Photon statistics in saturated m-photon amplification and attenuation of coherent light

The change of photon statistics of a nearly coherent single-mode light beam travelling through a saturable m-photon-amplifying or absorbing medium (m = 1, 2, …) is theoretically investigated. With the help of an approximation scheme valid for $\text{n}$ ? 1, Δn² ? $\text{n}$² ($\text{n}$ mean value and Δn² variance of the photon number) an analytical expression is derived for the quantity Δn²/$\text{n}$. The results holds for arbitrary values of the initial population inversion and of the degree of saturation. It turns out that for both amplification and attenuation processes after sufficiently strong interaction Δn²/$\text{n}$ tends to an asymptotic value.     

Die reaktion von 4-(α-hydroxyalkyliden)-Δ2-5-isoxazolonen mit bifunktionellen stickstoffbasen

The 4-(α-hydroxyalkylidene)-Δ²-5-isoxazolones2 exist in the β-ketoenol form (“vinyloge car?ylic acids”),2a,c react with guanidine and amidines to give only the enolates4, whereas they react both with hydrazines and 1,2-diamines to form the enamines6 and9 (“vinyloge amids”). The 4-(α-ethoxyalkylidene)-Δ²-5-isoxazolones 7 (“vinyloge esters”) condense with guanidine, benzamidine, and urea to affort the enamines8. Attempted ring-opening by bases failed whilst catalytic hydrogenation of the enamines6 and8 yielded the pyrazoles10,11 and diazepines12. The structures of the compounds have been elucidated by NMR and IR-spectra.     

The Influence of Multi-Photon Absorption on Photon Statistics

A previous approximation scheme [6] which allowed to calculate, in a simple manner, the quantity Δn²/n (n mean value and Δn² variance of the photon number) in the course of a multi-photon absorption process, is extended to study the change of the shape of the photon distribution, too. It turns out that there is a tendency to symmetrize the distribution. Moreover, an approximative expression for the asymptotic distribution to which the distribution tends after a sufficiently strong absorption, irrespective of the initial distribution, is found in form of a Gaussian.     

Ein lexikographischer Suchalgorithmus zur Lösung allgemeiner ganzzahliger Programmierungsaufgaben

Zusammenfassung In dieser Arbeit wird ein slexikographischer Suchalgorithmus zur Lösung von allgemeinen diskreten Optimierungsaufgaben, bei denen Zielfunktion und Restriktionen beliebige Funktionen sein können, angegeben. Es handelt sich hierbei um ein spezielles Branch-and-Bound Verfahren, bei welchem die übliche Schrankenbedingung (Bound) nicht als Auswahlkriterium, sondern nur als Verwerfkriterium benutzt wird. Die Auswahlstrategie ist lexikographisch. Die Anwendbarkeit des Verfahrens auf ganzzahlige und gemischt-ganzzahlige Programmierungsprobleme und auf besondere Spezialfälle sowie auf diophantische Gleichungs- und Ungleichungssysteme wird diskutiert. Außerdem werden alle anderen bekannten Verfahren zur ganzzahligen Programmierung kurz erwähnt und deren Rechenzeiten und Effizienz mit den entsprechenden Daten des Suchalgorithmus an Hand von zahlreichen Testbeispielen verglichen.

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Summary This paper presents a lexicographic search algorithm for solving general discrete optimization problems with arbitrary objective functions and constraints. It is a special branch-and-bound method in which the bound condition is used only as a reject criterion, but not as choice criterion. The choice strategy of the algorithm is lexicographical. The practical use of this method for integer and mixed integer programming and for solving systems of diophantine equations and inequalities is demonstrated. Moreover, there is a short discussion of all other known integer programming methods and of their computing time and efficiency compared with the search algorithm. This comparison is made by means of numerous test problems.

     

Cycloaddition von N-sulfinylaminen an ketene

Aromatic and aliphatic N-sulphinyl amines add smoothly to diphenyl and biphenylene ketene forming substituted 1,2-thiazetidinone-(3)-oxides-(1). An addition of ketene itself to N-sulphinyl cyclohexyl amine can be concluded from secondary products only.