The microstructure evolution of Ti–43Al–3Si (at-) alloy solidified in alumina crucible was investigated by directional solidification technology. After directional solidification, the microstructure of the alloy is consisted of γ-TiAl, α2-Ti3Al, ξ-Ti5Si3 phases and Al2O3 particles. There are three morphologies of ξ phases formed in the alloy, namely, long rod-like, cluster-like with eutectic morphology, and needle-like shape. The volume fraction of ξ phases decreases with increasing growth rates. Al2O3 particles broke from the crucible and enter into the melt by the thermal physical erosion. Al2O3 particles enrich in the liquid phase with the moving of solid-liquid interface, and are captured or entrapped by dendrites during solidification. The Al2O3 particles mainly distributed in the interdendritic region, and some particles exist in dendrites.

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The paper deals with the global existence of weak solutions for a weakly dissipative µ-Hunter-Saxton equation by using smooth data approximate to the initial data and Helly's theorem. Розглянуто проблему глобального iснування слабких розв'язкiв слабкодисипативного µ-рiвняння Хантера-Сакстона за допомогою гладких даних, що є наближенням до початкових даних, та теорему Хеллi.