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1
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EN
We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using multifractal detrended fluctuation analysis. By calculating the singularity spectra f(α) we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, which is manifested by larger values of the corresponding Hölder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.
EN
Sediments found in waterways around the world may contain toxic compounds of anthropogenic origin that can harm the environment and human health. As a result, it is often necessary to remove them and find disposal methods that are environmentally and economically acceptable. Here, we report on results obtained in an experimental program to characterize the nature of the sediment contamination. The objective was to gain a better understanding of the properties of the sediments to develop better methods for understanding the fate and transport of the contaminants and for improving methods for their removal from the sediments. Our investigations made use of X-ray facilities at the Brookhaven National Synchrotron Light Source and the European Synchrotron Radiation Facility at Grenoble, France. The experiments included: measurements of the microstructure of the sediments using computed microtomography, X-ray absorption, and fluorescence microscopy with resolutions as low as 0.2 micrometers to obtain information on the relationships of organic and mineral components of the sediments and on the distribution of contaminants on the surfaces of the sediment grains, investigation of functional groups of chemical compounds using X-ray absorption near-edge spectroscopy and Fourier transform infrared spectroscopy. Scanning electron microscopy and electron probe measurements were made to ascertain the morphology of the sediment surfaces and the distribution of metals on individual sediment grains.
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Structural Sustainability of the Polish Trade System

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Acta Physica Polonica A
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2016
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vol. 129
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issue 5
1004-1007
EN
We use multi-region Input-Output databases to show the sustainability of the Polish trade system. Analyses of the robustness of the supply system as a whole are missing in the literature, in strong contrast with a wide variety of network analyses inquiring into the resilience of financial systems. We represent the trade system as a flow network, and use information-theoretic approach to address growth and development of such a system. We perform an analysis of the development, robustness, and structural sustainability of the Polish trade system based on national Input-Output Tables (in current prices) for Poland for the years between 1995 and 2011. As such, we are also able to comment on the changes of the studied characteristics over the years. Further, we compare the results with the results obtained for the global supply system based on the multi-region Input-Output Tables. We find the Polish supply system to be much less organised than the global supply system. We also quantify the effect of the 2008 financial crisis on the size and organisation of the trade system in Poland.
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Acta Physica Polonica A
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2016
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vol. 129
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issue 5
955-958
EN
In this paper the notion of the preference homogeneity is extended. We determine the value functions under the cumulative prospect theory such that the certainty equivalents related to them are invariant with respect to some classes of transformations.
EN
We found a unified formula for description of the household incomes of all society classes, for instance, of those of the European Union in year 2007. This formula is a stationary solution of the threshold Fokker-Planck equation (derived from the threshold nonlinear Langevin one). The formula is more general than the well known that of Yakovenko et al. because it satisfactorily describes not only household incomes of low- and medium-income society classes but also the household incomes of the high-income society class.
EN
In this work we compared the empirical data of annual income of Polish and European households as well as annual income of individuals in United States (e.g. for years 2006 and 2008) with predictions of the most popular theoretical models. Particularly good agreements with Pareto distribution and prediction of the Yakovenko model were obtained. For the low society class well agreement with prediction of the cumulative exponential distribution was gained. However, it turned out that the cumulative distribution of annual income of Polish households can be described quite well by the Generalised Lotka-Volterra model.
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issue 4
615-618
EN
At the end of 19th century Vilfredo Pareto, as the first tried by using power-laws to describe wealth and income distributions in society. We applied early works of Pareto as well as Gibrat (i.e. laws of Pareto and rules of proportionate growth, respectively). Furthermore, we used recent and advanced models: the Generalised Lotka-Volterra model and collision models. By using empirical data for annual income of Polish households, e.g. for years 2003 and 2006, the comparison with these theoretical models was successfully made. The surprisingly good agreements with Pareto distribution were obtained, where Pareto exponents near the cubic law were found for middle class. For the low class very good agreement with prediction of the cumulative log-normal distribution was gained. Hence, it was possible to establish the border between low and middle society levels. The same was possible for the border between high and middle classes as the ranking for the former follows (to some extent) the Zipf law.
EN
We prove that the most rafined approach - our extension of the Yakovenko et al. model - is a universal in the sense that it well describes both household incomes in the European Union and the individual incomes in the United States for all income social classes. This prove was based on our comparative study of various kinds of incomes. The study constitutes a basis for the finding of an impact of the recent world-wide financial crisis on the volatility of various temporary Pareto exponents and on other parameters of the model.
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Naming Boys after U.S. Presidents in 20th Century

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EN
This paper deals with the popularity of given names in the United States, for the period 1885-2009. Based on the data obtained from the website of U.S. Social Security Administration, it was demonstrated that the fashion of naming babies after the incumbent American president passed away in the '60s. At the same time, however, examples were given, mainly concerning celebrities, after whom babies are still named. The above theses were strengthened with the aid of quantitative data analysis by constructing an index dedicated to the specifics of the task under investigation. The obtained results were discussed in the terms of the rally effect and of the Simmel theory of fashion.
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Real Estate Market under Catastrophic Change

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EN
Within the last decade, real estate prices in Poland have changed significantly. We believe that these prices inevitably reflect the dynamics of the real estate market, and therefore they can be used to track its evolution path. To study whether and how the prices (regarded as a state variable) change over time depending on such control variables as gross domestic product and central bank interest rates, the theory of discontinuous change (also known as the catastrophe theory) was used. Catastrophic model assumes that small price fluctuations are associated with stable, long-term development of the market, whereas rapid changes are always due to short-term instabilities. In such a picture, the system evolution path draws a smooth curve within the stability area passing continuously between neighboring equilibrium states, and it rarely enters into the instability area to jump over the potential barrier to another equilibrium state.
11
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issue 4
677-687
EN
This paper presents an exactly solvable (by applying the fractional calculus) the rheological model of fractional dynamics of financial market conformed to the principle of no arbitrage present on financial market. The rheological model of fractional dynamics of financial market describes some singular, empirical, speculative daily peaks of stock market indices, which define crashes as a kind of phase transition. In the frame of the model the plastic market hypothesis and financial uncertainty principle were formulated, which proposed possible scenarios of some market crashes. The brief presentation of the model was made in our earlier work (and references therein). The rheological model of fractional dynamics of financial market is a deterministic model and it is complementary to already existing other ones; together with them it offers possibility for thorough and widespread technical analysis of crashes. The constitutive, fractional integral equation of the model is an analogy of the corresponding one, which defines the fractional Zener model of plastic material. The fractional Zener model is the canonical one for modern rheology, polymer physics and biophysics concerning non-Debye relaxation of viscoelastic biopolymers. The useful approximate solution of the constitutive equation of the rheological model of fractional dynamics of financial market consists of two parts: (i) the first one connected with long-term memory present in the system, which is proportional to the generalized exponential function defined by the Mittag-Leffler function and (ii) the second one describing oscillations (e.g. beats or oscillations having two slightly shifted frequences). The shape exponent leading the Mittag-Leffler function, defines here the order of the phase transition between bullish and bearish states of the financial market, in particular, for recent hossa and bessa on some small, middle and large stock markets. It happened that this solution also successfully estimated some long-term price dynamics on the hypothetical market in United States.
EN
We propose that a two-dimensional electric network may be used for fundamental studies of wave function properties, transport, and related statistics. Using Kirchhoff's current law and the jω-method we find that the network is analogous to a discretized Schrödinger equation for quantum billiards and dots. Thus the complex electric potentials play the role of quantum mechanical wave functions.
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Cross-Correlations in Warsaw Stock Exchange

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EN
We study the inter-stock correlations for the largest companies listed on Warsaw Stock Exchange and included in the WIG20 index. Our results from the correlation matrix analysis indicate that the Polish stock market can be well described by a one-factor model. We also show that the stock- stock correlations tend to increase with the timescale of returns and they approach a saturation level for the timescales of at least 200 min, i.e. an order of magnitude longer than in the case of some developed markets. We also show that the strength of correlations among the stocks crucially depends on their capitalization. These results combined with our earlier findings together suggest that now the Polish stock market situates itself somewhere between an emerging market phase and a mature market phase.
EN
Detailed knowledge about the temperature distribution achieved in the target area is essential for the development of magnetic hyperthermia treatments. However, the temperature inhomogeneity was found in all local hyperthermia studies. As a consequence of the impossibility of guaranteeing the temperature and thus the thermal dose distribution, hyperthermia is never applied as a single treatment modality. We suggest a model that enables the calculations and optimization of the spatial-time distribution of the temperature in the target volume (i.e. tumor) caused by magnetically heated elements: (i) arrays of clusters of iron oxides magnetite (Fe_3O_4) magnetic nanoparticles, and (ii) arrays of magnetic needles. In order to find the spatial-time temperature distribution in tumor, the bioheat transfer equation is solved for the two above-mentioned arrays of magnetically heated sources embedded in the tumor. The temporal and spatial temperature distributions were calculated with regard to the effect of blood perfusion in the tumor. It is shown that a matrix of magnetic micro-needles injected in the tumor could provide rather uniform tumor heating with the center-edge temperature difference smaller than 3°C at any times during the magnetic hyperthermia treatments. The temperature profiles can be suitably adjusted by a proper choice of the magnetic nanoparticles arrangement.
Acta Physica Polonica A
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2018
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vol. 133
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issue 6
1414-1416
EN
We consider structural change of a world trade-flow network for different commodities from 1995 to 2013. A minimum spanning tree is generated from the trade flow data, and we investigate the hierarchical organization of the tree by changing the hub node. Only a few countries are the hub nodes for many of the commodities. We observed the structural transitions, from a chain-like tree (many countries are hub nodes) to a bi-starlike tree (only two countries are hub nodes). In the bi-starlike tree, China and Germany are the only two hub nodes.
Acta Physica Polonica A
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2013
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vol. 124
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issue 2
173-180
EN
Bibliometric data on the growth dynamics of papers devoted to the Czochralski method of crystal growth and citations to these papers published in the scientific literature are analyzed using mathematical functions based on progressive nucleation mechanism and power-law approaches. It is shown that the basic concepts of progressive nucleation mechanism originally developed for crystal growth can satisfactorily be applied to explain the citation behavior of papers published on the Czochralski method of crystal growth. It is also found that: (1) cumulative number N(t) of papers and cumulative number L(t) of citations to them at time t are mutually related, and (2) as determined by the plot of the parameter L(t)/t^2 against the number Δ N(t) of papers published per year, the citation behavior of papers published on the Czochralski method follows three distinct periods: 1954-1988, 1988-2001 and 2001-2012, which are related to the dependence of the number Δ N(t) of papers published per year on publication time t.
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Multifractal Dynamics of Stock Markets

