• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.231-240
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• 2013

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.105-122
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• 2023

We present explicit formulas for the spectra of higher spin operators on the subbundle of the bundle of spinor-valued trace free symmetric tensors that are annihilated by Clifford multiplication over the standard sphere in odd dimension. In the even dimensional case, we give the spectra of the square of such operators. The Dirac and Rarita-Schwinger operators are zero-form and one-form cases, respectively. We also give eigenvalue formulas for the conformally invariant differential operators of all odd orders on the subbundle of the bundle of spinor-valued forms that are annihilated by Clifford multiplication in both even and odd dimensions on the sphere.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.807-814
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• 1996

Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x \times Y \to S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X \times RP^{2n-k} \to S^{2n}$ is homotopically trivial.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.739-744
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• 2002

Recently we have discovered that sediments should be separated from lithosphere, and soil should be separated from biosphere, both sediment and soil will be mixed sediments-soil-sphere (Seso-sphere), which is using particulate mechanics to be solved. Erosion and sediment both are moving by particulate matter with water or wind. But ancient sediments will be erosion same to soil. Nowadays, real soil has already reduced much more. Many places have only remained sediments that have ploughed artificial farming layer. Thus it means sediments-soil-sphere. This paper discusses sediments-soil-sphere erosion modeling. In fact sediments-soil-sphere erosion is including water erosion, wind erosion, melt-water erosion, gravitational water erosion, and mixed erosion. We have established geographical remote sensing information modeling (RSIM) for different erosion that was using remote sensing digital images with geographical ground truth water stations and meteorological observatories data by remote sensing digital images processing and geographical information system (GIS). All of those RSIM will be a geographical multidimensional gray non-linear equation using mathematics equation (non-dimension analysis) and mathematics statistics. The mixed erosion equation is more complex that is a geographical polynomial gray non-linear equation that must use time-space fuzzy condition equations to be solved. RSIM is digital image modeling that has separated physical factors and geographical parameters. There are a lot of geographical analogous criterions that are non-dimensional factor groups. The geographical RSIM could be automatic to change them analogous criterions to be fixed difference scale maps. For example, if smaller scale maps (1:1000 000) that then will be one or two analogous criterions and if larger scale map (1:10 000) that then will be four or five analogous criterions. And the geographical parameters that are including coefficient and indexes will change too with images. The geographical RSIM has higher precision more than mathematics modeling even mathematical equation or mathematical statistics modeling.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.220-223
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• 2008

A test facility to measure the performance of a KM(Kick Motor) is constructed, and prediction of blast wave propagation over the facility is performed to check if the safety of test personnel in MCC(Main Control Center) can be guaranteed even for the most severe explosion. Assuming that the initial explosion energy is contained in a sphere under the pressure of 500, 1000, 1500 psi, respectively, the radius of the sphere is determined for each pressure to set the mass of contained explosion gas to 35 kg. The material properties of explosion gas are set to be the ones of KM propellant combustion gas under normal condition. To reduce the effort and time required for a complex three-dimensional modeling, the flowfield is approximated to axismmetry. Calculations are performed for all three initial pressure conditions, and the analysis of the result is given for 1500 psi which is expected to be the worst case. The maximum pressure is 3.5 psig while the minimum pressure is -1.2 psig on the outer wall of MCC, and the maximum pressure difference between the inner and outer walls of protection wall amounts to 3.0 psi.

• KIPS Transactions on Software and Data Engineering
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• v.8 no.2
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• pp.89-96
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• 2019

360 degree 3-dimensional lidar sensors and vision cameras are commonly used in the development of autonomous driving techniques for automobile, drone, etc. By the way, existing calibration techniques for obtaining th e external transformation of the lidar and the camera sensors have disadvantages in that special calibration objects are used or the object size is too large. In this paper, we introduce a simple calibration method between two sensors using a spherical object. We calculated the sphere center coordinates using four 3-D points selected by RANSAC of the range data of the sphere. The 2-dimensional coordinates of the object center in the camera image are also detected to calibrate the two sensors. Even when the range data is acquired from various angles, the image of the spherical object always maintains a circular shape. The proposed method results in about 2 pixel reprojection error, and the performance of the proposed technique is analyzed by comparing with the existing methods.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.185-191
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• 2006

