Anna M. Barańska

In a democratic country, every citizen has the right to information about the environment in which he or she lives – therefore, there should be some procedure of conventional, formal evaluation of an urbanized area with reference to its local fragments. Such kind of the procedure has been proposed in this article. The procedure is based on the conventional scoring of local areas, which can be assigned weights representing positive and negative features. The procedure provides for variants of preconditions and continuation of considerations for source data variables. The method of assessing the quality of life in the local area should serve the broad local community, therefore the intermediate and final results of the considerations are presented not only in the form of maps, but also in an illustrative way – in the form of three-dimensional (3D) images, with colors easily associated with positive or negative features. A wide range of tools from the professional GIS package – ArcGIS version 10 was used to perform the task. These tools allow to solve complex spatial problems as well as to visualize the results in an effective way.

The objective of this research paper is to establish the relationship between a randomly selected point of the field of play and the target. The analysis has been based on an exemplary pitch and the rules of football. A decision to desist from the field gain and to take a shot must take into account the relationship between the possible angle of dispersion and the angle at which the goal can be seen. The latter one (denoted as γ) has been devoted special attention here. Then, we have paid special attention to the fact that the view of the goal decreases as the player moves away from the longitudinal axis of the pitch. By turning the direction of the goal line b to the direction that is perpendicular to the line of shot, we obtain a decreased projection of the goal t. The indicators such as angle γ, projection t and its quotient version N aptly define various spatial situations that occur in the field of play. However, in order to add better illustration to the assessment, another indicator (V) has been proposed. It treats the changing view of the goal as an “aiming target” observed from varying distances. The comparability of the opportunities has also been demonstrated in the form of circle-shaped isolines, based on the chord of the goal. The performed analyses have legitimised the standard rule and aim of football which involves favourable field gain along the wings and finally crossing the ball into the middle field.

The main objective of this publication was to present a two-stage algorithm of modelling random phenomena, based on multidimensional function modelling, on the example of modelling the real estate market for the purpose of real estate valuation and estimation of model parameters of foundations vertical displacements. The fi rst stage of the presented algorithm includes a selection of a suitable form of the function model. In the classical algorithms, based on function modelling, prediction of the dependent variable is its value obtained directly from the model. The better the model refl ects a  relationship between the independent variables and their effect on the dependent variable, the more reliable is the model value. In this paper, an algorithm has been proposed which comprises adjustment of the value obtained from the model with a random correction determined from the residuals of the model for these cases which, in a separate analysis, were considered to be the most similar to the object for which we want to model the dependent variable. The effect of applying the developed quantitative procedures for calculating the corrections and qualitative methods to assess the similarity on the fi nal outcome of the prediction and its accuracy, was examined by statistical methods, mainly using appropriate parametric tests of signifi cance. The idea of the presented algorithm has been designed so as to approximate the value of the dependent variable of the studied phenomenon to its value in reality and, at the same time, to have it “smoothed out” by a well fi tted modelling function.