Solvability of Minimal Graph Equation Under Pointwise Pinching Condition for Sectional Curvatures

We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan–Hadamard manifold M whose radial sectional curvatures outside a compact set satisfy an upper bound

$$\begin{aligned} K(P)\le - \frac{\phi (\phi -1)}{r(x)^2} \end{aligned}$$

and a pointwise pinching condition

$$\begin{aligned} |K(P) |\le C_K|K(P') | \end{aligned}$$

for some constants \(\phi >1\) and \(C_K\ge 1\), where P and \(P'\) are any 2-dimensional subspaces of \(T_xM\) containing the (radial) vector \(\nabla r(x)\) and \(r(x)=d(o,x)\) is the distance to a fixed point \(o\in M\). We solve the asymptotic Dirichlet problem with any continuous boundary data for dimensions \(n=\dim M>4/\phi +1\).

     

A Grobman–Hartman Theorem for Control Systems

We consider the problem of locally linearizing a control system via topological transformations. According to [2,3], there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of under-determined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman–Hartman theorem for control systems.     

Nonribosomal peptide synthesis in animals: the cyclodipeptide synthase of Nematostella

Cyclodipeptide synthases (CDPSs) are small enzymes structurally related to class-I aminoacyl-tRNA synthetases (aaRSs). They divert aminoacylated tRNAs from their canonical role in ribosomal protein synthesis, for cyclodipeptide formation. All the CDPSs experimentally characterized to date are?bacterial. We show here that a predicted CDPS from the sea anemone Nematostella vectensis is an active CDPS catalyzing the formation of various cyclodipeptides, preferentially containing tryptophan. Our findings demonstrate that eukaryotes encode active CDPSs and suggest that all CDPSs have?a similar aminoacyl-tRNA synthetase-like architecture and ping-pong mechanism. They also raise questions about the biological roles of the cyclodipeptides produced in bacteria and eukaryotes.     

Synthesis and luminescence properties of new red-shifted absorption lanthanide(III) chelates suitable for peptide and protein labelling

The synthesis and photo-physical properties of an original bis-pyridinylpyrazine chromophore efficiently sensitising europium(III) and samarium(III) are described. The corresponding lanthanide(III) complexes display in aqueous solutions a maximum excitation wavelength which is significantly red-shifted compared to the usual terpyridine-based chelates, and a valuable luminescence brightness above 2,000 dm(3) mol(-1) cm(-1) at 345 nm was obtained with a europium(III) derivative. Further functionalisation with three different bioconjugatable handles was also investigated and their ability to efficiently label a model hexapeptide was evaluated and compared. Finally, the best bioconjugatable europium(III) chelate was used in representative labelling experiments involving monoclonal antibodies and the luminescence features of the corresponding bioconjugates remained satisfactory.     

Magnetic and conduction properties in 1D organic radical materials: an ab initio inspection for a challenging quest

The chemical control of magnetic and conduction properties for organic radicals is mainly based on t, the resonance integral, and U, the on-site repulsion, used in the Hubbard model. A qualitative analysis based on the competition between the kinetic and the Coulomb contribution, and the expression of the magnetic exchange coupling suggests that U should be roughly 800 cm(-1) while the resonance integral |t| should be 200 cm(-1) to reach bifunctionality. Ab initio wavefunction-based calculations allowed us to quantitatively measure those quantities for several organic materials considered as 1D systems starting from their reported crystal structures. The extraction of t and U parameters from the exchange coupling constants between neighbouring radicals allowed us to anticipate a possible metallic behaviour. Finally, the impact of chemical changes in the constitutive units is measured to rationalize the macroscopic behaviour modifications. It is shown that the intriguing regime characterized by simultaneous itinerant and localized electrons might be achieved by molecular engineering.     

Atlas motion platform generalized kinematic model

Conventional training simulators commonly use a hexapod configuration to provide motion cues. While widely used, studies have shown that hexapods are incapable of producing the range of motion required to achieve high fidelity simulation required in many applications. A novel alternative is the Atlas motion platform. This paper presents a new generalized kinematic model of the platform which can be applied to any spherical platform actuated by three omnidirectional wheels. In addition, conditions for slip-free and singularity-free motions are identified. Two illustrative examples are given for different omnidirectional wheel configurations.     

Oxo-15 dihydro-15,20S catharanthine,nouvel intermédiaire dans l'hémisynthèse de l'anhydrovinblastine

15-Oxo-15,20S-dihydrocatharanthine 4a has been converted stereospecifically into 15R-acetoxy-15,20S-dihydrocatharanthine 10a. The coupling reaction of the corresponding N_b-oxide 11 with vindoline 14 afforded the pivotal anti-tumour alkaloid anhydrovinblastine 1.