Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M m...Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.展开更多
Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equil...Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.展开更多
A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generall...A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative tri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.展开更多
A matrix whose entries are +,-, and 0 is called a sign pattern matrix. For a sign pattern matrix A , if A 3=A , then A is said to be sign tripotent. In this paper, the characterization of the n by n(n...A matrix whose entries are +,-, and 0 is called a sign pattern matrix. For a sign pattern matrix A , if A 3=A , then A is said to be sign tripotent. In this paper, the characterization of the n by n(n≥2) sign pattern matrices A which are sign tripotent has been given out. Furthermore, the necessary and sufficient condition of A 3=A but A 2≠A is obtained, too.展开更多
A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .Ak≤0. Further, we determine the maximum number of negative ...A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .Ak≤0. Further, we determine the maximum number of negative entries that can occur in A whenever Ak≤0. Finally, we give a necessity and sufficiency condition for A2≤0.展开更多
文摘Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.
基金Project supported by the National Natural Science Foundation of China (Nos. 50378083 and 50638050)the Research Foundation for the Doctoral Program of Higher Education of China (No. 20050335097)
文摘Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.
文摘A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative tri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.
基金Project supported by the National Natural Science Foundation of China(1 9971 0 86)
文摘A matrix whose entries are +,-, and 0 is called a sign pattern matrix. For a sign pattern matrix A , if A 3=A , then A is said to be sign tripotent. In this paper, the characterization of the n by n(n≥2) sign pattern matrices A which are sign tripotent has been given out. Furthermore, the necessary and sufficient condition of A 3=A but A 2≠A is obtained, too.
基金Supported by Shanxi Natural Science Foundation(20011006)
文摘A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .Ak≤0. Further, we determine the maximum number of negative entries that can occur in A whenever Ak≤0. Finally, we give a necessity and sufficiency condition for A2≤0.
