A new approach for solving mechanical problems of Linear Lagrangian systems using the Hamilton–Jacobi formulation is proposed. The equations of motion are recovered from the action integral. It has been proved that there is no need to follow the consistency conditions of the Dirac approach.

The study aimed to determine the effect of goat breed (Shami, Mountain Black and Hybrid) on testicular and epididymal sperm reserves. The study was conducted at Mutah University Animal Farm, Jordan in March 2016. The study area lies between Latitude of 31°27 ′′ N, Longitude of 35°74 ′′ W, and an altitude of 960 m. Average temperature and relative humidity recorded during the study were 14.6°C and 59.0%, respectively. Hybrid had the heaviest (P = 0.04) right tail epididymal weight (6.36 ± 0.3 g), the highest (P = 0.03) epididymosomatic index (0.60 ± 0.1 g/kg), and the widest (P = 0.02) testicular width (0.32 ± 0.03 cm/kg) relative to body weight. Epididymal sperm concentrations in the right testicular side were the highest (P = 0.04) in Hybrid (0.530 ± 0.15 × 10 9 sperm/ml) compared to Shami (0.386 ± 0.04 × 10 9 sperm/ml) and Mountain Black (0.322 ± 0.10 × 10 9 sperm/ml). Total testicular-epididymal sperm concentrations in both testes were the highest (P = 0.04) in Hybrid (0.810 ± 0.20 × 10 sperm/ml) compared to Shami (0.764 ± 0.09 × 10 9 sperm/ml) and Mountain Black (0.716 ± 0.12 × 10 9 sperm/ml). Furthermore, Hybrid had the highest (P = 0.05) epididymal body sperm concentrations (0.252 ± 0.05 × 10 9 sperm/ml) in both testes compared to Mountain Black and Shami. Taken together, the outcomes of this work highlighted the testicular and epididymal sperm traits in bucks of three breeds native to the semiarid region of Jordan. Hybrid displayed greater testicular traits than Shami and Mountain Black.

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The enhancement spectra of the collision-induced absorption of D2 in its fundamental band region 2600–4000 cm−1 in the binary mixtures D2–He, D2–Ar and D2–Kr are investigated at 298 K. The binary absorption coefficients of the band are determined from the measured integrated absorption coefficients and compared with previous results. An analysis of the experimental spectra is carried out by assuming appropriate line-shape functions for the overlap and the quadrupole transitions.