Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X...Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.展开更多
The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special...The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.展开更多
In the field of aerospace, theodolite system is often used in the inspection of large object. A new measurement system that consists of four theodolites is presented in this paper, with which the "blind" pro...In the field of aerospace, theodolite system is often used in the inspection of large object. A new measurement system that consists of four theodolites is presented in this paper, with which the "blind" problem raised in Original dual-theodolite system can be overcome. The principle of multi-theodolite system, together with the mathematicalmodel (both of calibration and of measurement) is given. And also the calibration process is discussed.展开更多
Continuous flow intersections (CFIs), also known as displaced left turns (DLTs), are a type of alternative intersection designed to improve operations at locations with heavy left-turn movements by reallocating these ...Continuous flow intersections (CFIs), also known as displaced left turns (DLTs), are a type of alternative intersection designed to improve operations at locations with heavy left-turn movements by reallocating these vehicles to the left side of opposing traffic. Currently, simulation is commonly used to evaluate operational performance of CFIs. However, this approach requires significant on-site data collection and is highly dependent on the analyst’s ability to correctly model the intersection and driver behavior. Recently, connected vehicle (CV) trajectory data has become widely available and presents opportunities for the direct measurement of traffic signal performance measures. This study utilizes CV trajectory data to analyze the performance of a CFI located in West Valley City, UT. Over 4500 trajectories and 105,000 GPS points are analyzed from August 2021 weekday data. Trajectories are linear-referenced to generate Purdue Probe Diagrams (PPDs) and extended PPDs to estimate split failures (SF), arrivals on green (AOG), traditional Highway Capacity Manual (HCM) level of service (LOS), and the distribution of stops. The estimated operational performance showed effective progression during the PM peak period at all the critical internal storage areas with AOG levels at exit traffic signals between 83% and 100%. In contrast, all external approaches with longer queue storage areas had AOG values ranging from 2% to 81% during the same time period. The presented analytical techniques and summary graphics provide practitioners with tools to evaluate the performance of any CFI where CV trajectories are available without the need for on-site data collection.展开更多
A dual-CCD simulating human eyes and neck (DSHEN) vision system is putforward. Its structure and principle are introduced. The DSREN vision system can perform somemovements simulating human eyes and neck by means of f...A dual-CCD simulating human eyes and neck (DSHEN) vision system is putforward. Its structure and principle are introduced. The DSREN vision system can perform somemovements simulating human eyes and neck by means of four rotating joints, and realize preciseobject recognizing and distance measuring in all orientations. The mathematic model of the DSHENvision system is built, and its movement equation is solved. The coordinate error and measureprecision affected by the movement parameters are analyzed by means of intersection measuringmethod. So a theoretic foundation for further research on automatic object recognizing and precisetarget tracking is provided.展开更多
In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give i...In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give its fractal characterization. We find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from translating the vector （x,y） with its radix expansion.展开更多
基金supported by the National Natural Science Foundation of China(12371150,11971432)the Natural Science Foundation of Zhejiang Province(LY21G010003)+2 种基金the Management Project of"Digital+"Discipline Construction of Zhejiang Gongshang University(SZJ2022A012,SZJ2022B017)the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)the Scientific Research Projects of Universities in Anhui Province(2022AH050955)。
文摘Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.
基金supported by Shanghai Pujiang Program (No.2019PJC062)the Natural Science Foundation of Shandong Province (No.ZR2021MG003)the Research Project on Undergraduate Teaching Reform of Higher Education in Shandong Province (No.Z2021046).
文摘The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.
文摘In the field of aerospace, theodolite system is often used in the inspection of large object. A new measurement system that consists of four theodolites is presented in this paper, with which the "blind" problem raised in Original dual-theodolite system can be overcome. The principle of multi-theodolite system, together with the mathematicalmodel (both of calibration and of measurement) is given. And also the calibration process is discussed.
基金Supported by National Natural Science Foundation of China （60874063） and Innovation and Scientific Research Foundation of Graduate Student of Heilongjiang Province （YJSCX2012-263HLJ）
文摘Continuous flow intersections (CFIs), also known as displaced left turns (DLTs), are a type of alternative intersection designed to improve operations at locations with heavy left-turn movements by reallocating these vehicles to the left side of opposing traffic. Currently, simulation is commonly used to evaluate operational performance of CFIs. However, this approach requires significant on-site data collection and is highly dependent on the analyst’s ability to correctly model the intersection and driver behavior. Recently, connected vehicle (CV) trajectory data has become widely available and presents opportunities for the direct measurement of traffic signal performance measures. This study utilizes CV trajectory data to analyze the performance of a CFI located in West Valley City, UT. Over 4500 trajectories and 105,000 GPS points are analyzed from August 2021 weekday data. Trajectories are linear-referenced to generate Purdue Probe Diagrams (PPDs) and extended PPDs to estimate split failures (SF), arrivals on green (AOG), traditional Highway Capacity Manual (HCM) level of service (LOS), and the distribution of stops. The estimated operational performance showed effective progression during the PM peak period at all the critical internal storage areas with AOG levels at exit traffic signals between 83% and 100%. In contrast, all external approaches with longer queue storage areas had AOG values ranging from 2% to 81% during the same time period. The presented analytical techniques and summary graphics provide practitioners with tools to evaluate the performance of any CFI where CV trajectories are available without the need for on-site data collection.
基金Aerospace Technology Support Foundation (No.HT2001-zjdx)Science and Technology Development Project of Hangzhou City(No.2001121C42)
文摘A dual-CCD simulating human eyes and neck (DSHEN) vision system is putforward. Its structure and principle are introduced. The DSREN vision system can perform somemovements simulating human eyes and neck by means of four rotating joints, and realize preciseobject recognizing and distance measuring in all orientations. The mathematic model of the DSHENvision system is built, and its movement equation is solved. The coordinate error and measureprecision affected by the movement parameters are analyzed by means of intersection measuringmethod. So a theoretic foundation for further research on automatic object recognizing and precisetarget tracking is provided.
基金Supported by the National Science Foundation of China (10671180) and Jiangsu University (05JDG041)
文摘In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give its fractal characterization. We find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from translating the vector （x,y） with its radix expansion.
