— In this paper we show that the invariant polynomial ring of the associated Clifford-Weil group can be embedded into the ring of Jacobi modular forms over the totally real field, so, therefore, that of Hilbert modular forms over the totally real field. Résumé (Anneau des invariants du groupe de Clifford-Weil, et forme de Jacobi sur un corps totallement réel) Dans cet article nous démontrons qu...

We find a minimal set of generators for the coordinate ring Calogero-Moser space ${\boldsymbol {\mathcal {C}}}_{\boldsymbol {3}}$ and algebraic relations among them explicitly. give new presentation algebra 3×3 invariant matrices involving defining ${\mathbb {C}}[\boldsymbol {C}}_{\boldsymbol {3}}]$ . Furthermore, we an explicit description GL3-invariant commuting variety its orbits under actio...

Template matching is a widely used technique in many of image processing and machine vision applications. In this paper we propose a new as well as a fast and reliable template matching algorithm which is invariant to Rotation, Scale, Translation and Brightness (RSTB) changes. For this purpose, we adopt the idea of ring projection transform (RPT) of image. In the proposed algorithm, two novel s...

Our main result is the description of generators of the total coordinate ring of the blow-up of P in any number of points that lie on a rational normal curve. As a corollary we show that the algebra of invariants of the action of a two-dimensional vector group introduced by Nagata is finitely generated by certain explicit determinants. We also prove the finite generation of the algebras of inva...

The state realization is called minimal if it is either accessible and observable or its state dimension is minimal. In the linear case those two definitions are equivalent, but not for nonlinear time-invariant systems. It is shown that definitions remain equivalent in case one is searching for minimal realization in a larger class of nonlinear time-varying systems. First, nonlinear realization...

Much of the wonderful invariant theory of the 19 century worked over fields of characteristic zero, while the theory for prime characteristic lagged behind. However, the Frobenius (p power) map in characteristic p > 0 leads to a rich theory of invariants in prime characteristic. This theory is closely bound up with the Steenrod Algebra, which allows us to derive new invariants from known invari...

1.1 Let V be a finite dimensional vector space and G a group of linear automorphisms of V , Then G acts by transposition on the dual V ∗ of V and hence on the space of regular functions R[V ∗] on V ∗, which may be identified with the symmetric algebra S(V ) of V , that is to say, the polynomial algebra generated by a basis of V . A basic problem of algebraic invariant theory is to determine S(V...

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.Over the past several years QTAG-modules have been the subject of intense investigation yet there is much to explore.The impetus for these efforts stems from the fact that the rings considered here are almost restriction free....

We use extensions to study the semi-simple quotient of the group ring FpAut(P ) of a finite p-group P . For an extension E : N → P → Q, our results involve relations between Aut(N), Aut(P ), Aut(Q) and the extension class [E] ∈ H(Q,ZN). One novel feature is the use of the intersection orbit group Ω([E]), defined as the intersection of the orbits Aut(N) · [E] and Aut(Q) · [E] in H(Q,ZN). This gr...

We discuss geometrical properties of the horizon surface of five-dimensional rotating black holes and black rings. Geometrical invariants characterizing these 3D geometries are calculated. We obtain a global embedding of the 5D rotating black horizon surface into a flat space. We also describe the Kaluza-Klein reduction of the black ring solution (along the direction of its rotation) which rela...