Conformal metrics with prescribed Q-curvature on S n

In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with n????5, and study the related fourth order elliptic equation. We prove new existence results based on a new type of Euler?CHopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal metrics having the same Q-curvature.     

Selective Detection of Dopamine in Presence of Ascorbic Acid by Use of Glassy‐Carbon Electrode Modified with Amino‐β‐Cyclodextrin and Carbon Nanotubes

A glassy carbon electrode modified with per‐6‐amino‐β‐cyclodextrin (β‐CDNH₂) and functionalized single‐walled carbon nanotubes (SWCNT‐COOH) was elaborated. This structure was investigated for the detection of dopamine acid (DA) in presence of ascorbic acid (AA). The sensor behavior was studied by cyclic voltammetry, square wave voltammetry and electrochemical impedance spectroscopy. The analysis results show that the electrode modification with CD derivative improves the sensitivity and selectivity of the DA recognition; the electrochemical response was further improved by introduction of SWCNT‐COOH. The sensor shows good and reversible linear response toward DA within the concentration range of 7×10^?7–10^?4 M with a detection limit of 5×10^?7 M.     

Synthesis and in vivo evaluation of 4-deoxy-4,4-difluoro-KRN7000

The synthesis of 4-deoxy-4,4-difluoro-KRN7000 starting from phytosphingosine is described. Key steps include a regioselective benzylation of azidophytosphingosine and a deoxofluor-mediated fluorination of the corresponding 4-ketone. This fluorination failed completely when the adjacent 3-OH was protected as benzyl ether but proceeded well when a benzoyl group was used. The biological evaluation reveals a bias toward Th1 cytokine induction upon Natural Killer T cell activation.     

Frobenius–Schur Factorization for Multivalued $${\varvec{2\times 2}}$$ Matrices Linear Operator

In this paper, a new concept for a \(2\times 2\) block relation matrix is studied in a Banach space. We define a matrix linear relation and present some of its properties. It is shown that, under certain condition, we can investigate the Frobenius–Schur of relation matrices.     

Glaucasides A-C, three saikosaponins from Atriplex glauca L. var. ifiniensis (Caball) Maire

From the roots of Atriplex glauca L. var. ifiniensis (Caball) Maire (syn. of Atriplex parvifolia Lowe var. genuina Maire), three new saikosaponins designated as glaucasides A-C (1-3) were isolated together with the known 3-O-β-D-glucopyranosyl-(1 → 2)-β-D-galactopyranosyl-saikogenin F (4). The structures of the new compounds were elucidated by extensive analysis of one-dimensional and two-dimensional NMR spectroscopy, FABMS, HR-ESIMS and chemical evidence as 13β,28-epoxy-16β,21β-dihydroxyolean-11-en-3β-yl O-β-D-[2-O-sulfate]-glucopyranosyl-(1 → 2)-α-L-arabinopyranoside (1), 13β,28-epoxy-16β,21β-dihydroxyolean-11-en-3β-yl O-β-D-[2-O-sulfate]-glucopyranosyl-(1 → 2)-α-L-arabinopyranosyl 21-O-{4-(secbutylamido)-butanoyl ester} (2) and 3-O-β-D-glucopyranosyl-(1 → 2)-β-D-galactopyranosyl saikogenin G (3). The cytotoxic activities of these compounds were evaluated against the HT-29 and HCT 116 human colon cancer cell lines.     

A note on the essential pseudospectra and application

In this research article, we work with the notion of essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving the definition and we investigate the characterization, the stability and some properties of these essential pseudospectra.     

On the equilibrium equation for a generalized biological membrane energy by using a shape optimization approach

A mechanical equilibrium equation of a vesicle membrane under a generalized elastic bending energy is obtained in this paper. Moreover, the derivation of this equilibrium equation is based on some shape optimization tools. This approach is new and more concise than the tensorial tools used previously for this problem.     

STABILITY OF THE S-LEFT AND S-RIGHT ESSENTIAL SPECTRA OF A LINEAR OPERATOR

In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space.     

Chemical composition and in vitro evaluation of antimicrobial and anti-acetylcholinesterase properties of the flower oil of Ferula lutea

The present work describes the chemical composition and evaluates the antimicrobial and the anti-acetylcholinesterase properties of the flower oil from the Tunisian Ferula lutea obtained by hydrodistillation and analyzed by combination of GC/FID and GC/MS. The chemical composition of the flower oil of this species is reported for the first time. Seventeen compounds were identified accounting for 94.3% of the total oil. The chemical composition of this essential oil was characterized by a high proportion of monoterpene hydrocarbons (80.4%) among which delta-3-carene (31.2%) and alpha-pinene (25.8%) were the predominant compounds. The oxygenated monoterpenes represent the second major fraction (12.0%), 2,3,6-trimethylbenzaldehyde (10.9%) being the predominant one. Furthermore, the isolated oil was tested for its antimicrobial activity using the disc-diffusion and the microdilution assays against six Gram-positive and five Gram-negative bacteria as well as towards eight Candida species. It was found that flower oil of F. lutea exhibited interesting antibacterial and anticandidal activity (MIC = 39 mcirog/mL against Escherichia coli, Staphylococcus aureus and S. epidermidis and MIC = 156 microg/mL against Candida albicans). The anti-acetylcholinesterase effect of this oil was also evaluated in this work. Results showed that this oil exhibits significant activity (IC50 =70.25 +/- 5.41 microg/mL).     

Controlled adhesion of Salmonella Typhimurium to poly(oligoethylene glycol methacrylate) grafts

Poly(oligoethylene glycol methacrylate), POEGMA, brushes were prepared by surface‐initiated atom transfer radical polymerization (SI‐ATRP) on gold‐coated silicon wafers. Prior to ATRP, the substrates were grafted by brominated aryl initiators via the electrochemical reduction of a noncommercial parent diazonium salt of the formula BF₄^?, ⁺N₂‐C₆H₄‐CH(CH₃)Br. The diazonium‐modified gold plates (Au‐Br) served as macroinitiators for ATRP of OEGMA which resulted in hydrophilic surfaces (Au‐POEGMA) that could be used for two distinct objectives: (i) resistance to fouling by Salmonella Typhimurium; (ii) specific recognition of the same bacteria provided that the POEGMA grafts are activated by anti‐Salmonella. The Au‐POEGMA plates were characterized by XPS, polarization modulation‐infrared reflection‐absorption spectroscopy (PM‐IRRAS) and contact angle measurements. Both Beer‐Lambert equation and Tougaard's QUASES software indicated a POEGMA thickness that exceeds the critical ～10 nm value necessary for obtaining a hydrophilic polymer with effective resistance to cell adhesion. The Au‐POEGMA slides were further activated by trichlorotriazine (TCT) in order to covalently bind anti‐Salmonella antibodies (AS). The antibody‐modified Au‐POEGMA specimens were found to specifically attach Salmonella Typhimurium bacteria. This work is another example of the diazonium salt/ATRP process to provide biomedical polymer surfaces. Copyright © 2011 John Wiley & Sons, Ltd.