Related papers: Hyper Space Complex Number
Strong dynamics constitutes one of the pillars of the standard model of particle interactions, and it accounts for the bulk of the visible matter in the universe. It is therefore a well posed question to ask if the rest of the universe can…
We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It…
The usual extensions of supersymmetry require the existence of a complex structure and the formulation of the theory on K\"{a}hler manifolds. It is shown, that by relaxing the constraints on the algebra of supercharges we can get new…
This work is meant to demonstrate new class of prime numbers -- cyclic prime numbers, that can be derived from any prime number at certain numeric systems. Cyclic prime numbers are also related to the cyclic numbers and full reptend prime…
The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
In this book for the first time the authors introduce the notion of real neutrosophic complex numbers. Further the new notion of finite complex modulo integers is defined. For every $C(Z_n)$ the complex modulo integer $i_F$ is such that…
We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an…
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product(STP) of matrices are…
A new approach to special relativity is presented which introduces coordinate systems with imaginary time axes, observation systems, and coordinate bases.
It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.
The possibility that spacetime is extended beyond the familiar 3+1-dimensions has intrigued physicists for a century. Indeed, the consequences of a dimensionally richer spacetime would be profound. Recently, new theories with higher…
Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this fact states that every polytope is…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Hyperdimensional (HD) computing is built upon its unique data type referred to as hypervectors. The dimension of these hypervectors is typically in the range of tens of thousands. Proposed to solve cognitive tasks, HD computing aims at…
In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN).…
In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining…