Toward microphase separation in epoxy systems containing PEO–PPO–PEO block copolymers by controlling cure conditions and molar ratios between blocks

Nanostructuring of thermosetting systems using the concept of templating and taking advantage of the self-assembling capability of block copolymers is an exciting way for designing new materials for nanotechnological applications. In this first part of the work, reactive blends based on stoichiometric amounts of a diglycidylether of bisphenol-A epoxy resin and 4,4′-diaminodiphenylmethane cure agent modified with three poly(ethylene oxide)-co-poly(propylene oxide)-co-poly(ethylene oxide) block copolymers were studied. Cure advancement of these systems was analyzed by differential scanning calorimetry. The experimental results show a delay of cure rate, which increases as copolymer content and PEO molar ratio in the block copolymer rise. Infrared spectroscopy shows that PEO block is mainly responsible of physical interactions between the hydroxyl groups of growing epoxy thermoset and ether bonds of block copolymer. These interactions are mainly responsible for the delaying of cure kinetics. The molar ratio between blocks also has a critical influence on the delaying of the cure rate. A mechanistic approach of cure kinetics allows us to relate the delay of cure as a consequence of block copolymer adding to physical interactions between components.     

Categorical group invariants of 3-manifolds

For a given class \({\mathcal{G}}\) of groups, a 3-manifold M is of \({\mathcal{G}}\) -category \({\leq k}\) if it can be covered by k open subsets such that for each path-component W of the subsets the image of its fundamental group \({ \pi_1(W) \rightarrow \pi(M )}\) belongs to \({\mathcal{G}}\) . The smallest number k such that M admits such a covering is the \({\mathcal{G}}\) -category, \({cat_{\mathcal{G}}(M)}\) . If M is closed, it has \({\mathcal{G}}\) -category between 1 and 4. We characterize all closed 3-manifolds of \({\mathcal{G}}\) -category 1, 2, and 3 for various classes \({\mathcal{G}}\) .     

Research topics in discrete estimation of distribution algorithms based on factorizations

In this paper, we identify a number of topics relevant for the improvement and development of discrete estimation of distribution algorithms. Focusing on the role of probability distributions and factorizations in estimation of distribution algorithms, we present a survey of current challenges where further research must provide answers that extend the potential and applicability of these algorithms. In each case we state the research topic and elaborate on the reasons that make it relevant for estimation of distribution algorithms. In some cases current work or possible alternatives for the solution of the problem are discussed.     

Stiefel-Whitney surfaces and decompositions of 3-manifolds into handlebodies

Every closed nanorientable 3-manifold M can be obtained as the union of three orientable handlebodies V₁, V₂, V₃ whose interiors are pairwise disjoint. If g_i denotes the genus of V_i, g₁g₂g₃, we say that M has tri-genus (g₁, g₂, g₃), if in terms of lexicographical ordering, the triple (g₁, g₂, g₃) is minimal among all such decompositions of M into orientable handlebodies. We relate the tri-genus of M to the genus of a surface that represents the dual of the first Stiefel-Whitney class of M. This is used to determine g₁ and g₂.     

Stiefel–Whitney surfaces and the tri-genus of non-orientable 3-manifolds

Every non-orientable 3-manifold M can be expressed as a union of three orientable handlebodies V ₁,V ₂,V ₃ whose interiors are pairwise disjoint. If g _i denotes the genus of ∂V _i and g ₃≤g ₂≤g ₃, then the tri-genus of M is the minimum triple (g ₁,g ₂,g ₃), ordered lexicographically. If the Bockstein of the first Stiefel–Whitney class βw ₁(M)=0, then M has tri-genus (0,2g,g ₃), where g is the minimal genus of a 2-sided Stiefel Whitney surface of M. In this paper it is shown that, if βw ₁(M)≠0, then M has tri-genus (1,2g−1,g ₃), where g is the minimal genus of a (1-sided) Stiefel–Whitney surface. As an application the tri-genus of certain graph manifolds is computed. Received: 28 April 1999     

A 3D-analysis of the Cl?�Cbenzene dimer solvation by Ar atoms

The solvation of the Cl^??Cbenzene (Cl^??CBz) aggregate by Ar atoms has been investigated employing molecular dynamics (MD) simulations. The gradual evolution from cluster rearrangement to solvation dynamics is discussed by considering ensembles of n (n = 1,...,30) Ar atoms around the Cl^??CBz clusters. The energetic of the solvated cluster is decomposed as a sum of pairs (including both the Ar?CAr and the Cl^??CAr terms), Cl^??CBz and Ar?CBz interactions and their relative contributions are analyzed as a function of the cluster size. The geometrical distribution of Ar atoms around Cl^??CBz is investigated in terms of radial distribution functions (RDF), bidimensional (2D) angular distributions and tridimensional (3D) probability densities. The variation on the spatial distribution of the Ar atoms around Cl^??CBz when the Ar number increases is investigated from a novel prospective, employing spherical coordinates of the solvent atoms within an inertial reference frame. Isomerization processes are also studied.     

The extension of the $$D(-k)$$ D ( - k ) -pair $$\{k,k+1\}$$ { k,k + 1 } to a quadruple

Periodica Mathematica Hungarica - Let $$n\ne 0$$ be an integer. A set of m distinct positive integers $$\{a_1,a_2,\ldots ,a_m\}$$ is called a D(n)-m-tuple if $$a_ia_j + n$$ is a perfect square for...