Projected Measures: A Simple Way to Characterize Fractal Structures and Interfaces

Fractals ◽  
1997 ◽  
Vol 05 (02) ◽  
pp. 295-308
Author(s):  
Massimiliano Giona ◽  
Manuela Giustiniani ◽  
Oreste Patierno
Keyword(s):  
Closed Form ◽  
Fourier Transforms ◽  
Fractal Structures ◽  
Multifractal Spectra ◽  
Self Similar ◽  
The Moment ◽  
Dynamic Phenomena

The properties of projected measures of fractal objects are investigated in detail. In general, projected measures display multifractal features which play a role in the evolution of dynamic phenomena on/through fractal structures. Closed-form results are obtained for the moment hierarchy of model fractal interfaces. The distinction between self-similar and self-affine interfaces is discussed by considering the properties of multifractal spectra, the orientational effects in the behavior of the moment hierarchies, and the scaling of the corresponding Fourier transforms. The implications of the properties of projected measures in the characterization of transfer phenomena across fractal interfaces are briefly analyzed.

La structure de classes québécoise au 19e siècle et le problème de l'articulation des modes de production

1981 ◽  
Vol 14 (3) ◽  
pp. 487-518
Author(s):  
Gérald Bernier
Keyword(s):  
Census Data ◽  
New France ◽  
Class Structure ◽  
Capitalist Development ◽  
Single Class ◽  
The Moment ◽  
Empirical Demonstration ◽  
Work Done ◽  
The Impact

The study of social classes in the nineteenth century requires the development of conceptual tools able to explain the impact of the Conquest on the pre-existant social structures in determining transformations of the class structure during the subsequent decades.This article examines the work done on this question by Marxist writers. The author criticizes certain conclusions which have been drawn and which suggest deficiencies at a theoretical level. The objections relate to the marked tendency of these conclusions to perceive the structural effects of the Conquest in terms of the formation of a double-class structure characterized by “ethnic origins.” Specifically, the author challenges the notion of the division itself, as well as the criterion on which the division is based.The author proposes that an analysis centred upon the concepts relating to a problem of the transition and linkage of different modes of production permits a more satisfying interpretation, if accompanied by a certain number of considerations of the “upside” and “downside” of the Conquest. To this end, the argument is based on a characterization of New France in terms of the domination of the relations of production of the feudal type and on an analysis of metropolitan centres with intent to evaluate their level of capitalist development at the moment of their respective colonial penetration in Canada. The results of this approach permit one to posit the existence of a single-class structure, characterized principally by the existence of elements connecting diverse modes and forms of production, whose origin reflects the unequal state of economic development in the two metropolitan centres.The empirical demonstration rests on the census data of 1851–1852 and on the complementary information drawn from the works of historians.

scholarly journals One-relator groups and algebras related to polyhedral products

2021 ◽  
pp. 1-20
Author(s):  
Jelena Grbić ◽  
George Simmons ◽  
Marina Ilyasova ◽  
Taras Panov
Keyword(s):  
Homology Group ◽  
Homotopy Theory ◽  
Commutator Subgroup ◽  
Homology Groups ◽  
Homological Characterization ◽  
One Relator Groups ◽  
Combinatorial Condition ◽  
The Moment ◽  
Necessary And Sufficient

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$ , we specify a necessary and sufficient combinatorial condition for the commutator subgroup $RC_K'$ of a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex $\mathcal {R}_K$ , to be a one-relator group; and for the Pontryagin algebra $H_{*}(\Omega \mathcal {Z}_K)$ of the moment-angle complex to be a one-relator algebra. We also give a homological characterization of these properties. For $RC_K'$ , it is given by a condition on the homology group $H_2(\mathcal {R}_K)$ , whereas for $H_{*}(\Omega \mathcal {Z}_K)$ it is stated in terms of the bigrading of the homology groups of $\mathcal {Z}_K$ .

