• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.271-287
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• 2022

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant Ω_X(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of Ω_X(α) and γ_X(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1569-1575
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• 2019

In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness of the associated spaces. We obtain that the three constants are the same as those for $L^1$ and $L^{\infty}$ spaces.

• Transactions of the Korean Society of Automotive Engineers
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• v.1 no.1
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• pp.66-79
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• 1993

To construct the design back data for a lean-burn gas engine, we have designed a constant volume combustion chamber with sub-chamber. With constant volume ratio of main-sub combustion chamber and constant equivalence ratio of methane-air mixture, the influence of geometric configurations(diameter, injection angle, number, length) of passagehole upon combustion characteristics were studied. It was found that combustion characteristics in the main combustion chamber were greatly influenced by the injection angle and length of passagehole.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.157-161
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• 1996

In the geometric accuracy, most of studies have been concentrated on the analysis of the geometric error, or a control path of grinding using the value of measured geometric error. In this paper, by using the value of measured motor current through hall sensor, detection of the geometric error have been accomplished, and in-process control path of grinding for improvement geometric accuracy, too.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.317-323
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• 2018

We study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact manifolds with zero boundary condition. In particular, we obtain some geometric estimates for the first eigenvalue.

• Journal of Ocean Engineering and Technology
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• v.13 no.3 s.33
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• pp.12-20
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• 1999

In this paper, method for mapping a three-dimensional shape into the two-dimensional plane will be introduced. This method is referred to geometric modelling and means a transformation between the flat sheet and final surface. The initial blank shape represents the original configuration of the final shape formed into three dimensional surface. The initial constant constant area mapping hypothesis was used in this paper. This technique will be applied to the basic data for an interactive computer design capable of dealing with typical stamping process, including deep parts and complex shapes.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1587-1598
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• 2013

In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation $$\frac{{\partial}u}{{\partial}t}={\triangle}u-b(x,t)u^{\sigma}$$ under general geometric flow on complete noncompact manifolds, where 0 < ${\sigma}$ < 1 is a real constant and $b(x,t)$ is a function which is $C^2$ in the $x$-variable and $C^1$ in the$t$-variable. As an application, we get an interesting Harnack inequality.

• Journal of Ocean Engineering and Technology
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• v.29 no.3
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• pp.263-269
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• 2015

This paper proposes a new approach for solving the weather routing problem by dividing it into two phases with the goal of fuel saving. The problem is to decide two optimal variables: the heading angle and speed of the ship under several constraints. In the first phase, the optimal route is obtained using the Real-Time Adaptive A* algorithm with a fixed ship speed. In other words, only the heading angle is decided. The second phase is the speed scheduling phase. In this phase, the original problem, which is a nonlinear optimization problem, is converted into a geometric programming problem. By solving this geometric programming problem, which is a convex optimization problem, we can obtain an optimal speed scheduling solution very efficiently. A simple case of numerical simulation is conducted in order to validate the proposed method, and the results show that the proposed method can save fuel compared to a constant engine output voyage and constant speed voyage.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.4 s.175
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• pp.1039-1046
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• 2000

This paper introduces the control and measurement of a double parallel robot manipulator applied for unknown geometric surface grinding. A measurement system is developed to recognize a grinding path by a vision camera and to observe a grinding load by a current sensor. With the measured fusion information, an intelligent controller identifies the unknown geometric surface and moves the robot along the grinding path with a constant grinding load.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.575-589
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• 2010

Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.