On the development of layouts on construction and renovation of marshalling complexes

Objective: Further improvement of organizational management methods for construction and renovation of railroad stations by the example of marshalling complexes infrastructure. Methods: By means of the methods of continuous construction theory, depending on technological arrangement and structure of facilities of railroad stations, an optimum amount of work was singled out for the purpose of construction lines development. Effective variants of organizational management were selected according to rational coefficient values of combining the facility and specialized flows, in case of which the maximum possible (for conditions of construction and renovation) estimated capacity of the station was preserved. Results: The dependencies of estimated capacity and the amount of work for construction and renovation of marshalling complexes of different types (one-way, combined, etc.) were determined. Practical importance: The data presented in the article is of high practical relevance due to the absence of modern research and industrial regulatory documents on construction and renovation management of the given type of transport facilities.

A factorisation procedure for two by two matrix functions on the circle with two rationally independent entries

SynopsisThe aim of this paper is the explicit canonical or standard factorisation of matrix functions with Wiener algebra elements. The present approach covers all regular 2 × 2 matrices where two entries are arbitrary and the remaining two are linear combinations of the former with rational coefficient functions. It is based on the knowledge of how to factorise scalar functions and rational matrix functions. In general, one also needs the approximation of any scalar Wiener algebra function with a rational function. However, this can be easily circumvented in many applications by intuitive manipulations with rational matrix functions.

Some remarks concerning Demazure’s construction of normal graded rings

In [1], Demazure showed a new way of constructing normal graded rings using the concept of “rational coefficient Weil divisors” of normal projective varieties and he showed, among other things, the followingTHEOREM ([1], 3.5). If R = ⊕n ≥ 0Rn is a normal graded ring of finite type over a field k and if T is a homogeneous element of degree 1 in the quotient field of R, then there exists unique divisor D ∈ Div (X, Q) (X = Proj (R)), such that for every n ≧ 0.(See (1.1) for the definition of