Related papers: First and Second Fundamental Theorems for Invarian…

We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric…

Let the finite group $G$ act linearly on the vector space $V$ over the field $k$ of arbitrary characteristic. If $H<G$ is a subgroup the extension of invariant rings $k[V]^G\subset k[V]^H$ is studied using modules of covariants. An example…

The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M.…

Let $R$ be a ring and $P$ a prime ideal of $R.$ In this paper, we establish some commutativity criteria for the factor ring $R/P$ in terms of derivations of $R$ satisfying some algebraic identities involving a new kind of involution in…

Two classical rings of invariants are shown to be Frobenius split: for the special linear group acting on the direct sum of several copies of the defining representation and several copies of the dual of the defining representation; and for…

In this work we derive important properties regarding matrix invariants which occur in the theory of differential equations with reflection.

The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…

For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…

In this paper, we consider the degenerate Stirling polynomials of the second kind which are derived from the generating function. In addition, we give some new identities for these polynomials.

In this paper, we study the ring of invariants under the action of SL(m,K)\times SL(n,K) and SL(m,K)\times SL(n,K)\times SL(2,K) on the 3-dimensional array of indeterminates of form m\times n\times 2, where K is an infinite field. And we…

The degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…

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…

We present an algorithmic framework for computing generators for the ring of invariants of an Artin-Schreier curve. We give explicit invariants for almost all Artin-Schreier curves of genus up to~8 in standard form, and for a handful of…

Let $G$ be the cyclic group of order $n$ and suppose ${\bf F}$ is a field containing a primitive $n^\text{th}$ root of unity. We consider the ring of invariants ${\bf F}[W]^G$ of a three dimensional representation $W$ of $G$ where $G…

For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental…

It is shown that laminar vortex rings can be generated by impulsive body forces having particular spatial and temporal characteristics. The method produces vortex rings in a fluid initially at rest, and once generated, the flow field…

The content of this preprint together with additional material appears now in 0706.2154.

We use recent results on matrix semi-invariants to give degree bounds on generators for the ring of semi-invariants for quivers with no oriented cycles.

Sturm theory for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. Here we propose a Sturm oscillation theorem for indefinite systems of even…

This article evaluates the determinants of two classes of special matrices, which are both from a number theory problem. Applications of the evaluated determinants can be found in [arXiv:math.NT/0509523]. Note that the two determinants are…