Related papers: The rational iteration method by Georges Lemaitre …
In this paper, we will apply the ideas from the mirror symmetry of Calabi-Yau threefolds to study the modular forms and one-parameter family of K3 surfaces found by Beukers and Peters, which provide enlightenment to the two mysterious…
The Dumont differential system on the Jacobi elliptic functions was introduced by Dumont (Math Comp, 1979, 33: 1293--1297) and was extensively studied by Dumont, Viennot, Flajolet and so on. In this paper, we first present a labeling scheme…
Riemann numerically approximated at least three zeta zeros. According to Edwards, Riemann even took steps to verify that the lowest zero he computed was indeed the first zeta zero. This approach to verification is developed, improved, and…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that…
These notes were written from a series of lectures given in March 2010 at the Universidad Complutense of Madrid and then in Barcelona for the centennial anniversary of the Spanish Mathematical Society (RSME). Our aim is to give an…
Arthur Stanley Eddington was one of the leading astronomers and theorists of his generation and a prominent proponent of the general theory of relativity. Yet when his former assistant Georges Lemaitre sent him a paper in 1927 suggesting…
The purpose of this note consists of discrete rational reconstruction which took place during the years 1609-1630 and 1630-1666, ie, the year of the publication of their Astronomia Nova and the year of death of the great German astronomer…
This article presents the emergence of formal methods in theory of partial differential equations (PDE) in the french school of mathematics through Janet's work in the period 1913-1930. In his thesis and in a series of articles published…
We develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and discrete Abelian integrals to their continuous…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
In 1962, astronomers Michel H\'enon and Carl Heiles studied orbits of stars around centers of galaxies to determine the third integral of motion in galactic dynamics. In order to do this, they reduced the system down to a 2-dimensional…
The Rutherford scattering experiment, conceived by Ernest Rutherford and carried out by Hans Geiger and Ernest Marsden, provided the first direct evidence of a compact atomic nucleus, fundamentally altering the understanding of atomic…
Recently much attention has been paid to the discovery of Hubble's law: the linear relation between the rate of recession of the distant galaxies and distance to them. Though we now mention several names associated with this law instead of…
We study the following system of two rational difference equations x_n=({\beta}_k x_(n-k)+{\gamma}_k y_(n-k))/(A+\Sigma_(j=1)^l[B_j x_(n-j) ]+\Sigma_(j=1)^l[C_j y_(n-j) ]), n \in N, y_n=({\delta}_k x_(n-k)+\in_k…
The Lagrangian theory of gravitational instability of homogeneous-isotropic Friedman-Lemaitre cosmogonies investigated and solved in the series of papers by Buchert (1989), (1992), Buchert & Ehlers (1993), Buchert (1993a,b), Ehlers &…
Considerable thought has been devoted to an adequate definition of the class of infinite, random binary sequences (the sort of sequence that almost certainly arises from flipping a fair coin indefinitely). The first mathematical exploration…
The paper revises the explicit integration of the classical Steklov--Lyapunov systems via separation of variables, which was first made by F. K\"otter in 1900, but was not well understood until recently. We give a geometric interpretation…
Image processing is an increasingly important aspect for analysis of data from X and $\gamma$-ray astrophysics missions. In this paper, I review a method proposed by Kebede (L. W. Kebede 1994, ApJ, 423, 878), and point out an error in the…
In 1776, L. Euler proposed three methods, called prima methodus, secunda methodus and tertia methodus, to calculate formulae for double zeta values. However strictly speaking, his last two methods are mathematically incomplete and require…