The 1:1 resonance in Hamiltonian systems

Two-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as parameters, the system undergoes a bifurcation when the frequencies pass through a resonance. These bifurcations are well understood for most resonances $k:l$, but not the semisimple cases $1:1$ and $1:?1$. A two-degree-of-freedom Hamiltonian system can be approximated to any order by an integrable normal form. The reason is that the normal form of a Hamiltonian system has an additional integral due to the normal form symmetry. The latter is intimately related to the ratio of the frequencies. For a rational frequency ratio this leads to $S^1$-symmetric systems. The question we wish to address is about the co-dimension of such a system in $1:1$ resonance with respect to left-right-equivalence, where the right action is $S^1$-equivariant. The result is a co-dimension five unfolding of the central singularity. Two of the unfolding parameters are moduli and the remaining non-modal parameters are the ones found in the linear unfolding of this system.     

Tuning the Product Spectrum of a Glycoside Hydrolase Enzyme by a Combination of Site-Directed Mutagenesis and Tyrosine-Specific Chemical Modification

Selective chemical modification of proteins plays a pivotal role for the rational design of enzymes with novel and specific functionalities. In this study, a strategic combination of genetic and chemical engineering paves the way for systematic construction of biocatalysts by tuning the product spectrum of a levansucrase from Bacillus megaterium (Bm-LS), which typically produces small levan-like oligosaccharides. The implementation of site-directed mutagenesis followed by a tyrosine-specific modification enabled control of the product synthesis: depending on the position, the modification provoked either enrichment of short oligosaccharides (up to 800 % in some cases) or triggered the formation of high molecular weight polymer. The chemical modification can recover polymerization ability in variants with defective oligosaccharide binding motifs. Molecular dynamic (MD) simulations provided insights into the effect of modifying non-native tyrosine residues on product specificity.     

Asymmetric transfer hydrogenation of imines catalyzed by a Noyori-type Ru(II) complex—a parametric study

We present, to the best of our knowledge, the first parametric study of the asymmetric transfer hydrogenation of imines catalyzed by a Noyori-type catalytic complex based on ruthenium. A model imine for this study was 1-methyl-3,4-dihydroisoquinoline, and a well-known complex RuCl(η⁶-p-cymene)((1S,2S)-N-p-toluenesulfonyl-1,2-diphenylethylenediamine) was chosen as the model catalyst. The reactions were performed in the presence of a formic acid–triethylamine mixture as the source of hydrogen.The parameters examined include general parameters, for example, concentration, temperature, and substrate-to-catalyst molar ratio, as well as parameters specific to this particular reaction, such as the amount of the hydrogenation mixture used, the ratio of its components, or the inhibitive effect of carbon dioxide. During this study, several unexpected parameters worth further investigation have emerged.     

Fluorotrimethyl[(Z)-pentafluoropropen-1-yl]phosphorane: Structure,Bonding, and Reactivity

In this contribution we report on fluorotrimethyl[(Z)-pentafluoropropen-1-yl]phosphorane as a phosphorus based fluorinating reagent. Its solid state structure can be described as a trigonal bipyramid featuring elongated axial bonds due to the formation of a 3-center 4-electron bond. Abstraction of the fluoride ion leads to a shortening of the axial P–C bond. Thus the title compound can be utilized for substitution of bromine with fluorine and for the transfer of fluoride ions onto electrophilic compounds. Reaction with Sn(C₂F₅)₂Br₂ afforded salt [P(CH₃)₃(C₃F₅)]₂[Sn(C₂F₅)₂F₄]. When fluorotrimethyl[(Z)-pentafluoropropen-1-yl]phosphorane was treated with P(C₂F₅)₂F the primarily produced anion is sufficiently nucleophilic to attack the propenyl group of the cation in β-position to the phosphorus atom to yield zwitterionic [Me₃PCF=C(CF₃)–PF₃(C₂F₅)₂].     

Promising new catalytic properties of a Co (II)-carboxamide complex and its derived Co3O4 nanoparticles for the Mizoroki-Heck and the Epoxidation reactions

The new Co(II) - carboxamide complex ( 1 ) and Co₃O₄ nanoparticles ( 2 ), by way of thermal decomposition of ( 1 ) have been efficiently synthesised in the environment-friendly. X-ray diffraction reveals a slightly distorted octahedral coordination of cobalt (four nitrogens and two oxygens) in ( 1 ) and regular octahedral or tetrahedral ones (oxygens only) in ( 2 ). The investigation of ( 1 ) and ( 2 ) in the Mizoroki-Heck and epoxidation of alkens reactions showed them both to be powerful, green and inexpensive catalysts.