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issue 4
623-629
EN
We present a comparative analysis of multifractal properties of financial time series built on stock indices from developing (WIG) and developed (S&P500) financial markets. It is shown how the multifractal image of the market is altered with the change of the length of time series and with the economic situation on the market. We emphasize that the proper adjustment of scaling range for multiscaling power laws is essential to obtain the multifractal image of time series. We analyze in this paper multifractal properties of real financial time series using Hölder f(α) representation and multifractal-detrended fluctuation analysis method. It is also investigated how multifractal properties of stocks change with variety of "surgeries" done on the initial real financial time series. This way we reveal main phenomena on the market influencing its multifractal dynamics. In particular, we focus on examining how multifractal picture of real time series changes when one cuts off extreme events like crashes or rupture points, and how fluctuations around the main trend in time series influence the multifractal behavior of financial series in the long-time horizon for both developed and developing markets.
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Singular Dynamics of Various Macroeconomic Sectors

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EN
In this work we applied our original solution of the literal Rheological Model of Fractional Dynamics of Financial Market, i.e., the time-dependent solution proportional to the Mittag-Leffler function superposed with oscillations, not only to describe the singular dynamics of financial markets but also to study the singular dynamics of various macroeconomic sectors. The approach makes possible to sufficiently estimate (among others) the time of crash as well as its order. Thus we demonstrate, perhaps useful for stock market investors as well as for various macroeconomic agents, the technical analysis of bubble and crash, which is complementary to the famous one supplying power-law superposed with log-periodic oscillations.
EN
We make the comparative study of scaling range properties for detrended fluctuation analysis (DFA), detrended moving average analysis (DMA) and recently proposed new technique called modified detrended moving average analysis (MDMA). Basic properties of scaling ranges for these techniques are reviewed. The efficiency and exactness of all three methods towards proper determination of scaling Hurst exponent H is discussed, particularly for short series of uncorrelated and persistent data.
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Catastrophes and Chaos in Business Cycle Theory

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EN
The primary thesis of this paper is that a nonlinear dynamical systems theory provides a basis for conducting all kinds of comparisons in the theory of business cycles, and it also enables its further development. A cognitive aim was to show that applying the theory of bifurcations and morphogenesis in the domain of economic fluctuations allows us to construct models of the cycle with greater explicatory and utility values than there were so far. In this way, the precision and consistency of the theory increases. In this field, applications of catastrophe theory are of great importance. Another fact was indicated, namely the theory of deterministic chaos places the issues of explanation and forecasting in economics in a totally different light. It turns out that we are dealing with at least three sources of complexity in economic systems: chaotic attractors, invariant chaotic sets that are not attracting in the form of chaotic saddles and the effects of fractal basin boundaries. This, in turn, limits the effectiveness of traditional economic policy. Economic management should be based on procedures that lower complexity of economic systems, however sometimes lower complexity incurs bigger instability. The paper is a survey of applications of nonlinear dynamical systems to mathematical business cycle models. The survey encompasses both earlier models that were built in 1970s, as well as later concepts. The paper also features a few of my newest results of numerical studies of some nonlinear economic systems.
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