Domination of uniformly continuous semigroups

We prove that a bounded operator on a Banach lattice, satisfying a growth condition, is regular. Also, we prove that the generator of a C ₀-semigroup on such a lattice for which such an operator exists is bounded.     

Beitrag zur Frage der qualitativen und quantitativen Bestimmung einiger Pyridinderivate mit Hilfe der IR-Absorptionsspektroskopie

Zusammenfassung Es wird die Möglichkeit einer qualitativen und quantitativen Reinheitsprüfung mit Mitteln der IR-Absorptionsspektroskopie an einer Anzahl von Pyridinderivaten untersucht. Zu diesem Zweck werden die IR-Absorptionsspektren der reinen Substanzen, sowie von binären und ternären Gemischen aufgenommen. Die Spektren werden aus-gewertet und die Nachweisgrenzen angegeben.Dem Verband der Chemischen Industrie und der Deutschen Forschungsgemeinschaft danken wir für die Unterstützung dieser Arbeit.     

TEAD–YAP Interaction Inhibitors and MDM2 Binders from DNA-Encoded Indole-Focused Ugi Peptidomimetics

DNA-encoded combinatorial synthesis provides efficient and dense coverage of chemical space around privileged molecular structures. The indole side chain of tryptophan plays a prominent role in key, or “hot spot”, regions of protein–protein interactions. A DNA-encoded combinatorial peptoid library was designed based on the Ugi four-component reaction by employing tryptophan-mimetic indole side chains to probe the surface of target proteins. Several peptoids were synthesized on a chemically stable hexathymidine adapter oligonucleotide “hexT”, encoded by DNA sequences, and substituted by azide-alkyne cycloaddition to yield a library of 8112 molecules. Selection experiments for the tumor-relevant proteins MDM2 and TEAD4 yielded MDM2 binders and a novel class of TEAD-YAP interaction inhibitors that perturbed the expression of a gene under the control of these Hippo pathway effectors.     

The Laplacian with Wentzell-Robin Boundary Conditions on Spaces of Continuous Functions

We investigate the Laplacian on a smooth bounded open set Rn with Wentzell-Robin boundary condition $\beta u+\frac{\partial u}{\partial \nu} + \Delta u=0$ on the boundary . Under the assumption $\memb$ C() with $\geq$ 0 , we prove that generates a differentiable positive contraction semigroup on $C(\bar{\Omega})$ and study some monotonicity properties and the asymptotic behaviour.     

Dirichlet and Neumann boundary conditions: What is in between?

Given an admissible measure μ on where is an open set, we define a realization of the Laplacian in with general Robin boundary conditions and we show that generates a holomorphic C ₀ -semigroup on which is sandwiched by the Dirichlet Laplacian and the Neumann Laplacian semigroups. Moreover, under a locality and a regularity assumption, the generator of each sandwiched semigroup is of the form . We also show that if contains smooth functions, then μ is of the form (where σ is the (n-1)-dimensional Hausdorff measure and β a positive measurable bounded function on ); i.e. we have the classical Robin boundary conditions. RID="h1" ID="h1"Dédié à Philippe Bénilan RID="*" ID="h1"This work is part of the DGF-Project: "Regularit?t und Asymptotik für elliptische und parabolische Probleme".     

Dialkyl Ether Formation by Nickel‐Catalyzed Cross‐Coupling of Acetals and Aryl Iodides

A new substrate class for nickel‐catalyzed C(sp³) cross‐coupling reactions is reported. α‐Oxy radicals generated from benzylic acetals, TMSCl, and a mild reductant can participate in chemoselective cross‐coupling with aryl iodides using a 2,6‐bis(N‐pyrazolyl)pyridine (bpp)/Ni catalyst. The mild, base‐free conditions are tolerant of a variety of functional groups on both partners, thus representing an attractive C? C bond‐forming approach to dialkyl ether synthesis. Characterization of a [(bpp)NiCl] complex relevant to the proposed catalytic cycle is also described.     

J. L. Lions’ problem on maximal regularity

This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It also contains two new results showing the limits of the theory.