Generalizing the Quinn–Wójs theorem on distinct multiplets of composite Fermions

The combinatorial tool of generating functions for restricted partitions is used to generalize a quantum physics theorem relating distinct multiplets of different angular momenta in the composite Fermion model of the fractional quantum Hall effect. Specifically, if g_ℓ(N,M) denotes the number of distinct multiplets of angular momentum ℓ and total angular momentum M, we prove that

where the sum is taken over all positive divisors of N and L(k)=kℓ-kN/2+3k/2-N+N/(2k)-1/2. The original Quinn–Wójs theorem results when k=1 and it appears that this generalization will be useful in further investigations of nuclear shells modeling elementary particle interactions when the particles are clustered together.     

On global minima of semistrictly quasiconcave functions

This paper studies the global behaviour of semistrictly quasiconcave functions with (possibly) nonconvex domain in the presence of global minima. We mainly present necessary conditions for the existence of global minima of a semistrictly quasiconcave real-valued function f with domain , and we show how the geometric structure of its graph and the cardinality of its range depend on the location of global minimum points. Our main result states that if a global minimum of f is achieved in the algebraic interior of K, then f can attain at the most n + 1 distinct function values, and the graph of f has a simple structure determined by a sequence of nested affine subspaces such that, essentially, f is constant on the set difference of each pair of successive affine subspaces.     

Positive solutions of p-type retarded functional differential equations

For systems of retarded functional differential equations with unbounded delay and with finite memory sufficient and necessary conditions of existence of positive solutions on an interval of the form [_t0,∞)$[t_0,\infty )$ are derived. A general criterion is given together with corresponding applications (including a linear case, too). Examples are inserted to illustrate the results.     

Applying the threshold accepting metaheuristic to curriculum based course timetabling

The article presents a study of local search algorithms for timetabling problems, with the particular goal of providing a contribution to competition track 3 of the International Timetabling Competition 2007 (ITC 2007). In this track, a formulation of a curriculum based course timetabling has been published, and novel benchmark instances have been presented that allow the comparison of optimization approaches.     

Quasi–Monte Carlo rules for numerical integration over the unit sphere {\mathbb{S}^2}

We study numerical integration on the unit sphere ${\mathbb{S}^2 \subseteq\mathbb{R}^3}$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a (0, m, 2)-net given in the unit square [0, 1]² to the sphere ${\mathbb{S}^2}$ by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J Sci Comput 18(2):595–609, 1997]. We prove three results. The first one is that the construction is (almost) optimal with respect to discrepancies based on spherical rectangles. Further we prove that the point set is asymptotically uniformly distributed on ${\mathbb{S}^2}$ . And finally, we prove an upper bound on the spherical cap L ₂-discrepancy of order N ^?1/2(log N)^1/2 (where N denotes the number of points). This improves upon the bound on the spherical cap L ₂-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Commun Pure Appl Math 39(S, suppl):S149–S186, 1986] by a factor of ${\sqrt{\log N}}$ . Numerical results suggest that the (0, m, 2)-nets lifted to the sphere ${\mathbb{S}^2}$ have spherical cap L ₂-discrepancy converging with the optimal order of N ^?3/4.     

Сцинтилляционный сп ектрометр с сложение м импулъсов от двух кри сталлов

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Die Lumineszenz,Verfärbung und Exoelektronenemission von Nach Verschiedenen Arten Gefärbten Ca2F-Kristallen

Zusammenfassung Anführung der Ergebnisse eines komplexen Studiums einiger optischer und elektrischer Erscheinungen bei natürlichen und künstlichen Kristallen von CaF₂ verschiedener Herkunft, die photochemisch, additiv oder gleichzeitig auf beide Arten (kombiniert) gefärbt waren. Untersucht wurden vor allem die Absorption bei konstanter und gleichmäßig ansteigender Temperatur (Thermoabsorption), die integrale Lumineszenz und deren Spektralanalyse und die Exoelektronenemission.Auszug aus einem Artikel, der in tschechischem Wortlaut in der Zeitschr. s. as. Fys.8 (1958) veröffentlicht wurde.     

Le pouvoir résolvant du système „objectif-émulsion“

Sans résumé

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Smolyak algorithms based on digital (t, α, d)-sequences for multivariate integration

We use so-called (t, α, d)-sequences and Smolyak's algorithm to construct d × l -dimensional integration rules with optimal convergence rates in a suitable function space. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)