THE DRAZIN INVERSE OF MATRICES OF QUATERNIONS

Let H be the real quaternion field,C and R be the complex and real field respectively.Clearly R（?）C（?）H. Let Hm×n denote the set of all m×n matrices over H.If A=(ars)∈Hm×n,then there exist A1 and A2∈Cm×n such that A=A1+A2j.Let AC denote the complexrepresentation of A,that is the 2m×2n complex matrix Ac=（（A1/A2）（-A2/A1））（see[1,2]）.We denote by AD the Drazin inverse of A∈Hm×n which is the unique solution of the e-

REVERSE ORDER LAW FOR GROUP INVERSE OF PRODUCT OF MATRICES ON SKEW FIELDS

Let Kn×n be the set of all n×n matrices and Krn×n the set {A∈Kn×n|rankA=r} on askew field K. Zhuang [1] denotes by A# the group inverse of A∈Kn×n which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.

AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES

is gained by deleting the kth row and the kth column （k=1,2,...,n） from Tn.We put for-ward an inverse eigenvalue problem to be that:If we don’t know the matrix T1,n,but weknow all eigenvalues of matrix T1,k-1,all eigenvalues of matrix Tk+1,k,and all eigenvaluesof matrix T1,n could we construct the matrix T1,n.Let μ1,μ2,…,μk-1,μk,μk+1,…,μn-1,

The Explicit Expressions of Level- k(r1 ,r2 ,… ,rk) Circulant Matrices and Their Some Properties

In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.

The Explicit Expressions of Level-k Circulant Matrices of Type(n_1,n_2.…,n_k) and Their Some Properties

In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.

ANALYSIS AND SIMULATION OF CONTROL MIXER CONCEPT FOR A CONTROL RECONFIGURABLE AIRCRAFT

In today's aircraft,the hardware redundancy is driven by the critical surfaces resulting in single point-failures.Reconfiguration technology remoVes the single surface criticality by employing control surfaces with aerodynamic redundancy.This paper studies a control reconfiguration scheme based on Control Mixer Concept.A technique for the design of a control mixer for an aircraft with damaged surfaces/actuators using the pseudo-inverse is developed and applied.This paper discusses its applications and limitations based on linear analysis and computer simulation.

Study on unknown input reduced-order observer for fault diagnosis

A novel unknown input reduced-order observer (UIRO) design scheme is presented. It is proved that unknown input appearing in measurement can be eliminated by a simple algebraic transformation. Then, a new UIRO design scheme is proposed via a transformation under no unknown input existing in measurement. Compared with other known results, the condition is weaker than others. So it was further reasonable. The design procedure proposed is simple and straightforward enough to be applied. An example is given to show its efficiency in fault diagnosis.

Type Synthesis of Fully-Decoupled 3R2T Parallel Mechanisms Based on Driven-Chain Principle

To avoid the existence of nonlinear and strong coupling in parallel mechanisms,it is necessary to address special care to the type synthesis of mechanisms,especially for the type synthesis of fully-decoupled parallel mechanisms. Based on the screw theory and the driven-chain principle,a methodology of structural synthesis for fully-decoupled three-rotational( 3R) and two-translational( 2T)parallel mechanisms was proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms.Firstly,according to the desired kinematic characteristics of fullydecoupled parallel mechanisms,a method was presented by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices. Secondly,according to the feature of the direct and the inverse Jacobian matrices,the effective screws,the actuated screws and the mobile un-actuated screws of each leg were established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements were obtained.Finally,the desired fully-decoupled parallel mechanisms could be synthesized by using the structural synthesis rule and structural synthesis of fully-decoupled 3R2 T parallel mechanisms could be obtained exploiting the abovementioned methodology. Furthermore,the Jacobian matrix of a synthesized 3R2 T parallel mechanism was deduced to demonstrate the decoupling feature of the parallel mechanism,which also validated the correctness of the methodology of the type synthesis for fully-decoupled 3R2 T parallel mechanisms.

Correspondence Between Bell Bases and Oriented Links in Knot Theory

From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage in knot theory.

Load Forecasting Technique for System Expansion in Isolated Area Using Time Invariant Socio-Economic Factors of Identical Agglomerations

Load forecasting is a critical issue for operational planning as well as grid expansion to ensure an uninterruptable electric power system. Being a small but densely populated country in South Asia, Bangladesh has many isolated places which are not connected to national grid yet. If concern authority opts to expand grid to those areas, they need reliable demand data for designing and dimensioning of different power system entities, e.g., capacity, overhead line capacity, tie line capacity, spinning reserve, load-shedding scheduling, etc., for reliable operation and to prevent possible obligatory redesigning. This paper represents an analysis to forecast the electricity demand of an isolated island in Bangladesh where past history of electrical load demand is not available. The analysis is based on the identification of factors, e.g., population, literacy rate, per capita income, occupation, communication, etc., on which electrical load growth of an area depends. Data has been collected from the targeted isolated area and form a grid connected area which is similar to target area from social and geographical perspective. Weights of those factors on load have been calculated by matrix inversion. Demand of the new area is forecasted using these weights factors by matrix multiplication.

ON THE GENERALIZED INVERSE NEVILLE-TYPE MATRIX-VALUED RATIONAL INTERPOLANTS

A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

ON LOWNER-ORDERING ANTITONICITY OF MATRIX INVERSION

A new condition for the antitoulcity of the inverse of Herndtian matrices with respect tothe Lowner Partial ordering is derived. The basic result is estabhebed by applying directly anelementary formula for a sum of matrices.