The analytic torsion of a cone over an odd dimensional manifold

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem [3, 2] for a manifold with boundary, according to Bruning and Ma (2006) [5]. We also prove Poincare duality for the analytic torsion of a cone. (C) 2010 Elsevier B.V. All rights reserved.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Evaluation of a simple hyphenated system for flow injection solid-phase pre-concentration and capillary electrophoresis

In this work, the development and evaluation of a hyphenated flow injection-capillary electrophoresis system with on-line pre-concentration is described. Preliminary tests were performed to investigate the influence of flow rates over the analytical signals. Results revealed losses in terms of sensitivity of the FIA-CE system when compared to the conventional CE system. To overcome signal decrease and to make the system more efficient, a lower flow rate was set and an anionic resin column was added to the flow manifold in order to pre-concentrate the analyte. The pre-concentration FIA-CE system presented a sensitivity improvement of about 660% and there was only a small increase of 8% in total peak dispersion. These results have confirmed the great potential of the proposed system for many analytical tasks especially for low concentration samples.

The Effects of Commercially Available Preservative-Free FDA-Approved Triamcinolone (Triesence (R)) on Retinal Cells in Culture

Purpose: To evaluate the effects of Triesence (R) (TRI), a new preservative-free triamcinolone approved by the U. S. Food and Drug Administration (FDA) for intraocular use, on human retina pigment epithelial (ARPE-19) and rat neurosensory (R28) cells in culture. Methods: ARPE-19 and R28 cell cultures were treated 24 h with 1,000, 500, 200, or 100 mu g/mL of crystalline (cTRI) or 1,000, 500, or 200 mu g/mL of solubilized (sTRI). TRI was solubilized by centrifuging the drug, discarding the supernatant containing the vehicle and then resuspending the drug pellet in an equivalent amount of Dimethyl sulfoxide to achieve the same concentration as the commercial preparation. Percentage of cell viability (CV) was evaluated by a trypan blue dye-exclusion assay. The mitochondrial membrane potential (Delta Psi m) was analyzed with the JC-1 assay. The caspase-3/7 activity was measured by a fluorochrome assay. Results: In the ARPE-19 cultures, the cTRI caused a decrease in CV at 1,000 mg/mL (13.03 +/- 6.51; P < 0.001), 500 mu g/mL (28.87 +/- 9.3; P < 0.001), 200 mu g/mL (54.93 +/- 5.61; P < 0.001), and 100 mu g/mL (82.53 +/- 0.65; P < 0.005) compared with the untreated controls (96.98 +/- 0.16). In R28 cultures, the cTRI treatment also reduced CV values significantly (P < 0.001) for the 1,000 mu g/mL (22.73 +/- 2.44), 500 mu g/mL (34.63 +/- 1.91), 200 mu g/mL (58.70 +/- 1.39), and 100 mu g/m (75.33 +/- 2.47) compared with the untreated controls (86.08 +/- 3.54). Once the TRI was solubilized (sTRI), the CV and Delta Psi m remained similar to the untreated controls for both ARPE-19 and R28 cells. The sTRI treatment with 1,000, 500, and 200 mu g/mL increased in caspase-3/7 activity in ARPE-19 cells (P < 0.01) and in R28 cells (P < 0.05) compared with dimethyl sulfoxide equivalent controls. Conclusion: The crystalline form of TRI (cTRI) can cause a significant decrease in CV to cultured retinal cells. Once the TRI is solubilized (sTRI), at the same concentrations, the cells remain viable with no decrease in CV or Delta Psi m. The sTRI can, however, increase caspase-3/7 activity, thus suggesting some degree of apoptosis.

FLOWS WITHOUT WANDERING POINTS ON COMPACT CONNECTED SURFACES

Given a compact 2 dimensional manifold M we classify all continuous flows phi without wandering points on M. This classification is performed by finding finitely many pairwise disjoint open phi-invariant subsets {U(1), U(2), ..., U(n)} of M such that U(i=1)(n) (U(i)) over bar = M and each U(i) is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of phi.

AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter

The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial particle and heat transport. However, the transport poloidal profile is much influenced by the presence of chaotic magnetic field lines at the plasma edge caused by external perturbations. Contrary to many expectations, it has been observed that such a chaotic region does not uniformize heat and particle deposition on the inner tokamak wall. The deposition is characterized instead by structured patterns called magnetic footprints, here investigated for a nonmonotonic analytical plasma equilibrium perturbed by an ergodic limiter. The magnetic footprints appear due to the underlying mathematical skeleton of chaotic magnetic field lines determined by the manifold tangles. For the investigated edge safety factor ranges, these effects on the wall are associated with the field line stickiness and escape channels due to internal island chains near the flux surfaces. Comparisons between magnetic footprints and escape basins from different equilibrium and ergodic limiter characteristic parameters show that highly concentrated magnetic footprints can be avoided by properly choosing these parameters. (c) 2008 American Institute of Physics.

Equifocality of a singular Riemannian foliation

A singular foliation on a complete Riemannian manifold M is said to be Riemannian if each geodesic that is perpendicular to a leaf at one point remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. In addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. These results generalize previous results of the authors on singular Riemannian foliations with sections.

