Executive Summary Operational risk management inside banks and insurance companies is currently an important task. The computation of a risk measure associated to these kinds of risks lies on the knowledge of the so-called Loss Distribution Function (LDF). Traditionally this LDF is computed via Monte Carlo simulations or using the Panjer recursion which is an iterative algorithm. In this paper,...

In this article, we briefly discussed the definition of fractal, several important characters of fractal and the computation method of fractal dimensions with self-similarity. We also used the recursion algorithm to design a multi-colored fractal tree which was generated in computer by VB (Visual Basic) language, and formed a fractal tree user interface based on that. In addition, various forms...

Utilizing a method briefly hinted in the author’s paper written in 1991 jointly with V. C. Harris, we derive here a number of unpublished recursion formulae for a variety of product partition functions which we believe have not been considered before in the literature. These include the functionsp∗(n;k,h) (which stands for the number of product partitions ofn> 1 into k parts of which h are dist...

In this paper, we propose a new modified recursion scheme for the approximate solution of higher-order, multipoint, nonlinear boundary value problems with higher-order Robin-type boundary conditions by the Adomian decomposition method. Our new approach utilizes all of the boundary conditions to derive an equivalent nonlinear Fredholm-Volterra integral equation before establishing the new modifi...

In this correspondence, we present a general recursive approach for image segmentation by extending Otsu’s method. The new approach has been implemented in the scope of document images, specifically real-life bank checks. This approach segments the brightest homogeneous object from a given image at each recursion, leaving only the darkest homogeneous object after the last recursion. The major s...

Harrison, P.G. and H. Khoshnevisan, A new approach to recursion removal, Theoretical Computer Science 93 (1992) 91-113. Iterative forms are derived for a class of recursive functions, i.e. the recursion is “removed”. The transformation comprises first analysis of the defining equation of a recursive function and then synthesis of an imperative language loop from the primitive subexpressions so ...

A recent proposal (Hauser, Chomsky & Fitch, 2002) suggests that the crucial defining property of human language is recursion. In this paper, following a critical analysis of what is meant by the term, I examine three reasons why the recursion-only hypothesis cannot be correct: (i) recursion is neither unique to language in humans, nor unique to our species, (ii) human language consists of many ...

In this paper we discuss the concept of cosymmetries and co–recursion operators for difference equations and present a co–recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion op...

Several extensions of Gödel’s system T with new forms of recursion have been designed for the purpose of giving a computational interpretation to classical analysis. One can organise many of these extensions into two groups: those based on bar recursion, which include Spector’s original bar recursion, modified bar recursion and the more recent products of selections functions, or those based on...

A typed lambda calculus with recursion in all finite types is defined such that the first order terms exactly characterize the parallel complexity class NC. This is achieved by use of the appropriate forms of recursion (concatenation recursion and logarithmic recursion), a ramified type structure and imposing of a linearity constraint.