Asymptotics for the number of n-quasigroups of order 4

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.Comment: 15 p., 3 fi

A New High Energy Photon Tagger for the H1 - Detector at HERA

The H1 detector at HERA has been upgraded by the addition of a new electromagnetic calorimeter. This is installed in the HERA tunnel close to the electron beam line at a position 8m from the interaction point in the electron beam direction. The new calorimeter extends the acceptance for tagged photoproduction events to the high y range, 0.85 < y < 0.95, and thus significantly improves the capability of H1 to study high energy gamma-p processes. The calorimeter design, performance and first results obtained during the 1996-1999 HERA running are described.Comment: 17 pages, 16 figure

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Holy Synod and Political Crisis of Interregnum

The features of the development of the dynastic crisis of the interregnum of 1825 through the prism of the functioning of one of the key public authorities - the Holy Synod is discussed in the article. An analysis of the literature allows us to conclude that in modern historiography, the events of the oath to Grand Duke Konstantin received conflicting estimates. It is noted that as a result there were several interpretative schemes of what happened in the capital on November 27. An appeal to the workflow of the Synod makes it possible to assert that from the point of view of the logic of the functioning of the state apparatus, a coup d’etat took place. An analysis of everyday activities, the key bureaucratic formulas in the protocols leads to the conclusion that the bureaucratic reaction to the oath to Konstantin did not correspond to the established traditions and was distinguished by haste and internal contradictions. This was reflected primarily in the decisions of November 27: the Synod decides on the oath, relying on oral reports from the synodal members, but the next day duplicates its own decision, referring to the jurisdiction of the Senate. Moreover, a comparison with the events of December 12-14 shows that the accession to the throne of Nikolai Pavlovich was carried out in accordance with the order established in the previous century and was distinguished by deliberate legal accuracy and consistency

Tagging High Energy Photons in the H1 Detector at HERA

Measures taken to extend the acceptance of the H1 detector at HERA for photoproduction events are described. These will enable the measurement of electrons scattered in events in the high y range 0.85 < y < 0.95 in the 1998 and 1999 HERA run period. The improvement is achieved by the installation of an electromagnetic calorimeter, the ET8, in the HERA tunnel close to the electron beam line 8 m downstream of the H1 interaction point in the electron direction. The ET8 will allow the study of tagged gamma p interactions at centre-of-mass energies significantly higher than those previously attainable. The calorimeter design and expected performance are discussed, as are results obtained using a prototype placed as close as possible to the position of the ET8 during the 1996 and 1997 HERA running.Comment: 13 pages, 13 figure

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number $n_0$ of the sites in the system leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on $n_0$. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in $n_0$ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum Path-Integral Monte Carlo calculations.Comment: 12 pages, 8 Postscript figure

New model for system of mesoscopic Josephson contacts

Quantum fluctuations of the phases of the order parameter in 2D arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores filled with superfluid helium, or Josephson junctions in which the average number of particles $n_0$ (effective bosons, He atoms, and so on) is small, and the standard approach employing the phase operator and the particle number operator as conjugate ones is inapplicable. There is a large difference in the phase diagrams between arrays of macroscopic and mesoscopic objects for $n_0 < 5$ and $U<J$ ($U$ is the characteristic interaction energy of the particle per granule and $J$ is the Josephson coupling constant). Reentrant superconductivity phenomena are discussed.Comment: 4 pages, 3 Postscript figure

Representations of Menger (2,n)(2,n)-semigroups by multiplace functions

Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place functions is an $(n+1)$-ary superposition $[ ]$, but there are some other naturally defined operations, which are also worth of consideration. In this paper we consider binary Mann's compositions \op{1},...,\op{n} for partial $n$-place functions, which have many important applications for the study of binary and $n$-ary operations. We present methods of representations of such algebras by $n$-place functions and find an abstract characterization of the set of $n$-place functions closed with respect to the set-theoretic inclusion

Copper-Containing Magnesioferrite in Vesicular Trachyandesite in a Lava Tube from the 2012-2013 Eruption of the Tolbachik Volcano, Kamchatka, Russia

Cu-rich magnesioferrite was found in vesicular basaltic trachyandesite in one of lava tubes (Duplex) that formed during the 2012-2013 eruption of the Tolbachik volcano, Kamchatka. This mineral is commonly associated with hematite, tenorite, halite, sylvite, and Ca-rich silicates (mainly, esseneite and Na-rich melilite) in high-temperature (800-1000 degrees C) reactionary zones (up to 100 mu m) covering vesicular rocks and lava stalactites in the Duplex tube. The mineral relationships of this assemblage indicate the following crystallization sequence: Ca-rich silicates + hematite -> Cu-rich magnesioferrite -> tenorite -> chlorides. This formed due to the reaction of hot gases containing Cu, alkalis, and Cl with solidified lava rock. The composition of magnesioferrite varies strongly in CuO (5.8-17.3 wt %; cuprospinel end-member-15-47 mol %), whereas the contents of other oxides are minor, indicating the main isomorphic substitution is Mg2+ Cu2+. Compositions with maximal CuO content nominally belong to Mg-rich cuprospinel: (Cu0.48Mg0.41Mn0.09Zn0.02Ca0.02) (Fe1.943+Al0.03Ti0.02)O-4. Increasing CuO content of the Duplex Cu-rich magnesioferrite is reflected in Raman spectra by moderate right shifting bands at approximate to 700-710 and 200-210 cm(-1) and the appearance of an additional band at 596 cm(-1). This supports the main isomorphic scheme and may indicate a degree of inversion in the spinel structure.Peer reviewe