Related papers: Additive number theory and the ring of quantum int…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
It is shown how Dedekind cuts can be used to introduce the extended real numbers along with sound arithmetic laws via one simple rule for the addition of sets. The crucial idea is that the use of the lower and the upper part of the cuts,…
We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units.…
Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL.…
We introduce an addition law for the usual quantum matrices $A(R)$ by means of a coaddition $\underline{\Delta} t=t\otimes 1+1\otimes t$. It supplements the usual comultiplication $\Delta t=t\otimes t$ and together they obey a…
In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator. Also, we show between the q-Euler…
We consider the four structures $(\mathbb{Z}; \mathrm{Sqf}^\mathbb{Z})$, $(\mathbb{Z}; <, \mathrm{Sqf}^\mathbb{Z})$, $(\mathbb{Q}; \mathrm{Sqf}^\mathbb{Q})$, and $(\mathbb{Q}; <, \mathrm{Sqf}^\mathbb{Q})$ where $\mathbb{Z}$ is the additive…
We show that for infinitely many square-free integers q there exist infinitely many triples of rational numbers {a, b, c} such that a^2 + q, b^2 + q, c^2 + q, ab + q, ac + q and bc + q are squares of rational numbers.
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
A perturbative approach to quantum field theory involves the computation of loop integrals, as soon as one goes beyond the leading term in the perturbative expansion. First I review standard techniques for the computation of loop integrals.…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced…
Using an extension of the abundancy index to imaginary quadratic rings with unique factorization, we define what we call $n$-powerfully perfect numbers in these rings. This definition serves to extend the concept of perfect numbers that…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
In this paper we construct the $q$-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is…
In [2], I constructed the p-adic q-integral on Zp. In this paper, we consider the properties of the p-adic invariant p-adic q-integral in the ring of p-adic integers at q=-1. Finally we give the some applications of p-adic q-integration at…
We associate a half-integer number, called {\em the quantum index}, to algebraic curves in the real plane satisfying to certain conditions. The area encompassed by the logarithmic image of such curves is equal to $\pi^2$ times the quantum…