相关论文: Virtual Calculus - Part II
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
This work establishes the existence of addition theorems and double-angle formulas for Ck real scalar functions. Moreover, we determine necessary and sufficient conditions for a bivariate function to be an addition formula for a Ck real…
We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.
We consider the classes of quasimultiplicative, semimultiplicative and Selberg multiplicative functions as extensions of the class of multiplicative functions. We apply these concepts to Ramanujan's sum and its analogue with respect to…
We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…
In the context of the correspondence between real functions on the unit circle and inner analytic functions within the open unit disk, that was presented in previous papers, we show that the constructions used to establish that…
We construct a generic extension in which the aleph_2 nd canonical function on aleph_1 exists.
A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.
Work in progress concerning alternative formalizations of arithmetic.
We enlighten relations between the K\"all\'en function, allowing in a simple way to distinguish between virtual and real processes involving massive particles, and the dilogarithms occurring as results of loop calculations for such kind of…
We study first-order expansions of the reals which do not define the set of natural numbers. We also show that several stronger notions of tameness are equivalent to each others.
In the previous paper (Kiri Sakahara and Takashi Sato. Basic Topological Concepts and a Construction of Real Numbers in Alternative Set Theory. arXiv e-prints, arXiv:2005.04388, May 2020), the authors displayed basic topological concepts…
We introduce a formalism to analyze partially defined functions between ordered sets. We show that our construction provides a uniform and conceptual approach to all the main definitions encountered in elementary real analysis including…
In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.
Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine…
We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.
Every continuous function of two or more real variables can be written as the superposition of continuous functions of one real variable along with addition.
We introduce a class of rational functions $A:\,\mathbb C\mathbb P^1\rightarrow \mathbb C\mathbb P^1$ which can be considered as a natural extension of the class of Latt\`es maps and establish basic properties of functions from this class.