Employing distributed Gaussian bases (DGB) to expand the vibrational eigenfunctions of the Morse oscillator in calculations for reaction probabilities, the calculation method becomes efficiently simplifies.

In calculations, at the basis of the stream function-axial velocity equation and the boundary equation above, using the finite difference method, the numerical calculations of the distribution of the secondary flow of Power-law fluid in eccentric annulus with the inner cylinder executing a planetary motion are made out, and the distribution of the secondary flow are plotted, and the relations between the conformations of secondary flow and the eccentric distance, the rotation and revolution velocities of the inner cylinder are analyzed.

A theoretical study on the electuonic structures of (dmpe)_2HtCrBH_4(Ⅰ), (dmpe)_2HtCrlH_4(Ⅱ) and [(dmpe)_2HtCrAlH_4l_2(Ⅲ) dmpe=(CH_3)_2PCH_2CH_2P(CH_3)_2, inwhich we have used two H_3 instead of one dmpe in calculations has been carried out by cndol_2 method.The results showed: (1) in occupied Mo, 6b_1 (HOMO) and 7a_1 in(Ⅱ), Cr 3d orbital repulses with Hb ls orbital (Hb is bridge judrogen atom), bnt in (Ⅰ), this repulsion is weaken; Cr(u-Hb)_2B is more stable and in lower energy than Cr(u-Hb)_2Al. (2) In the electronic structure of(Ⅲ, the repulsion between Cr 3d and H ls is weaken largely; Al(u-Hb)_2Al is in low energy. Ht和Hb are active for theirr large contribution to higher occupied Mo and it may be the reason of easy cxchangc nctwccn Ht and Hb in solution. The differences in their electronic structurc are in agreement with experiment result.

Finally,we analyze the efficiency of the proposed sc heme and show that the scheme is more efficient than group signature schemes suc h as ACJT scheme in complexity.

3. The analysis on different empirical formulations of in-tube condensation heat transfer coefficients indicate that R404A can be treated as pure refrigrant when calculating it's in-tube condensation heat transfer coefficients.

Disadvan-tages of time consuming and inaccurate calculation results with MCNP4C when calculating the deep penetra-tion problems are avoided by step calculation.

oct file, the errors brought out by the interpolation of station' s coordinates can be reduced when calculating the ocean tidal displacement corrections,so as to increase the precision of GPS data processing.

Comparison of the Calculations of Three-Convolution Circular Arc Corrugated Diaphragms by Toroidal Shell Theory and by Orthogonal Anisotropy Plate Theory

The coefficients used in calculations were determined by us.

In calculations we used two models: continuous and discrete.

A software tool for application in calculations of the position and velocity vectors of spacecraft is presented.

In calculations of turbulent flows with combustion, it is often assumed that this distribution has a universal dependence on the mean concentration and the pulsations of the concentration, which are determined from the corresponding equations.

The effect is also obtained in calculations made within the framework of the Navier-Stokes equations.

Attention is given to polarographs and peripheral devices differing in complexity and analytical potentialities.

These generators are similar to Geffe's generator in complexity and random properties.

For the consideration of practical application, it is further simplified in complexity.

Compared with the original ML algorithm, the simplified ML algorithm can provide significant reduction in complexity with small degradation in performance.

In this paper, we apply the sampling method (Monte Carlo) to factor graphs, and then the integrals in the sum-product algorithm can be approximated by sums, which results in complexity reduction.

When calculating the dispersion attraction between nanoparticles in dispersions, we use Mitchell and Ninham equations for the case of small (compared to particle radii) interlayer thickness.

When calculating coordinates and velocities on the integration step (at given instants of time), the approximate Everhart formula was employed.

It is shown that, when calculating the transformation kinetics for the model under consideration, in the general case (at s ≠ 1/2), the effects of shielding in the particle growth must be taken into account.

These values are taken into account when calculating kinetic parameters of the NaVO3 electroreduction.

It is emphasized that one should take into account the effect of thermoelastic stress when calculating this energy.

