scholarly journals The Assouad dimension of randomly generated fractals

2016 ◽  
Vol 38 (3) ◽  
pp. 982-1011 ◽  
Author(s):  
JONATHAN M. FRASER ◽  
JUN JIE MIAO ◽  
SASCHA TROSCHEIT
Keyword(s):  
Topological Structure ◽  
Packing Dimension ◽  
Sample Space ◽  
The Other ◽  
Random Fractals ◽  
Assouad Dimension ◽  
Self Similar ◽  
Stark Contrast

We consider several different models for generating random fractals including random self-similar sets, random self-affine carpets, and Mandelbrot percolation. In each setting we compute either thealmost sureor theBaire typicalAssouad dimension and consider some illustrative examples. Our results reveal a phenomenon common to each of our models: the Assouad dimension of a randomly generated fractal is generically as big as possible and does not depend on the measure-theoretic or topological structure of the sample space. This is in stark contrast to the other commonly studied notions of dimension like the Hausdorff or packing dimension.

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

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.

Structural role of copper in the minerals of the pearceite-polybasite group: the case of the new minerals cupropearceite and cupropolybasite

2007 ◽  
Vol 71 (06) ◽  
pp. 641-650 ◽  
Author(s):  
L. Bindi ◽  
M. Evain ◽  
P. G. Spry ◽  
K. T. Tait ◽  
S. Menchetti
Keyword(s):  
Chemical Characterization ◽  
Sample Space ◽  
The Other ◽  
Crystal Chemical ◽  
Structural Position ◽  
Space Group ◽  
Cu Content ◽  
Own Name

Abstract The pearceite-polybasite group of minerals, general formula [M6T2S7][Ag9CuS4] with M = Ag, Cu; and T = As, Sb, show a crystal structure which can be described as the succession, along the c axis, of two pseudo-layer modules: a [M6T2S7]2– A module layer and a [Ag9CuS4]2+ B module layer. Copper is present in one structural position of the B module layer and replaces Ag in the only fully occupied M position of the A module layer. When the Cu content is >4.00 a.p.f.u., the structural position of the A module layer becomes Cu-dominant and, consequently, the mineral deserves its own name. In this paper we report the crystal-chemical characterization of two Cu-rich members exhibiting the 111 unitcell type (corresponding to the Tac polytype). One sample (space group (P )m1, a 7.3218(8), c 11.8877(13) Å, V 551.90(10) Å3, Z = 1) having As >Sb and with the structural position of the A module layer dominated by Cu, has been named cupropearceite and the other sample (space group (P3̄)m1, a 7.3277(3), c 11.7752(6) Å, V 547.56(8) Å3, Z = 1) having Sb >As has been named cupropolybasite. Both the new minerals and mineral names have been approved by the IMA-CNMNC.

TWO FAMILIES OF EXACT DISKS WITH A CENTRAL BLACK HOLE

1996 ◽  
Vol 05 (01) ◽  
pp. 53-63 ◽  
Author(s):  
JOSÉ P.S. LEMOS ◽  
PATRICIO S. LETELIER
Keyword(s):  
Black Hole ◽  
Topological Defect ◽  
Rotational Velocity ◽  
The Other ◽  
Central Black Hole ◽  
Counter Rotation ◽  
Infinite Extent ◽  
Self Similar ◽  
Physical Effects ◽  
Many Particles

The gravitational field of a configuration formed by a static disk and a Schwarzschild black hole is analysed for two families of disks. The matter of the disks is made of counter-rotating particles with as many particles rotating to one side as to the other, in such a way that the net angular momentum is zero and the disk is static. The first family consists of peculiar disks, in the sense that they are generated by two opposite dipoles. The particles of the disk have no pressure or centrifugal support. However, when there is a central black hole, centrifugal balance in the form of counter-rotation appears. The second family is a one parameter family of self-similar disks which includes at one end a Newtonian disk, and at the other a topological defect of spacetime. The presence of the black hole impresses more rotational velocity to the particles. These two families are of infinite extent. Some interesting physical effects are studied.

