相关论文: On radius of convergence of $q$-deformed real numb…
The concept of $q$-deformation, or ``$q$-analogue'' arises in many areas of mathematics. In algebra and representation theory, it is the origin of quantum groups; $q$-deformations are important for knot invariants, combinatorial…
The q-rational numbers and the q-irrational numbers are introduced by S. Morier-Genoud and V. Ovsienko. In this paper, we focus on q-real quadratic irrational numbers, especially q-metallic numbers and q-rational sequences which converge to…
For an integer $n\geq 1$, consider the $n$-th metallic number $\phi_n=\frac{n+\sqrt{n^2+4}}{2}$ (e.g. $\phi_1$ is the golden number) and denote by $[\phi_n]_q$ its $q$-deformation in the sense of S. Morier-Genoud and V. Ovsienko. This is an…
We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a "$q$-analogue of a real." The construction is based on the notion of $q$-deformed rational number introduced in…
In arXiv:1812.00170, S. Morier-Genoud and V. Ovsienko introduced the notion of the $q$-rational number $[x]_q$, $x\in \Bbb Q$, a rational function specializing to $x$ at $q=1$, obtained by $q$-deforming the continued fraction expansion of…
A few years ago Morier-Genoud and Ovsienko introduced an interesting quantization of the real numbers as certain power series in a quantization parameter $q.$ It is known now that the golden ratio has minimal radius among all these series.…
We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…
We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the…
We explain the notion of "$q$-deformed real numbers" introduced in our previous work and overview their main properties. We will also introduce $q$-deformed Conway-Coxeter friezes.
In this investigation our main aim is to determine the radius of uniform convexity of the some normalized q-Bessel and Wright functions. Here we consider six different normalized forms of q-Bessel functions, while we apply three different…
This paper is the survey of some of our results related to $q$-deformations of the Fock spaces and related to $q$-convolutions for probability measures on the real line $\mathbb{R}$. The main idea is done by the combinatorics of moments of…
A $q$--deformed anharmonic oscillator is defined within the framework of $q$--deformed quantum mechanics. It is shown that the Rayleigh--Schr\"odinger perturbation series for the bounded spectrum converges to exact eigenstates and…
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. A new class of fractional q-deformed Lie algebras is proposed, which for the…
We consider a natural $q$-deformation of the classical Markov numbers. This $q$-deformation is closely related to $q$-deformed rational numbers recently introduced by two of us. Both notions, those of $q$-rationals and $q$-Markov numbers,…
We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The q-deformed models are based on the representation theory of two copies of U_q(su(2)) at a root of…
We address the study of the thermodynamics of a crystalline solid by applying q-deformed algebras. We based part of our study by considering both Einstein and Debye models. We have mainly explored the q-deformed thermal and electric…
Within the formulation of a q-deformed Quantum Mechanics a qualitative undercut of the q-deformed uncertainty relation from the Heisenberg uncertainty relation is revealed. When $q$ is some fixed value not equal to one, recovering of…
Fix $n$ a positive integer. Take the $n$-th metallic number $\phi_n=\frac{n+\sqrt{n^2+4}}{2}$ (e.g. $\phi_1$ is the golden number) and let $\Phi_n(q)$ be its $q$-deformation in the sense of S. Morier-Genoud and V. Ovsienko. This is an…
In 1999, Reg Wood conjectured that the quotient of Q[x_1,...,x_n] by the action of the rational Steenrod algebra is a graded regular representation of the symmetric group S_n. As pointed out by Reg Wood, the analog of this statement is a…