Simultaneous optical and X-ray observations of flares and rotational modulation on the RS CVn binary HR 1099 (V711 Tau) from the MUSICOS 1998 campaign

We present simultaneous and continuous observations of the Hα, Hβ, He I D_3, Na I D_1,D_2 doublet and the Ca II H&K lines for the RS CVn system HR 1099. The spectroscopic observations were obtained during the MUSICOS 1998 campaign involving several observatories and instruments, both echelle and long-slit spectrographs. During this campaign, HR 1099 was observed almost continuously for more than 8 orbits of 2^d.8. Two large optical flares were observed, both showing an increase in the emission of Hα, Ca II H K, Hβ and He I D_3 and a strong filling-in of the Na I D_1, D_2 doublet. Contemporary photometric observations were carried out with the robotic telescopes APT-80 of Catania and Phoenix-25 of Fairborn Observatories. Maps of the distribution of the spotted regions on the photosphere of the binary components were derived using the Maximum Entropy and Tikhonov photometric regularization criteria. Rotational modulation was observed in Hα and He I D_3 in anti-correlation with the photometric light curves. Both flares occurred at the same binary phase (0.85), suggesting that these events took place in the same active region. Simultaneous X-ray observations, performed by ASM on board RXTE, show several flare-like events, some of which correlate well with the observed optical flares. Rotational modulation in the X-ray light curve has been detected with minimum flux when the less active G5 V star was in front. A possible periodicity in the X-ray flare-like events was also found.

Optical and ultraviolet observations of a strong flare in the young, single K2 dwarf LQ Hya

We present high-resolution optical echelle spectra and IUE observations during a strong flare on 1993 December 22 in the very active, young, rapidly rotating, single K2 dwarf LQ Hya. The initial impulsive phase of the flare, which started sometime between 2:42 ut and 4:07 ut, was characterized by strong optical continuum enhancement and blueshifted emission lines with broad wings. The optical chromospheric lines reached their maximum intensity at ≈ 5:31 ut, by which time the blueshift vanished and the optical continuum enhancement had sharply decreased. Thereafter, the line emission slowly decreased and the lines redshift in a gradual phase that lasted at least two more hours. The Mg II lines behaved similarly. Quiescent C IV flux levels were not recovered until 21 h later, though a data gap and a possible second flare make the interpretation uncertain. In addition to the typically flare-enhanced emission lines (e.g., H α and H β), we observe He I D_3 going into emission, plus excess emission (after subtraction of the quiescent spectrum) in other He I and several strong neutral metal lines (e.g., Mg I b). Flare enhancement of the far-ultraviolet continuum generally agrees with an Si I recombination model. We estimate the total flare energy, and discuss the broad components, asymmetries and Doppler shifts seen in some of the emission lines.

Auctioning versus grandfathering in cap-and-trade systems with market power and incomplete information

We compare auctioning and grandfathering as allocation mechanisms of emission permits when there is a secondary market with market power and firms have private information on their own abatement technologies. Based on real-life cases such as the EU ETS, we consider a multi-unit, multi-bid uniform auction. At the auction, each firm anticipates its role in the secondary market, either as a leader or a follower. This role affects each firms’ valuation of the permits (which are not common across firms) as well as their bidding strategies and it precludes the auction from generating a cost-effective allocation of permits, as it occurs in simpler auction models. Auctioning tends to be more cost-effective than grandfathering when the firms’ abatement cost functions are sufficiently different from one another, especially if the follower has lower abatement costs than the leader and the dispersion of the marginal costs is large enough.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.