相关论文: Observations about Leonardo's drawings for Luca Pa…

We show that an earlier conjecture of the author, on diophantine approximation of rational points on varieties, implies the ``abc conjecture'' of Masser and Oesterl'e. In fact, a weak form of the former conjecture is sufficient, involving…

The manuscripts that presumably contained Newton's early development of the fundamental concepts that led to his Principia have been lost. A plausible reconstruction of this development is presened based on Newton's exchange of letters with…

Brukner and Pienaar have critiqued the Relational Quantum Mechanics of Rovelli, and together with Di Biagio, the latter has replied. I point out a few places where, in my view, that reply needs clarification.

Linearly repetitive Delone sets are shown to be rectifiable by a bi-Lipschitz homeomorphisms of the Euclidean space that sends the Delone set to the set of points with integer coordinates.

During the early 1830's Bernard Bolzano, working in Prague, wrote a manuscript giving a foundational account of numbers and their properties. In the final section of his work he described what he called `infinite number expressions' and…

These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.

This is an exposition of Poincar\'e's 1883 paper, ``Sur les \'equations alg\'ebriques,'' which gives an important refinement of Descartes's rule of signs and was a precursor of P\' olya's Positivstellensatz.

Einstein's field equations with variable gravitational and cosmological ``constant'' are considered in presence of perfect fluid for Bianchi type-I spacetime. Consequences of the four cases of the phenomenological decay of $\Lambda$ have…

In this paper we describe the work of Luis Caffarelli in the area of fluid mechanics and related topics. Not only has his work on fluid mechanics been very influential, but many of his contributions that do not directly relate to fluid…

This paper presents an annotated English translation of Daniel Bernoulli's 1727 work A New Theory on the Motion of Waters through Channels of Any Kind, originally published in the Commentarii Academiae Scientiarum Imperialis Petropolitanae.…

In this note, we give a diffeomorphism (to $\mathbb{R}^n$) criterion via long-time Ricci flow and show some applications. In particular, we provide an affirmative answer that the conclusion in [Manifolds with small curvature concentration,…

Newton's Principia, when it appeared in 1687, was received with the greatest admiration, not only by the foremost mathematicians and astronomers in Europe, but also by philosophers like Voltaire and Locke and by members of the educated…

In his 1685 paper "Observationes cyclometricae" published in Acta Eruditorum, Adam Adamandy Kocha\'nski presented an approximate ruler-and-compass construction for rectification of the circle. It is not generally known that the first part…

This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…

This paper determines the general formula for describing differentials of composite functions in terms of differentials of their factor functions. This generalises the formula commonly attributed to Faa di Bruno to functions in locally…

In this paper, we prove a result of equivalence in law between a diffusion conditioned with respect to partial observations and an auxiliary process. By partial observations we mean coordinates (or linear transformation) of the process at a…

During the voyages that led him to discover the new continent bearing his name, Amerigo Vespucci made interesting astronomical observations of the southern sky. In the past, his data have been interpreted with criteria that do not follow…

Lecture given at the International Meeting ``Boltzmann's Legacy - 150 Years after his Birth'', organized by the Accademia Nazionale dei Lincei, 25 - 28 May 1994, in Rome, to be published in: ``Atti dell"Accademia Nazionale dei Lincei'',…

We dedicate this paper to investigate the most generalized form of Fibonacci Sequence, one of the most studied sections of the mathematical literature. One can notice that, we have discussed even a more general form of the conventional one.…

The notion of partial Jacobi manifold is introduced in the convenient ($c^\infty$-complete) framework of Fr\"olicher, Kriegl, and Michor. Explicit examples are provided in both finite and infinite dimensions, and the characteristic…