The phenomenon of the Steinhaus Seminar on Applied Mathematics: Topics

This article presents the subject of the Applied Mathematics Seminar, conducted in 1948-1960 by Professor Hugon Steinhaus in Wrocław and is an important supplement to the analysis presented in the work of Szczotka (2018). This topic is illustrated by a more detailed discussion of some of the works on this subject and some of the results obtained by the participants of the Seminar. The results are well-founded in mathematical journals.Niniejszy artykuł przedstawia tematyke Seminarium Matematyki Stosowanej, prowadzonego w latach 1948-1960 przez profesora Hugona Steinhausa we Wrocławiu i jest istotnym uzupełnieniem analizy przestawionej w pracy Szczotki (2018). Tematyke te ilustrujemy dokładniejszym omawianiem niektórych prac i rezultatów z tej tematyki uzyskanych przez uczestników Seminarium

GI/GI/1 queues with infinite means of service time and interarrival time

The main results deal with the GI/GI/1 queues with infinite means of the service times and interarrival times. Theorem 3.1 gives an asymptotic, in a heavy traffic situation, of the equence of waiting times of the consecutive customers. Theorem 4.1 gives an asymptotic of stationary waiting times in a heavy traffic situation. In a special case, the asymptotic stationary waiting times have an exponential distribution Corollary 4.1.The main results deal with the GI/GI/1 queues with infinite means of the service times and interarrival times. Theorem 3.1 gives an asymptotic, in a heavy traffic situation, of the equence of waiting times of the consecutive customers. Theorem 4.1 gives an asymptotic of stationary waiting times in a heavy traffic situation. In a special case, the asymptotic stationary waiting times have an exponential distribution Corollary 4.1

The case of the Steinhaus seminar on applied mathematics. Outline of the concept

This article is devoted to the Seminar on Applied Mathematics, conducted in 1948-1960 by Professor Hugo Steinhaus in Wroclaw. It is based on the protocols of this Seminar so far not discussed anywhere. Many facts related to Professor Hugo Steinhaus can be found easily in the literature, also in the diary of the professor \emph{Mathematician for all seasons--recollections and notes.} (2016). Steinhaus was an outstanding mathematician. He wrote his doctoral thesis under the direction of David Hilbert at the University of Göttingen. Already at that time, he was interested in applications of mathematics. He also used mathematics as the goal of life in various aspects of economic and social life. During the Wrocław period, when he was running the Applied Mathematics Seminar for people with different professions and interests, he gave the beginning of the Wrocław School of Applied Mathematics. All the problems considered in this Seminar are briefly signaled in the protocols that are presented in the article along with the supplement based on the publication.Niniejszy artykuł jest pierwszą częścią większego zamierzenia poświęconego Seminarium Matematyki Stosowanej, prowadzonego w latach 1948-1960 przez profesora Hugona Steinhausa we Wrocławiu. Jest oparty na protokołach z tego Seminarium, nigdzie dotąd nie omawianych. Próbujemy tutaj zastanowić się nad genezą tego Seminarium, jego celem, a także przedstawiamy atmosferę na nim panującą i jego formułę. Druga część naszego zamierzenia ,,Tematyka steinhausowskiego Seminarium Matematyki Stosowanej. Tematyka. (2019) będzie poświęcona omówieniu tematyki i problemów rozważanych na tym Seminarium oraz niektórych rezultatów uczestników Seminarium, publikowanych w czasopismach matematycznych