Related papers: On relations of invariants for vector-valued forms
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
It turns out that complex geodesics in Teichm\"uller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We describe this connection and show how geometric features…
The inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
In this work we introduce a new method for manufacturing minimal submanifolds in Riemannian geometry. For this we employ the so called complex-valued eigenfunctions. This is particularly interesting in the cases when the Riemannian ambient…
In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.
We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
A formula for the Riemannian metric tensor of differentiable manifolds of linear dynamical systems of same McMillan degree is presented in terms of their transfer function matrices. The necessary calculations for its application to ARMA and…
A general invariant manifold theorem is needed to study the topological classes of smooth dynamical systems. These classes are often invariant under renormalization. The classical invariant manifold theorem cannot be applied, because the…
The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalism is proved for $N=3$. More examples in higher dimensions show that the result might hold in…
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…
We introduce a generalization of structured manifolds as the most general Riemannian metric g associated to an affinor (tensor field of (1,1)-type) F and initiate a study of their semi-invariant submanifolds. These submanifolds are…
Using connections to random matrix theory and orthogonal polynomials, we develop a framework for obtaining explicit closed-form formulae for the number, $\mathscr{N}_{g}(2\nu,j)$, of connected $2\nu$-valent labeled graphs with $j$ vertices…
Two-term recurrence relations are supplied for indefinite integrals of functions that involve factors of the types ${P_2}^n$, ${P_3}^n$, ${P_4}^n$, ${P_1}^m {Q_1}^n$, $E_1 {P_1}^n$, ${P_1}^m {Q_2}^n$, $E_1 {P_2}^n$, ${P_2}^m {Q_2}^n$,…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…