Related papers: On the development of differential geometry in Est…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries,…
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.
Physics research complements traditional approaches, such as mathematical (stochastic) finance and econometrics in quantitative economics and finance. In the early years of this millennium, we embarked on an interdisciplinary research…
We trace the evolution of the theory of stochastic partial differential equations from the foundation to its development, until the recent solution of long-standing problems on well-posedness of the KPZ equation and the stochastic…
This Master's Thesis analyzes thoroughly the topic of the Mathematics Education in Russia and Mathematical Circles. It deals with the historical context of the Mathematics Education in Russia in the XVIIIth, XIXth and XXth centuries; the…
We show that a knowledge of diagonal partons at a low scale is sufficient to determine the off-diagonal (or skewed) distributions at a higher scale, to a good degree of accuracy. We quantify this observation by presenting results for the…
This paper examines the history of the development of dimensional analysis, from Euclidean geometry to hyperspace. This is largely a secondary source work intended to summarize, as briefly as possible, with enough mathematical rigor, the…
In this chapter, we survey some recent developments in the field of geophysical inversion. We aim to provide an accessible general introduction to the breadth of current research, rather than focussing in depth on particular topics. In…
This paper gives an overview of several key innovations in the 19th century which led to complex geometry in the 20th century. This includes the creation of the complex plane, the work of Abel on addition theorems for generalized elliptic…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon…
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…