The synthesis of 12-membered macrocycles containing a C1–C8 alkene unit via ring-closing metathesis

Model cross and ring-closing metathesis strategies toward the C1–C8-linear carbon skeleton are presented. The introduction of a four-atom tether enables the formation of 12-membered rings in good-to-excellent yields and stereoselectivity. Furthermore, the study revealed that the cross-metathesis approach and the formation of medium ring sizes via ring-closing metathesis are much less favorable.     

Lyapunov Functions and Cone Families

We describe systematically the relation between Lyapunov functions and nonvanishing Lyapunov exponents, both for maps and flows. This includes a brief survey of the existing results in the area. In particular, we consider separately the cases of nonpositive and arbitrary Lyapunov functions, thus yielding optimal criteria for negativity and positivity of the Lyapunov exponents of linear cocycles over measure-preserving transformations. Moreover, we describe converse results of these criteria with the explicit construction of eventually strict Lyapunov functions for any map or flow with nonzero Lyapunov exponents. We also construct examples showing that in general the existence of an eventually strict invariant cone family does not imply the existence of an eventually strict Lyapunov function.     

Computational Study of Supramolecular Bis-porphyrin “Molecular Tweezers”

A computational study of a series of space separated bis-porphyrin “molecular tweezers” using semiempirical (AM1) and DFT (B3LYP and PBE1PBE) methods has been carried out. It was found that polynorbornane bis-porphyrin systems are significantly less rigid than previously thought. The variation of the metal–metal separation distance between the two porphyrin centers does not cause a significant energy change thus enabling these molecules to easily adjust to the optimal coordination distance required for complexation by various bidentate 4-pyridyl ligands inside the cavity of these “tweezers”. Article 54, ECCC-10, April 1-30 2005, http://www.eccc.monmouth.edu     

Synthesis of bis-peptides attached on poly[n]norbornene molecular scaffolds with well-defined relative positions and distances

This article describes novel synthetic approaches to polynorbornene molecular scaffolds substituted with peptides at various, well-defined positions. A library of norbornene building blocks with attached peptides was prepared. Alkene cyclobutane epoxide (ACE) coupling method was used as a key step reaction for the connection of two norbornene building blocks into bis-peptide scaffolds. Photodimerization of cyclobutene diesters offers an alternative route to polynorbornene bis-peptides. Pyrrolo-peptides were used for preparation of peptide-substituted 7-aza norbornenes. Asymmetrical bis-peptide scaffolds were prepared by ACE coupling of peptide-norbornane epoxide with another norbornene-peptide block. Chemical elaboration of bridgehead dimethyl esters of ACE products or epoxide ACE reagents was also used for peptide attachment.     

Positive top Lyapunov exponent via invariant cones: Single trajectories

We establish criteria for the positivity of the top Lyapunov exponent of a nonautonomous dynamics in terms of invariant cone families, both for maps and flows. The families of cones are associated with quadratic forms of type (k,p−k)$(k,p-k)$ with k arbitrary. Our work can be seen as a counterpart of results in the context of ergodic theory, where the positivity of the top Lyapunov exponent is obtained for almost all trajectories although saying nothing about each specific trajectory.     

A version of the theorem of Johnson,Palmer, and Sell for quasicompact cocycles

We provide a classification of Einstein submanifolds in space forms with flat normal bundle and parallel mean curvature. This extends a previous result due to Dajczer and Tojeiro (Tohoku Math J (2) 45:43–49, 1993) for isometric immersions of Riemannian manifolds with constant sectional curvature.     

Transition from atomic to molecular adsorption of oxygen on tungsten monomer anion

Using vibrationally resolved ultraviolet photoelectron spectroscopy, we studied oxygen adsorption on W monomer anions. Three oxygen atoms are atomically bound in a WO3- compound, whereas in WO4- the fourth oxygen atom is attached to the oxygen, forming a di-oxygen species, implying that atom to molecule transition of O2 takes place when the number of oxygen atoms attached to a W monomer anion exceeds three. Our results indicate that molecular adsorption of oxygen is preferred on electron-deficient metals, showing that the driving force of the atom to molecule transition for the chemisorption of diatomic molecules can be the variations of electronic structures of metal hosts.