ترغب بنشر مسار تعليمي؟ اضغط هنا

On $q$-deformed real numbers

81   0   0.0 ( 0 )
 نشر من قبل Valentin Ovsienko Yu
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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 arXiv:1812.00170. Extending the construction to negative real numbers, we obtain certain Laurent series.

قيم البحث

اقرأ أيضاً

We study analytic properties of $q$-deformed real numbers, a notion recently introduced by two of us. A $q$-deformed positive real number is a power series with integer coefficients in one formal variable~$q$. We study the radius of convergence of th ese power series assuming that $q in C.$ Our main conjecture, which can be viewed as a $q$-analogue of Hurwitzs Irrational Number Theorem, provides a lower bound for these radii, given by the radius of convergence of the $q$-deformed golden ratio. The conjecture is proved in several particular cases and confirmed by a number of computer experiments. For an interesting sequence of Pell polynomials, we obtain stronger bounds.
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.
298 - Valentin Ovsienko 2021
This work is a first step towards a theory of $q$-deformed complex numbers. Assuming the invariance of the $q$-deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~$i$ compatible wi th this action. Obtained in such a way $q$-deformed Gaussian integers have interesting properties and are related to the Chebyshev polynomials.
Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of $q$-operations on the construction of $q$-numbers for all numerical sets. Based on such a construction, we present a new product that distributes over the $q$-sum. Finally, we present different patterns of $q$-Pascals triangles, based on $q$-sum, whose elements are $q$-numbers.
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا