Absorption Spectra of 4‐Nitrophenolate Ions Measured in Vacuo and in Solution

From blue to red: While four π‐conjugated nitrophenolates absorb within a relatively narrow region in solution, they cover the entire visible spectrum when isolated in vacuo (see picture). The work combines gas‐ and solution‐phase spectroscopy and provides the first benchmark of theoretical excitation energies for nitrophenolates.

     

Synthesis of Small‐Molecule Fluorescent Probes for the In Vitro Imaging of Calcium‐Activated Potassium Channel KCa3.1

Small‐molecule probes for the in vitro imaging of K_Ca3.1 channel‐expressing cells were developed. Senicapoc, showing high affinity and selectivity for the K_Ca3.1 channels, was chosen as the targeting component. BODIPY dyes 15 – 20 were synthesized and connected by a Cu^I‐catalyzed azide–alkyne [3+2]cycloaddition with propargyl ether senicapoc derivative 8 , yielding fluorescently labeled ligands 21 – 26 . The dimethylpyrrole‐based imaging probes 25 and 26 allow staining of K_Ca3.1 channels in NSCLC cells. The specificity was shown by removing the punctate staining pattern by pre‐incubation with senicapoc. The density of K_Ca3.1 channels detected with 25 and by immunostaining was identical. The punctate structure of the labeled channels could also be observed in living cells. Molecular modeling showed binding of the senicapoc‐targeting component towards the binding site within the ion channel and orientation of the linker with the dye along the inner surface of the ion channel.     

Time-Resolved Crystallography at X-ray Free Electron Lasers and Synchrotron Light Sources

Serial femtosecond crystallography with biological macromolecules is a rapidly developing method tailored to the immense brilliance of the emerging free electron lasers for hard X-rays (X-ray FELs). Recently, the first successful time-resolved serial femtosecond crystallographic experiment at near atomic resolution was conducted at the Linac Coherent Light Source. The X-ray FEL-based experiments will trigger new developments not only at the X-ray FELs, but also at existing synchrotron light sources. This review will attempt to summarize some of the most important experiments to date and give a brief outlook on what to expect.     

19F-detected dual-optimized inverted 1JCC 1,n-ADEQUATE

Modification of the recently reported ¹⁹F-detected 1,1-ADEQUATE experiment that incorporates dual-optimization to selectively invert a wide range of ¹J_CC correlations in a 1,n-ADEQUATE experiment is reported. Parameters for the dual-optimization segment of the pulse sequence were modified to accommodate the increased size of ¹J_CC homonuclear coupling constants of poly- and perfluorinated molecules relative to protonated molecules to allow broadband inversion of the ¹J_CC correlations. The observation and utility of isotope shifts are reported for the first time for 1,1- and 1,n-ADEQUATE correlations.     

W(bipy)(CN)6]-: a suitable metalloligand in the design of heterotrimetallic complexes. The first Cu(II)Ln(III)W(V) trinuclear complexes

The first 3d-4f-5d heterotrimetallic complexes using [W(V)(bipy)(CN)(6)](-) as a metalloligand were synthesized (bipy = 2,2'-bipyridine). The structural and magnetic properties of three [Cu(II)Ln(III)W(V)] complexes (Ln = Gd, Ho, Tb) are discussed.     

Real function reconstruction from sparse Fourier samples

In this paper we use the Prony method to reconstruct structured, real-valued functions from the smallest possible number of equidistantly distributed Fourier samples. In particular, we consider characteristic functions in whose supports are unit-height polygons in the plane with N vertices. We show that these functions can be recovered by 3N Fourier samples. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A posteriori bounds for linear functional outputs of Crouzeix–Raviart finite element discretizations of the incompressible Stokes problem

A finite element technique is presented for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions. The finite element discretization is effected by Crouzeix–Raviart elements, the discontinuous pressure approximation of which is central to this approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic ‘energy’ reformulation of the desired output, the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the inter‐sub‐domain continuity conditions on velocity. Appealing to the dual max–min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine‐mesh discretization. The Lagrange multipliers are generated by exploiting an associated coarse‐mesh approximation. In addition to the requisite coarse‐mesh calculations, the bound technique requires the solution of only local sub‐domain Stokes problems on the fine mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flow rate past and the lift force on a body immersed in a channel. Copyright © 2000 John Wiley & Sons, Ltd.     

Global Well-posedness of Incompressible Inhomogeneous Fluid Systems with Bounded Density or Non-Lipschitz Velocity

In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier–Stokes equations with initial data ${a_0 \in L^\infty (\mathbb{R}^d), u_0 = (u_0^h, u_0^d) \in \dot{B}^{-1+\frac{d}{p}}_{p, r} (\mathbb{R}^d)}$ , which satisfy ${(\mu \| a_0 \|_{L^\infty} + \|u_0^h\|_{\dot{B}^{-1+\frac{d}{p}}_{p, r}}) {\rm exp}(C_r{\mu^{-2r}}\|u_0^d\|_{\dot{B}^{-1+\frac{d}{p}}_{p,r}}^{2r}) \leqq c_0\mu}$ for some positive constants c ₀, C _r and 1 < p < d, 1 < r < ∞. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity fields. Furthermore, with additional regularity assumptions on the initial velocity or on the initial density, we can also prove the uniqueness of such a solution. We should mention that the classical maximal L ^p (L ^q ) regularity theorem for the heat kernel plays an essential role in this context.