ELEMENTARY AND Φ-FREE LIE TRIPLE SYSTEMS

We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.

Hybridisation in kiwi(Apteryx;Apterygidae)requires taxonomic revision for the Great Spotted Kiwi

Background:Kiwi(Apteryx spp.)are flightless ratites from New Zealand whose numbers and distributions have declined following human arrival.Some of the kiwi species are known to hybridise but the extent of hybridization is unknown.Methods:We reviewed hybridisation in kiwi(Apteryx spp.)and present new genetic data examining the extent of hybridisation between Rowi(A.rowi)and Little Spotted Kiwi(A.owenii)at Okarito,the location of the only remaining natural population of the threatened Rowi.We also genetically examined the syntype specimens of A.haastii Potts,1872,collected from near Okarito in the 1870s,which have unusual morphologies.Results:We found evidence of recurrent hybridisation between Rowi and Little Spotted Kiwi over the last 150 years,including one F1 hybrid found in the last 15 years,despite Little Spotted Kiwi’s likely extinction on the mainland in the 1970s.However,we found little evidence of introgression of Little Spotted Kiwi alleles into the extant Rowi popula-tion.The syntype specimens of A.haastii were also found to be hybrids between Little Spotted Kiwi and Rowi.Conclusions:Our genetic analyses indicate that,although we detected multiple instances of hybridisation between Rowi and Little Spotted Kiwi,it does not appear to be an ongoing threat to Rowi.Because the syntype specimens of A.haastii are hybrids and therefore not representative of the prevailing usage of the name for the Great Spotted Kiwi(A.haastii),we resurrect the nomen oblitum A.maxima Sclater and Hochstetter,1861 for the large spotted kiwi species.

The Transmigrating Evil Genius： From Boothby to Rohmer to Fleming

Literary characters possess a genealogy. Indeed, stock characters like the evil genius or super villain boast family trees that readers can trace not only through time--in this case, starting in the late 19th century--but also across borders. This study traces the genealogical roots of the modern super villain by examining, in turn, Ian Fleming＇s characters Ernst Blofeld and Dr. Julius No, Sax Rohmer＇s Dr. Fu Manchu, and Guy Boothby＇s Dr. Antonio Nikola. In ＂Orientalism＂, the author contends that the modern super villain is the embodiment of these writers＇ orientalist fantasies and fears. Finally, in ＂Mad Science＂, the argument is made that the evil geniuses of Fleming, Rohmer, and Boothby may very well be the offspring of an earlier stock character, the mad scientist, who trades monomania for megalomania.

A-Equation and Its Connections to Nonlinear Integrable System

A novel approach to inverse spectral theory for Schr&oumldinger Equation operators on a half-line was first introduced by Barry Simon and actively studied in recent literatures. The remarkable discovery is a new object A-function and intergo-differential Equation (called A-Equation) it satisfies. Inverse problem of reconstructing potential is then directly connected to finding solutions of A-Equation. In this work, we present a large class of exact solutions to A-Equation and reveal the connection to a class of arbitrarily large systems of nonlinear ordinary differential Equations. This non-linear system turns out to be C-integrable in the sense of F. Calogero. Integration scheme is proposed and the approach is illustrated in several examples.

Infinite-dimensional 3-Lie algebras and their ：onnections to Harish-Chandra modules

We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.

Some Results on Metric n-Lie Algebras

We study the structure of a metric n-Lie algebra G over the complex field C. Let G = S＋R be the Levi decomposition, where T4 is the radical of G and S is a strong semisimple subalgebra of G. Denote by re（G） the number of all minimal ideals of an indecomposable metric n-Lie algebra and R^⊥ the orthogonal complement of R. We obtain the following results. As S-modules, R^⊥ is isomorphic to the dual module of G/R. The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on G is equal to that of the vector space of certain linear transformations on G; this dimension is greater than or equal to rn（G） ＋ 1. The centralizer of T4 in G is equal to the sum of all minimal ideals; it is the direct sum of R^⊥and the center of G. Finally, G has no strong semisimple ideals if and only if R^⊥ R.