Spectral analysis of nonselfadjoint Schrödinger problem with eigenparameter in the boundary condition

In this paper we consider the nonselfadjoint (dissipative) Schrödinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrödinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrödinger boundary value problem are given.     

On Edge Singularity and Eigenvectors of Mixed Graphs

Let G be a mixed glaph which is obtained from an undirected graph by orienting some of its edges. The eigenvalues and eigenvectors of G are, respectively, defined to be those of the Laplacian matrix L（G） of G. As L（G） is positive semidefinite, the singularity of L（G） is determined by its least eigenvalue λ1 （G）. This paper introduces a new parameter edge singularity εs（G） that reflects the singularity of L（G）, which is the minimum number of edges of G whose deletion yields that all the components of the resulting graph are singular. We give some inequalities between εs（G） and λ1 （G） （and other parameters） of G. In the case of εs（G） = 1, we obtain a property on the structure of the eigenvectors of G corresponding to λ1 （G）, which is similar to the property of Fiedler vectors of a simple graph given by Fiedler.     

关于二元分式线性齐次复合函数的积分

通过把二重积分转化成曲线积分,得到二元分式线性齐次复合函数积分的两个定理及其若干推论,并构造一些比较典型的用一般方法难以计算的例子说明结论的应用.     

Organic reactions in water: an efficient one-pot synthesis of acyloxiranes from Baylis-Hillman adducts using hypervalent iodine

Treatment of Baylis-Hillman adducts with iodosobenzene (PhIO) in the presence of a catalytic amount of KBr in water at room temperature afforded the corresponding acyloxiranes in good yields.     

“一体两核四结合”的“原子物理学”线上线下混合教学模式的探索与实践

本文依托“原子物理学”省级线上线下混合式一流课程的建设,借助尔雅通识网络课程平台,运用学习通智慧教学软件,积极开展了“原子物理学”混合教学模式的探索与实践.通过在线资源建设、教学模式探索、教学模式实践等过程,转变教学观念,创新构建了“一体两核四结合”混合教学模式,为地方高校进行线上线下混合教学模式的改革提供一定的参考与借鉴.     

THE INTEGRAL AS A FUNCTlON OF THE UPPER LIMIT AND DEPENDING ON A PARAMETER TO SOLVE DRAWING THROUGH IDLING ROLLS

ＴＨＥＩＮＴＥＧＲＡＬＡＳＡＦＵＮＣＴｌＯＮＯＦＴＨＥＵＰＰＥＲＬＩＭＩＴＡＮＤＤＥＰＥＮＤＩＮＧＯＮＡＰＡＲＡＭＥＴＥＲＴＯＳＯＬＶＥＤＲＡＷＩＮＧＴＨＲＯＵＧＨＩＤＬＩＮＧＲＯＬＬＳＺｈａｏＤｅ－ｗｅｎ（赵德文）；ＺｈａｏＺｈｉ－ｙｅ（赵志业）；...     

Clay-anchored non-heme iron-salen complex catalyzed cleavage of CC bond in aqueous medium

Clay-anchored iron[N,N′-ethylenebis(salicylideneaminato)] complex, synthesized by direct exchange, oxidizes various olefins and chalcones in aqueous acetonitrile using hydrogen peroxide as terminal oxidant. Aldehyde and its derivatives are obtained as oxidation products by the cleavage of CC double bond. In comparison with the catalysis by iron-salen complex in solution, the clay catalyzed pathway not only increases the rate of reaction significantly, but also provides selective oxidation toward the aldehyde. Some chalcones also give very good yield in water, compared to the solution and clay catalyzed pathways.     

The effectiveness of resources created by students as partners in explaining the relevance of mathematics in engineering education

First-year engineering students often struggle to see the relevance of theoretical mathematical concepts for their future studies and professional careers. This is an issue, as students who do not see relevance in fundamental parts of their studies may disengage from these parts and focus their efforts on other subjects they think will be more useful to them. In this study, we surveyed engineering students enrolled in a first-year mathematics subject on their perceptions of the relevance of the individual mathematical topics taught. Surveys were administered at the start of semester when some of these topics were unknown to them, and again at the end of semester when students had not only studied all these topics but also watched a set of animated videos. These videos had been produced by higher-year students to explain where they had seen applications of the mathematical concepts presented in the first year. We notice differences between the perceived relevance of topics for future study and for professional careers, with relevance to study rated higher than relevance to careers. We also find that the animations are seen as helpful in understanding the relevance of first-year mathematics. The majority of students indicated that lecturers with students as partners should work collaboratively to produce future videos.     

On a Vector Version of a Fundamental Lemma of J. L. Lions

Let ? be a bounded and connected open subset of R~N with a Lipschitzcontinuous boundary,the set ? being locally on the same side of ??.A vector version of a fundamental lemma of J.L.Lions,due to C.Amrouche,the first author,L.Gratie and S.Kesavan,asserts that any vector field v =(vi) ∈(D′(?))~N,such that all the components 1/2(?_jv_i + ?_iv_j),1 ≤ i,j ≤ N,of its symmetrized gradient matrix field are in the space H~(-1)(?),is in effect in the space(L~2(?))~N.The objective of this paper is to show that this vector version of J.L.Lions lemma is equivalent to a certain number of other properties of interest by themselves.These include in particular a vector version of a well-known inequality due to J.Neˇcas,weak versions of the classical Donati and Saint-Venant compatibility conditions for a matrix field to be the symmetrized gradient matrix field of a vector field,or a natural vector version of a fundamental surjectivity property of the divergence operator.