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.     

A combined ESI- and MALDI-MS(/MS) study of peripherally persulfonylated dendrimers: false negative results by MALDI-MS and analysis of defects

Mass spectrometry, in particular MALDI-MS, has often been used as a valuable means to characterize dendritic molecules with respect to their molecular masses. Also, it is a valuable tool for analyzing potential defects in their structure which result from incomplete synthetic steps. This article presents a comparison of ESI and MALDI mass spectrometric experiments on dendrimers persulfonylated at their periphery. While the ESI mass spectra easily permit impurities and defects to be identified and thus provide evidence for sample purity, reactions with acidic matrices occur during the MALDI process. The resulting defects are identical to those expected from incomplete substitution. Thus, in these cases, MALDI-MS yields false negative results. With mass-selected, ESI-generated ions, collision experiments were performed in an FT-ICR mass spectrometer cell to provide detailed insight into the fragmentation patterns of the various dendrimers. Different fragmentation patterns are observed depending on the exact structure of the dendrimer. Also, the nature of the charge is important. The fragmentation reactions for protonated species differ much from those binding a sodium or potassium ion. These differences can be traced back to different sites for binding H+ versus Na+ or K+. Tandem MS experiments on mass-selected dendrimer ions with defects can be used to distinguish different types of defects. A concise structural assignment can thus be made on the basis of these experiments. Even mixtures of two isobaric defect variants with the same elemental composition can be identified.     

Chemical input multiplicity facilitates arithmetical processing

We describe the design and function of a molecular logic system, by which a combinatorial recognition of the input signals is utilized to efficiently process chemically encoded information. Each chemical input can target simultaneously multiple domains on the same molecular platform, resulting in a unique combination of chemical states, each with its characteristic fluorescence output. Simple alteration of the input reagents changes the emitted logic pattern and enables it to perform different algebraic operations between two bits, solely in the fluorescence mode. This system exhibits parallelism in both its chemical inputs and light outputs.     

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.     

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.     

On representations of the elliptic quantum groupE τ,η(sl 2)

We describe representation theory of the elliptic quantum groupE _,(sl ₂). It turns out that the representation theory is parallel to the representation theory of the YangianY(sl ₂) and the quantum loop group .We introduce basic notions of representation theory of the elliptic quantum groupE _,(sl ₂) and construct three families of modules: evaluation modules, cyclic modules, one-dimensional modules. We show that under certain conditions any irreducible highest weight module of finite type is isomorphic to a tensor product of evaluation modules and a one-dimensional module. We describe fusion of finite dimensional evaluation modules. In particular, we show that under certain conditions the tensor product of two evaluation modules becomes reducible and contains an evaluation module, in this case the imbedding of the evaluation module into the tensor product is given in terms of elliptic binomial coefficients. We describe the determinant element of the elliptic quantum group. Representation theory becomes special ifN=m+l, whereN,m,l are integers. We indicate some new features in this case.The authors were supported in part by NSF grants DMS-9400841 and DMS-9501290.     

Conformational Flexibility of Tetralactam Macrocycles and Their Intermolecular Hydrogen‐Bonding Patterns in the Solid State

Flexible rigidity : Tetralactam macrocycles of the Hunter type bear a rigid scaffold (see space‐filling representation), but can still widely adapt to the properties of a guest molecule inside their cavities. X‐ray crystal structures of a series of differently substituted macrocycles reveal a remarkably broad variety of intermolecular hydrogen‐bonding patterns organizing the macrocycles in the crystals in intriguingly different ways.

     

Equivariant Lefschetz number of differential operators

Let G be a compact Lie group acting on a compact complex manifold M by holomorphic transformations. We prove a trace density formula for the G-Lefschetz number of a holomorphic differential operator on M. We generalize the recent results of Engeli and the first author to orbifolds.     

5-μm vertical external-cavity surface-emitting laser (VECSEL) for spectroscopic applications

Mid-IR tunable VECSELs (Vertical External-Cavity Surface-Emitting Lasers) emitting at 4–7 μm wavelengths and suitable for spectroscopic sensing applications are described. They are realized with lead-chalcogenide (IV–VI) narrow band gap materials.