STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.

Identification Method for RLG Random Errors Based on Allan Variance and Equivalent Theorem

An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent m...

The Equivalence Theorem of Appoximation for Two-dimensional Baskakov Operators

In this paper, we study the convergence rate of two-dimensional Baakakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.

EQUIVALENCE THEOREM ON WEIGHTED SIMULTANEOUS L-APPROXIMATION BY MEANS OF SZASZ-KANTOROVICH OPERATORS AND BASKAKOV-KANTOROVICH OPERATORS

The intention of this paper is to give direct and converse results on weighted simultaneous approximation by means of Sz(?)sz-Kantorovich operators and Baskakov-Kantorovich operators in L_p-norms using the weighted Ditzian-Totik modulus of smoothness.

EVALUATION OF ELECTROMAGNETIC SCATTERING OF TWO DIMENSIONAL CONDUCTING OBJECTS--TE CASE

A hybrid technique is developed for the evaluation of two dimensional electromagnetic scattering from electrically large conducting bodies with cracks on their surfaces (TE case). The edge based finite element method (FEM) is employed to compute the scattering from the cracks. Physical optics (PO) and physical theory of diffraction (PTD) are utilized to evaluate the scattering from the large bodies with the cracks filled with perfect conductors. These two methods are combined by an efficient coupling scheme. Some of numerical results are presented. It is shown that the hybrid technique has some advantages over other methods in regard to saving computer memory units and CPU time.

POINTWISE SIMULTANEOUS APPROXIMATION BY LEFT GAMMA QUASI-INTERPOLANTS

Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. We consider left Gamma quasi-interpolants and give a pointwise simultaneous approximation equivalence theorem with ωφλ^2r（f,t）∞ by means of unified the classical modulus and Ditzian-Totick modulus.

Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam

In this paper based on the equivalence principle and the reciprocity theorem, the scattered field up to second-order by two parallel 2D targets arbitrarily located in a Gaussian beam is considered. The first-order solution can easily be obtained by calculating the scattered field from isolated targets when illuminated by a Gaussian beam. However, because of the difficulty in formulating the couple scattering field, it is almost impossible to find an analytical solution for the second-order scattered field if the shapes of 2D targets are not canonical geometries. In order to overcome this problem, in this paper, the second-order solution is derived by using the technique based on the reciprocity theorem and the equivalence principle. Meanwhile, the relation between the secondary scattered field from target #1 and target #2 is obtained. Specifically, the bi- and mono-static scattering of Gaussian beam by two parallel adjacent inhomogeneous plasma-coated conducting circular cylinders is calculated and the dependence of attenuation of the scattering width on the thickness of the coated layer, electron number density, collision frequency and radar frequency is discussed in detail.

Bistatic RCS Prediction with Graphical Electromagnetic Computing (GRECO) Method for Moving Targets

Graphical Electromagnetic Computing (GRECO) is recognized as one of the most valuable methods of the RCS (Radar Cross Section) computation for the high frequency region. The method of GRECO and Monostatic bistatic Equivalence Theorem was used to calculate the bistatic RCS for moving targets in the high frequency region. Some computing examples are given to verify the validity of the method. Excellent agreement with the measured data indicates that the method has practical engineering value.

A Wave Propagation Model Based on Monte-Carlo Particle-Tracing

This article describes a new wave propagation model based on Monte-Carlo particle-tracing. This model relies on Monte-Carlo integration and Huygens currents radiating. The particles used to compute the field permit to consider the interferences. This model includes the diffraction of the surface without edge computation. The implementation of this propagation model is based on a image synthesis renderer. The results of this model are studied in far field situation with perfectly conducting shapes, by comparing results with a classical MoM method.

EQUIVALENCY THEOREM FOR “SADDLE-POINT” FINITE ELEMENT SCHEMES AND TWO CRITERIA OF STRONG BABUSKA-BREZZI CONDITION

This paper is concerned with the general study in the existence,uniqueness and error estimationof finite element solutions for a larger class of 'saddle-point' schemes. The established theory inthe form of Lax-like equivalency theorem includes Brezzi’s theory that has been treated as a specialcase.Two criteria are presented so as to help the practical verification of S-Babuska condition.

An equivalence theorem of a class of Minkowski norms and its applications

In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifolds of dimension n 4 with vanishing Landsberg curvatures must be Berwald manifolds.

Weighted approximation by Bernstein quasiinterpolants for functions with singularities

We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of this modified quasi-interpolants. Some classical results on approximation of continuous functions are generalized to the weighted approximation of functions with singularities.

D-Optimal Designs for Hierarchical Linear Models with Heteroscedastic Errors

This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix.The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained.The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.

D-optimal population designs in linear mixed effects models for multiple longitudinal data

The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data.Observations of each response variable within subjects are assumed to have a first-order autoregressive structure,possibly with observation error.The equivalence theorems are provided to characterise theD-optimal population designs for the estimation of fixed effects in the model.The semi-Bayesian D-optimal design which is robust against the serial correlation coefficient is also considered.Simulation studies show that the correlation between multi-response variables has tiny effects on the optimal design,while the experimental costs are important factors in the optimal designs.

Pointwise Approximation by Szàsz-Mirakjan Quasi-Interpolants

Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szasz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus wφ^2r （f, t）. In this paper, we extend Diallo＇s result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f ∈ CB[0, ∞） by making use of the unified modulus wφ^2r（f, t） （0≤λ≤ 1）.