The normalized cyclomatic quotient associated with presentations of finitely generated groups

Given a presentation of ann-generated group, we define the normalized cyclomatic quotient (NCQ) of it, which gives a number between 1−n and 1. It is computed through an investigation of the asymptotic behavior of a kind of an “average rank”, or more precisely the quotient of the rank of the fundamental group of a finite subgraph of the corresponding Cayley graph by the size of the subgraph. In many ways (but not always) the NCQ behaves similarly to the behavior of the spectral radius of a symmetric random walk on the graph. In particular, it characterizes amenable groups. For some types of groups, like finite, amenable or free groups, its value equals that of the Euler characteristic of the group. We give bounds for the value of the NCQ for factor groups and subgroups, and formulas for its value on direct and free products. Some other asymptotic invariants are also discussed.     

The different aromatic characters of some localized benzene derivatives

Localized benzene derivatives can be separated into two classes, one that retains large diamagnetic ring currents and a second that loses the diamagnetic ring current. Energetic criteria and NICS scan are used to evaluate the nature of the two classes. Hückel-type treatment, MO analysis, and comparison to model compounds suggest that there is no connection between geometric localization and the loss of aromaticity.     

Peptide Bond Formation in the Protonated Serine Dimer Following Vacuum UV Photon-Induced Excitation

Possible routes for intra-cluster bond formation (ICBF) in protonated serine dimers have been studied. We found no evidence of ICBF following low energy collision-induced dissociation (in correspondence with previous works), however, we do observe clear evidence for ICBF following photon absorption in the 4.6–14 eV range. Moreover, the comparison of photon-induced dissociation measurements of the protonated serine dimer to those of a protonated serine dipeptide provides evidence that ICBF, in this case, involves peptide bond formation (PBF). The experimental results are supported by ab initio molecular dynamics and exploration of several excited state potential energy surfaces, unraveling a pathway for PBF following photon absorption. The combination of experiments and theory provides insight into the PBF mechanisms in clusters of amino acids, and reveals the importance of electronic excited states reached upon UV/VUV light excitation.     

Structural and spatial considerations in the N,N'-diacyl- and bis(alkoxycarbonyl)bispidinone series

Diamidic and dicarbamic bispidinones show trans-cis isomerism, the relative population in solution of the cis form increasing with solvent polarity. The mutual proximity of the two amide functions in 4a has no impact on the barrier to isomerization. The system represents a peculiar case of planar chirality posing a challenge to its specification.     

Electrically pumped edge-emitting photonic crystal lasers with angled facets

We demonstrate electrically pumped large-area edge-emitting InGaAsP/InP two-dimensional photonic crystal lasers with angled facets at room temperature. The laser uses a weak index perturbation surface photonic crystal structure to control optical modes in the wafer plane. Measurements of the laser spectra show that the modal selection is due to satisfying the Bragg resonance conditions in both the longitudinal and the transverse directions. The lasing wavelength is tuned lithographically by changing photonic crystal lattice constants. We demonstrate a fine lasing wavelength tuning sensitivity (change of lasing wavelength over change of lattice constant) of 0.08 through the transverse lattice constant tuning.     

The relationships between oxidase and synthase activities of flavin dependent thymidylate synthase (FDTS)

New findings lead to a revised understanding of the substrates' binding order, the role of the substrate as an activator, and the observed lag phase in the FDTS catalyzed reaction.     

MC elements in pronilpotent DG Lie algebras

Consider a pronilpotent DG (differential graded) Lie algebra over a field of characteristic 0. In the first part of the paper we introduce the reduced Deligne groupoid associated to this DG Lie algebra. We prove that a DG Lie quasi-isomorphism between two such algebras induces an equivalence between the corresponding reduced Deligne groupoids. This extends the famous result of Goldman–Millson (attributed to Deligne) to the unbounded pronilpotent case.In the second part of the paper we consider the Deligne 2-groupoid. We show it exists under more relaxed assumptions than known before (the DG Lie algebra is either nilpotent or of quasi quantum type). We prove that a DG Lie quasi-isomorphism between such DG Lie algebras induces a weak equivalence between the corresponding Deligne 2-groupoids.In the third part of the paper we prove that an L-infinity quasi-isomorphism between pronilpotent DG Lie algebras induces a bijection between the sets of gauge equivalence classes of Maurer–Cartan elements. This extends a result of Kontsevich and others to the pronilpotent case.