Related papers: Some constructions in the M\=anava \'Sulvas\=utra
This paper presents a case study in the use of a large language model to generate a fictional Buddhist "sutra"', and offers a detailed analysis of the resulting text from a philosophical and literary point of view. The conceptual subtlety,…
This is a short note on generalized $G_2$-structures obtained as a consequence of a $T$-dual construction given in a previous work of the authors together with Leonardo Soriani. Given classical $G_2$-structure on certain seven dimensional…
Some notes and observations on analytic functions defined on an annulus
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…
This paper deals with certain fundamental results about affine hulls and simplices in a real normed linear space. The framework of the paper is Bishop's constructive mathematics, which, with its characteristic interpretation of existence as…
Some new infinite families of simple, indecomposable $m$-factorizations of the complete multigraph $\lambda K_v$ are presented. Most of the constructions come from finite geometries.
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
Constructive arithmetic, or the Markov arithmetic MA, is obtained from intuitionistic arithmetic HA by adding the following two principles: the Markov principle M which distinguishes constructivism from intuitionism, and the so-called…
The mu-invariant mu = (\mu_1,\mu_2,\mu_3) of a rational space curve gives important information about the curve. In this paper, we describe the structure of all parameterizations that have the same mu-type, what we call a mu-stratum, and as…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
This paper is mainly devoted to a structure study of Hom-alternative algebras . Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are displayed. Moreover some results about Hom-alternative bimodule…
A More Sums Than Difference (MSTD) set is a finite set of integers $A$ where the cardinality of its sumset, $A+A$, is greater than the cardinality of its difference set, $A-A$. Since addition is commutative while subtraction isn't, it was…
There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and…
In this paper we overview the theory of conics and roulettes in four non-Euclidean planes. We collect the literature about these classical concepts, from the eighteenth century to the present, including papers available only on arXiv. The…
Classical results on aperiodic tilings are rather complicated and not widely understood. Below, an alternative approach is discussed in hope to provide additional intuition not apparent in classical works.
Generalizing work of Marin [12], we construct in a unified way all the "braids and ties'' algebras available in literature and new ones.
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…