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Yadav, R. P.; Dwivedi, S.; Mi, Fractal and multifractal analysis of LiF thin film surface //Applied Surface Science(NLD). 2012 г., т. 261, P.547-553

Fractal and multifractal analysis is performed on the atomic force microscopy (AFM) images of the surface morphologies of the LiF thin films of thickness 10 nm, 20 nm, and 40 nm, respectively. Autocorrelation function, height-height correlation function, and two-dimensional multifractal detrended fluctuation analysis (MFDFA) are used for characterizing the surface. It is found that the interface width, average roughness, lateral correlation length, and fractal dimension of the LiF thin film increase with the thickness of the film, whereas the roughness exponent decreases with thickness. Thus, the complexity and roughness of the LiF thin films increases as thickness increases. It is also demonstrated that the LiF thin films are multifractal in nature. Strength of the multifractality increases with thickness of the film. (C) 2012 Elsevier B. V. All rights reserved

Aschwanden M.J.A statistical fractal-diffusive avalanche model of a slowly-driven self-organized criticality system//Astronomy and Astrophysics(DEU). 2012 г., т. 539,pt.1,Number: A2

A statistical fractal-diffusive avalanche model of a slowly-driven self-organized criticality system By: Aschwanden, M. J. ASTRONOMY & ASTROPHYSICS Volume: 539 Article Number: A2 Published: MAR 2012 Full Text View AbstractClose AbstractAims. We develop a statistical analytical model that predicts the occurrence frequency distributions and parameter correlations of avalanches in nonlinear dissipative systems in the state of a slowly-driven self-organized criticality (SOC) system. Methods. This model, called the fractal-diffusive SOC model, is based on the following four assumptions: (i) the avalanche size L grows as a diffusive random walk with time T, following L proportional to T-1/2; (ii) the energy dissipation rate f (t) occupies a fractal volume with dimension D-S; (iii) the mean fractal dimension of avalanches in Euclidean space S = 1, 2, 3 is D-S approximate to (1+ S)/2; and (iv) the occurrence frequency distributions N(x). x(-ax) based on spatially uniform probabilities in a SOC system are given by N(L) proportional to L-S, with S being the Eudlidean dimension. We perform cellular automaton simulations in three dimensions (S = 1, 2, 3) to test the theoretical model

Castineira-Ibanez, Sergio; Rubio, Constanza; Romero-Garcia, Vicent; et al. Design, Manufacture and Characterization of an Acoustic Barrier Made of Multi-Phenomena Cylindrical //Archives of Acoustics(POL). 2012 г., т. 37, N 4, стр. 455-462

In this work we present the design and the manufacturing processes, as well as the acoustics standardization tests, of an acoustic barrier formed by a set of multi-phenomena cylindrical scatterers. Periodic arrangements of acoustic scatterers embedded in a fluid medium with different physical properties are usually called Sonic Crystals. The multiple scattering of waves inside these structures leads to attenuation bands related to the periodicity of the structure by means of Bragg scattering. In order to design the acoustic barrier, two strategies have been used: First, the arrangement of scatterers is based on fractal geometries to maximize the Bragg scattering; second, multi-phenomena scatterers with several noise control mechanisms, as resonances or absorption, are designed and used to construct the periodic array. The acoustic barrier reported in this work provides a high technological solution in the field of noise control

Chen, Yongping Optimal surface fractal dimension for heat and fluid flow in microchannels//Applied Physics Letters(USA). 2010 г., т. 97, N 8, art.084101.

The fractal Weierstrass-Mandelbrot function was introduced to characterize the multiscale self-affine rough surface of microchannels. Based on this fractal characterization, the role of the rough surface structure on the thermal and hydrodynamic properties in microchannels was evaluated using a computational fluid dynamic simulation. Once identified, these were used to determine the optimal surface dimension for heat and fluid flow. It was found that, no matter what the Reynolds number and roughness height are, the flow heat transfer performance is being optimized with increasing fractal dimension of the surface until to the dimension value of three (infinitely crumpled)

Chen, Zhen Long Hitting probabilities and fractal dimensions of multiparameter multifractional Brownian motion //Acta Mathematica Sinica(CHN). 2013 г., т. 29, N 9,стр. 1723-1742.

