Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.     

The Hoyle state in nuclear lattice effective field theory

We review the calculation of the Hoyle state of ¹²C in nuclear lattice effective field theory (NLEFT) and its anthropic implications in the nucleosynthesis of ¹²C and ¹⁶O in red giant stars. We also analyse the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the α nuclei ¹⁶O, ²⁰Ne, ²⁴Mg, and ²⁸Si by Euclidean time projection. Finally, we discuss recent NLEFT results for the spectrum, electromagnetic properties, and α-cluster structure of ¹⁶O.     

On array models theoretical predictions versus measurements for the growth of cells and dendrites in the transient solidification of binary alloys

Most of the theoretical studies of the growth of cells/dendrites in the literature are based on the assumption that it is a steady-state phenomenon. The analysis of cells/dendritic structures in the unsteady-state regime is very important, since it encompasses the majority of industrial solidification processes. The aim of the present investigation was to validate the predictions furnished by the cellular and primary dendritic growth models in the literature for unsteady-state conditions against a large spectrum of experimental data, which includes those for a variety of Al alloys (Al–Cu, Al–Si, Al–Fe, Al–Bi, Al–Ni, Al–Sn) and low thermal diffusivity alloys, such as Sn–Pb and Pb–Sb. The predictions furnished by the Hunt–Lu model do not match the cellular experimental scatter for any examined alloy system. However, this model matches well with the primary dendritic growth of Al alloys, with the exception of Al–Sn alloys, for which the Hunt–Thomas approach has to be applied. The primary dendritic predictions of Bouchard–Kirkaldy's model, performed with the originally suggested a ₁ calibration factors are, in most cases, located above the experimental points. Experimental growth laws relating cellular and dendritic spacings with the tip growth rate and the cooling rate, respectively, are established.     

Structure and optical properties of Ag/CeO2 nanocomposites

Silver/ceria (Ag/CeO₂) nanocomposites were prepared from Ce(NO₃)₃?6H₂O, AgNO₃, and NH₄OH with different molar ratios through a hydrothermal process, and then were completed by carrying out the precursors calcining at 750 °C for 2 h under air atmosphere. Below 1 % of Ag concentration in Ag/CeO₂ nanocomposites, the Ag crystalline structure does not appear. XRD and TEM results show evidence of two different effects (the agglomeration and the barrier effects) governing the process of crystal growth. HR-TEM image and EDX elemental analysis of the Ag/CeO₂ nanocomposite confirmed that isolated Ag nanocrystals are dispersed in the CeO₂ matrix. The red shifts are attributed to the quantum confinement effect and the valence change of the Ce⁺ ions. Ag nanoparticles can help to improve the absorption of visible light, enhancing the absorption intensity of Ag/CeO₂ nanocomposite. These results are of great significance for the control of microstructure, crystallinity, and applications for the development of nanocomposite materials.     

Differentiation of myeloma and metastatic cancer in the spine using dynamic contrast-enhanced MRI

Spinal myeloma and metastatic cancer cause similar symptoms and show similar imaging presentations, thus making them difficult to differentiate. In this study, dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) was performed to differentiate between 9 myelomas and 22 metastatic cancers that present as focal lesions in the spine. The characteristic DCE parameters, including the peak signal enhancement percentage (SE%), the steepest wash-in SE% during the ascending phase and the wash-out SE%, were calculated by normalizing to the precontrast signal intensity. The two-compartmental pharmacokinetic model was used to obtain K^trans and k_ep. All nine myelomas showed the wash-out DCE pattern. Of the 22 metastatic cancers, 12 showed wash-out, 7 showed plateau, and 3 showed persistent enhancing patterns. The fraction of cases that showed the wash-out pattern was significantly higher in the myeloma group than the metastatic cancer group (9/9 = 100% vs. 12/22 = 55%, P = .03). Compared to the metastatic cancer group, the myeloma group had a higher peak SE% (226% ± 72% vs. 165% ± 60%, P = .044), a higher steepest wash-in SE% (169% ± 51% vs. 111% ± 41%, P = .01), a higher K^trans (0.114 ± 0.036 vs. 0.077 ± 0.028 1/min, P = .016) and a higher k_ep (0.88 ± 0.26 vs. 0.49 ± 0.23 1/min, P = .002). The receiver operating characteristic analysis to differentiate between these two groups showed that the area under the curve was 0.798 for K^trans, 0.864 for k_ep and 0.919 for combined K^trans and k_ep. These results show that DCE-MRI may provide additional information for making differential diagnosis to aid in choosing the optimal subsequent procedures or treatments for spinal lesions.     

