Related papers: Tibetan calendar mathematics
The aim of this study is to clarify the consequences of recent theoretical results for the numerical computation of expectation by the shift method, and in particular to yield sufficient criteria for the existence of speed of convergence of…
We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arrangements, the computation of Tutte polynomials is then…
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
For the eigenvalues of $p$ complex hermitian $n\times n$ matrices coupled in a chain, we give a method of calculating the spacing functions. This is a generalization of the one matrix case which has been known for a long time.
In this note we prove a weighted version of the Khintchine inequalities.
The relation between algebraic and traditional calculations of molecular vibrations is investigated. An explicit connection between interactions in configuration space and the corresponding algebraic interactions is established.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
This is the "preprint" for a paper that came out in 1998 but for some reason wasn't posted then. Abstract:These lectures are for novices to lattice QCD. They introduce a set of simple ideas and numerical techniques that can be implemented…
The Gregorian calendar -- first established for daily use on Friday, October 15th, 1582 by Pope Gregory XIII in Catholic countries -- is presently the most pervasive calendar in the world. As such, algorithms for performing various…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
This paper proposes new explicit formulas for the doubling and addition step in Miller's algorithm to compute the Tate pairing. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric…
We explain the algebra needed to make sense of the log signature of a path, with plenty of examples. We show how the log signature can be calculated numerically, and explain some software tools which demonstrate it.
In this report we propose 50+ metrics which can be measured by organizations in order to identify improvements in various areas such as meeting efficiency, capacity planning or leadership skills, just to new a few. The notion of calendar…
In this paper we establish that the well-known Arithmetic System is consistent in the traditional sense. The proof is done within this Arithmetic System.
Estimation of time delays from a noisy and gapped data is one of the simplest data analysis problems in astronomy by its formulation. But as history of real experiments show, the work with observed data sets can be quite complex and…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the…
Lattice calculations of the mass of the strange quark are reviewed. In particular, the reason for the spread in values is explained with emphasis on the effects that recently implemented improvements have had on the lattice determinations.
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…