The asymptotic number of labeled graphs with given degree sequences

Asymptotics are obtained for the number of n × n symmetric non-negative integer matrices subject to the following constraints: (i) each row sum is specified and bounded, (ii) the entries are bounded, and (iii) a specified “sparse” set of entries must be zero. The result can be interpreted in terms of incidence matrices for labeled graphs.     

Endliche zweifach transitive Permutationsgruppen,deren Involutionen keine Fixpunkte haben

Ohne Zusammenfassung     

Solubility of Certain Pencils of Curves of Genus 1, and of the Intersection of two Quadrics in P4

The main part of the paper finds necessary conditions for solubilityof a pencil of curves of genus 1, each of which is a 2-coveringof an elliptic curve with at least one 2-division point. Asin previous work, these are proved subject to Schinzel's Hypothesisand to the finiteness of the Tate-afarevi group of ellipticcurves defined over a number field. It thus generalizes earlierwork of Colliot-Thélène, Skorobogatov and thesecond author. The final section gives necessary conditions (though of a ratherugly nature) for the solubility of a Del Pezzo surface of degree4. 2000 Mathematical Subject Classification: 11D25.     

Synthesis of Alkynylated Benzo[a]naphtho[2,3‐i]phenazine Derivatives

Thermal condensation of 2,3‐diamino‐1,4‐(bistriisopropylsilylethynyl)benzene, ‐naphthalene,‐anthracene, and ‐benzothiadiazole substrates with 1,2‐naphthalenedione forms bent benzophenazine‐type heteroarenes in a one‐step reaction in good to excellent yields. The targets are investigated by UV/Vis spectroscopy, cyclic voltammetry, and single‐crystal X‐ray crystallography. The packing of the targets in the solid state follows either a herringbone or a brick wall motif. In the case of 8,13‐bis(triisopropylsilylethynyl)dibenzo[a,i]phenazine, polymorphs with either packing result.     

Prediction of Pressure Oscillations in a Premixed Swirl Combustor Flow and Comparison to Measurements

The most common and reliable technique used for flame stabilization of industrial combustors with high thermal loads is the application of strongly swirling flows. In addition to stabilization, swirl flames offer the possibility to influence emission characteristics by simply changing the swirl intensity or the type of swirl generation. Despite of these major advantages, swirling flows tend to evolve flow instabilities, that considerably constitute a significant source of noise. In general, noise generation is substantially enhanced, when such a swirling flow is employed for flames. Thus, the minimization of the resulting noise emissions under conservation of the benefit of high ignition stability is one major design challenge for the development of modern swirl stabilized combustion devices. The present investigation makes an attempt to determine mechanisms and processes to influence the noise generation of flames with underlying swirling flows. Therefore, a new burner has been designed, that offers the possibility to vary geometrical parameters as well as the type of swirl generation, typically applied in industrial devices. Experimental data has been acquired for the isothermal flow as well as swirl flames by means of 3-D-LDV-diagnostics comprising the components of long-time averaged mean and rms-velocities as well as spectrally resolved velocity fluctuations for all components. The noise emission data was acquired with microphone probes resulting in sound pressure levels outside the zone of the perceptible fluid flow. Along to the experiments, numerical simulations using RANS and LES have been carried out for isothermal cases with different burner outlet geometries. The results of the measurements show a distinct rise of the sound pressure level, obtained by changing both the test setup from the isothermal into the flame configuration as well as the geometrical parameters. This is also resembled by the LES simulation results. Furthermore, a physical model has been developed from experiments and verified by the LES simulation, that explains the formation of coherent flow structures and allows to separate their contribution to the overall noise emission from ordinary turbulent noise sources.     

Porous Polymers Based on Aryleneethynylene Building Blocks

Porous conjugated polymers are synthesized by metal‐catalyzed coupling reactions. The progress for porous polymers when planar or tetrahedral building blocks are connected by alkyne units into novel materials is highlighted. The most prominent reaction for the buildup of the microporous alkyne‐bridged polymers is the Sonogashira reaction, connecting alkynes to aromatic iodides or bromides. The availability of the building blocks and the potency of the Sonogashira reaction allow preparing a large variety of intrinsically porous polymeric materials, in which rigid struts connect multipronged centers. The microporous polymers are used as catalysts and as storage materials for gases and sensors. Postfunctionalization schemes, understanding of structure‐property relationships, and the quest for high porosity are pertinent.