arXiv subjects

Milan Minarovjech

Publications and source records attributed to Milan Minarovjech.

3 recordsLinked to original sources

arXiv2009

The 2008 August 1 Eclipse Solar-Minimum Corona Unraveled

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 degrees. 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.

astro-ph.SR↗

arXiv2008

Ramanujan sums analysis of long-period sequences and 1/f noise

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.

math-ph↗

arXiv2006

The Projective Line Over the Finite Quotient Ring GF(2)[$x$]/$< x^{3} - x>$ and Quantum Entanglement II. The Mermin "Magic" Square/Pentagram

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 $3 \times 3$ 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 ${\rm GF}(2) \otimes \rm{GF}(2)$ 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)[$x$]/$ $. 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.

quant-ph↗