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In Fig. 2, we show the particular set of parameters that determines a period two-cycle, actually, with k= 0.22. Further growth ofkleads the attractor to follow a typical route of flip bifurcations in complex price dynamics: a sequence of flip　bifurcations generate a sequence of attracting cycles in period 2＾ｎ , which are followed by the creation of a chaotic attractor. In Fig. 3, a cycle of period four is shown. 独占企業における経済動学の文章です。どなたかお願いしますm(__)m

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  • oignies
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まず、正確に転記できていませんね。 ｏｆ　ｋｌｅｅｄｓの前後が何か英語としてつながらないようです。うつしまちがえて いませんか。 こまかいことは、わかりませんが 複雑な価格決定過程において、どのようなことがおきるか、を説明してい ます。 図が、２，３とあるようですが、図をみながらよめば、わかるのでは？ ３行目のａｔｔｒａｃｔは多分、ひきよせるという意味です。 第１期、第２期、第３期、第４期でおきることをそれぞれ、説明しているはず ですが、そういう風に図はなっていませんか。

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  • 英文和訳をお願いします。

    To clarify the dynamics depending on　k, we have reported a bifurcation diagram in Fig. 4. It shows different values of　quantity for different values of　k, particularly between 0.15 and 0.29. It is easily illustrated that we move from stability　through a sequence of a period doubling bifurcations to chaos.

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    3. Results and discussions Our new annual carbon-14 data for the EMMP not only confirm the relationship between the cycle length and solar activity level but also provide some important insights on the state of solar activity during this period. Fig. 1 shows the signal of solar cycles detected in the carbon-14 data and Fig. 2-a shows the frequency analysis of the data, exhibiting the change in solar cycles and their amplitude. The power spectrum remarkably indicates a 9-year cyclicity (± 1 for the 68% confidence level against the high-frequency noise (< 3 years) through 880–960 AD, together with an 18-year period of solar polarity reversals. The overall significances of the two signals are 3 sigma and 2.7 sigma, respectively. The length of the 11-year solar cycle is ~ 2 years shorter than that observed for the last 150 years, and ~ 5 years shorter than those during the Maunder Minimum.

  • 以下の英文の和訳をお願いします。

    Although the magnitude of the variations of carbon-14 is strongly attenuated through the carbon cycle after being produced by the GCRs in the atmosphere (Siegenthaler and Beer, 1988), carbon-14 in tree-rings preserve the information on the variations in solar cycles and the magnetic dipole polarity of the sun. Therefore, the variability of the “11-year” solar cycle in association with the century-scale variations of solar activity can be monitored to asses its influence on climate. The lengths of sunspot periods have been modulated by a few years since the 11-year sunspot cycle was firstly found by Schwabe (1843). The maximum range observed so far is ~ 9 to ~ 14 years, but most of the cycles fit in ~ 10–12 years with the overall average being 11 years. However, we have previously found a change in average cycle length during the Maunder Minimum ((Miyahara et al., 2004); see Supplementary Fig. S1). The sunspots were scarce through 1645–1715 AD due to the anomalous weakening of the magnetic activity at this time, yet the carbon-14 abundances show the appearance of significant cyclic changes in magnetic activity. The average length of the cycles through the 70 years was about 14 years with the 28-year period of magnetic polarity reversals. The relationship between the cycle length of the “11-year” variation in sunspots and its magnitude has been investigated in several papers (Clough, 1905, Solanki et al., 2002 and Rogers et al., 2006). A consistent feature is the inverse correlation between cycle amplitudes and cycle lengths that maybe related to the change of the meridional flows inside the convection zone of the sun (Hathaway et al., 2003).

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    Here we examine the relationship between the sun and climate by measuring the carbon-14 content in tree-rings with annual time resolution. The GCR flux and hence the activity level of the sun can be monitored by carbon-14. Our particular focus is around the period of the Maunder Minimum and the early Medieval Maximum Period (EMMP) in the 9–10th century. Sunspot numbers and the activity levels of the sun gradually change in time with quasi-cycles of about 11 years (Schwabe cycle).The polarity of the solar intrinsic magnetic field, which is more or less a simple dipole at every activity minima, reverses at every activity maximum. It changes the track of protons, the positively charged main constituent of GCRs, due to the spirally expanding interplanetary magnetic field formed by solar wind (Kota and Jokipii, 1983) and hence changes the attenuation level of GCRs in the heliosphere. Bulk of the GCRs comes from the polar region of the heliosphere when the polarity of the sun is positive, while GCRs come from the horizontal direction when negative.The attenuation of GCRs in the heliosphere is, therefore, more sensitive when the polarity is negative to the intensity of solar magnetic field and the tilt angle of the current sheets which expand horizontal direction. Thus the variation of the GCR flux on the earth has a “22-year” cyclic component, and will be transferred to the variations in carbon-14.

