Approximation by solutions of elliptic equations in semilocal spaces

In the present work, we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain Ω by solutions of the same equations in a larger domain. We construct an abstract framework which allows us to deal with such density questions, simultaneously for various norms. More specifically, we study approximations with respect to the norms of semilocal Banach spaces of distributions. These spaces are required to satisfy certain postulates. We establish density results for elliptic operators with constant coefficients which unify and extend previous results. In our density results Ω may possess holes and it is required to satisfy the segment condition. We observe that analogous density results do not hold in spaces where the infinitely smooth functions are not dense. Finally, we provide applications related to the method of fundamental solutions.     

Anisotropic equations in weighted Sobolev spaces of higher order

We consider the strongly nonlinear boundary value problem,

Liouville results for m-Laplace equations of Lane–Emden–Fowler type

We consider sign changing solutions of the equation −Δm(u)=|u|^p−1u$-{\mathrm{\Delta }}_m(u)={|u|}^{p-1}u$ in possibly unbounded domains or in RN${\mathbb{R}}^N$. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The results hold true for m>2$m>2$ and m−1m−1<p<pc(N,m). Here pc(N,m)$p_c(N,m)$ is a new critical exponent, which is infinity in low dimension and is always larger than the classical critical one.     

城市道路交通信号实时控制的数学模型与算法研究

研究了交通信号的实时配时控制问题.建立了在已有交通设施条件下,控制信号具有线性约束的非线性实时配时系统优化模型,设计了与模型相适应的实时CLY系列算法.重点讨论了点控制问题,建立了相应的数学优化模型,设计了CLY-Point1算法求解.还对线控制问题和面控制问题,建立了多层优化控制模型,并设计CLY-Point2、CLY-Line和CLY-Area算法进行求解.数值模拟结果表明,CLY系列算法具有很强的实时性,车辆平均等待时间比固定配时减少了约20%.     

Checking for normality in linear mixed models

Linear mixed models are popularly used to fit continuous longitudinal data,and the random effects are commonly assumed to have normal distribution.However,this assumption needs to be tested so that further analysis can be proceeded well.In this paper,we consider the Baringhaus-Henze-Epps-Pulley (BHEP) tests,which are based on an empirical characteristic function.Differing from their case,we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors.The test is consistent against global alternatives,and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/√ n where n is sample size.Furthermore,to overcome the problem that the limiting null distribution of the test is not tractable,we suggest a new method: use a conditional Monte Carlo test (CMCT) to approximate the null distribution,and then to simulate p-values.The test is compared with existing methods,the power is examined,and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.     

关于可靠性生存寿命分析中几类重要截尾分布函数参数的最佳有效无偏估计

在给出了可靠性生存寿命分析几类重要随机截尾分布函数的基础上,讨论了寿命分布函数参数的最佳有效无偏估计,为解决可靠性生存寿命分析以及通讯工程和电力负载预测中的最佳无偏误差估计问题提供了令人满意的可靠依据和有效算法．     

Optimal real-time estimation in diffusion tensor imaging

Diffusion tensor imaging (DTI) constitutes the most used paradigm among the diffusion-weighted magnetic resonance imaging (DW-MRI) techniques due to its simplicity and application potential. Recently, real-time estimation in DW-MRI has deserved special attention, with several proposals aiming at the estimation of meaningful diffusion parameters during the repetition time of the acquisition sequence. Specifically focusing on DTI, the underlying model of the noise present in the acquired data is not taken into account, leading to a suboptimal estimation of the diffusion tensor. In this paper, we propose an optimal real-time estimation framework for DTI reconstruction in single-coil acquisitions. By including an online estimation of the time-changing noise variance associated to the acquisition process, the proposed method achieves the sequential best linear unbiased estimator. Results on both synthetic and real data show that our method outperforms those so far proposed, reaching the best performance of the existing proposals by processing a substantially lower number of diffusion images.     

