Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior

In this paper, we present a family of optimal, in the sense of Kung–Traub’s conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun’s fourth-order method. We use the Ostrowski’s efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methods.     

Internal structure of coalitions in competitive and altruistic graphical coalitional games

This paper introduces a certain graphical coalitional game where the internal topology of the coalition depends on a prescribed communication graph structure among the agents. The game Value Function is required to satisfy four Axioms of Value. These axioms make it possible to provide a refined study of coalition structures on graphs by defining a formal graphical game and by assigning a Positional Advantage, based on the Shapley value, to each agent in a coalition based on its connectivity properties within the graph. Using the Axioms of Value the graphical coalitional game can be shown to satisfy properties such as convexity, fairness, cohesiveness, and full cooperativeness. Three measures of the contributions of agents to a coalition are introduced: marginal contribution, competitive contribution, and altruistic contribution. The mathematical framework given here is used to establish results regarding the dependence of these three types of contributions on the graph topology, and changes in these contributions due to changes in graph topology. Based on these different contributions, three online sequential decision games are defined on top of the graphical coalitional game, and the stable graphs under each of these sequential decision games are studied. It is shown that the stable graphs under the objective of maximizing the marginal contribution are any connected graph. The stable graphs under the objective of maximizing the competitive contribution are the complete graph. The stable graphs under the objective of maximizing the altruistic contribution are any tree.     

Methods for the determination of cyclopropenoid fatty acids. VII. The dilution-HBr-titration technique as a general method

The stepwise HBr titration method for the cyclopropenoid analysis of cottonseed oils is subject to serious inaccuracies when applied to samples containing higher cyclopropenoid concentrations, particularly if they contain appreciable amounts of alumina-adsorbable materials. A modification of the method is described which eliminates these sources of error. Its validity has been established by the analysis of a wide range of synthetic compositions including compositions containing massive amounts of interfering HBr-reactive substances and other alumina-adsorbable materials. The method with further modification can be used to analyze glycerides with the same high degree of accuracy. Presented at the AOCS Meeting in Houston, April 1965. So. Utiliz. Res. Dev. Div., ARS, USDA.     

Viscoelastic Effects in a Phosphate Glass-Metal Seal

A family of phosphate glasses has been developed with thermal expansion behavior in the elastic range that nearly matches the response of 304 stainless steel. Attempts to make concentric pin-shell seals consistently have yielded fractures between 400° and 300°C during cooling. Elastic stress analyses which neglect glass transitional behavior and utilize constant glassy ("elastic") thermal expansion coefficients predict a residual stress state that is compressive. However, viscoelastic computations which include the effects of structural relaxation during glass transtion show that tensile stresses sufficient to cause failure arise during cooldown of the seal.     

Epoxy fatty acid ester plasticizers. Preparation and properties

Summary The preparation of epoxy fatty acid ester plasticizers has been reviewed. These plasticizers can be prepared by epoxidation reactions, utilizing a preformed peracid or anin-situ technique. A newin-situ epoxidation process, utilizing hydrogen peroxide and acetic acid in the presence of strong acid catalyst, has been described. Excellent conversions to epoxide have been achieved with a series of monounsaturated and polyunsaturated esters. Epoxy fatty acid esters are excellent plasticizers for vinyl resins. Their performance in a series of additional epoxy plasticizers of vegetable and marine origin is described. Novel epoxy plasticizers based upon mixed acetylated mono- and di-glyceride have been prepared and are found to have excellent plasticizer performance. Presented at the 28th fall meeting, American Oil Chemists’ Society, October 1954, Minneapolis, Minn.     

Recent studies of self-condensation and co-condensation of melamine-formaldehyde resins; cure at low temperatures

Self-condensation: recent research on the chemical pathways by which alcoholated melamine-formaldehyde (MF) resins react with themselves and on the product structures is summarized. Model compound studies suggest that bridges are less stable than widely thought unless they are in hexahydro-1,3,5-triazine ring structures. In acyclic structures they are probably less stable than bridges. Co-condensation: studies of how the composition of MF resins influences the rates of reaction with poly(ol) co-reactant show that MF resins that contain very low levels of and/or functionality are quite reactive. Reactivities of a variety of poly(ester) and acrylic coreactants were studied. By combining reactive MF resins with reactive co-reactants one can formulate high solids enamels that cure by co-condensation in 30 min at 50 to 65 °C with 0.5 parts per hundred (phr) of p-toluenesulfonic acid (p-TSA) catalyst. Cure at 25 °C appears feasible with higher catalyst levels.     

Iridoid glycoside metabolism and sequestration byPoladryas minuta (Lepidoptera: Nymphalidae) feeding onPenstemon virgatus (Scrophulariaceae)

A bivoltine checkerspot butterfly,Poladryas minuta, is aPenstemon specialist, not known to utilize any other plant genus for oviposition and larval feeding. At several intermontane plains sites of central Colorado, the butterfly utilizesPenstemon virgatus as its sole host plant. Analysis of the host plant showed it to contain three cinnamyl-type catalpol esters (scutellarioside-II, globularin, globularicisin) and catalpol. The host plant contained an average of 10% dry weight iridoids, but some variation among individual plants and leaves within plants was noted. Field-collected butterflies contained 2.1–8.7% dry weight catalpol, but no other iridoids. Adults from larvae fedP. virgatus in the lab contained 4.2–9.0% dry weight catalpol and excreted large amounts of catalpol in the meconium. No catalpol was found in the larval frass. Larvae did not consume three alternate iridoid-containing host-plant species, and most eventually died rather than feed on the alternate plants. Larvae did consume small amounts of artificial diets containing the alternate species andP. virgatus, but most went into diapause and some died. Survival was good on artificial diet containing 10% dry weight of the iridoid esters fromP. virgatus. Only catalpol was found in pupae and adults, but it was absent from the larval frass. The cinnamic-type acids expected from larval hydrolysis of the esters were not found in larval frass, pupae, or adults. These results are contrasted with those found for another checkerspot,Euphydryas anicia, which consumes a different host-plant species but was present at one of the same sites withPoladryas minuta.Paper 15 in the series Chemistry of the Scrophulariaceae. Paper 14 Boros, C.M., Stermitz, F.R., and Harris, G.H. 1990.J. Nat. Prod. 5372–80.     

IMAGING OF PARTICLE MOTION IN FLUID-SOLID SYSTEMS USING A GAMMA CAMERA

A new approach is presented for the characterization of particle motion in fluid-solid systems based on dynamic imaging with a gamma scintillation camera. A two-dimensional spouted bed of 200-500 micron diameter anion exchange resin beads was used as a test system. One or several beads were radiolabeled with the 140 keV gamma emitting radionuclide 99m-Tc pertechnetate, and particle velocity, panicle path, the spatial distribution of particle residence times, and local bed density were determined from the measured temporal and spatial distributions of particle activity. While care must be exercised in the interpretation of data when the scale for changes in the spatial distribution of activity approaches the limits of camera resolution, the method is quantitative, non-invasive, and well suited to the study of systems having symmetry in one spatial dimension.     

Phase Stability of Fine-Grained (Mg,Y)-PSZ

A fine-grained zirconia, which has been costabilized with yttria and magnesia, has been prepared. Its stability during subeutectoid annealing at 1100^deg;C, and its hydrothermal stability during hydrothermal treatment at 180^deg;C, have been determined and they are compared to those of Y-TZP and Mg-PSZ materials .