New Weyl groups forA 1 (1) and characters of singular highest weight modules

We consider singular Verma modules overA ₁ ⁽¹⁾ , i.e., Verma modules for which the central charge is equal to minus the dual Coxeter number. We calculate the characters of certain factor modules of these Verma modules. In one class of cases we are able to prove that these factor modules are actually the irreducible highest modules for those highest weights. We introduce new Weyl groups which are infinitely generated abelian groups and are proper subgroups or isomorphic between themselves. Using these Weyl groups we can rewrite the character formulae obtained in the paper in the form of the classical Weyl character formula for the finite-dimensional irreducible representations of semisimple Lie algebras (respectively Weyl-Kac character formula for the integrable highest weight modules over affine Kac-Moody algebras) so that the new Weyl groups play the role of the usual Weyl group (respectively affine Weyl group).     

Preparation des reactifs organolithiens a partir des acides ω-cyanocarboxyliques dans l'ammoniac liquide

By treating ω-cyanocarboxylic acids with lithium amide in liquid ammonia, salts, of the type [NCCH(CH₂)_nCOOLi]Li are prepared. The formation of these salts is confirmed by their reaction with N-benzolydiphenylketimine and benzophenone to give ω-diarlylate, ω-benzoylamino- and ω-hydroxy-ψ-cyanocarboxylic acids respectively.     

Monotonicity in high‐order curvilinear finite element arbitrary Lagrangian–Eulerian remap

The remap phase in arbitrary Lagrangian–Eulerian (ALE) hydrodynamics involves the transfer of field quantities defined on a post‐Lagrangian mesh to some new mesh, usually generated by a mesh optimization algorithm. This problem is often posed in terms of transporting (or advecting) some state variable from the old mesh to the new mesh over a fictitious time interval. It is imperative that this remap process be monotonic, that is, not generate any new extrema in the field variables. It is well known that the only linear methods that are guaranteed to be monotonic for such problems are first‐order accurate; however, much work has been performed in developing non‐linear methods, which blend both high and low (first) order solutions to achieve monotonicity and preserve high‐order accuracy when the field is sufficiently smooth. In this paper, we present a set of methods for enforcing monotonicity targeting high‐order discontinuous Galerkin methods for advection equations in the context of high‐order curvilinear ALE hydrodynamics. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

A Simple Synthesis of Dimethylphosphinyl-Substituted Tetrahydropyrroles

Abstract

New dimethylphosphinyl-substituted tetrahydropyrroles 3, 5, 6 and 8 have been synthesized via 1,3-cycloaddition reaction of the N-(4-chlorophenylmethylene)aminomethyl-dimethylphosphinoxide (1) to benzylideneacetophenone, ethyl cinnamate and cinnamonitrile. The structure of the compounds was confirmed by elemental analysis, IR, ¹H-, and ³¹P¹H-NMR spectroscopy and in some cases by mass spectrometry, as well.     

Solvatochromic Determination of Second-order Polarizabilities of Chromophore-functionalized Dextran and Amylose Derivatives

Linear dextran and helix amylose were covalently bonded with nonlinear optical (NLO) chromophores. The influence of the conformation of the polymer matrix on the NLO behavior of the supramolecular structure has been studied. The second order hyperpolarizability depends not only on the secondary structure of the biopolymer, but also on the position of the chromophore towards the polymeric backbone. Functionalization of NLO-phores with biopolymers led to increased thermo- and photostability.     

Fast and efficient separation of cytokinins from auxin and abscisic acid and their purification using mixed-mode solid-phase extraction

A method for separation of cytokinins from auxin and abscisic acid, which allows further separation of cytokinin ribotides from cytokinin bases, ribosides and glucosides and their purification on a single Oasis MCX column was developed. Due to the mixed reversed-phase and cation-exchange mode of the Oasis MCX sorbent the cationic cytokinin bases, ribosides and glucosides as well as the anionic auxin, abscisic acid and cytokinin ribotides are retained and can be sequentially eluted by solvents containing different concentrations of methanol and ammonium hydroxide. Characteristics of the method are high recoveries of analyzed phytohormones and their sufficient purity for quantification by HPLC–ELISA (RIA) or HPLC–MS.     

Stiefel-Skyrme-Higgs models,their classical static solutions and Yang-Mills-Higgs monopoles

A new series of models is introduced by adding Higgs fields to the earlier proposed Euclidean four-dimensional Skyrme-like models with Yang-Mills composite fields constructed from Stiefel manifold-valued fields. The classical static versions of these models are discussed. The connection with the monopole solutions of the Yang-Mills-Higgs models in the Prasad-Sommerfield limit is pointed out and the BPS monopole is reobtained as an example. On leave of absence from the Institute of Nuclear Research and Nuclear Energy, Sofia, Bulgaria.     

Synthese und Umwandlungen der N-substituierten 3-Aminopropansäuren, 2. Mitt.: Darstellung von 1-Benzoyl-azetidinonen-(2)

Zusammenfassung Die durch Behandlung mit Essigsäureanhydrid bewirkte Wasserabspaltung der 3,3-Diaryl-3-benzoylaminopropansäuren führte zur Bildung von N-benzoylierten -Lactamen.

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On treatment with acetic anhydride, 3,3-diaryl-3-benzoyl-aminopropanoic acids lose water and form N-benzoyl--lactams.

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1. Mitt.:Chr. Ivanov, P. Markov undA. Dobrev, C. r. Acad. Bulg. Sci.15, Nr. 4, 403 (1962); Chem. Abstr.60, 4112 d (1964).     

Electro-responsive asymmetric nanopores in polyimide with stable ion-current signal

For the preparation of a single asymmetrically shaped nanopore in a polyimide membrane, Kapton foils were irradiated with single heavy ions and subsequently etched from one side in sodium hypochlorite (NaOCl). The other side of the membrane was protected from etching by a stopping medium containing a reducing agent for hypochlorite ions (OCl^-). The resulting conical nanopore rectified ion current and exhibited a stable ion-current flow. Received: 23 May 2002 / Accepted: 2 September 2002 / Published online: 15 January 2003 RID="*" ID="*"Corresponding author. Fax: +49-6159/712-179, E-mail: Z.Siwy@gsi.de