Related papers: Golden-Thompson's inequality for deformed exponent…
In a recent letter (EPL, 104 (2013) 60003) we suggested a way to avoid divergences inherent to the formulation of nonextensive statistical mechanics. They can be eliminated via the use of a q-Laplace transformation, which was illustrated…
We consider a ${\mu}$-deformation of the Segal-Bargmann transform, which is a unitary map from a ${\mu}$-deformed quantum configuration space onto a ${\mu}$-deformed quantum phase space (the ${\mu}$-deformed Segal-Bargmann space). Both of…
We first observe that the (co)domains of the q-deformed functions are some subsets of the (co)domains of their ordinary counterparts, thereby deeming the deformed functions to be incomplete. In order to obtain a complete definition of…
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…
We consider the logistic family and apply the $q$-deformation $\phi_q(x)=\frac{1-q^x}{1-q}$. We study the stability regions of the fixed points of the $q$-deformed logistic map and the regions where the dynamic is complex through…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…
We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of…
Suppose a residually finite group $G$ acts cocompactly on a contractible complex with strict fundamental domain $Q$, where the stabilizers are either trivial or have normal $\mathbb{Z}$-subgroups. Let $\partial Q$ be the subcomplex of $Q$…
In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they…
In statistical physics, entropy is generally logarithm of probability. Therefore, if dynamics is decomposed by log, entropy production should be decomposed properly. In the present work, log-decomposition of dynamics is introduced. By which…
This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part…
We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
In this communication, one shows that there exists in the literature a certain form of deformed derivative that can here be identified as the dual of conformable derivative. The deformed subtraction is used here, together with the duality…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla…
Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.