Computing the real roots of a polynomial by the exclusion algorithm

We describe a new algorithm for localizing the real roots of a polynomialP(x). This algorithm determines intervals on whichP(x) does not possess any root. The remainder set contains the real roots ofP(x) and can be arbitrarily small.     

Almost Connected Orders

One of the standard axioms for semiorders states that no three-point chain is incomparable to a fourth point. We refer to asymmetric relations satisfying this axiom as almost connected orders or ac-orders. It turns out that any relation lying between two weak orders, one of which covers the other for inclusion, is an ac-order (albeit of a special kind). Every ac-order is bracketed in a natural way by two weak orders, one the maximum in the set of weak orders included in the ac-order, and the other minimal, but not necessarily the minimum, in the set of weak orders that include the ac-order. The family of ac-orders on a finite set with at least five elements is not well graded (in the sense of Doignon and Falmagne, 1997). However, such a family is both upgradable and downgradable, as every nonempty ac-order contains a pair whose deletion defines an ac-order on the same set, and for every ac-order which is not a chain, there is a pair whose addition gives an ac-order.     

Kinetic Analysis of the Reactions between GG-Containing Oligonucleotides and Platinum Complexes. 1. Reactions of Single-Stranded Oligonucleotides with cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) and [Pt(NH(3))(3)(H(2)O)](2+)

Using concentration measurements based on high performance liquid chromatography, we have investigated the kinetics of reaction between single-stranded oligonucleotides containing a d(GpG) sequence, i.e., d(GG), d(TGG), d(TTGG), and d(CTGGCTCA), and the platinum complexes cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) (1) and [Pt(NH(3))(3)(H(2)O)](2+) (2). The rate constants for the substitution of one aqua ligand of platinum in 1 or 2 by each guanine of the oligonucleotides were individually measured, as well as, for 1, those for the subsequent conversion of the monoadducts to the diadduct. For the platination of d(GG) and d(TGG), the rate constants are similar for the 5'- and 3'-guanines. The longer oligonucleotides d(TTGG) and d(CTGGCTCA) are platinated slightly faster on the 5'-G than on the 3'-G. 2 shows a similar slight preference for the 5'-guanine, but it reacts by a factor of 4-10 more slowly than 1. For both complexes, the platination rate constants increase with increasing oligonucleotide length. Platination of the 5'-G by 1 is 1 order of magnitude faster on d(CTGGCTCA) than on d(GG). Concerning the chelation step giving the GG diadduct of 1, the longer the oligonucleotide, the larger is the ratio between the rates of the cyclization of the 3'- and 5'-monoadducts k(3)(')(c) and k(5)(')(c): k(3)(')(c)/k(5)(')(c) equals 1.4 for d(GG) and 3.3 for d(CTGGCTCA).     

Sterically congested uranyl complexes with seven-coordination of the UO2 unit: the peculiar ligation mode of nitrate in [UO2(NO3)2(Rbtp)] complexes

Addition of 1 or 2 molar equiv of Rbtp [Rbtp = 2,6-bis(5,6-dialkyl-1,2,4-triazin-3-yl)pyridine; R = Me, Pr ( n )] to UO 2(OTf) 2 in anhydrous acetonitrile gave the neutral compounds [UO 2(OTf) 2(Rbtp)] [R = Me ( 1), ( n )Pr ( 2)] and the cationic complexes [UO 2(Rbtp) 2][OTf] 2 [R = Me ( 3), Pr ( n ) ( 4)], respectively. No equilibrium between the mono and bis(Rbtp) complexes or between [UO 2(Rbtp) 2][OTf] 2 and free Rbtp in acetonitrile was detected by NMR spectroscopy. The crystal structures of 1 and 3 resemble those of their terpyridine analogues, and 3 is another example of a uranyl complex with the uranium atom in the unusual rhombohedral environment. In the presence of 1 molar equiv of Rbtp in acetonitrile, UO 2(NO 3) 2 was in equilibrium with [UO 2(NO 3) 2(Rbtp)] and the formation of the bis adduct was not observed, even with an excess of Rbtp. The X-ray crystal structures of [UO 2(NO 3) 2(Rbtp)] [R = Me ( 5), Pr ( n ) ( 6)] reveal a particular coordination geometry with seven coordinating atoms around the UO 2 fragment. The large steric crowding in the equatorial girdle forces the bidentate nitrate ligands to be almost perpendicular to the mean equatorial plane, inducing bending of the UO 2 fragment. The dinuclear oxo compound [U(CyMe 4btbp) 2(mu-O)UO 2(NO 3) 3][OTf] ( 7), which was obtained fortuitously from a 1:2:1 mixture of U(OTf) 4, CyMe 4btbp, and UO 2(NO 3) 2 [CyMe 4btbp = 6,6'-bis-(3,3,6,6-tetramethyl-cyclohexane-1,2,4-triazin-3-yl)-2,2'-bipyridine] is a very rare example of a mixed valence complex involving covalently bound U (IV) and U (VI) ions; its crystal structure also exhibits a seven coordinate uranyl moiety, with one bidentate nitrate group almost parallel to the UO 2 fragment. The distinct structural features of [UO 2(kappa (2)-NO 3) 2(Mebtp)], with its high coordination number and a noticeable bending of the UO 2 fragment, and of [UO 2(kappa (2)-NO 3)(kappa (1)-NO 3)(terpy)], which displays a classical geometry, were analyzed by Density Functional Theory, considering the bonding energy components and the molecular orbitals involved in the interaction between the uranyl, nitrate, and Mebtp or terpy moieties. The unusual geometry of the Mebtp derivative with the seven coordinating atoms around the UO 2 fragment was found very stable. In both the Mebtp and terpy complexes, the origin of the interaction appears to be primarily steric (Pauli repulsion and electrostatic); this term represents 62-63% of the total bonding energy while the orbital term contributes to about 37-38%.     

Investigation of double-stranded DNA/drug interaction by ESI/FT ICR: orientation of dissociations relates to stabilizing salt bridges

Noncovalent complexes of DNA and Hoechst 33258 were investigated by ESI-FT/ICR MS in various activation modes (collision-induced dissociation (CID), sustained off-resonance irradiation collision-induced dissociation (SORI-CID), infrared multiphoton dissociation (IRMPD) and electron detachment dissociation (EDD)). The binding selectivity of Hoechst 33258 was confirmed by the comparative study of its noncovalent association with different DNA sequences. The CID spectra of [ds + HO - 5H](5-) obtained with a linear hexapole ion trap resulted in unzipping of the strands. This outcome is a clue to the drug-binding mode, shading light on the localization of the binding sites of Hoechst 33258 to the DNA sequence. The IRMPD and SORI-CID experiments mainly gave DNA backbone cleavages and internal fragment ions. From this result, information on the localization of the binding sites of Hoechst 33258 in the DNA sequence was obtained. No sodium cationization was observed on the DNA sequence ions although they were present on fragmentation of the duplex, indicating that the backbone cleavages were generated from the single strand associated with the Hoechst 33258 where the number of alkali cation is restricted. Under electron detachment (ED) conditions, multiple EDs were achieved for the [ds + HO - 5H](5-) ion without any significant dissociation. The presence of drug appears to enhance the stability of the multiply charged system. It was proposed that the studied noncovalent complex involved the formation of zwitterions and consequently strong salt-bridge interactions between DNA and drug.     

