On Gradient Solitons of the Ricci–Harmonic Flow

In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.     

The localized longitudinal index theorem for Lie groupoids and the van Est map

We define the “localized index” of longitudinal elliptic operators on Lie groupoids associated with Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of the localized index, is an action of the Hopf algebroid of jets around the unit space, and the characteristic map it induces on Lie algebroid cohomology. This map can be globalized to differentiable groupoid cohomology, giving a definition of the “global index”, that can be computed by localization. This correspondence between the “global” and “localized” index is given by the van Est map for Lie groupoids.     

Overdetermined partial boundary value problems on finite networks

In this study, we define a class of non-self-adjoint boundary value problems on finite networks associated with Schrödinger operators. The novel feature of this study is that no data are prescribed on part of the boundary, whereas both the values of the function and of its normal derivative are given on another part of the boundary. We show that overdetermined partial boundary value problems are crucial for solving inverse boundary value problems on finite networks since they provide the theoretical foundations for the recovery algorithm. We analyze the uniqueness and the existence of solution for overdetermined partial boundary value problems based on the nonsingularity of partial Dirichlet-to-Neumann maps. These maps allow us to determine the value of the solution in the part of the boundary where no data was prescribed. We also execute full conductance recovery for spider networks.     

Sequences of harmonic maps in the 3‐sphere

We define two transforms of non‐conformal harmonic maps from a surface into the 3‐sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between harmonic maps into the 3‐sphere, H‐surfaces in Euclidean 3‐space and almost complex surfaces in the nearly Kähler manifold . As a consequence we can construct sequences of H‐surfaces and almost complex surfaces.     

Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: Pro or contra?

The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.     

硅衬底氮化镓基LED薄膜转移至柔性黏结层基板后其应力及发光性能变化的研究

本文将硅(Si)衬底上外延生长的氮化镓(GaN)基发光二极管(LED)薄膜转移至含有柔性黏结层的基板上, 获得了不受衬底和支撑基板束缚的LED薄膜. 利用高分辨率X射线衍射仪(HRXRD)研究了薄膜转移前后的应力变化, 同时对其光致发光(PL)光谱的特性进行了研究. 结果表明: 硅衬底GaN基LED薄膜转移至柔性基板后, GaN受到的应力会由转移前巨大的张应力变为转移后微小的压应力, InGaN/GaN量子阱受到的压应力则增大; 尽管LED薄膜室温无损转移至柔性基板其InGaN阱层的In组分不会改变, 然而按照HRXRD倒易空间图谱通用计算方法会得出平均铟组发生了变化; GaN基LED薄膜从外延片转移至柔性基板时其PL谱会发生明显红移.     

Phytochemical Analysis and Habitat Suitability Mapping of Glycyrrhiza glabra L. Collected in the Hatay Region of Turkey

The growth and quality of licorice depend on various environmental factors, including the local climate and soil properties; therefore, its cultivation is often unsuccessful. The current study investigated the key factors that affect the contents of bioactive compounds of Glycyrrhiza glabra L. root and estimated suitable growth zones from collection sites in the Hatay region of Turkey. The contents of three bioactive compounds (glycyrrhizic acid, glabridin, and liquiritin), soil factors (pH, soil bearing capacity, and moisture content), and geographical information (slope, aspect, curvature, elevation, and hillshade) were measured. Meteorological data (temperature and precipitation) were also obtained. An analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA) were performed on the data. The soil bearing capacity, moisture content, slope, aspect, curvature, and elevation of the study area showed statistically significant effects on the glycyrrhizic acid and liquiritin contents. A habitat suitability zone map was generated using a GIS-based frequency ratio (FR) model with spatial correlations to the soil, topographical, and meteorological data. The final map categorized the study area into four zones: very high (15.14%), high (31.50%), moderate (40.25%), and low suitability (13.11%). High suitability zones are recommended for further investigation and future cultivation of G. glabra.     

侧伏规律在岩质边坡结构面编录中的应用

理论上,据边坡设计坡面来编录展示结构面的迹线分布应与其在坡面内的侧伏交线一致。把握一定的侧伏规律,处以适当的素描技法,既可吻合实际情况,又可提高绘图效率和资料质量,对边坡结构模型的准确分析不无裨益。有鉴于此,经过现场观测总结,分析了结构面与坡面的各种交切关系及其迹线的侧伏特征。在侧伏规律公式推导的基础上,根据两者产状提出其特征三角形判别法,并编制相应的算图,可校核以及在适当条件下推测某一产状要素。讨论了实践中几类难以作图的特殊情况下侧伏规律的应用。     

基于主磁场长期变化模型的地磁导航基准图时变修正

地球主磁场长期变化是影响地磁导航基准图时效性的一个重要因素。提出一种以模型预测值对基准图进行时变修正的方法,利用主磁场长期变化模型解决临近空间地磁导航基准图的时变修正问题。基于WMM2010建立地球主磁场长期变化模型,在此基础上建立中国地区临近空间(海拔高度30 km)的主磁场长期变化模型,利用该模型计算出的地磁场分量长期变化率对基准图时变进行修正。仿真实验结果表明,修正后的地磁导航基准图的匹配概率可以达到90%以上,相比修正前有显著提高,且修正前后间隔时间越长效果越明显。利用主磁场长期变化模型修正后的地磁导航基准图具有良好的适配性。