Midwest cousins of Barnes-Wall lattices

Given a rational lattice and suitable set of linear transformations, we construct a cousin lattice. Sufficient conditions are given for integrality, evenness and unimodularity. When the input is a Barnes-Wall lattice, we get multi-parameter series of cousins. There is a subseries consisting of unimodular lattices which have ranks ²d−1±²d−k−1, for odd integers d?3 and integers . Their minimum norms are moderately high: .     

A class of bivariate negative binomial distributions with different index parameters in the marginals

In this paper, we consider a new class of bivariate negative binomial distributions having marginal distributions with different index parameters. This feature is useful in statistical modelling and simulation studies, where different marginal distributions and a specified correlation are required. This feature also makes it more flexible than the existing bivariate generalizations of the negative binomial distribution, which have a common index parameter in the marginal distributions. Various interesting properties, such as canonical expansions and quadrant dependence, are obtained. Potential application of the proposed class of bivariate negative binomial distributions, as a bivariate mixed Poisson distribution, and computer generation of samples are examined. Numerical examples as well as goodness-of-fit to simulated and real data are also given here in order to illustrate the application of this family of bivariate negative binomial distributions.     

On the classification of Hadamard matrices of order 32

All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13, 680, 757 Hadamard matrices of one type and 26, 369 such matrices of another type. Based on experience with the classification of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insignificant. © 2009 Wiley Periodicals, Inc. J Combin Designs 18:328–336, 2010     

Generating scenario trees: A parallel integrated simulation-optimization approach

A crucial issue for addressing decision-making problems under uncertainty is the approximate representation of multivariate stochastic processes in the form of scenario tree. This paper proposes a scenario generation approach based on the idea of integrating simulation and optimization techniques. In particular, simulation is used to generate outcomes associated with the nodes of the scenario tree which, in turn, provide the input parameters for an optimization model aimed at determining the scenarios’ probabilities matching some prescribed targets. The approach relies on the moment-matching technique originally proposed in [K. Høyland, S.W. Wallace, Generating scenario trees for multistage decision problems, Manag. Sci. 47 (2001) 295-307] and further refined in [K. Høyland, M. Kaut, S.W. Wallace, A heuristic for moment-matching scenario generation, Comput. Optim. Appl. 24 (2003) 169-185]. By taking advantage of the iterative nature of our approach, a parallel implementation has been designed and extensively tested on financial data. Numerical results show the efficiency of the parallel algorithm and the improvement in accuracy and effectiveness.     

A new branch-and-price algorithm for the traveling tournament problem

The traveling tournament problem (ttp) consists of finding a distance-minimal double round-robin tournament where the number of consecutive breaks is bounded. For solving the problem exactly, we propose a new branch-and-price approach. The starting point is a new compact formulation for the ttp. The corresponding extensive formulation resulting from a Dantzig-Wolfe decomposition is identical to one given by Easton, K., Nemhauser, G., Trick, M., 2003. Solving the traveling tournament problem: a combined interger programming and constraint programming approach. In: Burke, E., De Causmaecker, P. (Eds.), Practice and Theory of Automated Timetabling IV, Volume 2740 of Lecture Notes in Computer Science, Springer Verlag Berlin/Heidelberg, pp. 100–109, who suggest to solve the tour-generation subproblem by constraint programming. In contrast to their approach, our method explicitly utilizes the network structure of the compact formulation: First, the column-generation subproblem is a shortest-path problem with additional resource and task-elementarity constraints. We show that this problem can be reformulated as an ordinary shortest-path problem over an expanded network and, thus, be solved much faster. An exact variable elimination procedure then allows the reduction of the expanded networks while still guaranteeing optimality. Second, the compact formulation gives rise to supplemental branching rules, which are needed, since existing rules do not ensure integrality in all cases. Third, non-repeater constraints are added dynamically to the master problem only when violated. The result is a fast exact algorithm, which improves many lower bounds of knowingly hard ttp instances from the literature. For some instances, solutions are proven optimal for the first time.     

