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Number of results: 8
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Abstract

The paper proposes a list of five „stylized facts”, regarded as the main trends with respect to the development of the global economy in the 20th c. The author’s main purpose is to answer the question whether, in the light of the contemporary growth theory and demographic forecasts, these trends are likely to continue unchanged also in the 21st c. Taking into account this theory and those forecasts, the paper offers forecasts of the average GDP per capita for both the countries of the Technology Frontier Area (TFA) and the catching-up countries. By these forecasts, the strong divergence trend of the last two centuries will be replaced by a strong convergence trend during the 21st c. Moreover, the global rate of growth of the per capita GDP will continue to be high in the first half of the current century, but strongly declining in the second half.
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Abstract

This paper provides analyses of the accuracy and convergence time of the PPP method using GPS systems and different IGS products. The official IGS products: Final, Rapid and Ultra Rapid as well as MGEX products calculated by the CODE analysis centres were used. In addition, calculations with weighting function of the observations were carried out, depending on the elevation angle. The best results were obtained for CODE products, with a 5-minute interval precision ephemeris and precise corrections to satellite clocks with a 30-second interval. For these calculations the accuracy of position determination was at the level of 3 cm with a convergence time of 44 min. Final and Rapid products, which were orbit with a 15-minute interval and clock with a 5 minute interval, gave very similar results. The same level of accuracy was obtained for calculations with CODE products, for which both precise ephemeris and precise corrections to satellite clocks with the interval of 5 minutes. For these calculations, the accuracy was 4 cm with the convergence time of 70 min. The worst accuracy was obtained for calculations with Ultra-rapid products, with an interval of 15 minutes. For these calculations, the accuracy was 10 cm with a convergence time of 120 min. The use of the weighting function improved the accuracy of position determination in each case, except for calculations with Ultra-rapid products. The use of this function slightly increased the convergence time, in addition to the CODE calculation, which was reduced to 9 min.
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Abstract

In order to overcome the shortcomings of the dolphin algorithm, which is prone to falling into local optimum and premature convergence, an improved dolphin swarm algorithm, based on the standard dolphin algorithm, was proposed. As a measure of uncertainty, information entropy was used to measure the search stage in the dolphin swarm algorithm. Adaptive step size parameters and dynamic balance factors were introduced to correlate the search step size with the number of iterations and fitness, and to perform adaptive adjustment of the algorithm. Simulation experiments show that, comparing with the basic algorithm and other algorithms, the improved dolphin swarm algorithm is feasible and effective.
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Abstract

The paper deals with the problems of designing observers and unknown input observers for discrete-time Lipschitz non-linear systems. In particular, with the use of the Lyapunov method, three different convergence criteria of the observer are developed. Based on the achieved results, three different design procedures are proposed. Then, it is shown how to extend the proposed approach to the systems with unknown inputs. The final part of the paper presents illustrative examples that confirm the effectiveness of the proposed techniques. The paper also presents a MATLAB® function that implements one of the design procedures.
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Abstract

This work presents an innovative shaft-lining solution which, in accordance with a patent of the Republic of Poland, allows successive, periodic leaching of excess rock salt migrating to the shaft opening. As is commonly known, all workings in rock salt strata are exposed to an increased convergence of sidewalls, making it very difficult to use shafts properly. Rocks migrating towards the shaft opening cause very high stress on the shaft liner. As a result, if the lining does not show substantial deformability, it fails. Lining failure due to insufficient deformability has been extensively described in the literature. Also, throughout the history of mining construction, a number of solutions have been proposed for different types of lining-deformability enhancement. For instance, the KGHM mining corporation applied a deformable steel lining – a solution used in the mining construction of galleries – along a 155-m-long section of the SW-4 shaft with diameters of 7,5 m that passes through a rock salt strata. At KGHM, the SW-4 shaft passes through a rock salt strata along a section of 155 m, in which a deformable enclosed steel lining was made. After several years, the convergence of shaft sidewalls stabilised at a rate of 0.5 mm/day. This enormous activity of the rock mass made it necessary to reconstruct the entire shaft section after only four years. According to further predictions, it will be necessary to reconstruct this section at least four times by 2045. This paper discusses in short form the underlying weaknesses of the technology in question. As a solution to the problems mentioned above, the authors of this work present a very simple design of a shaft lining, called the tubing-aggregate lining, which utilises the leachability of salt rock massifs. The essential part of the lining is a layer of coarse aggregate set between the salt rock sidewall and the inner column of the tubing lining. One the one hand, coarse aggregate supports the salt rock sidewall and is highly deformable due to its compressibility, but on the other hand it allows water or low saturated brine to migrate and dissolve salt rock sidewalls. This paper presents the first stage of works on this subject. Patent No. PL 223831 B had been granted before these works commenced.
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Abstract

The article aims to explain whether in 2004–2015 Poland experienced economic convergence between regions and counties (Polish: powiat), and whether this process occurred within the regions (Polish: województwo). Following Poland’s EU accession, the Polish policy became dominated by the polarization and diffusion concept of regional development, which may cause differences in the short term, while in the long run it may contribute not only to the increased efficiency of public funds allocation, but also to the elimination of disparities in growth levels. In the analysed period Poland experienced a process of economic divergence between the regions, only the years 2006–2008 saw a short-term reduction in regional disparities. On the other hand, a slow process of reducing economic inequalities between counties took place after 2004. It was, however, varied – a clear reduction in disparities occurred between the land counties (Polish: powiat ziemski) in an almost monotonic manner, whereas city counties (Polish: miasto na prawach powiatu) did not undergo any convergence. Within the regions, the process of economic convergence varied: in five regions, β-convergence was identified, and σ-convergence occurred in all the regions. The process of reducing disparities was significantly dependent on the development pathway of the region.
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Abstract

In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.
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