轨形Gromov-Witten不变量沿光滑点的加权涨开公式

本文考虑,当一个紧辛轨形群胚(X,ω)沿着光滑点作加权涨开时,它的形如<α_1,…,α_m,[pt]>_(g,A)~X的轨形Gromov-Witten不变量的变化公式,其中[pt]∈H_(dR)~(2n)(X)是生成元,dimX=2n.我们证明了对于非零A∈H_2(|X|,Z),<α_1,…,α_m,[pt]>_(g,A)~X={_(g_1,pl(A)-e’)~xdimX=4,g≥0,∑((-1)g_1·2)/(2g_1+2)!_(g_2,pl(A)-e’)~xdimX=6,g≥0,_(g_1,pl(A)-e’)~xdimX≥8,g=0其中x是X沿一光滑点的权α=(α_1,…,α_n)的加权涨开,且α_1≥α_i,2≤i≤n.     

一种新的求非线性方程组的数值延拓法

针对迭代过程中的Jacobi奇异问题,本文提出了一种新的数值延拓法.通过构造双参数同伦算子,采用可控条件和适当选取参数的方式克服Jacobi奇异性,并分析了方法的收敛性.最后,通过数值实验对比,验证了方法的可行性和优越性.特别是具有可调控越过Jacobi奇异(点、线、面)的优势,从而也在某种程度上解决了数值延拓法严重依赖于初值的问题.     

High-order total variation-based Poissonian image deconvolution with spatially adapted regularization parameter

Images captured by image acquisition systems using photon-counting devices such as astronomical imaging, positron emission tomography and confocal microscopy imaging, are often contaminated by Poisson noise. Total variation (TV) regularization, which is a classic regularization technique in image restoration, is well-known for recovering sharp edges of an image. Since the regularization parameter is important for a good recovery, Chen and Cheng (2012) proposed an effective TV-based Poissonian image deblurring model with a spatially adapted regularization parameter. However, it has drawbacks since the TV regularization produces staircase artifacts. In this paper, in order to remedy the shortcoming of TV of their model, we introduce an extra high-order total variation (HTV) regularization term. Furthermore, to balance the trade-off between edges and the smooth regions in the images, we also incorporate a weighting parameter to discriminate the TV and the HTV penalty. The proposed model is solved by an iterative algorithm under the framework of the well-known alternating direction method of multipliers. Our numerical results demonstrate the effectiveness and efficiency of the proposed method, in terms of signal-to-noise ratio (SNR) and relative error (RelRrr).     

Davey-Stewartson系统粗糙爆破解的极限行为

研究了Davey-Stewartson系统(简记为D-S系统)粗糙爆破解的动力学性质.所谓粗糙爆破解即为正则性为H~s(s1)的爆破解,此时D-S系统粗糙解不再满足能量守恒率.利用I-方法与Profile分解理论,得到了D-S系统粗糙爆破解在H~s(R~2)(其中ss_0,且s_0≤(1+11~(1/2))/5≈0.8633)中的极限行为,包括L~2强极限的不存在性与L~2集中性质以及极限图景.     

Optimal replacement policy based on maximum repair time for a random shock and wear model

We study a \(\delta \) shock and wear model in which the system can fail due to the frequency of the shocks caused by external conditions, or aging and accumulated wear caused by intrinsic factors. The external shocks occur according to a Bernoulli process, i.e., the inter-arrival times between two consecutive shocks follow a geometric distribution. Once the system fails, it can be repaired immediately. If the system is not repairable in a pre-specific time D, it can be replaced by a new one to avoid the unnecessary expanses on repair. On the other hand, the system can also be replaced whenever its number of repairs exceeds N. Given that infinite operating and repair times are not commonly encountered in practical situations, both of these two random variables are supposed to obey general discrete distribution with finite support. Replacing the finite support renewal distributions with appropriate phase-type (PH) distributions and using the closure property associated with PH distribution, we formulate the maximum repair time replacement policy and obtain analytically the long-run average cost rate. Meanwhile, the optimal replacement policy is also numerically determined by implementing a two-dimensional-search process.     

