Single-commodity robust network design problem: Complexity,instances and heuristic solutions

We study a single-commodity Robust Network Design problem (RND) in which an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. In each scenario, a subset of the nodes is exchanging flow. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. Previously conducted computational investigations on the problem motivated the study of the complexity of some special cases and we present complexity results on them, including hypercubes. In turn, these results lead to the definition of new instances (random graphs with {−1, 0, 1} balances) that are computationally hard for the natural flow formulation. These instances are then solved by means of a new heuristic algorithm for RND, which consists of three phases. In the first phase the graph representing the network is reduced by heuristically deleting a subset of the arcs, and a feasible solution is built. The second phase consists of a neighborhood search on the reduced graph based on a Mixed-Integer (Linear) Programming (MIP) flow model. Finally, the third phase applies a proximity search approach to further improve the solution, taking into account the original graph. The heuristic is tested on the new instances, and the comparison with the solutions obtained by Cplex on a natural flow formulation shows the effectiveness of the proposed method.     

Controllability for systems governed by semilinear evolution inclusions without compactness

In this paper we study the controllability for a class of semilinear differential inclusions in Banach spaces. Since we assume the regularity of the nonlinear part with respect to the weak topology, we do not require the compactness of the evolution operator generated by the linear part. As well we are not posing any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. We are considering the usual assumption on the controllability of the associated linear problem. Notice that, in infinite dimensional spaces, the above mentioned compactness of the evolution operator and linear controllability condition are in contradiction with each other. We suppose that the nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. This regularity setting allows us to solve controllability problem under various growth conditions. As application, a controllability result for hyperbolic integro-differential equations and inclusions is obtained. In particular, we consider controllability of a system arising in a model of nonlocal spatial population dispersal and a system governed by the second order one-dimensional telegraph equation.     

Ferrocene‐modified thiopyrimidines: synthesis,enantiomeric resolution,antitumor activity

Ferrocenylalkyl thiopyrimidines ( 6a–d to 9a–d ) were prepared via the reaction of the α‐(hydroxy)alkyl ferrocenes, FcCHR(OH) ( 1a–d ; Fc = ferrocenyl; R = H, Me, Et, Ph), with 2‐thiopyrimidines ( 2 – 5 ) in acetone at room temperature in the presence of TFA, yielding 50–95%. The resulting enantiomers were resolved using HPLC on modified cellulose as chiral selector. The antitumor activities of S‐ferrocenylethyl 2‐thiopyrimidine ( 6b ) against two murine solid tumor models, carcinoma 755 (Ca755) and Lewis lung carcinoma (LLC) were evaluated in vivo. The strong antitumor effect of compound 6b on Ca755 and LLC was demonstrated. The index of tumor growth inhibition on Ca755 equaled 95% in comparison with control. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthesis,characterization and biological studies of alkenyl‐substituted titanocene(IV) carboxylate complexes

The carboxylate compounds [Ti(η⁵‐C₅H₅)(η⁵‐C₅H₄{CMe₂(CH₂CH₂CH?CH₂)})(O₂CCH₂SXyl)₂] (2; Xyl = 3,5‐Me₂C₆H₃) and [Ti(η⁵‐C₅H₅)(η⁵‐C₅H₄{CMe₂(CH₂CH₂CH?CH₂)})(O₂CCH₂SMesl)₂] (3; Mes 1 = 2,4,6‐Me₃C₆H₂) were synthesized by the reaction of [Ti(η⁵‐C₅H₅)(η⁵‐C₅H₄{CMe₂(CH₂CH₂CH?CH₂)})Cl₂] (1) with 2 equivalents of xylylthioacetic acid or mesitylthioacetic acid, respectively. Compounds 2 and 3 were characterized by spectroscopic methods. The cytotoxic activity of 1–3 was tested against human tumor cell lines from four different histogenic origins—8505C (anaplastic thyroid cancer), DLD‐1 (colon cancer) and the cisplatin sensitive A253 (head and neck cancer) and A549 (lung carcinoma)—and compared with those of the reference complex [Ti(η⁵‐C₅H₅)₂Cl₂] (R1) and cisplatin. Surprisingly, the cytotoxic activities of the carboxylate derivatives were lower than those of their corresponding dichloride analogue (1). However, complexes 1–3 were more active than titanocene dichloride against all the studied cells with the exception of complex 2 against A253 and A549 cell lines. DNA‐interaction tests were also carried out. Solutions of all the studied complexes were treated with different concentrations of fish sperm DNA, observing modifications of the UV spectra with intrinsic binding constants of 2.99 × 10⁵, 2.45 × 10⁵, and 2.35 × 10⁵ M ^?1 for 1–3. Structural studies based on density functional theory calculations of 2 and 3 were also carried out. Copyright © 2010 John Wiley & Sons, Ltd.     

Boundary conditions in rational conformal field theories

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformal boundary conditions are labelled by the nodes of G. This approach is carried to completion for sl(2) theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the A-D-E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalisation of the formalism of Cardy–Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk–boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints.     

Influence of exposure to vitrification solutions on 2-cell mouse embryos: I. Intracellular potassium and sodium content

Intracellular concentrations of potassium and sodium in two-cell mouse embryos in G1/S phase after exposure to vitrification solutions containing vitrificant agents (VFAs) ethane-1,2-diol (ethylene glycol, EG), propane-1,2-diol (propylene glycol, PG), or dimethyl sulfoxide (DMSO), and sucrose (S) after incubation in Dulbecco solution were measured by electron probe microanalysis (EPMA) as described earlier (CryoLetters, 2006, 27: 87-98). The 4-step protocol was as followed: 10% VFA for 10 min => 30% VFA + 0.7 M S for 1.5 min ==> 0.5 M S for 10 min ==> 10 min pure Dulbecco's. The cytoplasmic concentration of potassium and sodium in immediately flashed out from the oviduct embryos was in range of 120 +/- 2 mM, with good concordance with the previous data (CryoLetters, 2006, 27:87-98). Exposure in Dulbecco's for 30 min did not alter elemental composition, neither did exposure in PG or DMSO for 1.5 min. In contrast, exposure for 1.5 min in EG dropped the level of potassium to 96 +/- 2 mM while elevating level of cytoplasmic sodium to 136 +/- 3 mM. Further exposure to 30%-EG for 3 min led to a two-fold decrease of both elements (60 +/- 3 mM and 66 +/- 2 mM for K and Na, respectively).