Related papers: Differentiability of Palmer's linearization Theore…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
We present a brief overview of integrability of nonlinear ordinary and partial differential equations with a focus on the Painleve property: an ODE of second order has the Painleve property if the only movable singularities connected to…
It is proved a theorem providing necessary and sufficient conditions enabling one to map a nonlinear system of first order partial differential equations, polynomial in the derivatives, to an equivalent autonomous first order system…
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…
We investigate the electrochemical processes within an electrolyser cell, which are modelled by a coupled system of second-order quasi-linear elliptic PDEs. In this context, we study an inverse problem aiming to reconstruct both the…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…
For classical discrete system under constant composition, typically reffered to as substitutional alloys, correspondence between interatomic many-body interactions and structure in thermodynamic equilibrium exhibit profound, complicated…
A density-functional theory is established for inhomogeneous superfluids at finite temperature, subject to time-dependent external fields in isothermal conditions. After outlining parallelisms between a neutral superfluid and a charged…
A problem of the orientational and density structure properties of a confined three-dimensional (3D) and two-dimensional (2D) Hard Gausssian Overlap (HGO) ellipsoids has been revisited using the Onsager-type second virial approximation of…
We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…
Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…
An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…
In the presence of an inhomogeneous oscillatory electric field, charged particles experience a net force, averaged over the oscillatory timescale, known as the ponderomotive force. We derive a one-dimensional Hamiltonian model which…
In this paper we study the homeomorphic properties of the solutions to one dimensional backward doubly stochastic differential equations under suitable assumptions, where the terminal values depend on a real parameter. Then, we apply them…
In this paper, we study the asymptotic behavior of solution to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space $C_{\mathcal{H}_{t}(\Omega)}$. When the…
The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…
We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…
It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…