• Title/Summary/Keyword: Cauchy method

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REPRESENTATION OF THE GENERALIZED FUNCTIONS OF GELFAND AND SHILOV

  • Jae Young Chung;Sung Jin Lee
    • Communications of the Korean Mathematical Society
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    • v.9 no.3
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    • pp.607-616
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    • 1994
  • I. M. Gelfand and G. E. Shilov [GS] introduced the Gelfand-Shilov spaces of type S, generalized type S and type W of test functions to investigate the uniqueness of the solutions of the Cauchy problems of partial differential equations. Using the heat kernel method Matsuzawa gave structure theorems for distributions, hyperfunctions and generalized functions in the dual space $(S^s_r)'$ of the Gelfand-Shilov space of type S in [M1, M2 and DM], respectively. Also, we gave structure theorems for ultradistributions, Fourier hyperfunctions in [CK, KCK], respectively.

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HOLD EFFECT IN FINITE TORSION OF A COMPRESSIBLE ELASTIC TUBE

  • Akinola, A.P;Layeni, O.P;Ldejobi, O.A.;Umoru, L.E.
    • Journal of applied mathematics & informatics
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    • v.16 no.1_2
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    • pp.323-336
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    • 2004
  • We consider the application of complex variable method to elastic problem and investigate the nonlinear effect of finite torsion of a compressible elastic composite layer. We obtain that as a result of finite deformation approach, a tube subjected to torsion decreases in radius giving rise to a “hold effect”.

ON COMPLEX VARIABLE METHOD IN FINITE ELASTICITY

  • Akinola, Ade
    • Journal of applied mathematics & informatics
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    • v.12 no.1_2
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    • pp.183-198
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    • 2003
  • We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.

CORRIGENDUM TO "A DUAL ITERATIVE SUBSTRUCTURING METHOD WITH A SMALL PENALTY PARAMETER", [J. KOREAN MATH. SOC. 54 (2017), NO. 2, 461-477]

  • Lee, Chang-Ock;Park, Eun-Hee;Park, Jongho
    • Journal of the Korean Mathematical Society
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    • v.58 no.3
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    • pp.791-797
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    • 2021
  • In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

MAXIMAL DOMAINS OF SOLUTIONS FOR ANALYTIC QUASILINEAR DIFFERENTIAL EQUATIONS OF FIRST ORDER

  • Han, Chong-Kyu;Kim, Taejung
    • Journal of the Korean Mathematical Society
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    • v.59 no.6
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    • pp.1171-1184
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    • 2022
  • We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.

LONG TIME BEHAVIOR OF SOLUTIONS TO SEMILINEAR HYPERBOLIC EQUATIONS INVOLVING STRONGLY DEGENERATE ELLIPTIC DIFFERENTIAL OPERATORS

  • Luyen, Duong Trong;Yen, Phung Thi Kim
    • Journal of the Korean Mathematical Society
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    • v.58 no.5
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    • pp.1279-1298
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    • 2021
  • The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

Kernel Integration Scheme for 2D Linear Elastic Direct Boundary Element Method Using the Subparametric Element (저매개변수 요소를 사용한 2차원 선형탄성 직접 경계요소법의 Kernel 적분법)

  • Jo, Jun-Hyung;Park, Yeongmog;Woo, Kwang-Sung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.25 no.5
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    • pp.413-420
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    • 2012
  • In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

STRONG CONVERGENCE OF MONOTONE CQ ITERATIVE PROCESS FOR ASYMPTOTICALLY STRICT PSEUDO-CONTRACTIVE MAPPINGS

  • Zhang, Hong;Su, Yongfu;Li, Mengqin
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.763-771
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    • 2009
  • T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

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A Study on Structural Analysis for Aircraft Gas Turbine Rotor Disks Using the Axisymmetric Boundary Integral Equation Method (축대칭 경계적분법에 의한 항공기 가스터빈 로터디스크 구조해석에 관한 연구)

  • Kong, Chang-Duk;Chung, Suk-Choo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.8
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    • pp.2524-2539
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    • 1996
  • A design process and an axisymmetric boundary integral equation method for precise structural analysis of the aircraft gas turbine rotor disk were developed. This axisymmetric boundary integral equation method for stress and steady-state thermal analysis was improved in solution accuracy by appling an implicit technique for Cauchy principal value evaluation, a subelement technique for weak singular integral evaluation and a double exponentical integral technoque for internal point solution near boundary surfaces. Stresses, temperatures, low cycle fatigue lifes and critical speeds for the turbine rotor disk of the thrust 1421 N class turbojet engine were analysed in a pratical calculation model problem.

Crystallite Size Measurement of Uranium Oxide Fuel Powders by Neutron Diffraction (중성자 회절에 의한 산화우라늄 핵연료 분말의 결정크기 측정)

  • 류호진;강권호;문제선;송기찬;최용남
    • Journal of Powder Materials
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    • v.10 no.5
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    • pp.318-324
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    • 2003
  • The nano-scale crystallite sizes of uranium oxide powders in simulated spent fuel were measured by the neutron diffraction line broadening method in order to analyze the sintering behavior of the dry process fuel. The mixed $UO_2$ and fission product powders were dry-milled in an attritor for 30, 60, and 120 min. The diffraction patterns of the powders were obtained by using the high resolution powder diffractometer in the HANARO research reactor. Diffraction line broadening due to crystallite size was measured using various techniques such as the Stokes' deconvolution, profile fitting methods using Cauchy function, Gaussian function, and Voigt function, and the Warren-Averbach method. The non-uniform strain, stacking fault and twin probability were measured using the information from the diffraction pattern. The realistic crystallite size could be obtained after separation of the contribution from the non-uniform strain, stacking fault and twin.