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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…

We study a new class of so-called quasi-infinitely divisible laws, which is a wide natural extension of the well known class of infinitely divisible laws through the L\'evy--Khinchine type representations. We are interested in criteria of…

Let X\subsetneq\mathbb{P}_{\mathbb{C}}^{N} be an n-dimensional nondegenerate smooth projective variety containing an m-dimensional subvariety Y. Assume that either m>\frac{n}{2} and X is a complete intersection or that m\geq\frac{N}{2}, we…

We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…

In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…

We consider a class of particular solutions to the (2+1)-dimensional nonlinear partial differential equation (PDE) $u_t +\partial_{x_2}^n u_{x_1} - u_{x_1} u =0$ (here $n$ is any integer) reducing it to the ordinary differential equation…

We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold…

We analyse the structure of imprecise Markov chains and study their convergence by means of accessibility relations. We first identify the sets of states, so-called minimal permanent classes, that are the minimal sets capable of containing…

In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Since we work on a non-Markovian context, some technical…

We prove that the partial-dual genus polynomial considered as a function on chord diagrams satisfies the four-term relation. Thus it is a weight system from the theory of Vassiliev knot invariants.

In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…

The purpose of this note is to show that the subvarieties of small degree inside a general hypersurface of large degree come from intersecting with linear spaces or other varieties.

This text is a draft of the review paper on projectively dual varieties. Topics include dual varieties, Pyasetskii pairing, discriminant complexes, resultants and schemes of zeros, secant and tangential varieties, Ein theorems, applications…

In our previous paper [International Journal of Theoretical Physics, 41 (2002), 1165-1190] we have shown, following the tradition of synthetic differential geometry, that div and rot are uniquely determined, so long as we require that the…

We determine the non-compact form of Vishik's Elementary Discrete Invariant for quadrics.

We show that the principal types of the closed terms of the affine fragment of $\lambda$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry…

This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…

Recently, we have witnessed tremendous applications of algebraic intersection theory to branches of mathematics, that previously seemed very distant. In this article we review some of them. Our aim is to provide a unified approach to the…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defined, and trace and lifting results with respect to a…