Compactness and convergence rates in the combinatorial integral approximation decomposition

The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the \(\hbox {weak}^*\) topology of \(L^\infty \) if the grid constant of this decomposition is driven to zero. We exploit this insight to formulate a general approximation result for optimization problems, which feature discrete and distributed optimization variables, and which are governed by a compact control-to-state operator. We analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes. We use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations, the predominant case in the literature, and the effectiveness of the approach.

     

Measurement of γp→K + Λ and γp→K + Σ 0 at photon energies up to 1.47 GeV

The reactions pK ⁺ and pK ^{+ 0} have been measured with the multiparticle detector system SAPHIR at ELSA in Bonn. Besides the differential cross sections the polarization and, for the first time, the ⁰ polarization have been determined in a photon induced reaction. All data are presented as functions of the photon energy (from threshold up to 1.47 GeV) and of the kaon production angle (0°–180°). The polarization of both and ⁰ is substantial at all energies and varies strongly with the production angle.This work is supported by the Bundesminister für Forschung und Technologie (BMFT), FK 06 BN 621 I     

Darstellung neuer Spiro-Alkoxy-cyclophosphazatriene

Preparation of New Spiro-Alkoxy-Cyclophosphazatrienes New spiro-Alkoxy-cyclophosphazatrienes of the general formula are described. The preparation of the substances and their mass spectroscopic data are reported.     

Mixed-integer optimal control problems with switching costs: a shortest path approach

Mathematical Programming - We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling...     

kinetic energy reflection from polycrystals bombarded with Ar+, Kr+, and Xe+ ions

When the surface of a solid is bombarded with ions a fraction of the primary energy is reemitted by ion reflection and sputtering. The contribution of ion reflection or sputtering to energy reflection is determined by the mass ratio of the bombarding ions to the target atoms.^1,2 In the case of light ions the contribution of reflected ions is dominant. Results for He⁺ and Ne⁺ bombardment were described in a previous paper.³ The present paper deals with results for Ar⁺, Kr⁺, and Xe⁺ bombardment of the same targets as investigated before.³ The energies of the mass selected bombarding ions range from 9 to 16 keV. The measurements were carried out by means of the thermic detector described in a separate paper.⁴ For the given mass ratios most of the reemitted energy is related to sputtering.     

Comparison of HPLC Versus HPTLC-Densitometry for the Quantification of Chromone Glucosides in Saposhnikoviae divaricatae Radix

A HPLC and a HPTLC-densitometric method were developed for the quantification of prim-O-glucosylcimifugin and 4′-O-β-d-glucosyl-5-O-methylvisamminol the major chromone glucosides in the roots of Saposhnikovia divaricata. The validation of both methods resulted in comparable parameters regarding stability, specificity, linearity, robustness, precision and recovery, whereas complementary advantages were obtained concerning LOD and LOQ. The HPTLC-based densitometry revealed a lower LOD (1.11 versus 4.37 μg mL⁻¹ in HPLC) and LOQ (3.36 versus 13.24 μg mL⁻¹ in HPLC) for prim-O-glucosylcimifugin, whereas the HPLC resulted in a lower LOD (1.00 versus 4.10 μg mL⁻¹ in HPTLC-densitometry) and LOQ (3.04 versus 12.46 μg mL⁻¹ in HPTLC-densitometry) for 4′-O-β-d-glucosyl-5-O-methylvisamminol. Both methods revealed nearly matching contents of the chromones after analysis of different commercially available batches of Saposhnikoviae divaricatae radix with a total content for both chromone glycosides in the range from 0.31 ± 0.011 to 0.56 ± 0.021 % determined by HPLC and between 0.34 ± 0.011 and 0.61 ± 0.009 % determined by HPTLC. The plant material cultivated in Germany showed a very similar content and ratio of both chromone glucosides in comparison to the standard batches originating from China.

