The Bertini irreducibility theorem for higher codimensional slices

In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.     

局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.     

PSO-LSSVM对LIBS定量分析精度的提高

针对土壤定量分析受基体效应影响大，LIBS定量分析精度不佳等问题，采用粒子群算法对LSSVM进行优化，提高模型的精确度。选取Pb Ⅰ 405.78 nm和Cr Ⅰ 425.44 nm作为分析谱线进行分析。采集十二个不同浓度样品的特征光谱，每个浓度样品在不同点采集20组数据，将其中17组数据设为训练集，3组数据设为预测集，用LSSVM和PSO-LSSVM两种方法建立定标模型。对比两种模型的拟合相关系数（R2）、训练集均方根误差（RMSEC）和预测集均方根误差(RMSEP)。由于自吸收效应的影响，随着浓度的增加，预测值逐渐低于实际值，LSSVM定标模型的拟合程度较低，无法达到实验要求，模型性能有待提高。利用粒子群算法对LSSVM的模型参数惩罚系数和核函数参数进行优化，得到最佳的参数组合，Pb元素为(8 096.8, 138.865 7)，Cr元素为(4 908.6, 393.563 5)，用最佳的参数组合构建LSSVM的定标模型。相比于LSSVM，PSO-LSSVM定标模型的精确度更高，Pb和Cr元素的R2提高到了0.982 8和0.985 0，拟合效果明显提升。Pb和Cr元素的训练集均方根误差由0.026 0 Wt%和0.027 2 Wt%下降到0.022 4 Wt%和0.019 1 Wt%，预测集均方根误差由0.101 8 Wt%和0.078 8 Wt% 下降到0.045 8 Wt%和0.042 0 Wt%，模型的稳定性进一步提高。说明PSO-LSSVM算法能够更好地降低土壤基体效应和自吸收效应带来的影响，提高分析结果的精确度与稳定性。     

对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用，利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。     

Piperazine‐functionalized nickel ferrite nanoparticles as efficient and reusable catalysts for the solvent‐free synthesis of 2‐amino‐4H‐chromenes

Piperazine‐functionalized nickel ferrite (NiFe₂O₄) nanoparticles were synthesized as recoverable heterogeneous base catalysts using a routine method. The synthesized materials were characterized using various spectroscopic techniques such as infrared, X‐ray diffraction, scanning electron microscopy, energy‐dispersive X‐ray, thermogravimetry analysis, and vibrating sample magnetometry. Catalytic efficiency was investigated in the synthesis of 2‐amino‐4H‐chromene derivatives via a one‐pot three component reaction of aldehyde and malononitrile with β or α‐naphthol/5‐methyle resorcinol under solvent‐free conditions with good to high yields. This method is operationally simple and has several advantages such as good to high yield, short reaction times, solvent‐free conditions, and easy synthesis. Moreover, the catalyst was recovered easily using an external magnet and reused three times without distinctive loss in catalytic activity.     

XANES/EPR Evidence of the Oxidation of Nickel(II) Quinolinylpropioamide and Its Application in Csp3−H Functionalization

An in situ generated oxidation species of nickel quinolinylpropioamide intermediate was produced. Characterization by X-ray absorption near edge structure (XANES) and EPR provides complementary insights into this oxidized nickel species. With aliphatic amides and isocyanides as substrates, a nickel-catalyzed facile synthesis of structurally diverse five-membered lactams could be achieved.     

~(236)U Multi-modal Fission Paths on a Five-dimensional Deformation Surface

In this paper, we develop a new path search algorithm which considers all the degrees of freedom and apply it on our calculated five-dimensional potential energy surface(PES) of~(236) U. Asymmetric and symmetric fission paths and barriers are obtained.     

Strategies for Synthesis of Imidazo[1,2‐a]pyridine Derivatives: Carbene Transformations or C−H Functionalizations

The imidazo[1,2‐a]pyridines are an important target in organic synthetic chemistry and have attracted critical attention of chemists mainly due to the discovery of the interesting properties exhibited by a great number of imidazo[1,2‐a]pyridine derivatives. Although lots of synthetic methods of imidazo[1,2‐a]pyridines have been developed in the past years, the chemistry community faces continuing challenges to use green reagents, maximize atom economy and enrich the functional group diversity of product. Undoubtedly, with its low cost and lack of environmentally hazardous byproducts, cascade reactions and C?H functionalizations are ideal strategies for this field. In this record we highlight some of our progress toward the goal to synthesis of imidazo[1,2‐a]pyridine derivatives through carbene transformations or C?H functionalizations.