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Journal articles on the topic 'Gradually truncated power law'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Gupta, Hari M., and José R. Campanha. "The gradually truncated Lévy flight for systems with power-law distributions." Physica A: Statistical Mechanics and its Applications 268, no. 1-2 (June 1999): 231–39. http://dx.doi.org/10.1016/s0378-4371(99)00028-x.

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2

GUPTA, HARI M., JOSÉ R. CAMPANHA, and FERNANDO D. PRADO. "POWER LAW DISTRIBUTION IN EDUCATION: UNIVERSITY ENTRANCE EXAMINATION." International Journal of Modern Physics C 11, no. 06 (September 2000): 1273–79. http://dx.doi.org/10.1142/s0129183100001085.

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We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.

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3

Mashanova, Alla, Tom H. Oliver, and Vincent A. A. Jansen. "Evidence for intermittency and a truncated power law from highly resolved aphid movement data." Journal of The Royal Society Interface 7, no. 42 (May 27, 2009): 199–208. http://dx.doi.org/10.1098/rsif.2009.0121.

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Power laws are increasingly used to describe animal movement. Despite this, the use of power laws has been criticized on both empirical and theoretical grounds, and alternative models based on extensions of conventional random walk theory (Brownian motion) have been suggested. In this paper, we analyse a large volume of data of aphid walking behaviour (65 068 data points), which provides a highly resolved dataset to investigate the pattern of movement. We show that aphid movement is intermittent—with alternations of a slow movement with frequent change of direction and a fast, relatively directed movement—and that the fast movement consists of two phases—a strongly directed phase that gradually changes into an uncorrelated random walk. By measuring the mean-squared displacement and the duration of non-stop movement episodes we found that both spatial and temporal aspects of aphid movement are best described using a truncated power law approach. We suggest that the observed spatial pattern arises from the duration of non-stop movement phases rather than from correlations in turning angles. We discuss the implications of these findings for interpreting movement data, such as distinguishing between movement and non-movement, and the effect of the range of data used in the analysis on the conclusions.

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GUPTA, HARI M., JOSÉ R. CAMPANHA, and FÁBIO R. CHAVARETTE. "POWER LAW DISTRIBUTION IN EDUCATION: EFFECT OF ECONOMICAL, TEACHING, AND STUDY CONDITIONS IN UNIVERSITY ENTRANCE EXAMINATION." International Journal of Modern Physics C 14, no. 04 (May 2003): 449–57. http://dx.doi.org/10.1142/s0129183103004656.

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We studied the statistical distribution of student's performance, which is measured through their marks, in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) with respect to (i) period of study — day versus night period (ii) teaching conditions — private versus public school (iii) economical conditions — high versus low family income. We observed long ubiquitous power law tails in physical and biological sciences in all cases. The mean value increases with better study conditions followed by better teaching and economical conditions. In humanities, the distribution is close to normal distribution with very small tail. This indicates that these power law tails in science subjects are due to the nature of the subjects themselves. Further and better study, teaching and economical conditions are more important for physical and biological sciences in comparison to humanities at this level of study. We explain these statistical distributions through Gradually Truncated Power law distributions. We discuss the possible reason for this peculiar behavior.

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5

León, Carlos. "Scale-free tails in colombian financial indexes: a primer." ODEON, no. 9 (February 12, 2016): 233. http://dx.doi.org/10.18601/17941113.n9.06.

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<p>A maximum likelihood method for estimating the power-law exponent verifies that the positive and negative tails of the Colombian stock market index (IGBC) and the Colombian peso exchange rate (TRM) approximate a scale-free distribution, whereas none of the heavy tails of a local sovereign securities index (IDXTES) are a plausible case for such distribution. Results also (i) support critiques regarding the flaws of ordinary least squares estimation methods for scale-free distributions; (ii) question the validity of Zipf’s law; (iii) suggest that IGBC and TRM display the scale-free nature documented as a stylized fact of financial returns, and that they may be following a gradually truncated Lévy flight; and (iv) suggest that local financial markets are self-organizing systems.</p>

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6

BURROUGHS, STEPHEN M., and SARAH F. TEBBENS. "UPPER-TRUNCATED POWER LAW DISTRIBUTIONS." Fractals 09, no. 02 (June 2001): 209–22. http://dx.doi.org/10.1142/s0218348x01000658.

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Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhibit a "fall-off" from a power law at the largest object sizes. Previous work has often either ignored the fall-off region or described this region with a different function. We demonstrate that when a data set is abruptly truncated at large object size, fall-off from a power law is expected for the cumulative distribution. Functions to describe this fall-off are derived for both linearly and logarithmically binned data. These functions lead to a generalized function, the upper-truncated power law, that is independent of binning method. Fitting the upper-truncated power law to a cumulative number-size distribution determines the parameters of the power law, thus providing the scaling exponent of the data. Unlike previous approaches that employ alternate functions to describe the fall-off region, an upper-truncated power law describes the data set, including the fall-off, with a single function.

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7

Zhu, Hong, Yingchao Xie, and Maochao Xu. "Discrete Truncated Power-Law Distributions." Australian & New Zealand Journal of Statistics 58, no. 2 (June 2016): 197–209. http://dx.doi.org/10.1111/anzs.12162.

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8

Ren, Hehe, Shujin Laima, and Hui Li. "Numerical Investigation of Very-Large-Scale Motions in a Turbulent Boundary Layer for Different Roughness." Energies 13, no. 3 (February 4, 2020): 659. http://dx.doi.org/10.3390/en13030659.

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Wall-model large eddy simulations (WMLES) are conducted to investigate the spatial features of large-scale and very-large-scale motions (LSMs and VLSMs) in turbulent boundary flow in different surface roughnesses at a very high Reynolds number, O (106–107). The results of the simulation of nearly smooth cases display good agreement with field observations and experimental data, both dimensioned using inner and outer variables. Using pre-multiplied spectral analysis, the size of VLSMs can be reduced or even disappear with increasing roughness, which indirectly supports the concept that the bottom-up mechanism is one of the origins of VLSMs. With increases in height, the power of pre-multiplied spectra at both high and low wavenumber regions decreases, which is consistent with most observational and experimental results. Furthermore, we find that the change in the spectrum scaling law from −1 to −5/3 is a gradual process. Due to the limitations of the computational domain and coarse grid that were adopted, some VLSMs and small-scale turbulence are truncated. However, the size of LSMs is fully accounted for. From the perspective of the spatial correlation of the flow field, the structural characteristics of VLSMs under various surface roughnesses, including three-dimensional length scales and inclination angles, are obtained intuitively, and the conclusions are found to be in good agreement with the velocity spectra. Finally, the generation, development and extinction of three-dimensional VLSMs are analyzed by instantaneous flow and vorticity field, and it shows that the instantaneous flow field gives evidence of low-speed streamwise-elongated flow structures with negative streamwise velocity fluctuation component, and which are flanked on each side by similarly high-speed streamwise-elongated flow structures. Moreover, each of the low-speed streamwise-elongated flow structure lies beneath many vortices.

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9

Minasandra, Pranav, and Kavita Isvaran. "Truncated power-law distribution of group sizes in antelope." Behaviour 157, no. 6 (June 11, 2020): 541–58. http://dx.doi.org/10.1163/1568539x-bja10012.

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Abstract Quantifying and understanding group size distributions can be useful for understanding group behaviour in animal populations. We analysed group size data of the blackbuck, Antilope cervicapra, from six different field sites to estimate the group size distribution of this antelope. We used likelihood based methods (AICs and likelihood ratios) to show that an exponentially truncated power law is the distribution that best describes blackbuck group data, outperforming a simple power-law, an exponential distribution, and a lognormal distribution. Our results show that distribution parameters can be used to draw novel insights regarding group dynamics, and we demonstrate this by investigating how habitat openness affects group size distributions.

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10

Deluca, Anna, and Álvaro Corral. "Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions." Acta Geophysica 61, no. 6 (September 26, 2013): 1351–94. http://dx.doi.org/10.2478/s11600-013-0154-9.

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11

Torresetti, Roberto, and Claudio Nordio. "Truncated lognormals as a power-law mimic in operational risk." Journal of Operational Risk 10, no. 3 (September 2015): 21–41. http://dx.doi.org/10.21314/jop.2015.163.

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12

Sokolov, I. M., A. V. Chechkin, and J. Klafter. "Fractional diffusion equation for a power-law-truncated Lévy process." Physica A: Statistical Mechanics and its Applications 336, no. 3-4 (May 2004): 245–51. http://dx.doi.org/10.1016/j.physa.2003.12.044.

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13

Amar, Jacques G., and Fereydoon Family. "Crossover scaling in surface growth with truncated power-law noise." Journal de Physique I 1, no. 2 (February 1991): 175–79. http://dx.doi.org/10.1051/jp1:1991123.

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14

Felisa, G., A. Lenci, I. Lauriola, S. Longo, and V. Di Federico. "Flow of truncated power-law fluid in fracture channels of variable aperture." Advances in Water Resources 122 (December 2018): 317–27. http://dx.doi.org/10.1016/j.advwatres.2018.10.024.

