4. Because the errors caused by truncating the high modals are avoided, the perturbation solutions of eigenvalues and eigenvectors are high accurate perturbation solutions;

And finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

Then, a group of beelines are used to approximate the boundaries of the plates and the Fourier expansion method is applied to the boundary conditions along the plate boundaries. The frequency equation is given by truncating the orders of the expansion series.

The simplest normal forms of the non-resonant double Hopf bifurcation (DHB)with parameter are obtained without truncating the original differential equation, i.e.the perturbation parameter of the system is treated as one-dimensional state variable.

Therefore, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

The section error,the relative error between the biggest shearing stress of accurate stress field and the biggest one of approximate stress field around the peak of Ⅰ- Ⅱ compound crackles,has been analysed,which provides the theoretical evidence for photoelasticity to measure KⅠ and KⅡ's error.

Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage were derived,and the Galerkin method was applied to simplify the equations.

The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization.

The arbitrariness in the way of truncating a cone manifests itself in the possibility of adding various harmonic polynomials.

Using the boundary truncating technique, the solution process of Finite-Element Method (FEM) has been greatly simplified compared with other hybrid methods.

A novel stop mutation truncating critical regions of the cardiac transcription factor NKX2-5 in a large family with autosomaldom

Search for truncating mutations or CAG repeat expansion in CACNA1A was negative.

Significant and escalating truncation of the redusome DNA causes cell aging due to an arising and increasing deficit of fRNAs and, for this reason, the lack of required ions near certain structural genes.

The proposed algorithm is reduced to the stepwise application to the tree of truncation of its vertices.

It was shown that the removal of 9-aa fragment by trypsin does not affect the catalytic activity of the receptor, whereas the thermolysin-induced truncation of the rhodopsin C-terminus by 12 aa about 1.5-fold enhances its activity.

This approach makes it possible to avoid uncontrollable errors introduced in the truncation of infinite series, and the error of the approach itself does not exceed a few percent.

However, the truncation of the series is also possible.

The properies, limits and the method of the difference solution of the short wave equation-Boussinesq equation were investigated by the numerical simulation of one dimensional short wave.An implicit difference scheme was proposed. The analysis of truncation error shows the necessity of adding a correction term for keeping identical accuracy of each term in the difference equation. The dissipation and frequency dispersion of the difference equation were analysed and on which the effects of Boussinesq term and...

The properies, limits and the method of the difference solution of the short wave equation-Boussinesq equation were investigated by the numerical simulation of one dimensional short wave.An implicit difference scheme was proposed. The analysis of truncation error shows the necessity of adding a correction term for keeping identical accuracy of each term in the difference equation. The dissipation and frequency dispersion of the difference equation were analysed and on which the effects of Boussinesq term and correction term os well.One dimensional short wave propagating in a wave flume was observed. The measured data agree with the results calculated by using Boussinesq equation with the correction term.

An equivalent linearization method for obtaining the response of nonlinear multi-degree-of-freedom dynamic systems to nonstationary gaussian excitation with nonzero mean is presented. Using the property of gaussian vector processes, the closed formulas of the coefficients of the equivalent linear system are obtained. The linear coefficients obtained are as simple as those of the Atalik and Utku method in mathematical form. A method to treat stochastic dynamic equation of complicated structure by means of modal...

An equivalent linearization method for obtaining the response of nonlinear multi-degree-of-freedom dynamic systems to nonstationary gaussian excitation with nonzero mean is presented. Using the property of gaussian vector processes, the closed formulas of the coefficients of the equivalent linear system are obtained. The linear coefficients obtained are as simple as those of the Atalik and Utku method in mathematical form. A method to treat stochastic dynamic equation of complicated structure by means of modal truncation method and to compute response statistics of dynamic system in the time domain is presented. One numerical method to compute mean and covariance equations of stochastic dynamic system is presented.

By employing quantitative calculations, we discovered that the usual wi- lliams premier expansion, which considered only the order 1 and Its approa- ching coordioate relationship. can only be adaptable to tips within the range of 1/20 length of the crack Moreover, the errors are unacceptable. The results mentioned herein not only. help to estimate the components of stress, but also to provide useful reference to other studies.