First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction ...First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.展开更多
In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statisticall...We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statistically self similar sets as well.展开更多
The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have ...The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.展开更多
In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of a measure with t...In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of a measure with the property that its pushforward by the thinness function is a probability measure of truncated normal distribution. Finally, we improve this method to find a measure satisfying some important properties in geometric measure theory.展开更多
For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Ma...For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Max(CD) of CD with the relative Scott topology ishomeomorphic to the set of all Scott compact subsets of Max(D) with the topology induced bythe Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.展开更多
I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is the...I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.展开更多
基金Supported by the National Natural Science Foundation of China (10371092)the Foundation of Wuhan University
文摘First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.
基金supported by the National Natural Science Foundation of China(10371092)Foundation of Ningbo University(8Y0600036).
文摘In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
文摘We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statistically self similar sets as well.
基金The Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia has funded this project under Grant Number(G:220-247-1443).
文摘The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.
文摘In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of a measure with the property that its pushforward by the thinness function is a probability measure of truncated normal distribution. Finally, we improve this method to find a measure satisfying some important properties in geometric measure theory.
基金Project supported by the National Natural Science Foundation of Chian(No.19831040),the Doctoral Programme Foundation of the Ministry of Education of China(No.2000061019)and the 973 Project by the Science Commission of China.
文摘For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Max(CD) of CD with the relative Scott topology ishomeomorphic to the set of all Scott compact subsets of Max(D) with the topology induced bythe Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.
基金Project supported by the National Natural Science Foundation of China the Doctoral Progamme Foundation of China and the Foundation of Wuhan University.
文摘I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.
