Related papers: A new proposal to the extension of complex numbers

A construction of reversible extensions of dynamical systems which applies to arbitrary mappings (not necessarily with open range) is presented. It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to…

Given a linear category over a finite field such that the moduli space of its objects is a smooth Artin stack (and some additional conditions) we give formulas for an exponential sum over the set of absolutely indecomposable objects and a…

We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely…

We introduce the notion of a pseudomultiplier of a Hilbert space $\mathcal H$ of functions on a set $\Omega$. Roughly, a pseudomultiplier of $\mathcal H$ is a function which multiplies a finite-codimensional subspace of $\mathcal H$ into…

A complete set of inequivalent realizations of three- and four-dimensional real unsolvable Lie algebras in vector fields on a space of an arbitrary (finite) number of variables is obtained.

This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…

Let $\mathfrak g$ be an infinite-dimensional Lie algebra and $G$ be the algebraic completion of its module. Using a geometric interpretation in terms of sewing two Riemann spheres with a number of marked points, we introduce a…

In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…

We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…

We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…

For $\alpha>1$ we represent a real number in $(0,1]$ in the form \[ \sum_{i=1}^{\infty}(\alpha-1)^{i-1}\alpha^{-(d_{1}+\dots+d_{i})}\] with $d_{i}\in\mathbb{N}$. We discuss ergodic theoretical and dimension theoretical aspects of this…

For a simple Lie algebra, over $\mathbb{C}$, we consider the weight which is the sum of all simple roots and denote it $\tilde{\alpha}$. We formally use Kostant's weight multiplicity formula to compute the "dimension" of the zero-weight…

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…

In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to…

This article provides the domain of existence $\Omega$ of the Laplace transform of infinitely divisible negative multinomial distributions. We define a negative multinomial distribution on $\mathbb{N}^{n},$ where $\mathbb{N}$ is the set of…

In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also associate with that family of functions a dual pair of problems…

We highlight an intrinsic connection between classical quadrature domains and the well-studied theme of removable singularities of analytic sets in several complex variables. Exploiting this connection provides a new framework to recover…

We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a…

Complex geometry represents a fundamental ingredient in the formulation of the Dirac equation by the Clifford algebra. The choice of appropriate complex geometries is strictly related to the geometric interpretation of the complex imaginary…