Human-based genetic algorithms (HBGA) use both human evaluation and innovation to optimize a population of solutions (Kosorukoff, 2001). The novel contribution of HBGAs is an introduction of human-based innovation operators. However, there was no attempt to measure the effect of human-based innovation operators on the overall performance of GAs quantitatively, in particular, by comparing the pe...

The case where K and S are continuous on Lp[0,1] operators is well studied (see, e.g., [1] and the references therein). Here we suppose that the functions K(t,s) and B(t) may be nonintegrable at t = 0. More precisely, we will formulate conditions on operators K and S in Sections 2 and 3. Under such conditions, those operators are not bounded on L[0,1] and one has to choose other functional spac...

We use the second modulus of continuity to estimate approximations a bounded measurable function on segment [0, 1] by Kantorovich type operators $$ {B}_n(f)(x)=\sum \limits_{j=0}^n{C}_n^j{x}^j{\left(1-x\right)}^{n-j}{F}_j(f), where Fj are functionals with sufficiently small supports and certain symmetry. The result obtained is sharp.

The process of inverting Markov kernels relates to the important subject of Bayesian modelling and learning. In fact, Bayesian update is exactly kernel inversion. In this paper, we investigate how and when Markov kernels (aka stochastic relations, or probabilistic mappings, or simply kernels) can be inverted. We address the question both directly on the category of measurable spaces, and indire...

The process of inverting Markov kernels relates to the important subject of Bayesian modelling and learning. In fact, Bayesian update is exactly kernel inversion. In this paper, we investigate how and when Markov kernels (aka stochastic relations, or probabilistic mappings, or simply kernels) can be inverted. We address the question both directly on the category of measurable spaces, and indire...

Let (Ω,Σ) be a measurable space and let X be a Banach space. Throughout this paper G will be a countably additive vector measure G : Σ → X. Consider the space L1(G) of (classes of real) G-integrable functions, following the definition of Bartle, Dunford and Schwartz [1] and Lewis [9]. The properties of this space have been studied by Kluvánek and Knowles [7], Okada [10] and Curbera [2]. In the ...

This paper is a natural continuation of Krylov (2020), where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and nondegenerate diffusion drift Ld+1(Rd+1). Here we study some properties these such as higher summability Green’s functions, maximum principle for related transport equations irregular coefficients, boundedness resolvent op...

In 1955, A. Grothendieck proved a basic inequality which shows that any bounded linear operator between L(μ)-spaces maps (Lebesgue-) dominated sequences to dominated sequences. An elementary proof of this inequality is obtained via a new decomposition principle for the lattice of measurable functions. An exposition is also given of the M. Lévy extension theorem for operators defined on subspace...