Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,su...Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.展开更多
This paper presents a new design of robust optimal controller for multivariable system. The row characteristic functions of a linear multivariable system and dynamic decoupling of its equivalent system, were applied t...This paper presents a new design of robust optimal controller for multivariable system. The row characteristic functions of a linear multivariable system and dynamic decoupling of its equivalent system, were applied to change the transfer function matrix of a closed-loop system into a normal function matrix, so that robust H^∞ optimal stability is guaranteed. Furthermore, for the decoupled equivalent control system the I^∞ optimization approach is used to have the closed-loop system embody optimal time domain indexes. A successful application on a heater control system verified the excellence of the new control scheme.展开更多
In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized...In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.展开更多
A matrix A ∈ Mn（C） is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invarian...A matrix A ∈ Mn（C） is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained.展开更多
The performance evaluation of automatic carrier landing system(ACLS)is an important part in the field of carrier aircraft landing control.Combining grey analytic hierarchy theory and data normalization theory,an impro...The performance evaluation of automatic carrier landing system(ACLS)is an important part in the field of carrier aircraft landing control.Combining grey analytic hierarchy theory and data normalization theory,an improved grey analytic hierarchy method is introduced to evaluate the performance of ACLS.A complete performance evaluation indicators system of ACLS is established,and the definition and calculation formula of each indicator are provided.The grey analytic hierarchy model is modified to improve the real-time performance of the algorithm,where traditional expert scoring sampling matrix is substituted by an indicator normalized sample matrix.Taking a certain ACLS as an example,the experimental simulation is carried out,and the simulation results verify the reliability and the accuracy of the improved grey analytic hierarchy method.展开更多
We present additional equivalent conditions on the existence of a 0 1 symmetric matrix with given row sum vector. The case of a 0 1 normal matrix is also considered.
Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute t...Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute the number of the orbits of An（R） and then compute the order of the orthogonal group determined by the special symmetric matrix. Finally we get the number of the symmetric matrices which are in the same orbit with the special symmetric matrix.展开更多
A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for supera...A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.展开更多
文摘Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.
基金Project (No. 60274036) supported by the National Natural Science Foundation of China
文摘This paper presents a new design of robust optimal controller for multivariable system. The row characteristic functions of a linear multivariable system and dynamic decoupling of its equivalent system, were applied to change the transfer function matrix of a closed-loop system into a normal function matrix, so that robust H^∞ optimal stability is guaranteed. Furthermore, for the decoupled equivalent control system the I^∞ optimization approach is used to have the closed-loop system embody optimal time domain indexes. A successful application on a heater control system verified the excellence of the new control scheme.
文摘In this paper, we found the bounds of the extreme eigenvalues of normalized Laplacian matrices and signless Laplacian matrices by using their traces. In addition, we found the bounds for k-th eigenvalues of normalized Laplacian matrix and signless Laplacian matrix.
基金Natural Science Foundation of Jiangsu Province(BK2007030)the National Natural Science Foundation of China(10471037)the Natural Science Foundation of the Education Committee of Jiangsu Province(07KJD110207,06KJD110179).
文摘A matrix A ∈ Mn（C） is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained.
文摘The performance evaluation of automatic carrier landing system(ACLS)is an important part in the field of carrier aircraft landing control.Combining grey analytic hierarchy theory and data normalization theory,an improved grey analytic hierarchy method is introduced to evaluate the performance of ACLS.A complete performance evaluation indicators system of ACLS is established,and the definition and calculation formula of each indicator are provided.The grey analytic hierarchy model is modified to improve the real-time performance of the algorithm,where traditional expert scoring sampling matrix is substituted by an indicator normalized sample matrix.Taking a certain ACLS as an example,the experimental simulation is carried out,and the simulation results verify the reliability and the accuracy of the improved grey analytic hierarchy method.
文摘We present additional equivalent conditions on the existence of a 0 1 symmetric matrix with given row sum vector. The case of a 0 1 normal matrix is also considered.
基金the Key Project of Chinese Ministry of Education (03060)
文摘Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute the number of the orbits of An（R） and then compute the order of the orthogonal group determined by the special symmetric matrix. Finally we get the number of the symmetric matrices which are in the same orbit with the special symmetric matrix.
文摘A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.
