Related papers: Complexes from complexes
The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in a previous paper by the authors for scalar valued functions, or zero-forms, and represents a new…
We establish some connections between nonresonant $A$-hypergeometric systems and de Rham-type complexes. This allows us to determine which of these $A$-hypergeometric systems "come from geometry."
We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.
We introduce the notion of differential largeness for fields equipped with several commuting derivations (as an analogue to largeness of fields). We lay out the foundations of this new class of "tame" differential fields. We state several…
Our constructions provide a systematic way to study cohomology pre-algebraic structures via classical cohomology, simplifying computations and enabling the use of established techniques.
We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…
Singular degenerate differential operator equations are studied. The uniform separability of boundary value problems for degenerate elliptic equation and optimal regularity properties of Cauchy problem for degenerate parabolic equation are…
The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we investigate the Hodge Laplacian and related first order…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
The numerical invariants (global) cohomological length, (global) cohomological width, and (global) cohomological range of complexes (algebras) are introduced. Cohomological range leads to the concepts of derived bounded algebras and…
The main goal of this work is to present a detailed study of the foundations of Complex Geometry, highlighting its geometrical, topological and analytical aspects. Beginning with a preliminary material, such as the basic results on…
There are two de Rham complexes in diffeology. The original one is due to Souriau and the other one is the singular de Rham complex defined by a simplicial differential graded algebra. We compare the first de Rham cohomology groups of the…
Derived de Rham cohomology has been recently used in several contexts, as in works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical invariants for special values of zeta functions. Inspired by some results of Morin,…
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…