Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Co-stressors chilling and high light increase photooxidative stress in diuron-treated red alga Kappaphycus alvarezii but with lower involvement of H(2)O(2)

Diuron is one of the most commonly found N-phenylurea herbicides in marine/estuarine waters that promotes toxic effects by inhibiting photosynthesis and affecting the production of reactive oxygen species (ROS) in autotrophs. Since photo- and thermoacclimation are also ROS-mediated processes, this work evaluates a hypothetical additive effect of high light (HL) and chilling (12 degrees C) on 50 nM diuron toxicity to the highly-photosynthetically active apices of the red alga Kappaphycus alvarezii. Additive inhibition of photosynthesis was mainly evidenced by significant decreases of quantum yield of photosystem II and electron transfer rates upon co-stressors exposure to diuron-treated algae. Under extreme 12 degrees C/HL/diuron conditions, unexpected lower correlations between H(2)O(2) concentrations in seawater and radical-sensitive protein thiols were concomitantly measured with the highest indexes of photoinhibition (parameter beta). Altogether, these data support the hypothesis that co-stressors chilling/HL additively inhibit photosynthesis in diuron-exposed K. alvarezii but with less involvement of H(2)O(2) in injury effects than with only chilling or HL. (C) 2010 Elsevier Inc. All rights reserved.

Co/Mg/Al hydrotalcite-type precursor, promoted with La and Ce, studied by XPS and applied to methane steam reforming reactions

Catalysts` precursor of Co/Mg/Al promoted with Ce and La were tested in the steam reforming of methane (SRM). The addition of promoters was made by anion-exchange. The oxides characterization was made by X-ray Photoelectron Spectroscopy (XPS) analysis that confirmed Co(2+) species in free form on surface and interacted with Mg and Al in the form of solid solution. In the SRM with high fed molar ratio of H(2)O:CH(4) = 4:1, the catalysts showed a great affinity with water and immediately deactivated by oxidation of the active sites. In the stoichiometric ratio of H(2)O:CH(4) = 2: 1 the catalysts were active and presented low carbon deposition during the time reaction tested. Also a test with low fed molar ratio H(2)O:CH(4) = 0.5:1 was carried out to evaluate the stability of the catalysts by CH(4) decomposition and all the catalysts were stable during 6 h of reaction. Promoted catalysts presented lower carbon deposition. (C) 2009 Elsevier B. V. All rights reserved.

Study of Water-Gas-Shift Reaction over La((1-y))Sr(y)Ni(x)Co((1-x))O(3) Perovskite as Precursors

The performance of La((1-y))Sr(y)Ni(x)Co((1-x))O(3) perovskites for the water gas shift reaction (WGSR) was investigated. The samples were prepared by the co- precipitation method and were performed by the BET method, XRD, TPR, and XPS. The catalytic tests were performed at 300 and 400 A degrees C and H(2)O(v)/CO = 2.3/1 (molar ratio). The sample with the highest surface area is La(0.70)Sr(0.30)NiO(3). The XRD results showed the formation of perovskite structure for all samples, and the La(0.70)Sr(0.30)NiO(3) sample also presented peaks corresponding to La(2)NiO(4) and NiO, indicating that the solubility limit of Sr in the perovskite lattice was surpassed. The replacement of Co by Ni favored the reduction of the species at lower temperatures, and the sample containing Sr presented the highest amount of reducible species, as identified by TPR results. All samples were active, the Sr containing perovskite appearing the most active due to the highest surface area, presence of the La(2)NiO(4) phase, and higher content of Cu in the surface, as detected by XPS. Among the samples containing Co, the most active one was that with x = 0.70 (60% of CO conversion).