1. Introduction Let P(x,y) denote the number of integers specified in the title. A number of estimates and asymptotic formulae for this function have been given (cf. [1] and the literature mentioned there). Recently DE BRUIJN ([2]) proved an asymptotic formula for log f(x,y) which holds uniformly for 2 < y < x. Part of the proof consisted of showing that P(x y) > C 71(y) + u\ where u = [(log x)...

In the last years the evolutionary computation domain is developed more and more rapidly. Differential Evolution is one of the representatives of this domain. It is a recently invented evolutionary algorithm, which nowadays is gaining more and more popularity. Originally proposed for continuous unconstraint optimization, it have been enlarged both and for mixed optimization and for handling non...

Differential evolution (DE) algorithms are commonly used metaheuristics for global optimization, but there has been very little research done on the generation of their initial population. The selection of the initial population in a population-based heuristic optimization method is important, since it affects the search for several iterations and often has an influence on the final solution. I...

Recommender systems are the systems that try to make recommendations to each user based on performance, personal tastes, user behaviors, and the context that match their personal preferences and help them in the decision-making process. One of the most important subjects regarding these systems is to increase the system accuracy which means how much the recommendations are close to the user int...

Integrated treatment planning for cancer patients has high importance in intensity modulated radiation therapy (IMRT). Direct aperture optimization (DAO) is one of the prominent approaches used in recent years to attain this goal. Considering a set of beam directions, DAO is an integrated approach to optimize the intensity and leaf position of apertures in each direction. In this paper, first, ...

In recent years a new evolutionary algorithm for optimization in continuos spaces called Differential Evolution (DE) has developed. DE turns out to need only few evaluation steps to minimize a function. This makes it an interesting candidate for problem domains with high computational costs as for instance in the automatic generation of programs. In this paper a DE-based tree discovering algori...

This paper presents a new technique for optimizing binary problems with building blocks. The authors have developed a different approach to existing Estimation of Distribution Algorithms (EDAs). Our technique, called Phylogenetic Differential Evolution (PhyDE), combines the Phylogenetic Algorithm and the Differential Evolution Algorithm. The first one is employed to identify the building blocks...

semilinear stochastic evolution equations with multiplicative l&apos;evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollarie...