Related papers: Elements
The goal of this paper is introduction of a concept of natural multidimensional numbers and to construct a generalized Peano arithmetic of these multidimensional numbers. For this purpose we define a polymultiset as a special set-like form…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension $n$. Our aim is to present some analytical methods and to discuss…
The purpose of this book is to provide an overview of AI research, ranging from basic work to interfaces and applications, with as much emphasis on results as on current issues. It is aimed at an audience of master students and Ph.D.…
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the…
Measuring the unknown neutrino oscillation parameters is one of the main aims in neutrino physics today. The measurement of these parameters is severely affected by the presence of degeneracies in the parameter space. Various neutrino…
We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by $m$, appearing fewer than $m$ times, or differing by less than $m$. We find results on their behavior and…
An error analysis for some Newton-Cotes quadrature formulae is presented. Peano-like error bounds are obtained. They are generally, but not always, better than the usual Peano bounds.
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
At present a number of current or proposed experiments are directed towards a search for a `new physics' by detecting variations of fundamental physical constants or violations of certain basic symmetries. Various problems related to the…
Despite the effort put into the detection of academic plagiarism, it continues to be a ubiquitous problem spanning all disciplines. Various tools have been developed to assist human inspectors by automatically identifying suspicious…
Given the profound and uncritiqued changes that have been implemented in Aotearoa New Zealand education since the 1990s, this paper provides a critical commentary on the characterising features of the New Zealand mathematics' curriculum in…
In this report, we aim to exemplify concentration inequalities and provide easy to understand proofs for it. Our focus is on the inequalities which are helpful in the design and analysis of machine learning algorithms.
In this essay, I argue that modern science is not the dichotomous pairing of theory and experiment that it is typically presented as, and I offer an alternative paradigm defined by its functions as a human endeavor. I also demonstrate how…
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
We present a review of the present status of the problem of neutrino masses and mixing including a survey of theoretical motivations and models, experimental searches and implications of recently appeared solar and atmospheric neutrino…
In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of…