New sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of the form $\Omega(t) = \mathrm{sgn} \prod\limits_{k=1}^m t_k$ multivariate functions from Hölder spaces are obtained.

Adaptation in spatially extended populations entails the propagation of evolutionary novelties across habitat ranges. Driven by natural selection, beneficial mutations sweep through the population in a "wave of advance". The standard model for these traveling waves, due to R. Fisher and A. Kolmogorov, plays an important role in many scientific areas besides evolution, such as ecology, epidemiol...

A key points of new approach for modeling of the population dynamics in reactive environment are presented here: 1) generalization of the Logistic equation to the case of reactive environment for modeling of population dynamics (or for the fulfilling of the ecological niches); 2) new type of asymptotic solution for such equation (which is tested on human population growth); 3) reduction to the ...

Much recent literature is concerned with how variation among individuals (e.g., variability in their traits and fates) translates into higher-level (i.e., population and community) dynamics. Although several theoretical frameworks have been devised to deal with the effects of individual variation on population dynamics, there are very few reports of empirically based estimates of the sign and m...

Effective management of widespread invasive species such as wild pigs (Sus scrofa) is limited by resources available to devote to the effort. Better insight of the effectiveness of different management strategies on population dynamics is important for guiding decisions of resource allocation over space and time. Using a dynamic population model, we quantified effects of culling intensities and...

We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an arbitrary fixed product basis. We show that linear growth of separability entropy provides a stricter criterion of complexity than Kolmogorov-Sinai entropy,...