On the complete set packing and set partitioning polytopes: Properties and rank 1 facets

This paper studies two polytopes: the complete set packing and set partitioning polytopes, which are both associated with a binary $n$-row matrix having all possible columns. Cuts of rank 1 for the latter polytope play a central role in recent exact algorithms for many combinatorial problems, such as vehicle routing. We show the precise relation between the two polytopes studied, characterize the multipliers that induce rank 1 clique facets and give several families of multipliers that yield other facets.     

Existence of incomplete canonical Kirkman packing designs

For $u,v$ positive integers with $u\equiv v\equiv 4\left(mod6\right)$, let ICKPD$(u,v)$ denote a canonical Kirkman packing of order $u$ missing one of order $v$. In this paper, it is shown that the necessary condition for existence of an ICKPD$(u,v)$, namely $u\ge 3v+4$, is sufficient with a definite exception $(u,v)=(16,4)$, and except possibly when $v>76$, $v\equiv 4\left(mod12\right)$ and $u\in \{3v+4,3v+10\}$.     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.     

Optimal packings of two to four equal circles on any flat torus

We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory.     

Separation of Photosynthetic Pigments by High-performance Liquid Chromatography: Comparison of Column Performance,Mobile Phase,and Temperature

High-performance liquid chromatography (HPLC) has been commonly used as method of separating and identifying photosynthetic pigments such as chlorophylls and carotenoids because of such advantages as speed, high resolution and sensitivity. In this technique, high separation relies largely on the type of column material. This study compared the efficiency of five reverse-phase columns, C8, C18, C18 monolithic, π-NAP, and cholester, for separation of photosynthetic pigments at several fixed conditions of mobile phase and temperature. This investigation also analysed the parameters of Δt_R and t_R ratio for selected pigments and resolution for structural isomers, such as α- and β-carotene. Among above columns tested, cholester column is suitable for separation of pigments not only for a broad range of polarity, but also for hydrophobic pigments in a simple mobile phase. This finding can help in the selection of column and HPLC parameters in separating photosynthetic pigments.     

Planarity of benzoylthiocarbazate tuberculostatics. IV. Polymorphs of N′‐(1,3‐dithiolan‐2‐ylidene)‐4‐nitrobenzohydrazide

The search for new tuberculostatics is important considering the occurrence of drug‐resistant strains of Mycobacterium tuberculosis . Three polymorphs of N ′‐(1,3‐dithiolan‐2‐ylidene)‐4‐nitrobenzohydrazide (a potentially tuberculostatic agent), C₁₀H₉N₃O₃S₂, denoted (I1), (I2) and (I3), and the monohydrate of this compound, C₁₀H₉N₃O₃S₂·H₂O, (I4), have been characterized by single‐crystal X‐ray diffraction. The conformations of the molecules in all these structures are very similar. Structures (I1), (I2) and (I3) provide an example of packing polymorphism resulting from different intermolecular interactions.     

New upper bounds for online strip packing

In this paper, we consider the online strip packing problem, in which a list of online rectangles has to be packed without overlap or rotation into one or more strips of width 1 and infinite height so as to minimize the required height of the packing. By analyzing a two-phase shelf algorithm, we derive a new upper bound 6.4786 on the competitive ratio for online one strip packing. This result improves the best known upper bound of 6.6623. We also extend this algorithm to online multiple strips packing and present some numeric upper bounds on their competitive ratios which are better than the previous bounds.     

Constraints on the fundamental topological parameters of spatial tessellations

Tessellations of that use convex polyhedral cells to fill the space can be extremely complicated, especially if they are not “facet‐to‐facet”, that is, if the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. In a recent paper 15 , we have developed a theory which covers these complicated cases, at least with respect to their combinatorial topology. The theory required seven parameters, three of which suffice for facet‐to‐facet cases; the remaining four parameters are needed for the awkward adjacency concepts that arise in the general case. This current paper establishes constraints that apply to these seven parameters and so defines a permissible region within their seven‐dimensional space, a region which we discover is not bounded. Our constraints in the relatively simple facet‐to‐facet case are also new.     

浓悬浮体的屈服应力和最大填充率

对剪切稀化的浓悬浮体，假设在剪切状态下结构参数变化的速率服从一级动力学关系，在此基础上导出浓悬浮体最大填充率与剪应力、屈服应力与填充率之间关系的数学模型．用硅粉－甘油水溶液及可可粉－可可脂两种悬浮体的实验确认了模型对工业微米级颗粒悬浮体的适用性