Practical statistics for the voids between galaxies

Serbian Astronomical Journal ◽

10.2298/saj1081019z ◽

2010 ◽

pp. 19-29

Author(s):

L. Zaninetti

Keyword(s):

Exponential Function ◽

Voronoi Tessellation ◽

Survival Function ◽

The Self ◽

Similar Distribution ◽

Survival Functions ◽

Redshift Survey ◽

Galaxy Redshift ◽

Self Similar

The voids between galaxies are identified with the volumes of the Poisson Voronoi tessellation. Two new survival functions for the apparent radii of voids are derived. The sectional normalized area of the Poisson Voronoi tessellation is modelled by the Kiang function and by the exponential function. Two new survival functions with equivalent sectional radius are therefore derived; they represent an alternative to the survival function of voids between galaxies as given by the self-similar distribution. The spatial appearance of slices of the 2dF Galaxy Redshift Survey is simulated.

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Estimation of Strength of Rock Masses using the Self-similar Distribution of Discontinuities-An Application of Ladanyi's Theory to In-situ Rock Masses-

Journal of the Japan Society of Engineering Geology ◽

10.5110/jjseg.44.2 ◽

2003 ◽

Vol 44 (1) ◽

pp. 2-13

Author(s):

Tomio TANAKA

Keyword(s):

The Self ◽

Similar Distribution ◽

Rock Masses ◽

Self Similar

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ON THE SELF-SIMILAR DISTRIBUTION OF THE EMERGENCY WARD ARRIVALS TIME SERIES

Fractals ◽

10.1142/s0218348x02001464 ◽

2002 ◽

Vol 10 (04) ◽

pp. 413-427 ◽

Cited By ~ 4

Author(s):

ENRIC MONTE ◽

JOSEP ROCA ◽

LLUIS VILARDELL

Keyword(s):

Time Series ◽

Lognormal Distribution ◽

The Self ◽

Similar Distribution ◽

Hospital Emergency ◽

Emergency Ward ◽

Telephone Exchange ◽

Wide Range ◽

Self Similar ◽

High Level

Hospital emergency arrivals are often modeled as Poisson processes because of the similarity of the problem to a telephone exchange model, i.e. applications that involve counting the number of times a random event occurs in a given time, where the interval between individual counts follows the exponential distribution. In this paper, we propose a statistical modeling of hospital emergency ward arrivals, using self-similar processes. This modeling takes into account the fact that it is known empirically that the emergency time series consists of periods marked by "bursts" of high level demand peaks, followed by periods of lower demand. This is explained neither by a Poisson during fixed-lengths intervals nor by a lognormal distribution. We show that a self-similar distribution can model this phenomenon. We also show that the commonly used Poisson models seriously underestimate the "burstiness" of emergency arrivals over a wide range of time scales, and that the emergency time series cannot be modeled by a lognormal distribution. The self-similar distribution was tested by the Hurst parameter, which we have calculated using five different methods, all of which agree on the value of the parameter.

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Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

Calcutta Statistical Association Bulletin ◽

10.1177/0008068320971924 ◽

2020 ◽

Vol 72 (2) ◽

pp. 111-121

Author(s):

Abdurakhim Akhmedovich Abdushukurov ◽

Rustamjon Sobitkhonovich Muradov

Keyword(s):

Relative Risk ◽

Sample Size ◽

Censored Data ◽

Survival Function ◽

Survival Functions ◽

Power Structures ◽

Bivariate Survival ◽

Empirical Estimates ◽

Bivariate Survival Function ◽

Product Limit

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

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Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/prm.2020.89 ◽

2020 ◽

pp. 1-31

Author(s):

Balázs Bárány ◽

Károly Simon ◽

István Kolossváry ◽

Michał Rams

Keyword(s):

Hausdorff Measure ◽

Similar Case ◽

Iterated Function Systems ◽

The Self ◽

Dimensional Hausdorff Measure ◽

Assouad Dimension ◽

Iterated Function ◽

Self Similar ◽

Weak Separation ◽

Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

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Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽

10.3390/e23030314 ◽

2021 ◽

Vol 23 (3) ◽

pp. 314

Author(s):

Tianyu Jing ◽

Huilan Ren ◽

Jian Li

Keyword(s):

Hot Spot ◽

Mach Reflection ◽

Near Field ◽

The Self ◽

Small Scale ◽

Mach Stem ◽

Self Similarity ◽

Von Neumann ◽

Similarity Problem ◽

Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

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