Related papers: The work of James Maynard
This paper reviews the current state of the art of the mean value theorem due to Thomas M. Flett. We present the results with detailed proofs and provide many new proofs of known results. Moreover, some new observations and yet unpublished…
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have…
We give a survey on recent developments in the model theory of valued fields since the introduction of the notion of ``tame valued field'', and of the modifications and generalizations of this notion.
This is an expository article discussing some of the work of Uhlenbeck, focusing mainly on work concerning harmonic maps and Yang-Mills fields.
Abhyankar proved that every field of finite transcendence degree over $\mathbb{Q}$ or over a finite field is a homomorphic image of a subring of the ring of polynomials $\mathbb{Z}[T_1, \dots, T_n]$ (for some $n$ depending on the field). We…
We review selected achievements of the late Bogdan Mielnik in the field of theoretical physics, with an emphasis on his attempts to go beyond quantum mechanics. Some of his original views on the problems of contemporary society and…
We investigate the properties of the James function, associated with Bill James's so-called "log5 method," which assigns a probability to the result of a game between two teams based on their respective winning percentages. We also…
A recent essay [1] reminds us of how richly Boltzmann deserves to be admiringly commemorated for the originality of his ideas on the occasion of his 150th birthday. Without any doubt, the scientific community owes Boltzmann a great debt of…
This paper describes the work of Jesse Douglas on the Plateau problem, work for which he was awarded a Fields Medal in 1936, and considers the contributions Tibor Rado made in the 1930s.
We review some of the most important results obtained over the years on the study of Yang-Mills fields on the four dimensional torus at the classical level.
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
Overview of Burkholder's work on martingales and analysis
We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.
The authors provide a survey of certain aspects of their joint work with the late M. K. Vamanamurthy. Most of the results are simple to state and deal with special functions, a topic of research where S. Ramanujan's contributions are…
We introduce a ring and a field, generated by a semigroup, and we investigate some of their properties.
The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the "Lenard recursion formula". The story about the discovery of the formula told by Andrew Lenard is the subject of this article.
This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.
We present a review on the recent developments concerning rigorous mathematical results on Schr\"odinger operators with magnetic fields. This paper is dedicated to the sixtieth birthday of Barry Simon.