Let B be a biconnect domain in the extended complex plane R 2, Γ and Γ′ denote the curve family in B which separates and joins the two boundary components of B espectively, and M(Γ) and M(Γ′)denote the module of Γ and Γ′ respectively, we prove in this paper that M(Γ)=1M(Γ′).

In this paper, functions of the P-Sa-Sm-N surface family under constant amplitude cyclic loading are established by combining the P-S-N curve family and constant life diagrams,which is fcasible in engineering application. Meanwhile, the preconditions of mechanics and probability-statistics are clearly presented.

A new method for modification of curves is described in this paper. To modify an initial G~2 rational cubic Bezier curve,we give constrained boundaries,replace the curve segment intersecting the boundaries with one of its curve family,which is either tangent to the boundaries or passes their vertexes,and restore G~2 continuity according to the curvature.

Based on measured data of test piles and with full consideration of the varying conditions of site, concept and empirical equation of π-S curve family and numerical solution of relevant P-S curve are put forth.

The mathematical function of the equivalent damage curve family is well fitted with the test data. The damage cumulative model and fatigue life prediction in complex loading were derived from the damage curve family function.

In this method, firstly we compute the exterior trajectory and the rotational angular velocities of the projectiles along the trajectory, and then we obtain the curve ω-t of angular velocities vs. time of flight. Through the analysis of ω-t curve family under various angles of fire, we select a ω_(t0)~* which can meet the tactical requirements.

The curve family calculated from the formula covers all experimental points and the formula can naturally be reduced to some other late published formulas under the some specified conditions.

Since the demand curve family facing the perfectly competitive firm has the formP =a, there is only one supply curve in this case.

235 lgτ, using the single scattering theory modified with epicentral distance, we obtain the curve family of corrected coda amplitudeAc(r,t), andω/2Qc values for each time interval of coda.

Thus, extending the H-curves can unify both C-curves and H-curves into a curve family too.

Thus, extending the C-curves can unify both C-curves and H-curves into one curve family.

Generally, the Hilbert curve family exhibits good performance in these studies.

This paper presents a method for employing electronic computer of small and medium size to compute and select the angular velocity ω_(t0) of self-destruction device, and to determine the principal structural parameters of the device. In this method, firstly we compute the exterior trajectory and the rotational angular velocities of the projectiles along the trajectory, and then we obtain the curve ω-t of angular velocities vs. time of flight. Through the analysis of ω-t curve family under various angles...

This paper presents a method for employing electronic computer of small and medium size to compute and select the angular velocity ω_(t0) of self-destruction device, and to determine the principal structural parameters of the device. In this method, firstly we compute the exterior trajectory and the rotational angular velocities of the projectiles along the trajectory, and then we obtain the curve ω-t of angular velocities vs. time of flight. Through the analysis of ω-t curve family under various angles of fire, we select a ω_(t0)~* which can meet the tactical requirements. For various numbers and diameters of the steel balls, we can compute the curve of angular velocity ω_(t0) of self-destruction vs. oblique angle α of the bevel shaped edge of sleeve (Fig. 2) and we get a group of curves. Based on the ω_(t0)~* selected from the tactical requirememts, we can determine suitable structural parameters i, d and α. With this method we can easily reveal the conditions of the dispersion of the burst points and the relationship between the positions of burst points of self-destruction and the minimum angle of fire θ_(0min) under various angles of fire θ_0 so as to solve the problem of optimum design which needs large amount of calculations and requires a few but very comprehensive influencing factors.

The stress distribution in the plate with the storoidal opening and the stress concentration around the opening are investigated by finite element method in this paper. Storidal openings are formed by the storoidal curve family, which lies between the circle (or ellipse) and the squar (or rectangle). The storoidal curves are practical and versatical and meet opening designs in the machine, aircraft and shipbuilding fields. Seven cases of the stress analysis of opening are given in this paper. The...

The stress distribution in the plate with the storoidal opening and the stress concentration around the opening are investigated by finite element method in this paper. Storidal openings are formed by the storoidal curve family, which lies between the circle (or ellipse) and the squar (or rectangle). The storoidal curves are practical and versatical and meet opening designs in the machine, aircraft and shipbuilding fields. Seven cases of the stress analysis of opening are given in this paper. The numerical results are obtained and some are illustrated by figures. In analysing the stress of the storoidal opening by means of computer techniques, we have found that the storoidal openings are generally superior to some of the more common types of openings. We recommend that this new type of opening be used in the engineering design.

To analyze the effect of two important derivatives, C_m and C_m~a, on roots of the characteristic equation of Ram Wing Vehicles (R.W.V.), the parameter plane method(P. P. M. ) in Dynamic Systems Analysis is applied. The parameter plane of the longitudinal motion equation of R.W.V. is established herein. Both C_m, and C_m~a, are considered as adjustable parameters. After the characteristic roots on the boundaries and break line are analyzed, the existential conditions of various steady regions can be obtained....

To analyze the effect of two important derivatives, C_m and C_m~a, on roots of the characteristic equation of Ram Wing Vehicles (R.W.V.), the parameter plane method(P. P. M. ) in Dynamic Systems Analysis is applied. The parameter plane of the longitudinal motion equation of R.W.V. is established herein. Both C_m, and C_m~a, are considered as adjustable parameters. After the characteristic roots on the boundaries and break line are analyzed, the existential conditions of various steady regions can be obtained. The results indicate that these conditions strongly depend on the break line. By mapping various steady boundaries from the parameter plane to the complex plane, the regions of steady characteristic roots and the ends of characteristic curve families, Г,, Г_0 and Г, can be determined. Two examples are given for explaining the results.This parameter plane distinctly shows the relationship between the derivatives C_m and C_m~a and all characteristic roots of the equation. It can be used for improving design, properly choosing related derivatives and estimating errors.