• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1411-1425
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• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1233-1240
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• 2011

An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and ${\beta}$-mixing property with exponential decay rate are obtained.

• Korean Journal of Computational Design and Engineering
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• v.1 no.3
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• pp.215-223
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• 1996

Every mechanical part is fabricated with the variations in its size and shape, and the allowable range of the variation is specified by the tolerance in the design stage. Geometric tolerances specify the size or the thickness of each shape entity itself or its relative position and orientation with respect to datums while considering their order of precedence. It would be desirable if the assemblability of parts could be verified in the computer when the tolerances on the parts are store together with the geometric model of the parts of an assembly and their assembled state. Therefore, a new method is proposed to represent geometric tolerances and to determine the assemblability. This method determines the assemblability by subdividing the ranges of relative motion between parts until there exists the subdivided regions that do not cause the interference.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.9
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• pp.84-93
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• 1996

This paper describes the development of new feature positioning method which embedded into the top-down assembly modeling system supporting conceptual design. In this work, the user provides the geometric constraints representing the position and size of features, then the system calculates their proper solution. The use of geometric constraints which are easy to understand intuitively enables the user to represent his design intents about geometric shapes, and enables the system to propagate the changes automatically when some editing occurs. To find the proper solution of given constraints, the Selective Solving Method in which the redundant or conflict equations are detected and discarded is devised. The validity of feature shapes satisfying the constraints can be maintained by this technique, and under or over constrained user-defined constraints can also be estimated. The problems such as getting the initial guess, controlling the multiple solutions, and dealing with objects of rotational symmetry are also resolved. Through this work, the feature based modeling system can support more general and convenient modeling method, and keeps the model being valid during modifying models.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.04a
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• pp.367-372
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• 2000

Accuracy of a machined component is determined by the relative motion between the cutting tool and the workpiece. One of the important factors which affects the accuracy of this relative motion is the geometric error of machine tools. In this study, geometric error is modeled using form shaping motion of machine tool, where a form shaping function is derived from the homogeneous transformation matrix. Geometric errors are measured by laser interferometer. After that, the local positioning error can be estimated from the form shaping model and geometric error data base. From this information, we can remodel the part by shifting the design surface to the amount of positional error. By generating tool path to the redesigned surface, we can reduce the machining error.

• Korean Journal of Computational Design and Engineering
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• v.9 no.1
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• pp.19-26
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• 2004

It is not possible to exchange parametric information of CAD models based on the current version of STEP (Standard for the Exchange of Product model data). The designer intents are lost during the transfer of CAD models. To resolve this problem, the macro-parametric approach had been proposed. To enable this approach, a set of standard modeling commands has been defined. Errors or missing elements of the standard modeling commands can be discovered by implementing macro-parametric translators. But there is a limit to discover problems only by using translators. This paper proposes a method to verify the standard modeling commands by implementing a geometric modeler. First, each argument of a modeling command is verified. Second, the set of the standard modeling commands is applied to geometric modeling of commercially available product parts. For the geometric modeling, nine test models have been selected.

• Journal of the Society of Naval Architects of Korea
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• v.40 no.6
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• pp.30-36
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• 2003

To improve survivability of damaged ship, assessment of stability and structural safety, and behavior analysis in wave is required. Prediction of sinking time, damage stability and structural strength considering progressive flooding and dynamic force in wave is very important. To do it, a geometric model which can be express damaged ship is prepared. This paper described the geometric modeler for survivability assessment of damaged ship. The modeler is developed based on 3-D geometric modeling kernel, ACIS. The hull form and compartment definition is available fundamentally. And requirement for modeler contains data generation and interface for hydrostatic calculation, behavior analysis, and longitudinal strength analysis and so on. To easy access modeling system by conventional user such as crew, user interface is developing.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.260-268
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• 2007

Demand for the use of 3D CAD DMU systems over the Internet environment has been increased. However, transmission of commercial 3D kernels has delayed the communication effectiveness due to the kernel size. Light weight CAD geometric kernel design methodology is required for rapid transmission in the distributed environment. In this paper, an assembly data structure suitable for the top-down and bottom-up assembly models has been constructed. Part features are stored without a hierarchy so that they are created and saved in no particular order. In particular, this paper proposes a new assembly representation model, called multi-level assembly representation (MAR), for the PDM based assembly DMU system. Since the geometric kernel retains assembly hierarchy and topological information, it is applied to the web-viewer for the PDM based DMU system. Effectiveness of the proposed geometric kernel is confirmed through various case studies.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.2
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• pp.136-144
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• 1997

Usually triangular patches are used to transfer geometric shape in Rapid Prototyping CAM system. STL, a list of triangles, is de facto standard in RP industry. Because STL does not have topological infoma- tion, it can cause errornous results. So STL should be verified before using. After adding support structures to anchor the part to the platform and to prevent sagging or distortion, slicing and layer by layer manufactur- ing process are done. But triangular patch is surface model and cannot provide sufficient information on geometry in the above processes. So, geometric modeling is necessary in verifying STL, adding support structures and slicing. It is natural that triangle based modeling is the best when tringular patches are used as input. Considering support structures, solid and faces coexist in RP process. Therefore non-manifold modeler is required. In this study, triangle based non-manifold geometric modeling is proposed for RP sys- tem consistent with STL input.

• Journal of the Korean Society for Precision Engineering
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• v.30 no.10
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• pp.1087-1093
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• 2013

In this study, a measurement method of double ball-bar is proposed to measure the geometric errors of an ultra-precision roll mold machine tool. A volumetric error model of the machine tool is established to investigate the effects of the geometric errors to a radius error and a cylindricity of the roll mold. A measurement path is suggested for the geometric errors, and a ball-bar equation is derived to represent the relation between the geometric errors and a measured data of the double ball-bar. Set-up errors, which are inevitable at the double ball-bar installation, also are analyzed and are removed mathematically for the measurement accuracy. In addition, standard uncertainty of the measured geometric errors is analyzed to determine the experimental condition. Finally, the proposed method is tested and verified through simulation.