Search Results (3)

Let $G_p(x,y,z)={\parallel x+y+z\parallel }^p+{\parallel z\parallel }^p{-\parallel x+z\parallel }^p-{\parallel y+z\parallel }^p$ be defined on a normed space $\mathcal{X}$. The special case $G_2(x,y,z)=0,\forall z\in \mathcal{X}$, where $\mathcal{X}$ is a real normed linear space, coincides with the trapezoid orthogonality (T-orthogonality), which was originally proposed by Alsina et al. in 1999. In this paper, for the case where $\mathcal{X}$ is a complex inner product space endowed with the inner product $⟨·,·⟩$ and induced norm $\parallel ·\parallel$, it is proved that $Sgn\left(G_2(x,y,z)\right)=Sgn\left(Re⟨x,y⟩\right),\forall z\in \mathcal{X}$, and a geometric explanation for condition $Re⟨x,y⟩=0$ is provided. Furthermore, a condition $G_2(x,iy,z)=0,\forall z\in \mathcal{X}$ is added to extend the T-orthogonality to the general complex normed linear spaces. Based on some characterizations, the T-orthogonality is compared with several other well-known types of orthogonality. The fact that T-orthogonality implies Roberts orthogonality is also revealed. Full article

When peanuts are harvested, the high rate of pod crush and pods leakage are the main problems in the current peanut fruit picking process. Optimized peanut picking rollers help to improve peanut harvesting efficiency. This paper investigates the fruit picking system of a three-monopoly, six-row semi-feeding peanut combine harvester, in order to reduce the rate of crush and leakage of peanut pods during the picking process. Firstly, this article specifies the structure and basic parameters of peanut picking pairs of rollers. Secondly, this paper combines JKR (Johnson-Kendall-Roberts) model theory, crash model simulation analysis, a field test, and other methods. Motion and force analysis are presented in detail for the peanut picking mechanism and associated harvesting components. The optimum clamping chain speed, the angle of installation of the picking rollers to the clamping chain, and the picking rollers’ speed are determined. A three-factor, three-level regression orthogonal combination test was designed to obtain regression models for pod crushed and pods leakage rate. The regression model’s response surface analysis concluded that when the clamping chain speed is 0.84–1.2 m/s, the fruit picking roller angle is 10°–11.2° and the fruit picking roller speed is 442 r/min–500 r/min. It is the optimal working parameter for the three-monopoly six-row peanut combine harvester. At this point, the peanut harvesting requirements are met, and the overall performance is significantly improved. This paper lays the foundation for the development of the semi-feeding peanut picking system. Full article

After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value for the functions of the corresponding operator. Full article