Boundedness of solutions of a system of integro-differential equations

Let b: [?1, 0] →$\text{R}$ be a nondecreasing, strictly convex C²-function with b(? 1) = 0, and let g: $\text{R}$ⁿ → $\text{R}$ⁿ be a locally Lipschitzian mapping, which is the gradient of a function G: $\text{R}$ⁿ → $\text{R}$. Consider the following vector-valued integro-differential equation of the Levin-Nohel type

$\text{x}\text{?}\text{(t)=?∝}{}_{\mathrm{?1}}{}^0\text{b(θ)g(x(t + θ))dθ}$

. (E) This equation is used in applications to model various viscoelastic phenomena. By LaSalle's invariance principle, every bounded solution x(t) goes to a connected set of zeros of g, as time t goes to infinity. It is the purpose of this paper to give several geometric criteria assuring the boundedness of solutions of (E) or some of its components.     

1H MRS detection of glycine residue of reduced glutathione in vivo

Glutathione (GSH) is a powerful antioxidant found inside different kinds of cells, including those of the central nervous system. Detection of GSH in the human brain using ¹H MR spectroscopy is hindered by low concentration and spectral overlap with other metabolites. Previous MRS methods focused mainly on the detection of the cysteine residue (GSH-Cys) via editing schemes. This study focuses on the detection of the glycine residue (GSH-Gly), which is overlapped by glutamate and glutamine (Glx) under physiological pH and temperature. The first goal of the study was to obtain the spectral parameters for characterization of the GSH-Gly signal under physiological conditions. The second goal was to investigate a new method of separating GSH-Gly from Glx in vivo. The characterization of the signal was carried out by utilization of numerical simulations as well as experiments over a wide range of magnetic fields (4.0–14 T). The proposed separation scheme utilizes J-difference editing to quantify the Glx contribution to separate it from the GSH-Gly signal. The presented method retains 100% of the GSH-Gly signal. The overall increase in signal to noise ratio of the targeted resonance is calculated to yield a significant SNR improvement compared to previously used methods that target GSH-Cys residue. This allows shorter acquisition times for in vivo human clinical studies.     

The Gauge–Bethe Correspondence and Geometric Representation Theory

The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive. We argue here that geometrical representation theory is a mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.     

Evaluation of aortic stenosis severity using 4D flow jet shear layer detection for the measurement of valve effective orifice area

Aims

The objective of this study was to evaluate the potential of 4D flow MRI to assess valve effective orifice area (EOA) in patients with aortic stenosis as determined by the jet shear layer detection (JSLD) method.

Methods and Results

An in-vitro stenosis phantom was used for validation and in-vivo imaging was performed in 10 healthy controls and 40 patients with aortic stenosis. EOA was calculated by the JSLD method using standard 2D phase contrast MRI (PC-MRI) and 4D flow MRI measurements (EOA_JSLD-2D and EOA_JSLD-4D, respectively). As a reference standard, the continuity equation was used to calculate EOA (EOA_CE) with the 2D PC-MRI velocity field and compared to the EOA_JSLD measurements. The in-vitro results exhibited excellent agreement between flow theory (EOA = 0.78 cm²) and experimental measurement (EOA_JSLD-4D = 0.78 ± 0.01 cm²) for peak velocities ranging from 0.9 to 3.7 m/s. In-vivo results showed good correlation and agreement between EOA_JSLD-2D and EOA_CE (r = 0.91, p < 0.001; bias: − 0.01 ± 0.38 cm²; agreement limits: 0.75 to − 0.77 cm²), and between EOA_JSLD-4D and EOA_CE (r = 0.95, p < 0.001; bias: − 0.09 ± 0.26 cm²; limits: 0.43 to − 0.62 cm²).

Conclusion

This study demonstrates the feasibility of measuring EOA_JSLD using 4D flow MRI. The technique allows for optimization of the EOA measurement position by visualizing the 3D vena contracta, and avoids potential sources of EOA_CE measurement variability.     

High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip

We show that a concentration of light at a metal tip allows near-field optical imaging of single fluorescent dye molecules at very high resolution, despite strong quenching effects. Details as small as 10 nm were observed in the fluorescence patterns of single Cy-3 dyes bound to the termini of DNA. Data evaluation by model fitting determines the positions of the dyes to an accuracy even better than 1 nm and also yields their 3D orientation. The metal tip simultaneously provides high-resolution topographic imaging complementing the optical signal for a detailed surface examination.     

Convergence of nonconforming multigrid methods without full elliptic regularity

We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound () for the contraction number of the -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable -cycle algorithm is an optimal preconditioner.

     

High-sensitivity microchip electrophoresis determination of inorganic anions and oxalate in atmospheric aerosols with adjustable selectivity and conductivity detection

A sensitive and selective separation of common anionic constituents of atmospheric aerosols, sulfate, nitrate, chloride, and oxalate, is presented using microchip electrophoresis. The optimized separation is achieved in under 1 min and at low background electrolyte ionic strength (2.9 mM) by combining a metal-binding electrolyte anion (17 mM picolinic acid), a sulfate-binding electrolyte cation (19 mM HEPBS), a zwitterionic surfactant with affinity towards weakly solvated anions (19 mM N-tetradecyl,N,N-dimethyl-3-ammonio-1-propansulfonate), and operation in counter-electroosmotic flow (EOF) mode. The separation is performed at pH 4.7, permitting pH manipulation of oxalate's mobility. The majority of low-concentration organic acids are not observed at these conditions, allowing for rapid subsequent injections without the presence of interfering peaks. Because the mobilities of sulfate, nitrate, and oxalate are independently controlled, other minor constituents of aerosols can be analyzed, including nitrite, fluoride, and formate if desired using similar separation conditions. Contact conductivity detection is utilized, and the limit of detection for oxalate (S/N = 3) is 180 nM without stacking. Sensitivity can be increased with field-amplified sample stacking by injecting from dilute electrolyte with a detection limit of 19 nM achieved. The high-sensitivity, counter-EOF operation, and short analysis time make this separation well-suited to continuous online monitoring of aerosol composition.     

Application of 1,10-phenanthroline for preconcentration of selected heavy metals on silica gel

Stripping voltammetry analysis using a hemispheroidal mercury microelectrode has been previously assessed theoretically as a possible candidate ‘primary method’ for amount of substance measurement. It was shown that the measurement methodology can be described completely by a set of measurement equations when a novel quantification process is employed to measure the steady-state diffusion-limited deposition current over an optimum sampling time, instead of employing an analyte stripping step. The corollary is that, for solutions of known composition, the method may be used for highly accurate determination of diffusion coefficients. This investigation uses experimental data from steady-state diffusion-limited current measurements with sampling periods optimised using Allan deviation techniques, together with a full uncertainty analysis to estimate feasibility and likely accuracy of this method.