scholarly journals Equicontinuous Delone Dynamical Systems

2013 ◽  
Vol 65 (1) ◽  
pp. 149-170 ◽  
Author(s):  
Johannes Kellendonk ◽  
Daniel Lenz
Keyword(s):  
Dynamical Systems ◽  
The Other ◽  
Almost Periodic ◽  
Other Hand ◽  
Local Complexity ◽  
Dirac Comb ◽  
Delone Set ◽  
Delone Sets

AbstractWe characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with finite local complexity, the only equicontinuous systems are then shown to be the crystallographic ones. On the other hand, within the class without finite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical systems that are not crystallographic. Our results solve the problem posed by Lagarias as to whether a Delone set whose Dirac comb is strongly almost periodic must be crystallographic.

scholarly journals Construction of the Discrete Hull for the Combinatorics of a Regular Pentagonal Tiling of the Plane

2016 ◽  
Vol 119 (1) ◽  
pp. 39
Author(s):  
Maria Ramirez-Solano
Keyword(s):  
The Other ◽  
Usual Sense ◽  
Conformal Maps ◽  
Cantor Space ◽  
Geometric Properties ◽  
Other Hand ◽  
Local Complexity ◽  
Combinatorial Data

The article A "regular" pentagonal tiling of the plane by P. L. Bowers and K. Stephenson, Conform. Geom. Dyn. 1, 58-86, 1997, defines a conformal pentagonal tiling. This is a tiling of the plane with remarkable combinatorial and geometric properties. However, it doesn't have finite local complexity in any usual sense, and therefore we cannot study it with the usual tiling theory. The appeal of the tiling is that all the tiles are conformally regular pentagons. But conformal maps are not allowable under finite local complexity. On the other hand, the tiling can be described completely by its combinatorial data, which rather automatically has finite local complexity. In this paper we give a construction of the discrete hull just from the combinatorial data. The main result of this paper is that the discrete hull is a Cantor space.

scholarly journals Local Complexity of Delone Sets and Crystallinity

2002 ◽  
Vol 45 (4) ◽  
pp. 634-652 ◽  
Author(s):  
Jeffrey C. Lagarias ◽  
Peter A. B. Pleasants
Keyword(s):  
Growth Rates ◽  
Linear Growth ◽  
Closed Ball ◽  
Covering Radius ◽  
Ideal Crystal ◽  
Minimum Radius ◽  
Local Complexity ◽  
Delone Set ◽  
Delone Sets

AbstractThis paper characterizes when a Delone set X in is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let NX(T) count the number of translation-inequivalent patches of radius T in X and let MX(T) be the minimum radius such that every closed ball of radius MX(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a “gap in the spectrum” of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal.Explicitly, for NX(T), if R is the covering radius of X then either NX(T) is bounded or NX(T) ≥ T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions.For MX(T), either MX(T) is bounded or MX(T) ≥ T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has MX(T) ≥ c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

scholarly journals On groups Gnk, braids and Brunnian braids

2016 ◽  
Vol 25 (13) ◽  
pp. 1650078
Author(s):  
S. Kim ◽  
V. O. Manturov
Keyword(s):  
Dynamical Systems ◽  
Braid Group ◽  
General Position ◽  
Knot Theory ◽  
The Other ◽  
Geometric Meaning ◽  
Free Products ◽  
Other Hand ◽  
Abstract Structure

