Researchers have demonstrated a novel AI model that can predict which DNA molecules bind with which other DNA molecules. Providing a more thorough ...
Keywords: Sfiral Neural Networks, Split-Complex Numbers, Topological Protection, Phase Transition, Hypercomplex Algebra, Noise Immunity.
ABSTRACT: “All is Number”—the universe follows a few profound mathematical rules, and pure thought can grasp reality. This paper explores the first principles of fundamental physics, focusing on the ...
Quaternion matrix algebra extends classical matrix theory into the realm of hypercomplex numbers, enabling elegant representation and manipulation of three-dimensional rotations and rigid-body motions ...
Quaternionic and octonionic field theories extend the familiar framework of complex-valued fields by employing higher-dimensional hypercomplex algebras. Quaternions, discovered by Hamilton, are ...
Abstract: Hypercomplex signal and image processing extends upon conventional methods by using hypercomplex numbers in a unified framework for algebra and geometry. The special issue is divided into ...
Abstract: Hypercomplex signal and image processing extends upon conventional methods by using hypercomplex numbers in a unified framework for algebra and geometry. The special issue is divided into ...
In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit, and satisfying the equation i^2 = −1.
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebras (PHAs) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via ...
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