To solve the extended fuzzy description logic with qualifying number restriction （EFALCQ） reasoning problems, EFALCQ is discretely simulated by description logic with qualifying number restriction （ALCQ）, and ALCQ...To solve the extended fuzzy description logic with qualifying number restriction （EFALCQ） reasoning problems, EFALCQ is discretely simulated by description logic with qualifying number restriction （ALCQ）, and ALCQ reasoning results are reused to prove the complexity of EFALCQ reasoning problems. The ALCQ simulation method for the consistency of EFALCQ is proposed. This method reduces EFALCQ satisfiability into EFALCQ consistency, and uses EFALCQ satisfiability to discretely simulate EFALCQ satdomain. It is proved that the reasoning complexity for EFALCQ satisfiability, consistency and sat-domain is PSPACE-complete.展开更多
In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and e...In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and evaluation. The procedure is essentially a multiple criteria decision-making problem. The traditional multiple criteria programming is not flexible enough in executing the system evaluation algorithm due to both the limited experimental data and the lack of human experiences. To make the CBR tool to be more efficient, a new method for the best choice among the feasible schemes based on the Fuzzy AHP using Fuzzy numbers （FFAHP） is proposed. Since the final results become a problem of ranking the mean of fuzzy numbers by the optimism of decision-maker using the FFAHP, its execution is much more intuitive and effective than with the traditional method.展开更多
A complex number mode analysis approach is proposed for vibration reducing of structural flexible redundant manipulators by utilizing self motion. In the proposed approach, the self motion is evaluated to nullify th...A complex number mode analysis approach is proposed for vibration reducing of structural flexible redundant manipulators by utilizing self motion. In the proposed approach, the self motion is evaluated to nullify the modal exciting force of flexural motion, and the approach can be freely used when the degree of freedom of flexural motion is much greater than the available degree of reundancy. The availability and effectiveness of the proposed approach are demonstrated through numerical simulation with a four link spatial robotic manipulator possessing an end flexible link.展开更多
In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and pr...In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.展开更多
This paper presents building one-parameter motion by complex numbers on a time scale. Firstly, we assumed that E and E′ were moving in a fixed time scale complex plane and {0, e1,e2} and {0', e'1,e'2} ?we...This paper presents building one-parameter motion by complex numbers on a time scale. Firstly, we assumed that E and E′ were moving in a fixed time scale complex plane and {0, e1,e2} and {0', e'1,e'2} ?were their orthonormal frames, respectively. By using complex numbers, we investigated the delta calculus equations of the motion on T. Secondly, we gave the velocities and their union rule on the time scale. Finally, by using the delta-derivative, we got interesting results and theorems for the instantaneous rotation pole and the pole curves (trajectory). In kinematics, investigating one-parameter motion by complex numbers is important for simplifying motion calculation. In this study, our aim is to obtain an equation of motion by using complex numbers on the time scale.展开更多
In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder...In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.展开更多
In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,...In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,non-dangerous male,and female.By mathematical analysis,we obtain the basic reproduction number for the existence of endemic equilibrium and study the effects of various immunization schemes about different groups.Furthermore,numerical simulations are undertaken to verify more conclusions.展开更多
The additives such as phosphoric acid, calcium phosphate, calcium super phosphate, calcium over super phosphate, calcium carbonate, sodium hydrosulphite, etc. were used to produce furfural from the straw by hydrolys...The additives such as phosphoric acid, calcium phosphate, calcium super phosphate, calcium over super phosphate, calcium carbonate, sodium hydrosulphite, etc. were used to produce furfural from the straw by hydrolysis with sulfuric acid. The effect of amount of the additives, the content of the added substance and the conditions of distillation on the acidity of the residues were studied. The experiment results showed that the all residues became neutral complex fertilizer, and the productivity of furfural increases under the following conditions: sulfuric acid concentration is 20% (by weight), the ratio of liquid to solid is 3∶1—4∶1 (by weight), the ratio of the additives to straw is suitable.展开更多
To extract features of fabric defects effectively and reduce dimension of feature space,a feature extraction method of fabric defects based on complex contourlet transform （CCT） and principal component analysis （PC...To extract features of fabric defects effectively and reduce dimension of feature space,a feature extraction method of fabric defects based on complex contourlet transform （CCT） and principal component analysis （PCA） is proposed.Firstly,training samples of fabric defect images are decomposed by CCT.Secondly,PCA is applied in the obtained low-frequency component and part of highfrequency components to get a lower dimensional feature space.Finally,components of testing samples obtained by CCT are projected onto the feature space where different types of fabric defects are distinguished by the minimum Euclidean distance method.A large number of experimental results show that,compared with PCA,the method combining wavdet low-frequency component with PCA （WLPCA）,the method combining contourlet transform with PCA （CPCA）,and the method combining wavelet low-frequency and highfrequency components with PCA （WPCA）,the proposed method can extract features of common fabric defect types effectively.The recognition rate is greatly improved while the dimension is reduced.展开更多
High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms...High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.展开更多
In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued n...In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.展开更多
基金The National Natural Science Foundation of China(No60403016)the Weaponry Equipment Foundation of PLA Equip-ment Ministry (No51406020105JB8103)
文摘To solve the extended fuzzy description logic with qualifying number restriction （EFALCQ） reasoning problems, EFALCQ is discretely simulated by description logic with qualifying number restriction （ALCQ）, and ALCQ reasoning results are reused to prove the complexity of EFALCQ reasoning problems. The ALCQ simulation method for the consistency of EFALCQ is proposed. This method reduces EFALCQ satisfiability into EFALCQ consistency, and uses EFALCQ satisfiability to discretely simulate EFALCQ satdomain. It is proved that the reasoning complexity for EFALCQ satisfiability, consistency and sat-domain is PSPACE-complete.
