Sobolev H1 geometry of the symplectomorphism group

For a closed symplectic manifold $(M,\omega )$ with compatible Riemannian metric g we study the Sobolev $H^1$ geometry of the group of all $H^s$ diffeomorphisms on M which preserve the symplectic structure. We show that, for sufficiently large s, the $H^1$ metric admits globally defined geodesics and the corresponding exponential map is a non-linear Fredholm map of index zero. Finally, we show that the $H^1$ metric carries conjugate points via some simple examples.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

15-deoxy-isoxeniolide-A,new diterpenoid from a bornean soft coral,Xenia sp.

A new xenicane diterpenoid, 15-deoxy-isoxeniolide-A (1) along with four known compounds 9-deoxy-isoxeniolide-A (2), isoxeniolide-A (3), xeniolide-A (4) and coraxeniolide-B (5) were isolated from the Bornean soft coral Xenia sp. The structures of these metabolites were elucidated on the basis of spectral analysis, NMR and HRESIMS. Compound 5 showed cytotoxic activity against ATL cell line, S1T.     

Hyperplane sections of determinantal varieties over finite fields and linear codes

We determine the number of ${\mathbb{F}}_q$-rational points of hyperplane sections of classical determinantal varieties defined by the vanishing of minors of a fixed size of a generic matrix, and identify the hyperplane sections giving the maximum number of ${\mathbb{F}}_q$-rational points. Further we consider similar questions for sections by linear subvarieties of a fixed codimension in the ambient projective space. This is closely related to the study of linear codes associated to determinantal varieties, and the determination of their weight distribution, minimum distance, and generalized Hamming weights. The previously known results about these are generalized and expanded significantly. Connections to eigenvalues of certain association schemes, distance regular graphs, and rank metric codes are also indicated.     

The Szegö kernel on a class of non-compact CR manifolds of high codimension

We generalize Nagel’s formula for the Szegö kernel and use it to compute the Szegö kernel on a class of non-compact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szegö kernel.     

Approaching compositional limits of perovskite – type oxides and oxynitrides by synthesis of Mg0.25Ca0.65Y0.1Ti(O,N)3, Ca1–xYxZr(O,N)3 (0.1 ≤ x ≤ 0.4), and Sr1–xLaxZr(O,N)3 (0.1 ≤ x ≤ 0.4)

Partial substitution of cations and anions in perovskite-type materials is a powerful way to tune the desired properties. The systematic variation of the cations size, the partial exchange of O²⁻ for N³⁻ and their effect on the size of the optical band gap and the thermal stability was investigated here. The anionic substitution resulted in the formation of the orthorhombic perovskite-type oxynitrides Mg_0.25Ca_0.65Y_0.1Ti(O,N)₃, Ca_1-xY_xZr(O,N)₃, and Sr_1–xLa_xZr(O,N)₃. A two-step synthesis protocol was applied: i) (nano-crystalline) oxide precursors were synthesized by a Pechini method followed by ii) ammonolysis in flowing NH₃ at T = 773 K (Ti) and T = 1273 K (Zr), respectively. High-temperature synthesis of such oxide precursors by solid–state reaction generally resulted in phase separation of the different A-site cations. Changes of the crystal structures were investigated by Rietveld refinements of the powder XRD data, thermal stability by DSC/TG measurements in oxygen atmosphere, oxygen and nitrogen contents by O/N analysis using hot gas extraction technique, and optical band gaps by photoluminescence spectroscopy. By moving from Mg_0.25Ca_0.65Y_0.1Ti(O,N)₃ via Ca_1–xY_xZr(O,N)₃ to Sr_1–xLa_xZr(O,N)₃, the degree of tilting of the octahedral network is reduced, as observed by an increase in the B–X–B angles caused by the simultaneously increasing effective ionic radius of the A-site cation(s). In general, increasing substitution levels on the A-site (Y³⁺ and La³⁺) are accompanied by an enhanced replacement of O²⁻ by N³⁻. In all three systems, this anionic substitution resulted in a reduction of the optical band gap by approximately 1 eV (Ti) and up to 2.1 eV (Zr) compared to the respective oxides. For Mg_0.25Ca_0.65Y_0.1Ti(O,N)₃ an optical band gap of 2.2 eV was observed, appropriate for a solar water splitting photocatalyst. The Zr-based oxynitrides required a by a factor of 2 higher nitrogen contents to significantly reduce the optical band gap and the measured values of 2.9 eV–3.2 eV are larger compared to the Ti-based oxynitride. Bulk thermal stability was revealed up to T = 881 K. In general, the thermal stability decreased with increasing substitution levels due to an increasing deviation from the ideal anionic composition as demonstrated by O/N analysis.     