Computational-Based Discovery of the Anti-Cancer Activities of Pyrrole-Based Compounds Targeting the Colchicine-Binding Site of Tubulin

Despite the tubulin-binding agents (TBAs) that are widely used in the clinic for cancer therapy, tumor resistance to TBAs (both inherited and acquired) significantly impairs their effectiveness, thereby decreasing overall survival (OS) and progression-free survival (PFS) rates, especially for the patients with metastatic, recurrent, and unresectable forms of the disease. Therefore, the development of novel effective drugs interfering with the microtubules’ dynamic state remains a big challenge in current oncology. We report here about the novel ethyl 2-amino-1-(furan-2-carboxamido)-5-(2-aryl/tert-butyl-2-oxoethylidene)-4-oxo-4,5-dihydro-1H-pyrrole-3-carboxylates (EAPCs) exhibiting potent anti-cancer activities against the breast and lung cancer cell lines in vitro. This was due to their ability to inhibit tubulin polymerization and induce cell cycle arrest in M-phase. As an outcome, the EAPC-treated cancer cells exhibited a significant increase in apoptosis, which was evidenced by the expression of cleaved forms of PARP, caspase-3, and increased numbers of Annexin-V-positive cells. By using the in silico molecular modeling methods (e.g., induced-fit docking, binding metadynamics, and unbiased molecular dynamics), we found that EAPC-67 and -70 preferentially bind to the colchicine-binding site of tubulin. Lastly, we have shown that the EAPCs indicated above and colchicine utilizes a similar molecular mechanism to inhibit tubulin polymerization via targeting the T7 loop in the β-chain of tubulin, thereby preventing the conformational changes in the tubulin dimers required for their polymerization. Collectively, we identified the novel and potent TBAs that bind to the colchicine-binding site and disrupt the microtubule network. As a result of these events, the compounds induced a robust cell cycle arrest in M-phase and exhibited potent pro-apoptotic activities against the epithelial cancer cell lines in vitro.     

Current Status of the X + C2H6 [X ≡ H,F(2P), Cl(2P), O(3P), OH] Hydrogen Abstraction Reactions: A Theoretical Review

This paper is a detailed review of the chemistry of medium-size reactive systems using the following hydrogen abstraction reactions with ethane, X + C₂H₆ → HX + C₂H₅; X ≡ H, F(²P), Cl(²P), O(³P) and OH, and focusing attention mainly on the theoretical developments. These bimolecular reactions range from exothermic to endothermic systems and from barrierless to high classical barriers of activation. Thus, the topography of the reactive systems changes from reaction to reaction with the presence or not of stabilized intermediate complexes in the entrance and exit channels. The review begins with some reflections on the inherent problems in the theory/experiment comparison. When one compares kinetics or dynamics theoretical results with experimental measures, one is testing both the potential energy surface describing the nuclei motion and the kinetics or dynamics method used. Discrepancies in the comparison may be due to inaccuracies of the surface, limitations of the kinetics or dynamics methods, and experimental uncertainties that also cannot be ruled out. The paper continues with a detailed review of some bimolecular reactions with ethane, beginning with the reactions with hydrogen atoms. The reactions with halogens present a challenge owing to the presence of stabilized intermediate complexes in the entrance and exit channels and the influence of the spin-orbit states on reactivity. Reactions with O(³P) atoms lead to three surfaces, which is an additional difficulty in the theoretical study. Finally, the reactions with the hydroxyl radical correspond to a reactive system with ten atoms and twenty-four degrees of freedom. Throughout this review, different strategies in the development of analytical potential energy surfaces describing these bimolecular reactions have been critically analyzed, showing their advantages and limitations. These surfaces are fitted to a large number of ab initio calculations, and we found that a huge number of calculations leads to accurate surfaces, but this information does not guarantee that the kinetics and dynamics results match the experimental measurements.     

Superconvergence analysis of an energy stable scheme with three step backward differential formula-finite element method for nonlinear reaction–diffusion equation

A three step backward differential formula scheme is proposed for nonlinear reaction–diffusion equation and superconvergence results are studied with Galerkin finite element method unconditionally. Energy stability is testified for the constructed scheme with an artificial term. Splitting technique is utilized to get rid of the ratio between the time step size and the subdivision parameter . Temporal error estimate in H²-norm is derived, which leads to the boundedness of the solutions of the time-discrete equations. Unconditional spatial error estimate in L²-norm is deduced which help bound the numerical solutions in L^∞-norm. Superconvergent property of in H¹-norm with order is obtained by taking difference between two time levels of the error equations unconditionally. The global superconvergent property is deduced through the above results. Two numerical examples show the validity of the theoretical analysis.