The Hudson Laboratories microbarograph system: Results and future trends

The ultralow frequency microbarograph system is described, and some results for periods ranging from a few minutes to a few hours are presented. Problems encountered during operation of the system are also discussed

Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)

A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural representation V ([1,0,...,0]) of gl(m|n) with highest weight (1,0,. . . ,0) are computed. Both results are steps for the explicit construction of the parastatistics Fock space.Comment: 16 page

Extremal projectors for contragredient Lie (super)symmetries (short review)

A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as their quantum $q$-analogs) is given. Some bibliographic comments on the applications of extremal projectors are presented.Comment: 21 pages, LaTeX; typos corrected, references adde

Cybersecurity concepts’ taxonomy

Based on the previously accepted taxonomy of concepts, a classification of concepts is proposed that is related to cybersecurity (CS) of objects and currently has the maximum unambiguous correspondence between the terms denoting these concepts and the concepts themselves. When constructing the classification, an attempt was made to apply the fundamentals of the taxonomy theory (systematics), the results of which led to the conclusion that the considered structures of concept systems will be hierarchical (the basic principle of taxonomy) under certain conditions (for example, when using only concepts that relate to the categories of the subject (object)), process, or property). The approach considered made it possible to form a group of terms directly related to the concepts from the proposed classification. This set can be considered as a terminology system related to the object’s CS. The proposed terms and their definitions do not contradict similar ones being used, but are distinguished by consistency in relation to the terms (definitions) themselves and corresponding concepts, and also have a universal application, which allows their use for almost any CS objects related to information (for example, information and automated systems, informatization systems, sociotechnical systems, cyber-physical systems and information as an object). The results obtained also have practical significance for education in the formation of a modern, methodologically sound conceptual base of students

On irreducibility of tensor products of evaluation modules for the quantum affine algebra

Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules.Comment: 22 pages. Some references are adde

On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization

We study classical twists of Lie bialgebra structures on the polynomial current algebra $\mathfrak{g}[u]$, where $\mathfrak{g}$ is a simple complex finite-dimensional Lie algebra. We focus on the structures induced by the so-called quasi-trigonometric solutions of the classical Yang-Baxter equation. It turns out that quasi-trigonometric $r$-matrices fall into classes labelled by the vertices of the extended Dynkin diagram of $\mathfrak{g}$. We give complete classification of quasi-trigonometric $r$-matrices belonging to multiplicity free simple roots (which have coefficient 1 in the decomposition of the maximal root). We quantize solutions corresponding to the first root of $\mathfrak{sl}(n)$.Comment: 41 pages, LATE

Q-power function over Q-commuting variables and deformed XXX, XXZ chains

We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2). We determine the corresponding deformed trigonometric and rational quantum R-matrices, which then are used in the computation of deformed XXX and XXZ Hamiltonians.Comment: LaTeX, 12 page

The Stellar Populations of the Cetus Dwarf Spheroidal Galaxy

We present Hubble Space Telescope Wide Field Planetary Camera 2 photometry in the V and I passbands of the recently discovered Local Group dwarf spheroidal galaxy in Cetus. Our color-magnitude diagram extends from above the first ascent red giant branch (RGB) tip to approximately half a magnitude below the horizontal branch (HB). Adopting a reddening of E(B-V) = 0.03, the magnitude of the RGB tip yields a distance modulus of (m-M)o = 24.46 +/- 0.14. After applying the reddening and distance modulus, we have utilized the color distribution of RGB stars to determine a mean metal abundance of [Fe/H] = -1.7 on the Zinn & West scale with an intrinsic internal abundance dispersion of +/-0.2 dex. An indirect calculation of the HB morphology of Cetus based on the mean dereddened HB color yields (B-R)/(B+V+R) = -0.91 +/- 0.09, which represents an HB that is redder than what can be attributed solely to Cetus' metal abundance. As such, Cetus suffers from the `second parameter effect' in which another parameter besides metallicity is controlling the HB morphology. If we adopt the conventional `age hypothesis' explanation for the second parameter effect, then this implies that Cetus is 2-3 Gyr younger than Galactic globular clusters at its metallicity.Comment: 13 pages, 8 figures, Accepted for publication in the March 10, 2002 Ap

Generalized Paraxial Ray Trace Procedure Derived from Geodesic Deviation

Paraxial ray tracing procedures have become widely accepted techniques for acoustic models in seismology and underwater acoustics. To date a generic form of these procedures including fluid motion and time dependence has not appeared in the literature. A detailed investigation of the characteristic curves of the equations of hydrodynamics allows for an immediate generalization of the procedure to be extracted from the equation form geodesic deviation. The general paraxial ray trace equations serve as an ideal supplement to ordinary ray tracing in predicting the deformation of acoustic beams in random environments. The general procedure is derived in terms of affine parameterization and in a coordinate time parameterization ideal for application to physical acoustic ray propagation. The formalism is applied to layered media, where the deviation equation reduces to a second order differential equation for a single field with a general solution in terms of a depth integral along the ray path. Some features are illustrated through special cases which lead to exact solutions in terms of either ordinary or special functions.Comment: Original; 40 pages (double spaced), 1 figure Replaced version; 36 pages single spaced, 7 figures. Expanded content; Complete derivation of the equations from the equations of hydrodynamics, introduction of an auxiliary basis for three dimensional wave-front modeling. Typos in text and equations correcte

An E-ELT Case Study: Colour-Magnitude Diagrams of an Old Galaxy in the Virgo Cluster

One of the key science goals for a diffraction limited imager on an Extremely Large Telescope (ELT) is the resolution of individual stars down to faint limits in distant galaxies. The aim of this study is to test the proposed capabilities of a multi-conjugate adaptive optics (MCAO) assisted imager working at the diffraction limit, in IJHK$_s$ filters, on a 42m diameter ELT to carry out accurate stellar photometry in crowded images in an Elliptical-like galaxy at the distance of the Virgo cluster. As the basis for realistic simulations we have used the phase A studies of the European-ELT project, including the MICADO imager (Davies & Genzel 2010) and the MAORY MCAO module (Diolaiti 2010). We convolved a complex resolved stellar population with the telescope and instrument performance expectations to create realistic images. We then tested the ability of the currently available photometric packages STARFINDER and DAOPHOT to handle the simulated images. Our results show that deep Colour-Magnitude Diagrams (photometric error, $\pm$0.25 at I$\ge$27.2; H$\ge$25. and K$_s\ge$24.6) of old stellar populations in galaxies, at the distance of Virgo, are feasible at a maximum surface brightness, $\mu_V \sim$ 17 mag/arcsec$^2$ (down to M$_I > -4$ and M$_H \sim$ M$_K > -6$), and significantly deeper (photometric error, $\pm$0.25 at I$\ge$29.3; H$\ge$26.6 and K$_s\ge$26.2) for $\mu_V \sim$ 21 mag/arcsec$^2$ (down to M$_I \ge -2$ and M$_H \sim$ M$_K \ge -4.5$). The photometric errors, and thus also the depth of the photometry should be improved with photometry packages specifically designed to adapt to an ELT MCAO Point Spread Function. We also make a simple comparison between these simulations and what can be expected from a Single Conjugate Adaptive Optics feed to MICADO and also the James Webb Space Telescope.Comment: 17 pages, 22 figures, accepted on A&