Related papers: Cyclotomic Matrices and Power Difference Sets
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
The volume of a cyclic polytope can be obtained by forming an iterated integral along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly…
Amid the uncertainty regarding the fundamental nature of neutrinos, we adhere to the Dirac description, and construct a model in the framework of $\Delta(27)$ symmetry. The model successfully accounts for the hierarchical patterns of both…
The concept of centrally symmetric configurations of integer matrices is introduced. We study the problem when the toric ring of a centrally symmetric configuration is normal as well as is Gorenstein. In addition, Gr\"obner bases of toric…
It is shown that when the mass matrix changes in orientation (rotates) in generation space for changing energy scale, then the masses of the lower generations are not given just by its eigenvalues. In particular, these masses need not be…
The structure of weighting coefficient matrices of Harmonic Differential Quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric depending on the order of the corresponding derivatives. The properties of both matrices…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…
With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite fields. Also, we confirm some related conjectures posed by…
The power structure over the Grothendieck (semi)ring of complex quasi-projective varieties constructed by the authors is used to express the generating series of classes of Hilbert schemes of zero-dimensional subschemes on a smooth…
With the goal of providing the foundations for a rigorous study of modules of bicomplex holomorphic functions, we develop a general theory of functional analysis with bicomplex scalars. Even though the basic properties of bicomplex number…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…
We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that…
Let $K$ be an abelian extension of the rationals. Let $S(K)$ be the Schur group of $K$ and let $CC(K)$ be the subgroup of $S(K)$ generated by classes containing cyclic cyclotomic algebras. We characterize when $CC(K)$ has finite index in…
We use generalised Zeckendorf representations of natural numbers to investigate mixing properties of symbolic dynamical systems. The systems we consider consist of bi-infinite sequences associated with so-called random substitutions. We…
Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is…
We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…