Under the VC++6.0 environment, using Pro/Toolkit procedure development technology to carry on secondary development in Pro/E, and using Access2000 to build the database of GB dimentional tolerance, a set of software was designed which can automatic inquiry and sign note dimentional tolerance.

Combined with practical condition of safety control of geotechnical engineering, this paper probes into a set of analyzing methods which are fit for safety control of geotechnical engineering, and applies preferred plane theory in the safety control, which is propitious to the management of geotechnical engineering.

Closed orbits are described and a set of points of dense orbit is explicitly given.

If in addition {λn} is a set of uniqueness forEp, that is, if the relations f(λn)=0(-∞>amp;lt;n>amp;lt;∞), with f εEp, imply that f ≡0, then we call {λn} acomplete interpolating sequence.

In this note we prove that the Wigner distribution of an f ∈ L2(?n) cannot be supported by a set of finite measure in ?2n unless f=0.

We prove that the boundary of a bounded domain is a set of injectivity for the twisted spherical means on ?n for a certain class of functions on ?n.

This is used to investigate subspaces of the RKHS generated by a set of fundamental functions.

Although James and Coolidge (1933) solved the molecular hydrogen problem in almost complete agreement with experiment by using a 13-term 2-electron eigenfunction, his method can hardly be applied to more complex molecules. For this and other reasons (Coulson, 1938), it is still desirable to obtain a good one-electron eigenfunction, i.e., molecular orbital, for the hydrogen molecule. The best molecular orbital treatment available in the literature was given by Coulson (1938), who used a trial eigenfunction in...

Although James and Coolidge (1933) solved the molecular hydrogen problem in almost complete agreement with experiment by using a 13-term 2-electron eigenfunction, his method can hardly be applied to more complex molecules. For this and other reasons (Coulson, 1938), it is still desirable to obtain a good one-electron eigenfunction, i.e., molecular orbital, for the hydrogen molecule. The best molecular orbital treatment available in the literature was given by Coulson (1938), who used a trial eigenfunction in elliptical coordinates involving 5 parameters and obtained 3.603 eV for the binding energy of H_2, which is to be compared with the ex- perimental value of 4.72 eV. In the present investigation we have proposed a new type of trial eigenfunction for the molecular orbital: (1) with p = centers a, b, g, c, d,…… i = electron 1 or 2 (2) where the p's are centers along the bond axis a-b (Fig. 1). In this simple problem both the Fock and Hartree methods yield the same result. The molecular orbital ψ must satisfy the following integral equation: (3) where ε is the energy of the molecular orbital, F is the Fock operator which is equal to H+G(1), while H is the one-electron Hamiltonian operator: H = -1/2▽~2-1/r_a-1/r_b (4) and G(1) is the interaction potential (5) Substituting (1) into (3), we obtain the linear combination coefficients c_p, which must satisfy the following secular equation: (6) where is the solution of the secular determinant and The F_(pq)'s are not at first known, but depend upon the c_p's. A method of successive approximation must therefore be adopted. A set of c_p values may be assumed, the F_(pq)'s calculated, the secular determinant (7) solved, and a new set of c_p values found. This process is repeated until a "self-consistent" set of c_p values is obtained. The above procedure was first proposed by Roothaan (1951), not for H_2 but for more complex molecules. It was called by him the "LCAO SCF (linear combination of atomic orbitals self-consistent field) method". The new feature of the present investigation is that we not only use LCAO but also LCNAO (linear combination of non-atomic orbitals, such as x_g, x_c, x_d, …). The order of secular determinant (7) may be reduced to half if we replace the eigen- functions x_a, x_b .... by their symmetrical and anti-symmetrical linear combinations x_a + x_b and x_a-x_b. Numerical calculations have been carried out both for the three- and the two-centered molecular orbitals. The three-centered molecular orbital is (10) (11) where S_(ab) and S(ag) are the overlapping integrals between x_a and x_b, and between x_a and x_g respectively. The parameters a and g have 'been obtained to give minimum energy by the method described above. They are a=l.190, g=0.22, and the binding energy is 3.598 eV, which is almost as good as that obtained by Coulson (3.603 eV) using a trial function of 5 parameters. The two-centered molecular orbital is (12) (13) which gives a maximum binding energy of 3.630 eV for a=1.190 and R~(ac)=R(bd)=0.105 (Fig. 1). This result is 'better than Coulson's. If we allow different values for the ex-ponent α in x_a and x_g in equation (11), or if we use a four-centered molecular orbital, such as ψ=a(x_a + x_b) + b(x_c + x_d) with four parameters, namely α_a=α_b, α_c=α_d, R_(ac)=R_(bd) and the ratio b/a, it is possible to obtain a still better result. Extension of the present method to the treatment of more complex molecules is now under investigation.

