• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.239-246
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• 2005

We determine the genera of the Drinfeld modular curves $X_\Delta(n)$.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.805-812
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• 2021

In this study, we obtain various conditions for the non-null curve flows to be inextensible in the 6-dimensional Lorentzian space 𝕃⁶. Then, we find partial differential equations which characterize the family of inextensible non-null curves.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.549-555
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• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• East Asian mathematical journal
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• v.39 no.5
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• pp.529-536
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• 2023

This paper introduces the Frobenius endomophisms on the binary Hessian curves. It provides an efficient and computable homomorphism for computing point multiplication on binary Hessian curves. As an application, it is possible to construct the GLV method combined with the Frobenius endomorphism to accelerate scalar multiplication over the curve.

• ETRI Journal
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• v.26 no.3
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• pp.241-251
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• 2004

We propose two improved scalar multiplication methods on elliptic curves over $F_{{q}^{n}}$ $q= 2^{m}$ using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield $F_q$ can be sped up by Frobenius expansion. Previous methods are restricted to the case of a small m. However, when m is small, it is hard to find curves having good cryptographic properties. Our methods are suitable for curves defined over medium-sized fields, that is, $10{\leq}m{\leq}20$. These methods are variants of the conventional multiple-base binary (MBB) method combined with the window method. One of our methods is for a polynomial basis representation with software implementation, and the other is for a normal basis representation with hardware implementation. Our software experiment shows that it is about 10% faster than the MBB method, which also uses Frobenius expansion, and about 20% faster than the Montgomery method, which is the fastest general method in polynomial basis implementation.

• Structural Engineering and Mechanics
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• v.9 no.4
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• pp.375-382
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• 2000

Experimental investigation into the cyclic behaviour of sand plast brick masonry was performed on forty two square panels. The panels were subjected to cyclic uniaxial compression for two cases of loading: normal to bed joint and parallel to bed joint. Experimental data were used to plot the unloading-reloading curves for the entire range of the stress-strain curve. Mathematical expressions to predict the reloading and unloading stress-strain curves at various values of residual strain are proposed. A simple parabola and an exponential type formula are found adequate to model the unloading and reloading curves respectively. The models account for the potential effects of residual strain on these curves. Comparison of test results with the proposed mathematical expression shows good correspondence.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.245-252
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• 1996

We described a relationship of the $L_2$ norm of the $L_2$norm of a Bzier curve and l2 norm of its confrol points. The use of Bezier curves finds much application in the general description of curves and surfaces and provided the mathematical basis for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for the $L_2$ norm with respect to the $L_2$ norm for its control points for easy computation.

• Magazine of the Korean Society of Agricultural Engineers
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• v.45 no.6
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• pp.153-161
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• 2003

The purpose of this paper is to investigate the soil-water characteristic curves for an unsaturated soil. To this ends, a series of suction measured test was conducted on the selected 4 kinds of soils taken from different sites of Korea, using modified pressure plate apparatus. Form the test results, the water contents, degree of saturation and volumetric water contents were analyzed with the suction. And the soil-water characteristic curves of unsaturated soil were drawn from the test results for various factors. The characteristic curves drawn with water content vs matric suction were classified certainly the difference in wet side but were not classified in dry side. The characteristic curves drawn with degree of saturation vs matric suction for unsaturated soil were shown the opposite inclination as compared with the former curve. But the characteristic curve with volumetric water content vs matric suction was described suitably not only in wet side condition but also in dry side. And it was found that the volumetric water contents of loose soil was high at the initial condition but that of dense soil was high at final condition (dry side).

• Structural Engineering and Mechanics
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• v.39 no.3
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• pp.411-425
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• 2011

This paper illustrates the results of a seismic vulnerability study aimed to derive the fragility curves for typical Algerian reinforced concrete bridge piers using an analytical approach. Fragility curves express the probability of exceeding a certain damage state for a given ground motion intensity (e.g., PGA). In this respect, a set of 41 worldwide accelerometer records from which, 21 Algerian strong motion records are included, have been used in a non-linear dynamic response analyses to assess the damage indices expressed in terms of the bridge displacement ductility, the ultimate ductility, the cyclic loading factor and the cumulative energy ductility. Combining the damage indices defined for 5 damage rank with the ground motion indices, the fragility curves for the bridge piers were derived assuming a lognormal distribution.

• Korean Journal of Computational Design and Engineering
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• v.4 no.3
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• pp.269-283
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• 1999

Surface/surface intersection is a common and important problem in geometric modeling and CAD/CAM. Several methods have been used to approach this problem. All possible intersection curves can be obtained by using the subdivision algorithm, while it requires a great deal of memory and is somewhat inefficient. The tracing algorithm is much faster than the subdivision algorithm, and can find points on the intersection curve sequentially. But, the tracing algorithm has some problems in the intersection curves on surface boundaries. In this paper, an Improved tracing algorithm that includes some ideas such as a new trace-terminating condition for the intersection curves on surface boundaries, detecting closed intersections and extension for composite surfaces is suggested. This algorithm consists of three step: generating state points for curve tracing, tracing intersection curves and sorting pieces of the intersection curves. The results of this algorithm and comparisons to the 'DESIGNBASE' and 'ACIS' system are presented.