相关论文: Selection rules of canonical differential equation…

Intersection cohomology is a way to enhance classical cohomology, allowing us to use a famous result called Poincar\'e duality on a large class of spaces known as stratified pseudomanifolds. There is a theoretically powerful way to arrive…

Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify…

We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable…

A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…

A general method for establishing results over a commutative complete intersection local ring by passing to differential graded modules over a graded exterior algebra is described. It is used to deduce, in a uniform way, results on the…

We study the existence of log-canonical Poisson structures that are preserved by difference equations of special form. We also study the inverse problem, given a log-canonical Poisson structure to find a difference equation preserving this…

For several applications in the arithmetic of abelian varieties it is important to compute canonical heights. Following Faltings and Hriljac, we show how the canonical height on the Jacobian of a smooth projective curve can be computed…

The measure of distinguishability between two neighboring preparations of a physical system by a measurement apparatus naturally defines the line element of the preparation space of the system. We point out that quantum mechanics can be…

Conflict sets are loci of intersecting wavefronts emanating from $l$ different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in…

We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…

Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly…

We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…

In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…

For regular linear time-invariant DAEs the corresponding matrix pencil is regular and the computation of a standard canonical form is well-understood. Although the investigation of linear DAEs with time-varying coefficients is more complex,…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify…

We propose a new method for the evaluation of intersection numbers for twisted meromorphic $n$-forms, through Stokes' theorem in $n$ dimensions. It is based on the solution of an $n$-th order partial differential equation and on the…

Ordered pairs of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining…