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THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET 被引量:2
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作者 胡迪鹤 张晓敏 《Acta Mathematica Scientia》 SCIE CSCD 2007年第2期267-273,共7页
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
关键词 random sub-self-similar set random shift set Hausdorff dimension exact Hausdorff measure function Hausdorff metric
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THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS 被引量:2
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作者 ZhangXiaoqun LiuYanyan 《Acta Mathematica Scientia》 SCIE CSCD 2004年第3期485-492,共8页
A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..
关键词 random graph-directed self-similar set Hausdorff dimension box-counting dimension REGULAR
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THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET 被引量:1
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作者 胡迪鹤 张晓敏 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期561-573,共13页
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.
关键词 random sub-self-similar set random shift set Hausdorff dimension exact Hausdorff measure function Hausdorff metric
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A NEGATIVE ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS WITH OPEN SET CONDITION 被引量:5
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作者 Jiandong Yin 《Analysis in Theory and Applications》 2009年第2期182-200,共19页
Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answ... Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture. 展开更多
关键词 self-similar set best covering natural covering Hausdorff measure
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AN ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS 被引量:4
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作者 Baoguo Jia Shaoyuan Xu 《Analysis in Theory and Applications》 2007年第1期9-15,共7页
In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.
关键词 self-similar set best covering natural covering Hausdorff measure
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Passive target tracking with intermittent measurement based on random finite set 被引量:4
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作者 罗小波 范红旗 +1 位作者 宋志勇 付强 《Journal of Central South University》 SCIE EI CAS 2014年第6期2282-2291,共10页
In the tracking problem for the maritime radiation source by a passive sensor,there are three main difficulties,i.e.,the poor observability of the radiation source,the detection uncertainty(false and missed detections... In the tracking problem for the maritime radiation source by a passive sensor,there are three main difficulties,i.e.,the poor observability of the radiation source,the detection uncertainty(false and missed detections)and the uncertainty of the target appearing/disappearing in the field of view.These difficulties can make the establishment or maintenance of the radiation source target track invalid.By incorporating the elevation information of the passive sensor into the automatic bearings-only tracking(BOT)and consolidating these uncertainties under the framework of random finite set(RFS),a novel approach for tracking maritime radiation source target with intermittent measurement was proposed.Under the RFS framework,the target state was represented as a set that can take on either an empty set or a singleton; meanwhile,the measurement uncertainty was modeled as a Bernoulli random finite set.Moreover,the elevation information of the sensor platform was introduced to ensure observability of passive measurements and obtain the unique target localization.Simulation experiments verify the validity of the proposed approach for tracking maritime radiation source and demonstrate the superiority of the proposed approach in comparison with the traditional integrated probabilistic data association(IPDA)method.The tracking performance under different conditions,particularly involving different existence probabilities and different appearance durations of the target,indicates that the method to solve our problem is robust and effective. 展开更多
关键词 passive target tracking maritime target joint detection and tracking intermittent measurement random finite set poor observability
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FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES 被引量:1
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作者 陈振龙 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期969-992,共24页
This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary condition... This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity. 展开更多
关键词 random string process hitting probability polar set Hausdorff dimension
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Multiple-model Bayesian filtering with random finite set observation 被引量:1
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作者 Wei Yang Yaowen Fu Xiang Li 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第3期364-371,共8页
The finite set statistics provides a mathematically rig- orous single target Bayesian filter (STBF) for tracking a target that generates multiple measurements in a cluttered environment. However, the target maneuver... The finite set statistics provides a mathematically rig- orous single target Bayesian filter (STBF) for tracking a target that generates multiple measurements in a cluttered environment. However, the target maneuvers may lead to the degraded track- ing performance and even track loss when using the STBF. The multiple-model technique has been generally considered as the mainstream approach to maneuvering the target tracking. Moti- vated by the above observations, we propose the multiple-model extension of the original STBF, called MM-STBF, to accommodate the possible target maneuvering behavior. Since the derived MM- STBF involve multiple integrals with no closed form in general, a sequential Monte Carlo implementation (for generic models) and a Gaussian mixture implementation (for linear Gaussian models) are presented. Simulation results show that the proposed MM-STBF outperforms the STBF in terms of root mean squared errors of dynamic state estimates. 展开更多
关键词 finite set statistic (FISST) random finite set multiple- model technique maneuvering target tracking.
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ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION 被引量:2
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作者 Shaoyuan Xu Weiyi Su Zuoling Zhou 《Analysis in Theory and Applications》 2008年第1期93-100,共8页
In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition (OSC). As applications, we discuss a self-simila... In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition (OSC). As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure. 展开更多
关键词 self-similar set Hausdorff measure and Hausdorff dimension open set condition
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RANDOM SETS: A UNIFIED FRAMEWORK FOR MULTISOURCE INFORMATION FUSION 被引量:3
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作者 Xu Xiaobin Wen Chenglin 《Journal of Electronics(China)》 2009年第6期723-730,共8页
The more diverse the ways and means of information acquisition are,the more complex and various the types of information are. The qualities of available information are usually uncertain,vague,imprecise,incomplete,and... The more diverse the ways and means of information acquisition are,the more complex and various the types of information are. The qualities of available information are usually uncertain,vague,imprecise,incomplete,and so on. However,the information is modeled and fused traditionally in particular,name some of the known theories: evidential,fuzzy sets,possibilistic,rough sets or conditional events,etc. For several years,researchers have explored the unification of theories enabling the fusion of multisource information and have finally considered random set theory as a powerful mathematical tool. This paper attempts to overall review the close relationships between random set theory and other theories,and introduce recent research results which present how different types of information can be dealt with in this unified framework. Finally,some possible future directions are discussed. 展开更多
关键词 Multisource information fusion random set theory Imperfect information
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A NEW METHOD FOR CONSTRUCTING FUZZY EVIDENCE BASED ON THE NON-CONSONANT RANDOM SET 被引量:2
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作者 Xu Xiaobin Wen Chenglin Li Zhiliang 《Journal of Electronics(China)》 2009年第1期31-37,共7页
Natural-language information is often mathematically expressed by fuzzy sets. With the random set theory as a bridge, this kind of information can be transformed into fuzzy evidence in Dempster-Shafer (DS) theory. The... Natural-language information is often mathematically expressed by fuzzy sets. With the random set theory as a bridge, this kind of information can be transformed into fuzzy evidence in Dempster-Shafer (DS) theory. Then Dempster's combination rule or other combination rules of evi- dence can be used perfectly for fusing natural-language and other information. However, this traditional transformation involves the use of α -cutsets to construct the focal elements which have to be repre- sented as consonant sets. This construction is very inflexible and unreasonable in some practical ap- plications. In this paper, with the desire to overcome this limitation, a method for constructing more general non-consonant focal elements is proposed based on the random set theory. Some examples are given to show the generality and the efficiency of this new method. Finally, we validate that non-consonant constructions provide less degrees of total uncertainty than that of the consonant case in these examples by using the evaluation criterion of total uncertainty. 展开更多
关键词 random set theory Fuzzy set Dempster-Shafer (DS) theory Target recognition
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THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET 被引量:1
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作者 胡迪鹤 《Acta Mathematica Scientia》 SCIE CSCD 2003年第2期201-207,共7页
The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} ... The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer. 展开更多
关键词 a.s. self-similar set Hausdorff metric fixed point STRUCTURE APPROXIMATION
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The Structure and the Sufficent and Necessary Conditions for Generalized Statistically Self-Similar Sets 被引量:1
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作者 DENG Ai-jiao HU Di-he (College of Mathematics and Computer Science,Wuhan University,Wuhan 430072,China) 《Wuhan University Journal of Natural Sciences》 CAS 2000年第1期13-21,共9页
We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statist... We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours. 展开更多
关键词 statistically recursive set generalized statistically self-similar set Hausdorff metric
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A NEW APPROACH OF SIMULTANEOUS FAULTS DIAGNOSIS BASED ON RANDOM SETS AND DSMT 被引量:2
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作者 Li Zhiliang Xu Xiaobin Wen Chenglin 《Journal of Electronics(China)》 2009年第1期24-30,共7页
Simultaneous faults often occur in running equipments, in order to solve the problems of the simultaneous faults, a new approach based on random sets and Dezert-Smarandache Theory (DSmT) is proposed in this paper. Fir... Simultaneous faults often occur in running equipments, in order to solve the problems of the simultaneous faults, a new approach based on random sets and Dezert-Smarandache Theory (DSmT) is proposed in this paper. Firstly, the simultaneous faults' model is built based on the generalized frame of discernment in DSmT. Secondly, according to the unified description of combination rules in evidence reasoning based on random sets, a new combination rule for simultaneous faults diagnosis is proposed. Thirdly, according to the working characteristics and environment of the sensors used to acquire fault characteristic information, a new method to construct basic probability assignment function is pro- posed based on membership. Finally, diagnosis result is obtained by use of the new combination rule combined with decision rules. A case pertaining to the fault diagnosis for a multi-function rotor test-bed is given, and the result shows that the proposed diagnosis approach is feasible and efficient. 展开更多
关键词 random sets Dezert-Smarandache Theory (DSmT) Basic probability assignment Simultaneous fault DIAGNOSIS
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Memory Function and Fractional Intergral Associated to the Random Self-similar Fractal 被引量:1
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作者 LIANG Hong-liang,LIU Xiao-shu(Department of Mathematics, Shangqiu Teacher’s College, Shangqiu 476000, China) 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第2期186-191,共6页
For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fracti... For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al. 展开更多
关键词 random self-similar fractals memory functions memory measures Laplace transform
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ANALYSIS OF CIRCUIT TOLERANCE BASED ON RANDOM SET THEORY 被引量:1
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作者 Xu Xiaobin Wen Chenglin 《Journal of Electronics(China)》 2008年第6期852-859,共8页
Monte Carlo Analysis has been an accepted method for circuit tolerance analysis, but the heavy computational complexity has always prevented its applications. Based on random set theory, this paper presents a simple a... Monte Carlo Analysis has been an accepted method for circuit tolerance analysis, but the heavy computational complexity has always prevented its applications. Based on random set theory, this paper presents a simple and flexible tolerance analysis method to estimate circuit yield. It is the alternative to Monte Carlo analysis, but reduces the number of calculations dramatically. 展开更多
关键词 random set theory Evidence theory Tolerance analysis Monte Carlo analysis Circuit yield
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The Advances of the Research for Random Recursive Sets(Ⅰ)
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作者 HU Di\|he (College of Mathematics and Computer Science, Wuhan University,Wuhan 430072, China) 《Wuhan University Journal of Natural Sciences》 CAS 1999年第4期381-381,共1页
We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson construct... We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\; 展开更多
关键词 random recursive set statistically self\|similar set Hausdorff dimension exact measure function
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Nonlinear Random Motion Analysis of A Tension Leg Platform Consider- ing the Set-down Motion of A Floating Body 被引量:2
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作者 WANG Bin 《China Ocean Engineering》 SCIE EI CSCD 2017年第2期210-219,共10页
The dynamic analysis of a Tension Leg Platform (TLP) in random wave is investigated by considering the set-down of a floating body. The nonlinear restoring stiffness is derived with the set-down motion of a floating... The dynamic analysis of a Tension Leg Platform (TLP) in random wave is investigated by considering the set-down of a floating body. The nonlinear restoring stiffness is derived with the set-down motion of a floating body and the coupled motion of the tension leg and platform and the differential equations of the motion are established. The study focuses on the influence of the set-down motion on the nonlinear response of the platform. By considering different significant wave heights and currents, motion responses of the platform are calculated and compared. The analysis shows that the set-down motion significantly increases the heave motion with low frequency and the equilibrium position of the heave motion with the set-down motion is much lower than that without set-down motion. The results in this paper indicate that the set-down motion has a major impact on the safety of the platform inproduction operation, and it is also a threat to the strength of tension legs and risers. 展开更多
关键词 Tension Leg Platform (TLP) set-down NONLINEAR restoring stiffness random wave coupled motion
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The Fractal Structures of the Sample Path of a General Subordinator and the Random Re-orderings of the Cantor Set
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作者 Hu Xiaoyu Institute of Applied Mathematics, Chinese Academy of Science, Beijing 100080,China Department of Mathematics, Central China Normal University, Wuhan 430070, China 《Wuhan University Journal of Natural Sciences》 CAS 1997年第1期27-31,共5页
In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure... In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure. 展开更多
关键词 Hausdorff measure packing measure SUBORDINATOR random re ordering of the Cantor set
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FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS
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作者 余旌胡 范文涛 《Acta Mathematica Scientia》 SCIE CSCD 2000年第2期256-260,共5页
In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.
关键词 statistically self-similar set statistically self-similar measure dimension distribution contractive map
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