基于“学习金字塔理论”的物理化学实验教学模式改革实践

介绍了东北林业大学物理化学实验课程教学中基于"学习金字塔理论"进行教学模式改革实践的情况。在实施实验教学过程中,通过增加"学生通过在线实验视频预习""学生为学生讲解实验""操作前学生小组讨论"和"操作后学生小组总结讨论"等学习环节,建立了一种有效的"以学生为中心"的实验教学模式,促进了学生综合素质和创新能力的培养,取得了良好的教学效果。     

On the Number of k‐Dominating Independent Sets

We study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erd?s and Moser—is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of k‐dominating independent sets in n‐vertex graphs is between and if , moreover the maximum number of 2‐dominating independent sets in n‐vertex graphs is between and . Graph constructions containing a large number of k‐dominating independent sets are coming from product graphs, complete bipartite graphs, and finite geometries. The product graph construction is associated with the number of certain Maximum Distance Separable (MDS) codes.     

Graphs with No Induced Five‐Vertex Path or Antipath

We prove that a graph G contains no induced ‐vertex path and no induced complement of a ‐vertex path if and only if G is obtained from 5‐cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class‐preserving operation introduced here.     

Strongly Even‐Cycle Decomposable Graphs

A graph is strongly even‐cycle decomposable if the edge set of every subdivision with an even number of edges can be partitioned into cycles of even length. We prove that several fundamental composition operations that preserve the property of being Eulerian also yield strongly even‐cycle decomposable graphs. As an easy application of our theorems, we give an exact characterization of the set of strongly even‐cycle decomposable cographs.     

基于S-R和分解定理的几何非线性问题的数值计算分析

为了探究几何非线性问题的数值求解方法,采用理论推导、MATLAB编程计算、有限元模拟相结合的方法,基于S-R和分解定理及更新拖带坐标描述法,运用插值型无单元Galerkin方法对几何非线性问题的增量变分方程进行了推导,并通过四点Gauss积分法和不动点迭代法对其进行求解.最后以平面悬臂梁的大变形问题为例进行求解计算,发现与ANSYS的计算结果拟合相似度很高,说明了所采用的几何非线性力学理论及数值计算方法的正确性和合理性,为求解几何非线性问题提供了一种新的依据.     

半参数线性混合效应模型的联合变量选择

多数基于线性混合效应模型的变量选择方法分阶段对固定效应和随机效应进行选择,方法繁琐、易产生模型偏差,且大部分非参数和半参数的线性混合效应模型只涉及非参数部分的光滑度或者固定效应的选择,并未涉及非参变量或随机效应的选择。本文用B样条函数逼近非参数函数部分,从而把半参数线性混合效应模型转化为带逼近误差的线性混合效应模型。对随机效应的协方差矩阵采用改进的乔里斯基分解并重新参数化线性混合效应模型,接着对该模型的极大似然函数施加集群ALASSO惩罚和ALASSO惩罚两类惩罚,该法能实现非参数变量、固定效应和随机效应的联合变量选择,基于该法得出的估计量也满足相合性、稀疏性和Oracle性质。文章最后做了个数值模拟,模拟结果表明,本文提出的估计方法在变量选择的准确性、参数估计的精度两个方面均表现较好。     

Substituent Effect on the Electronic Properties and Nature of the W≡C Bond in trans‐Cl(OC)(H3P)3W(≡C‐para‐C6H4X) (X = H,F, SiH3, CN,NO2, SiMe3, CMe3, NH2, NMe2) Complexes: A Computational Quantum Chemistry Study

In this investigation, we describe substituent effect on the dipole moment, ionization potential, electron affinity, structure, frontier orbitals energy, in the trans‐Cl(OC)(H₃P)₃W(≡C‐para‐C₆H₄X) (X = H, F, SiH₃, CN, NO₂, SiMe₃, CMe₃, NH₂, NMe₂) complexes using MPW1PW91 quantum chemical calculations. The nature of chemical bond between the [Cl(OC)(H₃P)₃W]⁻ and [C‐para‐C₆H₄X]⁺ fragments was illustrated with energy decomposition analysis (EDA). Percentage composition in terms of the defined groups of frontier orbitals for these complexes was inspected to investigate the character in metal–ligand bonds. Quantum theory of atoms in molecules (QTAIM) was used for illustration of metal–ligand bonds in these complexes.     

Theoretical Study of Substituent Effects on Geometric and Spectroscopic Parameters (IR, 13C, 29Si NMR) and Energy Decomposition Analysis of the Bonding in Molybdenum Silylidyne Complexes CpMo(CO)2(≡Si‐para‐C6H4X)

In this study, we report the substituent effect on the structures, frontier orbital analysis, and spectroscopic properties (IR , ¹³C , ²⁹Si NMR ) in the molybdenum silylidyne complexes CpMo (CO )₂(≡Si‐para ‐C₆H₄X ) (X = H, F, Cl, CN , NO₂ , Me, OMe , NH₂ , NHMe ) using MPW1PW91 quantum chemical calculations. The calculated structural parameters and spectral parameters are compatible with the experimental values in similar complexes. The nature of the chemical bond between the [Cp(OC ) ₂Mo ]⁻ and [Si‐para ‐C₆H₄X ]⁺ fragments was explored with energy decomposition analysis (EDA ). The percentage composition in terms of the defined groups of frontier orbitals for CpMo (CO )₂(≡Si‐para ‐C₆H₄X ) complexes was investigated to explore the character of the metal–ligand bonds. The linear correlations between the properties and Hammett constants (σ _p) were illustrated. Natural bond orbital analysis (NBO ) was used to illustrate the electronic structure of the complexes.     

Regio-selective cyanation of (Z)-(1,2-dibromo-2-arylvinyl)triisopropylsilane with suppression of halogen elimination

Highly regio-selective cyanation of vicinal (Z)-dibromoalkenyl silanes was achieved by a vinylic Rosenmund-von Braun reaction, significantly suppressing side-production of alkyne. The alkyne was generated by a halogen elimination side-reaction that is an intrinsic problem in metal-activation of vicinal dihaloalkenes. We have studied to overcome the problem, and finally found the combination of CuCN and O = PPh₃ in toluene solvent effectively controlled the production of byproducts. The resultant single isomer has significance in potentially application as a multi-tunable synthetic scaffold.     

UV-mediated decomposition of diazomalonates in benzene: Unexpected access to functionalized bicyclo[3.2.0]heptane skeleton

Upon irradiation with 300-nm UV light, the photolysis of diazomalonates in benzene unexpectedly affords 2,6-dicarboxylate bicyclo[3.2.0]hepta-2,6-dienes in low yields. These products are proven to be derived from cyclohepta-1,3,5-triene intermediates presumably via a tandem 1,5-carboxylate migration/[2+2] cycloaddition sequence.