Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation

We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic, although it can be formulated also for solutions of the elliptic Ernst equation that are nowhere axis-accessible.Comment: 75 pages (plus optional table of contents). Sign errors in elliptic case equations (1A.13), (1A.15) and (1A.25) are corrected. Not relevant to proof contained in pape

In situ synthesis of size-controlled, stable silver nanoparticles within ultrashort peptide hydrogels and their anti-bacterial properties

We have developed a silver-releasing biomaterial with promising potential for wound healing applications. The material is made of ultrashort peptides which can self-assemble in water to form hydrogels. Silver nanoparticles (Ag NPs) were synthesized in situ within the biomaterial, using only UV irradiation and no additional chemical reducing agents. The synthetic strategy allows precise control of the nanoparticle size, with the network of peptide fibers preventing aggregation of Ag NPs. The biomaterial shows increased mechanical strength compared to the hydrogel control. We observed a sustained release of Ag NPs over a period of 14 days. This is a crucial prerequisite for effective anti-bacterial therapy. The ability to inhibit bacterial growth was tested using different bacterial strains, namely gram-negative Escherichia coli and Pseudomonas aeruginosa and gram-positive Staphylococcus aureus. Inhibition of bacterial growth was observed for all strains. The best results were obtained for Pseudomonas aeruginosa which is known for exhibiting multidrug resistance. Biocompatibility studies on HDFa cells, using Ag NP-containing hydrogels, did not show any significant influence on cell viability. We propose this silver-releasing hydrogel as an excellent biomaterial with great potential for applications in wound healing due to its low silver content, sustained silver nanoparticle release and biocompatibility

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Synthesis and bioactivity of a conjugate composed of green tea catechins and hyaluronic acid

(-)-Epigallocatechin-3-gallate (EGCG) is a green tea polyphenol that has several biological activities, including anti-cancer activity and anti-inflammation. Hyaluronic acid (HA) is a naturally-occurring polysaccharide that is widely used as a biomaterial for drug delivery and tissue engineering due to its viscoelastic, biocompatible and biodegradable properties. By conjugating HA with EGCG, the resulting HA-EGCG conjugate is expected to exhibit not only the inherent properties of HA but also the bioactivities of EGCG. Toward this end, we report the synthesis of an amine-functionalized EGCG as an intermediate compound for conjugation to HA. EGCG was reacted with 2,2-diethoxyethylamine (DA) under acidic conditions, forming ethylamine-bridged EGCG dimers. The EGCG dimers were composed of four isomers, which were characterized by HPLC, high-resolution mass spectrometry and NMR spectroscopy. The amine-functionalized EGCG dimers were conjugated to hyaluronic acid (HA) through the formation of amide bonds. HA-EGCG conjugates demonstrated several bioactivities which were not present in unmodified HA, including resistance to hyaluronidase-mediated degradation, inhibition of cell growth and scavenging of radicals. The potential applications of HA-EGCG conjugates are discussed

Observables for spacetimes with two Killing field symmetries

The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed directly in the Hamiltonian theory. The reduced system corresponds to the field equations of the SL(2,R) chiral model with additional constraints. On the classical phase space, a method of obtaining an infinite number of constants of the motion, or observables, is given. The procedure involves writing the Hamiltonian evolution equations as a single `zero curvature' equation, and then employing techniques used in the study of two dimensional integrable models. Two infinite sets of observables are obtained explicitly as functionals of the phase space variables. One set carries sl(2,R) Lie algebra indices and forms an infinite dimensional Poisson algebra, while the other is formed from traces of SL(2,R) holonomies that commute with one another. The restriction of the (complex) observables to the Euclidean and Lorentzian sectors is discussed. It is also shown that the sl(2,R) observables can be associated with a solution generating technique which is linked to that given by Geroch.Comment: 23 pages (LateX-RevTeX), Alberta-Thy-55-9

Risiko von Infektionen unter einer Behandlung mit Tumornekrosefaktor-α-Inhibitoren

Zusammenfassung: Tumornekrosefaktor-α (TNF) ist ein Zytokin, welches bei der Aktivierung von Entzündungszellen essenziell ist. Es ist bei der Granulombildung und -erhaltung im Rahmen von chronischen Infektionen beteiligt. Bei entzündlichen Prozessen kann sich die exzessive Produktion von TNF jedoch für den Patienten nachteilig auswirken. So spielt TNF eine wichtige Rolle bei der Entzündung chronischer Autoimmunkrankheiten. Medikamente zur Hemmung von TNF (Etanercept, Infliximab, Adalimumab) werden bei verschiedenen entzündlichen rheumatischen und autoimmunen Krankheiten mit Erfolg eingesetzt. Patienten unter einer Anti-TNF-Therapie haben ein erhöhtes Risiko, an Tuberkulose zu erkranken. Die Datenlage für andere infektiöse Erkrankungen ist weniger gut dokumentiert. Es gibt etliche anekdotische Fallberichte über die Assoziation von TNF-Hemmern und Infektionskrankheiten wie Histoplasmose, Listeriose, Kokzidioidomykose, Candidiasis und Aspergillose. Sie weisen auf eine erhöhte Infektionsanfälligkeit bei Patienten unter einer Anti-TNF-Therapie hin. In dieser Übersichtsarbeit erörtern wir zuerst die Bedeutung von TNF allgemein und spezifisch für die Infektionsabwehr, beschreiben kurz die Unterschiede der verfügbaren TNF-Hemmer und gehen im Detail die klinischen Daten durch, welche auf das erhöhte Infektionsrisiko unter einer Anti-TNF-Therapie hinweise

Growth control of GaAs nanowires using pulsed laser deposition with arsenic over pressure

Using pulsed laser ablation with arsenic over pressure, the growth conditions for GaAs nanowires have been systematically investigated and optimized. Arsenic over pressure with As$_2$ molecules was introduced to the system by thermal decomposition of polycrystalline GaAs to control the stoichiometry and shape of the nanowires during growth. GaAs nanowires exhibit a variety of geometries under varying arsenic over pressure, which can be understood by different growth processes via vapor-liquid-solid mechanism. Single-crystal GaAs nanowires with uniform diameter, lengths over 20 $\mu$m, and thin surface oxide layer were obtained and can potentially be used for further electronic characterization

Differentially rotating disks of dust: Arbitrary rotation law

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i. e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and Gravitation

Evidence of breakdown of the spin symmetry in diluted 2D electron gases

Recent claims of an experimental demonstration of spontaneous spin polarisation in dilute electron gases \cite{young99} revived long standing theoretical discussions \cite{ceper99,bloch}. In two dimensions, the stabilisation of a ferromagnetic fluid might be hindered by the occurrence of the metal-insulator transition at low densities \cite{abra79}. To circumvent localisation in the two-dimensional electron gas (2DEG) we investigated the low populated second electron subband, where the disorder potential is mainly screened by the high density of the first subband. This letter reports on the breakdown of the spin symmetry in a 2DEG, revealed by the abrupt enhancement of the exchange and correlation terms of the Coulomb interaction, as determined from the energies of the collective charge and spin excitations. Inelastic light scattering experiments and calculations within the time-dependent local spin-density approximation give strong evidence for the existence of a ferromagnetic ground state in the diluted regime.Comment: 4 pages, 4 figures, Revte