• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.801-810
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• 2022

In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.83-90
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• 2016

We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.205-210
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• 2001

In this work, virtual material characterization of 3D orthogonal woven composites is performed to predict the elastic properties by a full scale FEA. To model the complex geometry of 3D orthogonal woven composites, an accurate unit structure is first prepared. The unit structure includes warp yarns, filler yarns, stuffer yams and resin regions and reveals the geometrical characteristics. For this virtual experiments by using finite element analysis, parallel multifrontal solver is utilized and the computed elastic properties are compared to available experimental results and the other analytical results. It is founded that a good agreement between material properties obtained from virtual characterization and experimental results. Using the method of this virtual material characterization, the effects of inconsistent filler yarn distribution on the in-plane shear modulus and filler yarn waviness on the transverse Young's modulus are investigated. Especially, the stiffness knockdown of 3D woven composite structures is simulated by virtual characterization. Considering these results, the virtual material characterization of composite materials can be used for designing the 3D complex composite structures and may supplement the actual experiments.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1289-1300
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• 2006

It is well known that the twistor, section of twistor space, classify the orthogonal almost complex structure on even dimensional Riemannian manifold (X, g). We will show that existence of a harmonic and anti-holomorphic twistor is equivalent to having a symplectic structure on (X, g).

• Journal of Drive and Control
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• v.12 no.4
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• pp.8-14
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• 2015

A quick-acting hydraulic fuse, which is mainly composed of a poppet, a seat, and a spring, must be designed to minimize the leaked oil volume during fuse operation on a line rupture. The optimal design parameters of a quick-acting hydraulic fuse were searched using the design of experiments method and the complex method. First, the $L_{50}(5^4)$ orthogonal array is used to find the robust minimum point among the 625 points of design variables. The search range can then be narrowed around the robust minimum point. Second, the $L_{25}(5^4)$ orthogonal array is used to obtain the variations of the design variables in the narrowed search range. The variations of design variables are used to set the structure of a polynomial equation representing the leakage oil volume of the quick-acting hydraulic fuse. The least squares method is then applied to obtain the coefficients of polynomial equation. Finally, the complex method is used to find the optimal design parameters where the objective function is described by the polynomial equation.

• 한국전산유체공학회:학술대회논문집
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• 2004.10a
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• pp.53-59
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• 2004

A general purpose program NUFLEX for the analysis of 3-D heat/fluid flow in complex geometry with pre/post processor have been developed, which consists of a flow solver based on FVM and a dedicated pre/post processor. The program employs a general non-orthogonal grid system and solve laminar and turbulent (lows with standard and RNG $\kappa-\epsilon$ turbulence models. NUFLEX is capable of analysing two-phase flow with topologically complex interface, turbulent diffusion combustion, solidification problems and magnetic flow. For the purpose of verification of the program and testing the applicability, several practical problems are solved and compared with the available data. Comparison of the NUFLEX results with that by the STAR-CD program has been also made for the same flow configuration and grid structure.

• Journal of Biomedical Engineering Research
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• v.10 no.2
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• pp.157-164
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• 1989

Three-dimensional imaging and manipulation of CT data are becoming increasingly important for deterRing the complex structure and pathologies. Octree which is a hierarchical data model is used to reconstruct three- dimensional objects from CT scans. Orthogonal cross sections are displayed by traverse the octree partially. Arbitrary oblique planes are derived by intersecting the square region of plane and cubic volume of octal node. Thia method enables the display of multi-structured complex organ ann the realization by personal computer.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1621-1630
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• 2015

In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ${\xi}$ are studied.