Simplification Methods for Sum-of-Squares Programs

A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem. The computation required to solve the feasibility problem depends on the number of monomials used in the decomposition. The Newton polytope is a method to prune unnecessary monomials from the decomposition. This method requires the construction of a convex hull and this can be time consuming for polynomials with many terms. This paper presents a new algorithm for removing monomials based on a simple property of positive semidefinite matrices. It returns a set of monomials that is never larger than the set returned by the Newton polytope method and, for some polynomials, is a strictly smaller set. Moreover, the algorithm takes significantly less computation than the convex hull construction. This algorithm is then extended to a more general simplification method for sum-of-squares programming.Comment: 6 pages, 2 figure

Is Zc(3900)Z_c(3900) a molecular state

Assuming the newly observed $Z_c(3900)$ to be a molecular state of $D\bar D^*(D^{*} \bar D)$, we calculate the partial widths of $Z_c(3900)\to J/\psi+\pi;\; \psi'+\pi;\; \eta_c+\rho$ and $D\bar D^*$ within the light front model (LFM). $Z_c(3900)\to J/\psi+\pi$ is the channel by which $Z_c(3900)$ was observed, our calculation indicates that it is indeed one of the dominant modes whose width can be in the range of a few MeV depending on the model parameters. Similar to $Z_b$ and $Z_b'$, Voloshin suggested that there should be a resonance $Z_c'$ at 4030 MeV which can be a molecular state of $D^*\bar D^*$. Then we go on calculating its decay rates to all the aforementioned final states and as well the $D^*\bar D^*$. It is found that if $Z_c(3900)$ is a molecular state of ${1\over\sqrt 2}(D\bar D^*+D^*\bar D)$, the partial width of $Z_c(3900)\to D\bar D^*$ is rather small, but the rate of $Z_c(3900)\to\psi(2s)\pi$ is even larger than $Z_c(3900)\to J/\psi\pi$. The implications are discussed and it is indicated that with the luminosity of BES and BELLE, the experiments may finally determine if $Z_c(3900)$ is a molecular state or a tetraquark.Comment: 17 pages, 6 figures, 3 table

Calorific values and ash contents of different organs of Masson pine (Pinus massoniana) in southern China

Calorific values of plants are important indices for evaluating and reflecting material cycle and energy conversion in forest ecosystems. Based on the data of Masson Pine (Pinus massoniana) in southern China, the calorific values (CVs) and ash contents (ACs) of different plant organs were analyzed systematically using hypothesis test and regression analysis in this paper. The results show: (i) the CVs and ACs of different plant organs are almost significantly different, and the order by AFCV (ash-free calorific value) from the largest to the smallest is foliage (23.55 kJ/g), branches (22.25 kJ/g), stem bark (21.71 kJ/g), root (21.52 kJ/g) and stem wood (21.35 kJ/g); and the order by AC is foliage (2.35%), stem bark (1.44%), root (1.42%), branches (1.08%) and stem wood (0.33%); (ii) the CVs and ACs of stem woods on top, middle and lower sections are significantly different, and the CVs are increasing from top to lower sections of trunk while the ACs are decreasing; (iii) the mean GCV (gross calorific value) and AFCV of aboveground part are larger than those of belowground part (roots), and the differences are also statistically significant; (iv) the CVs and ACs of different organs are related, to some extent, to diameter, height and origin of the tree, but the influence degrees of the factors on CVs and ACs are not the same

Radio Sources in the NCP Region Observed with the 21 Centimeter Array

We present a catalog of 624 radio sources detected around the North Celestial Pole (NCP) with the 21 Centimeter Array (21CMA), a radio interferometer dedicated to the statistical measurement of the epoch of reionization (EoR). The data are taken from a 12 h observation made on 2013 April 13, with a frequency coverage from 75 to 175 MHz and an angular resolution of ~ 4 arcmin. The catalog includes flux densities at eight sub-bands across the 21CMA bandwidth and provides the in-band spectral indices for the detected sources. To reduce the complexity of interferometric imaging from the so-called "w" term and ionospheric effects, the present analysis are restricted to the east-west baselines within 1500 m only. The 624 radio sources are found within 5 degrees around the NCP down to ~ 0.1 Jy. Our source counts are compared, and also exhibit a good agreement, with deep low-frequency observations made recently with the GMRT and MWA. In particular, for fainter radio sources below ~ 1 Jy, we find a flattening trend of source counts towards lower frequencies. While the thermal noise (~0.4 mJy) is well controlled to below the confusion limit, the dynamical range (~10^4) and sensitivity of current 21CMA imaging is largely limited by calibration and deconvolution errors, especially the grating lobes of very bright sources, such as 3C061.1, in the NCP field which result from the regular spacings of the 21CMA. We note that particular attention should be paid to the extended sources, and their modeling and removals may constitute a large technical challenge for current EoR experiments. Our analysis may serve as a useful guide to design of next generation low-frequency interferometers like the Square Kilometre Array.Comment: 16 pages, 21 figures, 7 tables, 1 machine readable table, accepted for publication in Ap