Related papers: "Fractal Expression" in Chinese Calligraphy
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…
The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns with the mathematical form, defined in such a manner, were…
This letter is a comment on an article by T.C. Halsey and M.H. Jensen in Nature about using recurrence times as a reliable tool to estimate multifractal dimensions of strange attractors. Our aim is to emphasize that in the recent…
We prove the existence of fractal solutions to a class of linear ordinary differential equations.This reveals the possibility of chaos in the very short time limit of the evolution even of a linear one dimensional dynamical system.
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…
One hallmark of human language is its combinatoriality -- reusing a relatively small inventory of building blocks to create a far larger inventory of increasingly complex structures. In this paper, we explore the idea that combinatoriality…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a…
Crumpled paper or drapery patterns are everyday examples of how elastic sheets can respond to external forcing. In this Letter, we study experimentally a novel sort of forcing. We consider a circular flexible plate clamped at its center and…
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
The calculus of variations is a classical subject which has gain throughout the last three hundred years a level of rigor and elegance that only time can give. In this note we show that, contrary to the classical field, available…
The gravitational time advancement is a natural but a consequence of curve space-time geometry. In the present work the expressions of gravitational time advancement have been obtained for geodesic motions. The situation when the distance…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Linguistics holds unique characteristics of generality, stability, and nationality, which will affect the formulation of extraction strategies and should be incorporated into the relation extraction. Chinese open relation extraction is not…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
Causality has traditionally been a scientific way to generate knowledge by relating causes to effects. From an imaginery point of view, causal graphs are a helpful tool for representing and infering new causal information. In previous…
This paper is a sharp and focussed exploration of the Fibonacci substitution and the mathematical entity it gives rise to, the Fibonacci word. Our investigations are both of an algebraic and a geometric nature. Indeed, it is the combination…