The parsimony pressure method is perhaps the simplest and most frequently used method to control bloat in genetic programming. In this paper we first reconsider the size evolution equation for genetic programming developed in [24] and rewrite it in a form that shows its direct relationship to Price’s theorem. We then use this new formulation to derive theoretical results that show how to practi...

The parsimony pressure method is perhaps the simplest and most frequently used method to control bloat in genetic programming. In this chapter we first reconsider the size evolution equation for genetic programming developed in [28] and rewrite it in a form that shows its direct relationship to Price’s theorem. We then use this new formulation to derive theoretical results that show how to prac...

In this paper, we discuss methods and approaches for definition of multiplication distributions, which is not defined in general the classical theory. We show that problem related to fact operator by a smooth function nonclosable space distributions. give method construction new objects called or mnemofunctions, preserve essential properties usual distributions produce algebras as well. describ...

We consider PT-symmetric, discrete nonlocal nonlinear Schr\"{o}dinger equation on metric graphs. Soliton solutions are obtained for simplest graph topologies, such as star and tree Integrability of the problem is shown by proving existence infinite number conservation laws.

Abstract Using a series of fractional powers we present representation the solution to logistic equation is presented. To simplify consider simplest case and prove that power indeed exact solution. Some numerical approximations are presented show good obtained by truncating series.

1926 marked the beginning of a radically new chapter in the history of chemistry, for the advent of the Schrödinger equation finally transformed chemistry into a calculable science. The problem, of course, was the inordinate complexity of the equation for all but the simplest of atomic and molecular systems and the discipline of Quantum Chemistry may be usefully characterised as the development...

a 2-d heat conduction model has been solved by using the adomian decomposition method topredict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source.the laser source may operate in a continuous wave (cw) mode or repeated pulse (rp) mode and may havearbitrary, spatial and temporal profiles.a generalized solution containing five-terms approxim...

in recent years, numerous approaches have been applied for finding the solutions of functional equations. one of them is the optimal homotopy asymptotic method. in current paper, this method has been applied for obtaining the approximate solution of fisher equation. the reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

We consider localized states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable localized states is made possible by pinning to the underlying lattice; they do not exist in the equivalent continuum equation. In particular we address the existence of ‘isolas’: closed curves of ...

Let us remind that Sommerfeld model of charged rigid sphere [1] (Sommerfeld particle) is the simplest theoretical model to take into consideration the ”back-reaction” of self-electromagnetic field on equation of motion of a radiating extended charged body (for point-like charge we have the known LorentzDirac equation with all its problems: renormalization of mass, preacceleration, runaway solut...