scholarly journals Fractal structures in freezing brine

2017 ◽  
Vol 826 ◽  
pp. 975-995
Author(s):  
Sergey Alyaev ◽  
Eirik Keilegavlen ◽  
Jan Martin Nordbotten ◽  
Iuliu Sorin Pop
Keyword(s):  
Characteristic Length ◽  
Complex Problem ◽  
Rate Of Change ◽  
Critical Threshold ◽  
Fractal Structures ◽  
Primary Interest ◽  
External Temperature ◽  
Self Similar ◽  
Salt Diffusion ◽  
Heuristic Analysis

The process of initial ice formation in brine is a highly complex problem. In this paper, we propose a mathematical model that captures the dynamics of nucleation and development of ice inclusions in brine. The primary emphasis is on the interaction between ice growth and salt diffusion, subject to external forcing provided by temperature. Within this setting two freezing regimes are identified, depending on the rate of change of the temperature: a slow freezing regime where a continuous ice domain is formed; and a fast freezing regime where recurrent nucleation appears within the fluid domain. The second regime is of primary interest, as it leads to fractal-like ice structures. We analyse the critical threshold between the slow and fast regimes by identifying the explicit rates of external temperature control that lead to self-similar salt-concentration profiles in the fluid domains. Subsequent heuristic analysis provides estimates of the characteristic length scales of the fluid domains depending on the time-variation of the temperature. The analysis is confirmed by numerical simulations.

scholarly journals Preliminary Characterization of Wild Grapevine Populations (Vitis vinifera ssp. sylvestris) Grown Along the Danube River

2013 ◽  
Vol 41 (2) ◽  
pp. 472 ◽  
Author(s):  
Carmen F. POPESCU ◽  
Liviu C. DEJEU ◽  
Rafael R. OCETE
Keyword(s):  
Vitis Vinifera ◽  
Morphological Analysis ◽  
Danube River ◽  
Vitis Vinifera L ◽  
Meristematic Tissue ◽  
The Danube River ◽  
Wild Grapevine ◽  
The Moment

The individuals belonging to three different groups of wild grapevines populations Vitis vinifera L. ssp. sylvestris (Gmelin) Hegi harvested along, or near the Danube River, were described by means of usual ampelographic methods. The twenty standardized descriptors used for morphological analysis revealed obvious differentiation among analyzed populations. Out of 65 individuals, a half produced flowers with separate sex and a high proportion of them were males (70%). Pollen measurements on light microscope provided information on differences in pollen size among inside wild grapevine populations of V. sylvestris with the polar length varying between 15.3 and 23 μm and the equatorial length between 15.5 and 24.4μm. The in vitro regenerative potential from meristematic tissue tested with each phenotype showed that the moment of differentiation, the aspect of proliferative structures and the rate of multiplication varied inside these wild grapevine populations, without any correlation with the location of harvesting. Our results provided valuable information about these Vitis vinifera ssp. sylvestris populations, possible to be used as starting plant material for research in general and further breeding of cultivars and grapevine rootstocks.

scholarly journals Wavelet introscopy of human organism bionets

2021 ◽  
pp. 63-72
Author(s):  
Gennady M. Aldonin ◽  
◽  
Vasily V. Cherepanov ◽  
Keyword(s):  
Functional State ◽  
Human Body ◽  
Dynamic Models ◽  
Golden Ratio ◽  
The State ◽  
The Body ◽  
Human Organism ◽  
Fractal Structures ◽  
Self Similar ◽  
The Creation

In domestic and foreign practice, a great deal of experience has been accumulated in the creation of means for monitoring the functional state of the human body. The existing complexes mainly analyze the electrocardiogram, blood pressure and a number of other physiological parameters. Diagnostics is often based on formal statistical data which are not always correct due to the nonstationarity of bioprocesses and without taking into account their physical nature. An urgent task of monitoring the state of the cardiovascular system is the creation of effective algorithms for computer technologies to process biosignals based on nonlinear dynamic models of body systems since biosystems and bioprocesses have a nonlinear nature and fractal structure. The nervous and muscular systems of the heart, the vascular and bronchial systems of the human body are examples of such structures. The connection of body systems with their organization in the form of self-similar fractal structures with scaling close to the “golden ratio” makes it possible to diagnose them topically. It is possible to obtain detailed information about the state of the human body’s bio-networks for topical diagnostics on the basis of the wavelet analysis of biosignals (the so-called wavelet-introscopy). With the help of wavelet transform, it is possible to reveal the structure of biosystems and bioprocesses, as a picture of the lines of local extrema of wavelet diagrams of biosignals. Mathematical models and software for wavelet introscopy make it possible to extract additional information from biosignals about the state of biosystems. Early detection of latent forms of diseases using wavelet introscopy can shorten the cure time and reduce the consequences of disorders of the functional state of the body (FSO), and reduce the risk of disability. Taking into account the factors of organizing the body’s biosystems in the form of self-similar fractal structures with a scaling close to the “golden ratio” makes it possible to create a technique for topical diagnostics of the most important biosystems of the human body.

