How to find Steiner minimal trees in euclideand-space

This paper has two purposes. The first is to present a new way to find a Steiner minimum tree (SMT) connectingN sites ind-space,d >- 2. We present (in Appendix 1) a computer code for this purpose. This is the only procedure known to the author for finding Steiner minimal trees ind-space ford > 2, and also the first one which fits naturally into the framework of backtracking and branch-and-bound. Finding SMTs of up toN = 12 general sites ind-space (for anyd) now appears feasible.We tabulate Steiner minimal trees for many point sets, including the vertices of most of the regular and Archimedeand-polytopes with <- 16 vertices. As a consequence of these tables, the Gilbert-Pollak conjecture is shown to be false in dimensions 3–9. (The conjecture remains open in other dimensions; it is probably false in all dimensionsd withd 3, but it is probably true whend = 2.)The second purpose is to present some new theoretical results regarding the asymptotic computational complexity of finding SMTs to precision .We show that in two-dimensions, Steiner minimum trees may be found exactly in exponential time O(C ^N ) on a real RAM. (All previous provable time bounds were superexponential.) If the tree is only wanted to precision , then there is an (N/)^O(N)-time algorithm, which is subexponential if 1/ grows only polynomially withN. Also, therectilinear Steiner minimal tree ofN points in the plane may be found inN ^O(N) time.J. S. Provan devised an O(N ⁶/⁴)-time algorithm for finding the SMT of a convexN-point set in the plane. (Also the rectilinear SMT of such a set may be found in O(N ⁶) time.) One therefore suspects that this problem may be solved exactly in polynomial time. We show that this suspicion is in fact true—if a certain conjecture about the size of Steiner sensitivity diagrams is correct.All of these algorithms are for a real RAM model of computation allowing infinite precision arithmetic. They make no probabilistic or other assumptions about the input; the time bounds are valid in the worst case; and all our algorithms may be implemented with a polynomial amount of space. Only algorithms yielding theexact optimum SMT, or trees with lengths (1 + ) × optimum, where is arbitrarily small, are considered here.     

On the study of creep feed grinding of alumina

Several issues involved in creep feed grinding of alumina with diamond wheels were studied. Influences of variables on responses were investigated. Off-line optimization was performed by formulating the grinding process as a multi-objective nonlinear mixed integer problem. The dominant mechanism of material removal was determined. The grinding process was simulated to obtain the number of active cutting edges and the grinding parameters such as cutting length, maximum undeformed chip thickness, etc. Unit load distribution was characterized and then used to estimate the percentage of cutting edges that fracture or plastically cut the material and to derive the probability distribution function for substance cracks. Fractal concept was applied to characterize wheel profiles. Findings from these studies are reported in this paper. These studies are definitely not complete, but surely shed some light on the creep feed grinding process of ceramic materials.     

Aging Behavior of xPb(Fe2/3W1/3)O3· (1 –x)Pb(Fe1/2Nb1/2)O3 Ceramic

The aging behavior of a series of lead perovskite dielectrics with the compositions x Pb(Fe_2/3W_1/3)O₃·(1 – x )Pb(Fe_1/2-Nb_1/2)O₃, where 0 ≤ x ≤ 1, and the effect of dopants were studied. Below the Curie temperature ( T _c), the capacitance and the dissipation factor (tan δ) decrease approximately linearly with logarithmic time. The aging rate depends on the temperature difference, Δ T , between the aging temperature and T _c, and on the dopant concentration, but is independent of the measurement frequency between 1 and 1000 kHz. The maximum aging rate is about 3% per decade of time for capacitance and 5% per decade for tan δ at 1 mol% dopant concentration, and increases to 6.3% for capacitance and 8.5% for tan δ at 0.7 mol% dopant concentration. These results are consistent with an aging mechanism caused by changing ferroelectric domain structure with time, as proposed for BaTiO₃.     

Large-scale in vivo synthesis of the carbohydrate moieties of gangliosides GM1 and GM2 by metabolically engineered Escherichia coli

Two metabolically engineered Escherichia coli strains have been constructed to produce the carbohydrate moieties of gangliosides GM2 (GalNAcbeta-4(NeuAcalpha-3)Galbeta-4Glc; Gal = galactose, Glc = glucose, Ac = acetyl) and GM1 (Galbeta-3GalNAcbeta-4(NeuAcalpha-3)Galbeta-4Glc. The GM2 oligosaccharide-producing strain TA02 was devoid of both beta-galactosidase and sialic acid aldolase activities and overexpressed the genes for CMP-NeuAc synthase (CMP = cytidine monophosphate), alpha-2,3-sialyltransferase, UDP-GlcNAc (UDP = uridine diphosphate) C4 epimerase, and beta-1,4-GalNAc transferase. When this strain was cultivated on glycerol, exogenously added lactose and sialic acid were shown to be actively internalized into the cytoplasm and converted into GM2 oligosaccharide. The in vivo synthesis of GM1 oligosaccharide was achieved by taking a similar approach but using strain TA05, which additionally overexpressed the gene for beta-1,3-galactosyltransferase. In high-cell-density cultures, the production yields for the GM2 and GM1 oligosaccharides were 1.25 g L(-1) and 0.89 g L(-1), respectively.     