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15

Solís-Pérez, Jesús Emmanuel, and José Francisco Gómez-Aguilar. "Novel Fractional Operators with Three Orders and Power-Law, Exponential Decay and Mittag–Leffler Memories Involving the Truncated M-Derivative." Symmetry 12, no. 4 (April 15, 2020): 626. http://dx.doi.org/10.3390/sym12040626.

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In this research, novel M-truncated fractional derivatives with three orders have been proposed. These operators involve truncated Mittag–Leffler function to generalize the Khalil conformable derivative as well as the M-derivative. The new operators proposed are the convolution of truncated M-derivative with a power law, exponential decay and the complete Mittag–Leffler function. Numerical schemes based on Lagrange interpolation to predict chaotic behaviors of Rucklidge, Shimizu–Morioka and a hybrid strange attractors were considered. Additionally, numerical analysis based on 0–1 test and sensitive dependence on initial conditions were carried out to verify and show the existence of chaos in the chaotic attractor. These results showed that these novel operators involving three orders, two for the truncated M-derivative and one for the fractional term, depict complex chaotic behaviors.

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16

Lavrov, Alexandre. "Flow of truncated power-law fluid between parallel walls for hydraulic fracturing applications." Journal of Non-Newtonian Fluid Mechanics 223 (September 2015): 141–46. http://dx.doi.org/10.1016/j.jnnfm.2015.06.005.

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17

Tian, Guo-Liang, Man-Lai Tang, and Jun-Wu Yu. "Bayesian Estimation and Prediction for the Power Law Process with Left-Truncated Data." Journal of Data Science 9, no. 3 (April 5, 2021): 445–70. http://dx.doi.org/10.6339/jds.201107_09(3).0009.

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18

Fukushima, Toshio. "Numerical computation of gravitational field of infinitely-thin axisymmetric disc with arbitrary surface mass density profile and its application to preliminary study of rotation curve of M33." Proceedings of the International Astronomical Union 14, S344 (August 2018): 276–79. http://dx.doi.org/10.1017/s1743921318007081.

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AbstractWe developed a numerical method[-70pt] to compute the gravitational field of an infinitely-thin axisymmetric disc with an arbitrary surface mass density profile. We evaluate the gravitational potential by a split quadrature using the double exponential rule and obtain the acceleration vector by numerically differentiating the potential by Ridders’ algorithm. By using the new method, we show the rotation curves of some non-trivial discs: (i) truncated power-law discs, (ii) discs with a non-negligible center hole, (iii) truncated Mestel discs with edge-softening, (iv) double power-law discs, (v) exponentially-damped power-law discs, and (vi) an exponential disc with a sinusoidal modulation of the density profile. Also, we present a couple of model fittings to the observed rotation curve of M33: (i) the standard deconvolution by assuming a spherical distributin of the dark matter and (ii) a direct fit of infinitely-thin disc mass with a double power-law distribution of the surface mass density.

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19

Brown, J. C., J. Kašparová, A. M. Massone, and M. Piana. "Fast spectral fitting of hard X-ray bremsstrahlung from truncated power-law electron spectra." Astronomy & Astrophysics 486, no. 3 (June 4, 2008): 1023–29. http://dx.doi.org/10.1051/0004-6361:200809496.

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20

Müller, Sebastian, Falk Heße, Sabine Attinger, and Alraune Zech. "The extended generalized radial flow model and effective conductivity for truncated power law variograms." Advances in Water Resources 156 (October 2021): 104027. http://dx.doi.org/10.1016/j.advwatres.2021.104027.

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21

Asanjarani, A., S. Satouri, A. Alizadeh, and MH Kargarnovin. "Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 5 (June 18, 2014): 818–39. http://dx.doi.org/10.1177/0954406214539472.

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Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for ( SS− SL), ( CS− CL), and ( CS− SL) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

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22

Endharta, Alfonsus Julanto, Jongwoon Kim, and Sung-Soo Choi. "Study on Effect of Left-Truncated Data Rate on ML Estimation for Power Law Process." Journal of the Korean Society for Railway 22, no. 9 (September 30, 2019): 688–97. http://dx.doi.org/10.7782/jksr.2019.22.9.688.

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23

Heße, Falk, Vladyslav Prykhodko, Steffen Schlüter, and Sabine Attinger. "Generating random fields with a truncated power-law variogram: A comparison of several numerical methods." Environmental Modelling & Software 55 (May 2014): 32–48. http://dx.doi.org/10.1016/j.envsoft.2014.01.013.