Complete and defective agreement in Kutchi

2014 ◽  
Vol 14 (2) ◽  
pp. 243-288
Author(s):  
Stefan Keine ◽  
Trupti Nisar ◽  
Rajesh Bhatt
Keyword(s):  
The Other ◽  
Other Hand ◽  
The Subject ◽  
Stark Contrast ◽  
Verbal Agreement ◽  
And Gender ◽  
Split Ergativity ◽  
Do So

We describe and analyze the previously undocumented verbal agreement system of Kutchi (Indo-Aryan). We argue that Kutchi instantiates a novel type of split ergativity. First, it exhibits an aspect split in that agreement in non-perfective clauses behaves on a par with agreement in intransitive perfective clauses, in stark contrast to transitive perfective clauses. A striking property of Kutchi is that these asymmetries manifest themselves in the richness of agreement. In the former configurations, the verb agrees with the subject for person, number and gender. In the latter, on the other hand, agreement is systematically defective and reliable fails to cross-references certain φ-features. In addition to this aspect split, Kutchi displays a person split: While the verb normally agrees with the subject, it surprisingly fails to do so in transitive perfective clauses with a 1st person subject. Instead, it is the object that triggers agreement in these configurations, likewise in a defective manner. We will argue that these agreement asymmetries are syntactic in nature rather than morphological. Our analysis builds on, and extends, previous work by Laka (2006) and Coon (2010).

What Results from Resultant Luck?

2021 ◽  
pp. 29-51
Author(s):  
Gerald Lang
Keyword(s):  
Strict Liability ◽  
The Other ◽  
Stark Contrast

This chapter distinguishes, in a preliminary way, among different views on the role of luck in ascriptions of blameworthiness. First, there is the ‘Strict Liability Account’, which makes agents blameworthy if and only if their acts cause harm. Second, and in stark contrast, there is the ‘Anti-Luck Account’, which holds that any lucky differences between agents should be neutralized: any lucky differences between them should make no difference to how much agents are blamed. Third, there is the ‘Restricted Luck-Sensitive Account’, which appears to blend elements of these other views. The Restricted Account agrees with the Anti-Luck Account that agents are not eligible for blameworthiness unless they act either maliciously, or negligently, or recklessly. This is the ‘Internal Claim’. But the Restricted Account also contends that agents who have qualified for blameworthiness by satisfying the Internal Claim may then be blameworthy to different degrees, depending on how their acts turn out, even if the differences between them at this stage reflect luck. This is the ‘External Claim’. (The other chapters in Part I of the book will build up a case for the Restricted Account and against the Anti-Luck Account.) This chapter also searches for the fundamental constituents of the Anti-Luck Account, and identifies key roles for the ‘Irrelevance Intuition’ and ‘Fairness Intuition’, and for comparative luck. Finally, it takes issue with anti-luckist ‘accommodation strategies’, which attempt to explain away our habits of assigning different amounts of blameworthiness to agents who seem to be separated only by luck.

“Two Suns in One Firmament”: John Cotton, Thomas Hooker, and the 1655 New Haven Sodomy Statute

2018 ◽  
Vol 87 (4) ◽  
pp. 1003-1028
Author(s):  
Sandra Slater
Keyword(s):  
Seventeenth Century ◽  
New England ◽  
The Other ◽  
Massachusetts Bay ◽  
New Haven ◽  
Sexual Activities ◽  
Legal Code ◽  
Legal Traditions ◽  
Stark Contrast

This piece explores the origins of the anomalous 1655 New Haven statute against sodomy that broke with legal traditions and codes both in England and New England. A lengthy and extraordinarily specific piece of legislation, the New Haven law stands in stark contrast to the minimalist language favored by the English in the early seventeenth century. When viewed within the larger context of clerical animosities, particularly between Thomas Hooker and John Cotton, there is a strong circumstantial case to make for its implementation as an extension of John Cotton's rejected Massachusetts Bay legal code,Moses His Judicials, applied by his friend and admirer John Davenport in New Haven. A devout disciple of John Cotton, John Davenport's New Haven colony relied on Cotton's influence and stood as a rebuke to Thomas Hooker's Connecticut settlements, often criticized as too spiritually lax by those in Massachusetts Bay and New Haven. While seeking to demonstrate greater piety and rigidity, John Cotton and Thomas Hooker sought to exert dominance over the other, with Cotton employing Davenport's colony as an effective castigation of Hooker's perceived liberality. This piece is reflective of trends in studies of sexuality which suggest that ideas and identities related to sexuality do not operate in isolation, but often mirror anxieties not necessarily connected to the regulation of sexual activities. This article situates the 1655 Sodomy Statue within a broader context in order to understand its origins and animosities that potentially motivated its inclusion into the New Haven legal statutes.

