Protecting Entanglement in a Common Phase Decoherence Environment using Weak Measurement and Quantum Measurement Reversal

Protection of entanglement from disturbance of the environment is an essential task in quantum information processing. We investigate the entanglement protection of a qubit-qubit system interacting with a phase decoherence reservoir by employing the weak measurement (WM) and quantum measurement reversal (QMR). We show explicitly that the quantum entanglement can be obviously protected by means of the proper WM and QMR. In particular, we found that there is a specific initial state parameter region, the entanglement protection ratio, which is determined only by the initial state parameter and independent of the form of the spectral density of the reservoir.     

Regular and Chaotic Spatial Distribution of Bose-Einstein Condensed Atoms in a Ratchet Potential

We study the regular and chaotic spatial distribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction in a ratchet potential. There exists in the system a space-dependent atomic current that can be tuned via Feshbach resonance technique. In the presence of the space-dependent atomic current and a weak ratchet potential, the Smale-horseshoe chaos is studied and the Melnikov chaotic criterion is obtained. Numerical simulations show that the ratio between the intensities of optical potentials forming the ratchet potential, the wave vector of the laser producing the ratchet potential or the wave vector of the modulating laser can be chosen as the controlling parameters to result in or avoid chaotic spatial distributional states.     

Traveling wave fronts in a delayed lattice competitive system

This paper is concerned with the existence, asymptotic behavior, strict monotonicity, and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed lattice competitive system. We first prove the existence of traveling wave fronts by constructing upper and lower solutions and Schauder’s fixed point theorem, and then, for sufficiently small intraspecific competitive delays, prove that these traveling wave fronts decay exponentially at both infinities. Furthermore, for system without intraspecific competitive delays, the strict monotonicity and uniqueness of traveling wave fronts are established by means of the sliding method. In addition, we give the exact decay rate of the stronger competitor under some technique conditions by appealing to uniqueness.     

K_m~-□P_n的交叉数

Klesc等人先后确定了K_m~-□P_n(4≤m≤6)的交叉数,本文利用构造法确定了K_m-2K_2(4≤m≤12,m≠10,12)的交叉数.在此基础上,可进一步确定K_m~-□P_n(4≤m≤9,m≠8)的交叉数.相比而言,我们所采用的方法更具一般性.     

SMITH NORMAL FORMAL OF DISTANCE MATRIX OF BLOCK GRAPHS

A connected graph, whose blocks are all cliques (of possibly varying sizes), is called a { block graph.} Let D(G) be its distance matrix. In this note, we prove that the Smith normal form of D(G) is independent of the interconnection way of blocks and give an explicit expression for the Smith normal form in the case that all cliques have the same size, which generalize the results on determinants.     

Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system

In this paper, we develop a stochastic programming model for economic dispatch of a power system with operational reliability and risk control constraints. By defining a severity-index function, we propose to use conditional value-at-risk (CVaR) for measuring the reliability and risk control of the system. The economic dispatch is subsequently formulated as a stochastic program with CVaR constraint. To solve the stochastic optimization model, we propose a penalized sample average approximation (SAA) scheme which incorporates specific features of smoothing technique and level function method. Under some moderate conditions, we demonstrate that with probability approaching to 1 at an exponential rate with the increase of sample size, the optimal solution of the smoothing SAA problem converges to its true counterpart. Numerical tests have been carried out for a standard IEEE-30 DC power system.     

The Spectrality of a Class of Fractal Measures on $$\mathbb{R}^{n}$$

Acta Mathematica Sinica, English Series - Let $$M=\rho^{-1}I\in M_{n}(\mathbb{R})$$ be an expanding matrix with 0 < ∣ ρ ∣ < 1 and $$D\subset\mathbb{Z}^{n}$$ be a...     

All-in-one phototheranostics based on BTP-4F-DMO nanoparticles for NIR-II fluorescence/photoacoustic dual-mode imaging and combinational therapy

Various phototheranostics have recently been developed for phototherapy. Through proper molecular design, the photochemical and photophysical properties of these phototheranostics can be promoted. Herein, an acceptor-donor-acceptor (A-D-A)-structured dye, BTP-4F-DMO, was synthesized and prepared into water-soluble nanoparticles (NPs). The obtained BTP-4F-DMO NPs had strong absorption from 650 nm to 850 nm and a fluorescence emission peak at ∼900 nm that tailed to ∼1100 nm. The NPs showed a superhigh photothermal conversion efficiency of 90.5% ± 5% and could simultaneously generate ^•OH and ¹O₂ with a ¹O₂ generation quantum yield of 4.6% under 808 nm laser irradiation. Due to these advanced properties, BTP-4F-DMO NPs can switch the role of autophagy from pro-survival to pro-death, thereby further promoting cancer cell death. These features make BTP-4F-DMO NPs a promising multifunctional phototheranostic agent for NIR-II fluorescence/photoacoustic dual-mode imaging-guided synergetic photodynamic/photothermal therapy. In general, this work provides a strategy for expanding the biomedical applications of organic A-D-A-structured phototheranostics.     

Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

We show that a constant-potential time-independent Schrödinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.     

对氯苄基锡酰腙配合物的合成、抗肿瘤活性及其与DNA相互作用

用二对氯苄基二氯化锡分别与对甲基苯甲酰肼缩苯甲酰甲酸及苯甲酰肼缩苯甲酰甲酸反应,合成了2个对氯苄基锡配合物(C1、C2),通过元素分析、IR、1 H NMR、13C NMR、119Sn NMR、HRMS以及X射线单晶衍射等表征了配合物结构。测试了配合物C1、C2的热稳定性以及配合物对癌细胞NCI?H460、HepG2、MCF7的体外抑制活性,发现配合物C2对癌细胞NCI?H460、HepG2、MCF7等均表现出良好的抑制作用。利用紫外吸收光谱、荧光猝灭光谱以及粘度法研究了配合物C2与ct?DNA之间的相互作用,结果表明配合物C2以插入模式与DNA结合。