A theory of many-body wave scattering is developed under the assumption a << d << λ, where a is the characteristic size of the small body, d is the distance between neighboring bodies and λ is the wave-length in the medium in which the bodies are embedded. The multiple scattering is essential under these assumptions. The author’s theory is used for creating materials with a desired refraction coefficient. This theory can be used in practice. A recipe for creating materials with a desired refraction coefficient is formulated. Materials with a desired radiation pattern, for example, wave-focusing materials, can be created.

Forest ecological benefit compensation plays a promoting role in improving the enthusiasm of forest ecological builders and maintainers, maintaining the legitimate economic interests of forest owners, and coordinating the fairness between the “clear water and green mountains” protectors and the “gold and silver mountains” beneficiaries. Comprehensive combed the domestic forest ecological benefit compensation mechanism, including the compensation scope, compensation subject, compensation object, the research progress of compensation standard, summarized the forest ecosystem benefits measurement, including physical appraisal method, the value evaluation method, energy analysis method and the characteristics and application research progress of ecological model method. This paper discusses the research status and existing problems of the calculation basis of compensation standard, the origin, research emphasis and progress of forest ecological service payment abroad in recent years, and the mechanism of forest ecological service payment in many countries. Finally, some suggestions are put forward to improve the compensation mechanism of forest ecological benefits in China. On the one hand, it is necessary to broaden the source of funds through various ways of marketization and scientifically evaluate the forest ecological benefits. On the other hand, the compensation standard should be established scientifically and reasonably to achieve different compensation levels or compensation intervals.

In this study, we define the unrestricted Pell and Pell-Lucas quaternions. We give generating functions, Binet formulas and some generalizations of well-known identities such as Vajda’s, Catalan’s, Cassini’s d’Ocagne’s identities.

Dushan county, Guizhou province, is located in the southernmost tip of Guizhou province. It belongs to the temperate climate of the subtropical region and is one of the centers of the karst east Asia area. The total area of the county is 242220 hectares, of which 169142 hectares are rocky desertifi cation or endangered desertification state. At present, the problem of rocky desertification has seriously affected the ecological environment of the county, which is one of the important factors that restrict the local social living standard and economic development. Therefore, it is of great significance to promote the social and economic development of the county by investigating and analyzing the spatial differentiation rules, present situation and harm of rocky desertification in Dushan county.

The objective of this work was to evaluate the combined effect of bovine manure, Pseudomonas putida and Trichoderma aureoviride on the development of lettuce (Lactuca sativa). The promotion of plant growth by microorganisms may be a viable and sustainable alternative for lettuce crop management. The experimental design was entirely randomized with five treatments: T0 (witness without fertilization, P. putida and T. aureoviride), TE (cattle manure), TEB (cattle manure + P. putida), TEF (cattle manure + T. aureoviride), TEFB (cattle manure + P. putida + T. aureoviride) and ten repetitions each. The following variables were analyzed: germination velocity index (GVI), first count (FC), germination percentage (GP), leaf area index and productivity. The TEFB treatment proved to be a viable alternative for the production of lettuce, especially for small producers, since all the vegetable production in the region comes from family farming.