Related papers: The simple complex numbers
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
There has been always an ambiguity in division when zero is present in the denominator. So far this ambiguity has been neglected by assuming that division by zero as a non-allowed operation. In this paper, I have derived the new set of…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
Wigner had expressed the opinion that the impossibility of exact measurements of single operators like position operators rendered the notion of geometrical points somewhat dubious in physics. Using Sewell's recent resolution of the…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Logic gates can be written in terms of complex differential operators, where the inputs and outputs are holomorphic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection…
Polygons are compound geometric objects, but when trying to understand the expected behavior of a large collection of random polygons -- or even to formalize what a random polygon is -- it is convenient to interpret each polygon as a point…
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We…
We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.
Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…
In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…
The science of complex networks is a new interdisciplinary branch of science which has arisen recently on the interface of physics, biology, social and computer sciences, and others. Its main goal is to discover general laws governing the…
This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
We propose a new geometrical model of matter, in which neutral atoms are modelled by compact, complex algebraic surfaces. Proton and neutron numbers are determined by a surface's Chern numbers. Equivalently, they are determined by…
An outline of recent work on complex networks is given from the point of view of a physicist. Motivation, achievements and goals are discussed with some of the typical applications from a wide range of academic fields. An introduction to…
In this work, I propose a way to help high school students and the general population understand quantum concepts by adopting a new inherently dual representation. Major difficulties in explaining to people the basic concepts of quantum…