This article focuses on the application of given data of flight delays at the airport Koˇsice and its adaptation for further processing. These data were recorded from 2006 till 2009. The airport Koˇsice did not do the data-processing of delays yet. Since the results of this process are useful in the planning or scheduling, we try to establish a methodology for analysing these data. The values of basic statistical parameters for different airlines and different types of flights are shown. We publish their short analysis and commentary. We try to show the problem of prediction of development of these delays at the airport using statistical test.

In this paper the quadratic programming problem with linear constraints containing absolute values of variables (QPPLCAV) is considered. Hessian matrix is presumed to be positive definite. The problem is transformed to the larger problem with double number of variables with the same number of linear constraints without absolute values and with additional nonnegativity conditions (one inequality containing n absolute values could be ‘directly’ substituted by the system of 2n inequalities without absolute values). This problem may have several solutions. The relations between the original and the transformed problems are studied. In order to obtain stable approximations to the normal solution to the transformed problem corresponding to the unique solution of the original problem a regularization technique is proposed. A numerical example is given.

The crossing numbers of Cartesian products of all graphs of order at most four with cycles are known. The crossing numbers of Cartesian products G2Cn for several graphs G on five and six vertices and the cycle Cn are also given. In this paper, we extend these results by determining crossing numbers of Cartesian products G2Cn for some specific six vertex graphs G and for some fixed number n = 3; 4; 5.

In this paper we first present a theoretical approach to study mathematics teacher knowledge and conditions for developing it. Then some interesting activities and games are presented. As a result, this paper supplies teachers with information that may be useful in better understanding the nature of games, activities and their role in teaching and learning mathematics. At the age of 10 pupils can concentrate less than 20 minutes during a lesson. However, a lesson in primary and secondary schools lasts for 45 minutes and 50 at universities. What a contradiction! To solve this problem we try to attract their attention with different techniques. As children and adults enjoy playing games we can teach and learn mathematics through games and activities. Experience reveals that games can be very productive learning activities. Are some games better than others? What educational benefits are there to be gained from games? How to integrate games in mathematics lessons? How to distinguish between ‘activity’ and ‘game’? How to teach students specialising in electrical engineering and informatics using such an approach?

Packing colouring of a graph G is a partitioning of the vertex set of G with the property that vertices in i-th class have pairwise distance greater than i. The packing chromatic number of G is the smallest integer k such that the vertex set of G can be partitioned as X1;X2; : : : ;Xk where Xi is an i-packing for each i. In the paper, the packing chromatic numbers for all Platonic solids as well as for all prisms are given.

The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. Only few results concerning crossing numbers of graphs obtained as join product of two graphs are known. There was collected the exact values of crossing numbers for join of all graphs of at most four vertices and of several graphs of order five with paths and cycles. We extend these results by giving the crossing numbers for join products of the special graph on six vertices with n isolated vertices as well as with the path on n vertices and with the cycle on n vertices.

The present paper offers a generalization of the modeling by matrices for the complex numbers and quaternions to hypercomplex numbers of dimensions 2, 4 and 8. The given matrix model seems to be a suitable tool to study further properties of the hypercomplex numbers too. The matrix model used here was well known for modeling 2 dimensional complex and hypercomplex numbers, even for quaternions (see [4]), and we extend its use to the case of 4 and 8 dimensional hypercomplex numbers.

The exact crossing number is known only for few specific families of graphs. According to their special structure, Cartesian products of two graphs are one of few graph classes for which the exact values of crossing numbers were obtained. Let Pn be a path with n+1 vertices and P^k_N n be the k-power of the graph P_n. Very recently, some results concerning crossing numbers of P^k_N were obtained. For the Cartesian product of P²_N n with the cycle of length three, the value 3n􀀀3 for its crossing number is given. In this paper, we extend this result by proving that the crossing numbers of the Cartesian product P² _n C4 is 4n􀀀4.

Classical problem of the motion of two bodies under gravitational interaction will be analyzed and simulated in GeoGebra. The two-body problem will be reduced to the single-body problem in central force field. Solutions of the single-body problem will be mapped onto solutions of the two-body problem and their correspondence will be analyzed. Finally, simulation of the two-body problem in a moving frame will be shown.

Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by  and , where ab = maxfa;bg; a b = minfa;bg. An orbit of A generated by x is called stable if per(A;x) = 1. An interval orbit of an interval matrix A and an interval vector X and the weak stability of an interval orbit are defined. A necessary and sufficient condition for the weak stability of interval orbits of circulant matrices is introduced and justified.

Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by  and , where ab = maxfa;bg; a b = minfa;bg. A vector x is an eigenvector of a matrix A if A x = x. An interval vector X and the possible and universal eigenvectors are defined. A necessary and sufficient condition for the possible and universal eigenvectors of a circulant matrix are proved and several examples are given.

In the paper a relatively simple yet powerful and versatile technique for forecasting time series data – simple exponential smoothing is described. The simple exponential smoothing (SES) is a short-range forecasting method that assumes a reasonably stable mean in the data with no trend (consistent growth or decline). It is one of the most popular forecasting methods that uses weighted moving average of past data as the basis for a forecast. The procedure gives heaviest weight to more recent observations and smaller weight to observations in the more distant past. The accuracy of the SES method strongly depends on the optimal value of the smoothing constant a. To determine the optimal a value in the paper was used a traditional optimalization method based on the lowest mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE).

We discuss several facts related to numerical-analytic methods for boundary value problems for first order ordinary and functional differential equations. A numerical-analytic scheme of investigation of a two-point boundary value problem for functional differential equations is stated.

We consider the integral boundary-value problem for a certain class of non-linear system of ordinary differential equations. We give a new approach for studying this problem, namely by using an appropriate parametrization technique the given problem is reduced to the equivalent parametrized two-point boundary-value problem with linear boundary conditions without integral term. To study the transformed problem we use a method based upon a special type of successive approximations, which are constructed analytically.

The aim of this contribution is to analyze the application of informatics software package GeoGebra in the modeling of options strategy. Several specific examples are presented. The object of this study is behavior of overall profit in different options strategies, observed from graphic point of view. Based on the analyzed examples using GeoGebra slider feature we conclude that bull spread and bear spread both provide limited profit and loss. In addition, for specific values of parameters profit is strictly positive.