The paper evaluates the relationship between the selection of the probability density function and the construction price, and the price of the building's life cycle, in relation to the deterministic cost estimate in terms of the minimum, mean, and maximum. The deterministic cost estimates were made based on the minimum, mean, and maximum prices: labor rates, indirect costs, profit, and the cost of equipment and materials. The net construction prices received were given different probability density distributions based on the minimum, mean, and maximum values. Twelve kinds of probability distributions were used: triangular, normal, lognormal, beta pert, gamma, beta, exponential, Laplace, Cauchy, Gumbel, Rayleigh, and uniform. The results of calculations with the event probability from 5 to 95% were subjected to the statistical comparative analysis. The dependencies between the results of calculations were determined, for which different probability density distributions of price factors were assumed. A certain price level was assigned to specific distributions in 6 groups based on the t-test. It was shown that each of the distributions analyzed is suitable for use, however, it has consequences in the form of a final result. The lowest final price is obtained using the gamma distribution, the highest is obtained by the beta distribution, beta pert, normal, and uniform.

The problem of query selectivity estimation for database queries is critical for efficientquery execution by database management systems. A query execution method strongly depends on earlyestimated size of a query result. This estimation determines a data access method used later during thequery execution. The selectivity parameter is a fraction of table rows that satisfy a single-table querycondition. For a selection condition of a range query where an attribute has a continuous domain, theselectivity is equivalent to a definite integral form probability density function (PDF) of attribute valuesdistribution. For a compound selection condition based on many attributes we need a multidimensionalspace-efficient non-parametric estimator of multivariate PDF of attribute values distribution. A knownapproach based on Discrete Cosine Transform (DCT) spectrum as an representation of multidimensionalPDF is considered. The energy compaction property of DCT lets omit a region of spectrum coefficientswith small absolute values without significant losing an accuracy of selectivity estimation. An area ofrelevant spectrum coefficients is called a sampling zone. Results of experiments from previous worksshows that applying the reciprocal shape of the sampling zone gives the least selectivity estimation errorsubject to a predetermined size of the zone. The main result of this work is a theoretical confirmation of onlyexperimental results from previous works. The paper presents the proof of the theorem that the reciprocalshape of the sampling zone is asymptotically error-optimal. The proof is based on calculus of variationsand the isoperimetric problem.

In the paper, the Hasofer-Lind index is applied for determining the probability of stability loss oftruss structure under random load. In 1974 Hasofer-Lind proposed a modified reliability index thatdid not exhibit the invariance problem. The “correction” is the evaluation the limit state functionat a point known as the “design point”, instead of the mean values. The design point is generallynot known a priori, an iteration technique must be used to find out the reliability index. The papershows how the reliability index changes under the influence of different variables mean value,standard deviation, and probability density function.

The Vistulian decline was a period of rapid environmental events. The authors correlated ages of the last Scandinavian Ice Sheet limits in northern Poland with ages of prominent events adapting the conditions of periglacial environment of Central Poland in response to the Late Vistulian climate warming. Ages from previous thematic geological and palaeogeographical studies were collected. The approach used indicates that despite methodological uncertainties and sometimes inconsistency of ages, it is especially helpful in timing of first warming signals (ca. 19–18 cal ka BP) and establishing of environmentally bipartite 3 millennia of the Oldest Dryas in the extraglacial zone. Abrupt warming at the onset of the Bølling-Allerød is well registered in biotic and abiotic archives available from Central Poland and remains in agreement with the large recession of the southern ice sheet margin.