On reading P. Harzer's paper on the mathematics in Japan.
On results of Jan Mařík in the theory of derivatives
Results of Jan Marik on the theory of derivatives of real functions are described.
On Ryszard Syski.
On stable polynomials
The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
On Stefan Banach and some of his results.
On the exchanges between Wolfgang Doeblin and Bohuslav Hostinský
We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.
On the expansion of a function in terms of spherical harmonics in arbitrary dimensions.
On the genesis of symbolic dynamics as we know it
We trace the beginning of symbolic dynamics-the study of the shift dynamical system-as it arose from the use of coding to study recurrence and transitivity of geodesics. It is our assertion that neither Hadamard's 1898 paper, nor the Morse-Hedlund papers of 1938 and 1940, which are normally cited as the first instances of symbolic dynamics, truly present the abstract point of view associated with the subject today. Based in part on the evidence of a 1941 letter from Hedlund to Morse, we place the...
On the genesis of the concept of covariant differentiation
The purpose of this paper is to reconsider the genesis of the concept of covariant differentiation, which is interpreted as arising out of two traditions running through 19th-century research work. While the first tradition, of an algebraic nature, was responsible for the “algorithmic” emergence of the concept, the second, analytical in character, was essentially concerned with the import of covariant differentiation as a broader kind of differentiation. The methodological contrast that these two...
On the history of martingales in the study of randomness.
On the history of suspension bridge theory
A linearized formulation of the elastic theory of suspension bridges is confronted with early investigations in the field. For decades, the structure was schematized as a beam (deck or girder) relieved by a one parameter distribution of forces exerted by the cable, disregarding the influence of beam deflection on that distribution as given by the linearized approach. An anonymous note presented the essential conclusions of this theory anticipating results of investigations following the methods...
On the history of unified field theories.
On the logical development of statistical models.
This paper presents a classification of statistical models using a simple and logical framework. Some remarks are made about the historical appearance of each type of model and the practical problems that motivated them. It is argued that the current stages of the statistical methodology for model building have arisen in response to the needs for more sophisticated procedures for building dynamic-explicative types of models. Some potentially important topics for future research are included.
On the mathematical work of Gheorge Tzitzeica.
On the Mathematical Work of Hans Reiter.
On the -th birthday of Semen Samsonovich Kutateladze for .
On the Non-Euclidian Geometry
On the problem of Baer and Kolchin in the Picard-Vessiot theory
We present the history of the development of Picard-Vessiot theory for linear ordinary differential equations. We are especially concerned with the condition of not adding new constants, pointed out by R. Baer. We comment on Kolchin's condition of algebraic closedness of the subfield of constants of the given differential field over which the equation is defined. Some new results concerning existence of a Picard-Vessiot extension for a homogeneous linear ordinary differential equation defined over...
On the remainder term of the de Moivre-Laplace formula.
On the Representation and Multiplication of Basic Alternating Cycle Matrices