The main goal of this paper is to study the sample path properties for the harmonisabletype N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an (N, d)-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets

6.U 03066
de Amo, E (de Amo, Enrique); Carrillo, MD (Diaz Carrillo, Manuel); Sanchez, JF (Fernandez Sanchez, Juan); Salmeron, A (Salmeron, Antonio)Moments and associated measures of copulas with fractal support //

Copulas are closely related to the study of distributions and the dependence between random variables. In this paper we develop a recurrence formula for the moments of a measure associated with a copula (a bivariate distribution function with uniform one-dimensional marginals) in the case that its support is a fractal set. We do the same for its principal and secondary diagonals. We also study certain measures of dependence or association for these copulas with fractal supports

Dong, Jun; Zheng, Hairong; Li, Xuqiang; et al.Surface-enhanced fluorescence from silver fractallike nanostructures decorated with silver nanoparti,//Applied Optics(USA). 2011 г., т. 50, N 31, стр. G123-G126

Fluorescence emission of fluorophore molecules in the close vicinity of a nanostructured metal surface can be enhanced through a local electromagnetic field with the help of surface plasmon resonance. The fluorescence enhancement effect is very sensitive to the topography and dielectric property of the metal substrate. In the current work, metal substrates with complex structures, which are made of silver fractallike structures and nanoparticles (NPs), are prepared through electrochemical reduction followed by physical deposition. The surface-enhanced fluorescence of Rhodamine 6G monolayer molecules deposited on the prepared complex substrates are investigated with the laser spectroscopic technique. The experimental results show that the fractallike structure decorated with silver NPs presents stronger fluorescence enhancement, compared with silver NPs or pure silver fractallike structures. (C) 2011 Optical Society of America

Fernandes, B.; Gregorio-Hetem, J.; Hetem, A., Jr Probing the anomalous extinction of four young star clusters: the use of colour-excess, main-sequenc//Astronomy and Astrophysics(DEU). 2012 г., т. 541, N 1, , Art.number: A95.

Aims. We studied four young star clusters to characterise their anomalous extinction or variable reddening and asses whether they could be due to contamination by either dense clouds or circumstellar effects. Methods. We evaluated the extinction law (R-V) by adopting two methods: (i) the use of theoretical expressions based on the colour-excess of stars with known spectral type; and (ii) the analysis of two-colour diagrams, where the slope of the observed colour distribution was compared to the normal distribution. An algorithm to reproduce the zero-age main-sequence (ZAMS) reddened colours was developed to derive the average visual extinction (A(V)) that provides the closest fit to the observational data. The structure of the clouds was evaluated by means of a statistical fractal analysis, designed to compare their geometric structure with the spatial distribution of the cluster members

French, Jason E Dendritic zircon formation by deterministic volume-filling fractal growth: Implications for the mechanisms of branch formation in dendrites //American Mineralogist(USA). 2010 г., т. 95, N 5, (стр. 706-716 ).

In this paper, I demonstrate that the complex structure observed in natural dendritic zircon, which crystallized from a mafic magma, can be approximated by a simple model of deterministic volume-filling fractal growth. The model comprises a novel dendritic growth process that reveals a previously unrecognized underlying structure to complex dendritic crystals, and provides an ideal way of maximizing surface area at the crystal-melt interface during dendritic crystal growth. This addresses the important kinetic effect of creating interfacial area. In turn, this relates to dissipation of the latent heat of fusion from the moving crystal-melt interface, which, in addition to chemical diffusion, is known to be a fundamental rate-controlling process in dendritic crystal growth

Gangopadhyay, Arnab; Sarkar, Aditi; Sarkar, Al A study on natural coral stone-a fractal solid //Applied Physics. A. Materials Science and Processing(DEU). 2012 г., т. 109, N 4,P.979-983.

