Explicit eigenvalues of certain scaled trigonometric matrices

In a very recent paper "\emph{On eigenvalues and equivalent transformation of trigonometric matrices}" (D. Zhang, Z. Lin, and Y. Liu, LAA 436, 71--78 (2012)), the authors motivated and discussed a trigonometric matrix that arises in the design of finite impulse response (FIR) digital filters. The eigenvalues of this matrix shed light on the FIR filter design, so obtaining them in closed form was investigated. Zhang \emph{et al.}\ proved that their matrix had rank-4 and they conjectured closed form expressions for its eigenvalues, leaving a rigorous proof as an open problem. This paper studies trigonometric matrices significantly more general than theirs, deduces their rank, and derives closed-forms for their eigenvalues. As a corollary, it yields a short proof of the conjectures in the aforementioned paper.Comment: 7 pages; fixed Lemma 2, tightened inequalitie

Transculturating the modern : Zhang Ruogu\u27s literary life in 1930s Shanghai

Zhang Ruogu 張若谷(1905-1967), now known primarily as an urban writer,2 began his literary career by translating and commenting on French literature in newspapers and journals and subsequently published several urban stories. He was also an active advocate of urban life and played an important role in the introduction of the ideas of the French-style café gathering and European cultural trends. Zhang Ruogu’s literary activities, his admiration of French literature and culture, and his works inspired by the French literary works that he admired or translated, are the focus of investigation of this paper. From Paris to Shanghai and from 19th-century French literature to urban stories of Shanghai of the 1930s, these literary trends and works advanced through a process of translation and interpretation. What occurred during this translation and interpretation process? How does this examination aid us in understanding Zhang Ruogu’s own work and modern Chinese literature? This paper addresses Zhang Ruogu’s translations, adaptations and interpretations of French literature as well as his own literary works

Persistence of Kardar-Parisi-Zhang Interfaces

The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18 \pm 0.08$ and $\theta_- = 1.64 \pm 0.08$. Bounds on $\theta_\pm$ are derived from the height autocorrelation function under the assumption of Gaussian statistics. The autocorrelation exponent $\bar \lambda$ for a $d$--dimensional interface with roughness and dynamic exponents $\beta$ and $z$ is conjectured to be $\bar \lambda = \beta + d/z$. For a recently proposed discretization of the KPZ equation we find oscillatory persistence probabilities, indicating hidden temporal correlations.Comment: 4 pages, 3 figures, uses revtex and psfi

Resources required for exact remote state preparation

It has been shown [M.-Y. Ye, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 69, 022310 (2004)] that it is possible to perform exactly faithful remote state preparation using finite classical communication and any entangled state with maximal Schmidt number. Here we give an explicit procedure for performing this remote state preparation. We show that the classical communication required for this scheme is close to optimal for remote state preparation schemes of this type. In addition we prove that it is necessary that the resource state have maximal Schmidt number.Comment: 7 pages, 1 figur

Multiwavelength analysis as a probe of accretion and radiative processes in LINERs

We study the multiwavelength properties of an optically selected sample of Low Ionization Nuclear Emission-line Regions (LINERs), in an attempt to determine the accretion mechanism powering their central engine. We show how their X-ray spectral characteristics, and their spectral energy distribution compare to luminous AGN, and briefly discuss their connection to their less massive counter-parts galactic black-hole X-ray binaries.Comment: 2 Pages. Proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez & S. N. Zhang (eds.

Unusual electronic ground state of a prototype cuprate: band splitting of single CuO_2-plane Bi_2 Sr_(2-x) La_x CuO_(6+delta)

By in-situ change of polarization a small splitting of the Zhang-Rice singlet state band near the Fermi level has been resolved for optimum doped (x=0.4) Bi$_{2}$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta}$ at the (pi,0)-point (R.Manzke et al. PRB 63, R100504 (2001). Here we treat the momentum dependence and lineshape of the split band by photoemission in the EDC-mode with very high angular and energy resolution. The splitting into two destinct emissions could also be observed over a large portion of the major symmetry line $\Gamma$M, giving the dispersion for the individual contributions. Since bi-layer effects can not be present in this single-layer material the results have to be discussed in the context of one-particle removal spectral functions derived from current theoretical models. The most prominent are microscopic phase separation including striped phase formation, coexisting antiferromagnetic and incommensurate charge-density-wave critical fluctuations coupled to electrons (hot spots) or even spin charge separation within the Luttinger liquid picture, all leading to non-Fermi liquid like behavior in the normal state and having severe consequences on the way the superconducting state forms. Especially the possibilty of observing spinon and holon excitations is discussed.Comment: 5 pages, 4 figure