Integral operators commuting with dilations and rotations in generalized Morrey-type spaces

We find conditions for the boundedness of integral operators $K$ commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of $Kf$ via spherical means of $f$. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others.     

Homogenization methods to approximate the effective response of random fibre-reinforced Composites

In this article a fibre-reinforced composite material is modelled via an approach employing a representative volume element with periodic boundary conditions. The effective elastic moduli of the material are thus derived. In particular, the method of asymptotic homogenization is used where a finite number of fibres are randomly distributed within the representative periodic cell. The study focuses on the efficacy of such an approach in representing a macroscopically random (hence transversely isotropic) material. Of particular importance is the sensitivity of the method to cell shape, and how this choice affects the resulting (configurationally averaged) elastic moduli. The averaging method is shown to yield results that lie within the Hashin–Shtrikman variational bounds for fibre-reinforced media and compares well with the multiple scattering and (classical) self-consistent approximations with a deviation from the latter in the larger volume fraction cases. Results also compare favourably with well-known experimental data from the literature.     

Biologically Relevant Molecular Transducer with Increased Computing Power and Iterative Abilities

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Global co-stationarity of the ground model from a new countable length sequence

Suppose are models of ZFC with the same ordinals, and that for all regular cardinals in , satisfies . If contains a sequence for some ordinal , then for all cardinals in with regular in and , is stationary in . That is, a new -sequence achieves global co-stationarity of the ground model.

     

A comparison of atomic force microscopy (AFM) and dynamic light scattering (DLS) methods to characterize nanoparticle size distributions

This paper compares the accuracy of conventional dynamic light scattering (DLS) and atomic force microscopy (AFM) for characterizing size distributions of polystyrene nanoparticles in the size range of 20–100 nm. Average DLS values for monosize dispersed particles are slightly higher than the nominal values whereas AFM values were slightly lower than nominal values. Bimodal distributions were easily identified with AFM, but DLS results were skewed toward larger particles. AFM characterization of nanoparticles using automated analysis software provides an accurate and rapid analysis for nanoparticle characterization and has advantages over DLS for non-monodispersed solutions.     

Anchor chain length alters the apparent mechanism of chloride channel function in SCMTR derivatives

Two membrane-anchored heptapeptides have been prepared and their pore-formation behavior in phospholipid bilayer membranes has been found to differ profoundly as a result only of alkyl chain length.     

Locality properties of radial basis function expansion coefficients for equispaced interpolation

Natasha Flyer ^{Many types of radial basis functions (RBFs) are global in termsof having large magnitude across the entire domain. Yet, incontrast, e.g. with expansions in orthogonal polynomials, RBFexpansions exhibit a strong property of locality with regardto their coefficients. That is, changing a single data valuemainly affects the coefficients of the RBFs which are centredin the immediate vicinity of that data location. This localityfeature can be advantageous in the development of fast and well-conditionediterative RBF algorithms. With this motivation, we employ hereboth analytical and numerical techniques to derive the decayrates of the expansion coefficients for cardinal data, in both1D and 2D. Furthermore, we explore how these rates vary in theinteresting high-accuracy limit of increasingly flat RBFs.}     

Linking local environments and hyperfine shifts: a combined experimental and theoretical (31)P and (7)Li solid-state NMR study of paramagnetic Fe(III) phosphates

Iron phosphates (FePO(4)) are among the most promising candidate materials for advanced Li-ion battery cathodes. This work reports upon a combined nuclear magnetic resonance (NMR) experimental and periodic density functional theory (DFT) computational study of the environments and electronic structures occurring in a range of paramagnetic Fe(III) phosphates comprising FePO(4) (heterosite), monoclinic Li(3)Fe(2)(PO(4))(3) (anti-NASICON A type), rhombohedral Li(3)Fe(2)(PO(4))(3) (NASICON B type), LiFeP(2)O(7), orthorhombic FePO(4)·2H(2)O (strengite), monoclinic FePO(4)·2H(2)O (phosphosiderite), and the dehydrated forms of the latter two phases. Many of these materials serve as model compounds relevant to battery chemistry. The (31)P spin-echo mapping and (7)Li magic angle spinning NMR techniques yield the hyperfine shifts of the species of interest, complemented by periodic hybrid functional DFT calculations of the respective hyperfine and quadrupolar tensors. A Curie-Weiss-based magnetic model scaling the DFT-calculated hyperfine parameters from the ferromagnetic into the experimentally relevant paramagnetic state is derived and applied, providing quantitative finite temperature values for each phase. The sensitivity of the hyperfine parameters to the composition of the DFT exchange functional is characterized by the application of hybrid Hamiltonians containing admixtures 0%, 20%, and 35% of Fock exchange. Good agreement between experimental and calculated values is obtained, provided that the residual magnetic couplings persisting in the paramagnetic state are included. The potential applications of a similar combined experimental and theoretical NMR approach to a wider range of cathode materials are discussed.