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24

Zimmerman, Donald W., and Bruno D. Zumbo. "Effect of Outliers on the Relative Power of Parametric and Nonparametric Statistical Tests." Perceptual and Motor Skills 71, no. 1 (August 1990): 339–49. http://dx.doi.org/10.2466/pms.1990.71.1.339.

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It is known that parametric statistical tests, such as t and F, are more powerful than their nonparametric counterparts, such as the Wilcoxon-Mann-Whitney test or the Kruskal-Wallis test, when the assumption of a normal population distribution is satisfied. However, it has been found that, for quite a few nonnormal distributions, the Wilcoxon-Mann-Whitney test ( W) is more powerful than the Student t-test ( t) both in the asymptotic limit and for small samples. The present computer-simulation study examined the role of outliers in determining the relative power of W and t. In a series of five steps, a standard normal distribution, as well as a uniform distribution, was altered so that extreme scores occurred with increasingly higher probability. It was found that the initial power advantage of t gradually diminished in favor of W. In contrast, in a series of five steps, exponential and Cauchy distributions were truncated at less and less extreme values, so that the influence of outliers was reduced, and the initial power advantage of W gradually diminished in favor of t. For all distributions, the ordinary Student t-test performed on the ranks of measures instead of the measures was affected by addition or elimination of outliers in the same way as W and yielded the same probabilities of Type I and Type II errors as W.

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25

PAUL, B. C., S. MUKHERJEE, and A. BEESHAM. "HIGHER DERIVATIVE THEORY WITH VISCOSITY." International Journal of Modern Physics D 07, no. 04 (August 1998): 499–507. http://dx.doi.org/10.1142/s0218271898000334.

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Cosmological solutions in a higher derivative theory have been obtained with an imperfect fluid. We consider both power law and exponential models of the early universe. We discuss cosmological models in the Eckart, truncated and full causal theories. In the full-causal theory, we distinguish between two cases, one with the temperature obeying a power law behavior and the other relaxing this assumption. The exponential solution permits a realistic scenario when the behavior of the temperature is not of the power-law type.

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Jung, Hohyun, and Frederick Kin Hing Phoa. "A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks." Entropy 23, no. 5 (April 22, 2021): 502. http://dx.doi.org/10.3390/e23050502.

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The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.

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27

Rigdon, Steven E., and Asit P. Basu. "Estimating the intensity function of a power law process at the current time: time truncated case." Communications in Statistics - Simulation and Computation 19, no. 3 (January 1990): 1079–104. http://dx.doi.org/10.1080/03610919008812906.

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28

Monereo Atienza, Cristina. "Derecho y Fotografía. La objetividad truncada | Photography and Law. The truncated objectivity." Cuadernos Electrónicos de Filosofía del Derecho, no. 38 (December 24, 2018): 143. http://dx.doi.org/10.7203/cefd.38.12480.

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Resumen: Este trabajo muestra que el discurso fotográfico está en estrecha conexión con la historia e ideología jurídicas. Las cuestiones que atañen a qué es una imagen, la relación entre imagen fotográfica, verdad y objetividad, o el poder de construcción narrativa de la imagen atañen directamente al concepto de Derecho. Como una fotografía, el Derecho moderno nació con el mismo afán de verdad y fe absoluta en la ciencia. Bajo el velo de la neutralidad y objetividad, buscaba la seguridad y control de las relaciones humanas, con la misma aspiración de poseer, cosificar y comercializar la naturaleza y lo humano. Como sucede con las primeras fotografías, el Estado y el Derecho modernos consiguieron acercarse supuestamente a la verdad al fundarse en lo empírico y también en lo espiritual, si bien una vez asentado el discurso narrativo burgués, con promesa de duración y permanencia, se olvidó el fundamento moral. Sin embargo, la otra faceta de la fotografía es subjetiva y creativa, y también lo es la del Derecho. Por eso, el Derecho no puede ser neutral. Muestra y genera un determinado discurso ideológico verosímil acerca de la forma de organización justa. Hablar del poder narrativo del Derecho, pone de manifiesto la capacidad jurídica de inventar la Justicia y, por tanto, sus peligros ideológicos y sus posibilidades emancipadoras. Abstract: This work shows that the photographic discourse is in close connection with the legal history and ideology. Questions that concern on what an image is, the relationship between photographic image, truth and objectivity, or the power of narrative construction of the image directly concern the concept of Law. Like a photograph, the Modern Law was born with the same zeal for truth and absolute faith in science. Under the veil of neutrality and objectivity, he sought the security and control of human relationships, with the same aspiration to possess, reify and commercialize Nature and Humanity. As it happens with the first photographs, the Modern State and Law managed to approach the truth by basing themselves on the empirical facts as well as on the spiritual ideas, although once the bourgeois narrative discourse was established, with promise of duration and permanence, the moral foundation was forgotten. However, the other facet of photography is subjective and creative, and so is that of Law. Therefore, the Law cannot be neutral. It shows and generates a certain credible ideological discourse about the form of just organization. Speaking of the narrative power of Law shows the legal capacity to invent Justice and, therefore, its ideological dangers and its emancipatory possibilities.

