We study the motivic Serre invariant of a smoothly bounded algebraic or rigid variety X over a complete discretely valued field K with perfect residue field k. If K has characteristic zero, we extend the definition to arbitrary K-varieties using Bittner’s presentation of the Grothendieck ring and a process of Néron smoothening of pairs of varieties. The motivic Serre invariant can be considered...

A time-scale invariant burst-detection algorithm for single-unit spike train is described. This burst analysis is an auto-adaptive algorithm that uses interand intra-burst intervals for identifying the burst itself. By using a self-adaptive algorithm, a burst is de$ned by the characteristic $ring patterns within and between bursts. Bursts are detected by auto-adaptive method when the inter-burs...

Let V be a representation of a finite group G over a field of characteristic p. If p does not divide the group order, then Molien’s formula gives the Hilbert series of the invariant ring. In this paper we find a replacement of Molien’s formula which works in the case that |G| is divisible by p but not by p. We also obtain formulas which give generating functions encoding the decompositions of a...

We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This implicitly gives a finite complete set of invariants for local unitary equivalence. This is done by showing that local unitary equivalence of density operators is e...

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

An absolute ideal of an Abelian group G is a subgroup that in every ring whose additive coincides with G. We describe reduced algebraically compact groups admit at least one structure R such (Problem 93 L. Fuchs’ book “Infinite Groups”). Reduced, compact, have only fully invariant subgroups as are characterized.

Let F be an affine flat group scheme over a commutative ring R, and S an F -algebra (an R-algebra on which F acts). We define an equivariant analogue QF (S) of the total ring of fractions Q(S) of S. It is the largest F -algebra T such that S ⊂ T ⊂ Q(S), and S is an F -subalgebra of T . We study some basic properties. Utilizing this machinery, we give some new criteria for factoriality (UFD prop...

This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its minimal resolution is acyclic. The results established track the change in this invariant under some standard operations in commutative algebra. As one of the ap...

For a connected reductive group G and a finite–dimensional G–module V , we study the invariant Hilbert scheme that parameterizes closed G–stable subschemes of V affording a fixed, multiplicity–finite representation of G in their coordinate ring. We construct an action on this invariant Hilbert scheme of a maximal torus T of G, together with an open T–stable subscheme admitting a good quotient. ...

A representation for a group or a monoid is called a representation with Borel mold if it can be normalized to a representation in upper triangular matrices whose image of the group or monoid generates the algebra of upper triangular matrices. In [Na2] the moduli of representations with Borel mold has been constructed for each group or monoid. The moduli of representations with Borel mold has s...