• The Pure and Applied Mathematics
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• v.13 no.2 s.32
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• pp.151-155
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• 2006

Let $\gamma$ be a $C_2$ curve in the open unit disk $\mathbb{D}. Flinn and Osgood proved that $K_{\mathbb{D}}(z,\gamma){\geq}1$ for all $z{\in}{\gamma}$ if and only if the curve ${\Large f}o{\gamma}$ is convex for every convex conformal mapping $\Large f$ of $\mathbb{D}, where $K_{\mathbb{D}}(z,\;\gamma)$ denotes the hyperbolic curvature of $\gamma$ at the point z. In this paper we establish a generalization of the Flinn-Osgood characterization for a curve with the hyperbolic curvature at least 1.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.123-132
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• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• Fashion & Textile Research Journal
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• v.13 no.5
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• pp.661-671
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• 2011

This study was designed to produce rounded belt pattern and tight-skirt pattern drafting method using 3D body scan data. Subjects were thirty women in their early twenties. In order to figure out the optimum cutting points, namely, where darts are made, using CAD program, curve ratio inflection points on the horizontal curve of waist, abdomen, and hip to find 1 point in the front, two points in the back part. The average length from center front point to maximum curve ratio was 7.7 cm(46.3%) on the waist curve; 7.9 cm(39.4%) on the abdomen curve. And the average length from center back point to maximum curve ratio point was 6.9 cm(39.0%) for first dart and 11.2 cm(63.3%) for second dart on the waist curve; 8.9 cm(35.8%) for first dart and 15.7 cm(63.3%) for second dart on the hip curve respectively. The cutting lines from were made up by connecting curve inflection points. After divided using cutting lines, each patch was flattened onto the plane and all the technical design factors related with patternmaking were measured, such as dart amount, lifting amount of side waist point, etc. Based on the results of correlation analysis among these factors, regression analysis was done to produce equations to estimate the variables necessary to draw up pattern draft method; F1=F8+1.1, $F4=2.5{\times}F2+0.9$, $F5=0.9{\times}F4+1.0$, $F6=0.3{\times}F4+0.4$, $B1=0.9{\times}B8+2.3$, $B4=2.1{\times}B2+1.3$, $B5=0.9{\times}B4+3.5$, and $B6=0.3{\times}B4+0.4$.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.159-169
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• 2005

An algorithmic approach to degree reduction of rational Bezier curves is presented. The algorithms are based on the degree reduction of polynomial Bezier curves. The method is introduced with the following steps: (a) convert the rational Bezier curve to polynomial Bezier curve by using homogenous coordinates, (b) reduce the degree of polynomial Bezier curve, (c) determine weights of degree reduced curve, (d) convert the Bezier curve obtained through step (b) to rational Bezier curve with weights in step (c).

• Journal of Information Processing Systems
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• v.4 no.4
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• pp.153-158
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• 2008

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

• Journal of the Korean Chemical Society
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• v.6 no.2
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• pp.104-107
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• 1962

It is thought that the adsorption isotherms in dyeing of cellulose by the direct cotton dyes are consisted of combined type of Langmuir and Freundlich as the opinion of Fujino, et al;$[D]_F=ab[D]_S/(1+b[D]_S)+k[D]_S$where a,b,k; constants, $[D]_F$; dye adsorption on the fiber, $[D]_S$; dye concentration in the bath. This means that the dyes adsorbed in cellulose present in the state of partly mono molecular and partly aggregate; the characteristic fading order curve will be expressed as the combined system of uniform particle size distribution and assumed that the slope of the theoretical models of Baxter, et al., and assumed that the slope of curve will be changed near the point of a, the saturation value of Langmuir isotherms in the above equation. Firstly, the theoretical fading rate curve was treated with small colour difference as the one step of experimental of above consideration.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.369-378
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• 2007

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d or d-1 on a smooth plane curve of degree d.

• Journal of Information Technology Services
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• v.12 no.3
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• pp.323-330
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• 2013

In this paper, miniaturized patch antenna operating at ISM band has been designed by applying the fractal technique. Various type of antenna structure, microstrip patch antenna and koch curve microstrip patch antenna has been proposed and simulated using Ansoft HFSS (High Frequency Structure Simulator). The area of microstrip patch antenna and koch microstrip patch antenna is 1,058 $mm^2$, and 891 $mm^2$ respectively, showing the size reduction ratio of 16%. The finally made koch curve microstrip patch antenna resonates at 2.45GHz with return loss of 22.69dB, VSWR of 1.2142, and antenna radiation gain of 3.26dBi.

• Journal of Animal Science and Technology
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• v.58 no.2
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• pp.8.1-8.14
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• 2016

In this research data representing 72,946 primiparous cows from 724 herds with 638,063 total test day records calved between 2001 and 2011. These data were analysed to determine the effect of age at first and season of calving on parameters of the Wood lactation curve. Also, genetic trend of the lactation curve parameters in different calving years were evaluated. The results indicate that the highest rate of atypical lactation curve was related to cows that calved in summer (28.05 %). The maximum phenotypic relationship between initial milk yield and total 305-d milk yield was observed in cows calved in spring (0.40). The role of peak yield is more than peak time on 305-d total milk yield in primiparous Holstein. One month increase in age at first calving from 18 to 26 month raised 305-d milk yield by around 138 kg and from 27 to 32 month decreased by 61 kg. The persistency of lactation between 101 and 200 days is higher than that of 201-305 days. Our results indicate that the shape of lactation curve is largely dependent on the season of calving (higher level of milk production in cows which calved in autumn and winter). The heritabilities of parameters of lactation curve and persistency measures were low. The genetic trends for peak time, peak yield and 305-d milk yields were positive and estimated to be 0.019, 0.021 and 8.13 kg/year respectively. So the range from 24 to 26.5 month of calving is the optimum calving time in primiparous Holstein for maximizing 305-d milk yield.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.99-105
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• 2009

Let $M=H_1{\cup}_SH_2$ be a Heegaard splitting of a 3-manifold M, D be an essential disk in $H_1$ and A be an essential annulus in $H_2$. Suppose D and A intersect in one point. First, we show that a Heegaard splitting admitting such a (D, A) pair satisfies the disjoint curve property, yet there are infinitely many examples of strongly irreducible Heegaard splittings with such (D, A) pairs. In the second half, we obtain another Heegaard splitting $M=H'_1{\cup}_{S'}H'_2$ by removing the neighborhood of A from $H_2$ and attaching it to $H_1$, and show that $M=H'_1{\cup}_{S'}H'_2$ also has a (D, A) pair with $|D{\cap}A|=1$.