This present research work contains the study of natural fractal material, coral stone. X-ray diffraction, FTIR, optical, DC and AC electrical characteristics are studied. The study includes Arrhenius like plots for both wafer and powder form of the material. Measurements show a possible partially irreversible phase transition occurs when coral is heated for a long time at an about 115 A degrees C. From the XRD data it has been also established that coral stone contains nano sized clusters which is supported by DC electrical measurement. The variation of AC conductivity of coral with thickness of the sample is studied and found exhibit an interesting feature of fractal solid. A scaling relation between AC conductivity and thickness has also been proposed here. The overall behavior of the specimen is like that of a fractal system

Hochman, Michael; Shmerkin, Pablo Local entropy averages and projections of fractal measures //Annals of Mathematics(USA). 2012 г., т. 175, N 3,P.1001-1059.

We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of "self-similarity" under the operation of re-scaling, the dimension of linear images of the measure behaves in a semi-continuous way. We apply this to prove the following conjecture of Furstenberg: if X, Y subset of [0, 1] are closed and invariant, respectively, under xm mod 1 and xn mod 1, where m, n are not powers of the same integer, then, for any t not equal 0, dim(X + tY) = min{1, dim X + dim Y}. A similar result holds for invariant measures and gives a simple proof of the Rudolph-Johnson theorem. Our methods also apply to many other classes of conformal fractals and measures. As another application, we extend and unify results of Peres, Shmerkin and Nazarov, and of Moreira, concerning projections of products of self-similar measures and Gibbs measures on regular Cantor sets. We show that under natural irreducibility assumptions on the maps in the IFS, the image measure has the maximal possible dimension under any linear projection other than the coordinate projections. We also present applications to Bernoulli convolutions and to the images of fractal measures under differentiable maps.

Ma, Lin Tao; Su, Wei Yi Two-dimensional Wave Equations with Fractal Boundaries//Acta Mathematica Sinica(CHN). 2013 г., т. 29, N 12,стр. 2321-2342.

This paper focuses on two cases of two-dimensional wave equations with fractal boundaries. The first case is the equation with classical derivative. The formal solution is obtained. And a definition of the solution is given. Then we prove that under certain conditions, the solution is a kind of fractal function, which is continuous, differentiable nowhere in its domain. Next, for specific given initial position and 3 different initial velocities, the graphs of solutions are sketched. By computing the box dimensions of boundaries of cross-sections for solution surfaces, we evaluate the range of box dimension of the vibrating membrane. The second case is the equation with p-type derivative. The corresponding solution is shown and numerical example is given

Ma, Lin Tao; Su, Wei Yi Two-dimensional Wave Equations with Fractal Boundaries//Acta Mathematica Sinica(CHN). 2013 г., т. 29, N 12,стр. 2321-2342.

This paper focuses on two cases of two-dimensional wave equations with fractal boundaries. The first case is the equation with classical derivative. The formal solution is obtained. And a definition of the solution is given. Then we prove that under certain conditions, the solution is a kind of fractal function, which is continuous, differentiable nowhere in its domain. Next, for specific given initial position and 3 different initial velocities, the graphs of solutions are sketched. By computing the box dimensions of boundaries of cross-sections for solution surfaces, we evaluate the range of box dimension of the vibrating membrane. The second case is the equation with p-type derivative. The corresponding solution is shown and numerical example is given

Manduteanu, Ileana; Pirvulescu, Monica; Gan, Ana Maria; et al Similar effects of resistin and high glucose on P-selectin and fractalkine expression and monocyte a//Biochemical and Biophysical Research Communications(USA). 2010 г., т. 391, N 3, стр. 1443-1448

