The pseudo-differential operator of parabolic equation is approximated to a wide-angle form by the Feit-Fleck method. The error brought by this approximation is analyzed.

In this approximation, it is assumed that the effect of radiative heat transfer would be so strong that the temperature of the medium could be regarded as uniform.

In NASA standard (NASA RP 1092), k was taken approximately as0.16,that if this approximation value is still suituble for the most resins in China is a question to be dis-cussed.

The unified-colored-noise approximation proposed by Jung and Hanggi is extended to the multi-dimensional case in this paper. Then, the Langevin equation and FokkerPlanck equation of colored cubic model for single mode dye-laser model are derived with this approximation method.

Taking the symmetric slab waveguide as an example,we show that radiation modes of a weakly guiding planar optical waveguide can be approximated by the free space modes,their field expression and normalization constants are simple and understandable physically and can be obtained directly without any calculation. By applying this approximation,the far field and radiation loss calculations caused by random wall imperfections have been significantly simplified.

The vibration energy or the electronic and vibration entropy of the gaseous molecules are approximately used as the energy or entropy of the solid. In this approximation, thermodynamic functions △H0, △S0, △G0 and hydrogen isotopes equilibrium pressure of the hydrogenating reaction have been calculated .

The vibrational energy, electronic and vibrational entropy of the molecules in their solid states are assumed, ΔHAEE, ΔS and ΔG and nitrogen equilibrium pressures of the nitrogenating reaction have been calculated based on this approximation.

With this approximation the measured contact angles of 1-bromonaphthalene anddiiodomethane on the silicagel plate are 16.1° and 35.8 ° respectively, well agreeing withliterature reported, and closed nonpolar component of the surface tension, 42.7 and41.7mN/m, are calculated correspondingly.

Δ H , ΔS , ΔG and hydrogen equilibrium pressure of the hydrogenating reaction have been calculated based on this approximation and very obvious isotope effects have been observed.

This approximation method is used to develop a simulation method of the sample path of linear fractional stable motions.

The comparison of the predictions of statistical approach with the results obtained on the basis of the approximation of homogeneous metastable phase made it possible to refine the domain of the applicability of this approximation.

The solutions obtained in this approximation describe only weak nonlinear effects and the region of their applicability is limited, naturally, to small values of the Grashof number (no larger than 103).

A solitary wave is characterized in this approximation by two variables - the energy density per unit length measured along its crest, and the direction of the normal to the wave crest.

The relaxation of harmonic perturbations in this approximation was considered by Levich [3].

In this paper, further simplifications are suggested for the two-fraction method based on the solubility function and the treatment of fractionation data by using Tung functipn which were proposed by the present authors in previous publications.The evaluation of the distribution parameters for a fraction from two intrinsic viscosity measurements in a good solvent and in a θ-solvent is shown to be not practical, because the required precision is not attainable in ordinary measurements. A new approximation is...

In this paper, further simplifications are suggested for the two-fraction method based on the solubility function and the treatment of fractionation data by using Tung functipn which were proposed by the present authors in previous publications.The evaluation of the distribution parameters for a fraction from two intrinsic viscosity measurements in a good solvent and in a θ-solvent is shown to be not practical, because the required precision is not attainable in ordinary measurements. A new approximation is suggested by taking the phase separation parameter Q to be equal to the volume ratio R of the concentrated and dilute phases. Then, the distribution parameters for the two-fraction method can be readily evaluated. Actual calculations show that the distribution parameters thus calculated is not very sensitive to the value of Q taken, and therefore this approximation is justified as a tentative simplification of the two-fraction method for the determination of molecular weight distributions.In the treatment of ordinary fractionation data by means of Tung function, all fractions except the first and the last ones can be approximated by a straight line for the integral distribution curve. The line passes through the points M(1 = 1/2) = Mη, M(1 = 0) = 1/2Mη which corresponds roughly to a straight line with equal slope as the Tung function at M1/2 with b = 2.7-3.0. This leads to a considerable saving in computation but very slight difference to the result.The suggested simplifications have been applied to a sample of PMMA. The integral distribution curve obtained by the suggested method are closer to the actual one obtained by sedmentation rate method than the usual Schulz-Dinlinger treatment.

The interrelation between traditional quantum field theory and composite quantized field theory is investigated. It is found that they are compatible and interrelated in the ladder approximation, whereas beyond this approximation the interrelation is not established.

Linear form functions are commonly used in a long time for a toroidal volume element swept by a triangle revolved about the symmetrical axis for general axisymmetrical stress problems. It is difficult to obtain the rigidity matrix by exact integration, and as approximations close to the symmetrical axis, the accuracy of this approximation deteriorates very rapidly. The exact integrations have been suggested by some authors for the calculation of rigidity matrix. However, it is shown in this paper that...

Linear form functions are commonly used in a long time for a toroidal volume element swept by a triangle revolved about the symmetrical axis for general axisymmetrical stress problems. It is difficult to obtain the rigidity matrix by exact integration, and as approximations close to the symmetrical axis, the accuracy of this approximation deteriorates very rapidly. The exact integrations have been suggested by some authors for the calculation of rigidity matrix. However, it is shown in this paper that these exact integrations can only be used for those axisymmetric elastic bodies with central hole. For solid axisymmetric body, it can be proved that the calculation fails due to the divergent property of rigidity matrix integration. In this paper, a new form function is suggested. In this new form function,the radial displacement u vanishes as radial coordinates r approach to zero. The calculated rigidity matrix is convergent everywhere, including these triangular toroidal element closed to the symmetrical axis. This kind of elenent is useful for the calculation of axisymmetric elastic body problem.