Dedekind Cuts and Long Strings of Zeros in Base Expansions

2021 ◽  
pp. 248-259
Author(s):  
Ivan Georgiev
Keyword(s):  
Long Strings ◽  
Dedekind Cuts

scholarly journals GAMMA RAYS FROM SMALL SCALE STRUCTURES ON LONG COSMIC STRINGS

1993 ◽  
Vol 02 (02) ◽  
pp. 183-195 ◽  
Author(s):  
M. MOHAZZAB ◽  
R. BRANDENBERGER
Keyword(s):  
Gamma Rays ◽  
Gamma Ray ◽  
Cosmic Strings ◽  
Unit Length ◽  
Formation Rate ◽  
Long Strings ◽  
Small Scale ◽  
Scale Structures ◽  
Cusp Formation ◽  
Small Scale Structures

The formation of cusps on long cosmic strings is discussed and the probability of cusp formation is estimated. The energy distribution of the gamma-ray background due to cusp annihilation on long strings is calculated and compared to observations. Under optimistic assumptions about the cusp formation rate, we find that strings with a mass per unit length μ less than Gμ=10−14 will have an observable effect. However, it is shown that the gamma-ray bursters cannot be attributed to long ordinary strings (or loops).

The Horse Fair

Black Beauty ◽  
2012 ◽  
Author(s):  
Anna Sewell
Keyword(s):  
Long Strings ◽  
Young Horses

No doubt a horse fair is a very amusing place to those who have nothing to lose; at any rate there is plenty to see. Long strings of young horses out of the country, fresh from the marshes; and droves of shaggy little Welsh ponies,...

scholarly journals The action of long strings in supersymmetric field theories

2019 ◽  
Vol 2019 (2) ◽  
Author(s):  
Tomer Solberg ◽  
Mykhailo Yutushui
Keyword(s):  
Long Strings ◽  
Field Theories ◽  
Supersymmetric Field Theories

scholarly journals ON THE NUMBER OF DEDEKIND CUTS AND TWO-CARDINAL MODELS OF DEPENDENT THEORIES

2015 ◽  
Vol 15 (4) ◽  
pp. 771-784 ◽  
Author(s):  
Artem Chernikov ◽  
Saharon Shelah
Keyword(s):  
Infinite Cardinal ◽  
Linear Orders ◽  
First Order ◽  
Dedekind Cuts

For an infinite cardinal ${\it\kappa}$, let $\text{ded}\,{\it\kappa}$ denote the supremum of the number of Dedekind cuts in linear orders of size ${\it\kappa}$. It is known that ${\it\kappa}<\text{ded}\,{\it\kappa}\leqslant 2^{{\it\kappa}}$ for all ${\it\kappa}$ and that $\text{ded}\,{\it\kappa}<2^{{\it\kappa}}$ is consistent for any ${\it\kappa}$ of uncountable cofinality. We prove however that $2^{{\it\kappa}}\leqslant \text{ded}(\text{ded}(\text{ded}(\text{ded}\,{\it\kappa})))$ always holds. Using this result we calculate the Hanf numbers for the existence of two-cardinal models with arbitrarily large gaps and for the existence of arbitrarily large models omitting a type in the class of countable dependent first-order theories. Specifically, we show that these bounds are as large as in the class of all countable theories.

scholarly journals COSMIC STRINGS, LOOPS, AND LINEAR GROWTH OF MATTER PERTURBATIONS

2002 ◽  
Vol 11 (01) ◽  
pp. 61-102 ◽  
Author(s):  
JIUN-HUEI PROTY WU ◽  
PEDRO P. AVELINO ◽  
E. P. S. SHELLARD ◽  
BRUCE ALLEN
Keyword(s):  
Dark Matter ◽  
Structure Formation ◽  
Cosmic String ◽  
Cold Dark Matter ◽  
Cosmic Strings ◽  
Topological Analysis ◽  
Long Strings ◽  
Source Spectrum ◽  
Galaxy Surveys ◽  
Network Properties

We describe a detailed study of string-seeded structure formation using high resolution numerical simulations in open universes and those with a non-zero cosmological constant. We provide a semi-analytical model which can reproduce these simulation results including the effect from small loops chopped of by the string network. A detailed study of cosmic string network properties regarding structure formation is also given, including the correlation time, the topological analysis of the source spectrum, the correlation between long strings and loops, and the evolution of long-string and loop energy densities. For models with Γ=Ω h=0.1 -0.2 and a cold dark matter background, we show that the linear density fluctuation power spectrum induced by cosmic strings has both an amplitude at 8 h-1 Mpc, σ8, and an overall shape which are consistent within uncertainties with those currently inferred from galaxy surveys. The cosmic string scenario with hot dark matter requires a strongly scale-dependent bias in order to agree with observations.

scholarly journals Dynamic changes in the higher-level chromatin organization of specific sequences revealed by in situ hybridization to nuclear halos.

1994 ◽  
Vol 126 (2) ◽  
pp. 289-304 ◽  
Author(s):  
M G Gerdes ◽  
K C Carter ◽  
P T Moen ◽  
J B Lawrence
Keyword(s):  
Dna Sequences ◽  
Residual Nucleus ◽  
Single Cells ◽  
Long Strings ◽  
Gene Clusters ◽  
S Phase ◽  
Fluorescence Signal ◽  
Intact Cells ◽  
Biochemical Fractionation ◽  
Specific Sequences

A novel approach to study the higher level packaging of specific DNA sequences has been developed by coupling high-resolution fluorescence hybridization with biochemical fractionation to remove histones and distend DNA loops to form morphologically reproducible nuclear "halos." Results demonstrate consistent differences in the organization of specific sequences, and further suggest a relationship to functional activity. Pulse-incorporated bromodeoxyuridine representing nascent replicating DNA localized with the base of the chromatin loops in discrete clustered patterns characteristic of intact cells, whereas at increasing chase times, the replicated DNA was consistently found further out on the extended region of the halo. Fluorescence hybridization to unique loci for four transcriptionally inactive sequences produced long strings of signal extending out onto the DNA halo or "loop," whereas four transcriptionally active sequences remained tightly condensed as single spots within the residual nucleus. In contrast, in non-extracted cells, all sequences studied typically remained condensed as single spots of fluorescence signal. Interestingly, two transcriptionally active, tandemly repeated gene clusters exhibited strikingly different packaging by this assay. Analysis of specific genes in single cells during the cell cycle revealed changes in packaging between S-phase and non S-phase cells, and further suggested a dramatic difference in the structural associations in mitotic and interphase chromatin. These results are consistent with and suggestive of a loop domain organization of chromatin packaging involving both stable and transient structural associations, and provide precedent for an approach whereby different biochemical fractionation methods may be used to unravel various aspects of the complex higher-level organization of the genome.

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