The structure of infinite Coxeter graphs whose largest eigenvalue belongs to the interval from √√5 + 2 to 3 3/√2] is investigated. In particular, such a graph is a tree, can have at most one label greater than 3 on its edges and such label does not exceed 6, can have only vertices with degree strictly less than 5, and among edges which are incident with vertex with degree 4 can be only one that is not incident with leaf. A number of other properties are also given for infinite Coxeter graphs with largest eigenvalue in the specified interval.
The Silesian Beskids (Poland), the westernmost part of the Carpathian Mountains is an area with long pastoral tradition. For centuries sheep grazed in clearings located among forested ridges have been an integral part of the mountain landscape and pastoral customs have become essential elements of regional cultural heritage. In the chapter, the history and the current state of pastoralism in the Silesian Beskids are presented. The specific pastoral system developed in the region, based on annual migration of flocks between summer highland and winter lowland pastures is described. Local breeds and specific regional sheep products are depicted. Furthermore, the importance of pastoralism for the environment, landscape and plant biodiversity is analysed and efforts to recover sheep grazing in the mountains after a period of a deep recession caused by social and economic transitions connected with the collapse of the communist system are presented. The approach to restoration of pastoralism is illustrated using a case study of a pastoral centre which combines traditional sheep grazing with cheese production, education and several activities to promote pastoral tradition.
The correlation indicators between the results of linear evaluation of first-born cows of two lines - Redad and Horror of Simmental combined breed by type and their milk productivity are given. Animals of both lines are characterized mainly by average values of linear characteristics of the type. At the same time, the highest score is given to first-born cows from the Redad line. There is a direct connection between the direction of the linear evaluation and the milk yield of the first-born from the Redad line in terms of height in the buttocks, depth of the torso, and angularity.
Carrying out a linear assessment of the first-born cows of the Simmental combined breed by type allows to identify defects in their exterior, which will further contribute to the effective selection and selection aimed at consolidating herds in accordance with the desired breed characteristics.
The growth of Redad cows was estimated at 5.8 points, and of Horror cows - 4.7 points. Animals from the Redad line had a larger chest width (0.6 points, P <0.01), a deep torso. According to the angularity (severity of the milk type), the animals of both lines received an average score (5 points). The depth of the udder is well expressed in the evaluated animals (6.2 and 6.1 points). Animals from the Horror line received the highest score for anterior udder attachment (P<0.05). Animals of both lines are well muscled, they have evenly placed pelvic limbs and strong hooves.
The studies showed a positive correlation between milk yield and height in the buttocks, body depth, angularity, anterior attachment of the udder in cows from the Redad line. Negative correlation between milking and central ligament, udder depth, teat length, pelvic limb angle.
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