Relative Entropy in Determining Degressive Proportional Allocations

The principle of degressively proportional apportionment of goods, being a compromise between equality and proportionality, facilitates the application of many different allocation rules. Agents with smaller entitlements are more interested in an allocation that is as close to equality as possible, while those with greater entitlements prefer an allocation as close to proportionality as possible. Using relative entropy to quantify the inequity of allocation, this paper indicates an allocation that neutralizes these two contradictory approaches by symmetrizing the inequities perceived by the smallest and largest agents participating in the apportionment. First, based on some selected properties, the set of potential allocation rules was reduced to those generated by power functions. Then, the existence of the power function whose exponent is determined so as to generate the allocation that symmetrizes the relative entropy with respect to equal and proportional allocations was shown. As a result, all agents of the apportionment are more inclined to accept the proposed allocation regardless of the size of their entitlements. The exponent found in this way shows the significant relationship between the problem under study and the well-known Theil indices of inequality. The problem may also be seen from this viewpoint.     

Minimum Query Set for Decision Tree Construction

A new two-stage method for the construction of a decision tree is developed. The first stage is based on the definition of a minimum query set, which is the smallest set of attribute-value pairs for which any two objects can be distinguished. To obtain this set, an appropriate linear programming model is proposed. The queries from this set are building blocks of the second stage in which we try to find an optimal decision tree using a genetic algorithm. In a series of experiments, we show that for some databases, our approach should be considered as an alternative method to classical ones (CART, C4.5) and other heuristic approaches in terms of classification quality.     

Study of heating effect and acoustic properties of dextran stabilized magnetic fluid

This paper presents acoustic properties of water-based biocompatible fluids in which magnetite particles (Fe₃O₄) were coated with two layers of surfactants: sodium oleate and dextran. The attenuation coefficient of ultrasonic wave measurements shows good structural stability of the fluid under the influence of a magnetic field. Hyperthermic tests proved that the magnetic fluid is suitable for therapeutic use as an agent which can release thermal energy (hyperthermia).     

柱塞泵油膜压力分析的高效有限单元法

The paper concerns numerical analysis of pressure distribution of an oil film on the valve plate in the variable height gap of an axial piston pump. The analysis employs the finite element method. For determination of oil pressure variations in the gap, the Reynolds equation, commonly applied in the theory of lubrication, is applied. The equation is solved numerically with the use of self-developed program based on the finite element method. In order to obtain high accuracy of the results, an adaptive mesh refinement based on residual estimations of solution errors is applied. The calculation results are represented as dependent on the geometric and working parameters of the pump.