Related papers: Composition of Bhargava's Cubes over Number Fields
An introduction to the theory of bundle gerbes and their relationship to Hitchin-Chatterjee gerbes is presented. Topics covered are connective structures, triviality and stable isomorphism as well as examples and applications.
In this paper, we present a complete classification of all imaginary $n$-quadratic fields of class number 1.
The P\'{o}lya group of an algebraic number field is the subgroup generated by the ideal classes of the products of prime ideals of equal norm inside the ideal class group. Inspired by a recent work on consecutive quadratic fields with large…
This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an integral basis for the maximal order of…
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
Equations which define classical configurations of strings in $R^3$ are presented in a simple form. General properties as well as particular classes of solutions of these equations are considered.
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
We test the applicability of the Bohigas conjecture to systems whose Hamiltonian is not written as a closed form analytic expression. A class of such Hamiltonians is created and appear to violate the conjecture. Numerical methods are…
Based on the works of M. Marshall on multirings, we propose the fundamentals for a \textbf{non reduced} abstract quadratic forms theory in general coefficients on rings, with the machinery of multirings and multifields.
We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic…
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted…
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
Y. Palu has generalized the cluster multiplication formulas to 2-Calabi-Yau categories with cluster tilting objects (\cite{Palu2}). The aim of this note is to construct a variant of Y. Palu's formula and deduce a new version of the cluster…
We argue that generic non-relativistic quantum field theories have a holographic description in terms of Horava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and…
An abstract $(v_k,b_r)$-configuration is a pair of finite sets of cardinalities $v$ and $b$ with a relation on the product of the sets such that each element of the first set is related to the same number $k$ of elements from the second set…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
Our primary purpose is to isolate the abstract, mathematical properties of circuits -- both classical Boolean circuits and quantum circuits -- that are essential for their computational interpretation. A secondary purpose is to clarify the…
Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…
Given any number field, we prove that there exist arbitrarily shaped constellations consisting of pairwise non-associate prime elements of the ring of integers. This result extends the celebrated Green-Tao theorem on arithmetic progressions…