On the Birkhoff factorization problem for the Heisenberg magnet and nonlinear Schroedinger equations

A geometrical description of the Heisenberg magnet (HM) equation with classical spins is given in terms of flows on the quotient space $G/H_+$ where $G$ is an infinite dimensional Lie group and $H_+$ is a subgroup of $G$. It is shown that the HM flows are induced by an action of $\mathbb{R}^2$ on $G/H_+$, and that the HM equation can be integrated by solving a Birkhoff factorization problem for $G$. For the HM flows which are Laurent polynomials in the spectral variable we derive an algebraic transformation between solutions of the nonlinear Schroedinger (NLS) and Heisenberg magnet equations. The Birkhoff factorization for $G$ is treated in terms of the geometry of the Segal-Wilson Grassmannian $Gr(H)$. The solution of the problem is given in terms of a pair of Baker functions for special subspaces of $Gr(H)$. The Baker functions are constructed explicitly for subspaces which yield multisoliton solutions of NLS and HM equations.Comment: To appear in Journal of Mathematical Physic

On the Topological Resonance Energy of Coumarin and Its Derivates

Topological resonance energies of coumarin and the following derivatives: 3-hydroxycoumarin, 4-hydroxycoumarin, 3,4-dihydro-. xycoumarin, 4,6-dihydroxycoumarin, 4,5,7-trihydroxycoumarin, 3- -carboxy-4-hydroxycoumarin, 3-bromo-4-hydroxycoumarin, and 6-bromo-4-hydroxycoumarin, are reported. Theoretical predictions that these all coumarins should exhibit aromatic properties are sustained by the ample experimental evidence. In addition, coumarin and isocoumarin are predicted to be much more stable than the corresponding quinonoid isomer

Neke ekološke karakteristike potočne vode

The water of a mountain brook was analysed and selected water quality parameters were determined. The pristine mountain brook water contained the smallest numbers of microorganisms whereas in the polluted water body downstream, the values of chemical oxygen demand, biochemical oxygen demand after five days and the count of specific indicator organisms (faecal coliforms) were increased.Ispitana su osnovna obilježja vodotoka Veliki Potok koji izvire u Zagrebačkoj gori i teče kroz zagrebačke općine Črnomerec i Trešnjevka. Uzorci vode uzimani su na sedam mjesta duž vodotoka i određivani su fizikalni (temperatura, pH, dubina), kemijski (otopljeni kisik, kemijska potrošnja kisika) i biološki (ukupni broj mikroorganizama, najvjerojatniji broj koliformnih bakterija, sulfitore-ducirajuće bakterije, biološka potrošnja kisika) pokazatelji onečišćenja vodotoka. Ustanovljeno je da je voda na izvorištu vrlo čista (prva kalegorija), no zbog aktivnosti okolnog stanovništva ona se postepeno zagađuje tako da pri utoku u potok Kustošak poprima karakteristike vodotoka četvrte kategorije kojom su obuhvaćene sve one vode koje se ne smiju koristiti za piće, u prehrambenoj industriji, za uzgoj riba i rekreaciju

Mapping the Asymmetric Thick Disk: The Hercules Thick Disk Cloud

The stellar asymmetry of faint thick disk/inner halo stars in the first quadrant first reported by Larsen & Humphreys (1996) and investigated further by Parker et al. (2003, 2004) has been recently confirmed by SDSS (Juric et al. 2008). Their interpretation of the excess in the star counts as a ringlike structure, however, is not supported by critical complimentary data in the fourth quadrant not covered by SDSS. We present stellar density maps from the Minnesota Automated Plate Scanner (MAPS) Catalog of the POSS I showing that the overdensity does not extend into the fourth quadrant. The overdensity is most probably not a ring. It could be due to interaction with the disk bar, evidence for a triaxial thick disk, or a merger remnant/stream. We call this feature the Hercules Thick Disk Cloud.Comment: 11 pages, 5 figures, to be published in Astrophysical Journal Letter

Differential algebras on kappa-Minkowski space and action of the Lorentz algebra

We propose two families of differential algebras of classical dimension on kappa-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl super-algebra. We also propose a novel realization of the Lorentz algebra so(1,n-1) in terms of Grassmann-type variables. Using this realization we construct an action of so(1,n-1) on the two families of algebras. Restriction of the action to kappa-Minkowski space is covariant. In contrast to the standard approach the action is not Lorentz covariant except on constant one-forms, but it does not require an extra cotangent direction.Comment: 16 page

Electrodynamics on κ\kappa-Minkowski space-time

In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to non-commutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this non-commutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.Comment: 16 pages,minor changes, paragraph added on page 13, two new references added, to appear in Phys.Rev.

The Blue Tip of the Stellar Locus: Measuring Reddening with the SDSS

We present measurements of reddening due to dust using the colors of stars in the Sloan Digital Sky Survey (SDSS). We measure the color of main sequence turn-off stars by finding the "blue tip" of the stellar locus: the prominent blue edge in the distribution of stellar colors. The method is sensitive to color changes of order 18, 12, 7, and 8 mmag of reddening in the colors u-g, g-r, r-i, and i-z, respectively, in regions measuring 90' by 14'. We present maps of the blue tip colors in each of these bands over the entire SDSS footprint, including the new dusty southern Galactic cap data provided by the SDSS-III. The results disfavor the best fit O'Donnell (1994) and Cardelli et al. (1989) reddening laws, but are well described by a Fitzpatrick (1999) reddening law with R_V = 3.1. The SFD dust map is found to trace the dust well, but overestimates reddening by factors of 1.4, 1.0, 1.2, and 1.4 in u-g, g-r, r-i, and i-z, largely due to the adopted reddening law. In select dusty regions of the sky, we find evidence for problems in the SFD temperature correction. A dust map normalization difference of 15% between the Galactic north and south sky may be due to these dust temperature errors.Comment: 18 pages, 22 figure

Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

We construct realizations of the generators of the $\kappa$-Minkowski space and $\kappa$-Poincar\'{e} algebra as formal power series in the $h$-adic extension of the Weyl algebra. The Hopf algebra structure of the $\kappa$-Poincar\'{e} algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on $\kappa$-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the $\kappa$-Minkowski space.Comment: 20 pages. Accepted for publication in International Journal of Modern Physics