Abstract This article provides a survey of key papers that characterise computable functions, but also some novel insights as follows. It is argued the power algorithms at least strong functions can be proved to totally in type-theoretic translations subsystems second-order Zermelo Fraenkel set theory. Moreover, it claimed typed systems lambda calculus give rise naturally functional interpretat...

We study numerical computation of conformal invariants domains in the complex plane. In particular, we provide an algorithm for computing capacity a condenser. The applies to wide variety geometries: are assumed have smooth or piecewise boundaries. method use is based on boundary integral equation developed and implemented [1]. A characteristic feature this that, with small changes code, spectr...

In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES alg...