Some new topological cardinal inequalities

In this paper we make use of the Pol-Šapirovski?'s technique to prove several cardinal inequalities, which generalize other well-known inequalities.     

Higher Loop Corrections to a Schwinger–Dyson Equation

We consider the effects of higher loop corrections to a Schwinger–Dyson equation for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess–Zumino model as a laboratory. We obtain the dominant contributions of the three and four-loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections.     

Renormalization group functions for the Wess–Zumino model: Up to 200 loops through Hopf algebras

We obtain the contributions to the renormalization group functions of all the diagrams containing the unique one-loop primitive divergence of a simple supersymmetric Wess–Zumino model, up to more than 200 loops. The asymptotic behavior of the coefficients in the expansion of the anomalous dimension is analysed.     

Sonochemical and sonophotocatalytic degradation of malachite green: the effect of carbon tetrachloride on reaction rates

A comparative study between the sonolytic, photocatalytic and sonophotocatalytic oxidation processes of aqueous solutions of malachite green was carried out in the presence of carbon tetrachloride, under a low power ultrasonic field (<15 W) and using titanium dioxide as a photocatalyst. The effect of a number of parameters such as ultrasonic intensity, TiO2 crystalline structure and the presence of CCl4 were studied using an inexpensive reactor. Enhanced rates of sonolytic degradation of malachite green in the presence of CCl4 were demonstrated. On the other hand, the simultaneous use of sonolysis and photocatalysis in the presence of CCl4 does not improve the degradation rate of malachite green in comparison with the one obtained using only sonolysis, but it makes possible a faster oxidative degradation of some reaction intermediaries. Finally, in air saturated solutions both processes, the sonolytic and the photocatalytic one, follow a first-order rate law.     

Fast method for the experimental determination of vaporization enthalpy by differential scanning calorimetry

A simple method is proposed to estimate the vaporization enthalpy of the palmitic acid (hexadecanoic acid) at its normal boiling temperature. Differential scanning calorimetry (DSC) was the technique used to directly measure these thermodynamic properties. The advantages of this method are its speed and small amount of sample required. In order to avoid evaporation and to ensure equilibrium conditions, the experiments were carried out including a-alumina in contact with the fatty acid. The effect of the alumina concentration is discussed. The obtained experimental data (T_bp=625.4±0.5 K, D_vap H=237.6±5.9 J g^-1) is compared with that obtained by using thermodynamic equations. This revised version was published online in August 2006 with corrections to the Cover Date.     

ACE-Inhibitory and Antioxidant Activities of Peptide Fragments Obtained from Tomato Processing By-Products Fermented Using <Emphasis Type="Italic">Bacillus subtilis</Emphasis>: Effect of Amino Acid Composition and Peptides Molecular Mass Distribution

The effects of amino acid composition and peptide molecular mass on ACE-inhibitory and antioxidant activities of protein fragments obtained from tomato waste fermented using Bacillus subtilis were evaluated. The addition of B. subtilis increased the relative amounts of aromatic and positively-charged amino acids which have been described to influence the biological activities of peptide fragments. IC₅₀ values of hydrolysates for ACE-inhibitory and 2, 2′-diphenyl-1-picrylhydrazyl (DPPH) scavenging activities were found to be 1.5 and 8.2 mg/mL, respectively. Size-exclusion chromatography (SEC) pattern of the hydrolysate indicated the breakdown of parent proteins to smaller peptides with molecular weights mainly below 1400 Da. MALDI-TOF mass spectrometry analysis revealed that the highest ACE-inhibitory activity was due to peptides showing molecular mass range 500–800 Da, while the most active antioxidant peptides were found to be mainly at the two different peptide weight ranges 500–800 Da and 1200–1500 Da.     

A Note on Schnyder’s Theorem

We give an alternate proof of Schnyder’s Theorem, that the incidence poset of a graph G has dimension at most three if and only if G is planar.     

Multilayered artifacts in the pre-Columbian metallurgy from the North of Peru

Three types of alloys were recognized when analyzing pre-Columbian artifacts from the North of Peru: gold, silver, and copper alloys; gilded copper and silver; silvered copper; tumbaga, i.e., copper or silver enriched on gold at the surface by depletion gilding. In this paper, a method is described to differentiate gold alloys from gilded copper and from copper–gold tumbaga, and silver alloys from silvered copper and copper–silver tumbaga. This method is based on the use of energy-dispersive X-ray fluorescence, i.e., on a sophisticated analysis of XRF-spectra carrying out an accurate determination of Cu(K _α /K _β ), Ag(K _α /K _β ), Au(L _α /L _β ), and Au-L _α /Cu-K _α or Ag-K _α /Cu-K _α ratios. That implies a dedicated software for the quantitative determination of the area of X-ray peaks. This method was first checked by a relevant number of standard samples and then it was applied to pre-Columbian alloys from the North of Peru.     

The number of self-dual codes over $${Z_{p^3}}$$

Let p be a prime number. In this paper, we consider codes over the ring of integers modulo p ³ and give a characterization of self-duality. This leads to a construction of self-dual codes and a mass formula, which counts the number of such codes over .