Context. The structure of the white-light and emission solar coronas and their MHD modelling are the context of our work. Aims. A comparison is made between the structure of the solar corona as observed during the 2008 August 1 total eclipse from Mongolia and that predicted by an MHD model. Methods. The model has an improved energy formulation, including the effect of coronal heating, conduction of heat parallel to the magnetic field, radiative losses, and acceleration by Alfvén waves. Results. The white-light corona, which was visible up to 20 solar radii, was of an intermediate type with well-pronounced helmet streamers situated above a chain of prominences at position angles of 48, 130, 241, and 322 degrees. Two polar coronal holes, filled with a plethora of thin polar plumes, were observed. High-quality pictures of the green (530.3 nm, Fe XIV) corona were obtained with the help of two narrow-passband filters (centered at the line itself and the vicinity of 529.1 nm background), with a FWHM of 0.15 nm. Conclusions. The large-scale shape of both the white-light and green corona was found to agree well with that predicted by the model. In this paper we describe the morphological properties of the observed corona, and how it compares with that predicted by the model. A more detailed analysis of the quantitative properties of the corona will be addressed in a future publication.

The coronal index (CI) of solar activity is the irradiance of the Sun as a star in the coronal green line (Fe XIV, 530.3 nm or 5303 Å). It is derived from ground‐based observations of the green corona made by the network of coronal stations (currently Kislovodsk, Lomnický Štít, Norikura, and Sacramento Peak). The CI was introduced by Rybanský (1975) to facilitate comparison of ground‐based green line measurements with satellite‐based extreme ultraviolet and soft X‐ray observations. The CI since 1965 is based on the Lomnický Štít photometric scale; the CI was extended to earlier years by Rybanský et al. (1994) based on cross‐calibrations of Lomnický Štít data with measurements made at Pic du Midi and Arosa. The resultant 1939–1992 CI had the interesting property that its value at the peak of the 11‐year cycle increased more or less monotonically from cycle 18 through cycle 22 even though the peak sunspot number of cycle 20 exhibited a significant local minimum between that of cycles 19 and 21. Rušin and Rybanský (2002) recently showed that the green line intensity and photospheric magnetic field strength were highly correlated from 1976 to 1999. Since the photospheric magnetic field strength is highly correlated with sunspot number, the lack of close correspondence between the sunspot number and the CI from 1939 to 2002 is puzzling. Here we show that the CI and sunspot number are highly correlated only after 1965, calling the previously‐computed coronal index for earlier years (1939–1965) into question. We can use the correlation between the CI and sunspot number (also the 2800 MHz radio flux and the cosmic ray intensity) to recompute daily values of the CI for years before 1966. In fact, this method can be used to obtain CI values as far back as we have reliable sunspot observations (∼1850). The net result of this exercise is a CI that closely tracks the sunspot number at all times. We can use the sunspot‐CI relationship (for 1966–2002) to identify which coronal stations can be used as a basis for the homogeneous coronal data set (HDS) before 1966. Thus we adopt the photometric scale of the following observatories for the indicated times: Norikura (1951–1954; the Norikura photometric scale was also used from 1939 to 1954); Pic du Midi (1955–1959); Kislovodsk (1960–1965). Finally, we revised the post‐1965 HDS and made several small corrections and now include data from Kislovodsk, Norikura, and Sacramento Peak to fill gaps at Lomnický Štít.