Metastable BrO(2+) and NBr(2+) molecules in the gas phase

The doubly positively charged gas-phase molecules BrO(2+) and NBr(2+) have been produced by prolonged high-current energetic oxygen (17 keV (16)O(-)) ion surface bombardment (ion beam sputtering) of rubidium bromide (RbBr) and of ammonium bromide (NH(4)Br) powdered ionic salt samples, respectively, pressed into indium foil. These novel species were observed at half-integer m/z values in positive ion mass spectra for ion flight times of roughly similar to 12 mu s through a magnetic-sector secondary ion mass spectrometer. Here we present these experimental results and combine them with a detailed theoretical investigation using high level ab initio calculations of the ground states of BrO(2+) and NBr(2+), and a manifold of excited electronic states. NBr(2+) and BrO(2+), in their ground states, are long-lived metastable gas-phase molecules with well depths of 2.73 x 10(4) cm(-1) (3.38 eV) and 1.62 x 10(4) cm(-1) (2.01 eV); their fragmentation channels into two monocations lie 2.31 x 10(3) cm(-1) (0.29 eV) and 2.14 x 10(4) cm(-1) (2.65 eV) below the ground state minimum. The calculated lifetimes for NBr(2+) (v '' < 35) and BrO(2+) (v '' < 18) are large enough to be considered stable against tunneling. For NBr(2+), we predicted R(e) = 3.051 a(0) and omega(e) = 984 cm(-1); for BrO(2+), we obtained 3.033 a(0) and 916 cm(-1), respectively. The adiabatic double ionization energies of BrO and NBr to form metastable BrO(2+) and NBr(2+) are calculated to be 30.73 and 29.08 eV, respectively. The effect of spin-orbit interactions on the low-lying (Lambda + S) states is also discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3562121]

Exploitation of a single interface flow system for on-line aqueous biphasic extraction

The exploitation of aqueous biphasic extraction is proposed for the first time in flow analysis This extraction strategy stands out for being environmentally attractive since it is based in the utilization of two immiscible phases that are intrinsically aqueous The organic solvents of the traditional liquid-liquid extractions ale no longer used, being replaced by non-toxic, non-flammable and non-volatile ones. A single interface flow analysis (SIFA) system was implemented to carry out the extraction process due to its favourable operational characteristics that include the high automation level and simplicity of operation, the establishment of a dynamic interface where the mass transfer occurred between the two immiscible aqueous phases, and the versatile control over the extraction process namely the extraction time The application selected to demonstrate the feasibility of SIFA to perform this aqueous biphasic extraction was the pre-concentration of lead. After extraction, lead reacted with 8-hydroxyquinoline-5-sulfonic acid and the resulting product was determined by a fluorimetric detector included in the flow manifold. Therefore, the SIFA single interface was used both as extraction (enrichment) and reaction interface. (C) 2010 Elsevier B.V All rights reserved.

Multi-commutation in spectrometry

We review recent developments in manifold components and the introduction of light-emitting-diode technology in spectroscopic detection in order to evaluate the tremendous possibilities offered by multi-commutation for infield and in-situ measurements, based on the use of multi-pumping and low-voltage, portable batteries, which make possible a dramatic reduction in size, weight and power requirements of spectrometric devices. (C) 2009 Elsevier Ltd. All rights reserved.

Total and inorganic mercury determination in fish tissue by flow injection cold vapour atomic fluorescence spectrometry

A simple and reliable method for Hg determination in fish samples has been developed. Lyophilised fish tissue samples were extracted in a 25% (w/v) tetramethylammonium hydroxide (TMAH) solution; the extracts were then analysed by FI-CVAFS. This method can be used to determine total and inorganic Hg, using the same FI manifold. For total Hg determination, a 0.1% (w/v) KMnO(4) solution was added to the FI manifold at the sample zone, followed by the addition of a 0.5% (w/v) SnCl(2) solution, whereas inorganic Hg was determined by adding a 0.1% (w/v) L-cysteine solution followed by a 1.0% (w/v) SnCl(2) solution to the FI system. The organic fraction was determined as the difference between total and inorganic Hg. Sample preparation, reagent consumption and parameters that can influence the FI-CVAFS performance were also evaluated. The limit of detection for this method is 3.7 ng g(-1) for total Hg and 4.3 ng g(-1) for inorganic Hg. The relative standard deviation for a 1.0 mu gL(-1) CH(3)Hg standard solution (n = 20) was 1.1%, and 1.3% for a 1.0 mu gL(-1) Hg(2+) standard solution (n = 20). Accuracy was assessed by the analysis of Certified Reference Material (dogfish: DORM-2, NRCC). Recoveries of 99.1% for total Hg and 93.9% inorganic Hg were obtained. Mercury losses were not observed when sample solutions were re-analysed after a seven day period of storage at 4 degrees C.

An expert flow system involving in-line prior assay for turbidimetric determination of chloride and sulphate in natural waters

A multi-pumping flow system exploiting prior assay is proposed for sequential turbidimetric determination of sulphate and chloride in natural waters. Both methods are implemented in the same manifold that provides facilities for: in-line sample clean-up with a Bio-Rex 70 mini-column with fluidized beads: addition of low amounts of sulphate or chloride ions to the reaction medium for improving supersaturation; analyte precipitation with Ba(2+) or Ag(+); real-time decision on the need for next assay. The sample is initially run for chloride determination, and the analytical signal is compared with a preset value. If higher, the sample is run again, now for sulphate determination. The strategy may lead to all increased sample throughput. The proposed system is computer-controlled and presents enhanced figures of merit. About 10 samples are run per hour (about 60 measurements) and results are reproducible and Unaffected by the presence of potential interfering ions at concentration levels usually found in natural waters. Accuracy was assessed against ion chromatography. (C) 2008 Elsevier B.V. All rights reserved.