A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Mechanism of the aromatic hydroxylation of thiophene by acid-catalyzed peracid oxidation

The oxidation of thiophene (1) with peracids in a strongly acidic environment yielded thiophen-2-one (4) as the product of an apparent direct hydroxylation of the thiophene aromatic ring together with the anticipated thiophene-S-oxide dimers, 2a,b, as the main products. Formation of the latter dimers can be rationalized in a straightforward manner by initial oxidation at the sulfur atom of thiophene (1) to yield thiophene-S-oxide followed by subsequent dimerization in a Diels-Alder type reaction. Trapping experiments in the presence of a competing dienophile indicated that thiophen-2-one (4) did not originate from the monomeric thiophene-S-oxide but was the product of an independent reaction pathway. The extent of thiophen-2-one (4) formation correlated with the acidity of the reaction medium and was suppressed in the presence of water, the latter presumably acting as a competing base. As evidenced by the use of 2,5-dideuterated thiophene (1-D), its mechanism of formation involved a 1,2-hydride shift, a feature commonly described in the peracid-mediated epoxidation of aromatic hydrocarbons and indicative for the occurrence of cationic intermediates. In agreement with all these observations we propose a mechanism involving initial protonation of thiophene followed by nucleophilic attack of the peracid in position 2 of the thiophene ring. Intramolecular epoxidation may lead to the formation of thiophene 2,3-epoxide as a highly reactive intermediate that then undergoes heterolytic ring opening and a 1,2-hydride shift to yield thiophen-2-one (4) after a final, acid-catalyzed, isomerization of the double bond.     

Über hexagonale Perowskite mit Kationenfehlstellen. XVII Strukturbestimmung an Ba9Nb6W□2O27 - der ersten Stapel-variante eines rhomboedrischen 27 L-Typs

On Hexagonal Perovskites with Cationic Vacancies. XVII. Structure Determination on Ba₉Nb₆W□₂O₂₇ – the First Stacking Polytype of a Rhombohedral 27 L-Type The hexagonal stacking polytype of rhombohedral 27 L -type, Ba₉Nb₆W□₂O₂₇, crystallizes in the space group R3 m with the sequence (4)1(3)1 ? (hhccchhcc)₃ and three formula units for the trigonal setting. The refined, intensity related, R'-value is 9.7percnt;. The octahedral net consists of blocks of three face connected octahedra which are linked to each other alternately through one or two octahedra connected exclusively by common vertices. The cationic vacancies are located in the centers of the groups of three octahedra. With this distribution direct contact between occupied face-sharing octahedra is avoided. The niobium and tungsten atoms are distributed statistically between the remaining octahedral holes. In the blocks of three octahedra they are displaced by ≈ 0.29 Å from their ideal positions in the direction of the central void. The Ba atoms neighbouring a vacancy (all in hexagonal packed BaO₃ sheets) are dislocated in the direction of the void, while the cubic packed BaO₃ sheets maintain nearly regular form.     

Über orthogonalisierbare nicht-archimedische Banachräume

Ohne Zusammenfassung     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Über Differentialgleichungen in n. a. Banachräumen,insbesondere ihre Lösung mittels eines „Wegintegrales“

Ohne Zusammenfassung     

Beitrag zur Kenntnis der Viskosezersetzung. Die Dissoziationskonstante der Cellulosexanthogensäure

Zusammenfassung Nachdem plausibel gemacht werden konnte, daß bei verschiedenen Zersetzungs- bzw. Regenerationsprozessen als Zwischenprodukt freie Cellulosexanthogensäure (CXS.) auftritt und dieselbe z. B. in vorliegender Arbeit im frisch gesponnenen Faden tatsächlich nachweisbar war, wurde auch versucht, die Dissoziationskonstante derselben abzuschätzen. Die dabei auftretenden Schwierigkeiten — sowohl hinsichtlich der experimentellen Durchführung wie auch die durch das Fehlen einer Theorie polyvalenter Makroionen — werden diskutiert. Aus mehreren unabhängigen Messungen, unter Bedachtnahme auf Ergebnisse an Celluloseglycolsäureäther vonKagawa undKatsuura, wird wahrscheinlich gemacht, daß die Dissoziationskonstante der verdünnten Säure zwischen 2,1 und 5,5·10^–5 liegt. Mithin ist die Cellulosexanthogensäure etwas stärker als Essigsäure, die im verdünnten Zustand bekanntlich Na-Cellulosexanthogenat ziemlich unzersetzt läßt^{2, 9, 12}.Abschließend wurde noch das Röntgendiagramm von präzipitiertem Na-Cellulosexanthogenat wiedergegeben.Mit 4 AbbildungenHerrn Prof. Dr.A. Skrabal zum 75. Geburtstag gewidmet.     

Multiple ionization of argon in coincidence with projectile ions in 60–120 MeV Si q+-Ar collisions

A projectile ion-recoil ion coincidence technique has been employed to study the multiple ionization and the charge transfer processes in collisions of 60–120 MeV Si ^q+ (q = 4−14) ions with neutral argon atoms. The relative contribution of different ionization channels, namely; direct ionization, electron capture and electron loss leading to the production of slow moving multiply charged argon recoil ions have been investigated. The data reported on the present collision system result from a direct measurement in the considered impact energy for the first time. The total ionization cross-sections for the recoil ions are shown to scale as q ^1.7/E _p ^0.5 , where E _p is the energy in MeV of the projectile and q its charge state. The recoil fractions for the cases of total- and direct ionizations are found to decrease with increasing recoil charge state j. The total ionization fractions of the recoils are seen to depend on q and to show the presence of a ‘shell-effect’ of the target. Further, the fractions are found to vary as 1/j ² upto j = 8+. The average recoil charge state 〈j〉 increases slowly with q and with the number of lost or captured electrons from or into the projectile respectively. The projectile charge changing cross-sections σ _qq′ are found to decrease with increasing q for loss ionization and to increase with q for direct-and capture ionization processes respectively. The physics behind various scaling rules that are found to follow our data for different ionization processes is reviewed and discussed.     

Theoretical vs. empirical classification and prediction of congested traffic states

Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss the terminology of traffic phases and give empirical evidence for the existence of a phase diagram of traffic states. In contrast to previously presented phase diagrams, it is shown that “widening synchronized patterns” are possible, if the maximum flow is located inside of a metastable density regime. Moreover, for various kinds of traffic models with different instability diagrams it is discussed, how the related phase diagrams are expected to approximately look like. Apart from this, it is pointed out that combinations of on- and off-ramps create different patterns than a single, isolated on-ramp.     

The effects of time delay on the decline and propagation processes of population in the Malthus-Verhulst model with cross-correlated noises

This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring, using a Fokker-Planck formalism. We will compare two different situations: (i) symmetrical interaction forces fulfilling Newton’s law of “actio = reactio” and (ii) asymmetric, forwardly directed interactions as, for example in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions for asymmetric interactions and driving terms agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. This analytical result is confirmed by computer simulations and establishes the possibility of approximating the steady state statistics in driven many-particle systems by Hamiltonian systems. Our finding is also useful to understand the various departure time distributions of queueing systems as a possible effect of interactions among the elements in the respective queue [Physica A 363, 62 (2006)].