Ground state systematics and collective dipole excitations of spheroidally deformed sodium clusters in a diffuse jellium model

We solve the Kohn-Sham equations self-consistently in the local density approximation for spheroidal sodium clusters in the particle range 8 ≤ Z ≤ 40. We use a smooth fermi-like jellium density to simulate the influence of the ions in the surface region and obtain similar results as Ekardt and Penzar, but slightly different regions of prolate-to-oblate transitions. We present the systematics of potential energy curves with respect to transitions between oblate, prolate and spherical shapes. Shape transitions occur at particle numbers 12/14 (prolate/oblate), 18/20/22 (oblate/spherical/prolate) and 30/32 (prolate/oblate), which are in good agreement with experimental results. The quadrupole and hexadecupole overlap of the electron density with the jellium is investigated, showing a strong hexadecupole dependence for selected clusters. Collective dipole resonances are described in a simple sum rule approach, which reveals a double splitting according to the different resonance frequencies along the principal axes of the spheroid. The systematics of the resonance peaks for the larger clusters with Z ≥ 20 is in good agreement with experimental results.     

Traditional organizations and crisis management in transition—Organizational perspectives on new dynamics of independent civil engagement

Digitalization and the trend towards more short‐term and project‐oriented social engagement have had a direct impact on traditional crisis management. This societal change has supported the evolution of new types of volunteers who use low‐threshold potentials to organize and maintain support independently. Traditional institutions like the German Red Cross are challenged to deal with these rapid changes regarding their own organizational culture in relation to the new phenomenon of so‐called unaffiliated volunteers. This paper investigates how unaffiliated volunteers influence and change the organizational culture of German disaster management by analysing and reflecting organizational adaptation processes in the aftermath of the German floods in 2013, the storm events in the west of Germany in 2014 and the refugee relief mission in 2015–2016. Therefore, semi‐structured interviews with experts of the German Red Cross were held to analyse their reactions towards unaffiliated Volunteers during the Floods in 2013 and the refugee relief missions, and further focus group interviews were conducted to validate the extracted results. Findings suggest that among professionals and leading entities in the German Red Cross, a process of rethinking has emerged, recognizing the importance and necessity to open up organizational structures for the collaboration and coordination of unaffiliated volunteers.     

The residue of vector sets with applications to decidability problems in Petri nets

Summary A set K of integer vectors is called right-closed, if for any elementmK all vectors mm are also contained in K. In such a case K is a semilinear set of vectors having a minimal generating set res(K), called the residue of K. A general method is given for computing the residue set of a right-closed set, provided it satisfies a certain decidability criterion.Various right-closed sets wich are important for analyzing, constructing, or controlling Petri nets are studied. One such set is the set CONTINUAL(T) of all such markings which have an infinite continuation using each transition infinitely many times. It is shown that the residue set of CONTINUAL(T) can be constructed effectively, solving an open problem of Schroff. The proof also solves problem 24 (iii) in the EATCS-Bulletin. The new methods developed in this paper can also be used to show that it is decidable, whether a signal net is prompt [23] and whether certain -languages of a Petri net are empty or not.It is shown, how the behaviour of a given Petri net can be controlled in a simple way in order to realize its maximal central subbehaviour, thereby solving a problem of Nivat and Arnold, or its maximal live subbehaviour as well. This latter approach is used to give a new solution for the bankers problem described by Dijkstra.Since the restriction imposed on a Petri net by a fact [11] can be formulated as a right closed set, our method also gives a new general approach for implementations of facts.     

Enzymatic esterification of glycerol II. Lipase-catalyzed synthesis of regioisomerically pure 1(3)-rac-monoacylglycerols

Regioisomerically pure 1(3)-rac-monoacylglycerols are conveniently prepared in high yields (>75%) and in multigram quantities by enzymatic esterification of glycerol in the presence of various lipases(Chromobacterium viscosum, Rhizopus delemar, Rhizomucor miehei) with a variety of different acyl donors, such as free fatty acids, fatty acid alkyl esters, vinyl esters and triacylglycerols, as well as natural fats and oils. All reactions are carried out in aprotic organic solvents with low water content, namelyn-hexane, diethyl ether, tBuOMe or mixtures of these solvents. Essential for the success of these transformations were the following two factors. First, the creation of an artificial interphase between the solvent-immiscible hydrophilic glycerol and the hydrophobic reaction medium by its adsorption onto a solid support. Second, a facile system for the separation of the desired monoacylglycerol from the reaction mixture, coupled with the continuous recycling of acyl donor and undesirable by-products.