Related papers: Jost B\"urgi's Method for Calculating Sines
In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
The Basel problem consists in finding the sum of the reciprocals of the squares of the positive integers. It was finally solved in 1735 by Leonhard Euler. In this paper, we propose a simple proof based on the Weierstrass Sine product…
The square peg problem asks whether every continuous curve in the plane that starts and ends at the same point without self-intersecting contains four distinct corners of some square. Toeplitz conjectured in 1911 that this is indeed the…
Background. Clustering analysis discovers hidden structures in a data set by partitioning them into disjoint clusters. Robust accuracy measures that evaluate the goodness of clustering results are critical for algorithm development and…
A Sinc-Nystr\"om method for Volterra integro-differential equations was developed by Zarebnia in 2010. The method is quite efficient in the sense that exponential convergence can be obtained even if the given problem has endpoint…
The main thrust of the article is to provide interesting example, useful for students of using bitwise operations in the programming languages C ++ and Java. As an example, we describe an algorithm for obtaining a Latin square of arbitrary…
Propagation Phase Contrast Synchrotron Microtomography (PPC-SR${\mu}$CT) is the gold standard for non-invasive and non-destructive access to internal structures of archaeological remains. In this analysis, the virtual specimen needs to be…
This paper presents a modification of Secant method for finding roots of equations that uses three points for iteration instead of just two. The development of the mathematical formula to be used in the iteration process is provided…
In a previous work, we developed the idea to solve Kepler's equation with a CORDIC-like algorithm, which does not require any division, but still multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler's…
This is a translation from Latin of E348 'Methodus facilis motus corporum coelestium utcunque perturbatos ad rationem calculi astronomici revocandi', in which Euler develops a method to alleviate the astronomical computations in a typical…
A determined algorithm is presented for solving the rSUM problem for any natural r with a sub-quadratic assessment of time complexity in some cases. In terms of an amount of memory used the obtained algorithm is the nlog^3(n) order. The…
Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more…
In [Solving second order ordinary differential equations by extending the Prelle-Singer method, J. Phys. A: Math.Gen., 34, 3015-3024 (2001)] we defined a function (we called S) associated to a rational second order ordinary differential…
We present a new systematic method for evaluating generalized log-sine integrals in terms of polylogarithms. Our approach is based on an identity connecting ordinary generating functions of polylogarithms to integrals involving the sine…
Decimal-to-binary conversion is important to modern binary computers. The classical method to solve this problem is based on division operation. In this paper, we investigate a decimal-to-binary conversion method based on addition…
A re-calculation of a known family of formulas of PI is carried out, revisiting the old Archimedes' algorithm. This allows to identify a general family equation and three new simple formulas of Pi in terms of the golden ratio PHI in the…
We demonstrate a new approach to the computation of ratios of elliptic integrals. It turns out that almost closed polygons interscribed between two conics retain some of the properties of such closed polygons. We apply these retained…
Plane partitions have been widely studied in Mathematics since MacMahon. See, for example, the works by Andrews, Macdonald, Stanley, Sagan and Krattenthaler. The Schur process approach, introduced by Okounkov and Reshetikhin, and further…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…