• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.433-446
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• 1997

In this paper we study an existence and the approxi-mation of the solution of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm Also we present some computational results by using fixed point method.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.65-70
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• 2007

We study the existence of nontrivial solutions of the Gradient type Dirichlet boundary value problem for elliptic systems of the form $-{\Delta}U(x)={\nabla}F(x,U(x)),x{\in}{\Omega}$, where ${\Omega}{\subset}R^N(N{\geq}1)$ is a bounded regular domain and U = (u, v) : ${\Omega}{\rightarrow}R^2$. To study the system we use the liking theorem on product space.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.125-133
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• 2023

We establish a characterization theorem of elliptic paraboloids in the (n+1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with extrinsic properties such as the (n+1)-dimensional volumes of regions enclosed by the hyperplanes and hypersurfaces, and the n-dimensional areas of projections of the sections of hypersurfaces cut off by hyperplanes.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.49 no.4
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• pp.23-35
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• 2012

This paper presents a 3-D pose (position and orientation) estimation method for an elliptic object in 3-D space. It is difficult to resolve the problem of determining 3-D pose parameters with respect to an elliptic feature in 3-D space by interpretation of its projected feature onto an image plane. As an alternative, we propose a two points-based pose estimation algorithm to seek the 3-D information of an elliptic feature. The proposed algorithm determines a homogeneous transformation uniquely for a given correspondence set of an ellipse and two coplanar points that are defined on model and image plane, respectively. For each plane, two triangular features are extracted from an ellipse and two points based on the polarity in 2-D projection space. A planar homography is first estimated by the triangular feature correspondences, then decomposed into 3-D pose parameters. The proposed method is evaluated through a series of experiments for analyzing the errors of 3-D pose estimation and the sensitivity with respect to point locations.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.37-49
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• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.363-388
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• 2022

In two previous papers the author presented a general construction of finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds. In this paper we restrict our attention to elliptic 3-manifolds. For illustration of our methods a constructive proof is given that orientation-reversing and fiber-preserving diffeomorphisms of Seifert manifolds do not exist for nonzero Euler class, in particular elliptic 3-manifolds. Each type of elliptic 3-manifold is then considered and the possible group actions that fit the given construction. This is shown to be all but a few cases that have been considered elsewhere. Finally, a presentation for the quotient space under such an action is constructed and a specific example is generated.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.419-428
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• 2009

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.3
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• pp.341-351
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• 2016

In this present work, the effect of hole shapes, orientation and hole arrangements on film cooling effectiveness has been carried out. For this work a flat plate has been considered for the computational model. Computational analysis of film cooling effectiveness using different hole shapes with no streamwise inclination has been carried out. Initially, the model with an inclination of $30^{\circ}$ has been verified with the experimental data. The validation results are well in agreement with the results taken from literature. Five different hole shapes viz. Cylindrical, Elliptic, Triangular, Semi-Cylindrical and Semi-Elliptic have been compared and validated over a wide range of blowing ratios. The blowing ratios ranged from 0.67 to 1.67. Later, orientation of holes have also been varied along with the number of rows and hole arrangements in rows. The performance of film cooling scheme has been given in terms of centerline and laterally averaged adiabatic effectiveness. Semi-elliptic hole utilizes half of the mass flow as in other hole shapes and gives nominal values of effectiveness. The triangular hole geometry shows higher values of effectiveness than other hole geometries. But when compared on the basis of effectiveness and coolant mass consumption, Semi-elliptic hole came out to give best results.