Phenanthroline-polyoxometalate hybrid compounds and the observation of intramolecular charge transfer

A phenanthroline ligand has been covalently modified at the 2 and 9 positions by an aminophenylhexamolybdate substituent. The 1H NMR spectrum indicated a strong electron-withdrawing effect of the hexamolybdate (Mo6O19(2-)) moiety on the phenanthroline ligand. UV-vis and cyclic voltammetry showed extended conjugation of the hybrid phenanthroline-polyoxometalate compound and the possibility of easy oxidation of the extended phenanathroline ligand. Further EPR experiments provided strong evidence for an intramolecular charge-transfer process with the formation of a phenanthroline cation radical and a reduced hexamolybdate.     

Peer methods for the one-dimensional shallow-water equations with CWENO space discretization

For many practical problems an efficient solution of the one-dimensional shallow-water equations (Saint–Venant equations) is important, especially when large networks of rivers, channels or pipes are considered. In order to test and develop numerical methods four test problems are formulated. These tests include the well-known dam break and hydraulic jump problems and two steady state problems with varying channel bottom, channel width and friction.The space discretization of the partial differential equations is based on a finite volume approach with central WENO interpolation and local Lax–Friedrich fluxes (Kurganov and Levy, 2000) [7]. For time-integration new linearly-implicit two-step peer methods of orders three and four are developed. These methods are especially adapted to the usage within the method of lines framework. They show a good performance compared to the well-established methods like ode15s, radau5 or rodasp.     

On q-analogues and stability theorems

In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.     

Interferometry of pions and kaons in high energy collisions

A hydrodynamic model which reproduces the observed rapidity and transverse momentum spectra of mesons and baryons is applied to the study of Bose-Einstein correlations. The pion correlations are found to be strongly affected by resonance decays, except for pairs of large transverse momenta.For S+S at 200 A GeV, in the central rapidity region the effective longitudinal source radii for pions and kaons differ by a factor of 2, the transverse radii by a factor of 1.3. The lifetime of the source can be extracted from kaon interferometry.     

Multiplicity distributions in hadronic and heavy ion reactions

It is shown that the study of multiplicity distributionsP(n) can provide valuable information about the reaction mechanism of strong interactions. The relation betweenP(n) and Bose-Einstein correlations is discussed and the recent Na³⁵ results are interpreted as possible evidence for the existence of a chaotic and a coherent component inP(n). An experiment to test the coherent nature of pion beams is proposed.     

Coherence and self-induced transparency in high-energy hadronic collisions

Two consequences of coherence of mesonic fields have been tested in proton-nucleus collisions. Multiplicity fluctuations measured in finite rapidity intervals are found to obey a Poisson distribution at large rapidities where nuclear transparency occurs. In close analogy to quantum optics we present a quark-parton model in which this link between coherence and transparency is realized via the phenomenon of self-induced transparency.     

From Dyck Paths to Standard Young Tableaux

Annals of Combinatorics - We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we...     

Dispersion-free fiber transmission for femtosecond pulses by use of a dispersion-compensating fiber and a programmable pulse shaper

We demonstrate nearly distortionless 2.5-km fiber transmission of sub-500-fs pulses, using a combination of standard single-mode fiber, dispersion-compensating fiber, and a programmable pulse shaper for simultaneous quadratic and cubic dispersion compensation. The dispersion-compensating fiber corrects the bulk of the quadratic and the cubic phases for the single-mode fiber, and the fiber-pigtailed programmable pulse shaper exactly compensates the residual dispersion terms. Together these elements permit complete recompression of pulses, which first broaden by ~400 times in the single-mode fiber.     

Numerical experiments with parallel two‐step W‐methods for DAEs

We study the numerical behavior of parallel two‐step W‐methods (PTSW methods) applied to index 2 and index 3 DAE test‐problems. In this experiments we do not observe an order reduction in the differential components of the solution and we obtain the same orders as in the ODE and index 1 case. Our methods perform comparably with RADAU for the test‐problems in sequential computations and superior in parallel mode. We conclude that PTSW methods are an interesting choice for solving DAEs, at least up to index 2.