The method of complementary I_0/I diagram for simplifying the computations of non-uniform beam constants is presented in this paper. The so-called "complementary I_0/I diagram" is the remaining I_0/I diagram of the haunched or de-haunched (or tapered) parts at the two ends of a beam after the I_0/I diagram of a non-uniform beam has been subtracted from the I_0/I = 1 diagram of a uniform beam.In the method of I_0/I diagram presented previously by the second author, the various momental areas have to be computed...

The method of complementary I_0/I diagram for simplifying the computations of non-uniform beam constants is presented in this paper. The so-called "complementary I_0/I diagram" is the remaining I_0/I diagram of the haunched or de-haunched (or tapered) parts at the two ends of a beam after the I_0/I diagram of a non-uniform beam has been subtracted from the I_0/I = 1 diagram of a uniform beam.In the method of I_0/I diagram presented previously by the second author, the various momental areas have to be computed for the entire length of a beam; in the method of complementary I_0/I diagram, the various momental areas need be computed for the lengths of the non-uniform sections at the two ends of the beam only. Hence the latter method is somewhat simpler than the former and may be considered as its improvement.The angle-change constants are the fundamental constants of a nonuniform beam, and only the coefficients of the angle-change constants need be computed. As any non-uniform beam may be considered as a uniform beam haunched or de-haunched or tapered at its one or both ends, the various anglechange coefficients φ may be computed separately in three distinct parts, viz., of a uniform beam, and φ~a and φ~b of the haunches at its two ends a and b, and then summed up as shown by the following general equation:φ=φ~a-φ~b (A) The values φ~a and φ~b are positive for haunched beams and negative for dehaunched or tapered beams, and either of them is zero for the end which is neither haunched nor de-haunched. To simplify the computations of the values of φ~a and φ~b, the complementary I_0/I diagram at each end of a beam is substituted by a cubic parabola passing through its two ends and the two intermediate points of the abscissas equal to 0.3 and 0.7 of its length. Then the value of φ~a or φ~b is computed with an error of usually less than 1% by the following formula:φ~a or φ~b = K_(0y0)+K_(3y3)+K_(7y7), (B) wherein y0, y3 and y7 are respectively the ordinates at the abscissa equal to 0, 0.3, and 0.7 of the length of the diagram, and the three corresponding values K_0, K_3 and K_7 are to be found from the previously computed tables.A set of the tables of K-values for calculating the values of φ~a and φ~b of the shape angle-changes and the load angle-changes under various loading conditions may be easily computed, which evidently has the following advantages: (1) As indicated by formulas (A) and (B), the computations of φ~a, φ~b and φ with K-values known are very simple; (2) the approximation of the results obtained is very close; (3) A single set of such K-value of the tables is applicable to non-uniform beams of any shape, any make-up, and any crosssection; and (4) as the K-values are by far easier to compute than any other constants, a comprehensive set of the tables of K-values with close intervals and including many loading conditions may be easily computed.Besides, by means of formulas (A), existing tables of constants such as A. Strassner's for beams haunched at one end only may be utilized to compute the shape and load constants for asymmetrical beams with entirely different haunches at both ends.Finally, five simple but typical examples are worked out first by the approximate method and then checked by some precise method in order to show that the approximation is usually extremely close.

The investigation of the properties of loess constitutes a highly specialized branch of soil engineering. The design and construction of foundations and earthwork in this soil involve many uncertainties that have not been solved. Among all uncertainties the following are considered the most important items:(1) the changes of bearing capacities caused by variations in the strength of the cohesive bond due to changes in its moisture content, and(2) the methods of ascertaining the amount of its settlement under...

The investigation of the properties of loess constitutes a highly specialized branch of soil engineering. The design and construction of foundations and earthwork in this soil involve many uncertainties that have not been solved. Among all uncertainties the following are considered the most important items:(1) the changes of bearing capacities caused by variations in the strength of the cohesive bond due to changes in its moisture content, and(2) the methods of ascertaining the amount of its settlement under the combined action of foundation loads and of percolating water.In order to prevent foundations against settlement the "Provisional Code for the Design of Natural Foundations" gives a set of rules of precautions for designers to observe, which include the prevention of water from getting into the foundations, artificial strengthening of the soil and the designing of superstructures in such a way that they will adjust themselves to settlement. Before the adoption of any of such precautions could be decided, the accuracy in evaluating the amount of possible settlement of the soil is a problem of prime importance, which unfortunately cannot be satisfactorily obtained.This paper attempts to give some predominent characteristics of loess, the points of contradiction between the assumptions made in the old designing code and the results derived from actual work, a comparison of the salient features of the old code with the new code of ordinance of the U. S. S. R., 1955, and some suggestions regarding further developments of this branch of soil engineering. Several cases of actual construction work in loess in recent years are also cited which, owing to our incomplete knowledge of the soils, nature, have inevitably either caused unnecessary expenses to the works, or brought about results detrimental to the stability of structures.In this branch of soil engineering have, therefore, many difficulties yet to be contended with. It is hoped that this paper could be of some reference value to research engineers in this line and the knowledge of loess be further developed in view of the increasing pressure of necessity in our present construction work.