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

Effects of land incremental value allocation on rural operational construction land (ROCL) under market mechanism: case study in China

The use of the market mechanism to convert the rural operational construction land (ROCL) into urban construction land without ownership changes is currently being introduced into reform pilot projects in China, changing the only form of governmental expropriation in the past. The new system allows rural collective economic organizations and members of the rural collective economy to directly participate in the allocation of land incremental value increases due to changes in land use. This replaces the previous way of allocating only the original use compensation from the government. This paper investigates the collectively owned new system, to establish the positive effects and shortcoming of the new model. Three cases are applied for the analysis using inductive-deductive reasoning methodology based on the property right and landrent theories. We have found that local government land adjustment charges on the transactions of rural construction land are suggested to be from 16 to 20 percent. The share ownership quantification model (SOQM) of land incremental value allocation between the collective economic organizations and members is effective and beneficial to the development of the rural collective economy and its members

Momentum Distribution of Near-Zero-Energy Photoelectrons in the Strong-Field Tunneling Ionization in the Long Wavelength Limit

We investigate the ionization dynamics of Argon atoms irradiated by an ultrashort intense laser of a wavelength up to 3100 nm, addressing the momentum distribution of the photoelectrons with near-zero-energy. We find a surprising accumulation in the momentum distribution corresponding to meV energy and a \textquotedblleft V"-like structure at the slightly larger transverse momenta. Semiclassical simulations indicate the crucial role of the Coulomb attraction between the escaping electron and the remaining ion at extremely large distance. Tracing back classical trajectories, we find the tunneling electrons born in a certain window of the field phase and transverse velocity are responsible for the striking accumulation. Our theoretical results are consistent with recent meV-resolved high-precision measurements.Comment: 5 pages, 4 figure

Spectroscopic Properties of QSOs Selected from Ultraluminous Infrared Galaxy Samples

We performed spectroscopic observations for a large infrared QSO sample with a total of 25 objects. The sample was compiled from the QDOT redshift survey, the 1 Jy ULIRGs survey and a sample obtained by a cross-correlation study of the IRAS Point Source Catalogue with the ROSAT All Sky Survey Catalogue. Statistical analyses of the optical spectra show that the vast majority of infrared QSOs have narrow permitted emission lines (with FWHM of Hbeta less than 4000 km/s) and more than 60% of them are luminous narrow line Seyfert 1 galaxies. Two of the infrared QSOs are also classified as low ionization BAL QSOs. More than 70% of infrared QSOs are moderately or extremely strong Fe II emitters. This is the highest percentage of strong Fe II emitters in all subclasses of QSO/Seyfert 1 samples. We found that the Fe II to Hbeta, line ratio is significantly correlated with the [OIII]5007 peak and Hbeta blueshift. Soft X-ray weak infrared QSOs tend to have large blueshifts in permitted emission lines and significant Fe II48,49 (5100--5400 A) residuals relative to the Boroson & Green Fe II template. If the blueshifts in permitted lines are caused by outflows, then they appear to be common in infrared QSOs. As the infrared-selected QSO sample includes both luminous narrow line Seyfert 1 galaxies and low ionization BAL QSOs, it could be a useful laboratory to investigate the evolutionary connection among these objects.Comment: 35 pages,14 figures, 4 tables, accepted for publication in A

Formation mechanism and control of the spiral marks of three-roll skew-rolled hollow axles

The spiral marks is one of the main surface quality defects of the three-roll skew rolled hollow axles. In order to eliminate the spiral marks, it is necessary to clarify the cause of the spiral marks on the surface of the rolled piece. Based on the analysis of the kinematics of the three-roll skew rolled hollow axles, the spiral marks is caused by the spiral pitch of the rolled piece being larger than the width of the finishing section of the roller. Increasing the rotation speed of the roller can reduce the spiral pitch of the rolled piece, thereby avoiding the appearance of spiral marks. The correctness of the proposed condition for preventing the defect of spiral marks is verified by simulation