The Lyman <span class='mathrm'>α</span> and Lyman <span class='mathrm'>β</span> lines in solar coronal streamers

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Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation

This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twisted derivations include regular derivations, difference and $q$-difference operators and superderivatives as special cases. Remarkably, the formulae for the iteration of Darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants. As an example, we revisit the Darboux transformations for the Manin-Radul super KdV equation, studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140, (1997). The new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants, covering all cases at once, rather than using several subcases. Then, by using a known relationship between quasideterminants and superdeterminants, we obtain expressions for these solutions as ratios of superdeterminants. This coincides with the results of Liu and Ma\~nas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression. Finally, we obtain another type of quasideterminant solutions to the Main-Radul super KdV equation constructed from its binary Darboux transformations. These can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary Darboux transformations in earlier work on this topic

ASAP : towards accurate, stable and accelerative penetrating-rank estimation on large graphs

Pervasive web applications increasingly require a measure of similarity among objects. Penetrating-Rank (P-Rank) has been one of the promising link-based similarity metrics as it provides a comprehensive way of jointly encoding both incoming and outgoing links into computation for emerging applications. In this paper, we investigate P-Rank efficiency problem that encompasses its accuracy, stability and computational time. (1) We provide an accuracy estimate for iteratively computing P-Rank. A symmetric problem is to find the iteration number K needed for achieving a given accuracy ε. (2) We also analyze the stability of P-Rank, by showing that small choices of the damping factors would make P-Rank more stable and well-conditioned. (3) For undirected graphs, we also explicitly characterize the P-Rank solution in terms of matrices. This results in a novel non-iterative algorithm, termed ASAP , for efficiently computing P-Rank, which improves the CPU time from O(n 4) to O( n 3 ). Using real and synthetic data, we empirically verify the effectiveness and efficiency of our approaches

Spectral properties of photon pairs generated by spontaneous four wave mixing in inhomogeneous photonic crystal fibers

The photonic crystal fiber (PCF) is one of the excellent media for generating photon pairs via spontaneous four wave mixing. Here we study how the inhomogeneity of PCFs affect the spectral properties of photon pairs from both the theoretical and experimental aspects. The theoretical model shows that the photon pairs born in different place of the inhomogeneous PCF are coherently superposed, and a modulation in the broadened spectrum of phase matching function will appear, which prevents the realization of spectral factorable photon pairs. In particular, the inhomogeneity induced modulation can be examined by measuring the spectrum of individual signal or idler field when the asymmetric group velocity matching is approximately fulfilled. Our experiments are performed by tailoring the spectrum of pulsed pump to satisfy the specified phase matching condition. The observed spectra of individual signal photons, which are produced from different segments of the 1.9 m inhomogeneous PCF, agree with the theoretical predictions. The investigations are not only useful for fiber based quantum state engineering, but also provide a dependable method to test the homogeneity of PCF.Comment: to appear in Phys. Rev.

Systemic risk in dynamical networks with stochastic failure criterion

Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use dynamical network approach to evaluate the collective financial failure---systemic risk---quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided on sub-periods, where within each sub-period banks may contiguously fail due to links to either (i) assets or (ii) other banks, controlled by two parameters, probability of internal failure $p$ and threshold $T_h$ ("solvency" parameter). The systemic risk non-linearly increases with $p$ and decreases with average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller $T_h$), the smaller the systemic risk---for some $T_h$ values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic (ii) controlled by probability $p_2$---a condition for the bank to be solvent (active) is stochastic---the systemic risk decreases with decreasing $p_2$. We analyse asset allocation for the U.S. banks.Comment: 7 pages, 7 figure

Low-temperature thermal conductivity of Dy_2Ti_2O_7 and Yb_2Ti_2O_7 single crystals

We study the low-temperature thermal conductivity (\kappa) of Dy_2Ti_2O_7 and Yb_2Ti_2O_7 single crystals in magnetic fields up to 14 T along the [111], [100] and [110] directions. The main experimental findings for Dy_2Ti_2O_7 are: (i) the low-T \kappa(H) isotherms exhibit not only the step-like decreases at the low-field (< 2 T) magnetic transitions but also obvious field dependencies in high fields (> 7 T); (ii) at T \le 0.5 K, the \kappa(H) curves show anisotropic irreversibility in low fields, that is, the \kappa(H) hysteresis locates at the first-order transition with H \parallel [100] and [110], while it locates between two successive transitions with H \parallel [111]; (iii) the \kappa in the hysteresis loops for H \parallel [100] and [110] show an extremely slow relaxation with the time constant of \sim 1000 min. The main experimental findings for Yb_2Ti_2O_7 are: (i) the zero-field \kappa(T) show a kink-like decrease at the first-order transition (\sim 200 mK) with decreasing temperature; (ii) the low-T \kappa(H) isotherms show a decrease in low field and a large enhancement in high fields; (iii) the low-T \kappa(H) curves show a sharp minimum at 0.5 T for H \parallel [110] and [111]. The roles of monopole excitations, field-induced transitions, spin fluctuations and magnetoelastic coupling are discussed.Comment: 15 pages, 11 figures, accepted for publication in Phys. Rev.

Imaging ionospheric inhomogeneities using spaceborne synthetic aperture radar

We present a technique and results of 2-D imaging of Faraday rotation and total electron content using spaceborne L band polarimetric synthetic aperture radar (PolSAR). The results are obtained by processing PolSAR data collected using the Phased Array type L-band Synthetic Aperture Radar (PALSAR) on board the Advanced Land Observation Satellite. Distinguished ionospheric inhomogeneities are captured in 2-D images from space with relatively high resolutions of hundreds of meters to a couple of kilometers in auroral-, middle-, and low-latitude regions. The observed phenomena include aurora-associated ionospheric enhancement arcs, the middle-latitude trough, traveling ionospheric disturbances, and plasma bubbles, as well as ionospheric irregularities. These demonstrate a new capability of spaceborne synthetic aperture radar that will not only provide measurements to correction of ionospheric effects in Earth science imagery but also significantly benefit ionospheric studies