Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.
The manual presents the main methods for studying fish. The general features of the external structure of fish are described: the shape of the body, external organs, the structure and functions of the fins, the types of scales, and the structure of the lateral line. The indicators of morphometric studies of fish with the use of meristic and plastic features according to the classical schemes of measuring fish are also presented. A short description of the statistical method of comparative study of two data samples using the Student's test is given. A method for determining the age of fish by scales is described, as well as a methodology for calculating the annual growth of fish. General information on anatomical structure of fishes is also given. Furthermore, methods of studying the fertility of fish, as well as assessing the nutrition of fish, are described. Particular attention is paid to creating fish preparations: the production of the skeleton of fish, the design of fixed moist preparations and the preparation of a stuffed fish. The presented material has visual illustrations, accompanied by short biological information and forms of tabular material design. The proffered material will be useful for students of the biological and ecological profile, students of natural and agrarian faculties, post-graduate students and young scientists.
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