Three Problems of the Theory of Choice on Random Sets

This paper discusses three problems which are united not only by the common topic of research stated in the title, but also by a somewhat surprising interlacing of the methods and techniques used. In the first problem, an attempt is made to resolve a very unpleasant metaproblem arising in general choice theory: why the conditions of rationality are not really necessary or, in other words, why in every-day life we are quite satisfied with choice methods which are far from being ideal. The answer, substantiated by a number of results, is as follows: situations in which the choice function "misbehaves" are very seldom met in large presentations. In the second problem, an overview of our studies is given on the problem of statistical properties of choice. One of the most astonishing phenomenon found when we deviate from scalar-extremal choice functions is in stable multiplicity of choice. If our presentation is random, then a random number of alternatives is chosen in it. But how many? The answer isn't trivial, and may be sought in many different directions. As we shall see below, usually a bottleneck case was considered in seeking the answer. It is interesting to note that statistical information effects the properties of the problem very much. The third problem is devoted to a model of a real life choice process. This process is typically spread in time, and we gradually (up to the time of making a final decision) accumulate experience, but once a decision is made we are not free to reject it. In the classical statement (i.e. when "optimality" is measured by some number) this model is referred to as a "secretary problem", and a great deal of literature is devoted to its study. We consider the case when the notions of optimality are most general. As will be seen below, the best strategy is practically determined by only the statistical properties of the corresponding choice function rather than its specific form

Investigation of the effect of beef moisture content on the amount of bound moisture with the calorimetric method

With the development of food processing and storage at near-cryoscopic temperatures, more and more attention is being paid to the development of methods for frozen out moisture and cryoscopic temperature calculating based on their component composition data. There is a significant dispersion among the existing experimental data of various researchers and calculation methods for beef thermophysical properties. In the study given, the authors determined the enthalpy of phase transitions, beet heat capacity with different moisture content and its cryoscopic temperature with the method of differential scanning calorimetry. With the analysis of the phase transitions enthalpy, it was found out that the share of non-freezing water for beef is n = 0.35 (g of water per 1 g of dry matter). The presence of the vitreous phase in the temperature range of about -85 ° С was established, most noticeably manifested when the moisture content of the samples is w = 37–45.8%, which indicates the formation of amorphous solutions in the process of food products freezing. Beginning of moisture melting peak Tm.b. takes place at temperatures range from -35 ° C till -25 ° C for the samples with low and normal moisture content respectively. Acccording to the theoretical Heldman ratio, a dependence for cryoscopic temperature calculating was proposed . The given semi-empirical dependences of the phase transitions enthalpy and the frozen moisture fraction provide an increase in the accuracy of calculations at low values of moisture content in the product. The research results can be used as input data in mathematical modeling of heat exchange processes and the development of calculating methods for the thermophysical properties of food products based on their composition