Gram Matrices of Mixed-State Ensembles

International Journal of Theoretical Physics - Gram matrices arise naturally in the consideration of pair-wise overlap of a family of vectors or quantum pure states, and play an important role in...     

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

Asymptotic Behavior of Least Energy Solutions for a Fractional Laplacian Eigenvalue Problem on ℝN

Acta Mathematica Sinica, English Series - We are interested in the existence and asymptotic behavior for the least energy solutions of the following fractional eigenvalue problem $$\left({\rm{P}}...     

Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by ${\text{TQS}}_{\lambda }\left(n\right)$, is a pair $\left(X,\mathrm{?}\right)$, where $X$ is an $n$‐set and $\mathrm{?}$ is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of $\mathrm{?}$. A ${\text{TQS}}_{\lambda }\left(n\right)$ is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS $\left(n\right)$ has been completely determined by Ji. In this paper, we show that there exists a pure ${\text{TQS}}_2\left(n\right)$ if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$. A corollary is that a simple ${\text{QS}}_4\left(n\right)$ also exists if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$.     

高压下β-InSe弹性常数、电子结构的第一性原理研究

基于密度泛函理论的第一性原理计算方法,本文研究了高压对β-InSe弹性常数、机械性能和电子结构的影响.在0～20 GPa范围内,随着压力的增大,β-InSe的晶格常数、晶胞体积逐渐减小,结构参数a/a_0、c/c_0、V/V_0单调减小.在0～12 GPa范围内,弹性模量G、E、B和泊松比v随着压力增大而增大,在16 GPa时大幅减小,G、E、B分别减小了34.9%、53.3%、82.9%.随着压力增大,Se-In和In-In原子之间的电荷密度增大,Se-In原子之间的共价键增强,层间距减小.而且,β-InSe在20 GPa时带隙消失,发生了半导体向半金属的相变.     

基质刚性影响声孔效应介导的单细胞基因转染

实验研究了基质刚性对单细胞质粒DNA转染效果的影响。实验采用高声压短脉冲(0.45MPa,10μs)条件的超声对培养在不同硬度凝胶基质(软的凝胶基质：0.2kPa,硬的凝胶基质：40kPa)上的力学敏感细胞NIH 3T3进行质粒DNA转染实验。实验结果表明,培养在硬的凝胶基质上的细胞,质粒DNA转染效率明显高于培养在软的凝胶基质上的细胞。进一步对质粒DNA进行荧光示踪可知培养在不同刚性基质上的细胞导入质粒DNA的方式不同。当细胞被培养在硬的凝胶基质上时,通过声致穿孔产生的小孔进入细胞内的质粒DNA更多,而培养在软的凝胶基质上的细胞,更多的质粒DNA可以通过非声致穿孔作用,例如内吞方式导入细胞。 细胞骨架蛋白分布规律表明,硬的凝胶基质上培养的细胞内有更多的F肌动蛋白微丝,可以更好地支撑起细胞的铺展形态,相对不容易发生内吞作用。而软的凝胶基质上培养的细胞内F肌动蛋白则更多以球形状态存在,细胞形貌骗向圆形,此时更容易发生胞吞作用。     

Effect of the dispersion on multipartite continuous-variable entanglement in optical parametric amplifier

Based on the quantum fluctuations, we adopt the method of generalized V1 criterion to investigate multipartite entanglement characteristics in an optical parametric amplification system with the consideration of dispersion. The nonlinear interaction becomes strong because of the existence of dispersion coefficient σ. Considering the influence of dispersion factor σ, with increasing the pump parameter μ, the value of minimum variance V1 decreases and the squeezing curve nearly equals 1/(1 + μ). The larger particle number N results in a smaller variance and higher entanglement.     

A self-penetrating and chemically stable zinc (ii)-organic framework as multi-responsive chemo-sensor to detect pesticide and antibiotics in water

Guided by the self-penetrating features can improve the stability of metal organic frameworks (MOFs), an unprecedented 3D self-penetrated framework, {[Zn (tptc)_0.5(bimb)]·H₂O}_n ( NUC-6 , here NUC corresponding to North University of China), with 3D (4,4)-c {8⁶} net, was designed. Benefit from the high chemical stability and excellent luminescent property, NUC-6 can be act as an efficient multi-response chemo-sensor in detecting dichloronitroaniline pesticide and nitrofuran antibiotics in water with the detection limits are 116 ppb for DCN pesticide, 16 ppb for NFT antibiotic, and 12 ppb for NTZ antibiotic. Besides, the mechanisms of luminescence quenching were revealed from the viewpoint of internal filter effect (IFE) and photo-induced electron transfer (PET), implied by the optical spectroscopy and quantum chemical calculation. This work provides a promising strategy to design stable MOFs by improving the self-penetrating features and to expand their practical applications in the detection of organic pollutants in aqueous medium.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.