This paper observes that the induced homomorphisms on cohomology groups by a cyclic map are trivial. For a CW-complex X, we use the fact to obtain some conditions of X so that the n-th Gottlieb group $G_n(X)$ is trivial for an even positive integer n. As corollaries, for any positive integer m, we obtain $G_{2m}(S^{2m})\;=\;0\;and\;G_2(CP^m)\;=\;0$ which are due to D. H. Gottlieb and G. Lang respectively, where $S^{2m}$ is the 2m- dimensional sphere and $CP^m$ is the complex projective m-space. Moreover, we show that $G_4(HP^m)\;=\;0\;and\;G_8(II)\;=\;0,\;where\;HP^m$ is the quaternionic projective m-space for any positive integer m and II is the Cayley projective space.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.661-668
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• 2012

For displaying multivariate numerical data on a 2D plane by the projection, principal components biplot and the GGobi are two main tools of data visualization. The biplot is very useful for capturing the global shape of the dataset, by representing $n$ observations and $p$ variables simultaneously on a single graph. The GGobi shows a dynamic movie of the images of $n$ observations projected onto a sequence of unit vectors floating on the $p$-dimensional sphere. Even though these two methods are certainly very valuable, there are drawbacks. The biplot is too condensed to describe the detailed parts of the data, and the GGobi is too burdensome for ordinary data analyses. In this paper, "the local projective display(LPD)" is proposed for visualizing multivariate numerical data. Main steps of the LDP are 1) $k$-means clustering of the data into $k$ subsets, 2) drawing $k$ principal components biplots of individual subsets, and 3) sequencing $k$ plots by Hurley's (2004) endlink algorithm for cognitive continuity.

• Journal of Electrical Engineering and Technology
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• v.2 no.1
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• pp.129-135
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• 2007

In this paper, we present a set of numerical schemes to solve the Muller integral equation for the analysis of electromagnetic scattering from arbitrarily shaped three-dimensional (3-D) dielectric bodies by applying the method of moments (MoM). The piecewise homogeneous dielectric structure is approximated by planar triangular patches. A set of the RWG (Rao, Wilton, Glisson) functions is used for expansion of the equivalent electric and magnetic current densities and a combination of the RWG function and its orthogonal component is used for testing. The objective of this paper is to illustrate that only some testing procedures for the Muller integral equation yield a valid solution even at a frequency corresponding to an internal resonance of the structure. Numerical results for a dielectric sphere are presented and compared with solutions obtained using other formulations.

• The Research Journal of the Costume Culture
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• v.17 no.5
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• pp.849-865
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• 2009

This research is a study of fashion design that applied formative features of formal beauty of architecture into clothing design; we focused on Gaudi's architectural style as well as Art Nouveau style that became popular from the end of the 19th century to the beginning of the 20th century. We noted that in general the simple and flat features of cloth impose a limitation on the expression of formal features in clothing design, but a unique diversity of designs can be achieved, evoking a sense of freshness by an ideal combination of flat patterns and draping. The aim of this research is to present a possibility of extending the sphere of design expression by creating three-dimensional clothes with pattern-cutting skills and applications of three-dimensional patterns as well as flat patterns found in Gaudi's works of architecture that are distinguished in curvaceousness and formal beauty. As for the research method, we reviewed previous studies by making a close review of books, papers, the pictures and web sites related to this topic. We made our clothes on the basis of this theoretical consideration. We found the following points. First, by presenting a work of fashion inspired by architectural designs, we realized that formal beauty in architect can become a motive for clothing design in a broad scale by noting the formal images, decoration details, and formative features of architectural works. Second, the characteristic lines of Gaudi's architecture are suitable to be adapted for expressing the detailed lines of decoration in clothes. Third, we can express formative beauty in clothes by highlighting the variation of shapes and lines through various attempts of change in background pattern, even though there is a limitation in the availability of cloth material because we must choose pieces of cloth with right texture and thickness that can be cut and sewn appropriately to express formative beauty. Fourth, we confirmed that it was possible to create unique formative designs by a creative application of both flat and three-dimensional cutting.