非齐度量测度空间上Morrey-Herz空间上的广义分数次积分算子及其交换子

设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性.     

Similar,or dissimilar,that is the question. How different are methods for comparison of compounds similarity?

Comparison of compounds similarity is one of the main strategies of virtual screening protocols. Both similarity and dissimilarity concepts are of great importance during the search for new active compounds. Similarity is important due to the assumption that underlies the process of searching for new drug candidates: structurally similar compounds should induce similar biological response. On the other hand, we are also interested in dissimilarity, as we usually aim to find structurally novel ligands. In the study, we compared several approaches of evaluating compound similarity. Various representations and metrics were applied and we indicated the rate of variation of the results that can occur when shifting from one strategy to another. We compared both general similarity of datasets using different approaches, as well as examined the changes in the set of nearest neighbors when changing one compound representation into another, and the influence of representation/metric settings on the clustering outcome. We hope that the study will be of great help during the preparation of virtual screening experiments, stressing the need for careful selection of the way, the compound similarity is assessed. The differences in the results that can be obtained via the application of particular strategy can significantly influence the outcome of comparison studies; therefore, its settings should be carefully selected beforerunning the comparison.     

桉树杂交种与其亲本的近红外光谱判别

研究桉树控制授粉后目标性状的基因作用方式是探索其基因重组规律的重要内容。常规的数量统计分析精度往往不高,而DNA分析的专业要求高,且费时费力。该研究利用近红外光谱(NIRs)研究不同基因型桉树杂交种、亲本及杂交种与亲本间近红外光谱信息的关系,探索NIRs用于桉树杂交种与其亲本判别的可行性和准确性。以控制授粉的桉树亲本及其杂交F1代材料为对象,每种基因型从各自田间试验分别选取10个单株,采集树冠中上部新鲜健康叶片。用手持式近红外仪Phazir Rx(1624)采集桉树杂交种与其亲本叶片的NIRs信息。每单株选10片完全生理成熟的健康叶片,避开叶脉扫描其正面光谱5次,以50条NIRs信息的均值代表单个叶片的NIRs信息,最终每个基因型获得10条NIRs信息。对原始NIRs采用二阶多项式S.G一阶导数预处理。预处理后的NIRs用于多元统计分析,首先对桉树杂交亲本和子代样本进行主成分分析(PCA),直观展示不同基因型的分类情况。然后运用簇类独立软模式(SIMCA)和偏最小二乘判别分析(PLS-DA)两种有监督的判别模式验证NIRs用于桉树杂交种与其亲本树种的分类判别效果。PCA结果显示,不同的亲本间、杂交种间及杂交种与亲本间样本的主因子得分可以清晰地将各基因型分开。SIMCA模式判别分析中,桉树杂交种样本到亲本PCA模型的样本距离显示,待判别样本能够形成单独的聚类,且能直观反映两者的遗传相似。PLS-DA判别结果显示,桉树杂交亲本的PLS模型能通过预测其杂交子代的响应变量将其与亲本准确分开。结果表明,桉树叶片的NIRs信息可以准确地反映桉树杂交子代遗传信息的传递规律,NIRs判别模型可以准确地将各种基因型予以区分。因此,NIRs信息不仅可用于桉树杂交种和纯种的定性判别,还可以分析桉树基因重组过程中加性遗传效应的大小,从而为桉树遗传基础分析及其育种改良研究提供理论支撑。