• Title/Summary/Keyword: approximate equivalence

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A NOTE ON APPROXIMATE SIMILARITY

  • Hadwin, Don
    • Journal of the Korean Mathematical Society
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    • v.38 no.6
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    • pp.1157-1166
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    • 2001
  • This paper answers some old questions about approximate similarity and raises new ones. We provide positive evidence and a technique for finding negative evidence on the question of whether approximate similarity is the equivalence relation generated by approximate equivalence and similarity.

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An Application of Homogenization Theory to the Coarse-Mesh Nodal Calculation of PWRs (PWR 소격격자 Nodal 계산에의 균질화 이론 적용)

  • Myung Hyun Kim;Jonghwa Chang;Kap Suk Moon;Chang Kun Lee
    • Nuclear Engineering and Technology
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    • v.16 no.4
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    • pp.202-216
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    • 1984
  • The success of coarse-mesh nodal solution methods provides strong motivation for finding homogenized parameters which, when used in global nodal calculation, will reproduce exactly all average nodal reaction rates for large nodes. Two approximate theories for finding these ideal parameters, namely, simplified equivalence theory and approximate node equivalence theory, are described herein and then applied to the PWR benchmark problem. Nodal code, ANM, is used for the global calculation as well as for the homogenization calculation. From the comparative analysis, it is recommended that homogenization be carried out only for the unique type of fuel assemblies and for core boundary color-sets. The use of approximate homogenized cross-sections and approximate discontinuity factors predicts nodal powers with maximum error of 0.8% and criticality within 0.1% error relative to the fine-mesh KIDD calculations.

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Sample Size Calculations for the Development of Biosimilar Products Based on Binary Endpoints

  • Kang, Seung-Ho;Jung, Ji-Yong;Baik, Seon-Hye
    • Communications for Statistical Applications and Methods
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    • v.22 no.4
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    • pp.389-399
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    • 2015
  • It is important not to overcalculate sample sizes for clinical trials due to economic, ethical, and scientific reasons. Kang and Kim (2014) investigated the accuracy of a well-known sample size calculation formula based on the approximate power for continuous endpoints in equivalence trials, which has been widely used for Development of Biosimilar Products. They concluded that this formula is overly conservative and that sample size should be calculated based on an exact power. This paper extends these results to binary endpoints for three popular metrics: the risk difference, the log of the relative risk, and the log of the odds ratio. We conclude that the sample size formulae based on the approximate power for binary endpoints in equivalence trials are overly conservative. In many cases, sample sizes to achieve 80% power based on approximate powers have 90% exact power. We propose that sample size should be computed numerically based on the exact power.

APPROXIMATE REACHABLE SETS FOR RETARDED SEMILINEAR CONTROL SYSTEMS

  • KIM, DAEWOOK;JEONG, JIN-MUN
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.469-481
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    • 2020
  • In this paper, we consider a control system for semilinear differential equations in Hilbert spaces with Lipschitz continuous nonlinear term. Our method is to find the equivalence of approximate controllability for the given semilinear system and the linear system excluded the nonlinear term, which is based on results on regularity for the mild solution and estimates of the fundamental solution.

APPROXIMATE CONTROLLABILITY AND REGULARITY FOR SEMILINEAR RETARDED CONTROL SYSTEMS

  • Jeong, Jin-Mun
    • Journal of applied mathematics & informatics
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    • v.9 no.1
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    • pp.213-230
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    • 2002
  • We deal with the approximate controllability for semilinear systems with time delay in a Hilbert space. First, we show the existence and uniqueness of solutions of the given systems with the mere general Lipschitz continuity of nonlinear operator f from $R\;\times\;V$ to H. Thereafter, it is shown that the equivalence between the reachable set of the semilinear system and that of its corresponding linear system. Finally, we make a practical application of the conditions to the system with only discrete delay.

APPROXIMATE IDENTITY OF CONVOLUTION BANACH ALGEBRAS

  • Han, Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.4
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    • pp.497-504
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    • 2020
  • A weight ω on the positive half real line [0, ∞) is a positive continuous function such that ω(s + t) ≤ ω(s)ω(t), for all s, t ∈ [0, ∞), and ω(0) = 1. The weighted convolution Banach algebra L1(ω) is the algebra of all equivalence classes of Lebesgue measurable functions f such that ‖f‖ = ∫0∞|f(t)|ω(t)dt < ∞, under pointwise addition, scalar multiplication of functions, and the convolution product (f ⁎ g)(t) = ∫0t f(t - s)g(s)ds. We give a sufficient condition on a weight function ω(t) in order that L1(ω) has a bounded approximate identity.

FINITE DIFFERENCE SCHEMES FOR CALCIUM DIFFUSION EQUATIONS

  • Choo, S.M.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.299-306
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    • 2008
  • Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^\infty$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

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FINITE DIFFERENCE SCHEMES FOR A GENERALIZED CALCIUM DIFFUSION EQUATION

  • Choo, Sang-Mok;Lee, Nam-Yong
    • East Asian mathematical journal
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    • v.24 no.4
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    • pp.407-414
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    • 2008
  • Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations with damping and convection terms, which describe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

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FINITE DIFFERENCE SCHEMES FOR A GENERALIZED NONLINEAR CALCIUM DIFFUSION EQUATION

  • Choo, S.M.
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1247-1256
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    • 2009
  • Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

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