Related papers: Tibetan calendar mathematics
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.
Presented with a new machine with a specific interconnect topology, algorithm designers use intuition about the symmetry of the algorithm to design time and communication-efficient schedules that map the algorithm to the machine. Is there a…
We describe a new arithmetic system for the Magma computer algebra system for working with $p$-adic numbers exactly, in the sense that numbers are represented lazily to infinite $p$-adic precision. This is the first highly featured such…
Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as…
Astronomical observations were used as a marker for time and the Calendar from ancient times. A more subtle calibration of epochs is thrown up by an observation of the position of the solstices and equinoxes, because these points shift in…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
We present some new mathematical tools which help to derive information about the quark mass matrices directly from experimental data and to elucidate the structure of these mass matrices.
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…
We propose a scheme or procedure for doing practical calculations with generalized seniority. It reduces the total computing time by calculating and storing in advance a set of intermediate quantities, taking advantage of the memory…
We examine in detail 15 Babylonian observations of lunar appulses and occultations made between 80 and 419 BC for the purpose of setting useful limits on Earth's clock error, as quantified by $\Delta$T, the difference between Terrestrial…
I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete…
In a recent work I developed a formula for efficiently calculating the number of abelian squares of length $t+t$ over an alphabet of size $d$, where $d$ may be very large. Here I show how the expressiveness of a certain class of…
Every human likes choices. But today's fast route planning algorithms usually compute just a single route between source and target. There are beginnings to compute alternative routes, but this topic has not been studied thoroughly. Often,…
We study properties of Euclidean affine functions (EAFs), namely those of the form $f(r) = (\alpha\cdot r + \beta)/\delta$, and their closely related expression $\mathring{f}(r) = (\alpha\cdot r + \beta)\%\delta$, where $r$, $\alpha$,…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
The problem of evaluating heat invariants can be computerized. Geometric symbol calculus of pseudodifferential operators is the main tool of such computerization.
The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical…
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
Old and new calculations of the Higgs mass quadratic divergence are compared.