Tetranuclear polybipyridyl complexes of Ru(II) and Mn(II), their electro- and photo-induced transformation into di-mu-oxo Mn(III)Mn(IV) hexanuclear complexes

Three heterotetranuclear complexes, [{Ru(II)(bpy)(2)(L(n))}(3)Mn(II)](8+) (bpy = 2,2'-bipyridine, n = 2, 4, 6), in which a Mn(II)-tris-bipyridine-like centre is covalently linked to three Ru(II)-tris-bipyridine-like moieties using bridging bis-bipyridine L(n) ligands, have been synthesised and characterised. The electrochemical, photophysical and photochemical properties of these complexes have been investigated in CH(3)CN. The cyclic voltammograms of the three complexes exhibit two successive very close one-electron metal-centred oxidation processes in the positive potential region. The first, which is irreversible, corresponds to the Mn(II)/Mn(III) redox system (E(pa) approximately 0.82 V vs Ag/Ag(+) 0.01 M in CH(3)CN-0.1 M Bu(4)NClO(4)), whereas the second which is, reversible, is associated with the Ru(II)/Ru(III) redox couple (E(1/2) approximately 0.91 V). In the negative potential region, three successive reversible four electron systems are observed, corresponding to ligand-based reduction processes. The three stable dimeric oxidized forms of the complexes, [Mn(2)(III,IV)O(2){Ru(II)(bpy)(2)(L(n))}(4)](11+), [Mn(2)(IV,IV)O(2){Ru(II)(bpy)(2)(L(n))}(4)](12+) and [Mn(2)(IV,IV)O(2){Ru(III)(bpy)(2)(L(n))}(4)](16+) are obtained in fairly good yields by sequential electrolyses after consumption of respectively 1.5, 0.5 and 3 electrons per molecule of initial tetranuclear complexes. The formation of the di-micro-oxo binuclear complexes are the result of the instability of the {[Ru(II)(bpy)(2)(L(n))](3)Mn(III)}(9+) species, which react with residual water, via a disproportionation reaction and the release of one ligand, [Ru(II)(bpy)(2)(L(n))](2+). A quantitative yield can be obtained for these reactions if the electrochemical oxidations are performed in the presence of an added external base like 2,6-dimethylpyridine. Photophysical properties of these compounds have been investigated showing that the luminescence of the Ru(II)-tris-bipyridine-like moieties is little affected by the presence of manganese within the tetranuclear complexes. A slight quenching of the excited states of the ruthenium moieties, which occurs by an intramolecular process, has been observed. Measurements made at low concentration (<1 x 10(-5) M) indicate that some decoordination of Mn(2+) arises in 1a-c. These measurements allow the calculation of the association constants for these complexes. Finally, photoinduced oxidation of the tetranuclear complexes has been performed by continuous photolysis experiments in the presence of a large excess of a diazonium salt, acting as a sacrificial oxidant. The three successive oxidation processes, Mn(II)--> Mn(III)Mn(IV), Mn(III)Mn(IV)--> Mn(IV)Mn(IV) and Ru(II)--> Ru(III) are thus obtained, the addition of 2,6-dimethylpyridine in the medium giving an essentially quantitative yield for the two first photo-induced oxidation steps as found for electrochemical oxidation.     

Reaction of quinine, 9-epiquinine and their acetates in superacid in the presence of hydrogen peroxide: an access to new fluorhydrins and/or ketones

In HF-SbF₅, in the presence of H₂O₂ (source of OH⁺ equivalent) quinine 1a yields 10-keto derivatives 4a and 5a and cyclic ether 3 as the major product. In the same conditions 1b, 2a, and 2b give the 10-keto and 10-fluoro-3-hydroxy analogs.     

One-electron reduction of superoxide radical-anions by 3-alkylpolyhydroxyflavones in micelles. Effect of antioxidant alkyl chain length on micellar structure and reactivity

In micellar solutions, one-electron reduction of (*)O 2 (-) radical-anions by 3-alkylpolyhydroxyflavones (FnH) with alkyl chains of n = 1, 4, 6, 10 carbons produces phenoxyl radicals ( (*)Fn) identical to those obtained by one-electron oxidation by (*)Br 2 (-) radical-anions or by repair of tryptophan radicals. In cetyltrimethylammonium bromide (CTAB), F1H localizes in the Stern layer, and alkyl chains of other FnH solubilize in the hydrophobic interior, interacting with cetyl tails. This interaction produces more compact micelles with lower intramicellar fluidity, as suggested by the increase in the pseudo-first-order rate constant of (*)Fn formation ( k 1) from approximately 390 s (-1) for n = 1 to 610 s (-1) for n = 10, leading to an intramicellar bimolecular rate constant of 1 x 10 (5) M (-1) s (-1). Additionally, (*)F1 and (*)F4 decay by intermicellar bimolecular reaction (2 k = 20 and 2 x 10 (5) M (-1) s (-1), respectively) whereas other (*)Fn radicals are stable over seconds due to increased localization with regards to the Stern layer. In contrast, the thick uncharged hydrophilic palisade layer and the compact hydrophobic core of Triton X100 micelles are responsible for a much higher microviscosity resulting in a decrease in k 1 from approximately 15.6 s (-1) for n = 1 to 9.6 s (-1) for n = 10.     

