Microstructural evolution of decagonal quasicrystal in the undercooled Al72Ni12Co16 alloy melts

The microstructure evolution of decagonal quasicrystals in Al₇₂Ni₁₂Co₁₆ alloy was investigated by the electromagnetic melting and cyclic superheating method. Single-phase decagonal quasicrystals have been obtained when the undercoolings were larger than 60 K. The decagonal quasicrystals formed at various undercoolings show different microstructural morphologies. Furthermore, grain refinement was found near the undercooling of 120 K. Based on current thermodynamic and dendrite growth theories, a dimensionless superheating parameter was adopted to explain the effect of processing conditions on the microstructure of Al₇₂Ni₁₂Co₁₆ alloy. The result indicate that the fine equiaxied microstructure of decagonal quasicrystal (D-phase) formed near on undercooling of 120 K originates from the break-up of dendrites.     

On the Zero-Energy-Limit Solution for the Modified Gross–Pitaevskii Equation

The modified Gross–Pitaevskii equation was derived and solved to obtain the 1D solution in the zero-energy limit. This stationary solution could account for the dominated contributions due to the kinetic effect as well as the chemical potential in inhomogeneous Bose gases.     

Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

The characteristic exponent α of a Lévy-stable law S _α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.      

Surface and interfacial properties of PVDF/acrylic copolymer blends before and after UV exposure

Morphological and chemical properties of both the surface and interface of poly(vinylidene fluoride)/poly(methyl methacrylate)-co-poly(ethyl acrylate) (PVDF/PMMA-co-PEA) blend films have been investigated before and after the samples were exposed to ultraviolet (UV) irradiation using a xenon arc lamp at 50 °C and 9% relative humidity (RH) for 7 months. Surface and interfacial morphologies were studied by atomic force microscopy (AFM). Chemical composition information was obtained by confocal Raman microscopy, attenuated total reflection-FTIR spectroscopy (ATR-FTIR), X-ray photoelectron spectroscopy (XPS), and contact angle measurements. Results show an enrichment of the PVDF material at the air surface, while the acrylic copolymer enriches the interface. Blends having greater than 50% mass fraction of PVDF show little change in the surface morphology after UV exposure for 7 months. However, for a lower PVDF content, blends exhibit significant degradation of PMMA-co-PEA copolymer and a much rougher surface after UV exposure. Microstructural changes in the PVDF spherulites are also observed after UV degradation. It is found that the surface and interfacial morphologies are correlated with the chemical properties.     

Products of residue currents of Cauchy–Fantappiè–Leray type

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy–Fantappiè–Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete intersection, the product of the residue currents of a tuple of sections coincides with the residue current of the direct sum of the sections.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev ratio.