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Wang, Zhi Ming. "Reliability Assessment Test Design for Numerical Control Machine Tools." Advanced Materials Research 542-543 (June 2012): 1218–21. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.1218.

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According to the required interval estimation precision of mean time between failures (MTBF) and reliability for numerical control (NC) machine tools, where failure processes can be described by the power law process model, the minimal testing truncated time and sample size of the reliability assessment test are given using Fisher information matrix method. The results show that there are two main factors which affect the truncated time and sample size. They are the log ratio of upper bound to lower bound and confidence of interval estimation for reliability indices, respectively. Among them, the minimal sample size increases significantly as the improvement of required precision of interval estimation for reliability indices and confidence increases, but the minimal testing truncated time is less affected by these two factors.

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Maschberger, Thomas, and Pavel Kroupa. "Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions." Monthly Notices of the Royal Astronomical Society 395, no. 2 (May 11, 2009): 931–42. http://dx.doi.org/10.1111/j.1365-2966.2009.14577.x.

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31

Guadagnini, A., M. Riva, and S. P. Neuman. "Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks." Hydrology and Earth System Sciences 16, no. 9 (September 10, 2012): 3249–60. http://dx.doi.org/10.5194/hess-16-3249-2012.

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Abstract. We analyze the scaling behaviors of two field-scale log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along three horizontal transects on a 21 m long and 6 m high outcrop of the Upper Cretaceous Straight Cliffs Formation, including lower-shoreface bioturbated and cross-bedded sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ(q) of separation scale or lag, s, over limited ranges of s. A procedure known as extended self-similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ξ(q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm or truncated fractional Gaussian noise (tfGn), stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm or tfGn and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm or tfGn functions.

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32

DeVore, J. G. "The Truncated Geometric Approximation and the Size Distribution of Small Atmospheric Particles." Journal of Atmospheric and Oceanic Technology 28, no. 6 (June 1, 2011): 779–86. http://dx.doi.org/10.1175/2010jtecha1513.1.

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Abstract This paper describes a simple relationship between the slope of particulate optical depth as a function of wavelength and the size distribution of spherical particles. It is based on approximating extinction using a truncated geometric optics relationship and is applicable when optical depth decreases with wavelength. The new relationship suggests that extinction versus wavelength measurements are most sensitive to particles that are comparable in size to the wavelength. When optical depth is expressed as a power-law function of wavelength, the resulting particle size distribution is also a power-law function of size, with the two exponents reproducing the well-known relationship between the Ångström and Junge exponents. Examples of applying the new relationship are shown using both numerical calculations based on Mie theory and measurements from the Aerosol Robotic Network (AERONET) sun photometer at NASA Goddard Space Flight Center (GSFC). Since the truncated geometric approximation makes no assumptions per se concerning the form of the particle size distribution, it may find application in supplementing solar aureole profile measurements in retrieving the size distributions of particles in thin clouds—for example, cirrus—or when they are present.

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33

Solomon, Sorin. "Generalized Lotka-Volterra (GLV) Models of Stock Markets." Advances in Complex Systems 03, no. 01n04 (January 2000): 301–22. http://dx.doi.org/10.1142/s0219525900000224.

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The Generalized Lotka-Volterra (GLV) model: [Formula: see text] provides a general method to simulate, analyze and understand a wide class of phenomena that are characterized by power-law probability distributions: [Formula: see text] and truncated Levy flights fluctuations [Formula: see text]. We show how the model applies to economic systems.

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PAUL, B. C., S. MUKHERJEE, and A. BEESHAM. "VISCOUS COSMOLOGICAL MODELS IN (1 + 1) DIMENSIONS." International Journal of Modern Physics D 07, no. 04 (August 1998): 567–79. http://dx.doi.org/10.1142/s0218271898000383.

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Cosmological solutions in (1 + 1) dimensions in the theory of gravity given by Mann have been obtained in the presence of dissipative phenomena. We have studied both the truncated Israel–Stewart theory and the full causal theory in these lower dimensions. In the full causal theory, we discuss two cases, one with the temperature obeying a power law behavior and the other without this assumption. Some of the solutions found in the truncated Israel–Stewart theory and in the full causal theory are comparable to those obtained by Chimento and Cossarini in (1 + 1) dimensions in Eckart theory.