Embedded silver ions-containing liposomes in polyelectrolyte multilayers: cargos films for antibacterial agents

A new antibacterial coating made of poly(L-lysine)/hyaluronic acid (PLL/HA) multilayer films and liposome aggregates loaded with silver ions was designed. Liposomes filled with an AgNO 3 solution were first aggregated by the addition of PLL in solution. The obtained micrometer-sized aggregates were then deposited on a PLL/HA multilayer film, playing the role of a spacer with the support. Finally, HA/PLL/HA capping layers were deposited on top of the architecture to form a composite AgNO 3 coating. Release of encapsulated AgNO 3 from this composite coating was followed and triggered upon temperature increase over the transition temperature of vesicles, found to be equal to 34 degrees C. After determination of the minimal inhibitory concentration (MIC) of AgNO 3 in solution, the antibacterial activity of the AgNO 3 coating was investigated against Escherichia coli. A 4-log reduction in the number of viable E. coli cells was observed after contact for 120 min with a 120 ng/cm (2) AgNO 3 coating. In comparison, no bactericidal activity was found for PLL/HA films previously dipped in an AgNO 3 solution and for PLL/HA films with liposome aggregates containing no AgNO 3 solution. The strong bactericidal effect could be linked to the diffusion of silver ions out of the AgNO 3 coating, leading to an important bactericidal concentration close to the membrane of the bacteria. A simple method to prepare antibacterial coatings loaded with a high and controlled amount of AgNO 3 is therefore proposed. This procedure is far superior to that soaking AgNO 3 or Ag nanoparticles into a coating. In principle, other small bactericidal chemicals like antibiotics could be encapsulated by this method. This study opens a new route to modify surfaces with small solutes that are not permeating phospholipid membranes below the phase transition temperature.     

Structural and luminescent properties of micro- and nanosized particles of lanthanide terephthalate coordination polymers

Reaction in water between rare earth ions (Ln = Y, La-Tm, except Pm) and the sodium salt of terephthalic acid leads to a family of lanthanide-based coordination polymers of general formula [Ln2(C8H4O4)3(H2O)4] n with Ln = La-Tm or Y. The isostructurality of the compounds with the previously reported Tb-containing polymer is ascertained on the basis of their X-ray powder diffraction diagrams. The coordination water molecules can be reversibly removed without destroying the crystal structure for compounds involving one of the lighter lanthanide ions (La-Eu). For compounds involving one of the heavier lanthanide ions (Tb-Tm) or yttrium, a structural change occurs during the drying process. X-ray diffraction data show this new anhydrous phase corresponding to the linking of pairs of Er(III) ions through mu-carboxylate bridges. Porosity profiles calculated for the anhydrous phases of Tb(III) and Er(III) show the presence of channels with very small sections. The luminescent properties of all the compounds have been recorded and the two most luminescent polymers, namely, the europium- and the terbium-containing ones, have been studied in more detail. Tb(III)-containing compounds display large quantum yields, up to 43%. Polyvinylpyrrolidone nanoparticles doped with [Ln2(C8H4O4)3(H2O)4] n (Ln = Eu, Tb, Er) have also been synthesized and characterized. The encapsulation of the coordination polymers results in somewhat reduced luminescence intensities and lifetime, but the nanoparticles can be dispersed in water and remain unchanged in this medium for more than 20 h.