Related papers: The q-Diode
The main purpose of this paper is to present a systemic study of some families of multiple $q$-Euler numbers and polynomials. In particular, by using the $q$-Volkenborn integration on $\Bbb Z_p$, we construct $p$-adic $q$-Euler numbers and…
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We…
We demonstrate electromagnetic interaction between distant quantum dots (QDs), as is observed from transient pump-probe differential reflectivity measurements. The QD-exciton lifetime is measured as a function of the probe photon energy and…
In this paper, we expand functions of specific $q$-exponential growth in terms of its even (odd) Askey- Wilson $q$-derivatives at $0$ and $\eta=(q^{1/4}+q^{-1/4})/2$. This expansion is a $q$-version of the celebrated Lidstone expansion…
The modified q-Bessel functions and the q-Bessel-Macdonald functions of the first and second kind are introduced. Their definition is based on representations as power series. Recurrence relations, the q-Wronskians, asymptotic…
Using the q,p-deformed oscillators as basic generating system, we obtain diverse classes (which form distinct sectors of functional continua) of novel versions of q-deformed oscillators, all of which share the property of "accidental"…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
We show that the two complementary parts of the dynamics associated to the Feigenbaum attractor, inside and towards the attractor, form together a q -deformed statistical-mechanical structure. A time-dependent partition function produced by…
Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a…
In this paper, we develop a new deformation and generalization of the Natural integral transform based on the conformable fractional $q$-derivative. We obtain transformation of some deformed functions and apply the transform for solving…
We develop a non-extensive thermodynamic formalism for the one-sided shift on a finite alphabet, inspired by Tsallis' generalization of Boltzmann entropy in statistical physics. We introduce notions of $q$-entropy, $q$-pressure, and…
Let $(a)_\infty = (a; q)_\infty = \prod_{n=0}^\infty (1-aq^n)$. An elegant result of Bloch and Okounkov [BO] states that if $x = e^z$, then $$ \frac{(xq)_\infty (x^{-1}q)_\infty}{(q)_\infty^2}, $$ which appears in various traces in…
We introduce four q-analogs of the double Laplace transform and prove some of their main properties. Next we show how they can be used to solve some q-functional equations and partial q-differential equations.
We study the possibility to use frequency dependent damping in RSFQ circuits as means to reduce dissipation and consequent decoherence in RSFQ/qubit circuits. We show that stable RSFQ operation can be achieved by shunting the Josephson…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.
We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are…
This paper describes an analytical evaluation of the quality factor Qz in a separable system in which the vector potential is known. The proposed method uses a potential definition of active and reactive power, implicitly avoiding infinite…
Previous work in hierarchical reinforcement learning has faced a dilemma: either ignore the values of different possible exit states from a subroutine, thereby risking suboptimal behavior, or represent those values explicitly thereby…
We explore a general diagrammatic framework to understand qudits and their braiding, especially in its relation to entanglement. This involves understanding the role of isotopy in interpreting diagrams that implement entangling gates as…
There exists a well-known relation between the zeros of sine function, Bernoulli numbers and the Riemann Zeta function. In the present paper, we find a similar relation for zeros of q-sine function. We introduce a new q-extension of the…