Related papers: Sheaves in Elementary Mathematics: The case of pos…

The purpose of this paper (which, in many passages, I take the liberty of writing in the first person singular for bringing a personal experience) is to show how teachers of Physics and Mathematics in Basic Education can teach, through a…

We introduce and study kernel algebras, i.e., algebras in the category of sheaves on a square of a scheme, where the latter category is equipped with a monoidal structure via a natural convolution operation. We show that many interesting…

This is a pedagogical article cited in the foregoing research note, quant-ph/9911050

We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…

Document subject classification is essential for structuring (digital) libraries and allowing readers to search within a specific field. Currently, the classification is typically made by human domain experts. Semi-supervised Machine…

We consider categorical and geometric purity for sheaves of modules over a scheme satisfying some mild conditions, both for the category of all sheaves and for the category of quasicoherent sheaves. We investigate the relations between…

These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a…

In this article, we will use elementary number theory techniques to investigate a sequence of integers defined by a sifting process called the lucky numbers. Ulam introduced lucky numbers as a sieve-based analogue of prime numbers. We…

Integration of heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful way to track…

Given an invertible sheaf on a fibre space between projective varieties of positive characteristic, we show that fibrewise semi-ampleness implies relative semi-ampleness. The same statement fails in characteristic zero.

For the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of, seed, by broadening the notion of generator. This new concept allows us to explore the semigroup tree in an alternative…

The phrase "(co)simplicial (pre)sheaf" can be reasonably interpreted in multiple ways. In this survey we study how the various notions familiar to the author relate to one another. We end by giving some example applications of the most…

In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…

Consider the case of many sensors, each returning very different types of data (e.g., a camera returning images, a thermometer returning probability distributions, a newspaper returning articles, a traffic counter returning numbers).…

We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good…

We present some new ideas on important problems related to primes. The topics of our discussion are: simple formulae for primes, twin primes, Sophie Germain primes, prime tuples less than or equal to a predefined number, and their…

The theory of grey systems plays an important role in science,engineering and in the everyday life in general for handling approximate data. In the present paper grey numbers are used as a tool for assessing with linguistic expressions the…

In this paper we introduce the notion of elementary numerosity as a special function defined on all subsets of a given set X which takes values in a suitable non-Archimedean field, and satisfies the same formal properties of finite…

The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.

A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected components. We consider the problem of deciding whether two…