相关论文: Twisted symmetries of differential equations

In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…

In this survey, we review recent developments in extending Hodge theory to differential forms with values in bundles equipped with singular metrics, based on joint work with Ya Deng, Christopher D. Hacon, and Mihai P\u{a}un.

Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first…

We prove an existence result for twisted K\"ahler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.

We introduce a theory of twisted simplicial distributions on simplicial principal bundles, which allow us to capture Bell's non-locality, and the more general notion of quantum contextuality. We leverage the classical theory of simplicial…

Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…

In the paper it is shown that, even without a knowledge of the concrete form of the equations of mathematical physics and field theories, with the help of skew-symmetric differential forms one can see specific features of the equations of…

A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.

We present an in-depth analysis of transverse momentum dependent (TMD) distributions of twist-three. In particular, we focus on evolution equations, symmetry relations, parameterization, interpretation, small-b asymptotic behaviour and the…

We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the…

We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…

The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…

We review recent experimental and theoretical progress in spin physics, as presented in the spin parallel session of DIS2006. In particular, we discuss the status of the nucleon spin structure, transverse polarized asymmetries, and recent…

Twisted links are a generalization of classical links and correspond to stably equivalence classes of links in thickened surfaces. In this paper we introduce twisted intersection colorings of a diagram and construct two invariants of a…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…

From its inception in statistical physics to its role in the construction and in the development of the asymmetric Yang-Mills phase in quantum field theory, the notion of spontaneous broken symmetry permeates contemporary physics. This is…

We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and…

This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.

In this work, we have introduced and studied some basic geometric properties of extended weakly symmetric spaces. After classification of this structure we have also established the existence of such a space by presenting a non-trivial…