In 1993, Mermin (Rev. Mod. Phys. 65, 803-815) gave lucid and strikingly simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of dimensions four and eight by making use of what has since been referred to as the Mermin(-Peres) "magic square" and the Mermin pentagram, respectively. The former is a 3 × 3 array of nine observables commuting pairwise in each row and column and arranged so that their product properties contradict those of the assigned eigenvalues. The latter is a set of ten observables arranged in five groups of four lying along five edges of the pentagram and characterized by similar contradiction. An interesting one-to-one correspondence between the operators of the Mermin-Peres square and the points of the projective line over the product ring GF(2) ⊗ GF(2) is established. Under this mapping, the concept "mutually commuting" translates into "mutually distant" and the distinguishing character of the third column's observables has its counterpart in the distinguished properties of the coordinates of the corresponding points, whose entries are both either zero-divisors, or units. The ten operators of the Mermin pentagram answer to a specific subset of points of the line over GF(2)[x]/ x 3 − x . The situation here is, however, more intricate as there are two different configurations that seem to serve equally well our purpose. The first one comprises the three distinguished points of the (sub)line over GF(2), their three "Jacobson" counterparts and the four points whose both coordinates are zero-divisors; the other features the neighbourhood of the point (1, 0) (or, equivalently, that of (0, 1)). Some other ring lines that might be relevant for BKS proofs in higher dimensions are also mentioned.

Ramanujan sums are exponential sums with exponent defined over the irreducible fractions. Until now, they have been used to provide converging expansions to some arithmetical functions appearing in the context of number theory. In this paper, we provide an application of Ramanujan sum expansions to periodic, quasiperiodic and complex time series, as a vital alternative to the Fourier transform. The Ramanujan-Fourier spectrum of the Dow Jones index over 13 years and of the coronal index of solar activity over 69 years are taken as illustrative examples. Distinct long periods may be discriminated in place of the 1/f α spectra of the Fourier transform.

We discuss results stemming from observations of the white-light and [Fe XIV] emission corona during the total eclipse of the Sun of 2008 August 1, in Mongolia (Altaj region) and in Russia (Akademgorodok, Novosibirsk, Siberia). Corresponding to the current extreme solar minimum, the white-light corona, visible up to 20 solar radii, was of a transient type with well-pronounced helmet streamers situated above a chain of prominences at position angles 48°, 130°, 241° and 322°. A variety of coronal holes, filled with a number of thin polar plumes, were seen around the poles. Furthering an original method of image processing, stars up to 12 magnitude, a Kreutz-group comet (C/2008 O1), and a coronal mass ejection (CME) were also detected, with the smallest resolvable structures being of, and at some places even less than, 1 arcsec. Differences, presumably motions, in the corona and prominences are seen even with the 19-min time difference between our sites. In addition to the high-resolution coronal images, which show the continuum corona (K-corona) that results from electron scattering of photospheric light, images of the overlapping green-emission-line (530.3 nm, [Fe XIV]) corona were obtained with the help of two narrow-passband filters (centered on the line itself and for the continuum in the vicinity of 529.1 nm, respectively), each with FWHM of 0.15 nm. Through solar observations, on whose scheduling and details we consulted, with the Solar and Heliospheric Observatory, Hinode's XRT and SOT, TRACE, and STEREO, as well as Wilcox Solar Observatory and SOHO/MDI magnetograms, we set our eclipse observations in the context of the current unusually low and prolonged solar minimum.

We discuss a remarkable brightening in a polar plume, as inferred from unique coordinated observations of the whitelight corona during the total eclipse of the Sun of 2006 March 29. The polar plume (also known as a polar ray, with distinctions that we discuss) was observed at the positional angle of 9 ; the velocity at which the brightening propagated was about 65 km s À1 , which is close to the values derived by modeling of mass/energy transfer in polar plumes/rays as well as to those acquired from images from the Extreme-ultraviolet Imaging Telescope on the European Space Agency/ NASA Solar and Heliospheric Observatory (SOHO/EIT). Comparing our data with those from the SOHO/LASCO C2 coronagraph, we estimate the lifetime of the polar ray to be less than 24 hr.

Time-latitudinal distributions of the solar-surface magnetic fields and the green corona (530.3 nm, Fe XIV) intensities in the period 1975 -2004 are analyzed.Meridional migration maps show that time-varying components consist of both the poleward and equatorward belts over a solar cycle. The green-corona maps are, for the first time, directly compared with magnetic flux charts, yielding a good association between the green corona and magnetic fields; this is most reliably seen at high latitudes.

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