ABSENCE OF LOCALIZATION IN SCHRÖDINGER OPERATORS WITH ARBITRARY DETERMINISTIC POTENTIAL SEQUENCES

1994 ◽  
Vol 08 (01) ◽  
pp. 29-40 ◽  
Author(s):  
KAZUMOTO IGUCHI
Keyword(s):  
Wave Function ◽  
Schrödinger Operators ◽  
The Other ◽  
Schrodinger Operators ◽  
Critical States ◽  
Other Hand ◽  
Extended States ◽  
Self Similar

The theory of localization in the Schrödinger operators with arbitrary deterministic potential sequences is studied herein. We classify all the systems of arbitrary substitutions into three categories in terms of the number of constituent atoms, r. If r=1, then all the states in the system belong to only extended states. If r=2, there appears a great variety of the systems on which the localization depends, where some systems show the transition between the extended and the critical states. On the other hand, if r≥3, then there is the universal criticality of the spectrum — all the states in the spectrum belong to only critical states, where the wave function is self-similar or fractal. Surprisingly, this result does not depend on any substitution scheme. Thus, the localization is absent in OUT systems.

Self-similar, time-dependent flows with a free surface

1976 ◽  
Vol 73 (4) ◽  
pp. 603-620 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Free Surface ◽  
Rational Functions ◽  
Rigid Wall ◽  
The Other ◽  
Three Dimensions ◽  
Simple Derivation ◽  
Similar Time ◽  
Self Similar ◽  
Parabolic Flow ◽  
Similar Flows

A simple derivation is given of the parabolic flow first described by John (1953) in semi-Lagrangian form. It is shown that the scale of the flow decreases liket−3, and the free surface contracts about a point which lies one-third of the way from the vertex of the parabola to the focus.The flow is an exact limiting form of either a Dirichlet ellipse or hyperbola, as the timettends to infinity.Two other self-similar flows, in three dimensions, are derived. In one, the free surface is a paraboloid of revolution, which contracts liket−2about a point lying one-quarter the distance from the vertex to the focus. In the other, the flow is non-axisymmetric, and the free surface contracts liket−5.The parabolic flow is shown to be one of a general class of self-similar flows in the plane, described by rational functions of degreen. The parabola corresponds ton= 2. Whenn= 3 there are two new flows. In one of these the scale varies ast12/7and the free surface has the appearance of a trough filling up. In the other, the free surface resembles flow round the end of a rigid wall; the scale varies ast−4·17.

DIMENSION ANALYSIS OF CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (01) ◽  
pp. 1730001 ◽  
Author(s):  
JUN WANG ◽  
KUI YAO
Keyword(s):  
Hausdorff Dimension ◽  
Fractal Dimensions ◽  
Continuous Functions ◽  
Packing Dimension ◽  
Box Dimension ◽  
Box Counting ◽  
Dimension Analysis ◽  
Box Counting Dimension ◽  
Self Similar

In this paper, we mainly discuss fractal dimensions of continuous functions with unbounded variation. First, we prove that Hausdorff dimension, Packing dimension and Modified Box-counting dimension of continuous functions containing one UV point are [Formula: see text]. The above conclusion still holds for continuous functions containing finite UV points. More generally, we show the result that Hausdorff dimension of continuous functions containing countable UV points is [Formula: see text] also. Finally, Box dimension of continuous functions containing countable UV points has been proved to be [Formula: see text] when [Formula: see text] is self-similar.

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