Elliptic CR-manifolds and shear invariant ODE with additional symmetries

We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast with the situation of hyperbolic CR-manifolds, where the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable istropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the manifold

Book Review: \u3ci\u3eConstructing Indian Christianities: Culture, Conversion, and Caste\u3c/i\u3e

Book review of Constructing Indian Christianities: Culture, Conversion, and Caste. Edited by Chad M. Bauman and Richard Fox Young. Abington, UK: Routledge, 2014, xxiii + 264 pages

Explicit description of spherical rigid hypersurfaces in C²

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Busting a myth with the Bayes Factor: Effects of letter bigram frequency in visual lexical decision do not reflect reading processes

Psycholinguistic researchers identify linguistic variables and assess if they affect cognitive processes. One such variable is letter bigram frequency, or the frequency with which a given letter pair co-occurs in an orthography. While early studies reported that bigram frequency affects visual lexical decision, subsequent, well-controlled studies not shown this effect. Still, researchers continue to use it as a control variable in psycholinguistic experiments. We propose two reasons for the persistence of this variable: (1) Reporting no significant effect of bigram frequency cannot provide evidence for no effect. (2) Despite empirical work, theoretical implications of bigram frequency are largely neglected. We perform Bayes Factor analyses to address the first issue. In analyses of existing large-scale databases, we find no effect of bigram frequency in lexical decision in the British Lexicon Project, and some evidence for an inhibitory effect in the English Lexicon Project. We find strong evidence for an effect in reading aloud. This suggests that, for lexical decision, the effect is unstable, and may depend on item characteristics and task demands rather than reflecting cognitive processes underlying visual word recognition. We call for more consideration of theoretical implications of the presence or absence of a bigram frequency effect

Free CR distributions

There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions $n$ and codimensions $n^2$ are among the very few possibilities of the so called parabolic geometries. Indeed, the homogeneous model turns out to be \PSU(n+1,n)/P with a suitable parabolic subgroup $P$. We study the geometric properties of such real $(2n+n^2)$-dimensional submanifolds in $\mathbb C^{n+n^2}$ for all $n>1$. In particular we show that the fundamental invariant is of torsion type, we provide its explicit computation, and we discuss an analogy to the Fefferman construction of a circle bundle in the hypersurface type CR geometry