Related papers: A note on integrating group scheme actions

We consider the formal reduction of a system of linear differential equations and show that, if the system can be block-diagonalised through transformation with a ramified Shearing-transformation and following application of the Splitting…

A new approach to the problem of group classification is applied to the class of first-order non-linear equations of the form $u_a u_a=F(t,u,u_t)$. It allowed complete solution of the group classification problem for a class of equations…

Due to the omission of a hypothesis from an elementary lemma in the author's paper "Gleason parts and point derivations for uniform algebras with dense invertible group", some of the proofs presented in that paper are flawed. We prove here…

In this paper we prove a Thomae derivative formula for trigonal curves admitting a non-singular affine model. This formula relates the derivatives of theta functions with rational characteristics on the curve to explicit expressions in the…

We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' theorem.

A new method for constructing aperiodic tilings is presented. The method is illustrated by constructing a particular tiling and its hull. The properties of this tiling and the hull are studied. In particular it is shown that these tilings…

We calculate explicitly an adelic quotient group for an excellent Noetherian normal integral two-dimensional separated scheme. An application to an irreducible normal projective algebraic surface over a field is given.

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…

We define the algebraic fundamental group functor of a reductive group scheme over an arbitrary (non-empty) base scheme and prove that this functor is exact.

In this paper we classify the irreducible integrable modules for the twisted toroidal extended affine Lie algebras with center acting non-trivially.

We introduce the concept of crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system.…

We extend the definition of fundamental group scheme to non reduced schemes over any connected Dedekind scheme. Then we compare the fundamental group scheme of an affine scheme with that of its reduced part.

The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…

Let G be a finite group and \rho: G--> End(E) be a group representation of G on a coherent sheaf over an integral scheme. The purpose of this paper shall give a decomposition theorem of such representations in non-splitting components and…

We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…

Every action of a finite group scheme $G$ on a variety admits a projective equivariant model, but not necessarily a normal one. As a remedy, we introduce and explore the notion of $G$-normalization. In particular, every curve equipped with…

We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results in a generalized setting using a ring with linear topology.

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…

We extend the theorem of Liouville on integration in finite terms to include dilogarithmic integrals. The results provide a necessary and sufficient condition for an element of the base field to have an antiderivative in a field extension…