ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

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Continuation methods in Banach manifolds

Sufficient conditions are given to assert that a perturbed mapping has a zero in a Banach manifold modelled over ℝⁿ. The zero is estimated by means of sequences of Newton's iterations. The proof of the result is constructive and is based upon continuation methods. This work is partially supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia.     

Synthesis,characterization and applications of polysiloxane networks with immobilized pyrogallol ligands

A porous, solid insoluble polysiloxane‐immobilized ligand system bearing pyrogallol active sites of the general formula P? (CH₂)₃? NH(CH₂)₃OC₆H₃(OH)₂ (where P represents [Si? O]_n siloxane network) has been prepared by the reaction of 3‐aminopropylpolysiloxane with 1,3‐dibromopropane followed by the reaction with pyrogallol. ¹³C CP‐MAS NMR and X‐ray photoelectron spectroscopy confirmed that the pyrogallol is chemically bonded to the siloxane backbone. Thermal analysis showed that the ligand system is stable under nitrogen at relatively high temperature. The polysiloxane–pyrogallol ligand system exhibits high potential for the uptake of the metal ions (Fe³⁺, Co²⁺, Ni²⁺ and Cu²⁺). Complexation of the pyrogallol ligand system for the metal ions at the optimum conditions was found to be in the order Fe³⁺ > Cu²⁺ > Ni²⁺ > Co²⁺. Copyright © 2005 John Wiley & Sons, Ltd.     

A REGULAR VALUE OF COMPACT DEFORMATION

Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one value in a specific open ball. The proof of the result is constructive and based upon continuation methods.     

Identification and separation of saxitoxins using hydrophilic interaction liquid chromatography coupled to traveling wave ion mobility‐mass spectrometry

The aim of this work was to develop a reliable and efficient analytical method to characterise and differentiate saxitoxin analogues (STX), including sulphated (gonyautoxins, GTX) and non‐sulphated analogues. For this purpose, hydrophilic interaction liquid chromatography (HILIC) was used to separate sulphated analogues. We also resorted to ion mobility spectrometry to differentiate the STX analogues because this technique adds a new dimension of separation based on ion gas phase conformation. Positive and negative ionisation modes were used for gonyautoxins while positive ionisation mode was used for non‐sulphated analogues. Subsequently, the coupling of these three complementary techniques, HILIC‐IM‐MS, permitted the separation and identification of STX analogues; isomer differentiation was achieved in HILIC dimension while non‐sulphated analogues were separated in the IM‐MS dimension. Additional structural characteristics concerning the conformation of STXs could be obtained using IM‐MS measurements. Thus, the collision cross sections (CCS) of STXs are reported for the first time in the positive ionisation mode. These experimental CCSs correlated well with the calculated CCS values using the trajectory method. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimization of Experimental Parameters to Explore Small‐Ligand/Aptamer Interactions through Use of 1H NMR Spectroscopy and Molecular Modeling

Aptamers constitute an emerging class of molecules designed and selected to recognize any given target that ranges from small compounds to large biomolecules, and even cells. However, the underlying physicochemical principles that govern the ligand‐binding process still have to be clarified. A major issue when dealing with short oligonucleotides is their intrinsic flexibility that renders their active conformation highly sensitive to experimental conditions. To overcome this problem and determine the best experimental parameters, an approach based on the design‐of‐experiments methodology has been developed. Here, the focus is on DNA aptamers that possess high specificity and affinity for small molecules, L ‐tyrosinamide, and adenosine monophosphate. Factors such as buffer, pH value, ionic strength, Mg²⁺‐ion concentration, and ligand/aptamer ratio have been considered to find the optimal experimental conditions. It was then possible to gain new insight into the conformational features of the two ligands by using ligand‐observed NMR spectroscopic techniques and molecular mechanics.