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For more than 50,000 years, Indigenous Australians have incorporated celestial events into their oral traditions and used the motions of celestial bodies for navigation, time-keeping, food economics, and social structure. In this paper, we…
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck…
We propose an extension of the join calculus with pattern matching on algebraic data types. Our initial motivation is twofold: to provide an intuitive semantics of the interaction between concurrency and pattern matching; to define a…
In this paper, we report on findings from an ethnographic study of how people use their calendars for personal information management (PIM). Our participants were faculty, staff and students who were not required to use or contribute to any…
The Ramayana is among the most influential literary traditions of South and Southeast Asia, transmitted across numerous linguistic and cultural contexts over two millennia. Despite extensive scholarship on regional Ramayana traditions,…
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.
In the early 1980's an elementary algorithm for computing conformal maps was discovered by R. K\"uhnau and the first author. The algorithm is fast and accurate, but convergence was not known. Given points z_0,...,z_n in the plane, the…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
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…
Noncommutativity lies in the heart of quantum theory and provides rich set of interesting questions in physics and mathematics. In this work I present some of them through the concept of Joint Numerical Range (JNR) - the set of…
The horologia are ancient ephemerides, tables of durations of the days and nights during all months of the year. The algorithms used to compute the horologia are here presented and the results are compared with the tables computed by…
In this paper, the term formula code refers to fragments of source code that implement a mathematical formula. We present empirical studies that analyze the diversity and frequency of formula code in open-source-software projects. In an…
A proper forecast of the menstrual cycle is meaningful for women's health, as it allows individuals to take preventive actions to minimize cycle-associated discomforts. In addition, precise prediction can be useful for planning important…
The arithmetic mean plays a central role in science and technology, being directly related to the concepts of statistical expectance and centrality. Yet, it is highly susceptible to the presence of outliers or biased interference in the…
By applying the derivative operator to the known identities from hypergeometric series or WZ pairs, we obtain seven series associated with harmonic numbers. Specifically, six of them are Ramanujan-like formulas for $1/\pi$ and the remaining…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…
This works presents a program which computes velocities of an Earth-bound observatory in the reference frame of the barycenter of the solar system. It feeds from ephemerides files of the Jet Propulsion Laboratory to extract the velocity of…
We extend Kaprekar's Routine for a large class of applications. We also give particular examples of this generalization as alternatives to Kaprekar's Routine and Number. Some open questions about the length of the iterations until reaching…
The Ramanujan Machine project detects new expressions related to constants of interest, such as $\zeta$ function values, $\gamma$ and algebraic numbers (to name a few). In particular the project lists a number of conjectures involving even…