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.     

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.     

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.     

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.     

Modeling and character analyzing of multiple fractional-order memcapacitors in parallel connection

Recently,the memory elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behaviors.Thus,the modeling and characterizing of the mem-elements become essential.In this paper,the analysis of the multiple fractional-order voltage-controlled memcapacitors model in parallel connection is studied.Firstly,two fractional-order memcapacitors are connected in parallel,the equivalent model is derived,and the characteristic of the equivalent memcapacitor is analyzed in positive or negative connection.Then a new understanding manner according to different rate factor K and fractional orderαis derived to explain the equivalent modeling structure conveniently.Additionally,the negative order appears,which is a consequence of the combination of memcapacitors in different directions.Meanwhile,the equivalent parallel memcapacitance has been drawn to determine that multiple fractional-order memcapacitors could be calculated as one composite memcapacitor.Thus,an arbitrary fractional-order equivalent memcapacitor could be constructed by multiple fractional-order memcapacitors.