Formal Symplectic Groupoid

The multiplicative structure of the trivial symplectic groupoid over ^d associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function in the direction of a non-trivial Poisson structure so that the multiplication remains associative. We prove that such a deformation is unique under some reasonable conditions and we give the explicit formula for it. This formula turns out to be the semi-classical approximation of Kontsevichs deformation formula. For the case of a linear Poisson structure, the deformed generating function reduces exactly to the CBH formula of the associated Lie algebra. The methods used to prove existence are interesting in their own right as they come from an at first sight unrelated domain of mathematics: the Runge–Kutta theory of the numeric integration of ODEs.A.S.C. acknowledges partial support of SNF Grant No. 20-100029/1.B.D. and G.F. acknowledge partial support of SNF Grant No. 21-65213.01.Acknowledgement The second author thanks Ernst Hairer for useful discussions, and suggestions.     

Renormalization group in the local potential approximation

In the local potential approximation, renormalization group equations reduce to a semilinear parabolic partial differential equation. We derive this equation and show the relation with the hierarchical model. We construct a family of non-trivial fixed points u _2n ^* ,n=2,3,4,..., which have the form ofn-well potentials and exist in the ranges of dimensions 2<d<d _n=2+2/(n?1). Asd←d _n u _2n ^* tends to zero. For the Wilson fixed pointu*₄, we give bounds on critical exponents. In the case of dipole gas in this approximation we show that no non-trivial fixed points exist.     

Construction of a non-trivial planar field theory with ultraviolet stable fixed point

We study a ₄ ⁴ planar euclidean quantum field theory with propagator 1/p ^2–/2,>0. With the help of the tree expansion of Gallavotti and Nicolò [1], this non-renormalizable theory is shown to have a non-trivial ultraviolet-stable fixed point at negative coupling constant. The vicinity of the fixed point is discussed.     

Initial conformations of macrocyclic compounds with rotational symmetry generated from a molecular fragment

An algorithm is described for generating atomic Cartesian coordinates of conformations of macrocyclic molecules possessing exact rotational or rotation-reflection symmetries. A fragment representing the asymmetric unit of the molecule is suitably oriented in space, and then a symmetry operator is applied to generate the initial coordinates of the molecule. An empirical force field of interatomic interactions is used to generate equilibrium conformations. Results of calculations performed on two cyclic polylactones and one crown ether using this approach are given. They reveal that symmetric conformations of these molecules are often preferred. Since the latter conformations are probably responsible for the specialized properties of these molecules, this method should facilitate doing theoretical studies on these kinds of compounds.     

Advances in clinical chemistry over the past 25 years

A survey is presented of developments over the past 25 years of several important areas of clinical chemistry. These areas are instrumentation, reagents, electrochemical sensors, computing, statistics, quality control, enzymology, drug monitoring, trace elements and nucleic acid probes.     

Röntgen-Kontrastmittel. 16. Mitteilung. Derivate von jodierten Benzoylamino-phenyl- und Benzoylamino-phenoxy-alkansäuren

A number of new [(3-amino-2,4,6-triiodo-benzoylamino)-phenyl- and -phenoxy]-alkanoic acids have been synthesized for evaluation as X-ray contrast agents. The toxicity, the bilitropism, and the urotropism of these compounds were determined.     

Skeleton inequalities and the asymptotic nature of perturbation theory for Φ4-theories in two and three dimensions

We use the polymer representation of ⁴-quantum field theories to prove an infinite family of correlation inequalities, called skeleton inequalities, for the 2n-point Green's functions. As an application, we show that they imply that Feynman perturbation theory is asymptotic in less than four dimensions.     

Effects of Non-planarity in the Radical Anions of Tribenzo[a,c,e]cyclooctenes

Reduction of tribenzo[a,c,e]cyclooctene ( 2 ) and its 2,3- and 1,4-dimethyl derivatives ( 4 and 5 ), as well as of 1,1-dimethyl-10,11-propane-2,2-diylidene-1H-benzo[5,6]cycloocta[1,2,3,4-def]fluorene ( 6 ) and its 5,6-didehydro derivative ( 7 ) was followed by cyclic voltammetry. The radical anions of these compounds and those of their derivatives (D) 2 , (D) 5 , and (D) 6 , deuteratsd at C(9) in 1 and 5 or in the corresponding position of 6, have been characterized with the use of ESR, ENDOR, and TRIPLE-resonance spectroscopy. The cyclic-voltammetric and proton-hyperfine data are consistent with the increasing deviations of the radical anions from planarity in the order These deviations, due to steric or interferences in the peri-positions 1?14 and 4?5, are removed in and by the introduction of bridging groups. The non-plalarity affects the thermodynamic and kinetic stabilities of the radical anions and causes a shift in the π-spin distribution away from that benzene ring which is linked to the two others by the essential single bonds C(4a)? C(4b) and C(14a)? C(14b). This finding suggests that the steric hindrance in , and is alleviated by twisting this ring out of coplanarity with the remaining (Z)-stilbene-like π-system.     

A Copper(I) Bis-phenanthroline Complex Buried in Fullerene-Functionalized Dendritic Black Boxes

Virtual inaccessibility to external contact was revealed by electrochemical investigations for a bis(1,10-phenanthroline)copper(I) core embedded in dendrimers with up to 16 peripheral fullerene units (shown schematically). With increasing numbers of fullerene units, less and less light is available to the core, and the small quantity of light energy that reaches the central Cu(I) complex is returned to the external fullerenes by energy transfer-the central core is buried in a dendritic black box.