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On equivalence relations Sigma_1^1-definable over H(kappa) [article]

Saharon Shelah, Pauli Väisänen
<span title="1999-11-29">1999</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Let kappa be an uncountable regular cardinal. Call an equivalence relation on functions from kappa into 2 Sigma_1^1-definable over H(kappa) if there is a first order sentence F and a parameter R subseteq H(kappa) such that functions f,g:kappa --> 2 are equivalent iff for some h:kappa --> 2, the structure (H(kappa),in,R,f,g,h) satisfies F, where in, R, f, g, and h are interpretations of the symbols appearing in F. All the values mu, 1 leq mu leq kappa^+ or mu=2^kappa, are possible numbers of
more &raquo; ... valence classes for such a Sigma_1^1-equivalence relation. Additionally, the possibilities are closed under unions of <=kappa-many cardinals and products of <kappa-many cardinals. We prove that, consistent wise, these are the only restrictions under the singular cardinal hypothesis. The result is that the possible numbers of equivalence classes of Sigma_1^1-equivalence relations might consistent wise be exactly those cardinals which are in a prearranged set, provided that the singular cardinal hypothesis holds and that some necessary conditions are fulfilled.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9911231v1">arXiv:math/9911231v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bezn222xm5cbvfzkjjmhunul5y">fatcat:bezn222xm5cbvfzkjjmhunul5y</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9911231/math9911231.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9911231v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

On ordinals accessible by infinitary languages

Saharon Shelah, Pauli Väisänen, Jouko Väänänen
<span title="">2005</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yeobluctzze7rfwekxs7sx2ayy" style="color: black;">Fundamenta Mathematicae</a> </i> &nbsp;
Let λ be an infinite cardinal number. The ordinal number δ(λ) is the least ordinal γ such that if φ is any sentence of L λ + ω , with a unary predicate D and a binary predicate ≺, and φ has a model M with D M , ≺ M a well-ordering of type ≥ γ, then φ has a model M ′ where D M ′ , ≺ M ′ is non-well-ordered. One of the interesting properties of this number is that the Hanf number of L λ + ω is exactly δ(λ) . It was proved in [BK71] that if ℵ 0 < λ < κ are regular cardinal numbers, then there is a
more &raquo; ... forcing extension, preserving cofinalities, such that in the extension 2 λ = κ and δ(λ) < λ ++ . We improve this result by proving the following: Suppose ℵ 0 < λ < θ ≤ κ are cardinal numbers such that • λ <λ = λ; • cf(θ) ≥ λ + and µ λ < θ whenever µ < θ; Then there is a forcing extension preserving all cofinalities, adding no new sets of cardinality < λ, and such that in the extension 2 λ = κ and δ(λ) = θ. 2000 Mathematics Subject Classification: 03C75, 03E35, 03C55.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm186-3-1">doi:10.4064/fm186-3-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/otmiuxk75rbq7f5ep2g6253zpy">fatcat:otmiuxk75rbq7f5ep2g6253zpy</a> </span>
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On the number of L_infty,omega_1-equivalent non-isomorphic models [article]

Saharon Shelah, Pauli Vaisanen
<span title="1999-08-30">1999</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that if ZF is consistent then ZFC+GCH is consistent with the following statement: There is for every k<omega a model of cardinality aleph_1 which is L_infty,omega_1-equivalent to exactly k non-isomorphic models of cardinality aleph_1. In order to get this result we introduce ladder systems and colourings different from the "standard" counterparts, and prove the following purely combinatorial result: For each prime number p and positive integer m it is consistent with ZFC+GCH that there
more &raquo; ... is a "good" ladder system having exactly p^m pairwise nonequivalent colourings.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9908160v1">arXiv:math/9908160v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v2iaq3og3jeu3be5yeeg7z4nea">fatcat:v2iaq3og3jeu3be5yeeg7z4nea</a> </span>
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On equivalence relations second order definable over H(κ)

