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.     

Extensions of Banach Lie-Poisson spaces

The extension of Banach Lie-Poisson spaces is studied and linked to the extension of a special class of Banach Lie algebras. The case of W∗-algebras is given particular attention. Semidirect products and the extension of the restricted Banach Lie-Poisson space by the Banach Lie-Poisson space of compact operators are given as examples.     

Noncommutative algebras related with Schubert calculus on Coxeter groups

For any finite Coxeter system (W,S) we construct a certain noncommutative algebra, the so-called bracket algebra, together with a family of commuting elements, the so-called Dunkl elements. The Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the Coxeter group W. We prove this conjecture for classical Coxeter groups and I₂(m). We define a “quantization” and a multiparameter deformation of our construction and show that for Lie groups of classical type and G₂, the algebra generated by Dunkl’s elements in the quantized bracket algebra is canonically isomorphic to the small quantum cohomology ring of the corresponding flag variety, as described by B. Kim. For crystallographic Coxeter systems we define the so-called quantum Bruhat representation of the corresponding bracket algebra. We study in more detail the structure of the relations in B_n-, D_n- and G₂-bracket algebras, and as an application, discover a Pieri-type formula in the B_n-bracket algebra. As a corollary, we obtain a Pieri-type formula for multiplication of an arbitrary B_n-Schubert class by some special ones. Our Pieri-type formula is a generalization of Pieri’s formulas obtained by A. Lascoux and M.-P. Schützenberger for flag varieties of type A. We also introduce a super-version of the bracket algebra together with a family of pairwise anticommutative elements, the so-called flat connections with constant coefficients, which describes “a noncommutative differential geometry on a finite Coxeter group” in the sense of S. Majid.     

On reproducing kernels and quantization of states

Quantization of a mechanical system with the phase space a Kähler manifold is studied. It is shown that the calculation of the Feynman path integral for such a system is equivalent to finding the reproducing kernel function. The proposed approach is applied to a scalar massive conformal particle interacting with an external field which is described by deformation of a Hermitian line bundle structure.     

Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.     

A holomorphic field theory

Starting from conformal kinematics we show that the complex Minkowski space as a model of time-space is as good as the real one. A holomorphic field theory is constructed on and it is shown that real field theory is a linear approximation of the holomorphic one.     

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.     

A history of chemical oscillations and waves

The history of the discovery and study of chemical oscillations and waves is presented from the very first accidental observations up to the systematic design of chemical oscillators. Special emphasis is devoted to the long-term debate over the possibility of pure chemical oscillations, i.e., concentration oscillations in homogeneous closed systems.     

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.