Two types of new Abel differential equation are structured by method of variation replacement, variation position transformation and compound function derivation law.

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Adamson reviews scholarship in sociolinguistics and second language acquisition, comparing theories of variation in first- and second-language speech, with special attention to the psychological underpinnings of variation theory.

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The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. The advantage is that the cost function variation is independent of the flow field variation, with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow-field evaluations. So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.

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The main results were as follows: 1.After being radiated with 60 Co-γ, seven types of mutated plants were obtained through morphologic observation on the aftergrowth of the regeneration plantlets. The mutation characters included the purple leaf vein and petiole, the spotted leaf, the strumae leaf, the acerose leaf, the tender stem, the leaf shape variation, and the leaf color variation.

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Using an airgun as a repeatable seismic source and recording the data at a fixed point, the variation of shear wave splitting parameters can indicate the variation of local stress-strain fields, and hence provides a method for earthquake stress-forecasting.

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But significant differences were found in coefficient of variation and broad-sense heritability (H2) of the three characters: CV and H2 of self-pollinated fruiting rate were both greatest, with the variation mainly resulted from inheritance, and high inheritance potential; H2 of fertile flower rate was the least and its variation was less from inheritance; CV of average fruit weight was the least and its inheritance potential is small. Thirdly, the ratios of sweet to bitter kernel of F1 progenies in positive and reverse crosses between Katy and Taianshuixing were 18∶16 and 13∶12, and were both in agreement with a 1∶1 segregation by χ2 test, which demonstrated that the bitter kernel character of Katy was heterozygous.

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For the leaf area index of the three forest types, there was a similar variation trend, i.e ., increased first and decreased then, with the maximum presented in mid-July or August for Q. mongolica and J.mandshurica forests while in mid-August or September for F. rhynchophulla forest. The canopy porosity of the three forest types also had a similar variation trend, but opposite to leaf area index, being decreased first and increased then, with the minimum presented in mid-June, July, August or September. The analysis of variation coefficients of leaf area index, transmitted direct gap light, and transmitted diffuse gap light indicated that the spatial pattern of leaf area index in July-September was the main factor affecting the spatial distribution of transmitted diffuse gap light.

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The study results show that:①The distribution of Cd in shallow surface soils is characterized as: The content of Cd in lacustrine deposit, alluvial lacustrine and alluvial-diluvial low-lying plain is 1.4 to 1.8 times as high as in alluvial-diluvial high valley flat and alluvial-diluvial high bank physiognomy areas.②The content variation of Cd in horizontal distribution was controlled by clay primarily and OrgC secondly. The variation of OrgC was major factor that affected the content variation of Cd in vertical distribution.

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Orthodox historical linguists ascribe variation to language-in or structural factors; functionalists attribute variation to external factors; and sociolinguists associate variation with change of social norms.

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