In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some propert...In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.展开更多
We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new...We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new starting vector,such that the occurrence of stagnation be mitigated or the convergence be accelerated.The more appealing utilization of the new method is in conjunction with a harmonic Ritz vector as the starting vector,which is discussed in detail.Numerical experiments are carried out to demonstrate that the proposed procedure can effectively mitigate the occurrence of stagnation due to the presence of small eigenvalues in modulus.展开更多
Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-princi...Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and l-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.展开更多
In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields...In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.展开更多
When the five-axis CNC system executes the 3D cutter radius compensation function,the angle between two adjacent radius compensation vectors might become very large and the linear axes would move too fast if the tool ...When the five-axis CNC system executes the 3D cutter radius compensation function,the angle between two adjacent radius compensation vectors might become very large and the linear axes would move too fast if the tool orientation vector is close to the surface normal.The reason that results in this phenomenon is analyzed based on building the transmission relationship between the cutter contact point and the cutter location point.By taking the square-end tool as an example,an optimization algorithm to control the undesired movements is advanced.For the singular area where sudden change exists,the number of interpolation cycles is determined by the cutter feedrate,the limit speeds of machine axes and the maximum allowable angle between radius compensation vectors of adjacent NC blocks.The radius compensation vector of each interpolation cycle is obtained by a kind of vector rotation method.By maintaining the perpendicularity between the radius compensation vector and the tool orientation vector,the rapid movements of the linear axes are eliminated.A trial-cut experiment is performed to verify the correctness and the effectiveness of the proposed algorithm.展开更多
文摘In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.
文摘We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new starting vector,such that the occurrence of stagnation be mitigated or the convergence be accelerated.The more appealing utilization of the new method is in conjunction with a harmonic Ritz vector as the starting vector,which is discussed in detail.Numerical experiments are carried out to demonstrate that the proposed procedure can effectively mitigate the occurrence of stagnation due to the presence of small eigenvalues in modulus.
基金Project supported by the National Natural Science Foundation of China (No. 10471087) the Zhejiang Provincial Natural Science Foundation of China (No.Y605044).
文摘Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and l-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.
文摘In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.
基金supported by the National Basic Research Program of China under Grant No.2011CB302400the National Key Technology Research and Development Program of China under Grant No.2012BAF13B08
文摘When the five-axis CNC system executes the 3D cutter radius compensation function,the angle between two adjacent radius compensation vectors might become very large and the linear axes would move too fast if the tool orientation vector is close to the surface normal.The reason that results in this phenomenon is analyzed based on building the transmission relationship between the cutter contact point and the cutter location point.By taking the square-end tool as an example,an optimization algorithm to control the undesired movements is advanced.For the singular area where sudden change exists,the number of interpolation cycles is determined by the cutter feedrate,the limit speeds of machine axes and the maximum allowable angle between radius compensation vectors of adjacent NC blocks.The radius compensation vector of each interpolation cycle is obtained by a kind of vector rotation method.By maintaining the perpendicularity between the radius compensation vector and the tool orientation vector,the rapid movements of the linear axes are eliminated.A trial-cut experiment is performed to verify the correctness and the effectiveness of the proposed algorithm.