Resistin and high glucose (HG) are concomitantly present at elevated concentration in diabetic's plasma; both are pro-inflammatory agents acting on vascular cells by mechanisms that are not fully understood. We questioned whether resistin and HG affect the expression of major adhesion molecules, P-selectin and fractalkine in human endothelial cells (HEC). The results showed that in HEC (i) resistin increased P-selectin expression; (ii) HG up-regulated Fk expression; (iii) P-selectin and fractalkine were functional increasing monocyte adhesion to activated cells. Co-stimulation with resistin and HG increased P-selectin and fractalkine mRNA and protein and induced monocyte adhesion, generated an increase in NADPH oxidase activity and of the intracellular reactive oxygen species and activated the NF-kB and AP-1 transcription factors at similar values as those of each activator. In conclusion in HEC, resistin and HG induce the up-regulation of P-selectin and fractalkine and the ensuing increased monocyte adhesion by a mechanism involving oxidative stress and NF-kB and AP-1 activation. (c) 2009 Elsevier Inc. All rights reserved

McKeague, Ian W. Sen, Bodhisattva FRACTALS WITH POINT IMPACT IN FUNCTIONAL LINEAR REGRESSION//Annals of Statistics(USA). 2010 г., т. 38, N 4,P. 2559-2586.

This paper develops a point impact linear regression model in which the trajectory of a continuous stochastic process, when evaluated at a sensitive time point, is associated with a scalar response. The proposed model complements and is more interpretable than the functional linear regression approach that has become popular in recent years. The trajectories are assumed to have fractal (self-similar) properties in common with a fractional Brownian motion with an unknown Hurst exponent. Bootstrap confidence intervals based on the least-squares estimator of the sensitive time point are developed. Misspecification of the point impact model by a functional linear model is also investigated. Non-Gaussian limit distributions and rates of convergence determined by the Hurst exponent play an important role

Miyamaru, Fumiaki; Kubot Terahertz Response of Split-Ring Resonators with Fractal Structures //Applied Physics Express (until 2008 see: Japanese J.of Applied Physics.2.)(JPN). 2012 г., т. 5, N 7, art. 072001

We investigate the electromagnetic characteristics of fractal split-ring resonators (SRRs) in the terahertz region by applying the fractal structure of a Koch curve to the SRRs in order to modify the electromagnetic response. The resonant frequency of the SRRs decreases as the fractal level of the Koch curve increases, indicating the possibility of fabricating metamaterials with extremely small unit cell sizes comparable to the wavelength of the electromagnetic waves at the operating frequency

Nedic, J.; Ganapathisubramani, B.; Vassilicos, J. C.; et al. Aeroacoustic Performance of Fractal Spoilers //AIAA JOURNAL Volume: 50 Issue: 12 P. 2695-2710 Published: DEC 2012

One of the major environmental problems facing the aviation industry is that of aircraft noise. The work presented in this paper, done as part of the European Union's Optimisation for Low Environmental Noise Impact Project, looks at reducing spoiler noise while maintaining aerodynamic performance, through means of large-scale fractal porosity. It is hypothesized that the highly turbulent flow generated by fractal grids from the way the multiple-length scales are organized in space, would reduce the impact of the recirculation region and, with it, the low-frequency noise it generates. In its place, a higher frequency noise is introduced, which is more susceptible to atmospheric attenuation and is less offensive to the human ear. A total of nine laboratory-scaled spoilers were looked at, seven of which had a fractal design, one with a regular grid design, and one solid for reference. The spoilers were inclined at an angle of 30 deg. Force, acoustic, and flow visualization experiments on a flat plate were carried out and it was found that the present fractal spoilers reduce the low-frequency noise by 2.5 dB. Results show that it is possible to improve the acoustic performance by modifying a number of parameters defining the fractal spoiler, some of them very sensitively. From these experiments, two fractal spoilers were chosen for a detailed aeroacoustic study on a three-element wing system, where it was found that the fractal spoilers had a reduction of up to 4 dB in the sound pressure level, while maintaining similar aerodynamic performances as conventional solid spoilers on the measured wing system

