Blow-up sets for linear diffusion equations in one dimension

We consider the heat equation in the half-line with Dirichlet boundary data which blow up in finite time. Though the blow-up set may be any interval [0,a], depending on the Dirichlet data, we prove that the effective blow-up set, that is, the set of points where the solution behaves like u(0,t), consists always only of the origin. As an application of our results we consider a system of two heat equations with a nontrivial nonlinear flux coupling at the boundary. We show that by prescribing the non-linearities the two components may have different blow-up sets. However, the effective blow-up sets do not depend on the coupling and coincide with the origin for both components.     

Theoretical investigation of substituted anthraquinone dyes

We have investigated with computational chemistry techniques the visible spectra of substituted anthraquinones. A wide panel of theoretical methods has been used, with various basis sets and density functional theory (DFT) functionals, in order to assess a level of theory that would lead to converged excitation energies. It turns out that the hybrid Becke-Lee-Yang-Parr and Perdew-Burke-Erzenrhof functionals with the 6-31G (d,p) atomic basis set provide reliable lambda(max) when the solvent effects are included in the model. Combining the results of both DFT schemes allows the prediction of lambda(max) with a standard deviation limited to 13 nm.     

Calorimetric determination of H+/M+ (M = Li,Cs) ion exchange inγ-titanium hydrogen phosphate

H⁺/M⁺ (M = Li, Cs) ion exchange in-titanium phosphate (-TIP) at 25°C and under static conditions has been studied. Titration and hydrolysis curves and the exchange isotherms were determined. The substitution was followed by X-ray diffraction. Direct calorimetric measurements were carried out at different degrees of conversion and the variation of the exchange enthalpy was obtained. The shape of the calorimetric curves is discussed. The results are compared to the values of H ⁰ obtained from titration data.     

Second-order Møller-Plesset evaluation of the bond length alternation of several series of linear oligomers

We investigate, at the second-order M?ller-Plesset level, the bond length alternation of 30 series of increasingly long linear oligomers for a total of more than 250 compounds, polyacetylene, polymethineimine, polyphosphinoborane, polyaminoborane, polyphosphazene, etc., for which, often for the first time, an accurate estimate of the polymeric bond length alternation is given. The variations induced either by chemical substitution of the backbone atoms or conformational modifications are discussed. Only three polymers present a large bond length alternation (>0.03 A). Systematic basis set effects have been unravelled, i.e., MP2/6-311G(2d) always overshoots the bond length alternation. Best estimates of the bond length alternation are provided for more than a dozen of polymers.     

Solvent-free synthesis of functionalized flavones under microwave irradiation

[reaction: see text] Eco-friendly direct solvent-free synthesis of flavones is achieved by microwave irradiation of phloroglucinol and beta-ketoesters. Heating with microwaves versus under classical conditions was shown to be higher yielding, cleaner, and faster. The reaction goes through a cycloaddition of an alpha-oxo ketene intermediate followed by an uncatalyzed thermal Fries rearrangement.     

Rotating charged black holes in Einstein-Born-Infeld theories and their ADM mass

In this work, the solution of the Einstein equations for a slowly rotating black hole with Born-Infeld charge is obtained. Geometrical properties and horizons of this solution are analyzed. The conditions when the ADM mass (as in the nonlinear static cases) and the ADM angular momentum of the system have been modified by the non linear electromagnetic field of the black hole, are considered.     

Improved anti-inflammatory and pharmacokinetic properties for superoxide dismutase by chemical glycosidation with carboxymethylchitin

O-carboxymethylchitin (molecular weight = 1.07 x 10(5), degree of carboxymethylation = 80%, degree of N-acetylation = 91%) was chemically attached to superoxide dismutase by the formation of amide linkages through a carbodiimide catalyzed reaction. The glycosidated enzyme contained about 1.8 mole of polysaccharide per mole of protein and retained 57% of the initial catalytic activity. The anti-inflammatory activity of the enzyme was 2.4 times increased after conjugation with the polysaccharide. The modified superoxide dismutase preparation was remarkably more resistant to inactivation with H(2)O(2) and its plasma half-life time was prolonged from 4.8 min to 69 h.     

Covalent polymer-drug conjugates

In this work, polymer-drugs conjugates used as drug delivery systems (DDS) are revised attending to their chemical conjugation. Namely, the classification of this type of DDS is based on the conjugation sites of the reactive groups (i.e., via end groups or pendant polymer groups). Advantages and limitations of these types of DDS are discussed through representative examples of polymer-drugs and polymer-proteins conjugates recently developed.     

Minimum energy requirements for quantum computation

A lower bound on the amount of energy needed to carry out an elementary logical operation on a quantum computer, with a given accuracy and in a given time, is derived. The bound arises from the requirement that the controls used to manipulate the qubits, which ultimately are themselves quan-tum mechanical systems, must nonetheless be classical to a sufficiently good approximation; it is expected to hold under a wide variety of conditions, and independently of the nature of the physical systems used to encode the qubits. This could have important consequences for very large-scale quantum computations.     

Patching and tearing single-wall carbon-nanotube ropes into multiwall carbon nanotubes

Bundles of single-wall carbon nanotubes (SWCNTs) coalesce forming multiwall carbon nanotubes (MWCNTs), containing from two to six nested tubes, under thermal treatment at high temperatures [(2200-2400) degrees C]. This structural transformation is confirmed by extensive molecular dynamics (MD) simulations. The simulations suggest a "patching-and-tearing" mechanism for the single-wall-to-multiwall transformation underlying the "concerted" coalescence of the tubes that begins with their polymerization. Tubes of different sizes and chiralities are considered.