Related papers: Some problems and conjectures about $L^2$-invarian…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences…
We analyze the particle spectrum of a second-order (in derivatives) theory based on a rank-2 tensor field with both symmetric and antisymmetric components. By demanding the existence of a propagating massless spin-2 particle and invariance…
We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polynomials with non-negative coefficients that are constant on…
It is understood now that all projective (and conformal) invariants of Riemannian metrics can be found by a transparent construction based on representation theory. So this article with a partial and quite cumbersome construction of…
Some Open Problems Concerning Orthogonal Polynomials.
We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…
This is Part II of the series of our papers under the title "Toward resolution of singularities over a field of positive characteristic (The Idealistic Filtration Program)". See http://arxiv.org/abs/math/0607009 for Part I.
Conjugations in space $L^2$ of the unit circle commuting with multiplication by $z$ or intertwining multiplications by $z$ and $\bar z$ are characterized. We also study their behaviour with respect to the Hardy space, subspaces invariant…
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse)…
We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
We study some new invariant measures arising from local inverse iterates. Examples are also given.
In this paper we briefly survey the classical problem of understanding which Lie algebras admit a complex structure, put in the broader perspective of almost complex structures with special properties. We focus on the different behavior of…
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.
It is well known that Rubik's cube has a set of group invariants. These values do not change if any layer was rotated, but they can change in case if some of the cubes were removed from the puzzle, mixed up and returned back. In this paper,…
This is a list of several open problems dealing mainly with univariate polynomials.
The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…