On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors

In estimating frequencies given that the signal waveforms are undersampled multiple times, Xia et. al. proposed to use a generalized version of Chinese remainder Theorem (CRT), where the moduli are $M_1, M_2, \cdots, M_k$ which are not necessarily pairwise coprime. If the errors of the corrupted remainders are within \tau=\sds \max_{1\le i\le k} \min_{\stackrel{1\le j\le k}{j\neq i}} \frac{\gcd(M_i,M_j)}4, their schemes can be used to construct an approximation of the solution to the generalized CRT with an error smaller than $\tau$. Accurately finding the quotients is a critical ingredient in their approach. In this paper, we shall start with a faithful historical account of the generalized CRT. We then present two treatments of the problem of solving generalized CRT with erroneous remainders. The first treatment follows the route of Wang and Xia to find the quotients, but with a simplified process. The second treatment considers a simplified model of generalized CRT and takes a different approach by working on the corrupted remainders directly. This approach also reveals some useful information about the remainders by inspecting extreme values of the erroneous remainders modulo $4\tau$. Both of our treatments produce efficient algorithms with essentially optimal performance. Finally, this paper constructs a counterexample to prove the sharpness of the error bound $\tau$

The Physical Connections Among IR QSOs, PG QSOs and Narrow-Line Seyfert 1 Galaxies

We study the properties of infrared-selected QSOs (IR QSOs), optically-selected QSOs (PG QSOs) and Narrow Line Seyfert 1 galaxies (NLS1s). We compare their properties from the infrared to the optical and examine various correlations among the black hole mass, accretion rate, star formation rate and optical and infrared luminosities. We find that the infrared excess in IR QSOs is mostly in the far infrared, and their infrared spectral indices suggest that the excess emission is from low temperature dust heated by starbursts rather than AGNs. The infrared excess is therefore a useful criterion to separate the relative contributions of starbursts and AGNs. We further find a tight correlation between the star formation rate and the accretion rate of central AGNs for IR QSOs. The ratio of the star formation rate and the accretion rate is about several hundred for IR QSOs, but decreases with the central black hole mass. This shows that the tight correlation between the stellar mass and the central black hole mass is preserved in massive starbursts during violent mergers. We suggest that the higher Eddington ratios of NLS1s and IR QSOs imply that they are in the early stage of evolution toward classical Seyfert 1's and QSOs, respectively.Comment: 32 pages, 6 figures, accepted by Ap

Skyrmion-skyrmion and skyrmion-edge repulsions in skyrmion-based racetrack memory

Magnetic skyrmions are promising for building next-generation magnetic memories and spintronic devices due to their stability, small size and the extremely low currents needed to move them. In particular, skyrmion-based racetrack memory is attractive for information technology, where skyrmions are used to store information as data bits instead of traditional domain walls. Here we numerically demonstrate the impacts of skyrmion-skyrmion and skyrmion-edge repulsions on the feasibility of skyrmion-based racetrack memory. The reliable and practicable spacing between consecutive skyrmionic bits on the racetrack as well as the ability to adjust it are investigated. Clogging of skyrmionic bits is found at the end of the racetrack, leading to the reduction of skyrmion size. Further, we demonstrate an effective and simple method to avoid the clogging of skyrmionic bits, which ensures the elimination of skyrmionic bits beyond the reading element. Our results give guidance for the design and development of future skyrmion-based racetrack memory.Comment: 15 pages, 6 figure

A review of process advancement of novel metal spinning

Metal spinning technology has seen a rapid development in recent years. Novel spinning processes, such as non-axisymmetrical spinning, non-circular cross-section spinning and tooth-shaped spinning, are being developed. This has challenged the limitation of traditional spinning technology being used for manufacturing axisymmetrical, circular cross-section, and uniform wall-thickness parts. In this paper, the classification of the traditional spinning processes is proposed based on the material deformation characteristics, the relative position between roller and blank, mandrel spinning and mandrel-free spinning, and temperature of the blank during spinning. The advancement of recently developed novel spinning processes and corresponding tool design and equipment development are reviewed. The classification of the novel spinning processes is proposed based on the relative position between the rotating axes, the geometry of cross-section and the variation of wall-thickness of the spun parts. The material deformation mechanism, processing failures and spun part defects of the aforementioned three groups of novel spinning processes are discussed by analyzing four representative spinning processes of industrial applications. Furthermore, other novel spinning processes and their classification as reported in the literature are summarized

Luminous Infrared Galaxies in the Local Universe

We study the morphology and star formation properties of 159 local luminous infrared galaxy (LIRG) using multi-color images from Data Release 2 (DR2) of the Sloan Digital Sky Survey (SDSS). The LIRGs are selected from a cross-correlation analysis between the IRAS survey and SDSS. They are all brighter than 15.9 mag in the r-band and below redshift ~ 0.1, and so can be reliably classified morphologically. We find that the fractions of interacting/merging and spiral galaxies are ~ 48% and ~ 40% respectively. Our results complement and confirm the decline (increase) in the fraction of spiral (interacting/merging) galaxies from z ~1 to z ~ 0.1, as found by Melbourne, Koo & Le Floc'h (2005). About 75% of spiral galaxies in the local LIRGs are barred, indicating that bars may play an important role in triggering star formation rates > 20 M_{sun}/yr in the local universe. Compared with high redshift LIRGs, local LIRGs have lower specific star formation rates, smaller cold gas fractions and a narrower range of stellar masses. Local LIRGs appear to be either merging galaxies forming intermediate mass ellipticals or spiral galaxies undergoing high star formation activities regulated by bars.Comment: 22 pages, 5 figures, accepted for publication in ApJ, title changed, typos corrected,major revisions following referee's comments,updated reference