Nestor Sanchez,Neyda Anez THE FRACTAL DIMENSION OF STAR-FORMING REGIONS AT DIFFERENT SPATIAL SCALES IN M33//Astrophysical Journal (USA). 2010 г., т. 720, N 2,стр. 541-547

We study the distribution of stars, H it regions, molecular gas, and individual giant molecular clouds in M33 over a wide range of spatial scales. The clustering strength of these components is systematically estimated through the fractal dimension. We find scale-free behavior at small spatial scales and a transition to a larger correlation dimension (consistent with a nearly uniform distribution) at larger scales. The transition region lies in the range similar to 500-1000 pc. This transition defines a characteristic size that separates the regime of small-scale turbulent motion from that of large-scale galactic dynamics. At small spatial scales, bright young stars and molecular gas are distributed with nearly the same three-dimensional fractal dimension (D-f,D-3D less than or similar to 1.9), whereas fainter stars and H II regions exhibit higher values, D-f,D-3D similar or equal to 2.2-2.5. Our results indicate that the interstellar medium in M33 is on average more fragmented and irregular than in the Milky Way.

Pasic, Mervan; Tanaka, Satoshi Fractal oscillations of self-adjoint and damped linear differential equations of second-order //9. Applied Mathematics and Computation(USA). 2012 г., т. 218, N 5,P. 2281-2293

For a prescribed real number s is an element of [1, 2), we give some sufficient conditions on the coefficients p(x) and q(x) such that every solution y = y(x), y is an element of C(2)((0, T]) of the linear differential equation (p(x)y')' + q(x) y = 0 on (0, T], is bounded and fractal oscillatory near x = 0 with the fractal dimension equal to s. This means that y oscillates near x = 0 and the fractal (box-counting) dimension of the graph Gamma(y) of y is equal to s as well as the s dimensional upper Minkowski content (generalized length) of Gamma(y) is finite and strictly positive. It verifies that y admits similar kind of the fractal geometric asymptotic behaviour near x = 0 like the chirp function y(ch)(x) = a(x)S(phi(x)), which often occurs in the time-frequency analysis and its various applications. Furthermore, this kind of oscillations is established for the Bessel, chirp and other types of damped linear differential equations given in the form y '' + (mu/x)y' + g(x)y = 0, x is an element of (0, T]. In order to prove the main results, we state a new criterion for fractal oscillations near x = 0 of real continuous functions which essentially improves related one presented in [1]. (C) 2011 Elsevier Inc. All rights reserved

Pu, Yang; Wang, Wubao; AL-Rubaiee, Mohammad; et al. Determination of Optical Coefficients and Fractal Dimensional Parameters of Cancerous and Normal Pro//Applied Spectroscopy(USA). 2012 г., т. 66, N 7,P.828-834

Optical extinction and diffuse reflection spectra of cancerous and normal prostate tissues in the 750 to 860 nm spectral range were measured. Optical extinction measurements using thin ex vivo prostate tissue samples were used to determine the scattering coefficient (mu(s)), while diffuse reflection measurements using thick prostate tissue samples were used to extract the absorption coefficient (mu(a)) and the reduced scattering coefficient (mu(s)'). The anisotropy factor (g) was obtained using the extracted values of mu(s) and mu(s)'. The values of fractal dimension (D-f) of cancerous and normal prostate tissues were obtained by fitting to the wavelength dependence of mu(s)'. The number of scattering particles contributing to mu(s) as a function of particle size and the cutoff diameter d(max) as a function of g were investigated using the fractal soft tissue model and Mie theory. Results show that d(max) of the normal tissue is larger than that of the cancerous tissue. The cutoff diameter d(max) is observed to agree with the nuclear size for the normal tissues and the nucleolar size for the cancerous tissues. Transmission spectral polarization imaging measurements were performed that could distinguish the cancerous prostate tissue samples from the normal tissue samples based on the differences between their absorption and scattering parameters

Timofte, A.; Botez, I. Casian; Scurtu, D.; et al.System Dynamics Control through the Fractal Potentia//4. Acta Physica Polonica. A. General Physics. Physics of Condensed Matter. Optics and Quantum Electronics. Atomic and Molecular Physics. Applied Physics(POL). 2011 г., т. 119, N 3,P. 304-311.

