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In the last decade the Fick-Jacobs approximation has been exploited to capture the transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show…

Markov cohort state-transition models have been the standard approach for simulating the prognosis of patients or, more generally, the life trajectories of individuals over a time period. Current approaches for estimating the variance of a…

Recent years have seen a great deal of progress in our understanding of bootstrap percolation models, a particular class of monotone cellular automata. In the two dimensional lattice there is now a quite satisfactory understanding of their…

We reformulate in a systematic way the conversional approach in its most general and compact form. We present a new definition of generalized Dirac bracket directly in terms of the super-observables commuting with the basic BFV-BRST charge.

In this paper, we investigate the existence of solution for systems of Fokker-Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are considered: a porous media congestion or \textit{soft}…

By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and…

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…

We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…

The derivation of effective evolution equations is central to the study of non-stationary quantum many-body sytems, and widely used in contexts such as superconductivity, nuclear physics, Bose-Einstein condensation and quantum chemistry. We…

We introduce some generalized topological concepts to deal with union-closed families, and show that one can reduce the proof of Frankl's conjecture to some families of so-called supratopological spaces. We prove some results on the…

After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary…

A geometric generalization of contraction theory called~$k$-contraction was recently developed using $k$-compound matrices. In this note, we focus on the relations between $k$-contraction and two other generalized contraction frameworks:…

A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized…

By means of a recent Birkhoff-Kellogg type theorem, we discuss the solvability of a fairly general class of parameter-dependent fourth order retarded differential equations subject to functional boundary conditions. We seek solutions within…

While behavioural equivalences among systems of the same type, such as Park/Milner bisimilarity of labelled transition systems, are an established notion, a systematic treatment of relationships between systems of different type is…

We aim to study the solutions of a fractional mesoscopic model of phase transitions in a periodic medium. After investigating the geometric properties of the interface of the associated minimal solutions, we construct minimal interfaces…

We propose a stable Petrov-Galerkin discretization of a kinetic Fokker-Planck equation constructed in such a way that uniform inf-sup stability can be inferred directly from the variational formulation. Inspired by well-posedness results…

In this paper we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate the periodic solutions of the complex cubic-quintic Ginzburg-Landau equation. The primary tools used here are Hopf…

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general…

We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the…