Saharon Shelah, Pauli Vaisanen
<span title="">2002</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yeobluctzze7rfwekxs7sx2ayy" style="color: black;">Fundamenta Mathematicae</a> </i> &nbsp;
Let κ be an uncountable regular cardinal. Call an equivalence relation on functions from κ into 2 second order definable over H(κ) if there exists a second order sentence φ and a parameter P ⊆ H(κ) such that functions f and g from κ into 2 are equivalent iff the structure H(κ), ∈, P, f, g satisfies φ. The possible numbers of equivalence classes of second order definable equivalence relations contains all the nonzero cardinals at most κ + . Additionally, the possibilities are closed under unions
more &raquo; ... and products of at most κ cardinals. We prove that these are the only restrictions: Assuming that GCH holds and λ is a cardinal with λ κ = λ, there exists a generic extension, where all the cardinals are preserved, there are no new subsets of cardinality < κ, 2 κ = λ, and for all cardinals µ, the number of equivalence classes of some second order definable equivalence relation on functions from κ into 2 is µ iff µ is in Ω, where Ω is any prearranged subset of λ such that 0 ∈ Ω, Ω contains all the nonzero cardinals ≤ κ + , and Ω is closed under unions and products of at most κ cardinals.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm174-1-1">doi:10.4064/fm174-1-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h4jz3yjfdze2hj2nwrseutbunu">fatcat:h4jz3yjfdze2hj2nwrseutbunu</a> </span>
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Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals [article]

Saharon Shelah, Pauli Väisänen
<span title="2002-12-04">2002</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
New Brunswick NJ, USA shelah@math.rutgers.edu Pauli Väisänen: Department of Mathematics University of Helsinki Finland pauli.vaisanen@helsinki.fi  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0212063v1">arXiv:math/0212063v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ozvuznpggbejtnzadwajefjfii">fatcat:ozvuznpggbejtnzadwajefjfii</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math0212063/math0212063.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0212063v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The number of L_infty,kappa-equivalent non-isomorphic models for kappa weakly compact [article]

Saharon Shelah, Pauli Väisänen
<span title="1999-11-29">1999</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For a cardinal kappa and a model M of cardinality kappa let No(M) denote the number of non-isomorphic models of cardinality kappa which are L_infty,kappa--equivalent to M. In [Sh:133] Shelah established that when kappa is a weakly compact cardinal and mu<=kappa is a nonzero cardinal, there exists a model M of cardinality kappa with No(M)=mu. We prove here that if kappa is a weakly compact cardinal, the question of the possible values of No(M) for models M of cardinality kappa is equivalent to
more &raquo; ... e question of the possible numbers of equivalence classes of equivalence relations which are Sigma^1_1-definable over V_kappa. In math.LO/9911231 we prove that, consistent wise, the possible numbers of equivalence classes of Sigma^1_1-equivalence relations can be completely controlled under the singular cardinal hypothesis. These results settle the problem of the possible values of No(M) for models of weakly compact cardinality, provided that the singular cardinal hypothesis holds.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9911232v1">arXiv:math/9911232v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pd3rk466jfcx3p2l566useedyq">fatcat:pd3rk466jfcx3p2l566useedyq</a> </span>
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Patterns of Genome-Wide VDR Locations

