• Title, Summary, Keyword: C-integral

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C-DUNFORD AND C-PETTIS INTEGRALS

  • Yu, Chao;Zhao, Dafang;Ye, Guoju
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.4
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    • pp.427-435
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    • 2008
  • In this paper, we give some extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We also discuss the relation among the C-Dunford integral, C-Pettis integral and C-integral.

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C-INTEGRAL AND DENJOY-C INTEGRAL

  • Zhao, Dafang;Ye, Guoju
    • Communications of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.27-39
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    • 2007
  • In this paper, we define and study the C-integral of functions mapping an interval [a,b] into a Banach space X and discuss the relations among Henstock integral, C-integral and McShane integral. We also study the Denjoy extension of the C-integral.

ON STRONG C-INTEGRAL OF BANACH-VALUED FUNCTIONS

  • Zhao, Dafang;Ye, Guoju
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.1-10
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    • 2007
  • In this paper, we define and study the Banach-valued C-integral and strong C-integral, We prove that the C-integral and the strong C-integral are equivalent if and only if the Banach space is finite dimensional. We also study the primitive of the strong C-integral in terms of the C-variational measures.

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C-DUNFORD INTEGRAL AND C-PETTIS INTEGRAL

  • Zhao, Dafang;You, Xuexiao
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.1
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    • pp.21-28
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    • 2008
  • In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We prove that a function f is C-Dunford integrable if and only if $x^*f$ is C-integrable for each $x^*{\in}X^*$ and prove the controlled convergence theorem for the C-Pettis integral.

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ON C-INTEGRAL OF BANACH-VALUED FUNCTIONS

  • Ye, Guoju;Zhao, Dafang
    • Korean Journal of Mathematics
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    • v.14 no.2
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    • pp.169-183
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    • 2006
  • In this paper, we define and study the C-integral and the strong C-integral of functions mapping an interval [a,b] into a Banach space X. We prove that the C-integral and the strong C-integral are equivalent if and only if the Banach space is finite dimensional, We also consider the property of primitives corresponding to Banach-valued functions with respect to the C-integral and the strong C-integral.

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Estimations of the C(t)-Integral in Transient Creep Condition for Pipe with Crack Under Combined Mechanical and Thermal Stress (I) - Elastic-Creep - (복합응력이 작용하는 균열 배관에 대한 천이 크리프 조건에서의 C(t)-적분 예측 (I) - 탄성-크리프 -)

  • Song, Tae-Kwang;Kim, Yun-Jae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.9
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    • pp.949-956
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    • 2009
  • The C(t)-integral describes amplitude of stress and strain rate field near a tip of stationary crack under transient creep condition. Thus the C(t)-integral is a key parameter for the high-temperature crack assessment. Estimation formulae for C(t)-integral of the cracked component operating under mechanical load alone have been provided for decades. However, high temperature structures usually work under combined mechanical and thermal load. And no investigation has provided quantitative estimates for the C(t)-integral under combined mechanical and thermal load. In this study, 3-dimensional finite element analyses were conducted to calculate the C(t)-integral of elastic-creep material under combined mechanical and thermal load. As a result, redistribution time for the crack under combined mechanical and thermal load is re-defined through FE analyses to quantify the C(t)-integral. Estimates of C(t)-integral using this proposed redistribution time agree well with FE analyses results.

THE INTEGRATION BY PARTS FOR THE C-INTEGRAL

  • Park, Jae Myung;Lee, Deok Ho;Yoon, Ju Han;Yu, Young Hyun
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.607-613
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    • 2009
  • In this paper, we define the C-integral and prove the integration by parts formula for the C-integral.

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ON C-STIELTJES INTEGRAL OF BANACH-VALVED FUNCTIONS

  • Zhang, Xiaojie;Zhao, Dafang;Ye, Guoju
    • The Pure and Applied Mathematics
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    • v.14 no.2
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    • pp.71-84
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    • 2007
  • In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.

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A NOTE ON THE INTEGRATION WITH RESPECT TO FINITELY ADDITIVE SET FUNCTIONS

  • Kim, Bong-Jin
    • The Pure and Applied Mathematics
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    • v.6 no.1
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    • pp.17-25
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    • 1999
  • In this paper, we investigate the properties of the Dunford-Schwartz integral (the integral with respect to a finitely additive measure). Though it is not equivalent to the cylinder integral, we can show that a cylinder probability v on (H, C) can be extend as a finitely additive probability measure $\hat{v}$ on a field $\hat{C}{\;}{\supset}{\;}C$ which is equivalent to the Dunford-Schwartz integral on ($H,{\;}\hat{C},{\;}\hat{v}$).

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