Relaxation of signed integral functionals in BV

For integral functionals initially defined for ${u \in {\rm W}^{1,1}(\Omega; \mathbb{R}^m)}$ by $$\int_{\Omega} f(\nabla u) \, {\rm d}x$$ we establish strict continuity and relaxation results in ${{\rm BV}(\Omega; \mathbb{R}^m)}$ . The results cover the case of signed continuous integrands ${f : \mathbb{R}^{m \times d} \to \mathbb{R}}$ of linear growth at infinity. In particular, it is not excluded that the integrands are unbounded below.     

BMO and uniform estimates for multi-well problems

We establish optimal local regularity results for vector-valued extremals and minimizers of variational integrals whose integrand is the squared distance function to a compact set K in matrix space ${{{\mathbb M}^{N \times n}}}$ . The optimality is illustrated by explicit examples showing that, in the nonconvex case, minimizers need not be locally Lipschitz. This is in contrast to the case when the set K is suitably convex, where we show that extremals are locally Lipschitz continuous. The results rely on the special structure of the integrand and elementary Cordes–Nirenberg type estimates for elliptic systems.     

Half-flat structures on S^3\times S^3

We describe left-invariant half-flat $ \mathrm{SU }(3) $ -structures on $ S^3\times S^3$ using the representation theory of $ \mathrm SO (4) $ and matrix algebra. This leads to a systematic study of the associated cohomogeneity one Ricci-flat metrics with holonomy $ \mathrm G _2$ obtained on $ 7 $ -manifolds with equidistant $ S^3\times S^3$ hypersurfaces. The generic case is analysed numerically.     

Fibronectin adsorption on tantalum: the influence of nanoroughness

The complex mechanisms of protein adsorption at the solid-liquid interface is of great importance in many research areas, including protein purification, biocompatibility of medical implants, biosensing, and biofouling. The protein adsorption process depends crucially on both the nanoscale chemistry and topography of the interface. Here, we investigate the adsorption of the cell-binding protein fibronectin on flat and nanometer scale rough tantalum oxide surfaces using ellipsometry and quartz crystal microbalance with dissipation (QCM-D). On the flat tantalum oxide surfaces, the interfacial protein spreading causes an increase in the rigidity and a decrease in the thickness of the adsorbed fibronectin layer with decreasing bulk protein concentration. For the tantalum oxide surfaces with well-controlled, stochastic nanometer scale roughness, similar concentration effects are observed for the rigidity of the fibronectin layer and saturated fibronectin uptake. However, we find that the nanorough tantalum oxide surfaces promote additional protein conformational changes, an effect especially apparent from the QCM-D signals, interpreted as an additional stiffening of the formed fibronectin layers.     

Benchmark density functional theory calculations for nanoscale conductance

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code in combination with maximally localized Wannier functions and the norm-conserving pseudopotential code SIESTA which applies an atomic orbital basis set. All calculations have been converged with respect to the supercell size and the number of k|| points in the surface plane. For all systems we find that the SIESTA transmission functions converge toward the plane-wave result as the SIESTA basis is enlarged. Overall, we find that an atomic basis with double zeta and polarization is sufficient (and in some cases, even necessary) to ensure quantitative agreement with the plane-wave calculation. We observe a systematic downshift of the SIESTA transmission functions relative to the plane-wave results. The effect diminishes as the atomic orbital basis is enlarged; however, the convergence can be rather slow.     

A Unique Tryptophan C‐Prenyltransferase from the Kawaguchipeptin Biosynthetic Pathway

Cyanobactins are a rapidly growing family of linear and cyclic peptides produced by cyanobacteria. Kawaguchipeptins A and B, two macrocyclic undecapeptides reported earlier from Microcystis aeruginosa NIES‐88, are shown to be products of the cyanobactin biosynthetic pathway. The 9 kb kawaguchipeptin (kgp) gene cluster was identified in a 5.26 Mb draft genome of Microcystis aeruginosa NIES‐88. We verified that this gene cluster is responsible for the production of the kawaguchipeptins through heterologous expression of the kgp gene cluster in Escherichia coli. The KgpF prenyltransferase was overexpressed and was shown to prenylate C‐3 of Trp residues in both linear and cyclic peptides in vitro. Our findings serve to further enhance the structural diversity of cyanobactins to include tryptophan‐prenylated cyclic peptides.     

Martin Boundary of a Fine Domain and a Fatou-Naïm-Doob Theorem for Finely Superharmonic Functions

Let Γ be a graph with the doubling property for the volume of balls and P a reversible random walk on Γ. We introduce H¹ Hardy spaces of functions and 1-forms adapted to P and prove various characterizations of these spaces. We also characterize the dual space of H¹ as a BMO-type space adapted to P. As an application, we establish H¹ and H¹- L¹ boundedness of the Riesz transform.     

ALD resist formed by vapor-deposited self-assembled monolayers

A new process of applying molecular resists to block HfO2 and Pt atomic layer deposition has been investigated. Monolayer films are formed from octadecyltrichlorosilane (ODTS) or tridecafluoro-1,1,2,2-tetrahydrooctyltrichlorosilane (FOTS) and water vapor on native silicon oxide surfaces and from 1-octadecene on hydrogen-passivated silicon surfaces through a low-pressure chemical vapor deposition process. X-ray photoelectron spectroscopy data indicates that surfaces blocked by these monolayer resists can prevent atomic layer deposition of both HfO2 and Pt successfully. Time-dependent studies show that the ODTS monolayers continue to improve in blocking ability for as long as 48 h of formation time, and infrared spectroscopy measurements confirm an evolution of packing order over these time scales.