• Journal of Ship and Ocean Technology
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• v.10 no.2
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• pp.24-36
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• 2006

Ship hullform is usually designed with a curve network, and smooth hullform surfaces are supposed to be generated by filling in (or interpolating) the curve network with appropriate surface patches. Tensor-product surfaces such as B-spline and $B\'{e}zier$ patches are typical representations to this interpolating problem. However, they have difficulties in representing the surfaces of irregular topological type which are frequently appeared in the fore- and after-body of ship hullform curve network. In this paper, we proposed a method that can automatically generate discrete $G^1$ continuous B-spline surfaces interpolating given curve network of ship hullform. This method consists of three steps. In the first step, given curve network is reorganized to be of two types: boundary curves and reference curves of surface patches. Especially, the boundary curves are specified for their surface patches to be rectangular or triangular topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. In the second step, surface fitting points and cross boundary derivatives are estimated by constructing virtual iso-parametric curves at discrete parameters. In the last step, discrete $G^1$ continuous B-spline surfaces are generated by surface fitting algorithm. Finally, several examples of resulting smooth hullform surfaces generated from the curve network data of actual ship hullform are included to demonstrate the quality of the proposed method.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.563-569
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• 2014

We investigate a minimal set of generators of a homogeneous ideal of a curve of degree d on a linearly normal smooth surface scroll W in $P^r$ whose arithmetic genus is maximal among curves of degree d on W.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.113-118
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• 2010

This paper proposed an ECAM (Electronic cam) control system which has simple and general structure. The proposed cam controller adopted the linear and polynomial curve-fitting method to generates a smooth cam profile curve function. Smooth motion trajectory of master actuator guarantees the good performance of slave motion and has an important effect on the interpolation quality of ECAM. The auto-tuning PID velocity controller was applied to overcome the uncertainties in ECAM, and the gains of the controller are updated continuously to ensure the consistency of system performance under varying working conditions. The robustness of system against the varying load torque disturbances and noises is guaranteed by using the load torque disturbance observer to suppress the disturbance on master actuator. The velocity compensator was applied to compensate the degradation of performance of slave motion caused from the varying driving speed of master motion. The stability and validity of the proposed ECAM control system was verified by simulation results.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1370
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• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.10
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• pp.1012-1017
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• 2006

By breaking the symmetry of the velocity profile in the S-curve, we developed a fast starting and smooth ending motion profile, named asymmetric S-curve(AS-curve). The problem for generating motion profile is formulated, and the algorithm for the AS-curve is derived and the flow chart of the AS-curve is illustrated. By various simulations, the derived algorithm is tested and shows the validity. This AS-curve can be applied to the high precision machines where fast and vibrationless motion is required in the near future.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.309-317
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• 2016

As a generalization of an inflection point, we consider a point P on a smooth plane curve C of degree m at which another curve C' of degree n meets C with high intersection multiplicity. Especially, we deal with the existence of two curves of degree m and n meeting at the unique point.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.6
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• pp.137-145
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• 2016

A novel tracking method is proposed to find coronary artery using high-order curve model in coronary CTA(Computed Tomography Angiography). The proposed method quickly generates numerous artificial trajectories represented by high-order curves, and each trajectory has its own cost. The only high-ranked trajectories, located in the target structure, are selected depending on their costs, and then an optimal curve as the centerline will be found. After tracking, each optimal curve segment is connected, where optimal curve segments share the same point, to a single curve and it is a piecewise smooth curve. We demonstrated the high-order curve is a proper model for classification of coronary artery. The experimental results on public data set sho that the proposed method is comparable at both accuracy and running time to the state-of-the-art methods.

• Korean Journal of Materials Research
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• v.26 no.11
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• pp.644-648
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• 2016

In order to examine how the solid-liquid interface responds to temperature variation depending on the materials characteristics, i.e. faceted phase or nonfaceted phase, the moving solid-liquid interface of transparent organic material, as a model substance for metallic materials (pivalic acid, camphene, salol, and camphor-50wt% naphthalene) was observed in-situ. Plots of the interface movement distance against time were obtained. The solid-liquid interface of the nonfaceted phase is atomically rough; it migrates in continuous mode, giving smooth curves of the distance-time plot. This is the case for pivalic acid and camphene. It was expected that the faceted phases would show different types of curves of the distance-time plot because of the atomically smooth solid-liquid interface. However, salol (faceted phase) shows a curve of the distance-time plot as smooth as that of the nonfaceted phases. This indicates that the solid-liquid interface of salol migrates as continuously as that of the nonfaceted phases. This is in contrast with the case of naphthalene, one of the faceted phases, for which the solid-liquid interface migrates in "stop and go" mode, giving a stepwise curve of the distance-time plot.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.1
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• pp.28-35
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• 1983

Quantitative analysis have been carried out on the micro-cracks on the surface and into the depth of unnotched smooth mild steel specimen under cyclic stains by rotating bending fatigue tests. Some of the results are; (1) Cracks initiate at the early stage of fatigue life N$_{I}$/ N$_{f}$=10 to 20%, and propagate during the rest of fatigue life. (2) Coalescence of highly crowded small fatigue cracks of random distribution seems to induce the final fracture at higher stress level. (3) The curves of crack initiation and the equal crack length on the graph of stress versus number of cycles are parallel to the S-N curve. (3) The curves of crack initiation and the equal crack length on the graph of stress versus number of cycles are parallel to the S-N curve. (4) The distributions of micro-surface crack length and depth show the composite Weibull distributions which are approximated to two straight lines separated by the value of transient region between stage I and stage II crack.k.k.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.377-386
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• 2011

For a smooth algebraic curve C of genus g $\geq$ 4, let $SU_C$(r, d) be the moduli space of semistable bundles of rank r $\geq$ 2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that $SU_C$(r, d) is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree $\geq$ r with respect to the ampl generator of Pic($SU_C$(r, d)). In this paper, we study the locus swept out by the rational curves on $SU_C$(r, d) of degree < r. As a by-product, we present another proof of Torelli theorem on $SU_C$(r, d).