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2 results

  • Appendix A - Some mathematical tools

  • Karim M. Abadir, Imperial College London, Risto D. H. Heijmans, Jan R. Magnus, Vrije Universiteit, Amsterdam
  • Book:
    Statistics
    Published online:
    11 June 2020
    Print publication:
    08 November 2018, pp 699-726

  • Summary

    This appendix collects mathematical tools that are needed in the main text. In addition, it gives a brief description of some essential background topics. It is assumed that the reader knows elementary calculus. The topics are grouped in four sections. First, we consider some useful methods of indirect proofs. Second, we introduce basic results for complex numbers and polynomials. The third topic concerns series expansions. Finally, some further calculus is presented, including difference calculus, Stieltjes integrals, and multivariable constrained optimization (covering also the case of inequality constraints).

  • Dynamic Problem Concerning Mode I Semi-Infinite Crack Propagation

  • N. C. Lü, Y. H. Cheng, X. G. Li, J. Cheng
  • Journal:
    Journal of Mechanics / Volume 29 / Issue 2 / June 2013
    Published online by Cambridge University Press:
    29 January 2013, pp. 309-318
    Print publication:
    June 2013

  • By the approaches of the theory of complex functions, dynamic problem concerning mode I semi-infinite crack propagation was studied. Analytical solutions are very easily obtained by application of the measures of self-similar functions. The problems researched can be changed into Riemann-Hilbert problems and analytical solutions to semi-infinite crack under the condition of impulse loads and increasing loads Pt located at the origin of the coordinates, respectively, are attained.