二元关系的性质测试及其复杂性分析

本文介绍了性质测试的基本原理,分析了用性质测试方法解决参数化问题的可行性,并将同构性质进行了参数化。研究了二元关系的性质测试以及参数化框架同构性质的测试问题,对固定的距离参数,证明了测试复杂性低于标准判定程序的复杂性。

Explanatory System of Support Vector Regression and Its Application in QSPR of Surfactants

In order to solve the problem of poor interpretability of support vector re- gression （SVR） applied in quantitative structure-property relationship （QSPR）, a com- plete set of explanatory system for SVR was established based on F-test, The nov- el explanatory system includes significance tests of model and single-descriptor im- portance, single-descriptor effect and sensitivity analysis, and significance tests of interaction between two descriptors, etc. The results of example indicated that the explanatory results of the new system were consistent well with those of stepwise linear regression model and quadratic polynomial stepwise regression model. The explanatory SVR model will play an important role in regression analysis such as QSPR.

Nakayama automorphisms of PBW deformations and Hopf actions

Poincaré-Birkhoff-Witt(PBW)deformations of Artin-Schelter regular algebras are skew CalabiYau.We prove that the Nakayama automorphisms of such PBW deformations can be obtained from their homogenizations.Some Calabi-Yau properties are generalized without Koszul assumption.We also show that the Nakayama automorphisms of such PBW deformations control Hopf actions on them.

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^(N+1)

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of all locally holomorphic auto-morphisms of these hypersurfaces near the origin.

Syntheses, characterization, and theoretical calculation of Rb2Mg3（P2O7）2 polymorphs with deep-ultraviolet cutoff edges

By the combination of the isolated P2O7 dimers and Mg O4 tetrahedra,α-andβ-Rb2Mg3(P2O7)2 polymorphs were synthesized by a high-temperature solution method.α-Rb2Mg3(P2O7)2 crystallizes in non-centrosymmetric space group P212121,whileβ-Rb2Mg3(P2O7)2 crystallizes in centrosymmetric P21/c.Both structures contain a three dimensional[Mg3P4O14]^2- anionic framework,while Rb^+ cations are in the space.Structure analyses show that the isolated P2O7 dimers can easily adjust their variable configurations and orientations to fit the different coordination environments of the cations,which is conducive to the formation of polymorphs.The phase transformation process fromα-toβ-Rb2Mg3(P2O7)2 was further investigated by powder X-ray diffraction and thermal gravimetric/differential scanning calorimetry measurements.In addition,UV-vis-NIR diffusion spectra indicate both materials have deep-ultraviolet cut-off edges(below 190 nm).α-Rb2Mg3(P2O7)2 is second-harmonic generation(SHG)-active and the origin of SHG response was investigated by the SHG density calculations.The first-principle calculations were also carried out to illuminate their structure-property relationships.

Honeycomb silicon: a review of silicene

Silicene, a new allotrope of silicon in a twodimensional honeycomb structure, has attracted intensive research interest due to its novel physical and chemical properties. Unlike carbon atoms in graphene, silicon atoms prefer to adopt sp2/sp3-hybridized state in silicene,enhancing chemical activity on the surface and allowing tunable electronic states by chemical functionalization. The silicene monolayers epitaxially grown on Ag(111) surfaces demonstrate various reconstructions with different electronic structures. In this article, the structure, phonon modes, electronic properties, and chemical properties of silicene are reviewed based on theoretical and experimental works in recent years.

Coprime action and arithmetical conditions on invariant conjugacy classes

Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. We show that if 4 divides no A-invariant conjugacy class size of G, then G is solvable. We also characterize the A-invariant structure of G under certain arithmetical conditions on the set of A-invariant class sizes of G by means of the fixed point subgroup, some of which imply the solvability of G. Thus, we extend, for coprime action, several results appeared in the literature on class sizes.