Polyacrylic acid macromolecule—complexed zinc phosphate crystal conversion coatings

When water-soluble polyacrylic acid (PAA) macromolecules are introduced into zinc phosphating liquids, significant improvements in the yield of conventional zinc phosphate conversion films deposited on carbon steel surfaces are obtained. The improvements include controllability of crystal dimensions, degree of crystallinity, and coating weight. The conversion layer formed is a composite microstructure consisting of a bulk PAA polymer and complexed PAA continuously overlaying a uniform array of fine dense zinc phosphate crystals. Interfacial studies of the composite layer using infrared spectroscopy, energy-dispersive X-ray spectrometry associated with scanning electron microscopy, and X-ray photoelectron spectroscopy indicated that the functional carboxylic acid groups in the PAA molecules were strongly chemisorbed by the Zn atoms at the outermost surface sites of the crystal layers. The intermolecular bridging action of the surface Zn atoms which connect the PAA and the zinc phosphate crystal layers results in good adhesion at the PAA–crystal interfaces. In addition, the plasticized complex formation plays an essential role in increasing the stiffness and the ductility of the normally conventional crystal films. The flexibility of the complex coating surface and the thickness and surface roughness of the thin PAA overlayer all affect the adhesive force at the interface between the organic polymer topcoat and the complexed coating.     

Stress–Strain Behavior of Nicalon-Fiber-Reinforced Calcium Aluminosilicate Composites under Tensile Fatigue Conditions

The unusual stress–strain hysteresis loop shape exhibited by ceramic-matrix composites under cyclic loading has previously been explained as a result of either strain rate dependence of the frictional shear stress or crack closure. This investigation has determined that the response is due to neither mechanism. Instead, it is proposed that a variation of interfacial shear strength occurs during each cycle. A static coefficient of friction dominates immediately after loading or unloading. A much lower dynamic coefficient of friction operates once fiber sliding begins. This dynamic coefficient appears to be very dependent on surface roughness.     

Adhesion aspects of levulinic-acid-modified furan polymers to crystalline zinc phosphate metal surfaces

The nature of the interfacial interactions between functional levulinic-acid-modified furan resin coatings and crystalline zinc phosphate hydrate films deposited on carbon steel surfaces has been systematically investigated. The typical surface topography of the highly crystallized zinc phosphate films was found to be characterized by the presence of a dendritic microstructure array of interlocking triclinic crystals. This structure acts significantly to develop mechanical interlocking bonds with the functional blend polymer which penetrates into the open surface structure of the films. Both the thickness of deposition film and the polar H₂O molecules of hydrate at the outermost film surface sites play essential roles in wetting by the functional liquid resin. When the polarized furan polymers spread on the oxide film surfaces, the carboxylate groups derived from the levulinic ester and acid molecules react to form strong hydrogen bonds with the crystallized H₂O molecules on the hopeite film. This formation of hydrogen bonding was shown to be a major factor affecting the chemical intermolecular attractions. A formulation consisting of 95 parts furan to 5 parts levulinic acid was found to yield the optimum protective coating. More than 5 parts levulinic acid resulted in the transformation of the characteristics of the polymer film from hydrophobic to hydrophilic.     

Mobil Zeolite Catalysts for Monomers

It has been about 20 years since Plank, Rosinski, and Hawthorne reported their spectacular results with metal-modified zeolite cracking catalysts for more efficient production of gasoline [1]. This discovery has saved an estimated 200 million barrels of crude oil each year in the United States alone [2]. In 1972, a patent by Argauer and Landolt described the preparation of a member of a generation of new synthetic zeolites, called ZSM- 5. It was unique because of its high silica/alumina ratio and greatly reduced coking rates for reactions with hydrocarbons by comparison with known low silica zeolites [3]. This material was an early member of a series of over 50 synthetic zeolitic substances prepared in Mobil laboratories.     

Use of15N for fertilizer N recovery and N mineralization studies in semi-arid Kenya

Maize and beans were grown on a ferralsol at Kiboko, Kenya, with up to 120 kg N ha^–1. Within the 10 kg N ha^–1 plots,¹⁵N labelled fertilizer was applied in microplots. There was no significant response in yield to fertilizer N and labelled N recovery was low, being 7.5% or less in one season and 17.7% or less in the second season. Samples of Kiboko soil at four different water contents were incubated and the rate of gross N mineralization over 7 days was calculated, utilizing¹⁵N labelling of the mineral N. Gross N mineralization increased greatly with soil moisture and a fitted relationship between gross N mineralization rate and soil water content was obtained. Using measurements of soil water content at the field site, daily values of the soil N supply by gross mineralization were calculated. On average, modelled gross soil N mineralized could supply much (> 69%) of the N removed from the plots. It is suggested that the lack of response to fertilizer N may be explained by the coincidence of a high rate of N mineralization, and increased crop demand, caused by the onset of rain.