• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.641-648
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• 1994

Let M be a minimally immersed closed hypersurface in $S^{n+1}$, II the second fundamental form and $S = \Vert II \Vert^2$. It is well known that if $0 \leq S \leq n$, then $S \equiv 0$ or $S \equiv n$ and totally geodesic hypersheres and Clifford tori are the only possible minimal hypersurfaces with $S \equiv 0$ or $S \equiv n$ ([6], [2]). From these results, Chern suggested some questions on the study of compact minimal hypersurfaces on the sphere with S =constant: what are the next possible values of S to n, and does in the ambient sphere\ulcorner By the way, S is defined extrinsically but, in fact, it is an intrinsic invariant for the minimal hypersurface, i.e., S = n(n-1) - R, where R is the scalar, curvature of M. Some partial answers have been obtained for dim M = 3: Assuming $M^3 \subset S^4$ is closed and minimal with S =constant, de Almeida and Brito [1] proved that if $R \geq 0$ (or equivalently $S \leq 6$), then S = 0, 3 or 6, Peng and Terng ([5]) proved that if M has 3 distint principal curvatures, then S = 6, and in [3] Chang showed that if there exists a point which has two distinct principal curvatures, then S = 3. Hence the problem for dim M = 3 is completely done. For higher dimensional cases, not much has been known and these problems seem to be very hard without imposing some more conditions on M.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2687-2694
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• 2002

A precision displacement measuring system is proposed, which can detect the 3-DOF translational motions of precision positioning devices. The optical system, which is composed of two diode-laser sources and two quadratic PSDs, is adapted to detect the position of the spherical reflector usually mounted on the platform of positioning devices. Each of the laser beams from diode-laser sources is reflected at the highly reflective surface of the sphere; hence, the 3-dimensional position of the sphere causes the directional change of the reflected beams, which is detected by the PSDs. In this paper, we define the relationships between the output values of the two PSDs and the 3-DOF translational motions of the sphere. Based on a deduced measurement model, we perform measurement simulation and evaluate the performance of the proposed measurement system: linearity, sensitivity, measuring range, and measurement error. The results show that the proposed measuring method is very useful for the measurement of the precision displacement of 3-DOF micro motions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.353-358
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• 2002

Human's vision is mostly confined to the area in the front and we, humans heavily depend on the sense of hearing to gather information in areas out of our sight. Thus, the virtual reality system consisting of the 3D sound effect gives the user a much better sense of reality than the system without the sound effect. Virtual 3D sound technology has mainly been researched with binaural system. The conventional binaural sound systems reproduce the desired sound at two arbitrary points using two channels in 3-D space. Head movement of listener might be change the nominal acoustic transfer function and deteriorate the performance of 3D sound system based on loudspeakers that needs a crosstalk canceller. In this paper, low kinds of sensitivity functions of sphere HRTF are derived to investigate the effect of head movement on HRTF in 3D sound system. Changes of HRTF caused by rotational and translational motion of head are obtained as we calculate the derivatives of HRTF with respect to angle and distance.

• Steel and Composite Structures
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• v.52 no.3
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• pp.377-390
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• 2024

Analyzing thermoelastic, elastoplastic, and residual stresses is pivotal for deepening our insights into material characteristics, particularly in the engineering of advanced materials like functionally graded materials (FGM). This research delves into these stress types within a thick-walled sphere composed of Al-SiC FGM, employing a detailed successive approximation method (SAM) to pinpoint stress distributions under varied loading scenarios. Our investigation centers on how the sphere's structure responds to different magnitudes of internal pressure. We discover that under various states-thermoelastic, elastoplastic, and residual-the radial stresses are adversely impacted, manifesting negative values due to the compressive nature induced by internal pressures. Notably, the occurrence of reverse yielding, observed at pressures above 410 MPa, merits attention due to its significant implications on the sphere's structural integrity and operational efficacy. Employing the SAM allows us to methodically explore the nuanced shifts in material properties across the sphere's thickness. This study not only highlights the critical behaviors of Al-SiC FGM spheres under stress but also emphasizes the need to consider reverse yielding phenomena to maintain safety and reliability in their application. We advocate for ongoing refinement of analytical techniques to further our understanding of stress behaviors in various FGM configurations, which could drive the optimized design and practical application of these innovative materials in diverse engineering fields.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.1-5
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• 2012

We study surfaces of revolution in the three dimensional Euclidean space $\mathbb{R}^3$ with two distinct axes of revolution. As a result, we prove that if a connected surface in the three dimensional Euclidean space $\mathbb{R}^3$ admits two distinct axes of revolution, then it is either a sphere or a plane.

