Related papers: Generalized Sprays and Nonlinear Connections

A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…

In a recent paper (arXiv:1501.06164) the author has introduced a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows the interpretation of merely measurable maps as solutions. This…

A nonlinear splitting on a fibre bundle is a generalization of an Ehresmann connection. An example is given by the homogeneous nonlinear splitting of a Finsler function on the total manifold of a fibre bundle. We show how homogeneous…

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on…

We consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and,…

Semilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such as complex conjugation. In particular, this generalization unifies the concepts of linear…

Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized…

Nonlinear relationships between covariates and a response variable of interest are frequently encountered in animal science research. Within statistical models, these nonlinear effects have, traditionally, been handled using a range of…

In earlier work, using the light cone picture, a world sheet field theory that sums planar phi^3 graphs was constructed and developed. Since this theory is both non-local and not explicitly Lorentz invariant, it is desirable to have a…

This paper develops a general approach to nonlinear circuit modelling aimed at preserving the intrinsic symmetry of electrical circuits when formulating reduced models. The goal is to provide a framework accommodating such reductions in a…

We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are…

Classical splines feature prominently in approximation theory and numerical analysis, while GKM theory arises in the study of equivariant cohomology. More recently, generalized splines have been studied which simultaneously generalize both…

By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…

Let G be a graph whose edges are labeled by ideals of a commutative ring. We introduce a generalized spline, which is a vertex-labeling of G by elements of the ring so that the difference between the labels of any two adjacent vertices lies…

In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain smoothing…

We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…

We present a novel theoretical framework for understanding the expressive power of normalizing flows. Despite their prevalence in scientific applications, a comprehensive understanding of flows remains elusive due to their restricted…

The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted…

We provide theoretical procedures and practical recipes to simulate non-Gaussian correlated, homogeneous random fields with prescribed marginal distributions and cross-correlation structure, either in a N-dimensional Cartesian space or on…

In Rips Complexes and Covers in the Uniform Category (arXiv:0706.3937) we define, following James, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. In this paper we investigate when these…