Robust linear optimization under general norms

We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.     

Poly(amidoamine) dendrimers peripherally modified with 1,8-naphthalimides. Photodegradation and photostabilization on polyamide matrix

Some novel fluorescent poly(amidoamine) dendrimers supported by a polyamide-6 matrix have been prepared and studied for the first time. The colour characteristics of the novel materials have been determined and found to be dependent on the nature of 1,8-naphthalimides bonded to their periphery amino groups. The materials have been treated with protons and cuprum cations. The resulting into changes in the colour characteristics and photostability of the dendrimers has been investigated. It has been shown that these ions inhibit the photodegradation of dendrimers molecules studied.     

Free-by-Demushkin pro-<Emphasis Type="Italic">p</Emphasis> groups

We give an example of a short exact sequence 1NGD1 of pro-p groups such that the cohomological dimension cd(G)=2, G is (topologically) finitely generated, N is a free pro-p group of infinite rank, D is a Demushkin group, for every closed subgroup S of G containing N and any natural number n the inflation map is an isomorphism but G is not a free pro-p product of a free pro-p group by a Demushkin group. This is a group theoretic version of a question raised by T. Würfel for some special Galois groups.Both authors are partially supported by bolsa de produtividade de pesquisa from CNPq, Brazil and CNPq grant 470272/2003-1.     

Finite Presentability and the Homological Type FP m for a Class of Hopf Algebras

We define and study the property finite presentability in the category  of Hopf algebras that are smash product of universal enveloping algebra of a Lie algebra by a group algebra. We show that for such Hopf algebras finite presentability is equivalent with finite presentability as an associative k-algebra.     

Tits alternative for 3-manifold groups

Let M be an irreducible, orientable, closed 3-manifold with fundamental group G. We show that if the pro-p completion of G is infinite then G is either soluble-by-finite or contains a free subgroup of rank 2. Both authors are partially supported by “Bolsa de produtividade de pesquisa” from CNPq, Brazil. Received: 16 February 2006     

Liquid crystalline polyfluorenes for blue polarized electroluminescence

A series of 9,9‐dialkyl‐poly(fluorene‐2,7‐diyl)s containing linear and branched alkyl substituents with a M_n of up to 200000 g/mol has been synthesized. Moreover, some of the polymers were end capped with a suitable hole transport functionality, such as a triphenylamine derivative, to improve their charge transport properties and to control the molecular weight. The thermal alignment of these novel polymers on a rubbed polyimide layer led to highly anisotropic film formation with dichroic ratios (absorption parallel and perpendicular to the rubbing direction) of up to 26 in absorption and 21 in emission.     

Homological properties of abstract and profinite modules and groups

Generalising the main results from [F. Grunewald, A. Jaikin, A. Pinto, P. Zalesskii, Normal subgroups of profinite groups of non-negative deficiency (preprint); D.H. Kochloukova, On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version, J. Pure Appl. Algebra 204 (3) (2006) 536-554; D.H. Kochloukova, Some Novikov rings that are von Neumann finite and knot-like groups, Comment. Math. Helv. 81 (4) (2006) 931-943] we study homological finiteness properties and projective dimensions of modules over groups G in the abstract and profinite case comparing with the same invariants for some specific normal subgroups N of G.     

On the homological finiteness properties of some modules over metabellian Lie algebras

We characterise the modulesB of homological typeFP _m over a finitely generated Lie algebraL such thatL is a split extension of an abelian idealA and an abelian subalgebraQ andA acts trivially onB. The characterisation is in terms of the invariant Δ introduced by R. Bryant and J. Groves and is a Lie algebra version of the generalisation [K 4, conjecture 1] of the still openFP _m -Conjecture for metabelian groups [Bi-G, Conjecture p. 367]. The casem=1 of our main result is treated separately, as there the characterisation is proved without restrictions on the type of the extension.     

On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version

A group G is knot-like if it is finitely presented of deficiency 1 and has abelianization G/G^′?Z. We prove the conjecture of E. Rapaport Strasser that if a knot-like group G has a finitely generated commutator subgroup G^′ then G^′ should be free in the special case when the commutator G^′ is residually finite. It is a corollary of a much more general result : if G is a discrete group of geometric dimension n with a finite K(G,1)-complex Y of dimension n, Y has Euler characteristics 0, N is a normal residually finite subgroup of G, N is of homological type FP_n-1 and G/N?Z then N is of homological type FP_n and hence G/N has finite virtual cohomological dimension vcd(G/N)=cd(G)-cd(N). In particular either N has finite index in G or cd(N)?cd(G)-1.Furthermore we show a pro-p version of the above result with the weaker assumption that G/N is a pro-p group of finite rank. Consequently a pro-p version of Rapaport's conjecture holds.     

Homological Invariants for pro-p Groups and Some Finitely Presented pro- C{\cal C} Groups

Let G be a finitely presented pro- C{\cal C} group with discrete relations. We prove that the kernel of an epimorphism of G to [^(\Bbb Z)]_C\hat{\Bbb Z}_{\cal C} is topologically finitely generated if G does not contain a free pro- C{\cal C} group of rank 2. In the case of pro-p groups the result is due to J. Wilson and E. Zelmanov and does not require that the relations are discrete ([15], [17]).For a pro-p group G of type FP_m we define a homological invariant C{\cal C} groups, pro-p groups, homological type FP_m, finite presentabilityBoth authors are partially supported by CNPq, Brazil.