Related papers: Prime and Co-prime Integer Matrices
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
In a prime number decomposition of integers in a given set, the occurrence frequencies of prime numbers are shown to satisfy a general forms of Zipf's law.
Continuing the study of the structure of semirings, we turn to the spectrum of prime congruences. Joo and Mincheva developed an elegant theory in the special case of idempotent semirings, which is generalized here to ``semiring pairs,''…
We present a simple, closed formula which gives all the primes in order. It is a simple product of integer floor and ceiling functions.
We investigate two one-sided orthogonalities of matrices, the first of which is left (right) $*$-orthogonality for rectangular matrices and the other is left (right) core-orthogonality of index $1$ matrices. We obtain some basic results for…
We are interested in classifying those sets of primes $\mathcal{P}$ such that when we sieve out the integers up to $x$ by the primes in $\mathcal{P}^c$ we are left with roughly the expected number of unsieved integers. In particular, we…
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…
In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…
Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in…
In this paper, we consider the simultaneous representation of pairs of sufficiently large integers. We prove that every pair of large positive odd integers can be represented in the form of a pair of one prime, four cubes of primes and 231…
We prove upper and lower bounds on the number of pairs of commuting $n\times n$ matrices with integer entries in $[-T,T]$, as $T\to \infty$. Our work uses Fourier analysis and leads us to an analysis of exponential sums involving matrices…
Due to their rich algebraic structures and various applications, circulant matrices have been of interest and continuously studied. In this paper, the notions of Binomial-related matrices have been introduced. Such matrices are circulant…
The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
In this paper, we continue the classification work done in the first paper of the same name. With careful modifications of our previous approach, we are able to deduce (with two notable exceptions) which members of the previously introduced…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…
We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many…
We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.