• Restorative Dentistry and Endodontics
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• v.43 no.2
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• pp.15.1-15.7
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• 2018

Objectives: The present study aimed to evaluate the shaping ability of 2 thermally treated nickel-titanium reciprocating systems in simulated curved canals. Materials and Methods: Forty simulated canals were prepared to apical size 25 using Reciproc Blue R25 (VDW) and WaveOne Gold Primary (Dentsply Sirona) instruments. Standard pre- and post-preparation images were taken and superimposed. The removal of resin material was measured at 5 standard points: the canal orifice, halfway between the canal orifice and the beginning of the curve, the beginning of the curve, the apex of the curve, and the end-point of the simulated canal. The data were analysed using the independent sample t-test with a 5% significance threshold. Results: The canals in which Reciproc Blue R25 was used showed a significantly greater widening than those in which WaveOne Gold was used at 4 of the 5 measurement points (p < 0.05). The Reciproc Blue R25 instrument removed significantly more resin from the inner aspect of the curve at 2 of the 5 points and similar amounts at the remaining 3 points. At the 2 apical points, there was no significant difference between the Reciproc Blue R25 and WaveOne Gold Primary instruments. Conclusion: Both instruments respected the original canal anatomy; however, WaveOne Gold resulted in a more conservative shape with less transportation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.88-93
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• 1998

It is frequently important to approximate a rational B$\acute{e}$zier curve by an integral, i.e., polynomial one. This need will arise when a rational B$\acute{e}$zier curve is produced in one CAD system and is to be imported into another system, which can only handle polynomial curves. The objective of this paper is to present an algorithm to approximate rational B$\acute{e}$zier curves with polynomial curves of higher degree.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.38-41
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• 2002

Many scientifc applications include manipulation of data points tying in a space. We describe a method, based on sector labeling to generate a space-filling curve for partitioning such given data points. Our method is straightforward and flexible, equipping a one-one correspondence between point-values on the curve and data points in space in more efficient than designated methods found in the literature. It is widely believed that the Hilbert curve achieves the desired properties on linear mappings due to the locality between data points. Therefore we focus on the Hilbert curve since, later on, we identify it as the most suitable for our application. We demonstrate on using our method for the data particles of an n-body simulation that based on Barnes-Hut algorithm.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.21-30
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• 2016

In this paper two procedures for determination of the elastic curve of the simply and multiple supported beams are developed. Determination of the elastic curve is complex as it requires to solve a strong nonlinear differential equation with given boundary conditions. For numerical solution the initial guess of the slope at the end of the beam is necessary. Two procedures for obtaining of the initial guess are developed: one, based on transformation of the supported beam into a clamped-free one, and second, on the linearization of the problem. Procedures are applied for calculating of elastic curve of a simply supported beam and a beam with three supports. Obtained results are compared. Advantages and disadvantages of both methods are discussed. It is proved that both suggested procedures give us technically accurate results.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.11 no.3
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• pp.80-85
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• 2002

The free curve gear is a non-circular gear without any relating center, which can perform free curve motion for complicated mechanisms, and minimize the work area. In this study, an algorithms for tooth profile generation of free curve involute gear is developed. The algorithm uses the involute gear creating principle in which a gear can be generated by rolling with another standard involute one. Cycloid me and third polynomial curve gears were designed and verified by computer graphics. These gears are manufactured in the wire-cut EDM and examined in engagement with a standard spur gear. The results showed that the proposed algorithm is successful to design and to manufacture the free curve gear with concave and convex profiles.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1101-1113
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• 2014

We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle E of rank r and degree d with gcd(r, d) = 1 is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.155-162
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• 2013

Although the snowflake curve, the boundary of the Koch snowflake, is one of the well-known fractals, there is no iterated function system (IFS) for it in the literature. In this study, we give an IFS for this familiar closed curve.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• Restorative Dentistry and Endodontics
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• v.47 no.2
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• pp.16.1-16.9
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• 2022

Objectives: This study compared the cyclic fatigue resistance of One Curve (C wire) and F6 Skytaper (conventional austenite nickel-titanium [NiTi]), and 2 instruments with thermos-mechanically treated NiTi: Protaper Next X2 (M wire) and Hyflex CM (CM wire). Materials and Methods: Ten new instruments of each group (size: 0.25 mm, 6% taper in the 3 mm tip region) were tested using a rotary bending machine with a 60° curvature angle and a 5 mm curvature radius, at room temperature. The number of cycles until fracture was recorded. The length of the fractured instruments was measured. The fracture surface of each fragment was examined with a scanning electron microscope (SEM). The data were analyzed using one-way analysis of variance and the post hoc Tukey test. The significance level was set at 0.05. Results: At 60°, One Curve, F6 Skytaper and Hyflex CM had significantly longer fatigue lives than Protaper Next X2 (p < 0.05). No statistically significant differences were found in the cyclic fatigue lives of One Curve, F6 Skytaper, and Hyflex CM (p > 0.05). SEM images of the fracture surfaces of the different instruments showed typical features of fatigue failure. Conclusions: Within the conditions of this study, at 60° and with a 5 mm curvature radius, the cyclic fatigue life of One Curve was not significantly different from those of F6 Skytaper and Hyflex CM. The cyclic fatigue lives of these 3 instruments were statistically significantly longer than that of Protaper Next.

• IE interfaces
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• v.23 no.3
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• pp.205-212
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• 2010

The learning curve model is a mathematical form which represents the relationship between the manufacturing experience and its effectiveness. The semiconductor manufacturing is widely known as an appropriate example for the learning effect due to its complicated manufacturing processes. In this paper, I propose a new compound learning curve model for semiconductor products in which the general learning curve model and the growth curve are composed. The dependent variable and the effective independent variables of the model were abstracted from the existing learning curve models and selected according to multiple regression processes. The simulation results using the historical DRAM data show that the proposed compound learning curve model is one of adequate models for describing learning effect of semiconductor products.