n)$ where ${\wp}_d(n)$ denotes the number of partitions of n arranged on a d-dimensional space. We also give an another definition of the d-dimensional partitions using the union of finite number of divisor sets of integers.

• Journal of Technologic Dentistry
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• v.23 no.1
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• pp.95-106
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• 2001

The purpose of this study was to show the method of three-dimensional morphometry developed recently and to compare the accuracy of three-dimensional morphometry with those of PA cephalometry, The three-dimensional morphometry analysis program and device were developed. Steel balls (1.2mm in diameter) were attached in twenty five landmarks of artificial human skull. This artificial human skull was used as experimental materials. From three-dimensional morphometry and PA cephalometry of artificial human skull. eleven linear measurements were acquired and made into asymmetry index. Right-left differences of measurements were used as asymmetry index. These measurements and asymmetry index were compared respectively with those of actual. The results were as follows: 1. Mean difference between three-dimensional morphometry and actual artificial human skull in linear measurements was $1.99{\pm}0.37mm$, and mean difference between PA cephalometry and actual was $21.12{\pm}0.45mm$. Both of all were reduced more than those of actual. 2. Mean difference between three-dimensional morphometry and actual artificial human skull in asymmetry index was $0.07{\pm}0.42$, and mean difference between PA cephalometry and actual was $3.63{\pm}0.60$. Three-dimensional morphometry was reduced while PA cephalometry was magnified more than that of actual. 3. Each eleven asymmetry index of three-dimensional morphometry was the same negative sign as those of actuals while only N-Z, ANS-J, Tr-Go, Tr-ANS asymmetry index were the same in PA cephalometry. These results suggest that the method of three-dimensional morphometry is more accurate than those of PA cephalometry in asymmetry analysis.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.53-64
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• 2008

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6. In the following series of two papers, we present a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor: I. The recurrence relations in 8-g-UFT II. The Einstein 's connection in 8-g-UFT In our previous paper [1], we investigated some algebraic structure in Einstein's 8-dimensional unified field theory (i.e., 8-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in 8-g-UFT. This paper is a direct continuation of [1]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 8-g-UFT and to display a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [1]. All considerations in this paper are restricted to the first class only of the generalized 8-dimensional Riemannian manifold $X_8$, since the cases of the second class are done in [2], [3] and the case of the third class, the simplest case, was already studied by many authors.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.32 no.2
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• pp.77-86
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• 2014

As raster-based high quality and resolution spatial information has appeared, 1/1,000 digital map lost either its recognition or uses because of insufficient new modified and updated information. Therefore, this study analyzed the linkage between three-dimensional spatial information and 1/1,000 digital map, and also suggested a modification plan of 1/1,000 digital map, made by three-dimensional spatial information. In fact, some area of Incheon and Busan were presented with the modification plan of 1/1,000 digital map as three-dimensional trial models. These trials reflected possibilities of modification by qualitative and quantitative analysis of 1/1,000 digital map, using three-dimensional object model.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.85-89
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• 2003

Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either of finite codimensional closed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphic vector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines $D_1$ R in the same system of lines on X the vector bundles E$\mid$D and E$\mid$R have the same splitting type.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.4
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• pp.289-294
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• 2018

In this work, a recently developed semi-analytic technique, so called the residual power series method, is generalized to process higher-dimensional linear and nonlinear partial differential equations. The solutions obtained takes a form of an infinite power series which can, in turn, be expressed in a closed exact form. The results reveal that the proposed generalization is very effective, convenient and simple. This is achieved by handling the (m+1)-dimensional Burgers equation.

• Journal of the Korean Applied Science and Technology
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• v.26 no.1
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• pp.45-50
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• 2009

Three-dimensional, statistical-mechanical formulations of problems are usually untractable analytically, and therefore they are commonly solved numerically. However, their one-dimensional counterparts are always to be solved analytically. In general analytical solutions sheds more insights to the problems than numerical solutions. Hence, solutions of one-dimensional problems may provide key properties to the problems, when they are extended to three dimensions. In this article, thermodynamic properties of one-dimensional fluid comprising molecules of rigid rods are analyzed statistical-mechanically. Molecules of rigid rods are characterized with repulsive or excluded volume effect. It is observed that this feature is well reflected in thermodynamic functions such as Helmholtz free energy. volumetric equation of state. chemical potential, entropy, etc.

• The Journal of Korean Academy of Prosthodontics
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• v.34 no.3
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• pp.574-592
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• 1996

This study investigated the time-dependent dimensional changes of elastomeric impression materials using holographic interferometry. Six commercial impression materials, Permlastic(polysulfide), Xantopren VL (condensation silicone), low and medium viscosity of Exafine, Provil (addition silicone), and Impregum(polyether), were selected. Steel plate was used as custom tray, and each impression specimen was 20 mm in width, 15 mm in length and 3 mm in thickness. Each impression material was evaluated at 30 minutes, 1, 2, 4, 6, 8 and 12 hours after setting using real-time holography. The results were as follow : 1. Xantopren VL and Permlastic showed relatively severe and continuous dimensional changes after setting. Low viscosity of Exafine, Provil, Impregum showed relatively slight dimensional changes with function of time and medium viscosity of Exafine showed almost no dimensional change from 2 hours after setting to 6 hours. 2. On initial dimensional changes within 1 hour, the amount of change in low viscosity of Exafine was the least and Xantopren VL was the largest. 3. On dimensional changes at 4 hours after setting, the amount of change in medium viscosity of Exafine was the least and tile change of Xantopren VL was the largest. 4. In overall dimensional stability during 12 hours, medium viscosity of Exafine was the most stable and Xantopren VL and Permlastic were least stable.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.131-140
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• 2005

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6, 7. In the following series of two papers, we present a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor: I. The recurrence relations in 8-g-UFT II. The Einstein's connection in 8-g-UFT In our previous paper [1], we investigated some algebraic structure in Einstein's 8-dimensional unified field theory (i.e., 8-g-UFT), with emphasis on the derivation of the recurrence relations of the third kind which hold in 8-g-UFT. This paper is a direct continuation of [1]. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 8-g-UFT and to display a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations of the third kind obtained in the first paper [1]. All considerations in this paper are restricted to the second class only of the generalized 8-dimensional Riemannian manifold $X_8$, since the case of the first class are done in [2], [3] and the case of the third class, the simplest case, was already studied by many authors.

• Journal of The Korean Astronomical Society
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• v.28 no.1
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• pp.61-65
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• 1995

We discuss a model4-dimensional Friedmann cosmology which may have evolved from a model of 4+D dimensions which admits spontaneous compactification of D dimensions (or N-dimensional variants of the Brans-Dicke (BD) theory). The BD parameter appearing in dimensional reduction is negative $-1<\omega<0$ (for the N-dimensional variants of the BD theory, $-1.5{\leq}{\omega})$. We find that if there had been inflationary transtion to the standard big-bang model, the Universe can undergoe a polar-type expansion during when the gravitational coupling becomes negative. The unique feature is that for the negative w, the density parameter of the post-inflationary Universe falls in a range 0<0<1 even if the Universe is geometrically flat (k = 0).