Probing the X-ray Variability of X-ray Binaries

Kilohertz quasi-periodic oscillations (kHz QPOs) has been regarded as representing the Keplerian frequency at the inner disk edge in the neutron star X-ray binaries. The so-called ``parallel tracks'' on the plot of the kHz QPO frequency vs. X-ray flux in neutron star X-ray binaries, on the other hand, show the correlation between the kHz QPO frequency and the X-ray flux on time scales from hours to days. This is suspected as caused by the variations of the mass accretion rate through the accretion disk surrounding the neutron star. We show here that by comparing the correlation between the kHz QPO frequency and the X-ray count rate on a certain QPO time scale observed approximately simultaneous in the Fourier power spectra of the X-ray light curve, we have found evidences that the X-ray flux of millihertz QPOs in neutron star X-ray binaries is generated inside the inner disk edge if adopting that the kilohertz QPO frequency is an orbital frequency at the inner disk edge. This approach could be applied to other variability components in X-ray binaries.Comment: 4 pages including 1 figure, To appear in "High Energy Processes and Phenomena in Astrophysics, IAU Symposium 214", X. Li, Z. Wang, V. Trimble (eds

Fingerprint of dynamical charge/spin correlations in the tunneling spectra of colossal magnetoresistive manganites

We present temperature-dependent scanning tunneling spectroscopy measurements on $La_{1-x}Ca_{x}MO_{3}$ ($x\sim0.33$) films with different degrees of biaxial strain. A depletion in normalized conductance around the Fermi level is observed both above and below the insulator-to-metal transition temperature $T_{MI}$, for weakly as well as highly-strained films. This pseudogap-like depletion globally narrows on cooling. The zero-bias conductance decreases on cooling in the insulating phase, reaches a minimum close to $T_{MI}$ and increases on cooling in the metallic phase, following the trend of macroscopic conductivity. These results support a recently proposed scenario in which dynamical short-range antiferromagnetic/charge order correlations play a preeminent role in the transport properties of colossal magnetoresistive manganites [R. Yu \textit{et al}., Phys. Rev. B \textbf{77}, 214434 (2008)].Comment: 9 pages, 4 figure

On generalized trigonometric functions and series of rational functions

Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$. We will show that those generalized trigonometric functions have algebraic identities which generalizes the well known $\sin^2(x)+\cos^2(x)=1$. One application of the generalized trigonometric functions is evaluating infinite series of rational functions.Comment: 14 page

On hyperbolic systems with time dependent H\"older characteristics

In this paper we study the well-posedness of weakly hyperbolic systems with time dependent coefficients. We assume that the eigenvalues are low regular, in the sense that they are H\"older with respect to $t$. In the past these kind of systems have been investigated by Yuzawa \cite{Yu:05} and Kajitani \cite{KY:06} by employing semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform property of the eigenvalues, we improve the Gevrey well-posedness result of \cite{Yu:05} and we obtain well-posedness in spaces of ultradistributions as well. Our main idea is a reduction of the system to block Sylvester form and then the formulation of suitable energy estimates inspired by the treatment of scalar equations in \cite{GR:11