Implications of the fractal potential in the system dynamics using an extended scale relativity model assuming the fractal character of the particle movements, are established. So, in the dissipative approximation of the model it is shown that the fractal potential comes from the non-differentiability of the space-time, i.e. by means of imaginary part of a complex speed field. In the dispersive approximation of the same model, the fractalization of the differential part of the complex speed field induces a normalized fractal potential which controls through coherence the system dynamics. In such context the type

Word, R. C.; Do Photoemission from localized surface plasmons in fractal metal nanostructures//Applied Physics Letters(USA). 2010 г., т. 96, N 25,art.251110

We use photoemission microscopy to characterize localized surface plasmon distributions in nanostructured gold layers on indium-tin-oxide/glass substrates. The Au films have a fractal dimension of similar to 1.3 and smallest feature sizes of similar to 100 nm. We use femtosecond laser pulses at a wavelength of similar to 800 nm for the plasmon excitation. Photoelectron emission occurs by a three-photon process in localized areas of indium-tin-oxide with similar to 70 nm diameter. In these areas the photoemission rate is enhanced several thousand fold compared to nonstructured surface areas. The results show that plasmon enhanced photoemission can be induced in a nonabsorbing material in proximity to a plasmon-active metal nanostructure

Yang, Y.; Zeng, J. F.; Volland Fractal growth of the dense-packing phase in annealed metallic , стр. 5260-5272//Acta Materialia (GBR). 2012 г., т. 60, N 13

Unlike crystalline metals, which have a well-understood periodical structure, the amorphous structure of metallic glasses (MGs) is still poorly understood, particularly when such a structure rearranges itself at the nanoscale under external agitations. In this article, we provide compelling evidence obtained from a recently developed high-resolution atomic force microscopy (HRAFM) technique that reveals the nanoscale structural heterogeneity after thermal annealing in a Zr-Ni metallic glass. Through the HRAFM technique, we are able to uncover the annealing-induced fractal growth of the dense-packing phases in the binary MG thin film, which exhibits a fractal dimension of similar to 1.7, in line with a two-dimensional diffusion limited aggregation process. The current findings not only reveal the evolution process of atomic packing in the annealed MG thin film, but also shed light on the possible cooling rate effect on the atomic structure of MGs.

Горяинов П.М., Иванюк Г.Ю., Калашников А, РЕЛЬЕФООБРАЗОВАНИЕ КАК ЭЛЕМЕНТ САМООРГАНИЗАЦИИ ЛИТОСФЕРЫ //Геология и геофизика (ВАК) 2013 г., т. 54, N 9, стр. 1366-1380

Различные по природе и масштабу геологические объекты демонстрируют взаимосвязь фрактальных свойств рельефа как с интенсивностью эндогенных энергопотоков, так и с вещественным составом геологических комплексов. Хорошая корреляция дифференцированности рельефа Хибинского массива с переменными различных уровней его структурно-вещественной организации (минеральный и химический составы пород и минералов, текстурные особенности горных пород и др.) свидетельствует о том, что рельефообразование является частью процесса самоорганизации Хибинского массива. Анализ фрактальной размерности рельефа Хибинского массива, Приморского края и детальных участков в Забайкалье выявил совпадение ее максимумов с положением рудных узлов, полей и месторождений, т.е. территорий с концентрацией элементов, существенно превышающей кларковую. Все это позволяет использовать фрактальные свойства рельефа в качестве поискового критерия.

