Counterions Control Whether Self‐Assembly Leads to Formation of Stable and Well‐Defined Unilamellar Nanotubes or Nanoribbons and Nanorods

Self‐assembly of the amphiphilic π‐conjugated carbenium ion ATOTA‐1⁺ in aqueous solution selectively leads to discrete and highly stable nanotubes or nanoribbons and nanorods, depending on the nature of the counterion (Cl^? vs. PF₆^?, respectively). The nanotubes formed by the Cl^? salt illustrate an exceptional example of a structural well‐defined (29±2 nm in outer diameter) unilamellar tubular morphology featuring π‐conjugated functionality and high stability and flexibility, in aqueous solution.     

Toward three-dimensional nanoengineering of heterogeneous catalysts

Cobalt-based Fischer-Tropsch systems are widely used to convert synthesis gas to clean hydrocarbon fuel. However, surprisingly little is known about the morphology of the catalysts on the nanoscale. Here we show that scanning transmission electron tomography reveals their true 3-D morphology and provides direct evidence that the support controls the final morphology of the catalyst. Such direct local three-dimensional measurements provide unprecedented insight into catalysis, and can henceforth transform our understanding of these complex materials.     

Separable states and positive maps

Using the natural duality between linear functionals on tensor products of C^∗-algebras with the trace class operators on a Hilbert space H and linear maps of the C^∗-algebra into B(H), we study the relationship between separability, entanglement and the Peres condition of states and positivity properties of the linear maps.     

Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property

In this paper we discuss the problem of finding optimal prefix-free codes for unequal letter costs, a variation of the classical Huffman coding problem. Our problem consists of finding a minimal cost prefix-free code in which the encoding alphabet consists of unequal cost (length) letters, with lengths α and β. The most efficient algorithm known previously requires O(n^{2 + max(α, β)}) time to construct such a minimal-cost set of n codewords, provided α and β are integers. In this paper we provide an O(n^max(α, β)) time algorithm. Our improvement comes from the use of a more sophisticated modeling of the problem, combined with the observation that the problem possesses a “Monge property” and that the SMAWK algorithm on monotone matrices can therefore be applied.     

Hydrodynamic impact of particle shape in slurry packed liquid chromatography columns

We report on a series of flow velocity and efficiency profiles, which were measured across the cross section of preparative chromatographic columns packed with different stationary phase materials using computed tomography. It is shown that this non-invasive technique is very useful for visualization of the inner part of a packed column and measurement of the spatial resolved column packing properties. For evaluation of the influence of the particle shape on the velocity distribution and column performance, irregular and spherical reversed phases were studied in detail. The results showed a decreasing velocity towards the column wall most certainly due to a lower permeability. This effect was much less pronounced in the case of spherical particles, indicating a more homogenous packing structure. The influence of the column packing pressure, as a possible measure for improvement of the packing homogeneity was also studied. It was shown that under the same packing conditions spherical particles always lead to a more homogeneous packing. The overall results of this work contribute to the origin of the fact that spherical material is superior to irregular one from the hydrodynamic point of view.     

(邻接)树图的同构及平面性

树图是非常有用的一类图.本文刻画了(邻接)树图分别为Pn,Cn,Kn的图类并且讨论了(邻接)树图的平面性.     

Thermooxidative degradation of polyethylene. I and II. Structural changes occurring in low-density polyethylene,high-density polyethylene,and tetratetracontane heated in air

Samples of low-density polyethylene (LDPE), high-density polyethylene (HDPE), and tetratetracontane (n-C₄₄H₉₀) free from additives were heated in air at temperatures between 120 and 180°C. As a comparison, “as received” HDPE containing unspecified additives has also been included. The structural changes have been studied with gel chromatography, viscometry, infrared spectroscopy, differential scanning calorimetry, and gravimetric measurements. LDPE, HDPE, and n-C₄₄H₉₀ follow the same course of thermooxidative degradation when they are free from additives and present in the molten state. Both molecular-diminishing and enlargement reactions occur. At temperatures below 150°C molecular enlargement is not observed until after rather long exposure times, whereas at higher temperatures enlargement occurs immediately. The difference is because “peroxide curing” becomes increasingly important above 150°C, whereas ester formation is operating at all temperature levels. Degradation below T_m is restricted to the amorphous phase that results in a different degradation pattern. In accelerated testing work extrapolations of the Arrhenius type in the prediction of structural change are thus not justified, even within the actual narrow temperature range. Neither are changes in commonly used standards like carbonyl content justified as a measure of the changes; for example, in mechanical properties. The stabilizer in the unpurified HDPE not only influences the induction period but also the course of the thermooxidative degradation.     

Presolving in linear programming

Most modern linear programming solvers analyze the LP problem before submitting it to optimization. Some examples are the solvers WHIZARD (Tomlin and Welch, 1983), OB1 (Lustig et al., 1994), OSL (Forrest and Tomlin, 1992), Sciconic (1990) and CPLEX (Bixby, 1994). The purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible.In this paper we present a comprehensive survey of presolve methods. Moreover, we discuss the restoration procedure in detail, i.e., the procedure that undoes the presolve.Computational results on the NETLIB problems (Gay, 1985) are reported to illustrate the efficiency of the presolve methods.This author was supported by a Danish SNF Research studentship.