Uniform estimates on paraproducts

We prove uniformL ^p estimates (Theorem 1.1) for a family of paraproducts and corresponding maximal operators.     

Darstellung und Eigenschaften von 1-Norbornylkupfer

Preparation and Properties of 1-Norbornyl Copper 1-Norbornyl copper was synthesized from copper(II) acetylacetonate and 1-norbornyl lithium. The compound shows an unexpected stability and decomposes only at ca. 80°C with precipitation of copper and formation of norbornyl radicals which were proved by spin-trap experiments. A further characterization was performed by the IR and ¹³C-NMR spectra.     

Die Kristallstrukturen und Phasentransformationen des tetramorphen RbGel3

Crystal Structures and Phase Transitions of the Tetramorphic RbGeI₃ The thermal behaviour of RbGeI₃ has been studied by X-ray diffraction, Raman spectroscopy, and DTA/DSC. The compound is tetramorphic. Yellow crystals of the LT-form have been obtained by crystallization from aqueous HI solutions. The orthorhombic crystal structure of LT? RbGeI₃ (space group P2₁2₁2₁; a = 10.1441(8) Å; b = 4.5460(5) Å; c = 16.8438(9) Å) shows a distorted NH₄CdCl₃ type structure with pyramidal GeI₃ anions. Three reversible phase transformations were found by heating. In a first step at 181°C LT? RbGeI₃ is transferred into the orthorhombic perovskite MT1—RbGeI₃ (red, space group Pn2₁a; a = 8.566(3) Å; b = 11.868(6) Å; c = 8.018(4) Å; RbGeBr₃ type structure) by a reconstructive phase transition. Subsequently at 221°C the phase MT2—RbGeBr₃ with a rhombohedrically deformed perovskite type structure (black, space group R3m; a = 5.990(2) Å; α = 88,89(3)°; CsGeCl₃ type structure) is formed. The high temperature modification HT? RbGeI₃ shows the cubic perovskite type structure (space group Pm3m; a = 5.994(3) (Å) and is stable above 244°C until decomposition occurs at 334°C.     

Recent advances in robust optimization: An overview

This paper provides an overview of developments in robust optimization since 2007. It seeks to give a representative picture of the research topics most explored in recent years, highlight common themes in the investigations of independent research teams and highlight the contributions of rising as well as established researchers both to the theory of robust optimization and its practice. With respect to the theory of robust optimization, this paper reviews recent results on the cases without and with recourse, i.e., the static and dynamic settings, as well as the connection with stochastic optimization and risk theory, the concept of distributionally robust optimization, and findings in robust nonlinear optimization. With respect to the practice of robust optimization, we consider a broad spectrum of applications, in particular inventory and logistics, finance, revenue management, but also queueing networks, machine learning, energy systems and the public good. Key developments in the period from 2007 to present include: (i) an extensive body of work on robust decision-making under uncertainty with uncertain distributions, i.e., “robustifying” stochastic optimization, (ii) a greater connection with decision sciences by linking uncertainty sets to risk theory, (iii) further results on nonlinear optimization and sequential decision-making and (iv) besides more work on established families of examples such as robust inventory and revenue management, the addition to the robust optimization literature of new application areas, especially energy systems and the public good.     

Multistep Continuous‐Flow Synthesis in Medicinal Chemistry: Discovery and Preliminary Structure–Activity Relationships of CCR8 Ligands

A three‐step continuous‐flow synthesis system and its application to the assembly of a new series of chemokine receptor ligands directly from commercial building blocks is reported. No scavenger columns or solvent switches are necessary to recover the desired test compounds, which were obtained in overall yields of 49–94 %. The system is modular and flexible, and the individual steps of the sequence can be interchanged with similar outcome, extending the scope of the chemistry. Biological evaluation confirmed activity on the chemokine CCR8 receptor and provided initial structure–activity‐relationship (SAR) information for this new ligand series, with the most potent member displaying full agonist activity with single‐digit nanomolar potency. To the best of our knowledge, this represents the first published example of efficient use of multistep flow synthesis combined with biological testing and SAR studies in medicinal chemistry.     

Additivity of the two-dimensional Miller ideal

Let J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} is bigger than the covering number of the ideal of the meager subsets of ^ω ω. We also show that Martin’s Axiom implies that the additivity of J (\mathbb M²){{\mathcal J}\,(\mathbb M^2)} is 2 ^ω .Finally we prove that there are no analytic infinite maximal antichains in any finite product of \mathfrakP(w)/fin{\mathfrak{P}{(\omega)}/{\rm fin}} .     

Driven drops on heterogeneous substrates: onset of sliding motion

Pinning and depinning of driven drops on heterogeneous substrates is studied as a function of the driving and heterogeneity amplitude. Two types of heterogeneity are considered: a "hydrophobic" defect that blocks the drop in front and a "hydrophilic" one that holds it at the back. Two different types of depinning leading to sliding motion are identified, and the resulting stick-slip motion is studied numerically.