     

Experimental investigation of vibrational excitations in230Th

Nuclear levels in²³⁰Th have been investigated in the decay of²³⁰Pa, the²³⁰Th(d, pn) reaction and the²³²Th(p, t) reaction. TheK =0 ₁ ⁺ , 2 ₁ ⁺ , and 2 ₂ ⁺ bands with band heads at 635, 781, and 1010 keV were observed up to the 8⁺, 9⁺, and 7⁺ levels, respectively. A second excited 0⁺ level was identified at 1297 keV which might be interpreted as the usual shape-oscillation. The branching ratios of theE2 transitions from the 0 ₁ ⁺ , 2 ₁ ⁺ , and 2 ₂ ⁺ bands are explained in the framework of the rotational model by taking into account the coupling of these bands with the ground-state band, and the coupling between the 0 ₁ ⁺ and 2 ₁ ⁺ band. A strong enhancement ofE2 transitions from the 2 ₁ ⁺ to the 0 ₁ ⁺ band reported earlier is not confirmed. For the octupole vibrations withK =0^–, 1^–, and 2^– theE1 branching ratios are analyzed in terms of the Coriolis coupling of these bands. An almost complete experimental set ofE1 transition moments from these negative-parity bands to the 0 _g ⁺ , 0 ₁ ⁺ , and 2 ₁ ⁺ bands was obtained. It is suggested that octupole correlations might be important in explaining theseE1 moments.We appreciate the help of Mr. Assmus with the proton irradiations and the financial support of the Kernforschungszentrum Karlsruhe GmbH. This work was supported by the Deutsche Forschungsgemeinschaft (grants Bo 1109/1-1, Gr 894/2-1, Gu 179/3-1 and He 1316/2-3) and by the Volkswagen Stiftung.     

Zur Strukturanalyse von einigen spiro-Alkoxychlorophosphazenen anhand von 31P- und 1H-KMR-Untersuchungen. Kopplung von zwei und drei Phosphorkernen

Zusammenfassung ³¹P- und ¹H-KMR-Spektren einiger mehrcyclischer Alkoxychlorophosphazene (s. Summary) werden analysiert und anhand der Wechselwirkung zweier und dreier Phosphorkerne wird die spiro-Struktur der Alkoxychlorophosphazene aufgezeigt.Wir danken Herrn Prof. Dr. H. Marsmann (Ruhr-Universität Bochum) für wertvolle Diskussionen und Herrn Dr. W. Dietrich (Ruhr-Universität Bochum) für die Anfertigung der KMR-Spektren.     

Comparison of HPLC Versus HPTLC-Densitometry for the Quantification of Chromone Glucosides in Saposhnikoviae divaricatae Radix

A HPLC and a HPTLC-densitometric method were developed for the quantification of prim-O-glucosylcimifugin and 4′-O-β-d-glucosyl-5-O-methylvisamminol the major chromone glucosides in the roots of Saposhnikovia divaricata. The validation of both methods resulted in comparable parameters regarding stability, specificity, linearity, robustness, precision and recovery, whereas complementary advantages were obtained concerning LOD and LOQ. The HPTLC-based densitometry revealed a lower LOD (1.11 versus 4.37 μg mL^?1 in HPLC) and LOQ (3.36 versus 13.24 μg mL^?1 in HPLC) for prim-O-glucosylcimifugin, whereas the HPLC resulted in a lower LOD (1.00 versus 4.10 μg mL^?1 in HPTLC-densitometry) and LOQ (3.04 versus 12.46 μg mL^?1 in HPTLC-densitometry) for 4′-O-β-d-glucosyl-5-O-methylvisamminol. Both methods revealed nearly matching contents of the chromones after analysis of different commercially available batches of Saposhnikoviae divaricatae radix with a total content for both chromone glycosides in the range from 0.31 ± 0.011 to 0.56 ± 0.021 % determined by HPLC and between 0.34 ± 0.011 and 0.61 ± 0.009 % determined by HPTLC. The plant material cultivated in Germany showed a very similar content and ratio of both chromone glucosides in comparison to the standard batches originating from China.     

Study of 227Th in the 226Ra(α,3n) reaction

The nuclear structure of ²²⁷Th was studied in the ²²⁶Ra (α,3n) reaction by gamma-ray and conversion-electron spectroscopy. Six rotational bands were identified with spins upto approximately 39/2. Attempts to connect these bands to the low-lying levels known from radioactive-decay work were not fully successful. Received: 25 June 1998