Interatomic potentials for the Na+—Rg complexes (Rg = He,Ne and Ar)

Interatomic potential energy curves are presented for the Na⁺—Rg (Rg = He, Ne and Ar) cationic complexes. The curves are calculated at the CCSD(T)/aug-cc-pVQZ level of theory, with correction for basis set superposition error being performed point-by-point. Ninety-six different bond lengths are used in the generation of the curves. From the curves rovibrational energy levels are calculated. These, in turn, are used to calculate the heat of formation of the cationic complexes, both by calculating partition functions under the assumption of a rigid rotor, harmonic oscillator, and also explicitly using the calculated rovibrational energy levels. The long range region of each of the curves is used to derive the D ₄ and D ₆ parameters, the former being used to derive the static polarizability a ₁ of each of the Rg atoms and the latter the first dispersion coefficients, C ₆(Na⁺—Rg).     

Hydration-induced conformational changes in protonated 2,4-pentanedione in the gas phase

Starting with H⁺[CH₃C(O)CH₂C(O)CH₃] (denoted H⁺PD), the protonated diketone-water clusters H⁺PD(H₂O) _n (n = 1–3) have been characterized by density functional theory calculations in combination with vibrational predissociation spectroscopy to explore the conformational changes of a protonated bifunctional ion solvated by water in the gas phase. Theoretical calculations for H⁺PD revealed that the ion contains an intramolecular hydrogen bond (IHB), with two oxygen atoms bridged by the extra proton in an O—H⁺ … O form. Attachment of one water molecule to it readily ruptures this IHB, replacing the H⁺ by the H₃O⁺ moiety. Further replacement of the IHB by two water molecules occurs at n = 2 and the ?C(O)CH₂C(O)- chain is fully opened (or unfolded) after transfer of the extra proton to the water trimer at n = 3. To verify the computational findings, infrared spectroscopic measurements were performed using a vibrational predissociation ion trap spectrometer to identify cluster isomers from the signatures of hydrogen bonded and non-hydrogen bonded OH stretching spectra of H⁺PD(H₂O)_2,3 produced in a corona discharge supersonic expansion. Besides open form isomers, evidence for the formation of water-bridged structures has been found for H⁺PD(H₂O)₃ at an estimated temperature of 200 K. A detailed illustration of the unfolding steps as well as the energy profiles for the evolution of a two-water bridge isomer from the protonated H⁺PD monomer are analysed pictorially (including both stable intermediates and transition states) in the present investigation.     

Forces between charged surfaces in a solvent primitive model electrolyte

Grand canonical Monte Carlo (GCMC) simulations have been performed to investigate the components of the force between parallel charged surfaces in an electrolyte. The solvent primitive model (SPM) was used to investigate the effect of neutral hard sphere solvent particles on the force between the surfaces. The effects of particle size, wall charge density, charge valency of the electrolyte, and the exclusion of neutral hard sphere are discussed. When solvent particles are considered, the total force between the charged surfaces is always repulsive, even for divalent counterions. This is different from the earlier conclusion reached with a restricted primitive model electrolyte. The repulsive force decreases in going from monovalent counterions to divalent counterions.     

Infrared spectra and isomeric structures of hydroxide ion-water clusters OH- (H2O)1-5: a comparison with H3O (H2O)1-5

Size-selected hydroxide ion water tetramers and pentamers [OH-(H₂O)_4,5], produced by a supersonic expansion, have been investigated using vibrational predissociation spectroscopy in conjunction with ab initio calculations based on density functional theory (DFT). The observed spectra in the frequency range 2650–3850 cm^?1 show some broad absorption bands attributed to the free and hydrogen bonded OH stretches of OH-(H₂O)_4,5 at an estimated cluster temperature of 170 K. DFT calculations performed at the B3LYP/6-31 + G* level reveal five and eight possible low lying isomeric forms for OH-(H₂O)₄ and OH-(H₂O)₅, respectively. The global minimum isomer of the tetramer is tri-solvated cyclic, which is energetically more stable than the tetra-solvated wheel-shaped form with an OH- ion at its centre. Compact cage-like lowest energy structures are found for the pentamer, in which the water molecules can act either as a single-donor-single-acceptor, as a double-proton-donor, or as a double-donor-single-acceptor in both the firs1183t a1192nd the second solvation shell of the OH- ion core. Interconversion among the isomers appears to be rapid as manifested in the observed spectra dominated by broad and congested absorptions. To understand the nature of spectral broadening and congestion, systemic comparisons of the results are made against those of the corresponding protonated cations, H+(H₂O)_n|1 and the corresponding halide anions, X-(H²O)ⁿ X = F, Cl, Br, and I. It is suggested that the spectral complexities observed for OH-(H₂O)_4,5 are predominantly a result of sampling configurations with a large distribution of O_solvent-O_ion-O_solvent angles and O_solvent … H-O_solvent distances between water molecules in the firs1175t a1181nd/or second hydration shells, together with the existence of more than one isomer in the supersonic expanson and rapid isomeric interconversion among them.     

Lie Derivations of Triangular Algebras

We investigate Lie derivations on a class of algebras called triangular algebras. In particular, we give sufficient conditions such that every Lie derivation on such an algebra <artwork name="GLMA31004ei1"> is a sum of derivation on <artwork name="GLMA31004ei2"> and a mapping from <artwork name="GLMA31004ei3"> to its centre.