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The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
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…
Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
A construction of integration, function calculus, and exterior calculus is made, allowing for integration of unital magma valued functions against (compactified) unital magma valued measures over arbitrary topological spaces. The Riemann…
We go into the need for, and the requirements on, a formal theory of budgets. We present a simple algebraic theory of rational budgets, i.e., budgets in which amounts of money are specified by functions on the rational numbers. This theory…
We use contemporary mathematical notation to describe the method for determining the age of the ecclesiastical moon as mandated by pope Gregory XIII and elaborated in the book of Christopher Clavius \emph{Romani calendarii explicatio}. The…
Working with letters that represent unknown constants, i.e., parameters, has been historically challenging for students. This is an important skill for their success in many future quantitative settings, and yet it appears this topic is…
In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove…
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…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…
Dimensions are an integral part of many models we use every day. Without thinking about it, we frequently use the time dimension: many financial and accounting spreadsheets have columns representing months or years. Representing a second…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.