scholarly journals The growth rate of tri-colored sum-free sets

2018 ◽  
Author(s):  
Robert Kleinberg ◽  
will sawin ◽  
David speyer
Keyword(s):  
Growth Rate ◽  
Free Sets

scholarly journals A DISTRIBUTION ON TRIPLES WITH MAXIMUM ENTROPY MARGINAL

2019 ◽  
Vol 7 ◽  
Author(s):  
SERGEY NORIN
Keyword(s):  
Growth Rate ◽  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Free Sets

We construct an $S_{3}$ -symmetric probability distribution on $\{(a,b,c)\in \mathbb{Z}_{{\geqslant}0}^{3}\,:\,a+b+c=n\}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\ldots ,n\}$ with mean $n/3$ . Existence of such a distribution verifies a conjecture of Kleinberg et al. [‘The growth rate of tri-colored sum-free sets’, Discrete Anal. (2018), Paper No. 12, arXiv:1607.00047v1], which is motivated by the study of sum-free sets.

The threshold energy for atom displacement in fcc metals

1990 ◽  
Vol 48 (4) ◽  
pp. 530-531
Author(s):  
Wilfried Sigle ◽  
Matthias Hohenstein ◽  
Alfred Seeger
Keyword(s):  
Growth Rate ◽  
Elevated Temperatures ◽  
Threshold Energy ◽  
Dislocation Loops ◽  
Absolute Minimum ◽  
Voltage Electron ◽  
Atom Displacement ◽  
Electron Microscopes ◽  
Fcc Metal

Prolonged electron irradiation of metals at elevated temperatures usually leads to the formation of large interstitial-type dislocation loops. The growth rate of the loops is proportional to the total cross-section for atom displacement,which is implicitly connected with the threshold energy for atom displacement, Ed . Thus, by measuring the growth rate as a function of the electron energy and the orientation of the specimen with respect to the electron beam, the anisotropy of Ed can be determined rather precisely. We have performed such experiments in situ in high-voltage electron microscopes on Ag and Au at 473K as a function of the orientation and on Au as a function of temperature at several fixed orientations.Whereas in Ag minima of Ed are found close to <100>,<110>, and <210> (13-18eV), (Fig.1) atom displacement in Au requires least energy along <100>(15-19eV) (Fig.2). Au is thus the first fcc metal in which the absolute minimum of the threshold energy has been established not to lie in or close to the <110> direction.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

TEMPERATURE DEPENDENCE OF THE CRYSTAL GROWTH RATE IN POLAR GLACIERS

1987 ◽  
Vol 48 (C1) ◽  
pp. C1-661-C1-662 ◽  
Author(s):  
J. R. PETIT ◽  
P. DUVAL ◽  
C. LORIUS
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Temperature Dependence ◽  
Crystal Growth Rate

Forming Sources of Long-run Growth: How to Understand Them?

2014 ◽  
pp. 4-20 ◽  
Author(s):  
G. Idrisov ◽  
S. Sinelnikov-Murylev
Keyword(s):  
Economic Growth ◽  
Growth Rate ◽  
Economic Policy ◽  
Business Cycle ◽  
Capital Markets ◽  
Productivity Growth ◽  
Government Spending ◽  
Long Run ◽  
Accelerate Growth ◽  
Budget Institutions

The paper analyzes the inconsequence and problems of Russian economic policy to accelerate economic growth. The authors consider three components of growth rate (potential, Russian business cycle and world business cycle components) and conclude that in order to pursue an effective economic policy to accelerate growth, it has to be addressed to the potential (long-run) growth component. The main ingredients of this policy are government spending restructuring and budget institutions reform, labor and capital markets reforms, productivity growth.

International trade: Research of the reasons for the fall

2019 ◽  
pp. 79-91 ◽  
Author(s):  
V. S. Nazarov ◽  
S. S. Lazaryan ◽  
I. V. Nikonov ◽  
A. I. Votinov
Keyword(s):  
Growth Rate ◽  
International Trade ◽  
Exchange Rate ◽  
Global Economy ◽  
Structural Changes ◽  
Global Value Chains ◽  
Value Chains ◽  
Negative Contribution ◽  
Basic Commodity ◽  
The Impact

The article assesses the impact of various factors on the growth rate of international trade. Many experts interpreted the cross-border flows of goods decline against the backdrop of a growing global economy as an alarming sign that indicates a slowdown in the processes of globalization. To determine the reasons for the dynamics of international trade, the decompositions of its growth rate were carried out and allowed to single out the effect of the dollar exchange rate, the commodities prices and global value chains on the change in the volume of trade. As a result, it was discovered that the most part of the dynamics of international trade is due to fluctuations in the exchange rate of the dollar and prices for basic commodity groups. The negative contribution of trade within global value chains in 2014 was also revealed. During the investigated period (2000—2014), such a picture was observed only in the crisis periods, which may indicate the beginning of structural changes in the world trade.

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