This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimens...This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimensional triangular cones (with multiple top vertexes). As a mathematical toy model of protein complexes, we consider complexes of closed trajectories of n-simplices (n=2,3,4...), where the design problem of protein complexes corresponds to an extended version of the Hamiltonian cycle problem. The problem is to find “a set of” closed trajectories of n-simplices which fills the n-dimensional region defined by a given pair of n+1 -dimensional triangular cones. Here we give a solution to the extended Hamiltonian cycle problem in the case of n=2 using the discrete differential geometry of triangles (i.e., 2-simplices).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 order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Fir...In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Firstly, the operation mechanism of the heald selection mechanism is analyzed in detail. The conjugate cam is mapped. The cam profile curve is fitted with cubic spline interpolation. Secondly, based on the overall analysis method and the complex vector method, the kinematics analysis of the key components after the high pair low generation is performed, and the angular displacement and angular velocity of each component are calculated with the rotation of the active cam. Finally, the movement curve diagram is drawn with Matlab, which lays the foundation for the dynamic analysis and in-depth study of the selection mechanism in the future.展开更多
文摘This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimensional triangular cones (with multiple top vertexes). As a mathematical toy model of protein complexes, we consider complexes of closed trajectories of n-simplices (n=2,3,4...), where the design problem of protein complexes corresponds to an extended version of the Hamiltonian cycle problem. The problem is to find “a set of” closed trajectories of n-simplices which fills the n-dimensional region defined by a given pair of n+1 -dimensional triangular cones. Here we give a solution to the extended Hamiltonian cycle problem in the case of n=2 using the discrete differential geometry of triangles (i.e., 2-simplices).
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.
文摘In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Firstly, the operation mechanism of the heald selection mechanism is analyzed in detail. The conjugate cam is mapped. The cam profile curve is fitted with cubic spline interpolation. Secondly, based on the overall analysis method and the complex vector method, the kinematics analysis of the key components after the high pair low generation is performed, and the angular displacement and angular velocity of each component are calculated with the rotation of the active cam. Finally, the movement curve diagram is drawn with Matlab, which lays the foundation for the dynamic analysis and in-depth study of the selection mechanism in the future.
