APPROXIMATIONS TO INVERSE FUNCTIONS OF HILL'S EQUATION, MCBAIN'S EQUATION AND ERROR FUNCTION

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Other Title
  • Hillの式, McBaionの式および誤差関数の逆関数の近似式

Description

Polynomials in the form of Eq. 5 can closely approximate Hill's and McBain's equation and their inverse functions at the initial to intermediate stage of dyeing. At the later stage, expressions in the form of Eq. 7 can closely approximate the inverse functions. where, P1…Pn and Q1…Qn-1, are constants. For the approximations to Hill's and McBain's equation, for the inverse functions, respectively.<br>The inverse function of error function is accurately approximated by the expression in the form of Eq. 9.<br>where g(X)=x, z=erfcx, and P0…Pn-1, Q0…Qn and a are constants.<br>Accurate diffusion coefficients of C. I. Disperse Violet 1 into poly (ethylene terephthalate) fiber and film were obtained from the experimental diffusion data by using the approximations.

Journal

  • Sen'i Gakkaishi

    Sen'i Gakkaishi 37 (1), T39-T47, 1981

    The Society of Fiber Science and Technology, Japan

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