Some remarks on the Jensen-Hadamard inequalities and applications

We provide some inequalities and integral inequalities connected to the Jensen-Hadamard inequalities for convex functions. In particular, we give some refinements to these inequalities. Some natural applications and further extensions are given.

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Sunto Forniamo alcune diseguaglianze e diseguaglianze integrali connesse alle dise-gueglianze di Jensen-Hadamard per funzioni convesse. In particolare, diamo qualche miglioramento di queste diseguaglianze. Alcune applicazioni naturali ed ulteriori estensioni sono date.

     

Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Intraspinal endodermal cyst: ultrastructural study of abnormal cilia.

Abnormal cilia were demonstrated in the lining epithelial cells of three cases of intraspinal endodermal (bronchogenic) cyst. The changes comprised a wide spectrum of ultrastructural abnormalities, including (a). cilia with abnormal axonemal microtubules, (b). swollen cilia, (c). compound cilia with or without excessive ciliary matrix, (d). naked cilia without limiting membrane, and (e). intracytoplasmic cilia and aggregates of microtubules. Of these, compound cilia and swollen cilia were most common. Cilia with dynein arm deficiency were not observed. Ciliary abnormalities found in the present study were very similar to those described in the bronchial epithelium of various diseases. The present findings suggest that the lining epithelium of intraspinal endodermal cyst shares similar ciliogenesis and susceptibility to abnormal ciliary formation as that of the bronchial epithelium.     

Solid state NMR characterization of formation of poly(ϵ‐caprolactone)/maghnite nanocomposites by in situ polymerization

Results of multinuclear MAS NMR spectroscopy are reported for poly (ε‐caprolactone)/maghnite nanocomposite formation, with ε‐caprolactone in situ polymerized in the presence of maghnite, a proton exchanged montmorillonite clay. Exfoliated and intercalated materials with different maghnite loading in the range 3–15 wt % were investigated. ¹H NMR evidences Brønsted acid hydroxyl groups in the silicate layers and shows that their broad signal at 7.6 ppm present in the parent clay disappears in the nanocomposite material. ²⁷Al MAS NMR results show that beside the hexacoordinated aluminum signal, two additional peaks corresponding to two different tetrahedral Al sites are present in the clay framework. The NMR signal intensity of only one of them was found to be affected in the nanocomposites compared with the parent maghnite, suggesting that these specific aluminum sites are the reactive ones at the initial stages of the polymerization. However almost no changes occurred in the ²⁹Si NMR spectra, confirming that the polymer grafting, as indicated earlier by atomic force microscopy, took place on the aluminum tetracoordinated sites rather than on the silicon sites. A mechanism of maghnite surface catalyzed polymerization of ε‐caprolactone was proposed, involving Brønsted and Lewis acid sites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3060–3068, 2007     

Short-range order and F ion diffusion inside the Pb1 − xAlxF2 + x solid solution Part II: Al NMR investigation and proposal of clustering process

A ²⁷Al nuclear magnetic resonance (NMR) investigation at room temperature of the Pb_{1 − x}Al_xF_{2 + x} (0 ≤ x ≤ 0.12) solid solution and of the ordered Pb₉Al₂F₂₄ phase is carried out. Two different types of aluminium ions are identified and their ratio is determined as a function of x. A clustering process based on the formation of column clusters, more and more extended when x increases, is proposed on the basis of results issued from the ¹⁹F (Part I) and ²⁷Al NMR investigations.     

Synthesis and antibacterial activities of water‐soluble methacrylate polymers containing quaternary ammonium compounds

New water‐soluble methacrylate polymers with pendant quaternary ammonium (QA) groups were synthesized and used as antibacterial materials. The polymers with pendant QA groups were obtained by the reaction of the alkyl halide groups of a previously synthesized functional methacrylate homopolymer with various tertiary alkyl amines containing 12‐, 14‐, or 16‐carbon alkyl chains. The structures of the functional polymer and the polymers with QA groups were confirmed with Fourier transform infrared and ¹H and ¹³C NMR. The degree of conversion of alkyl halides to QA sites in each polymer was determined by ¹H NMR to be over 90% in all cases. The number‐average molecular weight and polydispersity of the functional polymer were determined by size exclusion chromatography to be 32,500 g/mol and 2.25, respectively. All polymers were thermally stable up to 180 °C according to thermogravimetric analysis. The antibacterial activities of the polymers with pendant QA groups against Staphylococcus aureus and Escherichia coli were determined with broth‐dilution and spread‐plate methods. All the polymers showed excellent antibacterial activities in the range of 32–256 μg/mL. The antibacterial activity against S. aureus increased with an increase in the alkyl chain length for the ammonium groups, whereas the antibacterial activity against E. coli decreased with increasing alkyl chain length. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5965–5973, 2006     

Spectrofluorimetric determination of guanethidine sulphate,guanfacine hydrochloride,guanoclor sulphate and guanoxan sulphate in tablets and biological fluids,using benzoin

A sensitive and rapid Spectrofluorimetric method for the determination of guanethidine sulphate, guanfacine hydrochloride, guanoclor sulphate and guanoxan sulphate in tablets and spiked human serum and urine samples is described. The method is based on the reaction of monosubstituted guanidino compounds in an aqueous potassium hydroxide solution with benzoin, in the presence of -mercaptoethanol and sodium sulphite. Highly fluorescent derivatives were obtained, with excitation and emission maximum wavelengths around 325 and 430 nm, respectively. In optimal reaction conditions, the linearity ranges were 0.04–0.28 g/ml, with relative standard deviations less than 2%. The method has been successfully applied to the determination of these drugs in tablets. The results are highly correlated with the B.P. method. Chloroform (or for guanoxan dichloromethane) was used to extract the drugs from serum and urine at basic pH, followed by the proposed fluorimetric method. The limit of detection is 0.02 g/ml for the selected drugs.