Handful Of Solutions Research Articles

Quadratic closed G2$\mathrm{G}_2$‐structures

This article studies closed G 2 $\mathrm{G}_2$ -structures satisfying the quadratic condition, a second-order PDE system introduced by Bryant involving a parameter λ $\lambda$ . For certain special values of λ $\lambda$ the quadratic condition is equivalent to the Einstein condition for the metric induced by the closed G 2 $\mathrm{G}_2$ -structure (for λ = 1 / 2 $\lambda = 1/2$ ), the extremally Ricci-pinched (ERP) condition (for λ = 1 / 6 $\lambda =1/6$ ), and the condition that the closed G 2 $\mathrm{G}_2$ -structure be an eigenform for the Laplace operator (for λ = 0 $\lambda = 0$ ). Prior to the work in this article, solutions to the quadratic system were known only for λ = 1 / 6 $\lambda = 1/6$ , − 1 / 8 $-1/8$ , and 2 / 5 $2/5$ , and for these values only a handful of solutions were known. In this article, we produce infinitely many new examples of ERP G 2 $\mathrm{G}_2$ -structures, including the first example of a complete inhomogeneous ERP G 2 $\mathrm{G}_2$ -structure and a new example of a compact ERP G 2 $\mathrm{G}_2$ -structure. We also give a classification of homogeneous ERP G 2 $\mathrm{G}_2$ -structures. We provide the first examples of quadratic closed G 2 $\mathrm{G}_2$ -structures for λ = − 1 $\lambda = -1$ , 1 / 3 $1/3$ and 3 / 4 $3/4$ , as well as infinitely many new examples for λ = − 1 / 8 $\lambda = -1/8$ and 2 / 5 $2/5$ . Our constructions involve the notion of special torsion for closed G 2 $\mathrm{G}_2$ -structures, a new concept that is likely to have wider applicability. In the final section of the article, we provide two large families of inhomogeneous complete steady gradient solitons for the Laplacian flow, the first known such examples.

FIDDLE: powder pattern indexing and structure solution hand in hand

<i>FIDDLE</i>: powder pattern indexing and structure solution hand in hand

A Dynamic Scheduling Algorithm for Divisible Loads in Grid Environments

Divisible loads are those workloads that can be partitioned by a scheduler into any arbitrary chunks. The problem of scheduling divisible loads has been defined for a long time, however, a handful of solutions have been proposed. Furthermore, almost all proposed approaches attempt to perform scheduling in dedicated environments such as LANs, whereas scheduling in non-dedicated environments such as Grids remains an open problem. In Grids, the incessant variation of a worker's computing power is a chief difficulty of splitting and distributing workloads to Grid workers efficiently. In this paper, we first introduce a computation model that explains the impact of local (internal) tasks and Grid (external) tasks that arrive at a given worker. This model helps estimate the available computing power of a worker under the fluctuation of the number of local and Grid applications. Based on this model, we propose the CPU power prediction strategy. Additionally, we build a new dynamic scheduling algorithm by incorporating the prediction strategy into a static scheduling algorithm. Lastly we demonstrate that the proposed dynamic algorithm is superior to the existing dynamic and static algorithms by a comprehensive set of simulations.

Electrocatalytic Reduction of HNO2 by a Silicomolybdate Polyanion: A Differential Electrochemical Mass Spectrometry Study

AbstractElectrocatalytic activities towards the reduction of important analytes such as nitrite, bromate, chlorate and hydrogen peroxide have been demonstrated for numerous heteropolyanions (HPAs). In this paper, the behavior of a Keggin‐type HPA, SiMo12O, on the one hand in solution and on the other hand immobilized in a conducting polymer, polypyrrole (PPy), in the presence of nitrous acid (HNO2) is examined. It is shown that the PPy films codoped with SiMo12O and HSO ions could be used as sensitive part of an amperometric sensor even if the response is limited by HNO2 diffusion into the PPy film. Differential electrochemical mass spectrometry (DEMS) was used to determine the gas formed during nitrous acid reduction by H2SiMo12O. Under an applied cathodic potential, when both HNO2 and SiMo12O are present in the medium, NO gas is produced whereas, when SiMo12O ions are immobilized in a PPy film, N2O evolves and the NO concentration, notably due to the disproportionation of HNO2, decreases.