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We try to define the more general form of iterative processes in which the Pomeau-Manneville and the Feigenbaum scenario may occur along with their specific scaling properties. Doing this we need to generalize other basic concepts. Thus,…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
The aim of the paper is to give an `elementary' introduction to the theory of modules over operads and discuss three prominent examples of these objects - simplex, associahedron (= the Stasheff polyhedron) and cyclohedron (= the…
Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative.
We give an introductory account of functional determinants of elliptic operators on manifolds and Polyakov-type formulas for their infinitesimal and finite conformal variations. We relate this to extremal problems and to the Q-curvature on…
We give a natural cohomological interpretation of Letzter-Makar-Limanov invariants for rings of differential operators on algebraic curves.
Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…
In this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are widely used to represent multidimensional data, such as meshes, that are two dimensional complexes, or graphs, that can be…
This paper presents a study of the characterization of the singular manifold of the six-degree-of-freedom parallel manipulator commonly known as the Stewart platform. We consider a platform with base vertices in a circle and for which the…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
Given a compact oriented triangulated $3$-manifold we find a non-trivial condition satisfied by certain labelings of the tetrahedra by elements of an arbitrary abelian group which we call angle structures. Smoothness of the manifold is used…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
Our aim is to illustrate how one can effectively apply the basic ideas and notions of topological entropy and dynamical degrees, together with recent progress of minimal model theory in higher dimension, for an explicit study of birational…
We provide a brief survey of a certain algebra of operators on symmetric polynomials, and collect a number of previously known results in the field.
It is shown that eigenvalues of Laplace-Beltrami operators on compact Riemannian manifolds can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we…
In this paper we investigate composition operators on discrete spaces. We establish the classification of underlying graphs of such operators. For one class of such graphs, namely graphs with one cycle, we obtain a characterization of…
We introduce a (bi)category $\mathfrak{Sing}$ whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of…