A pointwise convergence for Sobolev space functions

Let 1<p<∞, and k,m be positive integers such that 0(k−2m)pn. Suppose ΩRⁿ is an open set, and Δ is the Laplacian operator. We will show that there is a sequence of positive constants c_j such that for every f in the Sobolev space W^k,p(Ω), for all xΩ except on a set whose Bessel capacity B_k−2m,p is zero.     

Investigating the effect of nanolayered silicates on blend segmental dynamics and minor component relaxation behavior in poly(ethylene oxide)/poly(methyl methacrylate) miscible blends

Polymer–silicate nanocomposites based on poly (ethylene oxide), PEO, poly(methyl methacrylate), PMMA, and sodium montmorillonite clay were fabricated and characterized to investigate the effect of nanolayered silicates on segmental dynamics of PEO/PMMA blends. X‐ray results indicate the formation of an exfoliated morphology in the nanocomposites. At low silicate contents, an enhancement in segmental dynamics of blend nanocomposites and also PEO, minor component in blend, is observed at temperature region below blend glass transition. This result can be attributed to the improvement of the confinement effect of rigid PMMA matrix on the PEO chains by introducing a low amount of layered silicates. On the other hand, at high silicate contents, an enhancement in segmental dynamics of blend nanocomposites and PEO is observed at temperature region above blend glass transition. This behavior could be interpreted based on the reduction of monomeric friction between two polymer components, which can facilitate segmental motions of blend components in nanocomposite systems. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Dehydration of acetonitrile using cross-linked sodium alginate membrane containing nano-sized NaA zeolite

Pervaporation (PV) separation of water–acetonitrile mixture using sodium alginate (NaAlg) based mixed matrix membranes (MMM) comprising different amounts of nano NaA zeolite (10, 20 and 30 wt%) is investigated in various concentrations of water and temperatures. The prepared membranes are modified by sulfosuccinic acid (SSA) as a crosslinking agent. NaAlg-NaA/SSA membranes are synthesized by a solution casting technique. The process and membrane performance including separation factor, flux and activation energy of permeation are determined. Results reveal that adding of nano zeolite may lead to an increase in the flux and the separation factor of sodium alginate membrane up to 123 and 169%. In addition, using MMM in dehydration of a feed containing 30 wt% of water shows much better performance than alginate membrane. Furthermore, the activation energy of water permeation through MMM is predicted lower than sodium alginate membrane which reflects the facilitated permeation of water through MMM.     

Adsorption Studies of Radionuclides and Toxic Metal Ions on a Modified Mesoporous Lanthanum(III) Silicate

A new adsorbent, modified mesoporous lanthanum(III) silicate, has been prepared with various molar ratios of Si/La (10, 20, 40, 80) and cethyltrimethylammonium bromide (CTAB) as structure directing agent. XRD, nitrogen sorption, SEM, IR, thermogravimetry and sorption of radionuclides and toxic metal ions have been studied. The results show that adsorption amount of some element such as Pb(II) and Th(IV) has been increased significantly by incorporation of lanthanum ions in the framework of adsorbent. Separation of Co(II)‐Th(IV), Co(II)‐U(VI) and Mo(VI)‐U(VI) has been developed on columns of this adsorbent.     

Fast and Efficient Nitration of Salicylic Acid and Some Other Aromatic Compounds over H_3PO_4/TiO_2-ZrO_2 Using Nitric Acid

TiO₂‐ZrO₂ (1/1)‐surf with Ti and Zr molar ratio of 1/1 was prepared with surfactant through a sol‐gel method. The optimum experimental condition was investigated for nitration of salicylic acid. Then, a number of nitration reactions were carried out with a variety of aromatic compounds in the optimum condition. The 25 wt% H₃PO₄/TiO₂‐ZrO₂ (1/1)‐surf catalyst showed good selectivity and yield in a short time for the nitration of salicylic acid and some other aromatic compounds.     

Preparation and biological evaluation of radiogallium labeled glucagon for SPECT imaging

In this work, recently prepared ⁶⁷Ga-labeled glucagon (⁶⁷Ga-DTPA-GCG) for imaging studies (radiochemical purity >94%; HPLC, S.A. 296–370 GBq/mM) was used in biological studies. The wild-type rat biodistribution results, 2 h post injection, demonstrated high tissue:muscle ratios for target tissues (liver, kidney, heart, spleen, fat intestine stomach and pancreas), 234, 18.45, 7.12, 1.75, 128.7, 4.9, 6.3 and 1.11, respectively. The tracer binding capacity using freshly prepared rat brain homogenate demonstrated significant specific binding of the tracer to neuronal GCG receptors (⁶⁷Ga-DTPA-GCG/⁶⁷Ga:3 and ⁶⁷Ga-DTPA-GCG/⁶⁷GaDTPA:2.2 at 90 min). SPECT images also demonstrated target specific binding of the tracer at 4 h. The data suggests the tracer is accumulated in GCGR rich tissues 2–4 h post injection, suggesting potentials of the tracer for future imaging studies in glocagonoma models.     

Lyapunov control of squeezed noise quantum trajectory

The quantum trajectory renders the optimal estimation of quantum state. It is a classical Itô stochastic differential equation. The Lyapunov global stabilization problem is solved for squeezed noise quantum trajectory. Lyapunov control stabilizes the quantum system toward one eigenstate. A two-level bistable quantum system is simulated as an example.     

An efficient chemoselective synthesis of O-vinylaryl systems using acetylenic esters and dihydroxybenzenes in the presence of triphenylphosphine or alkyl isocyanides

<正>The addition of 2,4-dihydroxyaceto(and benzo)phenone to propiolic ester is catalyzed by triphenylphosphine or tert-butyl isocyanide to form O-vinyl aryl derivatives in fairly good yields.     

On the hierarchy of cohomological dimensions of groups

Using Auslander’s G-dimension, we assign a numerical invariant to any group Γ. It provides a refinement of the cohomological dimension and fits well into the well-known hierarchy of dimensions assigned already to Γ. We study this dimension and show its power in reflecting the properties of the underlying group. We also discuss its connections to relative and Tate cohomology of groups.