Interlacing Log-concavity of the Boros-Moll Polynomials

We introduce the notion of interlacing log-concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq 0$. Interlacing log-concavity is stronger than the log-concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-concavity which implies that some classical combinatorial polynomials are interlacing log-concave.Comment: 10 page

Geometric phases induced in auxiliary qubits by many-body systems near its critical points

The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the qubit, respectively. As an example, we consider the XY spin-chain dephasingly couple to a qubit, the geometric phase induced in the qubit is presented and discussed. The results show that the geometric phase might be used to signal the critical points of the many-body system, and it tends to zero with the parameters of the many-body system going away from the critical points

Effect of Decoherence on the Dynamics of Bose-Einstein Condensates in a Double-well Potential

We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to environments. Two kinds of coupling are taken into account. With the first kind of coupling dominated, the decoherence can enhance the self-trapping by increasing the damping of the oscillations in the dynamics, while the decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.Comment: for color figures, see PR

A rapid staining-assisted wood sampling method for PCR-based detection of pine wood nematode Bursaphelenchus xylophilus in Pinus massoniana wood tissue

For reasons of unequal distribution of more than one nematode species in wood, and limited availability of wood samples required for the PCR-based method for detecting pinewood nematodes in wood tissue of Pinus massoniana, a rapid staining-assisted wood sampling method aiding PCR-based detection of the pine wood nematode Bursaphelenchus xylophilus (Bx) in small wood samples of P. massoniana was developed in this study. This comprised a series of new techniques: sampling, mass estimations of nematodes using staining techniques, and lowest limit Bx nematode mass determination for PCR detection. The procedure was undertaken on three adjoining 5-mg wood cross-sections, of 0.5 · 0.5 · 0.015 cm dimension, that were cut from a wood sample of 0.5 · 0.5 · 0.5 cm initially, then the larger wood sample was stained by acid fuchsin, from which two 5-mg wood cross-sections (that adjoined the three 5-mg wood cross-sections, mentioned above) were cut. Nematode-staining-spots (NSSs) in each of the two stained sections were counted under a microscope at 100· magnification. If there were eight or more NSSs present, the adjoining three sections were used for PCR assays. The B. xylophilus – specific amplicon of 403 bp (DQ855275) was generated by PCR assay from 100.00% of 5-mg wood cross-sections that contained more than eight Bx NSSs by the PCR assay. The entire sampling procedure took only 10 min indicating that it is suitable for the fast estimation of nematode numbers in the wood of P. massonina as the prelimary sample selections for other more expensive Bx-detection methods such as PCR assay

China's energy consumption in the building sector: A Statistical Yearbook-Energy Balance Sheet based splitting method

China's energy consumption in the building sector (BEC) is not counted as a separate type of energy consumption, but divided and mixed in other sectors in China's statistical system. This led to the lack of historical data on China's BEC. Moreover, previous researches' shortages such as unsystematic research on BEC, various estimation methods with complex calculation process, and difficulties in data acquisition resulted in “heterogeneous” of current BEC in China. Aiming to these deficiencies, this study proposes a set of China building energy consumption calculation method (CBECM) by splitting out the building related energy consumption mixed in other sectors in the composition of China Statistical Yearbook-Energy Balance Sheet. Then, China's BEC from 2000 to 2014 are estimated using CBECM and compared with other studies. Results show that, from 2000 to 2014, China's BEC increased 1.7 times, rising from 301 to 814 million tons of standard coal consumed, with the BEC percentage of total energy consumption stayed relatively stable between 17.7% and 20.3%. By comparison, we find that our results are reliable and the CBECM has the following advantages over other methods: data source is authoritative, calculation process is concise, and it is easy to obtain time series data on BEC etc. The CBECM is particularly suitable for the provincial government to calculate the local BEC, even in the circumstance with statistical yearbook available only