On properties of primitive sets of digraphs with common cycles

2019 ◽  
pp. 101-114
Author(s):  
Y. E. Avezova ◽  
Keyword(s):  
Common Cycles ◽  
Primitive Sets

scholarly journals The number of maximum primitive sets of integers

2021 ◽  
pp. 1-15
Author(s):  
Hong Liu ◽  
Péter Pál Pach ◽  
Richárd Palincza
Keyword(s):  
Related Problem ◽  
Maximum Size ◽  
Multiplicative Error ◽  
Coprime Integers ◽  
Primitive Sets

Abstract A set of integers is primitive if it does not contain an element dividing another. Let f(n) denote the number of maximum-size primitive subsets of {1,…,2n}. We prove that the limit α = lim n→∞ f(n)1/n exists. Furthermore, we present an algorithm approximating α with (1 + ε) multiplicative error in N(ε) steps, showing in particular that α ≈ 1.318. Our algorithm can be adapted to estimate the number of all primitive sets in {1,…,n} as well. We address another related problem of Cameron and Erdős. They showed that the number of sets containing pairwise coprime integers in {1,…n} is between ${2^{\pi (n)}} \cdot {e^{(1/2 + o(1))\sqrt n }}$ and ${2^{\pi (n)}} \cdot {e^{(2 + o(1))\sqrt n }}$ . We show that neither of these bounds is tight: there are in fact ${2^{\pi (n)}} \cdot {e^{(1 + o(1))\sqrt n }}$ such sets.

scholarly journals The probability of choosing primitive sets

2007 ◽  
Vol 125 (1) ◽  
pp. 39-49 ◽  
Author(s):  
Sergi Elizalde ◽  
Kevin Woods
Keyword(s):  
Primitive Sets

Common cycles in seasonally cointegrated time series

1996 ◽  
Vol 53 (3) ◽  
pp. 261-264 ◽  
Author(s):  
Sung K. Ahn
Keyword(s):  
Time Series ◽  
Common Cycles

Testing for Common Cycles in Money, Nominal Income and Prices

2003 ◽  
Vol 71 (s1) ◽  
pp. 68-84 ◽  
Author(s):  
Stephen Hall ◽  
David Shepherd
Keyword(s):  
Nominal Income ◽  
Common Cycles

scholarly journals Correlation between the Fluctuations in Worldwide Seismicity and Atmospheric Carbon Pollution

Sci ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 2 ◽  
Author(s):  
Alberto Carpinteri ◽  
Gianni Niccolini
Keyword(s):  
Seismic Activity ◽  
Nuclear Reactions ◽  
Active Faults ◽  
Earth’S Crust ◽  
Atmospheric Co2 ◽  
Geochemical Evolution ◽  
Geochemical Data ◽  
Common Cycles ◽  
Earth's Crust ◽  
Seismic Moment Release

The crucial stages in the geochemical evolution of the Earth’s crust, ocean, and atmosphere could be explained by the assumed low-energy nuclear reactions (LENR) that are triggered by seismic activity. LENR result in the fission of medium-weight elements accompanied by neutron emissions, involving Fe and Ni as starting elements, and C, N, O as resultants. Geochemical data and experimental evidences support the LENR hypothesis. A spectral analysis of the period 1955-2013 shows common cycles between interannual changes in atmospheric CO2 growth rate and global seismic-moment release, whereas the trending behavior of the atmospheric CO2 was in response to the anthropogenic emissions. Assuming a correlation between such seismic and atmospheric fluctuations, the latter could be explained by cycles of worldwide seismicity, which would trigger massively LENR in the Earth’s Crust. In this framework, LENR from active faults could be considered as a relevant cause of carbon formation and degassing of freshly-formed CO2 during seismic activity. However, further studies are necessary to validate the present hypothesis which, at the present time, mainly aims to stimulate debate on the models which regulates atmospheric CO2.

scholarly journals State-of-the-Art Water Treatment in Czech Power Sector: Industry-Proven Case Studies Showing Economic and Technical Benefits of Membrane and Other Novel Technologies for Each Particular Water Cycle

Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 98
Author(s):  
Jaromír Marek
Keyword(s):  
Water Treatment ◽  
Case Studies ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Power Plants ◽  
Water Cycle ◽  
Liquid Waste ◽  
Novel Technologies ◽  
Turbine Condensate ◽  
Common Cycles

The article first summarizes case studies on the three basic types of treated water used in power plants and heating stations. Its main focus is Czechia as the representative of Eastern European countries. Water as the working medium in the power industry presents the three most common cycles—the first is make-up water for boilers, the second is cooling water and the third is represented by a specific type of water (e.g., liquid waste mixtures, primary and secondary circuits in nuclear power plants, turbine condensate, etc.). The water treatment technologies can be summarized into four main groups—(1) filtration (coagulation) and dosing chemicals, (2) ion exchange technology, (3) membrane processes and (4) a combination of the last two. The article shows the ideal industry-proven technology for each water cycle. Case studies revealed the economic, technical and environmental advantages/disadvantages of each technology. The percentage of technologies operated in energetics in Eastern Europe is briefly described. Although the work is conceived as an overview of water treatment in real operation, its novelty lies in a technological model of the treatment of turbine condensate, recycling of the cooling tower blowdown plus other liquid waste mixtures, and the rejection of colloidal substances from the secondary circuit in nuclear power plants. This is followed by an evaluation of the potential novel technologies and novel materials.

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