Measurement of the intensity of total scattering of x-rays by a number of polyatomic gases was made for scattering angles between 15° and 130 ° using an ionization method of recording the scattered intensity. Balanced filters of ZrO2, and SrO were used to separate the MoKa rays and Soller slits were placed in front of the ionization chamber to obtain a definite scattering angle. The gases studied are CL2, CO2, N2O, H2S, CC14 and CHCl3. In each case the absolute values of the scattered intensity were determined...

Measurement of the intensity of total scattering of x-rays by a number of polyatomic gases was made for scattering angles between 15° and 130 ° using an ionization method of recording the scattered intensity. Balanced filters of ZrO2, and SrO were used to separate the MoKa rays and Soller slits were placed in front of the ionization chamber to obtain a definite scattering angle. The gases studied are CL2, CO2, N2O, H2S, CC14 and CHCl3. In each case the absolute values of the scattered intensity were determined by comparison with the scattering from oxygen, the results of Wollan for the latter gas being taken as correct. The experimental results are actually compared with Woo's theory of the scattering of x-rays by polyatomic gases and the agreement seems to be satisfactory.

A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two well-known theories,molecular orbital theory and electron-pair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the anti-symmetrical two-electron bond function ψ_i(v_(2i-1),v_(2i)).(If there exist one- electron,three-electron or many-electron bonds,they can be similarly described by the corresponding one-electron,three-electron...

A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two well-known theories,molecular orbital theory and electron-pair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the anti-symmetrical two-electron bond function ψ_i(v_(2i-1),v_(2i)).(If there exist one- electron,three-electron or many-electron bonds,they can be similarly described by the corresponding one-electron,three-electron or many-electron bond func- tions.) Then the stationary state of the molecule is represented by the follow- ing wave function Ψ, where the summation is over all permutations of 1,2,……,2n except those within the interior of the functions,since each ψ_i is already anti-symmetrical.Obviously (2~n/((2n)/!))~(1/2) is the normalization factor. By quantum mechanics the energy of the molecule equals (1) here H_i,T_(ij) and S_(11)' are respectively the following three kinds of operators, (2) (3) (4) The third term of equation (1) is the exchange integral of electrons 1 and 1', while (1,2') is that of electrons 1 and 2'.According to the definition of bond functions,ψ_i may be written as (5) Substituting equation (5) into equation (1) and carrying out the integration over spin coordinates,we obtain (6) It can be easily seen from equation (6) that the combining energy of a mole- cule consists of two parts,one being the binding energy of the bonds represent- ed by the first term of equation (6),and the other being the interaction energy of the bonds denoted by the second term of that equation. If we choose certain functions φ_i~('s) involving several parameters and substi- tute them into equation (6),we may determine the values of those parameters by means of the variation principle. For the discussion of bond interaction energies,we develop a new method for the evaluation of certain types of three-center and four-center integrals.The interaction energy of a unit positive charge and an electron cloud of cylindrical- symmetry distribution may be written as (7) where (8) and R_0~2=a~2+b~2+c~2 The interaction energy of two electron clouds both of cylindrical-symmetry distributions with respect to their own respective axes is evaluated to be (9) (10) where is to sum over j from zero to the lesser value of n-2i and m, is to sum over i from zero to the integral one of n/2 and (n-1)/2,and is to sum over all cases satisfying the relation =m-j,while b_(n,n-2i) represents the coefficient of x~(n-2i) in the n th Legendre polynomial.

In this paper is presented a method of finding the. reactive moments distributed along the clamped edges of a rectangular plate by means of double sine series. Plate with two opposite edges clamped and the other two opposite edges simply supported, and plate with all four edges fixed are used as illustrative examples; the load being uniformly disdributed. The results we obtained are certainly exactly the same that we had obtained by using the method of superposition. However, the method by the double series...

In this paper is presented a method of finding the. reactive moments distributed along the clamped edges of a rectangular plate by means of double sine series. Plate with two opposite edges clamped and the other two opposite edges simply supported, and plate with all four edges fixed are used as illustrative examples; the load being uniformly disdributed. The results we obtained are certainly exactly the same that we had obtained by using the method of superposition. However, the method by the double series has its advantages, when the loads acting on the plate are discontinous. Besides our method can be easily extended for solving the reactive moments of clamped edges of plates on the elastic foundation and under the combined action of lateral load and uniform compression or tension.