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.     

A general framework for describing photofission observables of actinides at an average excitation energy below 30 MeV

A reasonable prediction of photofission observables plays a paramount role in understanding the photofission process and guiding various photofission-induced applications, such as short-lived isotope production, nuclear waste disposal, and nuclear safeguards. However, the available experimental data for photofission observables are limited, and the existing models and programs have mainly been developed for neutron-induced fission processes. In this study, a general framework is proposed for characterizing the photofission observables of actinides, including the mass yield distributions (MYD) and isobaric charge distributions (ICD) of fission fragments and the multiplicity and energy distributions of prompt neutrons (n_p) and prompt γ rays (γ_p). The framework encompasses various systematic neutron models and empirical models considering the Bohr hypothesis and does not rely on the experimental data as input. These models are then validated individually against experimental data at an average excitation energy below 30 MeV, which shows the reliability and robustness of the general framework. Finally, we employ this framework to predict the characteristics of photofission fragments and the emissions of prompt particles for typical actinides including ²³²Th, ^{235, 238}U and ²⁴⁰Pu. It is found that the ²³⁸U(γ, f) reaction is more suitable for producing neutron-rich nuclei compared to the ²³²Th(γ, f) reaction. In addition, the average multiplicity number of both n_p and γ_p increases with the average excitation energy.     

Stabilized Nonconforming Mixed Finite Element Method for Linear Elasticity on Rectangular or Cubic Meshes

Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method.     

On weighted spectral radius of unraveled balls and normalized Laplacian eigenvalues

For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the $s^{\text{th}}$ (where $s\ge 2$) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when $s=2$, the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs.     

柠檬果茶中游离态和键合态挥发性成分分析

以柠檬果茶为研究对象,建立了顶空固相微萃取前处理结合气相色谱质谱联用技术测定其中挥发性化合物的分析方法。采用开水冲泡对样品进行提取,通过Amberlite XAD-2大孔吸附树脂对柠檬果茶中的糖苷类挥发性组分键合,分离游离态和键合态化合物,甲醇溶剂作为洗脱剂对键合态化合物进行洗脱,Almondsβ-D-葡萄糖苷酶对其酶解。使用气质联用对样品中游离态和键合态挥发性成分进行检测,其结果根据数据库匹配和对比文献保留时间定性,内标法进行定量。结果表明,柠檬果茶中含有游离态物质24种,键合态物质16种,主要为(+)-柠檬烯、1-辛醇、橙花醇、(-)-4-萜品醇、alpha-松油醇等。方法为花果茶干燥工艺提供参考。     

Trilinear Lp estimates with applications to the Cauchy problem for the Hartree-type equation

In this paper, $L^p$ estimates for a trilinear operator associated with the Hartree type nonlinearity are proved. Moreover, as application of these estimates, it is proved that after a linear transformation, the Cauchy problem for the Hartree-type equation becomes locally well posed in the Bessel potential and homogeneous Besov spaces under certain regularity assumptions on the initial data. This notion of well-posedness and the functional framework to solve the equation were firstly proposed by Y. Zhou.     

Synthesis of 1-aryl-3H-[1,2,5]triazepino[5,4-a]benzimidazol-4(5H)-ones and quantum chemical investigation of the rotamers of the Boc-protected hydrazide key intermediate

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PASE synthesis of 1-azolyl-1H-1,2,4-triazoles by the reaction of diazoazoles with ethyl isocyanoacetate

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Modeling of the glycine tripeptide cyclization in the Ser65Gly/Tyr66Gly mutant of green fluorescent protein

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