Abstract:
At present there are two trends in the market of rail freight transportation in Russia: freight owners put forward higher demands to the transportation quality (promptness of delivery) in an effort to reduce storage costs by means of reducing the size of freight shipment; the structure of railcar traffic volume of the railways of Russia is getting more complex due to the reduction of the average shipment size and due to the transfer of railcar fleet ownership to a large number of operating companies. These trends significantly complicate operational management supervision of railway stations and transport nodes. Application of typical data from the information system about the railcar location at the transportation node is not enough for the dispatchers to make the best decision concerning the car traffic management. The article is concerned with the description and development of the mathematical model of empty railcar distribution for loading at the railway transport node; this model will take into account the requirements of railcar owners in terms of their cars application, the operating work level of railroad stations of the transportation node and the possibility of adding the groups of empty railcars to the transfer trains, clean-up trains and industrial railway trains operating on a tight schedule. The developed model and the software package were implemented in the information system of the industrial railway of the major metallurgical enterprise - OJSC "Magnitogorsk Metallurgical Works", which processes up to two thousand of railcars belonging to different owners. This model made it possible to reduce the labour intensity of dispatcher operation planning the empty railcar distribution for loading and reduce the total time the railcars spend in the enterprise railway system.

Abstract:
Recent development in noncommutative geometry generalization of gauge theory is reviewed. The mathematical apparatus is reduced to minimum in order to allow the non-mathematically oriented physicists to follow the development in the interesting field of research. (Lectures presented at the Silesian School of Theoretical Physics: Standard Model and Beyond'93, Szczyrk (Poland), September 1993.)

Abstract:
We discuss the problem of determining the spacetime structure. We show that when we are using only topological methods the spacetime can be modelled as an R- or Q-compact space although the R-compact spaces seem to be more appropriate. Demanding the existence of a differential structure substantially narrows the choice of possible models. The determination of the differential structure may be difficult if it is not unique. By using the noncommutative geometry construction of the standard model we show that fundamental interactions determine the spacetime in the class of R-compact spaces. Fermions are essential for the process of determining the spacetime structure.

Abstract:
We investigate how exotic differential structures may reveal themselves in particle physics. The analysis is based on the A. Connes' construction of the standard model. It is shown that, if one of the copies of the spacetime manifold is equipped with an exotic differential structure, compact object of geometric origin may exist even if the spacetime is topologically trivial. Possible implications are discussed. An $SU(3)\otimes SU(2)\otimes U(1)$ gauge model is constructed. This model may not be realistic but it shows what kind of physical phenomena might be expected due to the existence of exotic differential structures on the spacetime manifold.

Abstract:
Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative.

Abstract:
The proposed by Bastianelli and van Nieuwenhuizen new method of calculations of trace anomalies is applied in the conformal gauge field case. The result is then reproduced by the heat equation method. An error in previous calculation is corrected. It is pointed out that the introducing gauge symmetries into a given system by a field-enlarging transformation can result in unexpected quantum effects even for trivial configurations.

Abstract:
It is argued that the noncommutative geometry construction of the standard model predicts a nonlinear symmetry breaking mechanism rather than the orthodox Higgs mechanism. Such models have experimentally verifiable consequences.

Abstract:
It is shown that the St\"uckelberg formalism can be regarded as a field-enlarging transformation that introduces an additional gauge symmetry to the considered model. The appropriate BRST charge can be defined. The physical state condition, demanding that that a physical state is to be anihilated by the BRST charge, is shown to be equivalent to the St\"uckelberg condition. Several applications of the new approach to the formalism are presented. The comparison with the BFV procedure is given. (The author field has been corrected.)

Abstract:
A field-enlarging transformation in the chiral electrodynamics is performed. This introduces an additional gauge symmetry to the model that is unitary and anomaly-free and allows for comparison of different models discussed in the literature. The problem of superfluous degrees of freedom and their influence on quantization is discussed. Several "mysteries" are explained from this point of view.

Abstract:
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history and basic ideas of quantum game theory. Description of Giffen paradoxes in this new formalism is discussed.