Pauli Tuoresmäki, Sami Väisänen, Antonio Neme, Sami Heikkinen, Carsten Carlberg, Andrzej T. Slominski
<span title="2014-04-30">2014</span> <i title="Public Library of Science (PLoS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s3gm7274mfe6fcs7e3jterqlri" style="color: black;">PLoS ONE</a> </i> &nbsp;
The genome-wide analysis of the binding sites of the transcription factor vitamin D receptor (VDR) is essential for a global appreciation the physiological impact of the nuclear hormone 1a,25-dihydroxyvitamin D 3 (1,25(OH) 2 D 3 ). Genome-wide analysis of lipopolysaccharide (LPS)-polarized THP-1 human monocytic leukemia cells via chromatin immunoprecipitation sequencing (ChIP-seq) resulted in 1,318 high-confidence VDR binding sites, of which 789 and 364 occurred uniquely with and without
more &raquo; ... ) 2 D 3 stimulation, while only 165 were common. We re-analyzed five public VDR ChIP-seq datasets with identical peak calling settings (MACS, version 2) and found, using a novel consensus summit identification strategy, in total 23,409 non-overlapping VDR binding sites, 75% of which are unique within the six analyzed cellular models. LPSdifferentiated THP-1 cells have 22% more genomic VDR locations than undifferentiated cells and both cell types display more overlap in their VDR locations than the other investigated cell types. In general, the intersection of VDR binding profiles of ligand-stimulated cells is higher than those of unstimulated cells. De novo binding site searches and HOMER screening for binding motifs formed by direct repeats spaced by three nucleotides (DR3) suggest for all six VDR ChIP-seq datasets that these sequences are found preferentially at highly ligand responsive VDR loci. Importantly, all VDR ChIP-seq datasets display the same relationship between the VDR occupancy and the percentage of DR3-type sequences below the peak summits. The comparative analysis of six VDR ChIP-seq datasets demonstrated that the mechanistic basis for the action of the VDR is independent of the cell type. Only the minority of genome-wide VDR binding sites contains a DR3-type sequence. Moreover, the total number of identified VDR binding sites in each ligand-stimulated cell line inversely correlates with the percentage of peak summits with DR3 sites.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pone.0096105">doi:10.1371/journal.pone.0096105</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24787735">pmid:24787735</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4005760/">pmcid:PMC4005760</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7j7k7k6yzbfutnibh2qzcazaya">fatcat:7j7k7k6yzbfutnibh2qzcazaya</a> </span>
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The number of L∞κ-equivalent nonisomorphic models for κ weakly compact

Saharon Shelah, Pauli Vaisanen
<span title="">2002</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yeobluctzze7rfwekxs7sx2ayy" style="color: black;">Fundamenta Mathematicae</a> </i> &nbsp;
For a cardinal κ and a model M of cardinality κ let No(M ) denote the number of nonisomorphic models of cardinality κ which are L ∞,κ -equivalent to M . We prove that for κ a weakly compact cardinal, the question of the possible values of No(M ) for models M of cardinality κ is equivalent to the question of the possible numbers of equivalence classes of equivalence relations which are Σ 1 1 -definable over V κ . By [SV] it is possible to have a generic extension where the possible numbers of
more &raquo; ... ivalence classes of Σ 1 1 -equivalence relations are in a prearranged set. Together these results settle the problem of the possible values of No(M ) for models of weakly compact cardinality. 2000 Mathematics Subject Classification: Primary 03C55; Secondary 03C75. Key words and phrases: number of models, infinitary logic.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/fm174-2-1">doi:10.4064/fm174-2-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kapsuiab5fcwldc63g4vftc3oi">fatcat:kapsuiab5fcwldc63g4vftc3oi</a> </span>
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On inverse gamma-systems and the number of L_infty,lambda-equivalent, non-isomorphic models for lambda singular [article]

Saharon Shelah, Pauli Väisänen
<span title="1998-07-15">1998</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Pauli Väisänen: Department of Mathematics P.O. Box 4 00014 University of Helsinki Finland pauli.vaisanen@helsinki.fi  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9807181v1">arXiv:math/9807181v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ne7psp4esbfe7bsktmbpgnicuu">fatcat:ne7psp4esbfe7bsktmbpgnicuu</a> </span>
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Almost free groups and Ehrenfeucht–Fraı̈ssé games for successors of singular cardinals

Saharon Shelah, Pauli Väisänen
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
We strengthen nonstructure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fra ssà e games between a ÿxed group of cardinality and a free Abelian group. A group is called -game-free if the isomorphism player has a winning strategy in the game (of the described form) of length ∈ . We prove for a large set of successor cardinals = + the existence of nonfree ( · !1)-game-free groups of cardinality . We concentrate on successors of singular cardinals. (S. Shelah), pauli.vaisanen@helsinki.ÿ (P. V ais anen).
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0168-0072(02)00037-4">doi:10.1016/s0168-0072(02)00037-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/upvdjksw7rg7jhuh5btpf5h3by">fatcat:upvdjksw7rg7jhuh5btpf5h3by</a> </span>
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Seven decades of neutron monitors (1951 – 2019): Overview and evaluation of data sources