scholarly journals Caracterización en línea de la dinámica temporal de señales para el monitoreo del sistema eléctrico de potencia

2020 ◽  
pp. 26-34
Author(s):  
Francisco Román Lezama-Zárraga ◽  
Jorge de Jesús Chan-González ◽  
Meng Yen Shih ◽  
Roberto Carlos Canto-Canul
Keyword(s):  
Nonlinear Oscillations ◽  
Electrical Power ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Electrical Power System ◽  
Transient Phenomena ◽  
On Line ◽  
Measurement Units ◽  
Dynamic Phenomena

The characterization of dynamic phenomena is essential for monitoring the Electrical Power System subject to disturbances. This article proposes an On-line time systematic approach to analyze and characterize the temporal evolution of transient and nonlinear oscillations in these systems. Two methods are used; the first method is based on a local decomposition of the signal under study into orthogonal basis functions to obtain the dynamics of transient oscillations. Next, a second method is applied to those orthogonal basis functions to obtain analytical signals and characterize the instantaneous amplitude, phase and frequency attributes of the oscillations and determine a physical interpretation of the system’s behavior. The proposed methodology is a time-frequencyenergy analysis which can be applied to the timesynchronized Phasor Measurement Units measurements. The results demonstrate that the proposed methodology provide an accurate characterization of transient phenomena with non-stationary effects.

scholarly journals A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

2021 ◽  
Vol 8 (1) ◽  
pp. 33-44
Author(s):  
Toufik Chaayra ◽  
Hussain Ben-azza ◽  
Faissal El Bouanani
Keyword(s):  
Closed Form ◽  
Fading Channels ◽  
Performance Metrics ◽  
Approximate Expression ◽  
Maximal Ratio Combining ◽  
Generalized Gamma ◽  
The Moment ◽  
Probability Density Function Pdf ◽  
Closed Form Approximation ◽  
Fox’S H Function

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.

WEAK SELF-SIMILAR SETS IN SEPARABLE COMPLETE METRIC SPACES

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750021
Author(s):  
R. K. ASWATHY ◽  
SUNIL MATHEW
Keyword(s):  
Metric Spaces ◽  
Complete Metric Space ◽  
Sufficient Conditions ◽  
Finite Union ◽  
Self Similarity ◽  
Complete Metric Spaces ◽  
Self Similar ◽  
Necessary And Sufficient ◽  
Physical Phenomena

Self-similarity is a common tendency in nature and physics. It is wide spread in geo-physical phenomena like diffusion and iteration. Physically, an object is self-similar if it is invariant under a set of scaling transformation. This paper gives a brief outline of the analytical and set theoretical properties of different types of weak self-similar sets. It is proved that weak sub self-similar sets are closed under finite union. Weak sub self-similar property of the topological boundary of a weak self-similar set is also discussed. The denseness of non-weak super self-similar sets in the set of all non-empty compact subsets of a separable complete metric space is established. It is proved that the power of weak self-similar sets are weak super self-similar in the product metric and weak self-similarity is preserved under isometry. A characterization of weak super self-similar sets using weak sub contractions is also presented. Exact weak sub and super self-similar sets are introduced in this paper and some necessary and sufficient conditions in terms of weak condensation IFS are presented. A condition for a set to be both exact weak super and sub self-similar is obtained and the denseness of exact weak super self similar sets in the set of all weak self-similar sets is discussed.

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