A generalization of Lomonosov's inequality and its applications to invariant subspaces

In this article we generalize Victor Lomonosov's famous inequality so as to be applicable to a wider class of functions. Then using it we prove that the adjoint of an algebra with a compactness property which is weaker than the PS property, employed by Victor Lomonosov, has nontrivial invariant subspaces.

     

Activation profiles of opioid ligands in HEK cells expressing δ opioid receptors

Background  

The aim of the present study was to characterize the activation profiles of 15 opioid ligands in transfected human embryonic kidney cells expressing only δ opioid receptors. Activation profiles of most of these ligands at δ opioid receptors had not been previously characterized in vitro. Receptor activation was assessed by measuring the inhibition of forskolin-stimulated cAMP production.     

Efficient synthesis of ferrocenylenones by Friedel-Crafts acylation with EtAlCl2-Me3Al

Efficient synthesis of ferrocenylenones using a Friedel-Crafts acylation reaction is described. Acryloyl, methacryloyl, crotonoyl, cinnamoyl, and β-methylcrotonoyl chlorides react with ferrocene in the presence of a Lewis acid (EtAlCl₂ or EtAlCl₂-Me₃Al) to give the corresponding ferrocenylenones (acryloyl, methacryloyl, crotonoyl, cinnamoyl, and methylcrotonoylferrocenes) in good isolated yields. Besides ferrocenylenones, chloroactylferrocene is also synthesised by this method.     

Nuclear forward scattering vs. conventional Mössbauer studies of atomically tailored Eu-based materials

With the decrease in size of devices, rapid characterization of nano-devices is an inevitable necessity. It is shown that Mössbauer spectroscopy using synchrotron radiation from the advanced photon source provides such a tool of investigation. Results are presented and compared for conventional Mössbauer and Nuclear Forward Scattering for ¹⁵¹Eu-doped magnesium sulfide as an example, especially at low concentrations.     

Synthesis and comparative solution properties of single‐, twin‐, and triple‐tailed associating ionic polymers based on diallylammonium salts

The cycloterpolymerizations of single‐, twin‐, and triple‐tailed hydrophobes with hydrophilic monomer N,N‐diallyl‐N‐carboethoxymethylammonium chloride and sulfur dioxide afforded a series of cationic polyelectrolytes (CPEs) in excellent yields. These CPEs, upon the acidic hydrolysis of the pendent ester groups, gave the corresponding pH‐responsive cationic acid salts, which, upon a treatment with sodium hydroxide, were converted to polybetaines (PBs), anionic polyelectrolytes (APEs), and PB/APE polymers containing various proportions of zwitterionic (PB) and anionic fractions (APE) in the polymer chain. At a shear rate of 0.36 s⁻¹ at 30 °C, salt‐free water solutions of the CPEs (2 g/dL) containing 8, 4, and 2.67 mol % of the single‐, twin‐, and triple‐tailed hydrophobes (all having 8 mol % octyloxy tails) had apparent viscosity values of 70, 2800, and 396,000 cps, respectively. The PB/APE polymer with a ratio of 33:67 for the zwitterionic and anionic fractions in the polymer chain gave the highest viscosity value. The superior viscosity behavior of the polymers containing the triple‐tailed hydrophobe was attributed to the blocky nature of the comonomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5480–5494, 2006     

Circles through two points that always enclose many points

This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under Grant CCR-8714565, by the second author has been partially supported by the Digital Equipment Corporation, by the fourth author has been partially supported by the Office of Naval Research under Grant N00014-86K-0416.     

1‐Methyl‐1H‐imidazo[4,5‐f]quinolin‐6‐ium chloride monohydrate

The title compound, C₁₁H₁₀N₃⁺·Cl^?·H₂O, belongs to the N1‐methyl‐substituted imidazo­[4,5‐f]­quinoline family, in which the heterocyclic ring is protonated at the pyridine rather than at the imidazole N atom. The mol­ecule as a whole is almost exactly planar. The molecular structure has been compared with that of the 2‐amino analogue described in the literature, and it was found that the extra amino group of the latter is involved in conjugation with the adjacent double bond, i.e. the conjugation does not extend over the entire heterocyclic system. The cation of the title compound forms a strong hydrogen bond with the Cl^? anion and the anions are interconnected by the water solvent mol­ecule.     

Chemical-effect variation of Kβ/Kα X-ray intensity ratios in 3d elements

Chemical effects on Kβ/Kα X-ray intensity ratios for some Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn compounds are studied experimentally. The X-ray spectra were measured by using a Si (Li) solid state detector with high resolution. The vacancies were produced by heavily filtered ²⁴¹Am gamma rays. It is found that the Kβ/Kα X-ray intensity ratios measured with compounds deviated up to 43% from the corresponding values of the pure elements. The values for pure elements are compared with the other experimental and with theoretical values.