Pauli Väisänen, Ilya Usoskin, Kalevi Mursula
<span title="2021-04-05">2021</span> <i title="American Geophysical Union (AGU)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2sveynknynaw7mfdpqacdjpeoq" style="color: black;">Journal of Geophysical Research - Space Physics</a> </i> &nbsp;
VÄISÄNEN ET AL.  ...  VÄISÄNEN ET AL.  ...  VÄISÄNEN ET AL. 10.1029/2020JA028941 5 of 11 Table 2 Continued 2 Notes. Prime stations are in bold.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1029/2020ja028941">doi:10.1029/2020ja028941</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r6gjlt3cajfyzfcqqcfjrl5siq">fatcat:r6gjlt3cajfyzfcqqcfjrl5siq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210717002344/https://agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/2020JA028941" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c4/03/c40371f564cbeb27c9c9795c3357dc2273432847.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1029/2020ja028941"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On inverse γ-systems and the number of L ∞λ-equivalent, non-isomorphic models for λ singular

Saharon Shelah, Pauli Väisänen
<span title="">2000</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4l7nckgxmbcgvj5vxsioq6qwyq" style="color: black;">Journal of Symbolic Logic (JSL)</a> </i> &nbsp;
Suppose λ is a singular cardinal of uncountable cofinality κ. For a model of cardinality λ, let No() denote the number of isomorphism types of models of cardinality λ which are L ∞λ-equivalent to . In [7] Shelah considered inverse κ-systems of abelian groups and their certain kind of quotient limits Gr()/ Fact(). In particular Shelah proved in [7, Fact 3.10] that for every cardinal Μ there exists an inverse κ-system such that consists of abelian groups having cardinality at most Μκ and
more &raquo; ... / Fact()) = Μ. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse κ-systems and possible values of No (under the assumption that θκ &lt; λ for every θ &lt; λ): if is an inverse κ-system of abelian groups having cardinality &lt; λ, then there is a model such that card() = λ and No() = card(Gr()/ Fact()). The following was an immediate consequence (when θκ &lt; λ for every θ &lt; λ): for every nonzero Μ &lt; λ or Μ = λκ there is a model , of cardinality λ with No() = Μ. In this paper we show: for every nonzero Μ ≤ λκ there is an inverse κ-system of abelian groups having cardinality &lt; λ such that card(Gr()/ Fact()) = Μ (under the assumptions 2κ &lt; λ and θ&lt;κ &lt; λ for all θ &lt; λ when Μ &gt; λ), with the obvious new consequence concerning the possible value of No. Specifically, the case No() = λ is possible when θκ &gt; λ for every λ &lt; λ.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2586536">doi:10.2307/2586536</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tnlaluhjwnc4doxnntvlo3svki">fatcat:tnlaluhjwnc4doxnntvlo3svki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921233933/http://shelah.logic.at/files/644.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8e/0c/8e0c5ebfbb82a3b36a773e197dbfaecddd0585a7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2586536"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>

Structure of the Power Spectral Density of Galactic Cosmic Ray Variation during 1953-2016

