Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetr...Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity.When the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.展开更多
Theory of uncertainty reasoning base on l-module of true value field,in this paper,an extended l-module was proposed,some properties and lattice measure were discussed,then the lattice integral on l-module was gained.
Aiming at the problem that the lattice feature exceeds the view field of the scanning electron microscope(SEM)measuring system,a new lattice measuring method is proposed based on integral imaging technology.When the s...Aiming at the problem that the lattice feature exceeds the view field of the scanning electron microscope(SEM)measuring system,a new lattice measuring method is proposed based on integral imaging technology.When the system works,the SEM measuring system is equivalent to an integral image acquisition system.Firstly,a lattice measuring method is researched based on integral imaging theory.Secondly,the system parameters are calibrated by the VLSI lattice standard.Finally,the value of the lattice standard to be tested is determined based on the calibration parameters and the lattice measuring algorithm.The experimental results show that,compared with the traditional electron microscope measurement method,the relative error of the measured value of the algorithm is maintained within 0.2%,with the same level of measurement accuracy,but it expands the field of view of the electron microscope measurement system,which is suitable for the measurement of samples under high magnification.展开更多
Based on the Lax pair formulation,we study the integrable conditions of the Osp(1|2)spin chain with open boundaries.We consider both the non-graded and graded versions of the Osp(1|2)chain.The Lax pair operators M_(&#...Based on the Lax pair formulation,we study the integrable conditions of the Osp(1|2)spin chain with open boundaries.We consider both the non-graded and graded versions of the Osp(1|2)chain.The Lax pair operators M_(±)for the boundaries can be induced by the Lax operator M_(j)for the bulk of the system.They correspond to the reflection equations(RE)and the Yang-Baxter equation,respectively.We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries.The double row monodromy matrix and transfer matrix of the spin chain have also been constructed.The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE.This construction is another way to prove the quantum integrability of the Osp(1|2)chain.We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.展开更多
基金The work was supported in part by NSF(DMS-1664561)NSFC(11975145 and 11972291)+1 种基金the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17KJB110020)Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT(2017XKZD11).
文摘Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity.When the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.
基金Supported by NSF of the Education Department of Henan Province(2009A110017)
文摘Theory of uncertainty reasoning base on l-module of true value field,in this paper,an extended l-module was proposed,some properties and lattice measure were discussed,then the lattice integral on l-module was gained.
基金supported by the National Key Research and Development Program(No.2019YFB2005503)。
文摘Aiming at the problem that the lattice feature exceeds the view field of the scanning electron microscope(SEM)measuring system,a new lattice measuring method is proposed based on integral imaging technology.When the system works,the SEM measuring system is equivalent to an integral image acquisition system.Firstly,a lattice measuring method is researched based on integral imaging theory.Secondly,the system parameters are calibrated by the VLSI lattice standard.Finally,the value of the lattice standard to be tested is determined based on the calibration parameters and the lattice measuring algorithm.The experimental results show that,compared with the traditional electron microscope measurement method,the relative error of the measured value of the algorithm is maintained within 0.2%,with the same level of measurement accuracy,but it expands the field of view of the electron microscope measurement system,which is suitable for the measurement of samples under high magnification.
基金supported by the National Natural Science Foundation of China(Grant Nos.12275214,11805152,12047502 and 11947301)the Natural Science Basic Research Program of Shaanxi Province Grant Nos.2021JCW-19 and 2019JQ-107Shaanxi Key Laboratory for Theoretical Physics Frontiers in China。
文摘Based on the Lax pair formulation,we study the integrable conditions of the Osp(1|2)spin chain with open boundaries.We consider both the non-graded and graded versions of the Osp(1|2)chain.The Lax pair operators M_(±)for the boundaries can be induced by the Lax operator M_(j)for the bulk of the system.They correspond to the reflection equations(RE)and the Yang-Baxter equation,respectively.We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries.The double row monodromy matrix and transfer matrix of the spin chain have also been constructed.The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE.This construction is another way to prove the quantum integrability of the Osp(1|2)chain.We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.
