The Degree of Word-Expansion of Lexicalized RRWW-Automata

Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based on the number of auxiliary symbols (categories) used for recognizing a language as the projection of its characteristic language onto its input alphabet. This type of recognition is typical for analysis by reduction, a method used in linguistics for the creation and verification of formal descriptions of natural languages. Our main results establish a hierarchy of classes of context-free languages and two hierarchies of classes of non-context-free languages that are based on the expansion factor of a language.

Tomographic imaging of molecular orbitals in length and velocity form

Recently Itatani et al. [Nature 432, 876 (2004)] introduced the new concept of molecular orbital tomography, where high harmonic generation (HHG) is used to image electronic wave functions. We describe an alternative reconstruction form, using momentum instead of dipole matrix elements for the electron recombination step in HHG. We show that using this velocity-form reconstruction, one obtains better results than using the original length-form reconstruction. We provide numerical evidence for our claim that one has to resort to extremely short pulses to perform the reconstruction for an orbital with arbitrary symmetry. The numerical evidence is based on the exact solution of the time-dependent Schrödinger equation for 2D model systems to simulate the experiment. Furthermore we show that in the case of cylindrically symmetric orbitals, such as the N2 orbital that was reconstructed in the original work, one can obtain the full 3D wave function and not only a 2D projection of it. Vor kurzem führten Itatani et al. [Nature 432, 876 (2004)] das Konzept der Molelkülorbital-Tomographie ein. Hierbei wird die Erzeugung hoher Harmonischer verwendet, um Bilder von elektronischen Wellenfunktionen zu gewinnen. Wir beschreiben eine alternative Form der Rekonstruktion, die auf Impuls- statt Dipol-Matrixelementen für den Rekombinationsschritt bei der Erzeugung der Harmonischen basiert. Wir zeigen, dass diese "Geschwindigkeitsform" der Rekonstruktion bessere Ergebnisse als die ursprüngliche "Längenform" liefert. Wir zeigen numerische Beweise für unsere Behauptung, dass man zu extrem kurzen Laserpulsen gehen muss, um Orbitale mit beliebiger Symmetrie zu rekonstruieren. Diese Ergebnisse basieren auf der exakten Lösung der zeitabhängigen Schrödingergleichung für 2D-Modellsysteme. Wir zeigen ferner, dass für zylindersymmetrische Orbitale wie das N2-Orbital, welches in der oben zitierten Arbeit rekonstruiert wurde, das volle 3D-Orbital rekonstruiert werden kann, nicht nur seine 2D-Projektion.

Nitrogen requirements of cassava in selected soils of Thailand

Cassava (Manihot esculenta) is one of the most important export crops in Thailand, yet the nitrogen requirement is unknown and not considered by growers and producers. Cassava requirements for N were determined in field experiments during a period of four years and four sites on the Satuk (Suk), Don Chedi (Dc), Pak Chong (Pc),and Ban Beung (BBg) soil series in Lopburi, Supanburi, Nakhon Ratchasima, and Chonburi sites, respectively. The fertilizer treatment structure comprised 0, 62.5, 125, 187.5, 250 and 312.5 kg N ha^(-1) as urea. At each site cassava was harvested at nine months and yield parameters and the minimum datasets were taken. The fertilizer rate which resulted in maximum yield ranged from 187.5 kg N ha^(-1) in Supanburi and Chonburi (fresh weight yield of 47,500 and 30,000 kg ha^(-1) respectively) to 250 kg N ha^(-1) in Lopburi and Nakhon Ratchasima (fresh weight yield of 64,100 and 46,700 kg ha^(-1) respectively). Yield appeared to decrease at the higher, 312 kg ha^(-1), at Supanburi and Lopburi, and 250 kg ha^(-1) (Chonburi) fertilizer N rates. Net revenue was 70.4 and 72.9 % higher than where no N was appliedLopburi and Nakhon Ratchasima sites. Net revenue at the Supanburi and Chonburi sites were 53.8 and 211.0 % higher than that where no N was applied. This study suggests that at all sites improved cassava production and net revenue could be obtained with the judicious application of higher quantities of N. The results provide needed guidance to nitrogen fertilization of the important industrial crop cassava in Thailand.