硼、磷共掺杂铁钴双金属材料的制备及其电催化析氧性能

采用一步水热法合成了硼、磷共掺杂铁钴材料(Fe-Co-B-P)。借助扫描电子显微镜(SEM)、X射线衍射(XRD)、X射线光电子能谱(XPS)、傅里叶变换红外光谱(FT-IR)等技术对所合成材料的形貌、结构和组成进行表征。利用线性扫描伏安(LSV)、循环伏安(CV)、电化学阻抗谱(EIS)等技术研究材料电化学析氧反应(OER)性能。结果表明,Fe-Co-B-P表面疏松且粗糙,颗粒间有许多空隙。在电流密度为10和100 mA·cm^-2时,其过电势分别为278和309 mV,Tafel斜率为24 mV·dec^-1,说明该材料具有较优的电催化析氧性能。其在连续进行10 h的计时电位测试过程中,电势基本保持在1.55 V(vs RHE),表明该催化剂具有较好的电化学稳定性。这是由于铁钴双金属与硼、磷非金属之间的协同作用促进了电子的传递。     

Bidirectionally polarizing surface chemistry of heteroatom-doped carbon matrix towards fast and longevous lithium-sulfur batteries

Herein, a bidirectional polarization strategy is proposed for hosting efficient and durable lithium-sulfur battery (Li-S) electrochemistry. By co-doping electronegative N and electropositive B in graphene matrix (BNrGO), the bidirectional electron redistribution enables a higher polysulfide affinity over its mono-doped counterparts, contributing to strong sulfur immobilization and fast conversion kinetics. As a result, BNrGO as the cathode host matrix realizes excellent cycling stability over 1000 cycles with a minimum capacity fading of 0.027% per cycle, and superb rate capability up to 10 C. Meanwhile, decent areal capacity (6.46 mAh/cm²) and cyclability (300 cycles) are also achievable under high sulfur loading and limited electrolyte. This work provides instructive insights into the interaction between doping engineering and sulfur electrochemistry for pursuing superior Li-S batteries.     

Current strategies for improving limitations of proteolysis targeting chimeras

Proteolysis targeting chimeras (PROTACs) are bifunctional degrader molecules via hijacking the ubiquitin-proteasome system (UPS) to specifically eliminate targeted proteins. PROTACs have gained momentum as a new modality of attractive technologies in the drug discovery landscape, since it allows to degrade disease-related proteins effectively. Although some PROTACs drugs reached the clinical research, they are still facing some bottlenecks and challenges that should not be neglected, such as poor oral bioavailability and potential toxic side effects. To overcome these limitations, herein, we provide an overview of recent strategies for improving the durability of PROTACs by enhancing cell permeability and reducing toxic side effects. Meanwhile, the impact of these strategies on improving oral bioavailability as well as their advantages and drawbacks will also be discussed. This review will give a useful reference toolbox for PROTACs design and further promote its clinical application.     

Electrochemical C–H/N–H cross-coupling of 2-phenylindolizines with phenothiazines to synthesize novel N-aryl phenothiazine derivatives

A facile and elegant method for synthesis of novel N–aryl phenothiazine derivatives from 2-phenylindolizines and phenothiazines through direct electrochemical oxidation has been developed. This approach was performed smoothly at room temperature without external oxidant and catalyst. Cyclic voltammetry and in situ FTIR techniques were applied to analyze the cross-coupling process of phenothiazines and 2-phenylindolizines, which helped to select the appropriate reaction potential. Under the optimized conditions, a broad range of substrates were well tolerated, affording the desired products in moderate to excellent isolated yields (up to 91%) with high regioselectivity. Meanwhile, a plausible mechanism involving a radical pathway has been proposed.     

Enhanced water-induced effects enabled by alkali-stabilized Pd-OHx species for oxidation of benzyl alcohol

The water promotion effects, where water can provide a solution-mediated reaction pathway in various heterogeneous chemical catalysis, have been presented and attracted wide attention recently, yet, the rational design of catalysts with a certain ability of enhancing water-induced reaction process is full of challenges and difficulties. Here, we show that by incorporating alkali (Na, K) cations as an electronic and/or structural promoter into Pd/rGO-ZnCr₂O₄ (rGO, reduced graphene oxide), the obtained Pd(Na)/rGO-ZnCr₂O₄ as a representative example demonstrates an outstanding benzyl alcohol oxidation activity in the Pickering emulsion system in comparison to the alkali-free counterpart. The response experiments of water injection confirm the enhanced activity, and the Na-modified catalyst can further enhance the promotion effects of water on the reaction. The effects of alkali cations for Pd nanoparticles are identified and deciphered by a series of experimental characterizations (XPS, in situ CO-DRIFTS, and CO-TPR coupled with MS), showing that there is abundant −OH on the surface of the catalyst, which is stabilized by the formation of Pd−OH_x. The alkali-stabilized Pd−OH_x is helpful to enhance the water-induced reaction process. According to the results of in situ Raman as well as UV-vis absorption spectra, the Na-modulated Pd(Na)/rGO-ZnCr₂O₄ enables the beneficial characteristics for distorting the benzyl alcohol structure and enhancing the adsorption of benzyl alcohol. Further, the mechanism for enhanced water promotion effects is rationally proposed. The strategy of alkali cations-modified catalysts can provide a new direction to effectively enhance the chemical reaction involving small molecule water.