The Alexander Phenomenon

A famous result of H. Alexander asserts that any proper holomorphic self-map  of the unit (Euclidean) ball in higher dimensions is an automorphism. Alexander's result has been extended to various classes of domains including strictly pseudoconvex domains (by Pinchuk) and weakly pseudoconvex domains with real-analytic boundary (by Bedford and Bell). It is conjectured that any proper holomorphic self-map of a smoothly bounded pseudoconvex domain in higher dimensions must be an automorphism. In this talk, I shall first briefly survey some of the prominent Alexander-type results.

Novel Approach for Drilling Exotic Engineering Materials

Inconel 718 is a Ni-Cr alloy which is used as drill collars in oil and gas industry. These drill collars for deep-water oil exploration have several deep holes which serve as conduits for power supply, data communication and remote monitoring & control with sensors and embedded electronics. Gundrilling is one of the machining processes which is widely employed for small deep holes due to its successful applications on several materials like Al alloys, cast irons and alloy steels.

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