Moment problems on subsemigroups of ℕ 0 k and ℤk

Sakakibara, Nobuhisa

doi:10.1007/bf03025764

Cited by 9 publications

(4 citation statements)

References 9 publications

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“…The black points in Figure 5f indicate Γ derived from the black points in Figures 5d and 5e, while the gray curve in Figure 5f shows Γ derived from the gray curves in Figures 5d and 5e for intense FDs. It is seen that Γ varies in a range of -1.2 < Γ < -0.6 in accord with most of the previous studies reporting Γ ∼ −1 (Lockwood 1960;Wada & Suda 1980;Sakakibara et al 1985Sakakibara et al , 1987Morishita et al 1990). The black points in E-events in the left panel of Figure 5f show a rapid decrease with increasing x during the recovery phase of the FD in x > +0.4 AU, implying that higher rigidity (60 GV) GCRs recover faster than lower rigidity (10 GV) GCRs.…”

Section: Average Features Of the Gcr Density Distributionsupporting

confidence: 89%

Average Spatial Distribution of Cosmic Rays Behind the Interplanetary Shock—global Muon Detector Network Observations

Kozai

Munakata

Kato

et al. 2016

ApJ

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We analyze the galactic cosmic ray (GCR) density and its spatial gradient in Forbush Decreases (FDs) observed with the Global Muon Detector Network (GMDN) and neutron monitors (NMs). By superposing the GCR density and density gradient observed in FDs following 45 interplanetary shocks (IP-shocks), each associated with an identified eruption on the sun, we infer the average spatial distribution of GCRs behind IP-shocks. We find two distinct modulations of GCR density in FDs, one in the magnetic sheath and the other in the coronal mass ejection (CME) behind the sheath. The density modulation in the sheath is dominant in the western flank of the shock, while the modulation in the CME ejecta stands out in the eastern flank. This east-west asymmetry is more prominent in GMDN data responding to ∼ 60 GV GCRs than in NM data responding to ∼ 10 GV GCRs, because of softer rigidity spectrum of the modulation in the CME ejecta than in the sheath. The GSE-y component of the density gradient, G y shows a negative (positive) enhancement in FDs caused by the eastern (western) eruptions, while G z shows a negative (positive) enhancement in FDs by the northern (southern) eruptions. This implies the GCR density minimum being located behind the central flank of IP-shock and propagating radially outward from location of the solar eruption. We also confirmed the average G z changing its sign above and below the heliospheric current sheet, in accord with the prediction of the drift model for the large-scale GCR transport in the heliosphere.

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Section: Average Features Of the Gcr Density Distributionsupporting

confidence: 89%

Average Spatial Distribution of Cosmic Rays Behind the Interplanetary Shock—global Muon Detector Network Observations

Kozai

Munakata

Kato

et al. 2016

ApJ

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“…But the right-hand side is equal to ξ(y)ξ(z) −1 dλ z (ξ )|G z , so the desired equality follows from (4). This proves (5). For x ∈ H + H + H and y ∈ H + H , since characters outside G vanish on H , by (3) and (5) we have…”

Section: Since These Two Measures Represent the Same Function Onmentioning

confidence: 53%

A reduction of the problem of characterizing perfect semigroups

Bisgaard¹,

Sakakibara²

2002

MATH. SCAND.

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“…For k , see [4], 6.4.8. These results are subsumed in the following result of Sakakibara [19]: A subsemigroup of k containing 0 is semiperfect if and only if it is {0} or isomorphic to or AE 0 .…”

Section: The Semigroup S Is Semiperfect If H(s) = P(s) and Perfect Imentioning

confidence: 91%

On the Stieltjes moment problem on semigroups

Bisgaard¹

2002

Czechoslovak Mathematical Journal

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Moment problems on subsemigroups of ℕ 0 k and ℤk

Cited by 9 publications

References 9 publications

Average Spatial Distribution of Cosmic Rays Behind the Interplanetary Shock—global Muon Detector Network Observations

Average Spatial Distribution of Cosmic Rays Behind the Interplanetary Shock—global Muon Detector Network Observations

A reduction of the problem of characterizing perfect semigroups

On the Stieltjes moment problem on semigroups

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