AN ACCELERATION FOR THE EIGENSYSTEM REALIZATION ALGORITHM WITH PARTIAL SINGULAR VALUES DECOMPOSITION

The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identify the dynamic parameter of spacecraftrapidly and accurately, an accelerated ERA with a partial singularvalues decomposition (PSVD) algorithm is presented. In the PSVD, theHankel matrix is reduced to dual diagonal form first, and thentransformed into a tridiagonal matrix.

Partial Fraction Decomposition by Repeated Synthetic Division

We present an efficient and elementary method to find the partial fraction decomposition of a rational function when the denominator is a product of two highly powered linear factors.

SnO_(2)/metal organic complex composite derived from low-temperature activated metal organic complex for advanced lithium storage

Sn-based metal organic complexes with coordination bonds,multi-active sites,and high theoretical capacity have attracted much attention as promising anodes for lithium ion batteries.However,the low electrical conductivity and huge volume changes restricted their electrochemical stability and practical utilization.Herein,Snbased anode with superior electrochemical performance,including a high reversible capacity of 1050.1 mAh·g^(-1)at 2 A·g^(-1)and a stable capacity of 1105.5 mAh·g^(-1)after 500 cycles at 1 A·g^(-1),was fabricated via a low-temperature calcination strategy from Sn metal organic complexes.The low-temperature calcination process regulates Sn-O bond and prevents the agglomeration of SnO_(2),generating highly dispersed SnO_(2) decorated metal organic complexes and providing sufficient active sites for ion storage.Ex situ characterizations expound that the undecomposed Sn-based metal organic complexes could be transformed into SnO_(2) during lithiation and delithiation,which enhances the electrical conductivity and induces a strong pseudo-capacitive behavior,accelerating the electrochemical kinetics;the multiple solid electrolyte interface with inflexible LiF and flexible ROCO_(2)Li buffers the volume variation of the electrode,resulting in its high electrochemical stability.This work provides a simple strategy for preparing excellent Sn-based anodes from metal organic complexes and reveals the lithium storage mechanism of the prepared Snbased anode.

STABILITY ANALYSIS FOR THE LARGE-SCALE SYSTEMS WITH TIME-DELAY

The stability analysis problems were put forward for the large-scale systems with time-delay by using the partial decomposition method. With the stability of the isolated subsystems without time- delay, some sufficient criterions for the asymptotical stability of the whole system were obtained by making a Lyapunov function with the Razumikhin condition and a Lyapunov functional for the retarded type and neutral type, respectively.

A complete algorithm for automated discovering of a class of inequality-type theorems

Making use of the discriminant sequence for polynomials, WR algorithm, Wu' s elimination and a partial cylindrical algebraic decomposition, we present here a practical algorithm for automated inequality discovering which can discover new inequalities automatically without requiring to put forward any conjectures beforehand. That is complete for an extensive class of inequality-type theorems. Also this algorithm is applied to the classification of the real physical solutions of geometric constraint problems. Many inequalities with various backgrounds have been discovered or rediscovered by our program, DISCOVERER, which implements the algorithm in Maple.

Real zeros of the zero-dimensional parametric piecewise algebraic variety

The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi-algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and sufficient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and sufficient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex.