Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method...Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method of the valid/invalid item is developed on the relation between reachability matrix and valid items. And valid items are explained from the perspective of graph theory. An incremental augment algorithm for constructing Qr matrix is proposed based on the idea of incremental forward regression, and its validity is theoretically considered. Results of empirical tests are given in order to compare the performance of the incremental augment algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms the Tatsuoka algorithm, and the analysis of the two algorithms also show linear growth with respect to the number of valid items. Mathematical models with 10 attributes are built for the two algorithms by the linear regression analysis.展开更多
With respect to the gamma spectrum, the energy resolution improves with increase in energy. The counts of full energy peak change with energy, and this approximately complies with the Gaussian distribution. This study...With respect to the gamma spectrum, the energy resolution improves with increase in energy. The counts of full energy peak change with energy, and this approximately complies with the Gaussian distribution. This study mainly examines a method to deconvolve the LaBr_3:Ce gamma spectrum with a detector response matrix constructing algorithm based on energy resolution calibration.In the algorithm, the full width at half maximum(FWHM)of full energy peak was calculated by the cubic spline interpolation algorithm and calibrated by a square root of a quadratic function that changes with the energy. Additionally, the detector response matrix was constructed to deconvolve the gamma spectrum. Furthermore, an improved SNIP algorithm was proposed to eliminate the background. In the experiment, several independent peaks of ^(152)Eu,^(137)Cs, and ^(60)Co sources were detected by a LaBr_3:Ce scintillator that were selected to calibrate the energy resolution. The Boosted Gold algorithm was applied to deconvolve the gamma spectrum. The results showed that the peak position difference between the experiment and the deconvolution was within ± 2 channels and the relative error of peak area was approximately within 0.96–6.74%. Finally, a ^(133) Ba spectrum was deconvolved to verify the efficiency and accuracy of the algorithm in unfolding the overlapped peaks.展开更多
Consistency test of the judgment matrix is an essential step in the aplication of Analytic Hierarchy Process (AHP). This thesis presents an algerithm concerning the adjustment of a judgment matrix when it failed to pa...Consistency test of the judgment matrix is an essential step in the aplication of Analytic Hierarchy Process (AHP). This thesis presents an algerithm concerning the adjustment of a judgment matrix when it failed to pass the consistency test.展开更多
K-means algorithm is one of the most widely used algorithms in the clustering analysis. To deal with the problem caused by the random selection of initial center points in the traditional al- gorithm, this paper propo...K-means algorithm is one of the most widely used algorithms in the clustering analysis. To deal with the problem caused by the random selection of initial center points in the traditional al- gorithm, this paper proposes an improved K-means algorithm based on the similarity matrix. The im- proved algorithm can effectively avoid the random selection of initial center points, therefore it can provide effective initial points for clustering process, and reduce the fluctuation of clustering results which are resulted from initial points selections, thus a better clustering quality can be obtained. The experimental results also show that the F-measure of the improved K-means algorithm has been greatly improved and the clustering results are more stable.展开更多
Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quant...Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.展开更多
An adaptive method for the solution of compressible flows is described. The idea results from the desire for an efficient grid system,and an accurate and robust solution method are used to resolve flow features of the...An adaptive method for the solution of compressible flows is described. The idea results from the desire for an efficient grid system,and an accurate and robust solution method are used to resolve flow features of the interest. The adaptation flow solution is proposed,including the detection of flow features based on the matrix error; the mesh adaptation using the mesh movement,the mesh refinement,the mesh coarsening,and their combination. The feature detection based on the matrix error can maintain the high resolution property for shock waves of the one-dimensional approximate Riemann solver and the higher order reconstruction scheme. The high grid efficiency is obtained with the anisotropically directional grid corresponding to feature directions,and the error of the flow-field is averaged. The procedure and its application to flow solutions of shock waves are described. Results validate that the method is reliable.展开更多
A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the enco...A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.展开更多
A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock...A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock absorption for a ship's tail shaft.A mathematic model of tail shaft flexural vibrations was built using the transfer matrix method.The nature frequency of flexural vibration for an electrically propelled ship's tail shaft was then analyzed,and an effective method for calculating it was proposed:a genetic algorithm(GA),which calculates the nature frequency of vibration of a system.Sample calculations,with comparisons by the Prohl method under conditions bearing isotropic support,showed this method to be practical.It should have significant impact on engineering design theory.展开更多
In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reco...In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.展开更多
There has been a growing interest in mathematical models to character the evolutionary algorithms. The best-known one of such models is the axiomatic model colled the abstract evolutionary algorithm. In this paper, we...There has been a growing interest in mathematical models to character the evolutionary algorithms. The best-known one of such models is the axiomatic model colled the abstract evolutionary algorithm. In this paper, we first introduce the definitions of the abhstract selection and evolution operators, and that of the abstract evolutionary algorithm, which describes the evolution as an abstract stochastic process composed of these two fundamental abstract operators. In particular, a kind of abstract evolutionary algorithms based on a special selection mechansim is discussed. According to the sorting for the state space, the properties of the single step transition matrix for the algorithm are anaylzed. In the end, we prove that the limit probability distribution of the Markov chains exists. The present work provides a big step toward the establishment of a unified theory of evolutionary computation.展开更多
基金Supported by the National Natural Science Foundation of China (30860084,60673014,60263005)the Backbone Young Teachers Foundation of Fujian Normal University(2008100244)the Department of Education Foundation of Fujian Province (ZA09047)~~
文摘Reduced Q-matrix （Qr matrix） plays an important role in the rule space model （RSM） and the attribute hierarchy method （AHM）. Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method of the valid/invalid item is developed on the relation between reachability matrix and valid items. And valid items are explained from the perspective of graph theory. An incremental augment algorithm for constructing Qr matrix is proposed based on the idea of incremental forward regression, and its validity is theoretically considered. Results of empirical tests are given in order to compare the performance of the incremental augment algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms the Tatsuoka algorithm, and the analysis of the two algorithms also show linear growth with respect to the number of valid items. Mathematical models with 10 attributes are built for the two algorithms by the linear regression analysis.
