On the Carleson Measure Criterion in Linear Systems Theory

In Ho and Russell (SIAM J Control Optim 21(4):614–640, 1983), and Weiss (Syst Control Lett 10(1): 79–82, 1988), a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation (L ²-admissibility on the state space ℓ ₂) to the more general situation of L ^p -admissibility on the state space ℓ _q . For analytic diagonal semigroups we present a new result that does not rely on Laplace transform methods. A comparison of both criteria leads to a result on L ^p -admissibility for reciprocal systems in the sense of Curtain (Syst Control Lett 49(2):81–89, 2003).     

Best constants in a borderline case of second-order Moser type inequalities

We study optimal embeddings for the space of functions whose Laplacian Δu   belongs to L¹(Ω)$L^1(\Omega )$, where Ω⊂RN$\Omega \subset {\mathbb{R}}^N$ is a bounded domain. This function space turns out to be strictly larger than the Sobolev space W2,1(Ω)$W^{2,1}(\Omega )$ in which the whole set of second-order derivatives is considered. In particular, in the limiting Sobolev case, when N=2$N=2$, we establish a sharp embedding inequality into the Zygmund space Lexp(Ω)$L_{\mathit{exp}}(\Omega )$. On one hand, this result enables us to improve the Brezis–Merle (Brezis and Merle (1991) [13]) regularity estimate for the Dirichlet problem Δu=f(x)∈L¹(Ω)$\mathrm{\Delta }u=f(x)\in L^1(\Omega )$, u=0$u=0$ on ∂Ω; on the other hand, it represents a borderline case of D.R. Adams' (1988) [1] generalization of Trudinger–Moser type inequalities to the case of higher-order derivatives. Extensions to dimension N?3$N?3$ are also given. Besides, we show how the best constants in the embedding inequalities change under different boundary conditions.     

Radial and non radial solutions for Hardy–Hénon type elliptic systems

We discuss existence and non-existence of positive solutions for the following system of Hardy and Hénon type: $$\left\{\begin{array}{ll} {-\Delta v=|x|^{\alpha}u^{p},\,-\Delta u=|x|^{\beta}v^{q} \,\,{\rm in}\, \Omega,}\\ {u=v=0 \quad\quad\quad\quad\quad\quad\quad\quad\quad{\rm on}\, \partial \Omega}, \end{array}\right.$$ where ${\Omega\ni 0}$ is a bounded domain in ${\mathbb{R}^{N}}$ , N ≥ 3, p, q > 1, and α, β > ?N. We also study symmetry breaking for ground states when Ω is the unit ball in ${\mathbb{R}^{N}}$ .     

An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics

This paper defines a new transport metric over the space of nonnegative measures. This metric interpolates between the quadratic Wasserstein and the Fisher–Rao metrics and generalizes optimal transport to measures with different masses. It is defined as a generalization of the dynamical formulation of optimal transport of Benamou and Brenier, by introducing a source term in the continuity equation. The influence of this source term is measured using the Fisher–Rao metric and is averaged with the transportation term. This gives rise to a convex variational problem defining the new metric. Our first contribution is a proof of the existence of geodesics (i.e., solutions to this variational problem). We then show that (generalized) optimal transport and Hellinger metrics are obtained as limiting cases of our metric. Our last theoretical contribution is a proof that geodesics between mixtures of sufficiently close Dirac measures are made of translating mixtures of Dirac masses. Lastly, we propose a numerical scheme making use of first-order proximal splitting methods and we show an application of this new distance to image interpolation.     

Harmonic Analysis for Real Spherical Spaces

We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.     

