• 대한수학회보
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• 제50권4호
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• pp.1099-1108
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• 2013

We define the Mannheim curve in a 3-dimensional Riemannian manifold, which is a generalization of the Mannheim curve in Euclidean space. In particular, we study the Mannheim curves and their partner curves in 3-dimensional space forms.

• 대한수학회보
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• 제52권6호
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• pp.2071-2093
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• 2015

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of ${\mathbb{E}}_1^n$. We determine the parametrizations of non-null self-similar curves in ${\mathbb{E}}_1^n$.

• 호남수학학술지
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• 제40권2호
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• pp.251-264
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• 2018

In the present study, we consider the curves in Galilean 4-space ${\mathbb{G}}_4$. We find out the involute curves of order k (k = 1, 2, 3) of a given curve. We get the relationships between the Frenet apparatus of a given curve and its involute curves of order k.

• 호남수학학술지
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• 제44권1호
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• pp.121-134
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• 2022

In this study, we obtain the spherical images of minimal curves in the complex space in ℂ⁴ which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.

• 호남수학학술지
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• 제45권3호
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• pp.513-541
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• 2023

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space ℝ³₁, Lorentzian sphere 𝕊²₁ and hyperbolic sphere ℍ²₀ of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in ℝ³₁ and draw the graphs of these indicatrix curves on the spheres.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.445-456
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• 2008

We characterize the helical polynomial space curves and solve the first-order Hermite interpolation problem for helical polynomial space quintics.

• 충청수학회지
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• 제26권3호
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• pp.541-545
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• 2013

In this paper, we explain how to get defining equations of the modular curves $X_1(2,2N)$ which show the moduli problems and present defining equations of $X_1(2,2N)$ for $N=2,3,{\ldots},8$.

• East Asian mathematical journal
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• 제26권1호
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• pp.69-73
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• 2010

We invoke the characterization of Pythagorean-hodograph polynomial curves and prove that it is impossible to parameterize any real curves, other than a straight line, by rational functions of its arc length.

• 호남수학학술지
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• 제46권2호
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• pp.181-197
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• 2024

In this study, we investigate Smarandache curves with Frenet-type frame in Myller configuration for Euclidean 3-space E₃. Also, we introduce some characterizations and invariants of them. Then, we construct a numerical example with respect to these special Smarandache curves in order to understand the obtained materials.

• 한국지진공학회논문집
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• 제11권4호
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• pp.13-23
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• 2007

This paper focuses on providing a practical approach for decision making in Performance-Based Design (PBD). Satisfactory performance is defined by several performance objectives that place limits on direct (monetary) loss and on a tolerable probability of collapse. No specific limits are placed on conventional engineering parameters such as forces or deformations, although it is assumed that sound capacity design principles are followed in the design process. The proposed design procedure incorporates different performance objectives up front, before the structural system is created, and assists engineers in making informed decisions on the choice of an effective structural system and its stiffness (period), base shear strength, and other important global structural parameters. The tools needed to implement this design process are (1) hazard curves for a specific ground motion intensity measure, (2) mean loss curves for structural and nonstructural subsystems, (3) structural response curves that relate, for different structural systems, a ground motion intensity measure to the engineering demand parameter (e.g., interstory drift or floor acceleration) on which the subsystem loss depends, and (4) collapse fragility curves. Since the proposed procedure facilitates decision making in the conceptual design process, it is referred to as a Design Decision Support System, DDSS. Implementation of the DDSS is illustrated in an example to demonstrate its practicality.