  • 次の英文の和訳をお願いします。

    Abstract The linkage between multi-decadal climate variability and activity of the sun has been long debated based upon observational evidence from a large number of instrumental and proxy records. It is difficult to evaluate the exact role of each of solar parameters on climate change since instrumentally measured solar related parameters such as Total Solar irradiance (TSI), Ultra Violet (UV), solar wind and Galactic Cosmic Rays (GCRs) fluxes are more or less synchronized and only extend back for several decades. Here we report tree-ring carbon-14 based record of 11-year/22-year solar cycles during the Maunder Minimum (17th century) and the early Medieval Maximum Period (9–10th century) to reconstruct the state of the sun and the flux of incoming GCRs. The result strongly indicates that the influence of solar cycles on climate is persistent beyond the period after instrumental observations were initiated. We find that the actual lengths of solar cycles vary depending on the status of long-term solar activity, and that periodicity of the surface air temperatures are also changing synchronously. Temperature variations over the 22-year cycles seem, in general, to be more significant than those associated with the 11-year cycles and in particular around the grand solar minima such as the Maunder Minimum (1645–1715 AD). The polarity dependence of cooling events found in this study suggests that the GCRs can not be excluded from the possible drivers of decadal to multi-decadal climate change.

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    There is a threshold value　for the reaction coefficient of the monopolist in such a way that the steady state is no longer stable. Mainly, the dynamic map(5) satisfies the canonical conditions required for the flip bifurcation [5,6].

  • この文章の和訳をお願いします。

    　　　In the chaotic zone, there are, of course, a great number of discrete collision orbits. Minimum separation distance in the chaotic zone near b=1.93 is enlarged in Fig.6, which is obtained from the calculation of 3000 orbits with b between 1.926 and 1.932. Even in this enlarged figure, r_min varies violently with b. Although the chaotic zones are not sufficiently resolved in our present study, the phase space occupied by collision orbits in the chaotic zones is much smaller than that in the regular collision bands. Even if all orbits in the chaotic zone are collisional, their contribution to the collision rate is less than 4% of the total: the width in b=2.30 and 2.48, we also found that the total width is much smaller than 0.001. This implies that in the evaluation of <P(e, i)>, we can neglect the contribution of collision orbits in the chaotic zones. 　　　These are n-recurrent collision orbits in the regular zones. Of these, 2-recurrent collision orbits are most important. The collisional band composed of them is found near b=2.34. Its width ⊿b is about 0.011, and the contribution to the collision is as large as 15%. No.3- and more –recurrent collision orbits were observed in regular zones. They were found only in the chaotic zones and, hence, can be neglected. 長いですが、よろしくお願いします。

  • この文章の和訳をよろしくお願いします。

    Fig. 3a and b. An example of recurrent non-collision orbits. The orbit with b=2.4784, e=0, and i=0 is illustrated. To see the orbital behavior near the protoplanet, the central region is enlarged in b; the circle shows the sphere of the two-body approximation and the small one the protoplanet. Fig. 4a and b. Same as Fig. 3 but b=2.341, e=0, and i=0. This is an example of recurrent collision orbits. Fig.5. Minimum separation distance r_min between the protoplanet and a planetesimal in the case of (e, i)=(0, 0). By solid curves, r_min in the first encounter is illustrated as a function of b. The level of protoplanetary radius is shown by a thin dashed line. The collision band in the second encounter orbits around b=2.34 is also shown by dashed curves. Fig. 6. Minimum distance r_min in the chaotic zone near b=1.93 for the case of (e, i)=(0, 0); it changes violently with b. Fig. 7a-c. Contours of minimum separation distance r_min in the first encounter for the case of (e, i)=(1.0, 0.5); b=2.3(a), 2.8(b), and 3.1 (c). Contours are drawn in terms of log_10 (r_min) and the contour interval is 0.5. Regions where r_min>1 are marked by coarse dots. Particles in these regions cannot enter the Hill sphere of the protoplanet. Fine dots denotes regions where r_min is smaller than the radius r_cr of the sphere of the two-body approximation (r_cr=0.03; log_10(r_cr)=-1.52). Fig. 3a and b.　および　Fig. 4a and b.　↓ http://www.fastpic.jp/images.php?file=3994206860.jpg Fig.5.　および Fig. 7a-c. 　↓ http://www.fastpic.jp/images.php?file=2041732569.jpg Fig. 6. ↓ http://www.fastpic.jp/images.php?file=2217998690.jpg お手数ですが、よろしくお願いします。