Development of an analytical approach for determination of total arsenic and arsenic (III) in airborne particulate matter by slurry sampling and HG-FAAS

Slurry sampling (SS) with hydride generation atomic absorption spectrometry (HG-AAS) was used to analyze 3 particulate matter samples collected in the Bananeira Village, Brazil, in 2005. The relative standard deviation (RSD), used to assess the precision, was lower than 4.8%. The accuracy of this method was confirmed by the analysis of certified atmospheric particulate matter urban dust reference material SRM 1649a. This method (SS/HG-AAS) was used to determine total arsenic and arsenic (III) in three particulate matter samples. In these samples, the total arsenic concentrations varied from 3.8 to 20.0 ng m^− 3, while As (III) concentrations varied from 2.7 to 10.5 ng m^− 3. All samples were also analyzed using acid digestion in digest block with cold finger and detection for HG-AAS. A paired t-test demonstrated no significant difference (95% CL) between the results obtained using these two sample preparation procedures. The limit of quantification, calculated considering the mass of particulate matter collected on every filter, was 0.6 ng m^− 3 for As total and 1.0 ng m^− 3 for As (III).     

分子水平研究不同嵌段结构苯乙烯/丁二烯共聚物的表面结构

利用具有准单分子层灵敏度的和频振动光谱(SFG)、原子力显微镜(AFM)和接触角(CA)测定技术研究链结构和溶剂对苯乙烯(S)/丁二烯(B)嵌段共聚物表面准分子层化学结构形成的影响.结果表明,两嵌段共聚物SB比三嵌段共聚物SBS更有利于聚丁二烯(PB)组分在膜表面富集.利用PB的选择性溶剂环己烷做溶剂时,SB膜表面层完全由纯的PB组分组成,而SBS表面则是聚苯乙烯(PS)与PB二组分共存.利用PS的选择性溶剂甲苯做溶剂时,SB与SBS表面都是PS与PB二组分共存,其中SBS表面PS组分的含量更高.原因是由于溶剂影响嵌段共聚物分子在溶液中的构象从而影响溶剂挥发后聚合物表面结构的形成.     

Comparative studies of photophysical and photochemical properties of solketal substituted platinum(II) and zinc(II) phthalocyanine sets

A complete set of platinum(II) solketal substituted phthalocyanines has been synthesized and characterized. To evaluate their potential as Type II photosensitizers for photodynamic therapy, comparative studies of their photophysical and photochemical properties with analogous zinc(II) series have been achieved: electronic absorption, fluorescence quantum yields, lifetimes, and fluorescence quenching by benzoquinone, as well as singlet oxygen generation and photodegradation. It appears that platinum(II) phthalocyanines are worth being used as Type II photosensitizers, as they exhibit good singlet oxygen generation and appropriate photodegradation.     

Exhaustive generation of k‐critical ‐free graphs

We describe an algorithm for generating all k‐critical ‐free graphs, based on a method of Hoàng et al. (A graph G is k‐critical H‐free if G is H‐free, k‐chromatic, and every H‐free proper subgraph of G is ‐colorable). Using this algorithm, we prove that there are only finitely many 4‐critical ‐free graphs, for both and . We also show that there are only finitely many 4‐critical ‐free graphs. For each of these cases we also give the complete lists of critical graphs and vertex‐critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the 3‐colorability problem in the respective classes. In addition, we prove a number of characterizations for 4‐critical H‐free graphs when H is disconnected. Moreover, we prove that for every t, the class of 4‐critical planar ‐free graphs is finite. We also determine all 52 4‐critical planar P₇‐free graphs. We also prove that every P₁₁‐free graph of girth at least five is 3‐colorable, and show that this is best possible by determining the smallest 4‐chromatic P₁₂‐free graph of girth at least five. Moreover, we show that every P₁₄‐free graph of girth at least six and every P₁₇‐free graph of girth at least seven is 3‐colorable. This strengthens results of Golovach et al.     

To the Problem of Single-Mode Operation in Smith-Purcell FEM

Realization of an effective single-mode oscillator based on the stimulated emission of radiation by relativistic electrons moving along a periodically corrugated waveguide, is theoretically shown to be possible in the regime, when the corrugation period is much larger than the operating wavelength.