Lifted inequalities for 0-1 mixed integer programming: Superlinear lifting

We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables, through the lifting of continuous variables fixed at their upper bounds. We introduce the concept of a superlinear inequality and show that, in this case, lifting is significantly simpler than for general inequalities. We use the superlinearity theory, together with the traditional lifting of 0-1 variables, to describe families of facets of the mixed 0-1 knapsack polytope. Finally, we show that superlinearity results can be extended to nonsuperlinear inequalities when the coefficients of the variables fixed at their upper bounds are large.This research was supported by NSF grants DMI-0100020 and DMI-0121495Mathematics Subject Classification (1991): 90C11, 90C27     

Nickel(II) and cerium(IV) ethyleneurea,ethylenethiourea and propyleneurea adducts

The NiCl₂ · 6eu, NiCl₂ · 6etu, Ce(SO₄)₂ · 6pu and Ce(SO₄)₂ · 6etu adducts (eu = ethyleneurea, etu = ethylenethiourea and pu = propyleneurea) were prepared by a solid state procedure, and characterized by C, H and N elemental analysis, i.r. spectroscopy, thermogravimetry (t.g.) and differential scanning calorimetry (d.s.c.). The i.r. results show that eu and pu coordinate through oxygen, whereas etu coordinates through nitrogen. The NiCl₂ · 6eu adduct is green, whereas the NiCl₂ · 6etu adduct is yellow. This fact suggests that the _o separation is larger for the latter adduct. On the other hand, both cerium adducts are white, suggesting that, for pu and etu cerium sulfate adducts, a ligand-to-metal charge-transfer promotes the reduction of Ce^IV to Ce^III. The t.g. thermal stability sequences are: etu > pu > eu and Ni > Ce. Cerium adducts release the six ligand molecules in a single mass loss step, suggesting that all ligand molecules are in equivalent coordinative positions (same bond length and strength). On the other hand, nickel adducts exhibit three mass loss steps in the thermal degradation (release of ligand molecules) process. This suggests that, for these compounds, there are three distinct coordinative positions, with distinct bond lengths and strengths, probably due to the Jahn–Teller effect. All four adducts melt before the onset of thermal degradation, with etu adducts exhibiting the higher melting temperatures and melting enthalpies, as a consequence of stronger intermolecular forces.     

Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms

We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables. We develop a lifting theory for the continuous variables. In particular, we present a pseudo-polynomial algorithm for the sequential lifting of the continuous variables and we discuss its practical use.This research was supported by NSF grants DMI-0100020 and DMI-0121495Mathematics Subject Classification (2000): 90C11, 90C27     

The Ion-exchange Capacity of Ti and Zr Lamellar Hydrogenphosphates. TG measurements

Thermogravimetric data were used to calculate the number of acidic Brönsted sites in lamellar α-titanium (α-TiP), γ-titanium (γ-TiP), α-zirconium (α-ZrP) and γ-zirconium (γ-ZrP) hydrogenphosphates. The numbers of acidic sites calculated for these lamellar compounds were 7.81, 5.67, 6.33 and 5.56 for α-TiP, γ-TiP, α-ZrP and γ-ZrP, respectively. These values are in good agreement with those found through potentiometric titration. The data obtained prove that thermogravimetric measurements can be used as a reliable analytical tool to follow the ion-exchange capacity of this kind of crystalline lamellar compounds.     

Determination of the antiretroviral drug nevirapine in diluted alkaline electrolyte by adsorptive stripping voltammetry at the mercury film electrode

This paper describes a stripping method for the determination of nevirapine at the submicromolar concentration levels. The method is based on controlled adsorptive accumulation of nevirapine at thin-film mercury electrode, followed by a linear cyclic scan voltammetry measurement of the surface species. Optimal experimental conditions include a 2.0 x 10(-3) mol L(-1) NaOH solution (supporting electrolyte), an accumulation potential of -0.20 V, and a scan rate of 100 mV s(-1). The response of nevirapine is linear over the concentration range 0.01-0.14 ppm. For an accumulation time of 6 minutes, the detection limit was found to be 0.87 ppb (3.0 x 10(-9) mol L(-1)). More convenient methods to measure the nevirapine in presence of the efavirenz, acyclovir, didanosine, indinavir, nelfinavir, saquinavir, lamivudine, zidovudine and metals ions were also investigated. The utility of this method is demonstrated by the presence of nevirapine together with ATP or DNA.     

Stabilization of catalytically active gold species in Fe-modified zeolites

The influence of iron additive on redox, electronic and catalytic properties of gold incorporated into zeolite catalysts has been studied by means of TEM, XPS, XRD, TPR, ICP and AES. The interaction of gold with iron modifier was observed in Y-zeolites and mordenites with different cations and method of Fe incorporation (impregnation or ion exchange). This interaction leads to mutual influence on redox properties of Fe and Au ionic species and facilitates their reduction. Limited diffusion of Au precursor after Fe species deposition in narrow mordenite channels does not permit to incorporate Au in adequate concentration, while in large super-cage of Y-zeolites this limitation is absent. The structure of Y-zeolites favors formation of active gold species. Catalytic tests in CO oxidation show that Fe additive stabilizes the gold active species active at low-temperature (partly charged clusters) and makes them insensitive to redox treatments.