Let S = K[x1, . . . , xn] be a polynomial ring over a field K, and E = ∧ 〈y1, . . . , yn〉 an exterior algebra. The linearity defect ldE(N) of a finitely generated graded E-module N measures how far N departs from “componentwise linear”. It is known that ldE(N) < ∞ for all N . But the value can be arbitrary large, while the similar invariant ldS(M) for an S-module M is always at most n. We will ...

LetGk,n be the Grassmannmanifold of k-planes inR . Borel showed that H∗ (Gk,n; Z2) = Z2 [w1, . . . , wk] /Ik,n where Ik,n is the ideal generated by the dual Stiefel-Whitney classes wn+1, . . . , wn+k. We compute Groebner bases for the ideals I2,2i−3 and I2,2i−4 and use these results along with the theory of modi ed Postnikov towers to prove new immersion results, namely that G2,2i−3 immerses in...

‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.

• EEG studies in Internet addiction are reviewed within a dual-process framework. • Internet addiction is associated with hypo-activated reflective-control system. • Internet addicts also appear to present an hyper-activated affective system. • Internet addiction may thus be characterized by an imbalance between systems. • Future works should explore Internet addiction subtypes and the role of ...

A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kähler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the Milnor linking number.

Energy bounds are derived for planar and compactified M2-branes in a hyper-Kähler background. These bounds are saturated, respectively, by lump and Q-kink solitons, which are shown to preserve half the worldvolume supersymmetry. The Q-kinks have a dual IIB interpretation as strings that migrate between fivebranes.