Classification of 1st order symplectic spinor operators over contact projective geometries

We give a classification of 1st order invariant differential operators acting between sections of certain bundles associated to Cartan geometries of the so-called metaplectic contact projective type. These bundles are associated via representations, which are derived from the so-called higher symplectic (sometimes also called harmonic or generalized Kostant) spinor modules. Higher symplectic spinor modules are arising from the Segal-Shale-Weil representation of the metaplectic group by tensoring it by finite dimensional modules. We show that for all pairs of the considered bundles, there is at most one 1st order invariant differential operator up to a complex multiple and give an equivalence condition for the existence of such an operator. Contact projective analogues of the well known Dirac, twistor and Rarita-Schwinger operators appearing in Riemannian geometry are special examples of these operators.     

Weakly non-linear analysis of Rayleigh-Benard convection with time periodic heating

The stability of a horizontal layer of fluid heated from below as well as from above is examined. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent part, which is oscillatory. The amplitude of temperature modulation is δ. By considering the weakly non-linear analysis, it is shown that the modulation produces a range of stable hexagons near the critical Rayleigh number. Some comparisons have been made with the other theoretical results.     

Covering theory for complexes of groups

We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and isometry of universal covers. We characterize faithful complexes of groups and prove a conjugacy theorem for groups acting freely on polyhedral complexes. We also define an equivalence relation on coverings of complexes of groups, which allows us to construct a bijection between such equivalence classes, and subgroups or overgroups of a fixed lattice Γ in the automorphism group of a locally finite polyhedral complex X.     

Simultaneous determination of five coumarins in Angelicae dahuricae Radix by HPLC/UV and LC‐ESI‐MS/MS

Rapid, simple and reliable HPLC/UV and LC‐ESI‐MS/MS methods for the simultaneous determination of five active coumarins of Angelicae dahuricae Radix, byakangelicol (1), oxypeucedanin (2), imperatorin (3), phellopterin (4) and isoimperatorin (5) were developed and validated. The separation condition for HPLC/UV was optimized using a Develosil RPAQUEOUS C₃₀ column using 70% acetonitrile in water as the mobile phase. This HPLC/UV method was successful for providing the baseline separation of the five coumarins with no interfering peaks detected in the 70% ethanol extract of Angelicae dahuricae Radix. The specific determination of the five coumarins was also accomplished by a triple quadrupole tandem mass spectrometer equipped with an electrospray ionization source (LC‐ESI‐MS/MS). Multiple reaction monitoring (MRM) in the positive mode was used to enhance the selectivity of detection. The LC‐ESI‐MS/MS methods were successfully applied for the determination of the five major coumarins in Angelicae dahuricae Radix. These HPLC/UV and LC‐ESI‐MS/MS methods were validated in terms of recovery, linearity, accuracy and precision (intra‐ and inter‐day validation). Taken together, the shorter analysis time involved makes these HPLC/UV and LC‐ESI‐MS/MS methods valuable for the commercial quality control of Angelicae dahuricae Radix extracts and its pharmaceutical preparations. Copyright © 2009 John Wiley & Sons, Ltd.     

Groupwise dense families

We show that the Filter Dichotomy Principle implies that there are exactly four classes of ideals in the set of increasing functions from the natural numbers. We thus answer two open questions on consequences of ? < ?. We show that ? < ? implies that ? = ?, and that Filter Dichotomy together with ? < ? implies ? < ?. The technical means is the investigation of groupwise dense sets, ideals, filters and ultrafilters. With related techniques we prove the new inequality ?≤ cf(?). Received: 9 October 1998 / Revised version: 18 August 1999 / Published online: 21 December 2000     

Noncompact homogeneous Einstein manifolds attached to graded Lie algebras

In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated nilmanifolds and solvmanifolds. We show that our solvmanifold is Einstein if the nilradical is two-step. New examples of Einstein solvmanifolds with three-step and four-step nilradicals are also given. This work was partially supported by Grant-in-Aid for Young Scientists (B) 14740049 and 17740039, The Ministry of Education, Culture, Sports, Science and Technology, Japan.     

A Multidimensional Generalization of Shukla's 8ψ8 Summation

   Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised ₈ ψ ₈ summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A _r-1 or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A _r-1 nonterminating very-well-poised ₆ φ ₅ summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.     

Homogeneous two-manifolds with an invariant two-form

We study a 2-dimensional manifold that admits a homogeneous action of a 3-dimensional Lie group G, and has a 2-form invariant under G. We show that such a manifold can be realized as a surface in the affine 3-space, and list such realizations.      

The duality of option investment strategies for hedge funds

This paper explores the structure of optimal investment strategies using stochastic programming and duality theory in investment portfolios containing options for a hedge fund manager who attempts to beat a benchmark. Explicit optimal conditions for option investments are obtained for several models. This research was supported by Inquire, the Social Sciences and Humanities Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the National Center of Competence in Research FINRISK, a research instrument of the Swiss National Science Foundation, and MIT’s Sloan School of Management. J. R. Rodríguez-Mancilla thanks Gabriel Casillas-Olvera, Deputy Manager of Risk Control at Banco de Mexico, who read several drafts of this paper and made many helpful comments. The opinions in this paper do not necessarily represent those of Banco de México.     

A non-D-space with large extent

We proved that ^?+ implies the existence of a non-D-space whose all closed subspace F satisfies e(F)=L(F). The existence of such a space under MA+¬CH or PFA is also discussed.