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Planetary gear train is mainly used for power transmission, so it is of great significance to study its self-locking and efficiency. In this study, the self-locking analysis and efficiency maximization design of a 3K-H planetary gear train are carried out. Firstly, the efficiency of the positive and negative mechanism of the gear train is calculated using the transmission ratio method. Then, a unified formula for the efficiency of the planetary gear train is summarized. Furthermore, the efficiency curve is drawn by Matlab. Next, the trend of efficiency change of the planetary gear train and the conditions for realizing self-locking are analyzed. Finally, how to maximize the efficiency of the opposite mechanism under the condition of self-locking is studied.

Polyoxometalates (POMs) have shown great potential for applications in photocatalysis due to their unique structural features, tunable band gap, and environmental benignity. Herein, a Fe ion-incorporated Co4W6O21(OH)2·4H2O sphere network POM was successfully synthesized via a simple hydrothermal process. A DFT calculation proved that the Fe ion partially replaced cobalt atoms, forming FexCo4−xWOH, which played a crucial role in modulating the electron state and the band structure. The as-prepared FexCo4−xWOH exhibited excellent Fenton-like photocatalytic activity; the degradation rate of RhB improved 3.69 times compared with the sample without doping. The favorable performance of FexCo4−xWOH is a result of the synergistic effects of the Fenton reaction and the activation of H2O2 under visible irradiation, which can generate a mass of •O2− and •OH species in the unique sphere network structure. This study supplied a new idea for designing highly-active Fenton-like POM photocatalysts for environmental remediation. [ABSTRACT FROM AUTHOR]

An explicit upper bound Z(2, n) ≤ n + m - 1 is derived for the number of zeros of Abelian integrals M1(h) = ∮γ(h) P(x, y) dy - Q(x, y) dx on the open interval (0, 1/6), where γ(h) is an oval lying on the algebraic curve Hλ = (1/2)x2 + (1/2)y2 - (1/3)x3 - λy3 = h, P(x, y), Q(x, y) are polynomials of x and y, and max{deg P(x, y), deg Q(x, y)} = n. The proof exploits the expansion of the first order Melnikov function M1(h, λ) near λ = 0 and assume (∂m/∂λm)M1(h, λ)|λ = 0 not vanish identically. [ABSTRACT FROM AUTHOR]