• Journal of the Korean Mathematical Society
• /
• v.36 no.6
• /
• pp.1169-1180
• /
• 1999

Two-point comparison theorems between hyperbolic and euclidean geometry for convex regions in the complex plane are known([5], [6]). We give new geometric proofs of sharp two-point comparison theorems for convex regions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.05a
• /
• pp.870-875
• /
• 2004

Beam stiffeners have frequently been used for raising natural frequencies of base structures. In stiffener layout optimization problems, most of the previous researches considering the position and/or the length of the stiffener as design variables dealt with structures having just simple convex shapes such as a square or rectangle. The reason is concave shape structures have difficulties ill formulating geometry constraints. In this paper, a new geometry constraint handling technique, which can define both convex and concave feasible lesions and measure a degree of geometry constraint violation, is proposed. Evolution strategies (ESs) is utilized as an optimization tool. In addition, the constraint-handling technique of EVOSLINOC (EVOlution Strategy for scalar optimization with Lineal and Nonlinear Constraints) is utilized to solve constrained optimization problems. From a numerical example, the proposed geometry constraint handling technique is verified and proves that the technique can easily be applied to structures in net only convex but also concave shapes, even with a protrusion or interior holes.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.721-727
• /
• 2021

The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.

• Korean Journal of Geomatics
• /
• v.4 no.1
• /
• pp.1-8
• /
• 2004

In the middle-resolution remote sensing, the Ground Sampled Distance (GSD) that the detector senses and samples is generally larger than the actual size of the objects (or materials) of interest, and so several objects are embedded in a single pixel. In this case, as it is impossible to detect these objects by the conventional spatial-based image processing techniques, it has to be carried out at sub-pixel level through spectral properties. In this paper, we explain the sub-pixel analysis algorithm, also known as the Linear Spectral Mixing (LSM) model, which has been experimented using the Hyperion data. To find Endmembers used as the prior knowledge for LSM model, we applied the concept of the convex geometry on the two-dimensional scatter plot. The Atmospheric Correction and Minimum Noise Fraction techniques are presented for the pre-processing of Hyperion data. As LSM model is the simplest approach in sub-pixel analysis, the results of our experiment is not good. But we intend to say that the sub-pixel analysis shows much more information in comparison with the image classification.

• Communications for Statistical Applications and Methods
• /
• v.25 no.1
• /
• pp.79-89
• /
• 2018

In this paper, we study the maximal property of the volume of the convex hull of d-dimensional independent random vectors. We show that the volume of the random convex hull from a multivariate location-scale family indexed by ${\Sigma}$ is stochastically maximized in simple stochastic order when ${\Sigma}$ is diagonal. The claim can be applied to a broad class of multivariate distributions that include skewed/unskewed multivariate t-distributions. We numerically investigate the proven stochastic relationship between the dependent and independent random convex hulls with the Gaussian random convex hull. The numerical results confirm our theoretical findings and the maximal property of the volume of the independent random convex hull.

• International Journal of Air-Conditioning and Refrigeration
• /
• v.16 no.3
• /
• pp.100-107
• /
• 2008

The heat transfer and friction characteristics of heat exchangers having convex louver fins are experimentally investigated, and the results are compared with those of wave fin counterparts. Eighteen samples (nine convex louver fin samples and nine wave fin samples) which had different fm pitches (1.81 mm to 2.54 mm) and tube rows (one to four) were tested. The convex angle was $11.7^{\circ}$. The j factors are insensitive to fin pitch, while f factors increase as fin pitch increases. The effect of fin pitch on f factor is more significant for the wave fin compared with the convex louver fin. It appears that the complex fin pattern of the convex louver fin induces intense mixing of the flow, and thus reduces the effect of fin pitch. Both the j and f factors decrease as the number of tube row increases. However, as the Reynolds number increases, the effect of tube row diminishes. Comparison of the convex louver fin j factors with those of wave fin reveals that convex louver fin j factors are 18% to 29% higher than those of wave fin. The f factors are 16% to 34% higher for the convex louver fin. The difference increases as fin pitch decreases. Existing correlation fails to adequately predict the present data. More data is needed for a general correlation of the convex louver fin geometry.

• Honam Mathematical Journal
• /
• v.31 no.3
• /
• pp.315-321
• /
• 2009

Erd$\"{o}$s posed the problem of determining the minimum number g(n) such that any set of g(n) points in general position in the plane contains an empty convex n-gon. In 1978, Harborth proved that g(5) = 10. We reprove the result in a geometric approach.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.1019-1045
• /
• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.279-289
• /
• 1999

Given n points in the plane the planar convex hull prob-lem in that of finding which of these points belong to the perimeter of the smallest convex region (a polygon) containing all n points. Here we suggest two kinds of methods. First we present a new sequential method for constructing the pla-nar convex hull O(1.5n) time in the quadratic decision tree model. Second using the sequential method we suggest a new parallel algo-rithm which solve the planar convex hull O(1.5n/p) time on a maspar Machine (CREW-PRAM) with O(n) processors. Also when we run on a maspar Machine we achieved a 37. 156-fold speedup with 64 pro-cessor.

• Journal of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1103-1118
• /
• 2020

In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These multiarc graphs naturally interpolate between arc graphs and flip graphs, both well studied objects in low dimensional geometry and topology. We show a number of rigidity results, namely showing that, under certain complexity conditions, that simplicial maps between them only arise in the "obvious way". We also observe that, again under necessary complexity conditions, subsurface strata are convex. Put together, these results imply that certain simplicial maps always give rise to convex images.