DESIGN OF DEEP-FERTILIZATION MECHANISM WITH DEFORMED GEARS AND PERFORMANCE TESTS

Deep-fertilization mechanism is a key part of deep-fertilization liquid fertilizer applicator. To obtain a good-performance deep-fertilization mechanism, this study developed a deep-fertilization mechanism with deformed gears and designed a deformed gear fertilization test bench. Single-factor and central composite design tests were performed with the planet carrier, spray hole size and pump pressure as the test factors, and the fertilizer amount as the test index. The results of the single-factor test showed a linear functional relationship between fertilizer amount and pump pressure, an exponential functional relationship between planet carrier velocity and fertilizer amount, and an exponential relationship between spray hole size and fertilizer amount. The rotating and perpendicular test data were analyzed and optimized using Design-Expert 8.0.5 software. The result of the optimization is: 10.5ml of fertilizer amount with pump pressure 0.36MPa, planet carrier velocity 82 r/min, and spray hole size 2 mm. The test result can meet the agronomic requirements.

On the finiteness and tails of perpetuities under a Lamperti–Kiu MAP

Consider a Lamperti–Kiu Markov additive process $(J, \xi)$ on $\{+, -\}\times\mathbb R\cup \{-\infty\}$, where J is the modulating Markov chain component. First we study the finiteness of the exponential functional and then consider its moments and tail asymptotics under Cramér’s condition. In the strong subexponential case we determine the subexponential tails of the exponential functional under some further assumptions.

On superstability of exponential functional equations

The aim of this paper is to prove the superstability of the following functional equations: $$\begin{aligned}& f \bigl(P(x,y) \bigr)= g(x)h(y), \\& f(x+y)=g(x)h(y). \end{aligned}$$ f ( P ( x , y ) ) = g ( x ) h ( y ) , f ( x + y ) = g ( x ) h ( y ) .