基金supported by the National Natural Science Foundation of China(Nos.41374130 and 41604154)
文摘With respect to the gamma spectrum, the energy resolution improves with increase in energy. The counts of full energy peak change with energy, and this approximately complies with the Gaussian distribution. This study mainly examines a method to deconvolve the LaBr_3:Ce gamma spectrum with a detector response matrix constructing algorithm based on energy resolution calibration.In the algorithm, the full width at half maximum(FWHM)of full energy peak was calculated by the cubic spline interpolation algorithm and calibrated by a square root of a quadratic function that changes with the energy. Additionally, the detector response matrix was constructed to deconvolve the gamma spectrum. Furthermore, an improved SNIP algorithm was proposed to eliminate the background. In the experiment, several independent peaks of ^(152)Eu,^(137)Cs, and ^(60)Co sources were detected by a LaBr_3:Ce scintillator that were selected to calibrate the energy resolution. The Boosted Gold algorithm was applied to deconvolve the gamma spectrum. The results showed that the peak position difference between the experiment and the deconvolution was within ± 2 channels and the relative error of peak area was approximately within 0.96–6.74%. Finally, a ^(133) Ba spectrum was deconvolved to verify the efficiency and accuracy of the algorithm in unfolding the overlapped peaks.
文摘Consistency test of the judgment matrix is an essential step in the aplication of Analytic Hierarchy Process (AHP). This thesis presents an algerithm concerning the adjustment of a judgment matrix when it failed to pass the consistency test.
文摘K-means algorithm is one of the most widely used algorithms in the clustering analysis. To deal with the problem caused by the random selection of initial center points in the traditional al- gorithm, this paper proposes an improved K-means algorithm based on the similarity matrix. The im- proved algorithm can effectively avoid the random selection of initial center points, therefore it can provide effective initial points for clustering process, and reduce the fluctuation of clustering results which are resulted from initial points selections, thus a better clustering quality can be obtained. The experimental results also show that the F-measure of the improved K-means algorithm has been greatly improved and the clustering results are more stable.
基金supported by the National Natural Science Foundation of China(Grant Nos.62071015 and 62171264)。
文摘Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.
文摘An adaptive method for the solution of compressible flows is described. The idea results from the desire for an efficient grid system,and an accurate and robust solution method are used to resolve flow features of the interest. The adaptation flow solution is proposed,including the detection of flow features based on the matrix error; the mesh adaptation using the mesh movement,the mesh refinement,the mesh coarsening,and their combination. The feature detection based on the matrix error can maintain the high resolution property for shock waves of the one-dimensional approximate Riemann solver and the higher order reconstruction scheme. The high grid efficiency is obtained with the anisotropically directional grid corresponding to feature directions,and the error of the flow-field is averaged. The procedure and its application to flow solutions of shock waves are described. Results validate that the method is reliable.
文摘A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.
基金the National Natural Science Foundation under Grant No.50675162
文摘A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock absorption for a ship's tail shaft.A mathematic model of tail shaft flexural vibrations was built using the transfer matrix method.The nature frequency of flexural vibration for an electrically propelled ship's tail shaft was then analyzed,and an effective method for calculating it was proposed:a genetic algorithm(GA),which calculates the nature frequency of vibration of a system.Sample calculations,with comparisons by the Prohl method under conditions bearing isotropic support,showed this method to be practical.It should have significant impact on engineering design theory.
基金supported by the National Natural Science Foundation of China (10971083, 10801063)the School of Mathematical Sciences Foundation of Jilin University
文摘In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.
基金Supported by the National Science Foundation of China(60133010)Supported by the Science Foundation of Henan Province(2000110019)
文摘There has been a growing interest in mathematical models to character the evolutionary algorithms. The best-known one of such models is the axiomatic model colled the abstract evolutionary algorithm. In this paper, we first introduce the definitions of the abhstract selection and evolution operators, and that of the abstract evolutionary algorithm, which describes the evolution as an abstract stochastic process composed of these two fundamental abstract operators. In particular, a kind of abstract evolutionary algorithms based on a special selection mechansim is discussed. According to the sorting for the state space, the properties of the single step transition matrix for the algorithm are anaylzed. In the end, we prove that the limit probability distribution of the Markov chains exists. The present work provides a big step toward the establishment of a unified theory of evolutionary computation.
