Synthese und Umwandlungen der N-substituierten 3-Aminopropansäuren, 3. Mitt.: Über die Umwandlung von 3-Hydroxyestern in N-benzoylierte 3-Aminosäuren nach der Reaktion vonRitter

Zusammenfassung Untersucht wurde der Einfluß der Substituenten in 3-Hydroxycarbonsäureestern auf ihre Umwandlung in 3-Benzoylaminopropansäuren nach der Reaktion vonRitter. Die Volumenvergrößerung der Substituenten in 3-Stellung hemmt den normalen Reaktionsablauf, wobei in den Fällen, wo in 2-Stellung ein Wasserstoffatom vorliegt, vorwiegend die konkurrierende Eliminierungsreaktion vor sich geht.2. Mitt.: Mh. Chem.96, 1746 (1965).     

Newq-Minkowski space-time and hierarchies ofq-difference conformal invariant equations

We propose several new infinite hierarchies ofq-conformal invariantq-difference equations, in particular, newq-Maxwell equations as the first member of one of these hierarchies. We use an indexless formulation in which all indices are traded for two conjugate variables,z, ¯z. We propose also newq-Minkowski coordinates which together withz, ¯z can be interpreted as the six local coordinates of aq-deformation of theSU (2, 2) flag manifold.Plenary lecture at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.     

Positive-energy irreps of the quantum anti de Sitter algebra

We obtain positive-energy irreducible representations of theq-deformed anti de Sitter algebraU _q (so(3, 2)) by deformation of the classical ones. When the deformation parameterq isN-th root of unity, all these irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than those of the corresponding finite-dimensional non-unitary representations ofso(3, 2). We discuss in detail the singleton representations, i.e. the Di and Rac. WhenN is odd, the Di has dimension 1/2(N ²–1) and the Rac has dimension 1/2(N ²+1), while ifN is even, both the Di and Rac have dimension 1/2N ². These dimensions are classical only forN=3 when the Di and Rac are deformations of the two fundamental non-unitary representations ofso(3, 2).Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.On leave from Bulgarian Acad. Sci., Institute of Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria.On leave from Pennsylvania State University (Fulbright scholar).     

Synthese und Umwandlungen der N-substituierten 3-Aminopropansäuren, 4. Mitt.: Darstellung von unterschiedlich am Stickstoff acylierten 3-Aminopropansäuren nachRitter

Zusammenfassung Die Umsetzung der Äthylester von 3-Hydroxycarbonsäuren mit unterschiedlichen Mono- und Dinitrilen in Gegenwart von Schwefelsäure führt meist zu den jeweiligen 3-(N-Acyl)-amino-carbonsäuren. Andere Versuche ergaben, daß der tert. Butylester der 2-(1-Hydroxycyclohexyl)-äthansäure direkt die erwartete N-Acylaminocarbonsäure liefert. In derselben Weise wurden einige N-Acylderivate der 2-(1-Aminocyclohexyl)-äthansäure synthetisiert, die aus dem Äthylester der eingesetzten Hydroxysäure nicht darstellbar sind.

---

Ethyl 3-hydroxycarboxylates react with mono- and dinitriles in the presence of sulfuric acid in most cases with the formation of the corresponding 3-(N-acyl)-amino acids. A direct formation of the N-acyl amino acid was observed in the case of (1-hydroxycyclohexyl)-acetic acidt-butyl ester. Several N-acyl derivatives of (1-aminocyclohexyl)-acetic acid, not obtainable from its ethyl ester, were synthesized using this procedure.

---

---

3. Mitt.: Mh. Chem.98, 2001 (1967).     

Structure investigations of N-acylated imines by means of UV-Vis spectroscopy

Summary The structures and twist angles about the single C-N bond in some N-acylated imines were determined on the basis of their absorption spectra. The overlapped individual spectral bands are resolved by means of an original computer-based program.

---

Strukturelle Untersuchungen von N-Acylierten Iminen mittels UV-Vis-Spektroskopie

Zusammenfassung Die Strukturen und Torsionswinkel um die C-N-Einfachbindung in einigen N-acylierten Iminen wurden auf Basis der Absorptionsspektren bestimmt. Die überlappenden individuellen Spektralbanden wurden mittels eines Computerprogramms analysiert.

     

Classification of conformal representations induced from the maximal cuspidal parabolic

In the present paper we continue the project of systematic construction of invariant differential operators on the example of representations of the conformal algebra induced from the maximal cuspidal parabolic.     

Contribution to the tin‐rich region of the Sn‐Zn‐Ti system

The tin‐rich region of the system Sn‐Zn‐Ti system has been studied by diffusion couples, differential scanning calorimetry and electron microprobe analyses. Ternary eutectic reaction occurs at 193.7°C near to the binary tin‐zinc eutectic point and titanium content less than 0.9 at.% Ti. Three ternary compounds with approximate formulae: Ti₈Sn₅Zn₂ to Ti₅Sn₃Zn, TiSn₄Zn₅ and Ti₂Sn₄Zn₃ have been observed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

α-Hydroxyalkylation of 3-Morpholinones with Aromatic Aldehydes and Chloral

Lithium derivatives of some 4-substituted 3-morpholinones react with aromatic aldehydes and with chloral to afford 4-alkyl-2-(1-hydroxy-alkyl)-3-morpholinones with good yields.     

Intertwining operator realization of non-relativistic holography

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory (without specifying any action). Further we show that these operators and the bulk-to-boundary operators are intertwining operators. In analogy to the relativistic case, we show that each bulk field has two boundary fields with conjugated conformal weights. These fields are related by another intertwining operator given by a two-point function on the boundary. Analogously to the relativistic result of Klebanov–Witten we give the conditions when both boundary fields are physical. Finally, we recover in our formalism earlier non-relativistic results for scalar fields by Son and others.     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.