Poincaré-Hopf inequalities

In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.

     

On the Spectral Rigidity of Hopf Manifolds

We characterize Hopf manifolds of complex dimension 3 (resp. 2) in the class of compact locally conformal Kaehler manifold ( resp. Hermitian manifold ) by the spectrum of the Laplacian acting on functions.     

Localising gravity in composite monopole brane worlds without bulk cosmological constant

We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e., a defect composed of a 't Hooft–Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space–time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without a priori introduction of a bulk cosmological constant.     

A calorimetric study of the different thermal behaviour of DNA in the isotropic and liquid-crystalline states

A difference between the thermal behaviour of the isotropic and liquid-crystalline state of sonicated DNA in aqueous salt solution containing poly(ethyleneglycol)(PEG) has been demonstrated. On cooling, a different degree of renaturation of thermally denaturated DNA is observed between samples which form the isotropic state and more concentrated samples which on cooling form the cholesteric state.     

Catalysis in aromatic nucleophilic substitution. Note II. Piperidino substitution reactions of some 2-l-3-nitrothiophenes and 2-l-5-nitrothiophenes in methanol and benzene

The rates of piperidino substitution of some 2-L-3-nitrothiophenes (I) and 2-L-5-nitrothiophenes (II) (L = Cl, Br, I, OC₆H₄NO₂-p, and SO₂Ph) have been measured in methanol and in benzene at various piperidine concentrations. The reactivity of compounds (I) is not affected by the piperidine concentration in both methanol and benzene, except for the case of L = I (Ic). Probably due to association effects, the reactivity of Ic in benzene decreases as the piperidine concentration is increased. The reactions of compounds II follow overall second order kinetics in methanol while in benzene a different behaviour is observed as a function of the nature of the leaving group. In fact, the piperidino substitutions of IIa-c (L = Cl, Br, I) are mildly accelerated at high piperidine concentrations (a moderate solvent effect); on the contrary the reactivity of IId and e shows a strong dependence on the piperidine concentration, pointing out a genuine base catalysis.     

Two-plane sub-bundles of nonorientable real vector-bundles

Let be a nonorientable m-plane bundle over a CW complex X of dimension m or less. Given a 2-plane bundle over X, we wish to know whether can be embedded as a sub-bundle of . The bundle need not be orientable. When is even-dimensional there is the added complication of twisted coefficients. In that case, we use Postnikov decomposition of certain nonsimple fibrations in order to describe the obstructions for the embedding problem. Emery Thomas [11] and [12] treated this problem for and both orientable. The results found here are applied to the tangent bundle of a closed, connected, nonorientable smooth manifold, as a special case.The writing of this paper was partially supported by CNPq grant     

On finite {1,2,3}-semiaffine planes

In this paper, we investigate {1,2,3}-semiaffine planes. All such planes of order n >51 shall be classified. It turns out that they are embeddable into projective planes of the same order n in the most natural way.Work supported by National Research Project on Strutture Geometriche Combinatoria, loro applicazioni of Italian M.P.I. and G.N.S.A.G.A. of C.N.R.     

Amphiphilic cyclodextrin carriers embedding porphyrins: charge and size modulation of colloidal stability in heterotopic aggregates

The interaction between the anionic 5,10,15,20-tetrakis(4-sulfonatophenyl)-21H,23H-porphyrin (TPPS) and cationic vesicles formed by heptakis(2-omega-amino-O-oligo(ethylene oxide)-6-hexylthio)-beta-cyclodextrin (SC6CDNH2) has been investigated in detail through a combination of elastic light scattering (ELS), quasi-elastic light scattering (QELS), zeta potential measurements, and time-resolved fluorescence anisotropy. ELS experiments provided the first structural characterization of these cationic vesicles both in the absence and in the presence of TPPS porphyrin, modeling the system as a spherical particle described by a single thin shell form factor. The structure of mixed hetero-aggregates is modulated by charge and size of the two components as function of different porphyrin/cyclodextrin (CD) molar ratios. At the limiting molar ratio studied, the absolute value of zeta potential (/zeta/ = 12.5 mV) seems to be a reference value for the formation of stable colloidal CD vesicular aggregates at thermodynamic equilibrium. New insights on the structure of these heterotopic colloids have been obtained by analysis of rotational correlation times at different molar ratios exploiting time-resolved fluorescence anisotropy experiments. At high porphyrin loads, the anisotropy decays behave as monoexponentials and the rotational correlation times (1-2 ns) together with the r(0) values close to zero suggest the presence of small amounts of TPPS embedded in a hydrophobic environment either in monomeric or in aggregated form. At the lower porphyrin/CD molar ratios, the anisotropy decays exhibit a double-exponential behavior showing a predominant component with a slow rotational correlation time (20-25 ns) and limiting anisotropy values of approximately 0.15. This component has been assigned to molecules that are more stabilized onto the CD vesicles, that is, porphyrins embedded into the oligo-ethylene "wall" of the CD vesicles. Scanning near-field optical microscopy of the samples evaporated on glass surfaces gave further insights on the morphology and optical properties of these systems, confirming the embedding of TPPS on the vesicles and evidencing the role of the solvent.     

Novel bifluorene based conjugated systems: synthesis and properties

A series of novel bifluorene based systems was synthesised by a convergent approach by means of a Suzuki cross-coupling between 7,7′-bis-(4,4,5,5-tetramethyl-[1,3,2]dioxaborolan-2-yl)-9,9,9′,9′-tetraoctyl-2,2′-bifluorene and suitable aryl-bromides. All the oligomers have been characterized by ¹H, ¹³C NMR, FT-IR, UV-vis, PL spectroscopy and mass analyses. In particular, it has been demonstrated that the presence of strong electron donor (amines) or withdrawing (carboxylic esters) groups causes a bathochromic shift of the optical properties with respect to those of unsubstituted molecules. The effects of these functional groups on the HOMO-LUMO energy levels were investigated by cyclic voltammetry. Remarkably, the LUMO energy level of 7,7′-bis-[5′-carbodecaoxy-2,2′-bithiophen-5-yl]-9,9,9′,9′-tetraoctyl-2,2′-bifluorene (−3.07 eV) is strongly influenced by the presence of the ester functional group.     

Synthesis and characterization of hybrid borosiloxane gels as precursors for Si–B–O–C fibers

The sol–gel method has been used for the synthesis of borosilicate gels from mixtures of methyltriethoxysilane (MTES) and dimethyldiethoxysilane (DMDES) and boric acid. The use of boric acid, B(OH)₃ allows the hydrolysis and condensation of hybrid silicon alkoxides without further addition of water or catalyst. The use of difunctional silicon units, –(CH₃)₂SiO– promote the formation, during the sol–gel process, of linear oligomers which facilitate fiber drawing before gelation. Gel characterization performed by FT-IR, XRD, TG-DTA and DCS analysis indicates the formation of a mixed network with incorporation of the boron units via =B-O-Si≡ bridges. The formation of borosiloxane bonds seems favored by the presence of DMDES. SiBOC glasses were obtained after pyrolysis of the borosilicate gels in argon atmosphere at 1000 °C. TG-DTA study indicates that the ceramic yield decreases by increasing the amount of DMDES. Gel fibers were successfully prepared from convenient partially-aged solutions by hand drawing. Pyrolysis of the obtained gel fibers under argon atmosphere at 1000 °C open the possibility to produce SiBOC homogeneous glass fibers with diameter as low as 10 μm.