Facial solar UV exposure of Austrian farmers during occupation

Optoelectronic personal UV-meters were used to monitor the occupational facial solar erythemally effective exposure of 12 Austrian full-time farmers with high temporal resolution. To ensure high quality measurements several quality assurance procedures were applied, like calibration with respect to solar elevation and total ozone column. From April to October the test persons carried the UV-meters on the forehead during working hours. A digital diary (activity, location, weather, photoprotective measures) was completed on an hourly basis. Our field test produced 1427 complete daily records (measurement and diary). The total exposures showed high variability (77 –757 standard erythema dose [SED]) which correlates with the number of working days and even stronger with the little numbers of days with high exposure (>10 SED). Risk factors for high exposures were: mixed-culture farms with aggravated working conditions, low degree of automation of working processes, inadequate operating logistics (summarized as manual work outdoor), driving machines without cabins, and female gender. UV exposure of female farmers was approximately twice as high as that of men: Women received 15% of ambient radiation while men got 8%. Avoiding daily exposure >10 SED could reduce exposure down to 40% and the risk in developing skin cancer by a factor of 40.     

Determination of heavy metals in activated charcoals and carbon black for Lyocell fiber production using direct solid sampling high-resolution continuum source graphite furnace atomic absorption and inductively coupled plasma optical emission spectrometry

Reactivity and concentration of additives, especially activated charcoal, employed for the Lyocell process, enhance the complexity of reactions in cellulose/N-methylmorpholine-N-oxide monohydrate solutions. Analytical control of the starting materials is a basic requirement to know the concentration of heavy metals, which are potential initiators of autocatalytic reactions. Seven activated charcoal and two carbon black samples have been analyzed regarding their content of seven elements, Cr, Cu, Fe, Mn, Mo, Ni and V using direct solid sampling high-resolution continuum source graphite furnace AAS (SS-HR-CS GF AAS) and inductively coupled plasma optical emission spectrometry (ICP OES) after microwave-assisted acidic digestion as a reference method. The limits of detection of the former technique are 1-2 orders of magnitude lower than those of ICP OES and comparable to those of more sophisticated techniques. For iron the working range of HR-CS GF AAS has been expanded by simultaneous measurement at two secondary absorption lines (344,099 nm and 344,399 nm). Partial least-squares regression between measured and calculated temperatures for beginning exothermicity (T_on) has been used to investigate the prediction capability of the investigated techniques. Whereas the ICP OES measurements for seven elements resulted in an error of prediction of 3.67%, the results obtained by SS-HR-CS GF AAS exhibited a correlation coefficient of 0.99 and an error of prediction of only 0.68%. Acceptable correlation has been obtained with the latter technique measuring only three to four elements.     

The protein kinase DYRK1A phosphorylates the splicing factor SF3b1/SAP155 at Thr434, a novel in vivo phosphorylation site

Background

Diacylglycerol acyltransferase (DGAT, EC 2.3.1.20) catalyzes the acyl-CoA-dependent acylation of sn-1, 2-diacylglycerol to generate triacylglycerol and CoA. The deduced amino acid sequence of cDNAs encoding DGAT1 from plants and mammals exhibit a hydrophilic N-terminal region followed by a number of potential membrane-spanning segments, which is consistent with the membrane-bound nature of this enzyme family. In order to gain insight into the structure/function properties of DGAT1 from Brassica napus (BnDGAT1), we produced and partially characterized a recombinant polyHis-tagged N-terminal fragment of the enzyme, BnDGAT1_(1–116)His₆, with calculated molecular mass of 13,278 Da.

Results

BnDGAT1_(1–116)His₆ was highly purified from bacterial lysate and plate-like monoclinic crystals were grown using this preparation. Lipidex-1000 binding assays and gel electrophoresis indicated that BnDGAT1_(1–116)His₆ interacts with long chain acyl-CoA. The enzyme fragment displayed enhanced affinity for erucoyl (22:1cis^Δ13)-CoA over oleoyl (18:1cis^Δ9)-CoA, and the binding process displayed positive cooperativity. Gel filtration chromatography and cross-linking studies indicated that BnDGAT1_(1–116)His₆ self-associated to form a tetramer. Polyclonal antibodies raised against a peptide of 15 amino acid residues representing a segment of BnDGAT1_(1–116)His₆ failed to react with protein in microsomal vesicles following treatment with proteinase K, suggesting that the N-terminal fragment of BnDGAT1 was localized to the cytosolic side of the ER.

Conclusion

Collectively, these results suggest that BnDGAT1 may be allosterically modulated by acyl-CoA through the N-terminal region and that the enzyme self-associates via interactions on the cytosolic side of the ER.