Periodic solutions to some problems of n-body type

We prove the existence of at least one T-periodic solution to a dynamical system of the type $$ - m_i \ddot u_i = \sum\limits_{j = 1,j \ne i}^n {\triangledown V_{ij} (u_i - u_j ,{\text{ }}t)}$$ (1) where the potentials V _ij are T-periodic in t and singular at the origin, u _i ε R ^k i=1, ..., n, and k≧3. We also provide estimates on the H ¹ norm of this solution. The proofs are based on a variant of the Ljusternik-Schnirelman method. The results here generalize to the n-body problem some results obtained by Bahri & Rabinowitz on the 3-body problem in [6].     

Reaction of Sulfene wild Heterocyclic N,N-Disubstituted α-Aminomethylene Ketones IV. Synthesis of 3,4-Dihydro-5H-[1]benzothiopyratio [3,4-e]-1,2-oxathiin and 2,3,6,7-Tetrahydro-5H-thiopyrano[3,4-e]-1,2-oxathiin Derivatives

The reaction of sulfene with N,N-disubstituted 3-aminomethylene-2,3-dihydro-4-thiochromanones and-2,3,5,6-tetrahydro-4-thiopyranones gave 1,4-cycloadducts which are derivatives of new heterocyclic systems, namely 3,4-dihydro-5H-[1]benzothiopyrano[3,4-e]-1,2-oxathiin and 3,4,7,8-tetrahydro-5H-thiopyrano[3,4-e]-1,2-oxathiin, respectively. Furthermore, some pyrazole derivatives VII and VIII were prepared from 3-hydroxymethylene-2,3-dihydro-4-thiochromanone or 2,3,5,6-tetrahydro-4-thiopyranone and hydrazines.     

Reaction of ketenes with N,N-disubstituted 2-aminomethylenecycloalkanones. V. Synthesis of N,N-disubstituted 4′-aminospiro [1,3-dithiane-2,3′-(5′,6′-polymethylene-3′,4′-dihydro-α-pyrones)]

The reaction of 2-carbonyl-1,3-dithiane, a sulfene prepared in situ from 2-chloroearbonyl-1,3-dithiane and triethylamine, with N,N-disubstituted 2-aminomethylvnecycloalkanones gave the 1,4-cycloadducts, namely N,N-disubstituted 4′-aminospiro[1,3-dithiane-2,3′-(5′,6′-poly-methylene-3′,4′-dihydro-α-pyrones)].     

DNA and RNA noncovalent interaction of platinum(II) polypyridine complexes

A comparative investigation of the noncovalent interaction of the platinum(II) polypyridine complexes [Pt(dipy)(n-Rpy)2]2+ and [Pt(4,4'-Me2dipy)(2-Rpy)2]2+ (dipy = 2,2'-dipyridine; Me = CH3; n = 2-4; R = H or CH3) with double-helical DNA (calf thymus) and RNA [poly(A).poly(U)] has been conducted. With the exception of [Pt(dipy)(2-Mepy)2]2+, all of the complexes interact strongly, by intercalation, with both nucleic acids giving rise to large changes in the electronic spectra and induced circular dichroism signals; in addition, viscosity experiments on rodlike DNA and RNA show that both biopolymers elongate upon interaction with the complexes. The binding constant values, KB, determined at 25 degrees C, indicate that, at 0.101 M ionic strength, the affinity for poly(A).poly(U) is strongly dependent on the complexes nature, while for DNA it is leveled off. [Pt(dipy)(2-Mepy)2]2+ binds to DNA but does not interact appreciably with poly(A).poly(U).     

Thermally stable polymers by condensation of diphenols with glyoxal

Polycondensation of bisphenol A, hydroquinone, or dihydroxynaphthalenes with glyoxal using methane sulphonic acid as condensing agent leads to polymeric materials having linear and ladder structure and high thermal stability. These polymers were characterized by NMR and TG. Oligomers (from dimer to tetramer) were isolated by GPC and their structures characterized.     

Highly sensitive fluorescent probe for detection of alkaloids

A new fluorescent probe, based on an amphiphilic Schiff-base zinc(II) complex, 1, for the sensitive detection of some important classes of alkaloids is presented. It exhibits optical absorption changes and fluorescence enhancement upon formation of 1:1 1·alkaloid adducts. Four diverse classes of alkaloids, represented by their basic structures and related representative prototypes, are investigated, through the study of optical and binding properties of 1·alkaloid adducts. It is found that the chromogenic and fluorogenic complex 1 is selective between these classes of alkaloids in the micromolar range, with a limit of quantification of 0.40 μM for nicotine and 0.43 μM for cinchonine.     

Some thoughts on electrospray ionization mechanisms

Electrospray ionization (ESI) mechanisms are highly complex, due to a series of physical and chemical phenomena taking place on a complex system, as a solution is. In fact, even if the solution of an analyte in a protic medium can be considered at first sight to be a two-component system, the presence of solvent dissociation equilibria and the possible interactions solvent-solvent dissociation products, solvent dissociation products-analyte make this system highly complex, also for the presence of possible ionic compounds (for example, Na(+), K(+)) which strongly affect the above equilibria. A high number of research articles have been published, mainly devoted to charged droplet production and to gas-phase ion generation. They all show the high complexity of the processes affecting electrospray measurements related to either the chemical equilibria present in the condensed phase and to electrolysis processes at the emitter tip or to the processes occurring in the sprayed droplets. As a result, the chemical composition inside the small droplets from which the analyte ions are generated can be significantly different from those in sprayed solution. In this review, after a short survey of the proposed ESI mechanisms, some experiments are described. They were performed to examine if ion mobility in solution, before the formation of the sprayed charged droplets, can affect the ESI results. The data, obtained by studying both inorganic and organic analytes, indicate that the ESI spectra are dependent on the analyte dimension and charge state which, as a consequence, affect their ion mobility in solution.     

Surfactant Hydrogels for the Dispersion of Carbon‐Nanotube‐Based Catalysts

Novel hydrogel phases based on positively charged and zwitterionic surfactants, namely, N‐[p‐(n‐dodecyloxybenzyl)]‐N,N,N‐trimethylammonium bromide (pDOTABr) and p‐dodecyloxybenzyldimethylamine oxide (pDOAO), which combine pristine carbon nanotubes (CNTs), were obtained, thus leading to stable dispersions and enhanced cross‐linked networks. The composite hydrogel featuring a well‐defined nanostructured morphology and an overall positively charged surface was shown to efficiently immobilise a polyanionic and redox‐active tetraruthenium‐substituted polyoxometalate (Ru₄POM) by complementary charge interactions. The resulting hybrid gel has been characterised by electron microscopy techniques, whereas the electrostatic‐directed assembly has been monitored by means of fluorescence spectroscopy and ζ‐potential tests. This protocol offers a straightforward supramolecular strategy for the design of novel aqueous‐based electrocatalytic soft materials, thereby improving the processability of CNTs while tuning their interfacial decoration with multiple catalytic domains. Electrochemical evidence confirms that the activity of the catalyst is preserved within the gel media.