Гиперболическое уравнение теплопроводности движущегося тела
Many structural elements in modern engineering and industry operate under conditions characterize... more Many structural elements in modern engineering and industry operate under conditions characterized by the unexpected changing of the heat flow. The thermal shock effect and, hence, the undesirable changing of thermal stress in construction material can result in the loss of capacity for work. The intensive introduction of modern technologies in a number of branches of the industry leads to the study of dependence of thermodynamical processes of different intensity on the behaviour of strained structural elements, especially the elements with cylindrical form. The hyperbolic heat conduction equation of a moving body is derived and solved in the cylindrical coordinate system (cylindrical frame of axes) in the way of Green's functions. Taking into consideration the finiteness of heat spreading speed, the solution corresponds to the hyperbolic theory of heat conduction, and makes it possible to settle strength standards for the components operating under thermodynamical loads, and t...
Математическая аналогия и следствия уравнений движения вязкой и упругой сред
Consequences of Navie-Sticks and Lame-Dyuamel-Neiman linearized equations are received on the bas... more Consequences of Navie-Sticks and Lame-Dyuamel-Neiman linearized equations are received on the base of mathematical analogy of methods of viscous and elastic mediums models construction. At the same time the components of curl's vectors satisfy diffusion equation independently of condensability properties of viscous medium in frame of using in work the linearized formulation of physical-mathematical model of viscous medium. Received equations include both as adiabatic as isothermal processes, which can conduct mechanical interactions depending on meanings of parameters characterized medium, and, consequently, can be used as for isoentropic (in case of reversible processes adiabatic) as for isothermal processes.
Model risk in credit scoring can be understood as the bank’s losses associated with a model quali... more Model risk in credit scoring can be understood as the bank’s losses associated with a model quality deterioration. Deterioration in model quality entails an incorrect assessment of the creditworthiness of borrowers and leads to an increase in potentially defaulting applications in the loan portfolio, as the bank relies on the model performance when making lending decisions. The relationship between model quality and financial performance is embedded in the confusion matrix, where the value of a type I error indicates the bank’s lost profit, and the value of a type II error is equivalent to losses in the event of a default. We propose estimating model risk based on the scenario forecast of model quality or the ranking ability of the Gini model over a given time interval. The result of the analysis is the assessment of the bank’s net present value for the current and modified models, depending on the approval level. The proposed approach allows us to solve the problem of the optimal c...
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