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.

The market demand for uniformity and productivity of commercial carrot roots has prioritized hybrid materials over open-pollinated varieties. In this sense, the objective of this work was to estimate the combining ability of carrot genitors for root productivity and resistance to leaf scorch. The experiments were conducted in Gama, DF, in the agricultural years 2012/13 and 2013/14. We evaluated 33 carrot hybrids, originated from crosses between three male-sterile populations, with 11 male-fertile S2 lines, all the genitors being of tropical origin. At 90 days after sowing, the severity of the leaf blight disease was estimated in the plots. At 100 days after sowing, harvesting was performed and root yield characters were evaluated. Analysis of variance and partial diallel analysis were performed for each year and jointly for both years. It was found that additive and non-additive genes are important in the manifestation of root yield and leaf blight resistance traits in carrot hybrids. The male-sterile parents with higher overall combining ability for root productivity are strains LM-649 and LM-650 and, among the male-fertile, strain LM-555-2-2. The best hybrids for root yield and leaf blight resistance are LM-649 × LM-555-11-1, LM-650 × LM-555-7-1 and LM-650 × LM-554-8-1.

In this paper, the pollination and biology of apricot in Hongfeng and New Century were studied. The results are as follows: (1) The est pollination with the red variety is early, new century's best pollinating varieties is camel yellow. (2) The flowering period of different cultivars was different, and the flowering period of Hongfeng and other varieties was 3 - 7 days later than that of Baxing water apricot and other varieties, which provided germplasm for further breeding of late flowering varieties. (3) Hongfeng, the new century and other varieties of self-flowering rate of 0 - 3.61% range, is self-incompatible varieties. (4) The pollen germination rate of different cultivars was higher than 50%, which indicated that the pollen was mature and the fertility was strong, and the reason of low percentage of self-pollination was pollen abortion, the main reason was self and so on.

The article examines the issues of application and improvement of the methodology for evaluating industrial enterprises as recipients of state support within the framework of the implementation of industrial policy. The authors considered approaches to the content of industrial policy, investigated the factors influencing its efficiency, identified aspects of its imperfections that arise when applying an incomplete list of important parameters of economic development and ambiguity in the interpretation of previously applied estimates. The article presents proposals to improve the methodology for assessing potential recipients of state support based on the development of a comprehensive indicator for assessing enterprises (recipients of support), taking into account not only the classical parameters of the economic efficiency of industrial enterprises applying for state financial assistance, but also such aspects as the development of budgetary funds, belonging to priority sectors of the economy, characteristics of sustainable development and export and innovation potential. Combining the results of a comprehensive assessment of the recipient of state support with a map of the business demography of the territory allows making a decision not only about the fact of support and its efficiency, but also to predict the assessment of the life cycle of the enterprise and its subsequent development.

Urban trees are one of the valuable storage in metropolitan areas. Nowadays, a particular attention is paid to the trees and spends million dollars per year to their maintenance. Trees are often subjected to abiotic factors, such as fungi, bacteria, and insects, which lead to decline mechanical strength and wood properties. The objective of this study was to determine the potential degradation of Elm tree wood by Phellinus pomaceus fungi, and Biscogniauxia mediteranae endophyte. Biological decay tests were done according to EN 113 standard and impact bending test in accordance with ASTM-D256-04 standard. The results indicated that with longer incubation time, weight loss increased for both sapwood and heartwood. Fungal deterioration leads to changes in the impact bending. In order to manage street trees, knowing tree characteristics is very important and should be regularly monitored and evaluated in order to identify defects in the trees.

Freshwater problems in coastal areas include the process of salt intrusion which occurs due to decreasing groundwater levels below sea level which can cause an increase in salt levels in groundwater so that the water cannot be used for water purposes, human consumption and agricultural needs. The main objective of this research is to implementation of RWH to fulfill clean water needs in tropical coastal area in Tanah Merah Village, Indragiri Hilir Regency, with the aim of providing clean water to coastal communities. The approach method used based on fuzzy logic (FL). The model input data includes the effective area of the house’s roof, annual rainfall, roof runoff coefficient, and water consumption based on the number of families. The BWS III Sumatera provided the rainfall data for this research, which was collected from the Keritang rainfall monitoring station during 2015 and 2021. The research findings show that FL based on household scale RWH technology is used to supply clean water in tropical coastal areas that the largest rainwater contribution for the 144 m² house type for the number of residents in a house of four people with a tank capacity of 29 m² is 99.45%.