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We develop a monotone finite volume element scheme for the diffusion problem on arbitrary polygonal grids inspired by the scheme in the literature ([35]). The main contributions of this paper include three aspects. Firstly, some auxiliary lines or points are introduced for any polygonal element so that it can be partitioned into two or more triangles, and one novel type of its control volume is concomitantly designed. In this paper, we mainly discuss quadrilateral grids. Secondly, some piecewise linear finite element spaces are imported for the trial spaces. Fictitious elements, continuous extensions and the nonlinear two-point flux idea can all be inherited from the triangular case. Therefore, the monotonicity of the scheme is easily proved only by the assembling of some triangles' element stiff matrices. Thirdly, the agreeable adaptability for distorted grids is completely borned. The strict convexity restriction on the grids can also be removed, the concave or severely distorted polygonal (such as quadrilateral) grids are transformed as the convex and general regular triangles. Finally, numerical results confirm its monotonicity, accuracy and stability. [ABSTRACT FROM AUTHOR]

The additive-multiplicative hazards (AMH) regression model specifies an additive and multiplicative form on the hazard function for the counting process associated with a multidimensional covariate process, which contains the Cox proportional hazards model and the additive hazards model as its special cases. In this paper, we study the AMH model with current status data, where the cumulative hazard hazard function is assumed to be nonparametric and is estimated using B-splines with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood estimation is proposed to estimate regression parameters. The proposed estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The B-splines estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and a real data example is presented for illustration. [ABSTRACT FROM AUTHOR]

Abstract: Partial substitution of Al by Mg was studied to reveal the influence of the neighboring element for glass forming ability (GFA) of La62Al14Cu24 alloy. A series of quaternary La62Al14−x Mg x Cu24 (x =2.8, 3.2, 3.5, 4.2, 5.0) alloys were cast by copper mold casting. As a result, the La–Al–Mg–Cu alloys with full glassy rods of 10mm in diameter were achieved, suggesting that partial substitution of Al by Mg dramatically enhances the GFA. The enhancement of GFA can be mainly attributed to the large atomic size ratios among these constituent elements. [ABSTRACT FROM AUTHOR]

Abstract: The preparation and application of overbased nanodetergents with excess alkaline calcium carbonate is a good example of nanotechnology in practice. The phase transformation of calcium carbonate is of extensive concern since CaCO3 serves both as an important industrial filling material and as the most abundant biomineral in nature. Industrially valuable overbased nanodetergents have been prepared based on calcium salts of heavy alkylbenzene sulfonate by a one-step process under ambient pressure, the carbonation reaction has been monitored by the instantaneous temperature changes and total base number (TBN). A number of analytical techniques such as TGA, DLS, SLS, TEM, FTIR, and XRD have been utilized to explore the carbonation reaction process and phase transformation mechanism of calcium carbonate. An enhanced understanding on the phase transformation of calcium carbonate involved in calcium sulfonate nanodetergents has been achieved and it has been unambiguously demonstrated that amorphous calcium carbonate (ACC) transforms into the vaterite polymorph rather than calcite, which would be of crucial importance for the preparation and quality control of lubricant additives and greases. Our results also show that a certain amount of residual Ca(OH)2 prevents the phase transformation from ACC to crystalline polymorphs. Moreover, a vaterite nanodetergent has been prepared for the first time with low viscosity, high base number, and uniform particle size, nevertheless a notable improvement on its thermal stability is required for potential applications. [Copyright &y& Elsevier]