• Proceedings of the KSRS Conference
• /
• 2008.10a
• /
• pp.141-144
• /
• 2008

Many studies have been conducted on extracting buildings from ALS(Airborne Laser Scanning) data. After segmentation or classification of building points, additional steps such as generalization is required to get straight boundary lines that better approximate the real ones. In much research, orthogonal constraints are used to improve accuracies and qualities. All the lines of the building boundaries are assumed to be either parallel or perpendicular mutually. However, this assumption is not valid in many cases and more complex shapes of buildings have been increased. A new algorithm is presented that is applicable to various complex buildings. It consists of three steps of boundary tracing, grouping, and regularization. The performance of our approach was evaluated by applying the algorithm to some buildings and the results showed that our proposed method has good potential for extracting building boundaries of various shapes.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.173-186
• /
• 2015

In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.681-693
• /
• 2003

In this paper, we first prove that there are no automorphism orbits accumulating at a boundary point of the largest isolated finite type. We also present a generalization of the results of Isaev and Krantz on the structure of the orbit accumulation points.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.439-454
• /
• 2014

We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

• Journal of the Korean Association of Geographic Information Studies
• /
• v.20 no.1
• /
• pp.137-151
• /
• 2017

The space between urban buildings becomes a waterway during rain events and requires a boundary condition in numerical calculations on grids to separate overland storm flows from building areas. Minimization of the building data distortion as a boundary condition is a necessary step for generating accurate calculation results. A building generalization is used to reduce the distortion of building shapes and areas during a raster conversion. The objective of this study was to provide the appropriate threshold value for building generalization and grid size in a numerical calculation. The impact of building generation on the connectivity of urban storm waterways were analyzed for a general residential area. The building generalization threshold value and the grid size for numerical analysis were selected as the independent variables for analysis, and the number and area of sinks were used as the dependent variables. The values for the building generalization threshold and grid size were taken as the optimal values to maximize the building area and minimize the sink area. With a 3 m generalization threshold, sets of $5{\times}5m$ to $10{\times}10m$ caused 5% less building area and 94.4% more sink area compared to the original values. Two sites representing general residential area types 2 and 3 were used to verify building generalization thresholds for improving the connectivity of storm waterways. It is clear that the recommended values are effective for reducing the distortion in both building and sink areas.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.3
• /
• pp.37-41
• /
• 2007

The semi-convexity for planar shapes has been recently introduced in [2]. As a generalization of the convextiy, semi-convexity is closed under the Minkowski sum. But the definition of semi-convexity requires that the shape boundary should satifisfy a differentiability condition $C^{1:1}$, which means that it should be possible to take the normal vector field along the domain's extended boundary. In view of the fact that the semi-convextiy is a most natural generalization of the convexity in many respects, this is a severe restriction for the semi-convexity, since the convexity requires no such a priori differentiability condition. In this paper, we generalize the semi-convexity to the closure of the class of semi-convex $\mathcal{M}$-domains for any Minkowski class $\mathcal{M}$, and show that this generalized semi-convexity is also closed under Minkowski sum.

• Korean Journal of Mathematics
• /
• v.17 no.1
• /
• pp.53-66
• /
• 2009

We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space $L_2({\Omega}{\times}(0 2{\pi}))$. We also use the variational linking theorem which is a generalization of the mountain pass theorem.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1669-1687
• /
• 2014

We consider a nonuniformly nonlinear elliptic systems with resonance part and nonlinear Neumann boundary condition on an unbounded domain. Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.571-579
• /
• 2007

Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with a periodic boundary condition, which is of the type $ut+\frac{{\partial}^2} {{\partial}x^2}\;g\;(u,\;u_x,\;u_{xx})=f(u,\;u_x,\;u_{xx})$. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Korean Journal of Mathematics
• /
• v.30 no.2
• /
• pp.375-389
• /
• 2022

In this paper, we prove some fixed-point theorems in partially ordered fuzzy metric spaces for (𝜙, 𝜓, 𝛽)-Geraghty contraction type mappings which are generalization of mappings with Geraghty contraction type condition. Application of the derived results are shown in proving the existence of unique solution to some boundary value problems.