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Eigenvector derivatives of eigenproblems analytically dependent on parameters are required in diverse technical fields such as structural design, system identification. Modal methods, a kind of popular methods in engineering problems, calculate eigenvector derivatives by expressing them as linear combinations of eigenvectors of eigenproblems. In this paper, an incomplete modal method is presented to compute eigenvector derivatives of polynomial eigenproblems analytically dependent on parameters. The proposed method only uses a small part of eigenvectors of polynomial eigenproblems. The contributions of other eigenvectors to eigenvector derivatives are approximated by an iterative formula. Our method can simultaneously compute the eigenvector derivatives corresponding to several eigenvalues, and it is effective whether the differentiated eigenvectors correspond to simple or semisimple eigenvalues, and whether the leading coefficient matrix is singular or not. Numerical examples are given to test the efficiency of the proposed method.

A new iterative method is proposed to compute the first-order and high-order derivatives of several eigenpairs of a quadratic eigenvalue problem (QEP). The derivatives of simple and semi-simple eigenpairs are simultaneously computed. The proposed method avoids to solve many different linear systems with the size of the QEP. Only the eigenpairs to be differentiated are required in our method. Convergence properties of the proposed iterative method are established. In order to accelerate the proposed iterative method, vector epsilon algorithm is applied and then an acceleration algorithm for our iterative method is presented and analyzed. Numerical experiments show that the proposed method is efficient for the computation of the first-order and high-order derivatives of eigenpairs of a QEP, especially for several eigenpair derivatives in moderate and large QEP.

A new receptance method is proposed for partial quadratic pole assignment problem (PQPAP) of asymmetric systems with multi-input. We use receptance matrices of symmetric parts of open-loop systems to express the solution of PQPAP. Then we derive the sensitivities of changed eigenvalues of close-loop system and give the measure of robustness. On these grounds, an algorithm for solving the robust and minimum norm PQPAP is put forward. Our method utilizes receptance matrices of symmetric parts of asymmetric systems and it is applicable to the systems with multi-input. Finally, numerical results are given to show the efficiency of our method.

This paper considers the partial quadratic eigenvalue assignment problem (PQEAP) in active vibration control using state feedback. A receptance method is proposed for PQEAP such that the norms of feedback matrices and the condition number of close-loop system are simultaneously minimized. The real form of the proposed method is developed. The proposed method only uses receptance matrices and the unwanted eigenpairs of open-loop system. The system matrices and the unchanged eigenpairs of open-loop system are not required. The efficiency of the proposed method is illustrated by some numerical examples.

BiVO4 is a promising photoanode material for solar assisted water splitting in a photoelectrochemical cell but has a propensity to degrade. Investigations carried out here in 0.1 M Na2SO4 electrolyte showed that degradation is by dissolution of V in the electrolyte while Bi is retained on the anode probably in the form of solid bismuth oxide (Bi2O3, Bi4O7). Accumulation of Bi oxide on the anode surface leads to passivation of the photoanode from further degradation. Thermodynamic modelling of possible degradation reactions has provided theoretical support to this mechanism. This self-passivation is accompanied by a decrease in photocurrent density but, it protects the anode against extensive photocorrosion and contributes to long-term stability. This disclosure is a more definitive understanding of degradation of BiVO4 during water splitting in a photoelectrochemical cell. This understanding is imperative for both fundamental and applied research.

In this paper, a new iterative method is proposed to calculate a few eigenpair derivatives of damped systems. The proposed method simultaneously computes the derivatives of several simple eigenvalues and their corresponding eigenvectors. Eigenpair derivatives are directly determined in n-space. Moreover, our method does not require the left eigenvectors. Convergence theory of the proposed method is given. On these grounds, using vector ϵ -algorithm, acceleration techniques for our method are provided and analyzed. Finally some numerical experiments are reported to show the efficiency of the proposed methods.

Novel cyclotriphosphazene based lubricant oil ( Lube-PN ) for heat-assisted magnetic recording media was synthesized by reacting hexachlorocyclotriphosphazene with pentafluorophenol, followed by treatment with a hydroxy-terminated perfluoropolyether in a high yield. Its chemical structure was confirmed by 1 H and 31 P NMR. Its properties including viscosity, thermal stability, tribology, laser resistance as well as mobility behaviour on the hard disk surface were investigated. The thermal properties of Lube-PN were analysed using thermogravimetric analysis, and the thermal aging results showed that the about 80% of Lube-PN was retained even after heating at 300 °C for 8 h. The Lube-PN also exhibited comparable bonding ratio, friction coefficient, moderate mobility and better laser resistance than commercial perfluoropolyether based lubricant oils.

A new iterative method is proposed for computing partial derivatives of many eigenpairs. This method simultaneously computes a few eigenpair partial derivatives. For each origin shift, partial derivatives of eigenpairs whose eigenvalues are closest to the origin shift can be computed. Hence, this method may be used for partial derivatives of all eigenpairs. Convergence of the proposed method is established. Finally numerical experiments are given to show the effectiveness of the proposed method.

This paper considers the sensitivity of semisimple multiple eigenvalues and corresponding generalized eigenvector matrices of a nonsymmetric matrix pencil analytically dependent on several parameters. The directional derivatives of the multiple eigenvalues are obtained, and the average of eigenvalues and corresponding generalized eigenvector matrices are proved to be analytic. The results can be used to define the sensitivity of the semisimple multiple eigenvalues and corresponding generalized eigenvector matrices. These are useful for investigating structural optimal design, model updating, and structural damage detection.

The major factors affecting the particle size and morphology of LaxSr1-xMnO3 powder produced by spray pyrolysis are found to be the pyrolysis temperature, the rate of gas to liquid flow rates and concentration of the raw materials. The powders consist mainly of less than 1 mu m spherical particles. The smaller particles are the perfect spheres. Particles greater than 2 Irm are mostly fragments of spheres. The chemical composition of LaxSr1-xMnO3 powder accords approximately with that of feed. The powder produced by spray pyrolysis is amorphous, which could be transformed into single structure of hexagonal-rhombohedral perovskite after being calcined at 1200 degrees C for 2 h in air and form the larger hard agglomerates. (C) 1997 Elsevier Science S.A.