Related papers: On Double-Entry Bookkeeping: The Mathematical Trea…
We review and interpret two basic propositions published by Ellerman (2014). The propositions address the algebraic structure of T accounts and double entry bookkeeping (DEB). The paper builds on this previous contribution with the view of…
Triple Entry (TE) is an accounting method that utilizes three accounts or 'entries' to record each transaction, rather than the conventional double-entry bookkeeping system. Existing studies have found that TE accounting, with its…
Triple-entry accounting (TEA) is simultaneously a novel application in the blockchain universe and one of the many concepts applied in blockchain technology. Its Wild Wild West status is accompanied by a lack of consistent and comprehensive…
To describe the dynamics of a size-structured population and its unstructured resource, we formulate bookkeeping equations in two different ways. The first, called the PDE formulation, is rather standard. It employs a first order partial…
We study the problem of differentially private (DP) secure multiplication in distributed computing systems, focusing on regimes where perfect privacy and perfect accuracy cannot be simultaneously achieved. Specifically, N nodes…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
Accounting frameworks follow stipulations of existing Accounting Theories. This exploratory research sets out to trace the evolution of accounting theories of Charge and Discharge Syndrome and the Corollary of Double Entry. Furthermore, it…
Bipartite graphs are commonly used to model relationships between two distinct entities in real-world applications, such as user-product interactions, user-movie ratings and collaborations between authors and publications. A butterfly (a…
Difference sets have been studied for more than 80 years. Techniques from algebraic number theory, group theory, finite geometry, and digital communications engineering have been used to establish constructive and nonexistence results. We…
We ask whether two or more images of arithmetic may inhabit the same space via different encodings. The answers have significance for a class of processor design that does all its computation in an encrypted form, without ever performing…
The quest for a precise and contextually grounded answer to the question in the present paper's title resulted in this stirred-not-shaken triptych, a phrase that reflects our desire to deepen the theoretical basis, broaden the practical…
What makes living things special is how they manage matter, energy, and entropy. A general theory of organismal metabolism should therefore be quantified in these three currencies while capturing the unique way they flow between individuals…
Discrete Euclidian Spaces (DESs) are the beginning of a journey without return towards the discretization of mathematics. Important mathematical concepts- such as the idea of number or the systems of numeration, whose formal definition is…
The Data Aggregation Problem occurs when a large collection of data takes on a higher security level than any of its individual component records. Traditional approaches of breaking up the data and restricting access on a "need to know"…
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have…
What makes sets, or more precisely, the category {\bf Set} important in Mathematics are the well known {\it two} specific ways in which arbitrary mappings $f : X \longrightarrow Y$ between any two sets $X, Y$ can {\it fail} to be…
The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-orderable, two-generated recursively presented solvable group…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of 'doubled kets' (i.e. mixing), and by tracing out part of a 'doubled' two-system ket (i.e. dilation). Both…
Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and…