Related papers: Twisted rational zeros of linear recurrence sequen…
This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem for them. The computation methods for their fundamental…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
An attempt to come closer to a resolution of the Collatz conjecture is presented. The central idea is the formation of a tree consisting of positive odd numbers with number 1 as root. Functions for generating the tree from the root are…
The author introduces the notion of a quantum form of an algebraic torus. In the case of diagonal algebraic torus we get the algebra of Laurent twisted polynomials. Quantum algebraic torus can be characterized in terms of exact sequences.…
Let $V_{n}$ denote the third order linear recursive sequence defined by the initial values $V_{0}$, $V_{1}$ and $V_{2}$ and the recursion $V_{n}=rV_{n-1}+sV_{n-2}+tV_{n-3}$ if $n\geq 3$, where $r$, $s$, and $t$ are real constants. The…
Using $n$ finite order automorphisms on a simple complex Lie algebra we construct twisted $n$-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case $n=2$ we list certain simple Lie algebras and…
In this paper we discuss the relationship between a TRO $\mathcal{T}$ and a sub-TRO $\mathcal{S}$ that is the range of a TRO-conditional expectation on $\mathcal{T}$, a \textit{ternary corner}, by investigating a special class $\mathcal{D}$…
Intersection numbers of twisted cocycles arise in mathematics in the field of algebraic geometry. Quite recently, they appeared in physics: Intersection numbers of twisted cocycles define a scalar product on the vector space of Feynman…
Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods…
In Communication theory and Coding, it is expected that certain circulant matrices having $k$ ones and $k+1$ zeros in the first row are nonsingular. We prove that such matrices are always nonsingular when $2k+1$ is either a power of a…
The rotation search problem aims to find a 3D rotation that best aligns a given number of point pairs. To induce robustness against outliers for rotation search, prior work considers truncated least-squares (TLS), which is a non-convex…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
We discuss properties of integers in base 3/2. We also introduce many new sequences related to base 3/2. Some sequences discuss patterns related to integers in base 3/2. Other sequence are analogues of famous base-10 sequences: we discuss…
We give some results on the existence of bounded remainder sets (BRS) for sequences of the form $(\{a_n\alpha\})_{n\geq 1}$, where $(a_n)_{n\geq 1}$ - in most cases - is a given sequence of distinct integers. Further we introduce the…
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless,…
A repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., a number has the form $d(10^m-1)/9$ for some $m\geq 1$ and $1 \leq d \leq 9$. Let $\left(T_n\right)_{n\ge0}$ be the sequence of Tribonacci.…
We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurcation that creates a ``twistless'' torus. At this…
Given a lower-triangular matrix of real numbers, one can ask the following four total-positivity questions: total positivity of the triangle itself; total positivity of its row-reversal; Toeplitz-total positivity of its row sequences…
For almost a century, the decidability of the Skolem Problem - that is, the problem of finding whether a given linear recurrence sequence (LRS) has a zero term - has remained open. A breakthrough in the 1980s established that the Skolem…
In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated…