The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper...The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we present new iterative algorithms for solving the split common fixed point problem of demimetric mappings in Hilbert spaces. Moreover, our algorithm does not need any prior information of the operator norm. Weak and strong convergence theorems are given under some mild assumptions. The results in this paper are the extension and improvement of the recent results in the literature.展开更多
The Electromagnetic Compatibility (EMC) of direct current (DC) motor windings is a system model which is used to reflect the functional characters of the system in the whole EMC specified frequency (150 KHz ~ 30 MHz)....The Electromagnetic Compatibility (EMC) of direct current (DC) motor windings is a system model which is used to reflect the functional characters of the system in the whole EMC specified frequency (150 KHz ~ 30 MHz). For most motor designing process, it is always used to evaluate the inductance of windings in lower or working frequency;however, when analyzing the conducted interference, it is necessary to take some pa-rameters in high frequency into account in building up the EMC model, such as the noticeable capacitance distributed among the windings or between windings and shells. Past research neglected the common-mode current generated by the high frequency interference within motor bearings coupled with shells, since the parasitic capacitance of rotor core comes from armature windings supplied sufficient paths. In EMC model-ing process for DC motor problem, first, test the impedance of windings by experiments;then, generate the equivalent circuit with overall parameters. At present, it is a difficulty that how to choose the parameters. Most researchers preferred to adopt analytical calculation results, however, it could not reflect the essence of the model since it requires many simplification. Based on this point, this paper adopted ant colony algorithm (ACA) with positive feedback to intelligently search and globally optimize the parameters of equivalent cir-cuit. Simulation result showed that the impedance of equivalent circuit calculated by this algorithm was the same as experimental result in the whole EMC frequency. In order to further confirm the validity of ACA, PSPICE circuit simulation was implemented to simulate the spectrum of common mode Electromagnetic Interference (EMI) of equivalent circuit. The simulation result accords well with the experiment result re-ceived by EMI receiver. So it sufficiently demonstrated correctness of ACA in the analysis of high frequency equivalent circuit.展开更多
Cooperative spectrum monitoring with multiple sensors has been deemed as an efficient mechanism for improving the monitoring accuracy and enlarging the monitoring area in wireless sensor networks.However,there exists ...Cooperative spectrum monitoring with multiple sensors has been deemed as an efficient mechanism for improving the monitoring accuracy and enlarging the monitoring area in wireless sensor networks.However,there exists redundancy among the spectrum data collected by a sensor node within a data collection period,which may reduce the data uploading efficiency.In this paper,we investigate the inter-data commonality detection which describes how much two data have in common.We define common segment set and divide it into six categories firstly,then a method to measure a common segment set is conducted by extracting commonality between two files.Moreover,the existing algorithms fail in finding a good common segment set,so Common Data Measurement(CDM)algorithm that can identify a good common segment set based on inter-data commonality detection is proposed.Theoretical analysis proves that CDM algorithm achieves a good measurement for the commonality between two strings.In addition,we conduct an synthetic dataset which are produced randomly.Numerical results shows that CDM algorithm can get better performance in measuring commonality between two binary files compared with Greedy-String-Tiling(GST)algorithm and simple greedy algorithm.展开更多
Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing...Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing from 0 and taking steps of length equal to <em>x</em>. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for <em>x</em> and <em>y</em>, whenever <em>y</em>/<em>x</em> is a rational number. In the case that <em>y</em>/<em>x</em> is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.展开更多
Different from the extended Euclidean algorithm which can compute directly only the multiplicative inverse of an element in Zm^＊ and the greatest common divisor of two integers, a recursive algorithm called REESSE is...Different from the extended Euclidean algorithm which can compute directly only the multiplicative inverse of an element in Zm^＊ and the greatest common divisor of two integers, a recursive algorithm called REESSE is designed by the authors, which can not only seek directly the multiplicative inverse and the greatest common divisor, but also solve directly a simple congruence for general solutions. This paper presents the definition and the two valuable properties of a simple congruence, analyzes in detail the reduction and recursion process of solving simple congruences, induces the recursive formula for solving simple congruences, and describes formally and implements in C language the recursive algorithm. At last, the paper compares REESSE with the extended Euclidean algorithm in thought, applicability and time complexity.展开更多
文摘The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we present new iterative algorithms for solving the split common fixed point problem of demimetric mappings in Hilbert spaces. Moreover, our algorithm does not need any prior information of the operator norm. Weak and strong convergence theorems are given under some mild assumptions. The results in this paper are the extension and improvement of the recent results in the literature.
文摘The Electromagnetic Compatibility (EMC) of direct current (DC) motor windings is a system model which is used to reflect the functional characters of the system in the whole EMC specified frequency (150 KHz ~ 30 MHz). For most motor designing process, it is always used to evaluate the inductance of windings in lower or working frequency;however, when analyzing the conducted interference, it is necessary to take some pa-rameters in high frequency into account in building up the EMC model, such as the noticeable capacitance distributed among the windings or between windings and shells. Past research neglected the common-mode current generated by the high frequency interference within motor bearings coupled with shells, since the parasitic capacitance of rotor core comes from armature windings supplied sufficient paths. In EMC model-ing process for DC motor problem, first, test the impedance of windings by experiments;then, generate the equivalent circuit with overall parameters. At present, it is a difficulty that how to choose the parameters. Most researchers preferred to adopt analytical calculation results, however, it could not reflect the essence of the model since it requires many simplification. Based on this point, this paper adopted ant colony algorithm (ACA) with positive feedback to intelligently search and globally optimize the parameters of equivalent cir-cuit. Simulation result showed that the impedance of equivalent circuit calculated by this algorithm was the same as experimental result in the whole EMC frequency. In order to further confirm the validity of ACA, PSPICE circuit simulation was implemented to simulate the spectrum of common mode Electromagnetic Interference (EMI) of equivalent circuit. The simulation result accords well with the experiment result re-ceived by EMI receiver. So it sufficiently demonstrated correctness of ACA in the analysis of high frequency equivalent circuit.
基金supported in part by the National Natural Science Foundation of China(No.61901328)the China Postdoctoral Science Foundation (No. 2019M653558)+1 种基金the Fundamental Research Funds for the Central Universities (No. CJT150101)the Key project of National Natural Science Foundation of China (No. 61631015)
文摘Cooperative spectrum monitoring with multiple sensors has been deemed as an efficient mechanism for improving the monitoring accuracy and enlarging the monitoring area in wireless sensor networks.However,there exists redundancy among the spectrum data collected by a sensor node within a data collection period,which may reduce the data uploading efficiency.In this paper,we investigate the inter-data commonality detection which describes how much two data have in common.We define common segment set and divide it into six categories firstly,then a method to measure a common segment set is conducted by extracting commonality between two files.Moreover,the existing algorithms fail in finding a good common segment set,so Common Data Measurement(CDM)algorithm that can identify a good common segment set based on inter-data commonality detection is proposed.Theoretical analysis proves that CDM algorithm achieves a good measurement for the commonality between two strings.In addition,we conduct an synthetic dataset which are produced randomly.Numerical results shows that CDM algorithm can get better performance in measuring commonality between two binary files compared with Greedy-String-Tiling(GST)algorithm and simple greedy algorithm.
文摘Let <em>x</em> and <em>y</em> be two positive real numbers with <em>x</em> < <em>y</em>. Consider a traveler, on the interval [0, <em>y</em>/2], departing from 0 and taking steps of length equal to <em>x</em>. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for <em>x</em> and <em>y</em>, whenever <em>y</em>/<em>x</em> is a rational number. In the case that <em>y</em>/<em>x</em> is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.
基金Supported by the National Key Promotion Plan for Science and Technology Results (2003EC000001)
文摘Different from the extended Euclidean algorithm which can compute directly only the multiplicative inverse of an element in Zm^＊ and the greatest common divisor of two integers, a recursive algorithm called REESSE is designed by the authors, which can not only seek directly the multiplicative inverse and the greatest common divisor, but also solve directly a simple congruence for general solutions. This paper presents the definition and the two valuable properties of a simple congruence, analyzes in detail the reduction and recursion process of solving simple congruences, induces the recursive formula for solving simple congruences, and describes formally and implements in C language the recursive algorithm. At last, the paper compares REESSE with the extended Euclidean algorithm in thought, applicability and time complexity.
