Lotketten in Hjelmslevgruppen

Ohne Zusammenfassung     

E-H-Zyklotronechos in Plasmen

A new echo type with free electrons in a slight inhomogeneous magnetic field excited by one electric and one magnetic pulse is calculated. Thus features of cyclotron echos and spin echoes are combined. The first electric pulse accelerates all (cold) particles to the same velocity as in the case of usual cyclotron echoes. The second magnetic pulse (at t = τ) rotates the plane of precession in phase space, quite in analogy to the motion of magnetic moments in the case of spin echoes. The echo arises at t = 2τ. The E-H echoes make relaxation and diffusion measurements in plasmas possible, using the methods proved useful in spin echo technique. There are no complications as in the case of E-E cyclotron echoes which are based on the fact that a velocity-dependent collision frequency is necessary for the nonlinearity of that echo mechanism.     

Paraelastisches Verhalten von S2 −-Zentren in Alkalihalogeniden

The reorientation of S₂ ^? molecule ions on anion sites in alkali halide crystals under mechanical stress has been investigated by means of electron spin resonance and optical measurements. The reorientation rate is given by an Arrhenius relation. Tunneling in the ground state of libration is unimportant contrary to the case of the O₂ ^? center. The stress-induced dichroism permitted identification and assignment of two optical absorption bands of the S₂ ^? center.     

The integrated prism interpretation of multileg Mach-Zehnder interferometers based on multimode interference couplers

To simplify the driving conditions as well as to improve the wavelength response of multileg Mach-Zehnder interferometers (MZI) based on multimode interference (MMI) couplers we develop a new interpretation of these devices. Used for optical switching and for wavelength filtering, they are shown to work as active or passive integrated prisms. This analogy greatly facilitates the design of such components and simplifies the understanding of their functionality. The driving conditions of optical switches based on such multileg MZI are easility studied and will be reduced to basic active phase shifts. For wavelength filtering applications using such elements, a new design of the phased waveguide array is proposed which improves the characteristics of the filters.     

Thermodynamics and kinetics of a Gō proteinlike heteropolymer model with two-state folding characteristics

We present results of Monte Carlo computer simulations of a coarse-grained hydrophobic-polar Gō-like heteropolymer model and discuss thermodynamic properties and kinetics of an exemplified heteropolymer, exhibiting two-state folding behavior. It turns out that general, characteristic folding features of realistic proteins with a single free-energy barrier can also be observed in this simplified model, where the folding transition is primarily driven by the hydrophobic force.     

Anti-Markovnikov additions to N-allylic derivatives involving ammonium-carbenium superelectrophiles

Anti-Markovnikov additions to non-conjugated unsaturated amines in superacid are reported. In situ NMR studies, DFT calculations and labelled substrates reactions support the involvement of new ammonium-carbenium superelectrophiles in this original process.     

Concentration for Poisson U-statistics: Subgraph counts in random geometric graphs

Concentration bounds for the probabilities $\mathbb{P}(N\ge M+r)$ and $\mathbb{P}(N\le M?r)$ are proved, where $M$ is a median or the expectation of a subgraph count $N$ associated with a random geometric graph built over a Poisson process. The lower tail bounds have a Gaussian decay and the upper tail inequalities satisfy an optimality condition. A remarkable feature is that the underlying Poisson process can have a.s. infinitely many points.The estimates for subgraph counts follow from tail inequalities for more general local Poisson U-statistics. These bounds are proved using recent general concentration results for Poisson U-statistics and techniques involving the convex distance for Poisson processes.     

The algebra of generating functions for multiple divisor sums and applications to multiple zeta values

We study the algebra \({{\mathrm{{\mathcal {MD}}}}}\) of generating functions for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in \({\mathbb {Q}}\) arising from the calculation of the Fourier expansion of multiple Eisenstein series. We show that the algebra \({{\mathrm{{\mathcal {MD}}}}}\) is a filtered algebra equipped with a derivation and use this derivation to prove linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). The (quasi-)modular forms for the full modular group \({{\mathrm{SL}}}_2({\mathbb {Z}})\) constitute a subalgebra of \({{\mathrm{{\mathcal {MD}}}}}\), and this also yields linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). Generating functions of multiple divisor sums can be seen as a q-analogue of multiple zeta values. Studying a certain map from this algebra into the real numbers we will derive a new explanation for relations between multiple zeta values, including those of length 2, coming from modular forms.