基金This project was partly supported bythe Key Programof the National Natural Science Foundation of China (79990580) .
文摘In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and evaluation. The procedure is essentially a multiple criteria decision-making problem. The traditional multiple criteria programming is not flexible enough in executing the system evaluation algorithm due to both the limited experimental data and the lack of human experiences. To make the CBR tool to be more efficient, a new method for the best choice among the feasible schemes based on the Fuzzy AHP using Fuzzy numbers （FFAHP） is proposed. Since the final results become a problem of ranking the mean of fuzzy numbers by the optimism of decision-maker using the FFAHP, its execution is much more intuitive and effective than with the traditional method.
文摘A complex number mode analysis approach is proposed for vibration reducing of structural flexible redundant manipulators by utilizing self motion. In the proposed approach, the self motion is evaluated to nullify the modal exciting force of flexural motion, and the approach can be freely used when the degree of freedom of flexural motion is much greater than the available degree of reundancy. The availability and effectiveness of the proposed approach are demonstrated through numerical simulation with a four link spatial robotic manipulator possessing an end flexible link.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60973162)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009GM037)+1 种基金the Science and Technology of Shandong Province, China(Grant No. 2010GGX10132)the Key Program of the Natural Science Foundation of Shandong Province, China (Grant No. Z2006G01)
文摘In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.
文摘This paper presents building one-parameter motion by complex numbers on a time scale. Firstly, we assumed that E and E′ were moving in a fixed time scale complex plane and {0, e1,e2} and {0', e'1,e'2} ?were their orthonormal frames, respectively. By using complex numbers, we investigated the delta calculus equations of the motion on T. Secondly, we gave the velocities and their union rule on the time scale. Finally, by using the delta-derivative, we got interesting results and theorems for the instantaneous rotation pole and the pole curves (trajectory). In kinematics, investigating one-parameter motion by complex numbers is important for simplifying motion calculation. In this study, our aim is to obtain an equation of motion by using complex numbers on the time scale.
基金the National Natural Science Foundation of China(Grant No.11871051).
文摘In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10901145)the Natural Science Foundation of Shanxi Province,China(Grant Nos. 2009011005-1 and 2012011002-1)the Top Young Academic Leaders of Higher Learning Institutions of Shanxi Province,China
文摘In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,non-dangerous male,and female.By mathematical analysis,we obtain the basic reproduction number for the existence of endemic equilibrium and study the effects of various immunization schemes about different groups.Furthermore,numerical simulations are undertaken to verify more conclusions.
文摘The additives such as phosphoric acid, calcium phosphate, calcium super phosphate, calcium over super phosphate, calcium carbonate, sodium hydrosulphite, etc. were used to produce furfural from the straw by hydrolysis with sulfuric acid. The effect of amount of the additives, the content of the added substance and the conditions of distillation on the acidity of the residues were studied. The experiment results showed that the all residues became neutral complex fertilizer, and the productivity of furfural increases under the following conditions: sulfuric acid concentration is 20% (by weight), the ratio of liquid to solid is 3∶1—4∶1 (by weight), the ratio of the additives to straw is suitable.
基金National Natural Science Foundation of China(No.60872065)the Key Laboratory of Textile Science&Technology,Ministry of Education,China(No.P1111)+1 种基金the Key Laboratory of Advanced Textile Materials and Manufacturing Technology,Ministry of Education,China(No.2010001)the Priority Academic Program Development of Jiangsu Higher Education Institution,China
文摘To extract features of fabric defects effectively and reduce dimension of feature space,a feature extraction method of fabric defects based on complex contourlet transform （CCT） and principal component analysis （PCA） is proposed.Firstly,training samples of fabric defect images are decomposed by CCT.Secondly,PCA is applied in the obtained low-frequency component and part of highfrequency components to get a lower dimensional feature space.Finally,components of testing samples obtained by CCT are projected onto the feature space where different types of fabric defects are distinguished by the minimum Euclidean distance method.A large number of experimental results show that,compared with PCA,the method combining wavdet low-frequency component with PCA （WLPCA）,the method combining contourlet transform with PCA （CPCA）,and the method combining wavelet low-frequency and highfrequency components with PCA （WPCA）,the proposed method can extract features of common fabric defect types effectively.The recognition rate is greatly improved while the dimension is reduced.
基金This project was supported by the Natural Science Foundation of Shaanxi Province.
文摘High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.
文摘In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.
