Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators

Let L =-?+V(x) be a Schr?dinger operator, where ? is the Laplacian on ■~n,while nonnegative potential V(x) belonging to the reverse H?lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schr?dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.     

High resolution NMR spectroscopy of rat brain in vivo through indirect zero-quantum-coherence detection

The time evolution of zero-quantum-coherences (ZQCs) is insensitive to magnetic field inhomogeneity. Using a 2D indirect ZQC detection method it is shown that high-resolution (1)H NMR spectra can be obtained from rat brain in vivo at 11.74T that are immune to magnetic field inhomogeneity. Simulations based on the density matrix formalism, as well as in vitro measurements are used to demonstrate the features of 2D ZQC NMR spectra. Unique spectral information which is normally not directly available from regular (1)H NMR spectra can be extracted and used for compound identification or improved prior knowledge during spectral fitting.     

Opioid ligands with mixed properties from substituted enantiomeric N-phenethyl-5-phenylmorphans. Synthesis of a micro-agonist delta-antagonist and delta-inverse agonists

Enantiomeric N-phenethyl-m-hydroxyphenylmorphans with various substituents in the ortho, meta or para positions of the aromatic ring in the phenethylamine side-chain (chloro, hydroxy, methoxy, nitro, methyl), as well as a pyridylethyl and a indolylethyl moiety on the nitrogen atom, were synthesized and their binding affinity to the mu-, delta-, and kappa-opioid receptors was examined. The higher affinity ligands were further examined in the [(35)S]GTPgammaS assay to study their function and efficacy. 3-((1R,5S)-(-)-2-(4-Nitrophenethyl)-2-aza-bicyclo[3.3.1]nonan-5-yl)phenol ((-)-) was found to be a mu-agonist and delta-antagonist in that functional assay and was about 50 fold more potent than morphine in vivo. 3-((1R,5S)-(-)-2-(4-Chlorophenethyl)-2-aza-bicyclo[3.3.1]nonan-5-yl)phenol ((-)-) and several other ligands displayed inverse agonist activity at the delta-opioid receptor. The absolute configuration of all of the reported compounds was established by chemical conversion of (-)- to 1R,5S-(-)-.HBr.     

Accelerating SNARE‐Mediated Membrane Fusion by DNA–Lipid Tethers

SNARE proteins are the core machinery to drive fusion of a vesicle with its target membrane. Inspired by the tethering proteins that bridge the membranes and thus prepare SNAREs for docking and fusion, we developed a lipid‐conjugated ssDNA mimic that is capable of regulating SNARE function, in situ. The DNA–lipid tethers consist of a 21 base pairs binding segment at the membrane distal end that can bridge two liposomes via specific base‐pair hybridization. A linker at the membrane proximal end is used to control the separation distance between the liposomes. In the presence of these artificial tethers, SNARE‐mediated lipid mixing is significantly accelerated, and the maximum fusion rate is obtained with the linker shorter than 40 nucleotides. As a programmable tool orthogonal to any native proteins, the DNA–lipid tethers can be further applied to regulate other biological processes where capturing and bridging of two membranes are the prerequisites for the subsequent protein function.     

Remarks on duality and semigroups

This paper discusses the duality theory for compact commutative idempotent semigroups and compact commutative inverse semigroups. The major difference from earlier work is the use of semicharacters which are measurable with respect to some measure on the semigroup. Duality theorems are proved using measures which give different dual spaces. This was written while the author was a guest of the Hebrew University of Jerusalem, Israel, and was supported in part by the National Science Foundation.     

A pseudopotential SCF-MO study of Te

A recently developed ab initio pseudopotential molecular orbital approach was applied to the Te ion, a system outside the practical reach of conventional all-electron treatments. Computations were carried out with a minimal STO -4G basis set. Results account reasonably well for the observed optical absorption spectrum and suggest the origin of a hitherto unassigned weak band. Ground-state properties, which included the structure, force field, and vibrational frequencies, were also investigated. Treated as a free, gas-phase ion, tetratellurium (II) yielded a bond length 0.05 Å shorter than the experimental value for the ion in a crystal lattice. Placement of static, point-charge counterions in the Te coordination sphere increased the bond length to a value 0.005 Å longer than derived by experiment. Calculations on neutral, cyclic Te₄ provided a theoretical single-bond reference length 0.09 Å longer than that obtained for the ion in a counterion environment. Comparisons between observed and calculated frequencies suggest an assignment of the vibrational spectrum different from the provisional assignment in the literature.     

Mapping phosphorylation rate of fluoro-deoxy-glucose in rat brain by F chemical shift imaging

¹⁹F magnetic resonance spectroscopy (MRS) studies of 2-fluoro-2-deoxy-d-glucose (FDG) and 2-fluoro-2-deoxy-d-glucose-6-phosphate (FDG-6P) can be used for directly assessing total glucose metabolism in vivo. To date, ¹⁹F MRS measurements of FDG phosphorylation in the brain have either been achieved ex vivo from extracted tissue or in vivo by unusually long acquisition times. Electrophysiological and functional magnetic resonance imaging (fMRI) measurements indicate that FDG doses up to 500 mg/kg can be tolerated with minimal side effects on cerebral physiology and evoked fMRI-BOLD responses to forepaw stimulation. In halothane-anesthetized rats, we report localized in vivo detection and separation of FDG and FDG-6P MRS signals with ¹⁹F 2D chemical shift imaging (CSI) at 11.7 T. A metabolic model based on reversible transport between plasma and brain tissue, which included a non-saturable plasma to tissue component, was used to calculate spatial distribution of FDG and FDG-6P concentrations in rat brain. In addition, spatial distribution of rate constants and metabolic fluxes of FDG to FDG-6P conversion were estimated. Mapping the rate of FDG to FDG-6P conversion by ¹⁹F CSI provides an MR methodology that could impact other in vivo applications such as characterization of tumor pathophysiology.     

Buildup of point-defect diffusion profiles in a foil during irradiation

The distribution of interstitials and vacancies in a foil under irradiation has been calculated as a function of both distance from the surface and irradiation time by solving the diffusion equation numerically on a computer. The defects were considered to annihilate at randomly distributed sinks, by mutual recombination, and by diffusion to the surface. Defect jump frequencies appropriate to silver at 125°C and foil thicknesses of 1 pm and 300 A were used. Large “humps” in the plot of vacancy concentration versus distance were found near the surface of the 1 pm foil at short irradiation times, unless the internal sink concentration was high. These humps may be responsible for some unusual void distributions observed near grain boundaries.     

From ordered bubbles to random stripes: Pattern formation in a hydrodynamic lattice gas

A two-component momentum-conserving lattice gas with competing interactions is introduced in two dimensions. One interaction acts at short range and produces interfaces with surface tension. The second interaction, the negative of the first, acts at rangea and produces modulated structures with approximate wavelength 2a. Depending on particle density, species concentration, and relative interaction strength, the equilibrium patterns formed by the model range from isotropic mixed and unmixed phases to hexagonally-ordered bubbles to randomly-oriented stripes. A Ginzburg-Landau equation is proposed that qualitatively captures the basic features of these phase transitions.