This study investigates the redesign of a structural system with the matrix modification. The inertia congruence transformation is adopted to find the latent roots of a dynamic stiffness matrix, and a method for deter...This study investigates the redesign of a structural system with the matrix modification. The inertia congruence transformation is adopted to find the latent roots of a dynamic stiffness matrix, and a method for determining its eigenvalue is proposed. The characteristics of the latent vector for a known latent root and a method for computing it are studied. The mode shapes of the redesigned structure must be differently handled based on whether the structure exhibits persistent or non-persistent natural frequencies.展开更多
Beal conjecture is a famous world mathematical problem and was proposed by American banker Beal, so to solve it is more difficult than Fermat’s last theorem. This paper uses relationship between the mathematical form...Beal conjecture is a famous world mathematical problem and was proposed by American banker Beal, so to solve it is more difficult than Fermat’s last theorem. This paper uses relationship between the mathematical formula and corresponding graph, and by characteristics of graph, combined with the algebraic transformation and congruence theory of number theory;it is proved that the equation can only be formed under having a common factor and Beal conjecture is correct.展开更多
In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformat...In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup Zn under multiplication modulo n. And, when Y lohtain in X, we do the same for the semigroup T（X, Y） consisting of all elements of T（X） whose range is contained in Y. We also characterise the minimal congruences on T（X. Y）.展开更多
文摘This study investigates the redesign of a structural system with the matrix modification. The inertia congruence transformation is adopted to find the latent roots of a dynamic stiffness matrix, and a method for determining its eigenvalue is proposed. The characteristics of the latent vector for a known latent root and a method for computing it are studied. The mode shapes of the redesigned structure must be differently handled based on whether the structure exhibits persistent or non-persistent natural frequencies.
文摘Beal conjecture is a famous world mathematical problem and was proposed by American banker Beal, so to solve it is more difficult than Fermat’s last theorem. This paper uses relationship between the mathematical formula and corresponding graph, and by characteristics of graph, combined with the algebraic transformation and congruence theory of number theory;it is proved that the equation can only be formed under having a common factor and Beal conjecture is correct.
文摘In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup Zn under multiplication modulo n. And, when Y lohtain in X, we do the same for the semigroup T（X, Y） consisting of all elements of T（X） whose range is contained in Y. We also characterise the minimal congruences on T（X. Y）.
