Related papers: Generalization of multifractal theory within quant…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
The probability density functions measured by Lewis and Swinney for turbulent Couette-Taylor flow, observed by Bodenschatz and co-workers in the Lagrangian measurement of particle accelerations and those obtained in the DNS by Gotoh et al.…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual…
We address the deformation quantization of generally parametrized systems displaying a natural time variable. The purpose of this exercise is twofold: first, to illustrate through a pedagogical example the potential of quantum phase space…
We introduce a $q$-deformation that generalises in a single framework previous works on classical and enriched $P$-partitions. In particular, we build a new family of power series with a parameter $q$ that interpolates between Gessel's…
In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized Fox--Wright function and the generalized M-series and…
Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
The generalized quantal distribution functions are investigated concerning systems of non-interacting bosons and fermions. The formulae for the number of particles and energy are presented and applications to the Chandrasekhar limit of…
Let $x \in [0,1)$ be a real number and denote its continued fraction expansion by $[a_1(x),a_2(x), a_3(x),\cdots]$. The convergence exponent of these partial quotients is defined as \[ \tau(x):= \inf\left\{s \geq 0: \sum_{n \geq 1}…
For a Borel measure and a sequence of partitions on the unit interval, we define a multifractal spectrum based on coarse Holder regularity. Specifically, the coarse Holder regularity values attained by a given measure and with respect to a…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The…
We consider KdV currents in a quantum field theory obtained by deforming a two dimensional conformal field theory on a cylinder via the irrelevant operator $T{\bar T}$. In this paper we determine their one-point functions modular…
Macroscopic systems often display phase transitions where certain physical quantities are singular or self-similar at different (spatial) scales. Such properties of systems are currently characterized by some order parameters and a few…
The wave functions of quantum Calogero-Sutherland systems for trigonometric case are related to polynomials in l variables (l is a rank of root system) and they are the generalization of Gegenbauer polynomials and Jack polynomials. Using…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…