• 대한수학회지
• /
• 제50권2호
• /
• pp.231-240
• /
• 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
• /
• 제63권1호
• /
• pp.105-122
• /
• 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.

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.807-814
• /
• 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.

• 대한원격탐사학회:학술대회논문집
• /
• 대한원격탐사학회 2002년도 Proceedings of International Symposium on Remote Sensing
• /
• pp.739-744
• /
• 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
• /
• 한국전산유체공학회 2008년도 춘계학술대회논문집
• /
• pp.220-223
• /
• 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.

• 정보처리학회논문지:소프트웨어 및 데이터공학
• /
• 제8권2호
• /
• pp.89-96
• /
• 2019

전방향 3차원 라이다 센서와 비전 카메라는 자동차나 드론 등의 자율주행기술 개발에 활용되고 있다. 한편 라이다 센서와 카메라 좌표계 사이의 변환 관계를 보정하기 위한 기존의 기술들은 특수한 보정물체를 제작하거나 보정물체의 크기가 큰 단점이 있다. 본 논문에서는 한 개의 구형물체를 사용하여 두 센서 사이의 기하보정을 간편하게 구현하는 방법을 소개한다. 구형 물체의 3차원 거리정보에서 RANSAC으로 네 개의 3차원 점을 선택하여 구의 중심좌표를 계산하고, 카메라 영상에서 물체의 2차원 중심점을 구하여 두 센서를 보정하였다. 구는 다양한 각도에서 영상을 획득하여도 항상 원형의 형상을 유지하기 때문에 데이터 획득 시 유리한 장점이 있다. 본 논문에서 제안하는 방법으로 약 2픽셀의 투영오차의 결과를 얻었고, 기존의 방법과의 비교실험을 통하여 제안 기술의 성능을 분석하였다.

• 대한수학회논문집
• /
• 제21권1호
• /
• pp.185-191
• /
• 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.

• 응용통계연구
• /
• 제25권4호
• /
• pp.661-668
• /
• 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
• /
• 제2권1호
• /
• pp.129-135
• /
• 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.

• 복식문화연구
• /
• 제17권5호
• /
• pp.849-865
• /
• 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.