Killing three birds with one stone--simultaneous operando EPR/UV-vis/Raman spectroscopy for monitoring catalytic reactions

For the first time, three operando methods, namely EPR, UV-vis and laser-Raman spectroscopy have been applied in parallel on the same V/TiO2 catalyst and under identical reaction conditions during oxidative dehydrogenation of propane to elucidate structure-reactivity relationships in status operandi.     

Using a factored dual in augmented Lagrangian methods for semidefinite programming

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further use the approximate maximum of the augmented Lagrangian with the aim of improving the convergence rate of alternating direction augmented Lagrangian frameworks. Numerical results are reported, showing the benefits of the approach.     

On properties of random dissections and triangulations

In this work we study properties of random graphs that are drawn uniformly at random from the class consisting of biconnected outerplanar graphs, or equivalently dissections of large convex polygons. We obtain very sharp concentration results for the number of vertices of any given degree, and for the number of induced copies of a given fixed graph. Our method gives similar results for random graphs from the class of triangulations of convex polygons.     

Statistical inference for the optimal approximating model

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ ²-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.     

Copper-facilitated Suzuki-Miyaura coupling for the preparation of 1,3-dioxolane-protected 5-arylthiophene-2-carboxaldehydes

5-Formyl-2-thiopheneboronic acid is a widely used building block for the synthesis of diverse structures, however, due to a significant instability its transformation to 5-arylthiophene-2-carboxaldehydes by CC couplings could be performed only in low yields. Herein, as a solution, a convenient technique is described for the preparation of 1,3-dioxolane-protected 5-arylthiophene-2-carboxaldehydes via a one-pot borylation–copper(I) chloride co-catalyzed Suzuki-Miyaura coupling reaction. The utilization of the in situ prepared 2-thiopheneboronic ester derivative is allowed by the method developed. Elimination of the crucial, acidic liberation step of boronic acid species resulted in improved yields and purities. In addition, comparison of various aryl bromides is shown to demonstrate the high tolerance of the transformation to functional groups.     

The connectivity of a graph and its complement

Let G be a graph with minimum degree δ(G), edge-connectivity λ(G), vertex-connectivity κ(G), and let be the complement of G.In this article we prove that either λ(G)=δ(G) or . In addition, we present the Nordhaus-Gaddum type result . A family of examples will show that this inequality is best possible.     

Synthesis and Magnetic Properties of Novel Azamacrocyclic LnIII,CuII, FeIII,and SrII Complexes and Conformational Analysis of the Ligands

Hexaalkoxy‐substituted azamacrocyclic metal complexes 1 · MX_n [MX_n = FeCl₃, CuCl₂, SrCl₂, Ln(NO₃)₃; Ln = La, Pr, Eu, Ho, Er] with various chain lengths were prepared by a convergent approach using 1,2‐bisalkoxy‐4,5‐diamines 3 and 4‐alkoxy‐pyridine‐2,6‐dicarbaldehydes 4 as key building blocks for template‐assisted cyclocondensation. Metal complexes 1 · MX_n were considered as potential metallomesogens. However, differential scanning calorimetry and optical polarizing microscopy of 1 · MX_n did not reveal any mesomorphism. The magnetic susceptibility shows deviation from Curie‐like behavior. Due to ligand field effects the effective magnetic moments are a function of the temperature. In order to obtain structural informations on the free ligand 1 , which is synthetically not accessible, theoretical calculations were carried out. For the free azamacrocycle 2a and the free hexamethoxy‐substituted azamacrocycle 1a the IR spectra were computed at the level of density functional theory. A planar and a saddle‐shaped conformation was considered. The IR spectra and especially the dependence of the C=N vibration on the structural parameters and the charge distribution are discussed.