Geometry and Classificatin of Solutions of the Classical Dynamical Yang–Baxter Equation

The classical Yang–Baxter equation(CYBE) is an algebraic equation central in the theory of integrable systems. Its nondegenerate solutions were classified by Belavin and Drinfeld. Quantization of CYBE led to the theory of quantum groups. A geometric interpretation of CYBE was given by Drinfeld and gave rise to the theory of Poisson–Lie groups. The classical dynamical Yang–Baxter equation (CDYBE) is an important differential equation analogous to CYBE and introduced by Felder as the consistency condition for the differential Knizhnik–Zamolodchikov–Bernard equations for correlation functions in conformal field theory on tori. Quantization of CDYBE allowed Felder to introduce an interesting elliptic analog of quantum groups. It becomes clear that numerous important notions and results connected with CYBE have dynamical analogs. In this paper we classify solutions to CDYBE and give geometric interpretation to CDYBE. The classification and interpretation are remarkably analogous to the Belavin–Drinfeld picture. Received: 24 March 1997 / Accepted: 20 June 1997     

Sets of sampling and interpolation in Bergman spaces

Properties of the unions of sampling and interpolation sets for Bergman spaces are discussed in conjunction with the examples given by Seip (1993). Their relationship to the classical interpolation sequences is explored. In addition, the role played by canonical divisors in the study of these sets is examined and an example of a sampling set is constructed in the disk.

     

Probability relations involving several subsystems

We consider the question of factorizability in tensor product spaces, and argue that the correlations associated with entangled states are even more problematic in the general case involving any tensor product of Hilbert spaces, than in the Einstein, Podolsky, and Rosen case with only two [1].     

Assembly of bifunctional receptors via the melamine-barbiturate structural motif

An assembly of cation receptor 1 and anion receptor 2 via the hydrogen bonding melamine-barbiturate structural motif complexes sodium thiocyanate, sodium iodide, and sodium azide in apolar solvents.     

Dextran-modified iron oxide nanoparticles

Dextran-modified iron oxide nanoparticles were prepared by precipitation of Fe（Ⅱ） and Fe（Ⅲ） salts with ammonium hydroxide by two methods. Iron oxide was precipitated either in the presence of dextran solution, or the dextran solution was added after precipitation. In the second method, the iron oxide particle size and size distribution could be controlled depending on the concentration of dextran in the solution. The nanoparticles were characterized by size-exclusion chromatography, transmission electron microscopy and dynamic light scattering. Optimal conditions for preparation of stable iron oxide colloid particles were determined, The dextran/iron oxide ratio 0-0,16 used in precipitation of iron salts can be recommended for synthesis of nanoparticles suitable for biomedical applications, as the colloid does not contain excess dextran and does not coagulate.     

Symmetries of space-time,conservation laws and forbidden motion i: General discussion

The classical (first integral) methods of studying restrictions on the possible motion of gravitationally interacting bodies are reviewed. The simple and flexible inequality method is extended to a similar approach to the relationship between possible forbidden motion and (asymptotic) symmetries in the relativistic few-body problem. This extended method is used to reproduce the standard results of bounded motion for a test particle in a Schwarzschild geometry. The existence of bounded motion is shown for the general relativistic few-body problem and the difficulties in determining such bounded motion is analysed. The use of this approach to obtaining a relativistic alternative to the classical Roche lobe analysis in contact binaries is discussed.