math updates on arXiv.orgMathematics (math) updates on the arXiv.org e-print archiveCompact supersymmetric solutions of the heterotic equations of motion in dimensions 7 and 8. (arXiv:0806.4356v1 math.DG)- (Found June 29, 2008 ) We construct explicit compact solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimension seven and eight, obeying the three form anomaly cancellation condition. Some of these manifolds are compact supersymmetric solutions of the heterotic equations of motion in dimensions seven and eight.http://arxiv.org/abs/0806.4356 Invariants associated with linear ordinary differential equations. (arXiv:0806.4352v1 math.AP)- (Found June 29, 2008 ) We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next, the method is used to obtain the invariants of low order linear ordinary differential equations, and the structure invariance group for an arbitrary order of these equations. Other properties of these equations are also discussed, including the exact number of.http://arxiv.org/abs/0806.4352 On cotilting cotorsion and torsion pairs. (arXiv:0806.4345v2 math.RA)- (Found June 29, 2008 ) In this paper we study cotorsion and torsion pairs induced by cotilting modules. We give a new characterization of cotilting cotorsion pairs of finite type, proving in particular that in the noetherian setting these are exactly those induced by a $Sigma$-pure injective cotilting module. Next we prove that a torsion pair is cogenerated by a $Sigma$-pure injective cotilting module if and only if its heart is a locally noetherian Grothendieck category. In particular we obtain that a ring admitting.http://arxiv.org/abs/0806.4345 Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen. (arXiv:0806.4294v1 math.ST)- (Found June 29, 2008 ) Pranab K. Sen has contributed extensively to many areas of Statistics including order statistics, nonparametrics, robust inference, sequential methods, asymptotics, biostatistics, clinical trials, bioenvironmental studies and bioinformatics. His long list of over 600 publications and 22 books and volumes along with numerous citations during the past 5 decades bear testimony to his work. All three of us have had the good fortune of being associated with him in different capacities. He has given..http://arxiv.org/abs/0806.4294 Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III. (arXiv:0806.4259v1 math.OA)- (Found June 29, 2008 ) We classify a certain class of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III. Our main technical tools are the structural analysis of type III factors and the theory of canonical extension of endomorphisms introduced by Izumi.http://arxiv.org/abs/0806.4259 |