• Proceedings of the KIEE Conference
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• 1993.11a
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• pp.219-221
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• 1993

In this study, piezoceramics/polymer composites with 3-3 connectivity were made by BURPS(Burnout Plastic Sphere) technique with PZT ceramics and plastic sphere. And the properties dependent on the Dextrin wt.% were investigated. The density of porous piezoceramic and piezoceramic/polymer composites were decreased almost linearly with increasing the Dextrin wt.%.

• Resources Recycling
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• v.17 no.4
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• pp.30-36
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• 2008

The preparation of porous lightweight materials as well as the measurement of physical properties has been performed by using SSA(sewage sludge ash) as the raw material. For this aim, two types of lightweight filler, that is, perlite and silica sphere were employed respectively and bentonite was also used as an inorganic binder. The properties of lightweight specimen calcined at 1,000 were measured in terms of density, compressive strength, thermal conductivity and sound absorption to examine the effect of material composition as well as the preparation condition on the properties of lightweight material. As a result, the density of specimen prepared with perlite was ranged from 1.23 to $1.37g/cm^3$ and the compressive strength was ranged from 242.3 to $370.5kg/cm^2$. In case of specimen prepared with silica sphere, it was found that the compressive strength was less than $100kg/cm^2$ even though density was lower than that of specimen with perlite. As far as the thermal conductivity of specimen was concerned, it was ranged from 0.3 to $0.5W/m^{\circ}K$ depending on material composition so that the insulation effect was superior to conventional concrete.

• Journal of Biomedical Engineering Research
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• v.26 no.2
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• pp.73-86
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• 2005

We need to flatten the brain cortex to smooth surface, sphere, or 2D plane in order to view the buried sulci. The rendered 3D surface of the segmented white matter and gray matter does not have the topology of a sphere due to the partial volume effect and segmentation error. A surface without correct topology may lead to incorrect interpretation of local structural relationships and prevent cortical unfolding. Although some algorithms try to correct topology, they require heavy computation and fail to follow the deep and narrow sulci. This paper proposes a method that corrects topology of the rendered surface fast, accurately, and automatically. The proposed method removes fractions beside the main surface, fills cavities in the inside of the main surface, and removes handles in the surface. The proposed method to remove handles has three-step approach. Step 1 performs smoothing operation on the rendered surface. In Step 2, vertices of sphere are gradually deformed to the smoothed surfaces and finally to the boundary of the segmented white matter and gray matter. The Step 2 uses multi-resolutional approach to prevent the deep sulci from geometrical intersection. In Step 3, 3D binary image is constructed from the deformed sphere of Step 2 and 3D surface is regenerated from the 3D binary image to remove intersection that may happen. The experimental results show that the topology is corrected while principle sulci and gyri are preserved and the computation amount is acceptable.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.3
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• pp.523-529
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• 2017

In this paper, we propose an efficient sphere decoding scheme that reduces computational complexity by combining receive and transmit ordering techniques in generalized spatial modulation systems, where the indexes of activated transmit antennas as well as the transmit symbols are exploited to transfer information to the receiver. In this scheme, the receive signals are optimally ordered so that the calculation for a candidate solution outside the sphere is terminated early to lower the computational complexity. In addition, the transmit ordering technique is applied to first search for candidate symbols and activated antennas having higher probabilities to further reduce the computational complexity. Simulation results show that the proposed doubly ordered sphere decoding scheme provides the same bit error rate performance with the conventional sphere decoding method and the sphere decoder employing only the receive ordering technique while it requires lower computational complexity.

• Korean Journal of Optics and Photonics
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• v.9 no.4
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• pp.258-263
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• 1998

Quasi-elastic light scattering is utilized to measure the mean diameter of the 0.3 $\mu\textrm{m}$-dimeter polystyrene sphere. The mean diameter of the polystyrene sphere is required to be known within the uncertainty of a few per centages. The systematic error has been considerably reduced by improving the system for the angle alignment and temperature measurement of cell. NIST SRM 1691 (0.269$\pm$0.007 $\mu\textrm{m}$: TEM; 0.275$\pm$0.007 $\mu\textrm{m}$: QELS) is measured to be 0.273 $\mu\textrm{m}$$\pm$0.006 $\mu\textrm{m}$ in mean diameter. Detailed description is given of the improved method and the resultant uncertainty, and the comparison of results with NIST is followed.