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We investigate high-order harmonic generation (HHG) from asymmetric molecules exposed to intense laser fields. We show that the emissions of odd and even harmonics depend differently on the orientation angle, the internuclear distance, as well as the effective charge. This difference mainly comes from different roles of intramolecular interference in the HHG of odd and even harmonics. These roles map the structure of the asymmetric molecule to the odd vs even HHG spectra.

This paper uses mathematical statistics method and analyzes the main scoring techniques: the serve technique, the jump smash technique, the net lob technique, the pushing backcourt ball technique and the smash technique by analyzing the data of the 29th Olympic Games by He Hanbin/Yu Yang (China) and Nova/Nasir (Indonesia). The analysis shows that: in the badminton mixed doubles match, since both sides are partners for many years, in order to win the game you must have good badminton technique; particularly the error rate of the net lob technique and the pushing backcourt ball technique is high, which needs further practice. The study plays a certain role in promoting the development of badminton technique and the popularization of badminton sports.

The Wiener index is a well-known measure of graph or network structures with similarly useful variants of modified and reverse Wiener indices. The Wiener index of a tree T obeys the relation W(T)=nT,1(e)·nT,2(e) where nT,1(e) and nT,2(e) are the number of vertices of T lying on the two sides of the edge e, and where the summation goes over all edges of T. The λ -modified Wiener index is defined as mWλ (T) =[nT,1(e)·nT,2(e)]λ . For each λ > 0 and each integer d with 3 ≤ d ≤ n− 2, we determine the trees with minimal λ -modified Wiener indices in the class of trees with n vertices and diameter d. The reverse Wiener index of a tree T with n vertices is defined as Λ(T)=½n(n-1)d(T)-W(T), where d(T) is the diameter of T. We prove that the reverse Wiener index satisfies the basic requirement for being a branching index.

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In order to improve the efficiency and robustness of reliability-based multidisciplinary design optimization (RBMDO), a new collaborative strategy (named C-RBMDO) which integrates performance measure approach (PMA) and concurrent subspace optimization strategy (CSSO) is proposed. Both the mathematical model and optimization procedure are put forward. The traditional triple-level nested flowchart of RBMDO is decoupled with the sequential optimization and reliability assessment (SORA). The deterministic multidisciplinary design optimization and the multidisciplinary reliability analysis are executed by CSSO and PMA respectively. Finally, the proposed method is verified through the design example of gear transmission.

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