Pauli Väisänen, Ilya Usoskin, Kalevi Mursula
<span title="">2017</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/djnl2eulfjdwxplyqzspykhc2m" style="color: black;">Proceedings of the International Astronomical Union</a> </i> &nbsp;
AbstractFluxes of galactic cosmic rays (GCR) observed at 1 AU are modulated inside the heliosphere at different time scales. Here we study the properties of the power spectral density (PSD) of galactic cosmic ray variability using hourly data from 31 neutron monitors (NM) from 1953 to 2016. We pay particular attention to the reliability of the used datasets and methods. We present the overall PSD and discuss different parts of the spectrum and the related periodicities. We find significant
more &raquo; ... ral peaks at the periods of 11 years, 1.75 years, 155 days, 27 days and 24 hours and the harmonics of the latter two peaks. We calculate a power law slope of −1.79 ± 0.13 for the period range between 50 and 130 hours and a slope of −1.34 ± 0.17 for the period range between 40 days and 3.4 years (1000 − 30000 h).
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1743921317010122">doi:10.1017/s1743921317010122</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pnyexquw7ncojchyavyqek4etm">fatcat:pnyexquw7ncojchyavyqek4etm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190428005520/http://jultika.oulu.fi/files/nbnfi-fe2018082233907.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a4/81/a4819e982cea94d9d9d20e459590d64302c5d4d6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1743921317010122"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> cambridge.org </button> </a>

Long-Term and Solar Cycle Variation of Galactic Cosmic Rays: Evidence for Variable Heliospheric Turbulence

Pauli Väisänen, Ilya Usoskin, Kalevi Mursula
<span title="2019-02-01">2019</span> <i title="American Geophysical Union (AGU)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2sveynknynaw7mfdpqacdjpeoq" style="color: black;">Journal of Geophysical Research - Space Physics</a> </i> &nbsp;
Pauli Väisänen acknowledges the personal research 297 grant from The Finnish Cultural Foundation.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1029/2018ja026135">doi:10.1029/2018ja026135</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ypjyjxrocrcxzkrt2znttko53y">fatcat:ypjyjxrocrcxzkrt2znttko53y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190429014757/http://jultika.oulu.fi/files/nbnfi-fe2019040511226.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a1/7f/a17f8bb527380e4c6cb6d3fe33a02544dff01ea0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1029/2018ja026135"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Spectral slope analysis of long-term cosmic-rayvariations at Earth

Ilya Usoskin, Pauli Väisänen, Kalevi Mursula
<span title="2019-07-22">2019</span> <i title="Sissa Medialab"> Proceedings of 36th International Cosmic Ray Conference — PoS(ICRC2019) </i> &nbsp; <span class="release-stage">unpublished</span>
The flux of galactic cosmic rays (GCR) at Earth is modulated in the heliosphere by the heliospheric magnetic field and solar wind, that vary in the course of solar cycle. The modulation is caused by diffusion, convection, adiabatic cooling and drifts, where very important is scattering of particles on magnetic inhomogeneities in the turbulent solar wind and heliospheric magnetic field (HMF). Turbulent variations are often characterized by a power law in the power spectrum of the cosmic-ray
more &raquo; ... tions. Previous works revealed a power law behaviour in the power spectral density (PSD) of GCR fluxes in the frequency range between 5.56 · 10 −6 and 2.14 −6 Hz (50 -130 hours) that varies with the solar cycle phases. Here we further develop these results by employing a broader and higher-quality dataset obtained from the world data repository (the WDCCR). Using data from 31 ground-based neutron monitors (NMs) spanning 65 years (nearly six solar cycles, 1953-2018) of measurements, we have studied the spectral slopes of the PSD of NM count rates. Using 2-year overlapping PSD intervals, we found that the spectral slope varies in time between approximately −1 and −2.6, with a mean value of −1.84 ± 0.01. Separating the results to specific solar cycle phases, we found that steep slopes close to −2.0 (typical for a random walk) appear during solar maximum times, and flatter slopes close to −1.7 (Kolmogorov-type spectrum) appear during solar cycle minimum times, indicating that different physical processes determine GCR transport in the Heliosphere at different phases of the solar cycle. We note that these results are in close agreement with the earlier results that used a different dataset.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22323/1.358.1165">doi:10.22323/1.358.1165</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e6qt7rz7wncsnd7me5y6whqybq">fatcat:e6qt7rz7wncsnd7me5y6whqybq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201111193732/https://pos.sissa.it/358/1165/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e4/59/e4592d76e8b349562b35cc00fdb77eaeb4298ac7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22323/1.358.1165"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>
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