相关论文: On consistency of perturbed generalised minimal mo…
Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
Motivated by recent developments of quasi-stationary Monte Carlo methods, we investigate the stability of quasi-stationary distributions of killed Markov processes under perturbations of the generator. We first consider a general bounded…
We introduce a new methodology for modeling regular spatial data using hyperuniform point processes. We show that, under some mixing conditions on the perturbations, perturbed lattices in general dimension are hyperuniform. Due to their…
A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be…
We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of Colombeau's simplified model. This generalizes the notion of G^{\infty }-regularity…
Admissible perturbations (i.e., perturbations that do not change the Mironenko reflecting function of the system) are obtained for an autonomous three-dimensional quadratic generalized Langford system with five parameters. The obtained…
We study continuity properties of Sobolev mappings $f \in W_{\mathrm{loc}}^{1,n} (\Omega, \mathbb{R}^n)$, $n \ge 2$, that satisfy the following generalized finite distortion inequality \[\lvert Df(x)\rvert^n \leq K(x) J_f(x) + \Sigma (x)\]…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. Indeed, we consider a family of such problems…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
We consider independent long-range percolation models on locally finite vertex-transitive graphs. Using coupling ideas we prove strict monotonicity of the critical points with respect to local perturbations in the connection function,…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
In this paper we prove a new abstract stability result for perturbed saddle-point problems based on a norm fitting technique. We derive the stability condition according to Babuska's theory from a small inf-sup condition, similar to the…
Generalized Lambda-semiflows are an abstraction of semiflows with non-periodic solutions, for which there may be more than one solution corresponding to given initial data. A select class of solutions to generalized Lambda-semiflows is…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
The framework of Baikov-Gazizov-Ibragimov approximate symmetries has proven useful for many examples where a small perturbation of an ordinary differential equation (ODE) destroys its local symmetry group. For the perturbed model, some of…
Let $A(x): =(A_{i, j}(x))$ be a continuous function defined on some subshift of $\Omega:= \{0,1, \cdots, m-1\}^\mathbb{N}$, taking $d\times d$ non-negative matrices as values and let $\nu$ be an ergodic $\sigma$-invariant measure on the…
We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing primal and dual quantitative sufficient and necessary…