• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.41-63
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• 2024

In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a parabolicity criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.109-112
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• 1997

In this paper, we study on a classification of hypersurfaces given by tansnormal functions on $R^{n+1}_1$. If M is a level set of a transnormal function on $R^{n+1}_1$, then it is one of a hyperplane, a cylinder around k-plane, a pseudo-sphere and a pseudo-hyperbolic space.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.587-596
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• 2007

In this paper, we study two-phase flow models. The chunk mix model of the two-phase flow equations is analyzed by a characteristic analysis. The model discussed herein has real characteristic values for all physically acceptable states and except for a set of measure zero has a complete set of characteristic vectors in state space.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.209-213
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• 2001

This paper describes the numerical solution to the hyperbolic system of magnetohydrodynamic (MHD) equations. First, by pointing out the approximations involved, the deal MHD equations are presented. Next, the MHD waves as well as the associated shocks and discontinuities, are presented. Then, based on the hyperbolicity of the ideal MHD equations, the application of upwind schemes, which have been developed for hydrodynamics, is discussed to solve the equations numerically. As an definite example, one and multi-dimensional codes based on the Total Variation Diminishing scheme are presented. The treatment in the multi-dimensional code, which maintains ${\nabla}{\cdot}$B = 0, is described. Through tests, the robustness of the upwind schemes for MHDs is demonstrated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.83-104
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• 1997

This paper studies parameter estimation for a first-order hyperbolic integro-differential equation modelling one-sex population dynamics. A second-order finite difference scheme is used to estimate parameters such as the age-specific death-rate and the age-specific fertility from fully discrete observations on the population. The function space parameter estimation convergence of this scheme is proved. Also, numerical simulations are performed.

• Journal of Korean Association for Spatial Structures
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• v.12 no.3
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• pp.47-54
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• 2012

The roof surface of spatial structures is often damaged or destroyed because of its light weight roof structure and materials. Many of large scale stadiums have roof structure framed with steel truss or stay cable and wrapped or covered with membrane material Teflon, and this membrane material is easily damaged and its loss is quite serious. Through such examples, it was found that the studies on wind proof design of roofs of large space structures were not sufficiently made. This study conducted wind pressure experiment and fluid analysis in order to examine the aerodynamic characteristic of the roof shape of hyperbolic paraboloid spatial structures. Although the biggest minimum peak wind pressure coefficient was shown in the edges of the roof in the wind origin direction, it decreases with the advancement to the longitudinal direction of the roof.

• Tunnel and Underground Space
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• v.16 no.5 s.64
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• pp.368-376
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• 2006

After heavy rainfall, It was occurred massive plane failure along bedding plane of shale in the center of rock slope. It was observed filling material and trace of underground water leakage around of the slope. We tried to find the cause for slope failure, and the result of examination showed that primary factors of the failure were low shear strength of clay filling material and water pressure formed within tension crack existed in the top of the slope. In this research, in order to examine the features of shear strength of filled rock joint, shear test of filled rock joint was conducted using of artificial filling material such as sand and clay..Also we made an investigation into the characteristics of shear strength with different thickness of filling materials.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.733-743
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• 2012

For the "Hopf bundle" $S^1{\rightarrow}S^{2n,1}{\rightarrow}\mathbb{C}H^n$, horizontal lifts of simple closed curves are studied. Let ${\gamma}$ be a piecewise smooth, simple closed curve on a complete totally geodesic surface $S$ in the base space. Then the holonomy displacement along ${\gamma}$ is given by $$V({\gamma})=e^{{\lambda}A({\gamma})i}$$ where $A({\gamma})$ is the area of the region on the surface $S$ surrounded by ${\gamma}$; ${\lambda}=1/2$ or 0 depending on whether $S$ is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group $\mathbb{R}{\rightarrow}\mathcal{H}^{2n+1}{\rightarrow}\mathbb{C}^n$.

• International Journal of Aerospace System Engineering
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• v.7 no.2
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• pp.6-12
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• 2020

The precise prediction of future position of satellite depends on the accurate determination of orbit, which is also helpful in performing orbit maneuvers and trajectory correction maneuvers. For estimating the orbit of satellite many methods are being used. Some of the conventional methods are based on (i) Differential Correction (DC) (ii) Extended Kalman Filter (EKF). In this paper, Differential Evolution (DE) is used to determine the orbit. Orbit Determination using DC and EKF requires some initial guess of the state vector to initiate the algorithm, whereas DE does not require an initial guess since a wide range of bounds for the design unknown variables (orbital elements) is sufficient. This technique is uniformly valid for all orbits viz. circular, elliptic or hyperbolic. Simulated observations have been used to demonstrate the performance of the method. The observations are generated by including random noise. The simulation model that generates the observations includes the perturbation due to non-spherical earth up to second zonal harmonic term.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1299-1320
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• 2023

In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hyper-cones whose centers lie on a non-null curve with non-null Frenet vector fields in E⁴₁ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in E⁴₁ by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.