Assuming that the drill stem is a homogeneous elastic pipe with constant section, articulated at both ends and without stabilizers, the author studies the effects of the flowage of drill fluid on the lateral vibration and stability of the drill stem, and derives the vibration frequency equation and the critical equation of destabilization.

The quality characteristics of 14 Chinese optimum coal types used in direct liquefaction have been analyzed. The optimum region and the critical equation have been worked out for the first time,Which are of great significance for guiding the research on coal liquefaction behaviors.

The differential equations of nonlinear vibration of the shell are obtained. The cusp catastrophe model of nonlinear dynamic buckling is developed by using catastrophe theory. The dynamic buckling conditions are discussed and the critical equation of dynamic buckling of the shell is obtained.

According to the principles of saving energy and water and raising economic benefit, in this paper are formulater the critical equations for gravity and water lifting irrigation, irrigation by canal and pipeline, and ground and micro-sprinkler irrigation.

secondly,me deep and perfect the model of G-C , get the critical function of supplier’strategic change in manufacturer innovation, and investigate the cooperative mode that the performance of supply chain is optimized;

This method is simpler and more convenient than that of solving the equation of stability critical condition, especially when the column is connected at its top with elastic beam, the results obtained by this method have the same precision as required.

Using the critical equation for the limiting regimes of a gas-liquid system with independent flow rate of the gaseous phase, experimental results on the stability of a two-phase mixture are generalized to thermosiphons.

In this work the critical equation together with the stationary thermal neutron distribution is stated for a cylindrical neutron-multiplying structure.

A critical equation is derived for determining extruder output in the case of a Newtonian liquid that adheres to the walls.

We also recover existence results for the critical equation.

This paper offers a simple method for computing the effective length of two-stepped columns. The mathematical model is based on the calculation of geometrical figures by graphic method and the solution is obtained by successive approximation. This method is simpler and more convenient than that of solving the equation of stability critical condition, especially when the column is connected at its top with elastic beam, the results obtained by this method have the same precision as required. Flow charts for calculation...

This paper offers a simple method for computing the effective length of two-stepped columns. The mathematical model is based on the calculation of geometrical figures by graphic method and the solution is obtained by successive approximation. This method is simpler and more convenient than that of solving the equation of stability critical condition, especially when the column is connected at its top with elastic beam, the results obtained by this method have the same precision as required. Flow charts for calculation are also given in this paper.

The critical equations of buckling of a rectangular sheet , which is compressed at two opposite simply supported edges and is stretched at the other two built-in edges , is obtained by the energy method. Analysis of the buckling of non-uniform stretching problems of sheets with this equation yields the critical load coefficent of buckling, with which it is proved that Yoshida Buckling Test (YBT) and the non-uniform stretching of a rectangular sheet which has relevent sizes are identical in their critical points...

The critical equations of buckling of a rectangular sheet , which is compressed at two opposite simply supported edges and is stretched at the other two built-in edges , is obtained by the energy method. Analysis of the buckling of non-uniform stretching problems of sheets with this equation yields the critical load coefficent of buckling, with which it is proved that Yoshida Buckling Test (YBT) and the non-uniform stretching of a rectangular sheet which has relevent sizes are identical in their critical points of buckling. That means as a simulative test YBT is feasible for non-uniform stretching problems.

In the formation of different grain harvest procedures in various districts,their historical and geographical causes are something and the local economical levels that play the decisive role are anything. By iscussion of critical equations for economic effects of machine unit, quantatively analyzed are four typical harvest processes-manual reap-ing-threshing,windrowing-power threshing,binder-thresher, and combine harvester; and their critical curves of economic effects plotted, giving a reference to selecting...

In the formation of different grain harvest procedures in various districts,their historical and geographical causes are something and the local economical levels that play the decisive role are anything. By iscussion of critical equations for economic effects of machine unit, quantatively analyzed are four typical harvest processes-manual reap-ing-threshing,windrowing-power threshing,binder-thresher, and combine harvester; and their critical curves of economic effects plotted, giving a reference to selecting mechanized harvest processes.