The structure of the gaussian auxiliary field approximation in the theory of phase ordering kinetics is analysed with the aim of placing the method within the context of a systematic theory. While we are unable to do this for systems with a scalar order parameter, where the approximation remains uncontrolled, a systematic development about the gaussian approximation can be outlined for systems ...

For finite semidistributive lattices the map κ gives a bijection between sets of completely join-irreducible elements and meet-irreducible elements. Here we study -map in context torsion classes. It is well-known that lattice classes for an artin algebra semidistributive, but general it far from finite. We show well-defined on set elements, even when infinite. then extend to which have canonica...

‎Let $R$ be a domain with quotiont field $K$‎, ‎and‎ ‎let $N$ be a submodule of an $R$-module $M$‎. ‎We say that $N$ is‎ ‎powerful (strongly primary) if $x,yin K$ and‎ ‎$xyMsubseteq N$‎, ‎then $xin R$ or $yin R$ ($xMsubseteq N$‎ ‎or $y^nMsubseteq N$ for some $ngeq1$)‎. ‎We show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $M$‎, ‎also we show tha...

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...

We state a conjecture which gives a combinatorial parametrization of the irreducible tempered representations with real central character of a graded Hecke algebra with unequal labels, associated to a root sytem of type B or C. This conjecture is based on a combinatorial generalization of the Springer correspondence in the classical (equal label) case. In particular, the described modules turn ...

It is a standard fact (see §2) that 7rr(4>) is of trace class. In particular, 7Tr(4>) is completely continuous for 4>eC7(G). This implies that L(r\G) decomposes into an orthogonal direct sum of irreducible invariant subspaces, {HjK°=i and for each i there are only a finite number of k so that H, is equivalent with Hk as a representation of G (cf. Gelfand, Graev, PyateckiïShapiro [9]). Let G den...

Let V be a simple vertex operator algebra and let G be a finite automorphism group of V . In [DY], it was shown that any irreducible V -module is a completely reducible V module where V G is the G-invariant sub-vertex operator algebra of V . In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V...

In this paper we study the variety Mnil of nilpotent elements of a reductive monoid M . In general this variety has a completely different structure than the variety Guni of unipotent elements of the unit group G of M . When M has a unique non-trivial minimal or maximal G×G-orbit, we find a precise description of the irreducible components of Mnil via the combinatorics of the Renner monoid of M...