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35

Molina-Garcia, Daniel, Trifce Sandev, Hadiseh Safdari, Gianni Pagnini, Aleksei Chechkin, and Ralf Metzler. "Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers." New Journal of Physics 20, no. 10 (October 18, 2018): 103027. http://dx.doi.org/10.1088/1367-2630/aae4b2.

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LaViolette, Randall A., W. E. Beyeler, R. J. Glass, K. L. Stamber, and Hamilton Link. "Sensitivity of the resilience of congested random networks to rolloff and offset in truncated power-law degree distributions." Physica A: Statistical Mechanics and its Applications 368, no. 1 (August 2006): 287–93. http://dx.doi.org/10.1016/j.physa.2005.12.049.

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37

Kitahama, Yasutaka, Takuji Nagahiro, Yoshito Tanaka, Tamitake Itoh, and Yukihiro Ozaki. "Analysis of blinking from multicoloured SERS-active Ag colloidal nanoaggregates with poly-L-lysine via truncated power law." Journal of Raman Spectroscopy 48, no. 4 (January 13, 2017): 570–77. http://dx.doi.org/10.1002/jrs.5079.

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38

Cheng, Ching-Yang. "Natural convection of a micropolar fluid from a vertical truncated cone with power-law variation in surface temperature." International Communications in Heat and Mass Transfer 35, no. 1 (January 2008): 39–46. http://dx.doi.org/10.1016/j.icheatmasstransfer.2007.05.018.

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39

Guadagnini, A., M. Riva, and S. P. Neuman. "Extended power-law scaling of heavy-tailed random fields or processes." Hydrology and Earth System Sciences Discussions 9, no. 6 (June 12, 2012): 7379–413. http://dx.doi.org/10.5194/hessd-9-7379-2012.

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Abstract. We analyze the scaling behaviors of two log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along two horizontal transects on a 21 m long outcrop of lower-shoreface bioturbated sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ (q) of separation scale or lag, s, over limited ranges of s. A procedure known as Extended Self-Similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ξ (q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm, stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm functions.

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Debnath, Partha Sarathi. "Observational constraints of bulk viscous Friedmann–Robertson–Walker cosmology with hybrid expansion law." International Journal of Modern Physics A 35, no. 27 (September 30, 2020): 2050173. http://dx.doi.org/10.1142/s0217751x20501730.

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In this work, we study bulk viscous Friedmann–Robertson–Walker cosmologies with hybrid expansion law. The bulk viscous theory of dissipative effects described by Eckart theory, truncated Israel–Stewart theory and full Israel–Stewart theory are implemented here. The hybrid expansion law model of scale factor is a general analytic type of evolution from which one can recover power-law and exponential expansion as a special cases. Hybrid expansion law model are applied to describe the present accelerating phase and early phases of evolution. We have determined the cosmological parameters such as Hubble parameter, deceleration parameter, jerk parameter, energy density, bulk viscous pressure and coefficient of bulk viscosity of the universe to construct physically acceptable cosmological model. We have considered both flat and closed space–time of Friedmann–Robertson–Walker cosmology to implement hybrid expansion law with dissipative effect. The variations of the coefficient of bulk viscosity with cosmic evolution are studied here in Eckart, truncated and full Israel–Stewart theory for flat and closed space–time to obtain physically acceptable hybrid expansion models driven by viscosity. We have also estimated observational constraints of the parameters of hybrid expansion law model by considering recent observational data set. We further reveal possible connections of our models with [Formula: see text] tension problem.

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Jiang, Jiachen, Felix Fürst, Dominic J. Walton, Michael L. Parker, and Andrew C. Fabian. "A NuSTAR view of GRS 1716−249 in the hard and intermediate states." Monthly Notices of the Royal Astronomical Society 492, no. 2 (January 7, 2020): 1947–56. http://dx.doi.org/10.1093/mnras/staa017.

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ABSTRACT We present a detailed analysis of the spectral properties of the black hole transient GRS 1716−249, based on the archival Swift and NuSTAR observations taken during the outburst of this source in 2016–2017. The first six NuSTAR observations show that the source is in a canonical hard state, where the spectrum is dominated by a power-law continuum. The seventh NuSTAR observation is taken during the intermediate state where both a disc thermal component and a power-law continuum are shown. All of our observations show a broad emission-line feature in the iron band and a Compton hump above 10 keV. We model the broad-band spectra using a high-density disc reflection model, where the soft X-ray emission in the hard state is interpreted as part of the disc reflection component. This model enables us to constrain the disc density parameter of GRS 1716−249 in the range of 1019–1020 cm−3. We only obtain an upper limit of the inner disc radius using high-density disc reflection spectroscopy and the results indicate either a non-truncated disc or a slightly truncated disc with Rin ≲ 20 rg.

