On the theory of collective motion in nuclei. II. Quantum theory

The collective Hamiltonian is assumed to be invariant under the orthogonal group O(A ? 1, $\text{R}$). It is shown that the quantum collective dynamics can be formulated on a coset space of the symplectic group $\text{sp}$(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the collective dynamics based on closed shells and leads to a Hilbert space of analytic functions in six complex collective quasiparticle variables. Dequantization of this scheme yields the classical dynamics described in I. In the limit A ? 1 one obtains a system of s- and d-bosons with symmetry group $\text{u}$ (6) in the collective state space.     

Untersuchung der endlichen Gruppen,deren eigentliche Untergruppen allei-stufig nilpotent sind

Ohne Zusammenfassung Wolfgang Gaschütz zum 60. Geburtstag gewidmet     

On λ-designs

A λ-design is a system of subsets S₁, S₂,…, S_n from an n-set S, n > 3, where |S_i ∩ S_j| = λ for i ≠ j, |S_j| = k_j > λ > 0, and not all k_j, are equal. Ryser [9] and Woodall [101 have shown that each element of S occurs either r₁, or r₂ times (r₁ ≠ r₂) among the sets S₁,…, S_n and r₁ +r₂ = n + 1. Here we: (i) mention most of what is currently known about λ-designs; (ii) provide simpler proofs of some known results; (iii) present several new general theorems; and (iv) apply our theorems and techniques to the calculation of all λ-designs for λ ? 5. In fact, this calculation has been done for all λ ?/ 9 and is available from the author.     

Some mutually disjoint steiner systems

A t-design λ; t-d-n is a system of subsets of size d (called blocks) from an n-set S, such that each t-subset from S is contained in precisely λ blocks. A Steiner system S(l, m, n) is a t-design with parameters 1; l-m-n. Two Steiner systems (or t-designs) are disjoint if they share no blocks. A search has been conducted which resulted in discovering 9 mutually disjoint S(5, 8, 24)'s, 24 mutually disjoint S(4, 7, 23)'s, 60 mutually disjoint S(3, 6, 22)'s, and 197 mutually disjoint S(2, 5, 21)'s. Taking unions of several mutually disjoint Steiner systems will then produce t-designs (with varying λ's) on 21, 22, 23, and 24 points.     

Economic lot sizes and vehicle scheduling

In this paper a relationship between the vehicle scheduling problem and the dynamic lot size problem is considered. For the latter problem we assume that order quantities for different products can be determined separately. Demand is known over our n-period production planning horizon. For a certain product our task is to decide for each period if it should be produced or not. If it is produced, what is its economic lot size? Our aim here is to minimize the combined set-up and inventory holding costs. The optimal solution of this problem is given by the well-known Wagner-Whitin dynamic lot size algorithm. Also many heuristics for solving this problem have been presented. In this article we point out the analogy of the dynamic lot size problem to a certain vehicle scheduling problem. For solving vehicle scheduling problems the heuristic algorithm developed by Clark and Wright in very often used. Applying this algorithm to the equivalent vehicle scheduling problem we obtain by analogy a simple heuristic algorithm for the dynamic lot size problem. Numerical results indicate that computation time is reduced by about 50% compared to the Wagner-Whitin algorithm. The average cost appears to be approximately 0.8% higher than optimum.     

Antiweb-wheel inequalities and their separation problems over the stable set polytopes

A stable set in a graph G is a set of pairwise nonadjacent vertices. The problem of finding a maximum weight stable set is one of the most basic ℕℙ-hard problems. An important approach to this problem is to formulate it as the problem of optimizing a linear function over the convex hull STAB(G) of incidence vectors of stable sets. Since it is impossible (unless ℕℙ=coℕℙ) to obtain a “concise” characterization of STAB(G) as the solution set of a system of linear inequalities, it is a more realistic goal to find large classes of valid inequalities with the property that the corresponding separation problem (given a point x ^*, find, if possible, an inequality in the class that x ^* violates) is efficiently solvable.?Some known large classes of separable inequalities are the trivial, edge, cycle and wheel inequalities. In this paper, we give a polynomial time separation algorithm for the (t)-antiweb inequalities of Trotter. We then introduce an even larger class (in fact, a sequence of classes) of valid inequalities, called (t)-antiweb-s-wheel inequalities. This class is a common generalization of the (t)-antiweb inequalities and the wheel inequalities. We also give efficient separation algorithms for them. Received: June 2000 / Accepted: August 2001?Published online February 14, 2002     

Application of an ePix100 detector for coherent scattering using a hard X‐ray free‐electron laser

A prototype ePix100 detector was used in small‐angle scattering geometry to capture speckle patterns from a static sample using the Linac Coherent Light Source (LCLS) hard X‐ray free‐electron laser at 8.34 keV. The average number of detected photons per pixel per pulse was varied over three orders of magnitude from about 23 down to 0.01 to test the detector performance. At high average photon count rates, the speckle contrast was evaluated by analyzing the probability distribution of the pixel counts at a constant scattering vector for single frames. For very low average photon counts of less than 0.2 per pixel, the `droplet algorithm' was first applied to the patterns for correcting the effect of charge sharing, and then the pixel count statistics of multiple frames were analyzed collectively to extract the speckle contrast. Results obtained using both methods agree within the uncertainty intervals, providing strong experimental evidence for the validity of the statistical analysis. More importantly it confirms the suitability of the ePix100 detector for X‐ray coherent scattering experiments, especially at very low count rates with performances surpassing those of previously available LCLS detectors.     

Settlement of Ulva zoospores on patterned fluorinated and PEGylated monolayer surfaces

Various designs for coatings that resist the attachment of marine organisms are based on the concept of "ambiguous" surfaces that present both hydrophobic and hydrophilic functionalities as surface domains. In order to facilitate the optimal design of such surfaces, information is needed on the scale of the domains that the settling stages of marine organisms are able to distinguish. Previous experiments showed that Ulva zoospores settle (attach) in high numbers onto fluorinated monolayers compared to PEGylated monolayers. The main aim of the present study was to determine, when zoospores of the green alga Ulva are presented with a choice of fluorinated or PEGylated surfaces, what the minimum dimensions of the two types of surface are that zoospores can detect and consequently settle on. Silicon wafers were chemically modified to produce a pattern of squares containing alternating fluorinated and PEGylated stripes of different widths on either a uniform fluorinated or PEGylated background. Each 1 cm x 1 cm square contained stripes with widths of 500, 200, 100, 50, 20, 5, or 2 microm as well as an unpatterned square with a chemistry opposite that of the background. Spores were selective in choosing where to settle, settling at higher densities on fluorinated stripes compared to PEGylated stripes. However, the magnitude of response, and the consequences for settlement on patterned areas overall, was dependent on both the width of the stripes and the chemistry of the background. The data are discussed in relation to the ability of spores to "choose" favorable sites for settlement and the implications for the development of novel antifouling coatings.