• Title/Summary/Keyword: reparametrization

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TIME REPARAMETRIZATION OF PIECEWISE PYTHAGOREAN-HODOGRAPH $C^1$ HERMITE INTERPOLANTS

  • Kong, Jae-Hoon;Kim, Gwang-Il
    • Journal of applied mathematics & informatics
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    • v.30 no.3_4
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    • pp.381-393
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    • 2012
  • In this paper, we show two ways of the time reparametrization of piecewise Pythagorean-hodograph $C^1$ Hermite interpolants. One is the time reparametrization with no shape change, and the other is that with shape change. We show that the first reparametrization does not depend on the boundary data and that it is uniquely determined by the size of parameter domain, up to the general cases. We empirically show that the second parametrization can cause the change of the shape of interpolant.

Bayesian Estimation for the Reliability of Stress-Strength Systems Using Noninformative Priors

  • Kim, Byung-Hwee
    • International Journal of Reliability and Applications
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    • v.2 no.2
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    • pp.117-130
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    • 2001
  • Consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions. We first treat the orthogonal reparametrization and then, using this reparametrization, derive Jeffreys'prior, reference prior, and matching priors. We next provide the suffcient condition for propriety of posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of the parameter of interest in some special cases.

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Surface Design Using B-spline Skinning of Cross-Sectional Curves under Volume Constraint (체적등의 구속조건하에서 단면곡선들로부터 B-spline Skinning을 사용한 곡면 디자인)

  • 김형철
    • Korean Journal of Computational Design and Engineering
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    • v.3 no.2
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    • pp.87-102
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    • 1998
  • Given a sequence of cross-sectional curves, the skinning method generates a freeform surface that interpolates the given curves in that sequence. This thesis presents a construction method of a B-spline skinning surface that is fair and satisfies volume constraints. The fairness metric is based on the parametric energy functional of a surface. The degrees of freedom in surface control are closely related lo control points in the skinning direction. The algorithm fur finding a skinning surface consists of two step. In the first step, an initial fair surface is generated without volume constraints and one coordinate of each control point is fixed. In the second step, a final surface that meets all constraints is constucted by rearranging the other coordinates of each control point that defines the initial surface A variational Lagrange optimization method produces a system of nonlinear equations, which can be solved numerically. Moreover, the reparametrization of given sectional curves is important for the construction of a reasonable skinning surface. This thesis also presents an intuitive metric for reparametrization and gives some examples that are optimized with respect to that metric.

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$C^1$ HERMITE INTERPOLATION WITH MPH QUARTICS USING THE SPEED REPARAMETRIZATION METHOD

  • Kim, Gwang-Il
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.131-141
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    • 2010
  • In this paper, we propose a new method to obtain $C^1$ MPH quartic Hermite interpolants generically for any $C^1$ Hermite data, by using the speed raparametrization method introduced in [16]. We show that, by this method, without extraordinary processes ($C^{\frac{1}{2}}$ Hermite interpolation introduced in [13]) for non-admissible cases, we are always able to find $C^1$ Hermite interpolants for any $C^1$ Hermite data generically, whether it is admissible or not.

Bayesian reliability estimation in a stress-strength system

  • Chang, In-Hong;Oh, Soo-Jin
    • Journal of Applied Reliability
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    • v.11 no.2
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    • pp.151-165
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    • 2011
  • We consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions with index, scale, and shape parameters. We first derive group-ordering reference priors using the reparametrization. We next provide the sufficient condition for propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of parameter of interest in some special cases.

A Method of Obtaning Least Squares Estimators of Estimable Functions in Classification Linear Models

  • Kim, Byung-Hwee;Chang, In-Hong;Dong, Kyung-Hwa
    • Journal of the Korean Statistical Society
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    • v.28 no.2
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    • pp.183-193
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    • 1999
  • In the problem of estimating estimable functions in classification linear models, we propose a method of obtaining least squares estimators of estimable functions. This method is based on the hierarchical Bayesian approach for estimating a vector of unknown parameters. Also, we verify that estimators obtained by our method are identical to least squares estimators of estimable functions obtained by using either generalized inverses or full rank reparametrization of the models. Some examples are given which illustrate our results.

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Bayesian Inference for Stress-Strength Systems

  • Chang, In-Hong;Kim, Byung-Hwee
    • 한국데이터정보과학회:학술대회논문집
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    • 2005.10a
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    • pp.27-34
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    • 2005
  • We consider the problem of estimating the system reliability noninformative priors when both stress and strength follow generalized gamma distributions. We first derive Jeffreys' prior, group ordering reference priors, and matching priors. We investigate the propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. We also examine whether the reference priors satisfy the probability matching criterion.

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A Study on Noninformative Priors of Intraclass Correlation Coefficients in Familial Data

  • Jin, Bong-Soo;Kim, Byung-Hwee
    • Communications for Statistical Applications and Methods
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    • v.12 no.2
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    • pp.395-411
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    • 2005
  • In this paper, we develop the Jeffreys' prior, reference prior and the the probability matching priors for the difference of intraclass correlation coefficients in familial data. e prove the sufficient condition for propriety of posterior distributions. Using marginal posterior distributions under those noninformative priors, we compare posterior quantiles and frequentist coverage probability.

Envelope of the Wallace-Simson Lines with Signed Angle ${\alpha}$

  • Bae, Sung Chul;Ahn, Young Joon
    • Journal of Integrative Natural Science
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    • v.5 no.1
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    • pp.38-41
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    • 2012
  • In this paper we show that for any triangle and any point on the circumcircle the envelope of the Wallace-Simson lines with signed angle ${\alpha}$ is a parabola. The proof is obtained naturally using polar coordinates. We also present the reparametrization of the envelope which is a linear normal curve.

EQUIVALENT DEFINITIONS OF RESCALED EXPANSIVENESS

  • Wen, Xiao;Yu, Yining
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.593-604
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    • 2018
  • Recently, a new version of expansiveness which is closely attached to some certain weak version of hyperbolicity was given for $C^1$ vector fields as following: a $C^1$ vector field X will be called rescaling expansive on a compact invariant set ${\Lambda}$ of X if for any ${\epsilon}$ > 0 there is ${\delta}$ > 0 such that, for any $x,\;y{\in}{\Lambda}$ and any time reparametrization ${\theta}:{\mathbb{R}}{\rightarrow}{\mathbb{R}}$, if $d({\varphi}_t(x),\,{\varphi}_{{\theta}(t)}(y)){\leq}{\delta}{\parallel}X({\varphi}_t(x)){\parallel}$ for all $t{\in}{\mathbb{R}}$, then ${\varphi}_{{\theta}(t)}(y){\in}{\varphi}_{(-{\epsilon},{\epsilon})}({\varphi}_t(x))$ for all $t{\in}{\mathbb{R}}$. In this paper, some equivalent definitions for rescaled expansiveness are given.