Vertices, sources and Green correspondents of the simple modules for the large Mathieu groups

We investigate the simple modules for the sporadic simple Mathieu groups M₂₂, M₂₃ and M₂₄ as well as those of the automorphism group, the covering groups and the bicyclic extensions of M₂₂ in characteristics 2 and 3. We determine the vertices and sources as well as the Green correspondents of these simple modules. We also find two 3-blocks with elementary abelian defect groups of order 9 in these groups which are Morita equivalent to their Brauer correspondents.     

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.     

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.

     

Hlawka’s functional inequality

The paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) $$f(x+y)+f(y+z)+f(x+z)\leq f(x+y+z)+f(x)+f(y)+f(z)$$ for the unknown mapping f defined on an Abelian group, on a linear space or on the real line. The study of the foregoing inequality is motivated by Hlawka’s inequality: $$\|x+y\|+\|y+z\|+\|x+z\|\leq\|x+y+z\|+\|x\|+\|y\|+\|z\|,$$ which in particular holds true for all x, y, z from a real or complex inner product space.     

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.     

Korn's inequalities for piecewise vector fields

Korn's inequalities for piecewise vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

     

Network information and connected correlations

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.     

Acoustic Radiation Force Impulse-Imaging for the evaluation of the thyroid gland: a limited patient feasibility study

Purpose

Real-time tissue elastography, a qualitative elastography method, has shown promising results in the diagnostic work up of thyroid nodules. However, to our knowledge no study has evaluated a quantitative elastography method in the thyroid gland. The present study is a feasibility study evaluating Acoustic Radiation Force Impulse-Imaging, a novel quantitative elastography method in the thyroid gland.

Methods

ARFI-imaging involves the mechanical excitation of tissue using short-duration acoustic pulses to generate localized displacements in tissue. The displacements induce a lateral shear-wave propagation which is tracked using multiple laterally positioned ultrasound “tracking“ beams. Inclusion criteria were: thyroid nodules ?1 cm, non-functioning or hypo-functioning on radionuclide scanning, and cytological/histological assessment of thyroid nodule as reference method. All patients received conventional ultrasound, and examination of the thyroid gland including Power Doppler Ultrasound using a 9 MHz linear transducer, in addition real-time elastography (RTE) was performed at 9 MHz frequency and ARFI-imaging was performed at 4 MHz using Siemens (ACUSON S2000) B-mode-ARFI combination transducer.

Results

Sixty nodules in 55 patients were analyzed. Three nodules were papillary carcinoma. The stiffer the tissue the faster the shear wave propagates. The results obtained indicated that the shear wave velocity in thyroid lobes ranged between 0.5 and 4.9 m/s. The median velocity of ARFI-imaging in the healthy nodule-free thyroid gland, as well as in benign and malignant thyroid nodules was 1.98 m/s (range: 1.20-3.63 m/s), 2.02 m/s (range: 0.92-3.97 m/s), and 4.30 m/s (range: 2.40-4.50 m/s), respectively. While no significant difference in median velocity was found between healthy thyroid tissue and benign thyroid nodules, a significant difference was found between malignant thyroid nodules on the one hand and healthy thyroid tissue (p = 0.018) or benign thyroid nodules (p = 0.014) on the other hand. Specificity of ARFI-imaging for the differentiation of benign and malignant thyroid nodules was comparable with RTE (91-95%).

Conclusions

ARFI can be performed in the thyroid tissue with reliable results.     

Adsorption of hydrogen and of oxygen on an open metal surface-HREELS investigation at Ni(311)

The adsorption behavior of hydrogen and oxygen on the stepped Ni(311) surface has been investigated by HREELS. A series of metastable phases was found for hydrogen adsorption at low temperatures with a succession of different adsorption sites indicated by the following loss peaks: 55 and 149 meV for the threefold site, shifting with higher coverage to 65 and 155 meV, respectively; 40 and 90 meV for the fourfold site, shifting to 35 and 85 meV with coverage; and 110 and 124 meV for an additional site between close packed rows. Room temperature adsorption of hydrogen leads to the reconstruction of the surface with occupation of three- and fourfold sites, represented by loss peaks at 60 and 145 meV for the threefold site and 74 meV for the fourfold site. This phase is the thermodynamically stable one. Oxygen is most likely initially adsorbed on a bridge site (loss peak at 66 meV). The stepped surface is already oxidized at very low exposures to oxygen, as seen by the characteristic vibration for oxide islands at 55 meV and later by the Fuchs-Kliewer mode of NiO at 68 meV.