Жуков С.А. ЗЕМНЫЕ ФРАКТАЛЫ//Земля из космоса(RUS). 2012 г.,N 15,стр. 32-43

Лекарство от смерти — жизнь, лекарство от жизни — творчество, а образец творчества — поверхность Земли. Творец бесконечно разнообразен в своих приемах. Один из приемов — достижение сложности через повторение. Картина создается из множества подобных элементов, то есть фракталов. Автор «путешествует» по Земле с помощью фотографий, полученных с борта МКС

Панычев С.Н., Фёдоров С.М. ОБЗОР МЕТОДОВ ПОСТРОЕНИЯ КВАЗИФРАКТАЛЬНЫХ АНТЕННЫХ РЕШЕТОК //Вестник Воронежского ГТУ (ВАК)(RUS). 2012 г., т. 8, N 4, стр. 32-35

В работе представлен обзор методов построения фрактальных антенных решеток с помощью фрактальных и апе- риодических плиток, также приведен метод оптимизации конструкции решетки для улучшения ее характеристик. Описа- ны основные достоинства и недостатки получаемых фрактальных решеток

Рудомёткин К.А. ПРИМЕНЕНИЕ ФРАКТАЛЬНОГО ФОРМАЛИЗМА ПРИ ОПИСАНИИ ФИЗИЧЕСКИХ ПРОЦЕССОВ И МЕХАНИЧЕСКИХ СВОЙСТВ КОНДЕНСИРОВАННЫХ МАТЕРИАЛОВ И ВЕЩЕСТВ//Известия Санкт-Петербургского гос.технологического института (технического ун-та) (ВАК)(RUS). 2013 г., т. , N 21, C.056-059

Рассмотрены примеры фрактального описания свойств материалов и физических процессов, которые характеризуются высокими скоростями подвода энергии. Такой подход для описания свойств и процессов необходим для обобщения постулатов классической физики быстропротекающих процессов и механики деформируемого твёрдого тела на структурированные среды

Фисенко В.Т., Фисенко Т.Ю. ФРАКТАЛЬНЫЕ МЕТОДЫ СЕГМЕНТАЦИИ ТЕКСТУРНЫХ ИЗОБРАЖЕНИЙ //Известия ВУЗов. Приборостроение (ВАК)(RUS). 2013 г., т. 56, N 5, стр. 63-70.

Представлены результаты разработки и исследования фрактальных методов сегментации цветных текстурных изображений. Цветовые характеристики текстуры использованы в качестве дополнительного признака для повышения эффективности сегментации. Рассмотрены особенности синтеза текстур на основе фрактальных свойств. Методы предназначены для автоматической обработки текстурных изображений

Шаталов В.М., Филиппов А.Э., Но, ПУЗЫРЬКОВАЯ ПРИРОДА ФЛУКТУАЦИЙ НЕКОТОРЫХ СВОЙСТВ ВОДНЫХ РАСТВОРОВ //Биофизика (ВАК)(RUS). 2012 г., т. 57, N 4 стр. 565-572).

C помощью математического моделирования процесса диффузии воздуха через поверхность воды с учетом обратного потока растущих пузырьков получены автоколебания концентрации растворенного воздуха. Cпектральная плотность этих колебаний имеет вид, характерный для 1/f-шума, что объясняет флуктуационную природу тех наблюдаемых свойств воды и биоэф- фектов, которые завиcят от количества растворенного в ней воздуха. Предложен механизм спонтанной люминесценции воды, которая наблюдается после облучения воды инфракрасным лазером. Pассчитанные автоколебания люминесценции имеют вид фрактала с бесконечной последовательностью периодов, эволюциониpующиx во времени, что в целом согласуется с экспериментом

Шкарупета Е.В., Смышляев В.А. ФРАКТАЛЬНЫЕ ОРГАНИЗАЦИИ В УСЛОВИЯХ ЭКОНОМИКИ ЗНАНИЙ //Вестник Воронежского ГТУ (ВАК)(RUS). 2012 г., т. 8, N 7.1,стр. 14-17).

В статье рассматривается новая, фрактальная форма существования организаций в условиях экономики знаний. Дается описание формирования фрактала с математической точки зрения, а также с помощью метода аналогии про-водится взаимосвязь между алгебраическими фракталами и фрактальными организациями

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