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This paper focuses on the vibration periodic property of Duffing oscillator with generalized initial conditions. Firstly, the undamped case is solved by Ji-Huan He’s frequency formulation; Secondly, the formulation is extended to the damped case. Numerical verification shows that the frequency formulation is mathematically simple and physically insightful and practically applicable. This paper paves a novel way for engineers to use the formulation to study nonlinear vibration system with ease and reliability. [ABSTRACT FROM AUTHOR]

The article presents a study on the phylogenetic relationships within Rhodiola (Crassulaceae) which has a high level of morphological diversity. Topics covered include the analysis of the sequences of the nuclear ribosomal internal transcribed spacers region and the plastid psbA-trnH and trnL-F markers, the monophyletic sections, and the well-supported clades formed. Also included is the evolution of dioecy and marcescent flowering stems.

In this study, chitosan-based silicon nanoparticles (Chsi-NPs) are prepared that primarily consists of C (57.9%), O (31.3%), N (5.6%), and Si (3.5%) and are 10–180 nm in size. We then explore the effect on the foliage applied on rice planted on soil contaminated with 104 mg·kg−1 arsenic (As); low (3 mg·L−1)and high (15 mg·L−1) doses of the foliar Chsi-NPs are administered during the rice grain filling stage. The results showed that the higher dose foliar Chsi-NPs treatment reduced the As concentration in the grain by 61.2% but increased As concentration in the leaves by 47.1% compared to the control treatment. The foliar spraying of the Chsi-NPs inhibited As transport to the grain by facilitating the attachment of As to the cell wall, with higher doses of the foliar Chsi-NPs treatment increased by 8.7%. The foliar spraying of Chsi-NPs increased the malondialdehyde levels by 18.4%, the catalase activity by 49.0%, and the glutathione activity by 99.0%. These results indicated that the foliar Chsi-NPs application was effective for alleviating As toxicity and accumulation in rice. This study provides a novel method for effectively alleviating As accumulation in rice. [Display omitted] • Foliar Chsi-NPs were used to improve the As tolerance of rice in soils. • Foliar Chsi-NPs application promotes the fixation of arsenic in the leaf cell wall. • Foliar Chsi-NPs treatments reduced the As concentration in the grain by 61.2%. [ABSTRACT FROM AUTHOR]

Abstract??Supergene Mn-oxide deposits are widely distributed in Guangxi, Guangdong, Yunnan, and Hunan Provinces, South China, accounting for 18% of the total Mn reserves in the country. Direct dating of supergene Mn enrichment, however, is lacking. In this paper, we present high-resolution40Ar/39Ar ages of Mn oxides from the Xinrong Mn deposit, western Guangdong, to place numerical constraints on the timing and duration of supergene Mn enrichment. A total of ten cryptomelane samples, spanning a vertical extent of 67?m, were dated using the40Ar/39Ar laser incremental heating technique, with seven samples yielding well-defined plateau or pseudo-plateau ages ranging from 23.48???0.91 to 2.06???0.05?Ma (2?). One sample yields a staircase spectrum that does not reach a plateau; the spectrum, however, indicates the presence of two or more generations of Mn oxides in the sample, whose ages are best estimated at 22.34???0.31 and 10.2???0.86?Ma, respectively. The remaining two samples gave meaningless or uninterpretable results due to significant39Ar recoil and contamination by old phases. The40Ar/39Ar data thus reveal a protracted history of weathering and supergene Mn enrichment that started at least in the end of the Oligocene or beginning of Miocene and extending into the latest Pliocene. Staircase-apparent age spectra, resulting from banded or botryoidal samples, yield an average growth rate of Mn oxides at 0.6?0.7???10?3?mm kyr?1. The values indicate that a 1-mm grain of Mn oxides may host minerals precipitated during a time span of ca. 1.5?m.y., and accumulation of Mn oxides to form economic deposits under weathering environments may take millions of years. The distribution of weathering ages shows that the oldest Mn oxides occur on the top of the profile, whereas the youngest minerals are found at the bottom, suggesting downward propagation of weathering fronts. However, two samples located at the intermediate depths of the profile yield ages comparable with those occurring at the highest elevations. Such a complexity of age distribution is interpreted in terms of preferential penetration of Mn-rich weathering solutions along more permeable fault zones, or as a result of multi stages of dissolution and re-precipitation of Mn oxides. A synthesis of geochronological and geological data suggests that formation of the Xinrong deposit was a consequence of a combination of favorable lithological, climatic, and structural conditions. Because the climatic and structural conditions are similar among the provinces of South China during the Cenozoic, the geochronological results obtained at Xinrong may also have implications for the timing of supergene Mn enrichment throughout South China. [ABSTRACT FROM AUTHOR]