We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as s-> 0^+ , dealing with classical fractional Sobolev spaces. As regards the limit as s->1^-, Young functions with an asymptotic linear growth are also considered in connection with the space of functions of bounded variation. Concerning the limit as s-> 0^+, Young functions fulfilling the \Delta_2-condition are admissible.

Over the last decade, significant attention has been devoted to Closed-Loop Supply Chain (CLSC) design problems. As such, this review aims at assessing whether the current modelling approaches for CLSC problems can support the transition towards a Circular Economy at a supply chain level. The paper comprehensively assesses the extent to which existing modelling approaches evaluate the performance of supply chains across the complete spectrum of sustainability dimensions.

We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s ->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as s->0^-, dealing with classical fractional Sobolev spaces. As regards the limit as s ->1^-, Young functions with an asymptotic linear growth are also considered in connection with the space of functions of bounded variation. Concerning the limit as s->0^+, Young functions fulfilling the \Delta_2-condition are admissible.

A reaction-diffusion system governing the prey-predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.

A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the "scattering holonomy", i.e. the integration (from the infinite past to the infinite future) of the differential spin evolution along the two worldlines of a binary system in hyperboliclike motion. We apply this approach to the computation, at the first post-Minkowskian approximation (i.e.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants.

We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

The optimal Orlicz target space and the optimal rearrangement-invariant tar- get space are exhibited for embeddings of fractional-order Orlicz-Sobolev spaces W^{s,A}(R^n). Related Hardy type inequalities are proposed as well. Versions for frac- tional Orlicz-Sobolev seminorms of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^- and of the Maz'ya-Shaposhnikova theorem on the limit as s ->0^+ are established. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.