相关论文: Some recent developments in quantization of fracta…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory,…
We generalize results of Fan and Zhang [6] on absolute continuity and singularity of the golden Markov geometric series to nonuniform stochastic series given by arbitrary Markov process. In addition we describe an application of these…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental testing process. Recently, there have been some attempts to analyze the…
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…
We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…
We survey recent developments in fractal analysis of regular and slow-fast dynamical systems using Minkowski dimension. Our focus is on spiral trajectories near monodromic limit periodic sets in regular systems and entry-exit sequences in…
In this article, the so-called "Nystr\"om method" is tested to compute optimal quantizers of Gaussian processes. In particular, we derive the optimal quantization of the fractional Brownian motion by approximating the first terms of its…
The objective of this study is to better understand the influence of fractures on the possibility of free convection in porous media. To this aim, we introduce a mathematical model for density driven flow in the presence of fractures, and…
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
In quantum metrology, entangled states of many-particle systems are investigated to enhance measurement precision of the most precise clocks and field sensors. While single-parameter quantum metrology is well established, many metrological…
We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear…
This article introduces a concept and measure of graph compartmentalization. This new measure allows for principled comparison between graphs of arbitrary structure, unlike existing measures such as graph modularity. The proposed measure is…
In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy…
We compute a minimum degree threshold sufficient for 3-partite graphs to admit a fractional triangle decomposition. Together with recent work of Barber, K\"uhn, Lo, Osthus and Taylor, this leads to bounds for exact decompositions and in…
In this paper, random and stochastic processes are defined on fractal curves. Fractal calculus is used to define cumulative distribution function, probability density function, moments, variance and correlation function of stochastic…