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Burroughs, S. M. "The Upper-Truncated Power Law Applied to Earthquake Cumulative Frequency-Magnitude Distributions: Evidence for a Time-Independent Scaling Parameter." Bulletin of the Seismological Society of America 92, no. 8 (December 1, 2002): 2983–93. http://dx.doi.org/10.1785/0120010191.

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SLANINA, FRANTIŠEK. "COMPLEX TEMPORAL STRUCTURE OF ACTIVITY IN ON-LINE ELECTRONIC AUCTIONS." Advances in Complex Systems 15, supp01 (June 2012): 1250053. http://dx.doi.org/10.1142/s0219525912500531.

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We analyze empirical data from the internet auction site Aukro.cz. The time series of activity shows truncated fractal structure on scales from about 1 min to about 1 day. The distribution of waiting times as well as the distribution of number of auctions within fixed interval is a power law, with exponents 1.5 and 3, respectively. Possible implications for the modeling of stock-market fluctuations are briefly discussed.

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Gorev, V. N., A. Yu Gusev, V. I. Korniienko, and A. A. Safarov. "ON THE KOLMOGOROV-WIENER FILTER FOR RANDOM PROCESSES WITH A POWER-LAW STRUCTURE FUNCTION BASED ON THE WALSH FUNCTIONS." Radio Electronics, Computer Science, Control, no. 2 (June 26, 2021): 39–47. http://dx.doi.org/10.15588/1607-3274-2021-2-4.

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Context. We investigate the Kolmogorov-Wiener filter weight function for the prediction of a continuous stationary random process with a power-law structure function. Objective. The aim of the work is to develop an algorithm of obtaining an approximate solution for the weight function without recourse to numerical calculation of integrals. Method. The weight function under consideration obeys the Wiener-Hopf integral equation. A search for an exact analytical solution for the corresponding integral equation meets difficulties, so an approximate solution for the weight function is sought in the framework of the Galerkin method on the basis of a truncated Walsh function series expansion. Results. An algorithm of the weight function obtaining is developed. All the integrals are calculated analytically rather than numerically. Moreover, it is shown that the accuracy of the Walsh function approximations is significantly better than the accuracy of polynomial approximations obtained in the authors’ previous papers. The Walsh function solutions are applicable in wider range of parameters than the polynomial ones. Conclusions. An algorithm of obtaining the Kolmogorov-Wiener filter weight function for the prediction of a stationary continuous random process with a power-law structure function is developed. A truncated Walsh function expansion is the basis of the developed algorithm. In opposite to the polynomial solutions investigated in the previous papers, the developed algorithm has the following advantages. First of all, all the integrals are calculated analytically, and any numerical calculation of the integrals is not needed. Secondly, the problem of the product of very small and very large numbers is absent in the framework of the developed algorithm. In our opinion, this is the reason why the accuracy of the Walsh function solutions is better than that of the polynomial solutions for many approximations and why the Walsh function solutions are applicable in a wider range of parameters than the polynomial ones. The results of the paper may be applied, for example, to practical traffic prediction in telecommunication systems with data packet transfer.

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Yang, S. W., Y. X. Hao, W. Zhang, and S. B. Li. "Nonlinear Dynamic Behavior of Functionally Graded Truncated Conical Shell Under Complex Loads." International Journal of Bifurcation and Chaos 25, no. 02 (February 2015): 1550025. http://dx.doi.org/10.1142/s021812741550025x.

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Nonlinear dynamic behaviors of ceramic-metal graded truncated conical shell subjected to complex loads are investigated. The shell is modeled by first-order shear deformation theory. The nonlinear partial differential governing equation in terms of transverse displacements of the FGM truncated conical shell is derived from the Hamilton's principle. Galerkin's method is then utilized to discretize the partial governing equations to a two-degree-of-freedom nonlinear ordinary differential equation. The temperature-dependent materials properties of the constituents are graded in the radial direction in accordance with a power-law distribution. The aerodynamic pressure can be calculated by using the first-order piston theory. The temperature field is assumed to be a steady-state constant-temperature distribution. Bifurcation diagrams, the maximum Lyapunov exponents, wave forms and phase portraits are obtained by numerical simulation to demonstrate the complex nonlinear dynamics response of the FGM truncated conical shell. The influences of the semi-vertex angle, the material gradient index, in-plane and aerodynamic load on the nonlinear dynamics are studied.

