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The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equations for linear isotropic bodies - in a modern…
The article provides an historical survey of the early contributions on the applications of fractional calculus in linear viscoelasticty. The period under examination covers four decades, since 1930's up to 1970's and authors are from both…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…
In this study, we continue to present profiles of some distinguished graduates in mathematics of the Jagiellonian University from the years 1918-1939. We discuss their professional paths and scholarly achievements, instances of scientific…
Technology has helped to innovate in the teaching-learning process. Today's students are more demanding actors when it comes to the environment, they have at their disposal to learn, experiment and develop critical thinking. The area of…
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…
In this survey paper we analyze the development of Fractional Calculus in Russia at the end of XIX century, in particular, the results by A.V.Letnikov, N.Ya.Sonine and P.A.Nekrasov. Some of the discussed results are either unknown or…
In this contribution we briefly review some of the current issues and promises for the future by asteroseismology. We are entering a new phase in this field driven by the wealth of data that has been collected and data that will soon be…
Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…
Development of optometry in western countries was studied on a viewpoint of the history of science. It was revealed that optometry had been formed on the basis of optics, a branch of physics, to which biomedical study was added. Optometry…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
The paper suggests a short survey of integration algorithms which evolved since 1982. These theorems and algorithms form discrete versions of the calculus theorems.
Over the past two decades, the field of high-dimensional statistics has experienced substantial progress, driven largely by technological advances that have dramatically reduced the cost and effort for data collection and storage across a…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…
In this study, we present profiles of some distinguished graduates in mathematics of the Jagiellonian University from the years 1918-1939. We discuss their professional paths and scholarly achievements, instances of scientific…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…