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  • Title/Summary/Keyword: weak regularity

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FURTHER RESULTS ON MULTISPLITTING AND TWO-STAGE MULTISPLITTING METHODS

  • Kim, Sang-Wook;Han, Yu-Du;Yun, Jae-Heon
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.25-35
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    • 2009
  • In this paper, we study the regularity of induced splittings from multisplitting and two-stage multisplitting methods of monotone matrices under the assumption that splittings are weak regular, and we also study some comparison theorems for two-stage multisplitting methods of monotone matrices.

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Test for Parameter Change based on the Estimator Minimizing Density-based Divergence Measures

  • Na, Ok-Young;Lee, Sang-Yeol;Park, Si-Yun
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.05a
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    • pp.287-293
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    • 2003
  • In this paper we consider the problem of parameter change based on the cusum test proposed by Lee et al. (2003). The cusum test statistic is constructed utilizing the estimator minimizing density-based divergence measures. It is shown that under regularity conditions, the test statistic has the limiting distribution of the sup of standard Brownian bridge. Simulation results demonstrate that the cusum test is robust when there arc outliers.

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Limiting Distributions of Trimmed Least Squares Estimators in Unstable AR(1) Models

  • Lee, Sangyeol
    • Journal of the Korean Statistical Society
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    • v.28 no.2
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    • pp.151-165
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    • 1999
  • This paper considers the trimmed least squares estimator of the autoregression parameter in the unstable AR(1) model: X\ulcorner=ØX\ulcorner+ε\ulcorner, where ε\ulcorner are iid random variables with mean 0 and variance σ2> 0, and Ø is the real number with │Ø│=1. The trimmed least squares estimator for Ø is defined in analogy of that of Welsh(1987). The limiting distribution of the trimmed least squares estimator is derived under certain regularity conditions.

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THE NAVIER-STOKES EQUATIONS WITH INITIAL VALUES IN BESOV SPACES OF TYPE B-1+3/qq,

  • Farwig, Reinhard;Giga, Yoshikazu;Hsu, Pen-Yuan
    • Journal of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1483-1504
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    • 2017
  • We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ΩR3 with initial value u0L2σ(Ω). It is known that a weak solution is a local strong solution in the sense of Serrin if u0 satisfies the optimal initial value condition u0B1+3/qq,sq with Serrin exponents sq > 2, q > 3 such that 2sq+3q=1. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class T0(ταu(τ)q)s dτ < with 2s+3q=12α, 0 < α < 12. This regularity is guaranteed if and only if u0 is contained in the Besov space B1+3/qq,s. In this article we consider the limit case of initial values in the Besov space B1+3/qq, and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.

ANALYTIC SMOOTHING EFFECT AND SINGLE POINT SINGULARITY FOR THE NONLINEAR SCHRODINGER EQUATIONS

  • Kato, Keiichi;Ogawa, Takayoshi
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.1071-1084
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    • 2000
  • We show that a weak solution of the Cauchy problem for he nonlinear Schrodinger equation, {i∂(sub)t u + ∂2(sub)x u = f(u,u), t∈(-T,T), x∈R, u(0,x) = ø(x).} in the negative solbolev space H(sup)s has a smoothing effect up to real analyticity if the initial data only have a single point singularity such as the Dirac delta measure. It is shown that for H(sup)s (R)(s>-3/4) data satisfying the condition (※Equations, See Full-text) the solution is analytic in both space and time variable. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [18] and previous work by Kato-Ogawa [12]. We give an improved new argument in the regularity argument.

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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR IN A THREE-DIMENSIONAL TWO-SPECIES CHEMOTAXIS-STOKES SYSTEM WITH TENSOR-VALUED SENSITIVITY

  • Liu, Bin;Ren, Guoqiang
    • Journal of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.215-247
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    • 2020
  • In this paper, we deal with a two-species chemotaxis-Stokes system with Lotka-Volterra competitive kinetics under homogeneous Neumann boundary conditions in a general three-dimensional bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some Lp-estimate techniques, we show that the system possesses at least one global and bounded weak solution, in addition to discussing the asymptotic behavior of the solutions. Our results generalizes and improves partial previously known ones.

The Development of Performance Measures in Railway Services (철도서비스 평가를 위한 항목 및 지표의 선정방안)

  • Kim Yeon-Kyu
    • Proceedings of the KSR Conference
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    • 2003.05a
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    • pp.222-231
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    • 2003
  • After the reform of rail industry, a system to evaluate service qualities is required for the continuous improvement of railway service and the strength of competitiveness. This research provides evaluation categories and indices which are considered to be suited to the evaluation of rail service qualities. This study provides 4 categories and 11 indices to assess the rail service qualities: provision-operation interval/average operation speed, reliability-regularity/operation cancellation rate, safety- train usage term/facilities for the weak, client satisfaction- easiness of reserving and purchasing of tickets/comfort of queuing facilities/ kindness of train crews/ pleasantness of trains/provision of information, etc.

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ENDPOINT ESTIMATES FOR MAXIMAL COMMUTATORS IN NON-HOMOGENEOUS SPACES

  • Hu, Guoen;Meng, Yan;Yang, Dachun
    • Journal of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.809-822
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    • 2007
  • Certain weak type endpoint estimates are established for maximal commutators generated by CalderˊonZygmund operators and OscexpLγ(μ) functions for γ1 under the condition that the underlying measure only satisfies some growth condition, where the kernels of CalderˊonZygmund operators only satisfy the standard size condition and some H¨ormander type regularity condition, and OscexpLγ(μ) are the spaces of Orlicz type satisfying that OscexpLγ(μ) = RBMO(μ) if γ = 1 and OscexpLγ(μ)RBMO(μ) if γ > 1.

ELLIPTIC OBSTACLE PROBLEMS WITH MEASURABLE NONLINEARITIES IN NON-SMOOTH DOMAINS

  • Kim, Youchan;Ryu, Seungjin
    • Journal of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.239-263
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    • 2019
  • The Calderˊon-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity a(ξ,x1,x) is assumed to be only measurable in one spatial variable x1 and has locally small BMO semi-norm in the other spatial variables x', uniformly in ξ variable. Regarding non-smooth domains, we assume that the boundaries are locally flat in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.

DYNAMIC BEHAVIOR OF CRACKED BEAMS AND SHALLOW ARCHES

  • Gutman, Semion;Ha, Junhong;Shon, Sudeok
    • Journal of the Korean Mathematical Society
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    • v.59 no.5
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    • pp.869-890
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    • 2022
  • We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of beams and arches is studied under the assumptions of the weak and strong damping. The presence of cracks forces weaker regularity results for the arch motion, as compared to the beam case.