  • この英文の和訳をお願いします。

    As mentioned above, there are two peaks in R(e,i) in the e-i diagram: one is at e≒1 (i<1) and the other at i≒3 (e<0.1). The former corresponds directly to the peak in R(e,0) at e≒1 found in the two-dimensional case. The latter is due to the peculiar nature to the three-dimensional case, as understood in the following way. Let us introduce r_min (i, b,ω) in the case of e=0, which is the minimum distance during encounter between the protoplanet and a planetesimal with orbital elements i, b, and ω. In Fig. 16, r_min(i,b)=min_ω{r_min(i,b,ω)} is plotted as a function of b for various i, where r_min<r_p (=0.005) means “collision”; there are two main collision bands at b≒2.1 and 2.4 for i=0. For i≦2, these bands still exist, shifting slightly to small b. This shift is because a planetesimal feels less gravitational attracting force of the protoplanet as i increases. As i increases further, the bands approach each other, and finally coalesce into one large collision band at i≒3.0; this large band vanish when i≧4. In this way, the peculiar orbital behavior of three-body problem makes the peak at i≒3 (e<0.1). Though there are the peaks in R(e,i), the peak values are not so large: at most it is as large as 5. This shows that the collisional rate is well described by that of the two-body approximation <P(e,i)>_2B except for in the vicinity of v, i→0 if we neglect a difference of a factor of 5. Now we propose a modified form of <P(e,i)>_2B which well approximates the calculated collisional rate even in the limit of v, i→0. We find in Fig.14 that <P(e,i)> is almost independent of i, i.e., it behaves two-dimensionally for i≦{0.1 (when e≦0.2), {0.02/e (when e≧0.2). (35) This transition from three-dimensional behavior to two-dimensional behavior comes from the fact that the isotropy of direction of incident particles breaks down for the case of very small i (the expression <P(e,i)>_2B given by Eq. (29) assumes the isotropy). In other words, as an order of magnitude, the scale height of planetesimals becomes smaller than the gravitational radius r_G=σ_2D/2 (σ_2D given by Eq. (3)) and the number density of planetesimals cannot be uniform within a slab with a thickness σ_2D for small i. Table 4. Numbers of three-dimensional collision events found by orbital calculations for the representative sets of e and i. In the table r_p is the radius of the protoplanet. Table 5. The three-dimensional collision rate <P(e,i)> for the case of r_p=0.005 (r_p being the protoplanetary radius), together with two-dimensional <P(e,i=0)> Fig. 14. Contours of the evaluated <P(e,i)>, drawn in terms of log_10<P(e,i)> Fig. 15. Contours of the enhancement factor R(e,i) Table 4.↓ http://www.fastpic.jp/images.php?file=1484661557.jpg Table 5.↓ http://www.fastpic.jp/images.php?file=6760884829.jpg Fig. 14. ＆Fig. 15.↓ http://www.fastpic.jp/images.php?file=8798441290.jpg 長文になりますが、よろしくお願いします。

  • この文章の和訳をお願いします。

    Fig. 8. Contours of minimum separation distance r_min in the second encounter for the case of (e, i, b)=(1.0, 0.5, 2.8). Dots have the same meanings as those in Fig. 7. Fig. 9. The “Differential” collisional rate <p(e, i, b)> (defined by Eq. (24)) is plotted as a function of b in the case of (e, i)=(1.0, 0.5). Fig. 8.↓ http://www.fastpic.jp/images.php?file=4403322728.jpg Fig. 9.↓ http://www.fastpic.jp/images.php?file=9905093670.jpg よろしくお願いします。

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