This issue is dedicated to Professor Wei Lin on the occasion of his 80th birthday, and to Professor Robert Gilbert for the 40th anniversary of his first academic visit to China.
Professor Wei Lin is a renowned mathematician and our respectable teacher.
Professor Lin was born on 7 September 1934, in Guangdong province, China. He left his hometown of Shantou in September 1952, was admitted to Zhongshan University (Sun Yat-sen University) initially as a student, and ultimately became a teacher there. He became a full professor in 1983. He served as the Chairman of the Department from 1984 to 1992 and played a major role in many other activities of the mathematical community. He was the Chairman of the Mathematical Society of Guangdong (1990–1995) and a member of the board of directors of ISAAC (the International Society for Analysis, its Applications and Computation, 1997–2002). The reader may refer to [Applicable Analysis, 85(2006), 1003–1009] for a more complete list of his editorship, society membership, and the visits he paid to fellow institutions over the world.
Professor Lin’s research work started in the early 1960s with a systematic study of the systems of partial differential equations, with a complex analysis background. This was a joint work with Hua Loo Keng and Wu Ciqian. Together, they completed the classification of the system with two variables and two unknown functions, underwent theoretical analysis of the canonic systems, and found applications in mathematical physics, such as elasticity. Results in this respect were put into a book (Science Press, China, 1979) in Chinese. An enriched English version appeared later as (Research Notes in Mathematics, Vol. 128, Pitman Publishing Inc).
In 1970, Professor Lin turned to a brand new, yet still mathematical related field, namely automatic control theory and applications. Theoretically, Lin and his colleagues worked on the distributed control systems, bearing an impact of the partial differential equations. On the application side, they designed and eventually built a digitally controlled steel-cutting machine for Wen Chong Shipyard in Guangzhou.
In 1982, Professor Lin visited Professor Robert Gilbert at the University of Delaware. During this one-year visit, Lin’s warm and friendly personality helped to build the bridge for long-lasting international collaborations among Gilbert, Lin, Begehr, and other mathematicians in analysis, applications, and computation. Throughout most of the 1980s, he worked on function theoretic methods in partial differential equations, initially jointly with Professor R. Gilbert and later with junior collaborators. He started his frequent visits to oversea universities. A topic of interest in the period was the inverse scattering method in ocean acoustics.
Since the 1990s, his focus has been wavelet theory. The topics of his papers have range from theoretic analysis, such as the non-uniform sampling problems in the shift-invariant spaces, to numerical calculation, such as the Galerkin method and the subdivision algorithm, with applications in elasticity.
Among his 20 Ph.D. students and roughly 30 Master’s students, we have benefited much from Professor Lin’s inspirational advising. As graduate students, and then as colleagues, we have had the invaluable opportunity to work with and learn from him. Professor Lin has been very strict with his habits, from academics and work to diet and exercise. He is, as he has always been, an exercise lover. We are delighted to know that he still swims in the summer every day, followed by Tai Chi each afternoon with his wife, Jinyi Wu, and a crowd of students.
It is worth mentioning that 2014 is also the 40th year of Professor Robert Gilbert’s first visit to China in 1984. Through Wei Lin’s support, Gilbert gained access into China. It was Gilbert who has encouraged the study of function theoretical methods in PDE and advertised Clifford analysis in China. Nowadays, this subject is well studied in many universities in China. As a consequence of his visit, Gilbert’s first monograph Function Theoretic Methods in Partial Differential Equations was translated into Chinese. More than 7500 copies have been sold. Also thanks to Wei Lin, Gilbert has received many Ph.D. students from China, Yongzhi Steve Xu being one of them. Xu was a Master’s student of Wei Lin’s, working on generalized bi-analytic functions. He came to the United States to finish his Ph.D. studies with Gilbert, and has worked closely with him since then. Xu remains grateful for Gilbert’s guidance and advice, about mathematics and beyond.
This issue includes 17 original research papers from colleagues, friends, and students of Professor Lin and Professor Gilbert on function theoretical methods in partial differential equations, wavelets, applied partial differential equations, and related problems.
Together with all contributors, we wish Professor Lin and Professor Gilbert health and happiness for years to come.
10 September 2014
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