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CARP, Radu. "COMBINING SOFT POWER WITH THE GEOPOLITICAL APPROACH - HOW DIFFICULT IS FOR THE EU TO CHANGE ITS ATTITUDE?" STRATEGIES XXI - National Defence College 1, no. 72 (July 15, 2021): 189–95. http://dx.doi.org/10.53477/2668-5094-21-14.

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After gradually evolving from an economic project to a political one, European Union leaders declare nowadays that it is time to go forward and to build a geopolitical actor on the international stage. This paper does make an account on the current stage of relevant geopolitical actors and how they view EU. In order to address this issue, EU have to focus more on its soft power instruments, like multilateralism and the promotion of democracy, rule of law and human rights, and also climate change, apart from hard power instruments like trade, security and defense, cybersecurity and data privacy.Keywords: democracy, European Union, geopolitics, human rights, multilateralism, rule of law, soft power.

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Kitahama, Yasutaka, Ai Enogaki, Yuhei Tanaka, Tamitake Itoh, and Yukihiro Ozaki. "Truncated Power Law Analysis of Blinking SERS of Thiacyanine Molecules Adsorbed on Single Silver Nanoaggregates by Excitation at Various Wavelengths." Journal of Physical Chemistry C 117, no. 18 (April 26, 2013): 9397–403. http://dx.doi.org/10.1021/jp312530j.

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Kuti, Csongor. "Between a Rock and a Hard Place: Constitutional Conflict Cases before The Romanian Constitutional Court." Hungarian Journal of Legal Studies 60, no. 3 (January 22, 2021): 281–95. http://dx.doi.org/10.1556/2052.2019.00017.

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For the rule of law-based democratic regimes, at least two types of significant political challenges can be identified:1. Challenges coming from outside of the democratic regime, in the form of movements which, by making use of the constitutionally guaranteed rights and liberties, attempt to destroy the democratic establishment.2. Challenges coming from inside the democratic regime, in the form of authoritarian movements, which are attempting to overcome their political opponents and consolidate their power by the misuse of the institutions found under their control according to the constitutional blueprint.This paper is concerned with the second type of challenges and examines how the power struggle reflects in constitutional adjudication. Focusing on the case law of the Romanian Constitutional Court, it analyzes the trends in the evolution of the Court’s interpretation of constitutional conflict issues. The paper argues that in periods of great political fragmentation and power-struggle, constitutional conflict cases are more present in the Court’s docket and they result in much more disputed decisions, as actors attempt to present political conflicts as judicial ones. The Court itself is getting more drawn into these struggles and gradually loses its ‘independent arbitrator’ stance.

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Laidoudi, Houssem, and Mohamed Bouzit. "Non-Newtonian Power-Law Flows around Circular Cylinder under Aiding/Opposing Thermal Buoyancy." Diffusion Foundations 16 (June 2018): 45–56. http://dx.doi.org/10.4028/www.scientific.net/df.16.45.

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This paper presents a comprehensive computational work on hydrodynamic and thermal phenomena of upward flow separation around a confined circular cylinder by aiding/opposing thermal buoyancy. For that purpose, let us consider a confined flow of Non-Newtonian power-law fluid around a heated/cooled circular cylinder in a two-dimensional vertical channel. The effects of thermal buoyancy and power-Law index on the flow separation and the average Nusselt number are studied for the conditions: (10 ≤ Re ≤ 40), (0.4≤ n ≤ 1.2), (-0.5 ≤ Ri ≤ 0.8), Pr = 50 and blockage ratio β = 0.2. In the steady flow regime the results show that the augmentation of the power-law index in the absence of thermal buoyancy causes a separation to grow. The adding buoyancy effect delays the separation in different power-law indices gradually and at some critical value of the buoyancy parameter it completely disappears resulting a stuck flow around a cylinder, whereas the opposing buoyancy effect causes an earlier wake behind cylinder. Moreover, the recirculation length is calculated to support the above finding. The decrease in the power-Law index increases the heat transfer rate. The Nusselt numbers are computed to predict the heat transfer rates of power-law fluids under the aiding/opposing thermal buoyancy condition.

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Kitahama, Yasutaka, Daichi Araki, Yuko S. Yamamoto, Tamitake Itoh, and Yukihiro Ozaki. "Different behaviour of molecules in dark SERS state on colloidal Ag nanoparticles estimated by truncated power law analysis of blinking SERS." Physical Chemistry Chemical Physics 17, no. 33 (2015): 21204–10. http://dx.doi.org/10.1039/c4cp05070c.

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