In [V. O. Manturov, arXiv:1501.05208v1 ], the second author defined the [Formula: see text]-free braid group with [Formula: see text] strands [Formula: see text]. These groups appear naturally as groups describing dynamical systems of [Formula: see text] particles in some “general position”. Moreover, in [V. O. Manturov and I. M. Nikonov, J. Knot Theory Ramification 24 (2015) 1541009] the second author and Nikonov showed that [Formula: see text] is closely related to classical braids. The authors showed that there are homomorphisms from the pure braids group on [Formula: see text] strands to [Formula: see text] and [Formula: see text] and they defined homomorphisms from [Formula: see text] to the free products of [Formula: see text]. That is, there are invariants for pure free braids by [Formula: see text] and [Formula: see text]. On the other hand in [D. A. Fedoseev and V. O. Manturov, J. Knot Theory Ramification 24(13) (2015) 1541005, 12 pages] Fedoseev and the second author studied classical braids with addition structures: parity and points on each strands. The authors showed that the parity, which is an abstract structure, has geometric meaning — points on strands. In [S. Kim, arXiv:submit/1548032], the first author studied [Formula: see text] with parity and points. the author constructed a homomorphism from [Formula: see text] to the group [Formula: see text] with parity. In the present paper, we investigate the groups [Formula: see text] and extract new powerful invariants of classical braids from [Formula: see text]. In particular, these invariants allow one to distinguish the non-triviality of Brunnian braids.

scholarly journals A dynamical-systems approach to the evolution of morphonotactic and lexical consonant clusters in English and Polish

2016 ◽  
Vol 2 (1) ◽  
pp. 115-139 ◽  
Author(s):  
Andreas Baumann ◽  
Kamil Kaźmierski
Keyword(s):  
Mathematical Model ◽  
Dynamical Systems ◽  
Evolutionary Dynamics ◽  
Systems Approach ◽  
The Other ◽  
Consonant Clusters ◽  
Other Hand ◽  
Signaling Function ◽  
Language Data ◽  
The One

Abstract Consonant clusters appear either lexically within morphemes or morphonotactically across morpheme boundaries. According to extant theories, their diachronic dynamics are suggested to be determined by analogical effects on the one hand as well as by their morphological signaling function on the other hand. This paper presents a mathematical model which allows for an investigation of the interaction of these two forces and the resulting diachronic dynamics. The model is tested against synchronic and diachronic language data. It is shown that the evolutionary dynamics of the cluster inventory crucially depend on how the signaling function of morphonotactic clusters is compromised by the presence of lexical items containing their morpheme internal counterparts.

scholarly journals Number of bounded distance equivalence classes in hulls of repetitive Delone sets

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Dirk Frettlöh ◽  
Alexey Garber ◽  
Lorenzo Sadun
Keyword(s):  
Equivalence Class ◽  
Equivalence Relation ◽  
Equivalence Classes ◽  
Bounded Distance ◽  
Local Complexity ◽  
Delone Set ◽  
Delone Sets ◽  
Uniformly Bounded

<p style='text-indent:20px;'>Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many.</p>

On braids and groups Gnk

2015 ◽  
Vol 24 (13) ◽  
pp. 1541009 ◽  
Author(s):  
Vassily Olegovich Manturov ◽  
Igor Mikhailovich Nikonov
Keyword(s):  
Dynamical Systems ◽  
Braid Group ◽  
Knot Theory ◽  
Free Groups ◽  
Braid Groups ◽  
The Other ◽  
Pure Braid Group ◽  
And Topology ◽  
Other Hand ◽  
Definition Of

In [Non-reidemeister knot theory and its applications in dynamical systems, geometry, and topology, preprint (2015), arXiv:1501.05208.] the first author gave the definition of [Formula: see text]-free braid groups [Formula: see text]. Here we establish connections between free braid groups, classical braid groups and free groups: we describe explicitly the homomorphism from (pure) braid group to [Formula: see text]-free braid groups for important cases [Formula: see text]. On the other hand, we construct a homomorphism from (a subgroup of) free braid groups to free groups. The relations established would allow one to construct new invariants of braids and to define new powerful and easily calculated complexities for classical braid groups.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

Can the Academic Self-Concept be Positive and Realistic?

2005 ◽  
Vol 19 (3) ◽  
pp. 129-132 ◽  
Author(s):  
Reimer Kornmann
Keyword(s):  
Academic Performance ◽  
Opposite Effect ◽  
Self Esteem ◽  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
High Ability ◽  
Self Image ◽  
Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

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