Minimal kernels of Dirac operators along maps

Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels .     

Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

Top-down synthesis of polyoxometalate-like sub-nanometer molybdenum-oxo clusters as high-performance electrocatalysts

The top-down fabrication of catalytically active molecular metal oxide anions, or polyoxometalates, is virtually unexplored, although these materials offer unique possibilities, for catalysis, energy conversion and storage. Here, we report a novel top-down route, which enables the scalable synthesis and deposition of sub-nanometer molybdenum-oxo clusters on electrically conductive mesoporous carbon. The new approach uses a unique redox-cycling process to convert crystalline Mo^IVO₂ particles into sub-nanometer molecular molybdenum-oxo clusters with a nuclearity of ∼1–20. The resulting molybdenum-oxo cluster/carbon composite shows outstanding, stable electrocatalytic performance for the oxygen reduction reaction with catalyst characteristics comparable to those of commercial Pt/C. This new material design could give access to a new class of highly reactive polyoxometalate-like metal oxo clusters as high-performance, earth abundant (electro-)catalysts.

The top-down synthesis and deposition of polyoxometalate-like clusters on porous carbon is reported together with the high electrocatalytic oxygen reduction reactivity of the composite.     

DFT Study of the Molybdenum‐Catalyzed Deoxydehydration of Vicinal Diols

The mechanism of the molybdenum‐catalyzed deoxydehydration (DODH) of vicinal diols has been investigated using density functional theory. The proposed catalytic cycle involves condensation of the diol with an Mo^VI oxo complex, oxidative cleavage of the diol resulting in an Mo^IV complex, and extrusion of the alkene. We have compared the proposed pathway with several alternatives, and the results have been corroborated by comparison with the molybdenum‐catalyzed sulfoxide reduction recently published by Sanz et al. and with experimental observations for the DODH itself. Improved understanding of the mechanism should expedite future optimization of molybdenum‐catalyzed biomass transformations.     

Definitive Structural Assessment of Enterococcal Diheteroglycan

Enterococcus faecalis is one of most important nosocomial and often multi‐antibiotic resistant pathogens responsible for infections that are difficult to treat. Previously, a cell‐wall polysaccharide termed diheteroglycan (DHG) was isolated and characterized as a promising vaccine candidate. However, the configuration of its lactic acid (LA) residue attached to the galactofuranoside unit was not assessed, although it influences conformation of DHG chain in terms of biological recognition and immune evasion. This study proves the R configuration of the LA residue by means of chemical analysis, investigation of intramolecular NMR nuclear Overhauser effects and molecular dynamics simulations of native DHG and corresponding R and S models, which were obtained by using pyranoside‐into‐furanoside rearrangement. As alternative treatment and prevention strategies for E. faecalis are desperately needed, this discovery may offer the prospect of a synthetic vaccine to actively immunize patients at risk.     

DYNAMIC STEREOCHEMISTRY OF SYMMETRICALLY BUT DIFFERENTLY SUBSTITUTED DIPHOSPHANES

Abstract

The main interest of our work in Bonn during the last years was in the field of phosphorus-carbon compounds with multiple bonds. Beside the synthesis of new classes of compounds we were particularly interested in the amazing analogy between the PC- and the CC-double bond, which could be proved by evidence of E/Z isomers and a clear indication of pericyclic reactions.