A second-order nonlinear neutral delay differential equation was studied, and some sufficient conditions for existence of positive solutions for this equation were established. The advantage of the results is omitting the restriction condition of for any， must be negative. Furthermore, some examples were presented to illustrated that the results is more effective.

When the gas-liquid two-phase flows through tee pipeline, the distribution of two phase in two branch pipes is always uneven. There may be only gas branch in pipelines when it is serious, while the other export tube may be full of liquid. The numerical simulation on oil-gas two phase fluxion in different time by CFD was made and the oil and gas separation characteristics in branch pipes were get. The results show that there will be gas-liquid separation phenomenon in branch pipe when the oil and gas flow through branch pipe of tee pipeline, and close to the mouth branch the separation phenomenon is obvious. There is almost no separation phenomenon in certain distance of the branch mouth.

 

A type Ⅳ functional response predator-prey system was studied.The existence of global limit cycle was investigated by using qualitative analysis and the ideas of Poincaré-Bendixson theory, and some biological illustrations were given.