Cauchy boundary andb-incompleteness of space-time

It is shown that if a space-time (M, g) is time-orientable and its Levi-Civita connection [in the bundle of orthonormal frames over (M, g)] is reducible to anO(3) structure, one can naturally select a nonvanishing timelike vector field and a Riemann metricg ⁺ onM. The Cauchy boundary of the Riemann space (M, g ⁺) consists of endpoints ofb-incomplete curves in (M, g); we call it theCauchy singular boundary. We use the space-time of a cosmic string with a conic singularity to test our method. The Cauchy singular boundary of this space-time is explicitly constructed. It turns out to consist of what should be expected.     

Cobaltchelate als Hydrierkatalysatoren. II). Hydridbildung beim [Co(dmgH)2]- und [Co(dpnH)]+ -Komplex

Cobalt Chelates for Hydrogenation Catalysts. II. Hydride Formation with [Co(dmgH)₂] and [Co(dpnH)]⁺ In the presence of benzil as scavanger for the hydridocomplexes [Co(dpnH)]⁺ and [Co(dmgH)₂] the hydride formation in water/n-propanol (50% v/v) becomes the rate determining step, and the ligand hydrogenation is completely suppressed in the case of [Co(dpnH)]⁺, but only partially in the case of [Co(dmgH)₂]. The rate of hydride formation in both cases is 2^nd order with respect to the complex, and the activation parameters ([Co(dmgH)₂]: ΔH^≠ = 48.4 ± 1.0 kJ · mol–¹, ΔS^≠ = ?57.4 ± 3.4J · mol^?1 · K^?1, [Co(dpnH)]⁺: ΔH^≠ = 52.7 = 0.4 kJ · mol^?1, ΔS^≠ = ?59.8 ± 1.2J · mol^?1 · K^?1) indicate a H₂-activation by homolytic splitting for both complexes. Some sources of error and possible causes for the missing activity of [Co(tim)]²⁺ are discussed.     

Coupled Sliding Discharges: A Scalable Nonthermal Plasma System Utilizing Positive and Negative Streamers on Opposite Sides of a Dielectric Layer

A nonthermal plasma system based on simultaneously formed positive and negative streamers on either side of a dielectric layer is described. The coupled sliding discharge (CSD) reactor based on this concept was found to be scalable by stacking and operating multiple electrode assemblies in parallel, similarly to the shielded sliding discharge (SSD) reactor reported earlier. A comparison of the two systems showed that although the energy density in the CSD reactor was lower, the efficiency for NO conversion and ozone synthesis from dry air were significantly higher. The energy cost for 50 % NO removal was ~30 eV/molecule compared to ~60 eV/molecule in the case of the SSD under the same conditions of 330 ppm initial NO concentration in air. The energy cost decreased to ~12 eV/molecule in both cases when NO was mixed with plasma-activated air at the outlet of the reactor to utilize ozone for NO conversion i.e., indirect plasma treatment. The energy yield for ozone generation from dry air was at ~70 g/kWh, comparable in both systems. The results show that the concept of a CSD, as that of SSDs, allows the construction of compact, efficient plasma reactors.     

cyc-DEP: Cyclic immunofluorescence profiling of particles collected using dielectrophoresis

Cancer is a highly heterogenous disease that requires precise detection tools and active surveillance methods. Liquid biopsy assays provide an agnostic way to follow the complex trajectory of cancer, providing better patient stratification tools for optimized treatment. Here, we present the development of a low-volume liquid biopsy assay called cyc-DEP (cyclic immunofluorescent imaging on dielectrophoretic chip) to profile biomarkers collected on a dielectrophoretic microfluidic chip platform. To enable on-chip cyclic imaging, we optimized a fluorophore quenching method and sequential rounds of on-chip staining with fluorescently conjugated primary antibodies. cyc-DEP allows for the quantification of a multiplex array of proteins using 25 µl of a patient plasma sample. We utilized nanoparticles from a prostate adenocarcinoma (LNCaP) cell line and a panel of six target proteins to develop our proof-of-concept technique. We then used cyc-DEP to quantify blood plasma levels of target proteins from healthy individuals, low-grade and high-grade prostate cancer patients (n = 3 each) in order to demonstrate that our platform is suitable for liquid biopsy analysis in its present form. To ensure accurate quantification of signal intensities and comparisons between different samples, we incorporated a signal intensity normalization method (fluorescent beads) and a custom signal intensity quantification algorithm that account for the distribution of signal across hundreds of collection regions on each chip. Our technique enabled a threefold improvement in multiplicity for detecting proteins associated with fluid samples, opening doors for early detection, and active surveillance through quantification of a multiplex array of biomarkers from low-volume liquid biopsies.     

Photochemical Hydrogen Evolution at Metal Centers Probed with Hydrated Aluminium Cations,Al+(H2O)n,n=1–10

Hydrated aluminium cations have been investigated as a photochemical model system with up to ten water molecules by UV action spectroscopy in a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. Intense photodissociation was observed starting at 4.5 eV for two to eight water molecules with loss of atomic hydrogen, molecular hydrogen and water molecules. Quantum chemical calculations for n=2 reveal that solvation shifts the intense 3s–3p excitations of Al⁺ into the investigated photon energy range below 5.5 eV. During the photochemical relaxation, internal conversion from S₁ to T₂ takes place, and photochemical hydrogen formation starts on the T₂ surface, which passes through a conical intersection, changing to T₁. On this triplet surface, the electron that was excited to the Al 3p orbital is transferred to a coordinated water molecule, which dissociates into a hydroxide ion and a hydrogen atom. If the system remains in the triplet state, this hydrogen radical is lost directly. If the system returns to singlet multiplicity, the reaction may be reversed, with recombination with the hydroxide moiety and electron transfer back to aluminium, resulting in water evaporation. Alternatively, the hydrogen radical can attack the intact water molecule, forming molecular hydrogen and aluminium dihydroxide. Photodissociation is observed for up to n=8. Clusters with n=9 or 10 occur exclusively as HAlOH⁺(H₂O)_n-1 and are transparent in the investigated energy range. For n=4–8, a mixture of Al⁺(H₂O)_n and HAlOH⁺(H₂O)_n-1 is present in the experiment.     

Comparing the weak and strong gate‐coupling regimes for nanotube and graphene transistors

We present an experimental and theoretical comparison of the weak and strong gate‐coupling regimes that arise for carbon nanotube (CNT) and graphene field‐effect transistors (FETs) in back‐gated and liquid‐gated configuration, respectively. We find that whereas the back‐gate efficiency is suppressed for a liquid‐gated CNT FET, the back gate is still effective in case of a liquid‐gated graphene FET. We calculate the gate‐induced Fermi‐level shifts and induced charge densities. In both strong and weak coupling regimes, nonlinearities occur in the gate dependence of these parameters, which can significantly influence the electronic transport. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)