More on the Isomorphism SU(2)⊗SU(2)≅SO(4)SU(2)\otimes SU(2)\cong SO(4)

In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3

Optical Spectroscopy of Type Ia Supernovae

We present 432 low-dispersion optical spectra of 32 Type Ia supernovae (SNe Ia) that also have well-calibrated light curves. The coverage ranges from 6 epochs to 36 epochs of spectroscopy. Most of the data were obtained with the 1.5m Tillinghast telescope at the F. L. Whipple Observatory with typical wavelength coverage of 3700-7400A and a resolution of ~7A. The earliest spectra are thirteen days before B-band maximum; two-thirds of the SNe were observed before maximum brightness. Coverage for some SNe continues almost to the nebular phase. The consistency of the method of observation and the technique of reduction makes this an ideal data set for studying the spectroscopic diversity of SNe Ia.Comment: Accepted for publication in the Astronomical Journal, 109 pages (including data table), 44 figures, full resolution figures at http://www.noao.edu/noao/staff/matheson/Iaspec.ps.g

Distances on the tropical line determined by two points

Let $p',q'\in R^n$. Write $p'\sim q'$ if $p'-q'$ is a multiple of $(1,\ldots,1)$. Two different points $p$ and $q$ in $R^n/\sim$ uniquely determine a tropical line $L(p,q)$, passing through them, and stable under small perturbations. This line is a balanced unrooted semi--labeled tree on $n$ leaves. It is also a metric graph. If some representatives $p'$ and $q'$ of $p$ and $q$ are the first and second columns of some real normal idempotent order $n$ matrix $A$, we prove that the tree $L(p,q)$ is described by a matrix $F$, easily obtained from $A$. We also prove that $L(p,q)$ is caterpillar. We prove that every vertex in $L(p,q)$ belongs to the tropical linear segment joining $p$ and $q$. A vertex, denoted $pq$, closest (w.r.t tropical distance) to $p$ exists in $L(p,q)$. Same for $q$. The distances between pairs of adjacent vertices in $L(p,q)$ and the distances \dd(p,pq), \dd(qp,q) and \dd(p,q) are certain entries of the matrix $|F|$. In addition, if $p$ and $q$ are generic, then the tree $L(p,q)$ is trivalent. The entries of $F$ are differences (i.e., sum of principal diagonal minus sum of secondary diagonal) of order 2 minors of the first two columns of $A$.Comment: New corrected version. 31 pages and 9 figures. The main result is theorem 13. This is a generalization of theorem 7 to arbitrary n. Theorem 7 was obtained with A. Jim\'enez; see Arxiv 1205.416

On the Low-Energy Effective Action of N=2 Supersymmetric Yang-Mills Theory

We investigate the perturbative part of Seiberg's low-energy effective action of N=2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on $U(1)_R$ anomaly and non-perturbative $\beta$-function arguments.Comment: 27 pages, RevTex, no figure

Scattering matrices and expansion coefficients of Martian analogue palagonite particles

We present measurements of ratios of elements of the scattering matrix of Martian analogue palagonite particles for scattering angles ranging from 3 to 174 degrees and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0 to 180 degrees. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty Martian atmosphere.Comment: 34 pages 7 figures 1 tabl

Choosing a measure of GRB brightness that approaches a standard candle

Studies using the GRB brightness as a distance indicator require a measure of brightness with a small intrinsic dispersion (close to a standard candle). There is unfortunately no general agreement on the definition of such a quantity. We show here that the comparison of the size-frequency curves obtained with various measures of brightness can be used to select the quantity which is closer to a standard candle. Our method relies on a few general assumptions on the burster spatial distribution, namely that nearby bursters are homogeneously distributed in an Euclidean space with no density or luminosity evolution. We apply it to 5 measures of GRB brightness in the Current BATSE Catalog and we find that the GRB size-frequency distribution depends significantly on the energy window used to measure the GRB brightness. The influence of the time window being, in comparison, negligible. Our method suggests that the best distance indicator in this Catalog is the fluence measured below 100 keV, indicating that GRB luminosities have a smaller intrinsic dispersion below 100 keV than above.Comment: 5 pages (LateX), 2 Postscript figures, Proceedings of the 4th Huntsville GRB Worksho

Sampling of conformational ensemble for virtual screening using molecular dynamics simulations and normal mode analysis

Aim: Molecular dynamics simulations and normal mode analysis are well-established approaches to generate receptor conformational ensembles (RCEs) for ligand docking and virtual screening. Here, we report new fast molecular dynamics-based and normal mode analysis-based protocols combined with conformational pocket classifications to efficiently generate RCEs. Materials \& methods: We assessed our protocols on two well-characterized protein targets showing local active site flexibility, dihydrofolate reductase and large collective movements, CDK2. The performance of the RCEs was validated by distinguishing known ligands of dihydrofolate reductase and CDK2 among a dataset of diverse chemical decoys. Results \& discussion: Our results show that different simulation protocols can be efficient for generation of RCEs depending on different kind of protein flexibility