Related papers: Chirality in a quaternionic representation of the …
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
For quaternionic signal processing algorithms, the gradients of a quaternion-valued function are required for gradient-based methods. Given the non-commutativity of quaternion algebra, the definition of the gradients is non-trivial. The HR…
Classifications and representations are two main topics in the theory of quadratic forms. In this paper, we consider these topics of ternary quadratic forms. For a given squarefree integer $N$, first we give the classification of positive…
The notion of chiral prime concatenations is studied as a recursive construction of prime numbers starting from a seed set and with appropriate blocks to define the primality growth, generation by generation, either from the right or from…
Conceptualizing planetary habitability depends on understanding how living organisms originated and what features of environments are essential to foster abiogenesis. Estimates of the abundance of life's building blocks are confounded by…
We suggest an enhancement to structural coding through the use of (a) causally bound codes, (b) basic constructs of graph theory and (c) statistics. As is the norm with structural coding, the codes are collected into categories. The…
The Chiral Quark-Soliton Model of nucleons is based on two ideas: 1) the major role of spontaneous chiral symmetry breaking in hadron physics and 2) the relevance of the large number of colours limit for the real world. In these lectures I…
Fix a quadratic order over the ring of integers. An embedding of the quadratic order into a quaternionic order naturally gives an integral binary hermitian form over the quadratic order. We show that, in certain cases, this correspondence…
Binding energy is a fundamental thermodynamic property that governs molecular interactions, playing a crucial role in fields such as healthcare and the natural sciences. It is particularly relevant in drug development, vaccine design, and…
In eukaryote nucleosome, DNA wraps around a histone octamer in a left-handed way. We study the process of chirality formation of nucleosome with Brownian dynamics simulation. We model the histone octamer with a quantitatively adjustable…
The seven binary quantum numbers that distinguish fundamental fermions have been shown to be conserved in decays and interactions. Here applications of this law are clarified to take account of odd (uct) and even (dsb) parity quarks…
This work is devoted to the study of representations of finite subgroups of the group of units of quaternion division algebras over a global or local field arising from the inclusion via extension of scalars splitting the algebra. Following…
A dynamical model is presented for chiral change in DNA molecules. The model is an extension of the conventional elastic model which incorporates the structure of base pairs and uses a spinor representation for the DNA configuration…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
Modelising the translation errors by suitable mathematical operators in the crystal basis model of the genetic code and requiring that codons prone to be misread encode the same amino-acid, the main features of the organisation in…
DNA monolayers with inherent chirality play a pivotal role across various domains, including biosensors, DNA chips, and bioelectronics. Nonetheless, conventional DNA chiral monolayers, typically constructed from single-stranded DNA (ssDNA)…
Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…
Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in…
Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic…