• 대한수학회지
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• 제44권2호
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• pp.407-442
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• 2007

The study of Euclidean submanifolds with finite type "classical" Gauss map was initiated by B.-Y. Chen and P. Piccinni in [11]. On the other hand, it was believed that for spherical sub manifolds the concept of spherical Gauss map is more relevant than the classical one (see [20]). Thus the purpose of this article is to initiate the study of spherical submanifolds with finite type spherical Gauss map. We obtain several fundamental results in this respect. In particular, spherical submanifolds with 1-type spherical Gauss map are classified. From which we conclude that all isoparametric hypersurfaces of $S^{n+1}$ have 1-type spherical Gauss map. Among others, we also prove that Veronese surface and equilateral minimal torus are the only minimal spherical surfaces with 2-type spherical Gauss map.

• Journal of Electrical Engineering and Technology
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• 제11권3호
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• pp.759-768
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• 2016

Direction of arrival (DOA) estimation of multiple sources using sensor arrays has been widely studied in the last few decades, particularly, the spherical harmonic analysis utilizing a spherical array. Both the number of sensors on the aperture and size of the sphere can affect the estimation accuracy dramatically. However, those two factors are conflicted to each other in a single spherical array. In this paper, a multiple spherical arrays structure is proposed to provide an alternative design to the traditional single spherical array for the spherical harmonic decomposition, to obtain better localization performance. The new structure consists of several identical spheres in a given area, and the microphones are placed identically on each sphere. The spherical harmonic analysis algorithm using the new multiple array structure for the problem of multiple acoustic sources localization is presented. Simulation results show that the multiple spherical arrays can provide a more accurate direction of arrival (DOA) estimation for the multiple sources than that of a single spherical array, distinguish several adjacent sources more efficiently, and reduce the number of microphones on each sphere without decreasing its’ estimation accuracy.

• 한국수학사학회지
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• 제36권2호
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• pp.21-34
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• 2023

Spherical trigonometry refers to the geometry related to spherical triangles. It has been an important tool for studying astronomy since ancient times. In trigonometry, concepts such as trigonometric functions naturally emerge from the relationship between arcs and chords of a circle. In this paper, we briefly examine the origin of spherical trigonometry. To introduce the basics of spherical trigonometry, we present fundamental and important theorems such as Menelaus's theorem, the law of sines and the law of cosines on a sphere, along with their proofs. Furthermore, we discuss the educational value and potential applications of spherical trigonometry.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.821-834
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• 2019

The reductivity of a spherical curve is the minimal number of times a particular local transformation called an inverse-half-twisted splice is required to obtain a reducible spherical curve from the initial spherical curve. It is unknown if there exists a spherical curve whose reductivity is four. In this paper, an unavoidable set of configurations for a spherical curve with reductivity four is given by focusing on 5-gons. It has also been unknown if there exists a reduced spherical curve which has no 2-gons and 3-gons of type A, B and C. This paper gives the answer to this question by constructing such a spherical curve.

• 한국공간구조학회논문집
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• 제2권4호
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• pp.45-52
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• 2002

Research about spherical shells been applying most usually is achieved by many investigators already and generalized equation has been derived. But, existent research is limited in case that spherical shell's roof rigidity is isotropy or orthotropy, and research that consider periodicity of rigidity-distribution that can happen by doing spherical shell's roof system by lattice system is not gone entirely. The purpose of this paper is applying Galerkin method to spherical shell that model periodicity of roof rigidity distribution that appear by roof lattice form of large space structure and develop structural analysis program that formularize. Rigidity-model of this research selects that of spherical shell which has 2-way grid. In this paper, buckling-strength and deformation distribution of isotopic spherical shell and 2-way grid spherical shell obtained by developed program could confirm the reliability by comparison with result of existent research.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.410-415
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• 2002

In this article, spatial filtering procedures with application to spherical acoustical holography are discussed. Planar and cylindrical holography are the most widely used amongst the various nearfield acoustical holography techniques. However, when the geometry of a source is similar to a sphere, spherical holography may yield better results than other types of holography since there are no errors due to truncation of the sound field in the spherical case. Spatial filtering affects the accuracy of spherical acoustical holography critically, especially in the case of backward projection. Thus spatial filtering is essential for successful application of spherical holography. In the present work, various filtering methods were evaluated in simulations made using sound pressure fields of various types and with different levels of random spatial noise. It was found that a procedure based on eliminating spherical harmonic coefficients that contribute insignificantly to the total sound power of the source gave the best results on average of the different procedures considered here. Spherical holography procedures were also verified experimentally. Reliable results were obtained using the power filtering algorithm. Thus it was concluded that spherical holography combined with power filtering may prove to be a useful tool for noise source identification.

• 한국공간구조학회논문집
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• 제4권4호
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• pp.77-84
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• 2004

Researches on spherical shell which is most usually applied have been completed by many investigators already and generalized numerical formula was derived. But the existent researches are limited to those on spherical shell with isotropic or orthotropic roof stiffness, periodic distribution of roof stiffness that can be caused by spherical and latticed roof system is not considered. Therefore, the object of this study is to develop a structural analysis program to analyze spherical shells that have periodicity of roof stiffness distribution caused by latticed roof of large space structure, grasp buckling characteristics and behavior of structure.

• 전기학회논문지
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• 제62권11호
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• pp.1541-1543
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• 2013

This paper presents a spherical motor which can control in multi-degree of freedom operation. The spherical motor has been researched by many types of structure. Thhis paper shows a spherical shaped airgap and surfaced permanent magnets. Especially, The motor consists of dual rotor cores. Unlike a cylindrical motor, the spherical motor design can be considered with azimuth direction on spherical coordinates. Therefore the permanent magnet surfaced on the rotor need to be designed optimally in order to generate a sinusoidal magnetic flux density in the airgap. This paper presents results of optimal design for reducing torque ripple of the multi-degree of freedom spherical motor.

• Journal of the Optical Society of Korea
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• 제17권2호
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• pp.219-223
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• 2013

The purpose of this study was to determine the relationship between the spherical equivalent visual acuity (VA) and uncorrected astigmatism. On 108 emmetropic eyes, the spherical equivalent VA was measured for cross cylindrical lens (CC lens)-induced astigmatic eyes and the VA-astigmatism relation determined. On 158 astigmatic eyes, the spherical equivalent VA and corrected astigmatism were measured and the measured values were compared with the calculated values from the VA-astigmatism relation by correlation coefficient analysis. Subsequent to that, the relationship between spherical equivalent VA and uncorrected astigmatism was made. The relationship was fitted for an exponential equation. Correlation coefficient between calculated values by equation and measured values for astigmatic eyes was 0.991 (p<0.01). The relationship between the spherical equivalent VA and the uncorrected astigmatism was decided as follows (spherical equivalent VA / uncorrected astigmatism): 1.0 / 0.25 D, 0.9 / 0.50 D, 0.8 / 0.75 D, 0.7 / 1.00 D, 0.6 / 1.25 D, 0.5 / 1.50 D, 0.4 / 2.00 D, 0.3 / 2.50 D, 0.2 / 3.00 D, 0.1 / 4.00 D, and 0.05 / 4.75 D. In conclusion, the relationship table devised from this study is a useful reference for predicting uncorrected astigmatism by measurement of decimal VA in spherical equivalent.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 춘계학술대회 논문집
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• pp.52-55
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• 2002

In this research, the modification method of spherical aberration, and aspherical lens shape design method were investigated. Spherical aberration affects lens's performance directly. Many studies have attempted to remove spherical aberration with a lot of methods in order to reduce the bad effect of spherical aberration. The approach to lens shape design was base on the ray tracing method. From the result, it was confirmed that ray reverse-tracing method was convenient to remove spherical aberration, and could be used very effectively and usefully for aberration-free aspherical lens design.