Integral geometry of translation invariant functionals,II: The case of general convex bodies

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

Decimation of the Dyson–Ising ferromagnet

We study the decimation to a sublattice of half the sites of the one-dimensional Dyson–Ising ferromagnet with slowly decaying long-range pair potentials of the form $\frac{1}{{|i?j|}^{\alpha }}$, deep in the phase transition region ($1<\alpha \le 2$ and low temperature). We prove non-Gibbsianness of the decimated measures at low enough temperatures by exhibiting a point of essential discontinuity for the (finite-volume) conditional probabilities of decimated Gibbs measures. This result complements previous work proving conservation of Gibbsianness for fastly decaying potentials ($\alpha >2$) and provides an example of a “standard” non-Gibbsian result in one dimension, in the vein of similar results in higher dimensions for short-range models. We also discuss how these measures could fit within a generalized (almost vs. weak) Gibbsian framework. Moreover we comment on the possibility of similar results for some other transformations.     

Continuous spin models on annealed generalized random graphs

We study Gibbs distributions of spins taking values in a general compact Polish space, interacting via a pair potential along the edges of a generalized random graph with a given asymptotic weight distribution $P$, obtained by annealing over the random graph distribution.First we prove a variational formula for the corresponding annealed pressure and provide criteria for absence of phase transitions in the general case.We furthermore study classes of models with second order phase transitions which include rotation-invariant models on spheres and models on intervals, and classify their critical exponents. We find critical exponents which are modified relative to the corresponding mean-field values when $P$ becomes too heavy-tailed, in which case they move continuously with the tail-exponent of $P$. For large classes of models they are the same as for the Ising model treated in Dommers et al. (2016). On the other hand, we provide conditions under which the model is in a different universality class, and construct an explicit example of such a model on the interval.     

Gabor systems and almost periodic functions

Inspired by results of Kim and Ron, given a Gabor frame in $L^2(\mathbb{R})$, we determine a non-countable generalized frame for the non-separable space ${\mathit{AP}}_2(\mathbb{R})$ of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of ${\mathit{AP}}_2(\mathbb{R})$ are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

新型手性硫醚-亚磷酰胺配体的设计与应用

根据模块组合法原理,设计并合成了一种具有亚磷酰胺结构的硫醚配体,该配体具有原料便宜易得、合成步骤简单、易于修饰和结构稳定等特点。以配体/钯络合物催化的丙二酸二甲酯与1,3-二苯基烯丙基醋酸酯的烯丙基化反应作为模板反应,探究了溶剂、碱对其立体控制的影响。随后探究了中心手性与轴手性的匹配/错配现象以及硫醚片段的空间位阻、电性对反应立体控制的作用。在最佳条件下,产物的对映选择性能够达到-76% ee。     

How Ligand Geometry Affects the Reactivity of Co(II) Cyclam Complexes

Cobalt complexes are extensively studied as bioinspired models for non-heme oxygenases as they facilitate both the stabilization and characterization of metal-oxygen intermediates. As an analog to the well-known Co(cyclam) complex Co{N₄} (cyclam=1,4,8,11-tetraazacyclotetradecane), the Co^II complex Co{i-N₄} with the isomeric isocyclam ligand (isocyclam=1,4,7,11-tetraazacyclotetradecane) was synthesized and characterized. Despite the identical N₄ donor set of both complexes, Co{i-N₄} enables the 2e⁻/2H⁺ reduction of O₂ with a lower overpotential (η_eff of 385 mV vs. 540 mV for Co{N₄} ), albeit with a diminished turnover frequency. Characterization of the intermediates formed upon O₂ activation of Co{i-N₄} reveals a structurally identified stable μ-peroxo Co^III dimer as the main product. A superoxo Co^III species is also formed as a minor product, as indicated by EPR spectroscopy. In further reactivity studies, the electrophilicity of these in situ generated Co−O₂ species was demonstrated by the oxidation of the O−H bond of TEMPO−H (2,2,6,6-tetramethylpiperidin-1-ol) via a H atom abstraction process. Unlike the known Co(cyclam), Co{i-N₄} can be employed in oxygen atom transfer reactions oxidizing triphenylphosphine to the corresponding phosphine oxide highlighting the impact of geometrical modifications of the ligand while preserving the ring size and donor atom set on the reactivity of biomimetic oxygen activating complexes.     

酸溶-电感耦合等离子体发射光谱法测定白云石和菱镁石中主次元素

利用电感耦合等离子体原子发射光谱仪( ICP-AES)建立白云石和菱镁石中铝、钙、铁、镁、锰、磷、硅、锶的测定方法。研究了酸体系、温度及消解方式对试样消解的影响,结果表明,使用5 mL盐酸和硝酸混合酸(1：3)-0.75 mL氢氟酸-5 mL水以密闭消解的方式在150 ℃下消解白云石和菱镁石30min,并以2mL饱和硼酸络合多余的氢氟酸,可以得到澄清消解液。通过白云石和菱镁石中铝、钙、铁、镁、锰、磷、硅、锶的谱线干扰情况,选择Al 308.215 nm、Ca 318.127 nm、Fe 261.187 nm、Mg 277.983 nm、Mn 257.61 nm、P 213.618 nm、Si 251.611 nm、Sr 421.552 nm作为分析线,各元素的校准曲线在线性范围内线性关系良好,相关系数均不小于0.999。按照实验方法测定白云石和菱镁石标准物质,各元素结果的相对标准偏差 (RSD, n=6)为0.89~3.19%,测定值与认定值无显著性差异。本方法有效解决了白云石和菱镁石快速有效溶解及准确测定问题。