Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity

We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of Colombeau's simplified model. This generalizes the notion of G^{\infty }-regularity introduced by M. Oberguggenberger. A key point is that these regularities can be characterized, for compactly supported generalized functions, by a property of their Fourier transform. This opens the door to microanalysis of singularities of generalized functions, with respect to these regularities. We present a complete study of this topic, including properties of the Fourier transform (exchange and regularity theorems) and relationship with classical theory, via suitable results of embeddings.Comment: Submitted to the Journal of Mathematical Analysis and Application

1D-confined crystallization routes for tungsten phosphides

Topological materials confined in one-dimension (1D) can transform computing technologies, such as 1D topological semimetals for nanoscale interconnects and 1D topological superconductors for fault-tolerant quantum computing. As such, understanding crystallization of 1D-confined topological materials is critical. Here, we demonstrate 1D-confined crystallization routes during template-assisted nanowire synthesis where we observe diameter-dependent phase selectivity for topological metal tungsten phosphides. A phase bifurcation occurs to produce tungsten monophosphide and tungsten diphosphide at the cross-over nanowire diameter of ~ 35 nm. Four-dimensional scanning transmission electron microscopy was used to identify the two phases and to map crystallographic orientations of grains at a few nm resolution. The 1D-confined phase selectivity is attributed to the minimization of the total surface energy, which depends on the nanowire diameter and chemical potentials of precursors. Theoretical calculations were carried out to construct the diameter-dependent phase diagram, which agrees with experimental observations. Our find-ings suggest a new crystallization route to stabilize topological materials confined in 1D.Comment: 5 figure

Nguyễn Ái Quốc với công tác giao thông liên lạc truyền bá chủ nghĩa Mác - Lênin vào Việt Nam

255 tr. ; 20 cm

Oral History of Khoan Huu Le

Mr. Khoan Huu Le, a retired Boeing engineer arrived in the United States as a Vietnamese boat refugee. He was born in Long Xuyen, Vietnam in 1940. The interview is focuses on four major events in Mr. Le’s life, beginning with his early education and career path as a teacher in French education system, followed by his experiences during the war and communist occupation, his experiences as a refugee, and finally re-establishment in the United States.Recorded Digitall