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.     

The effect of random step changes of system parameters on the stability of steady vibration of nonlinear systems

Summary The author proposes a method of analysing the effect of random step changes of system parameters on the stability of steady solution of a nonlinear system in case this steady solution is not the only one. The method is based on the assumption that the time between successive step changes is comparatively long against the period of steady vibration so that transients become stabilized after each parameter change. The parameter is free to vary on a finite interval of values.

---

Übersicht Es wird ein Verfahren vorgeschlagen, um die Auswirkung von zufälligen Sprungstörungen der Systemparameter auf die Stabilität von stationären Lösungen nichtlinearer Systeme zu untersuchen. Dabei wird vorausgesetzt, daß es mehrere stationäre Lösungen gibt. Es wird angenommen, daß die Zeit zwischen den nacheinander folgenden Sprungstörungen vergleichsweise lang gegenüber der Periode der stationären Schwingung ist, so daß die Einschwingvorgänge nach jeder Parameteränderung abgeklungen sind. Der Parameter kann sich dabei in einem endlichen Wertcbcreich ändern.

---

---

Herrn Professor Dr. K. Klotter zum 70. Geburtstag gewidmet.     

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.     

Longitudinal waves in a damped layered system

Summary In the paper a layered system with a finite length connected to discrete elements is considered. It is assumed that the layers of the system as well as the discrete elements undergo longitudinal deformations only. In the considerations a wave method taking into account all wave reflections is utilized. Exemplary numerical calculations are carried out for a two-layered system. These concern the determination of the ranges and locations of resonant regions for selected cross-sections and for various mechanical properties of the layers.

---

Longitudinalwellen in einem geschichteten system mit dämpfung

Übersicht Betrachtet wird ein geschichtetes Kontinuum endlicher Abmessung, das mit diskreten Feder/Dämpfer/Masse-Elementen verbunden ist. Es wird angenommen, daß sowohl der Schichtwerkstoff als auch die diskreten Elemente nur longitudinale Verformungen erleiden. Bei den Betrachtungen wird eine auf den Wellenlösungen aufbauende Methode benutzt, die alle Wellenreflektionen berücksichtigt. Exemplarische numerische Rechnungen werden für ein Zweischichten-System mit ausgewählten Querschnitten und verschiedenen Stoffeigenschaften durchgeführt.

     

A fluorescent assay for chloride transport; identification of a synthetic anionophore with improved activity

A fluorescent assay based on the chloride-sensitive probe, lucigenin, is developed for monitoring chloride transport into vesicles, and used to compare the effectiveness of three steroid-derived transporters.     

A variational approach of the rank function

In the same spirit as the one of the paper (Hiriart-Urruty and Malick in J. Optim. Theory Appl. 153(3):551–577, 2012) on positive semidefinite matrices, we survey several useful properties of the rank function (of a matrix) and add some new ones. Since the so-called rank minimization problems are the subject of intense studies, we adopt the viewpoint of variational analysis, that is the one considering all the properties useful for optimizing, approximating or regularizing the rank function.