Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

Liquid-Liquid Equilibrium of Copolymer Solutions with Broad and Asymmetric Chemical Distributions

ABSTRACT

A solution of a random copolymer showing polydispersity only with respect to chemical composition is considered. A model distribution very flexible in its breadth and in its asymmetry is used to describe the polydispersity. Based on continuous thermodynamics, equations for the cloud-point curve, the shadow curve, the spinodal, the critical point, and the heterogeneous double critical point are derived. the activity coefficients are calculated with the aid of Huggins' χ-parameter concept assuming χ to depend linearly on the average chemical composition of the copolymer. the influence of the breadth and the asymmetry of the distribution on the liquid-liquid equilibrium of the copolymer solution is discussed.     

Do halogen and methyl substituents have electronic effects on the structures of simple disilanes? An experimental and theoretical study of the molecular structures of the series X3SiSiMe3 (X = H, F, Cl and Br)

The gas-phase molecular structures of a series of halogen-substituted disilanes [X₃SiSiMe₃ (X = H, F, Cl and Br)], 1,1,1-trimethyldisilane (H₃SiSiMe₃), 1,1,1-trifluoro-2,2,2-trimethyldisilane (F₃SiSiMe₃), 1,1,1-trichloro-2,2,2-trimethyldisilane (Cl₃SiSiMe₃) and 1,1,1-tribromo-2,2,2-trimethyldisilane (Br₃SiSiMe₃), have been determined in the gas phase by electron diffraction. Ab initio calculations at the HF and MP2 level were used to support the experimental investigation using the SARACEN method. All of the investigated structures were determined to adopt a staggered structure with C _3v symmetry. The effect of substitution on the Si–Si bond and the Si–Si–X bond angle was investigated and these results were compared to results obtained from a recent study of halogen-substituted disilanes [X₃SiSiXMe₂ (X = F, Cl, Br and I)] to consider the effect of the methyl groups on the substituted disilanes.     

Maritime inventory routing with multiple products: A case study from the cement industry

This paper considers a maritime inventory routing problem faced by a major cement producer. A heterogeneous fleet of bulk ships transport multiple non-mixable cement products from producing factories to regional silo stations along the coast of Norway. Inventory constraints are present both at the factories and the silos, and there are upper and lower limits for all inventories. The ship fleet capacity is limited, and in peak periods the demand for cement products at the silos exceeds the fleet capacity. In addition, constraints regarding the capacity of the ships’ cargo holds, the depth of the ports and the fact that different cement products cannot be mixed must be taken into consideration. A construction heuristic embedded in a genetic algorithmic framework is developed. The approach adopted is used to solve real instances of the problem within reasonable solution time and with good quality solutions.     

Service network design with management and coordination of multiple fleets

We present a new optimization model for the tactical design of scheduled service networks for transportation systems where several entities provide service and internal exchanges and coordination with neighboring systems is critical. Internal exchanges represent border crossings necessitating changes of vehicles, while the coordination with neighboring systems represents intermodal operations. For a given demand, the model determines departure times of the services such that throughput time of the demand in the system is minimized. The model is an extension of the design-balanced capacitated multicommodity network design model that we denote service network design with asset management and multiple fleet coordination to emphasize the explicit modeling of different vehicle fleets. Data from a real-world problem addressing the planning of new rail freight services across borders serves to illustrate the capabilities of the formulation. We analyze how synchronization with collaborating services and removal of border-crossing operations impact the throughput time for the freight. We identify a significant potential for system performance enhancement from synchronization among collaborating services for the problem studied.     

Aliphatic hydroxylation and epoxidation of capsaicin by cytochrome P450 CYP505X

Microbial cytochrome P450 enzymes (CYPs) are able to mimic the metabolism of human CYPs. One challenge is to identify the respective drug metabolites and to compare substrate specificities to those of the human enzymes. In this study, a class VIII self-sufficient CYP from Aspergillus fumigatus (CYP505X) and variants of this enzyme were heterologously expressed in E. coli. The substrate scope of the variants was determined using active pharmaceutical ingredients (APIs) and (hetero)cyclic compounds. Capsaicin – the active compound in chili peppers – was oxidized most efficiently (4.36?μM/min) in a whole cell mediated biotransformation. The products were isolated, purified and their structures elucidated by 1D and 2D NMR. The two major metabolites showed modifications on the lipophilic side chain. Specifically, capsaicin was hydroxylated at position 8 to give (E)-8-hydroxy-N-(4-hydroxy-3-methoxybenzyl)-8-methylnon-6-enamide and epoxidized at the double bond to give N-(4-hydroxy-3-methoxybenzyl)-5-(3-isopropyloxiran-2-yl)-pentanamide.     

Die Bestimmung von Spuren von Quecksilber

Ohne Zusammenfassung     

APplication of Continuous Thermodynamics to the Stability of Polymer Systems. II

A determinant criterion for the critical state in solutions and mixtures of polydisperse polymers is established within the general framework of Gibbs theory. The treatment continues an earlier paper by considering more general Gibbs free energy relations: The function replacing the x-term in the classic Flory-Huggins equation is permitted to depend on a finite number of moments of the polymer distribution(s) so as to embrace most Gibbs free energy relations of practical use. The new criterion leads to a very large reduction of computer time and of needed storage capacity compared to the traditional Gibbs determinant criterion. Some relations known from the literature are shown to be special cases of the established new criterion.     

Substituent Effects on Oxidation‐Induced Formation of Quinone Methides from Arylboronic Ester Precursors

A series of arylboronic esters containing different aromatic substituents and various benzylic leaving groups (Br or N⁺Me₃Br^?) have been synthesized. The substituent effects on their reactivity with H₂O₂ and formation of quinone methide (QM) have been investigated. NMR spectroscopy and ethyl vinyl ether (EVE) trapping experiments were used to determine the reaction mechanism and QM formation, respectively. QMs were not generated during oxidative cleavage of the boronic esters but by subsequent transformation of the phenol products under physiological conditions. The oxidative deboronation is facilitated by electron‐withdrawing substituents, such as aromatic F, NO₂, or benzylic N⁺Me₃Br^?, whereas electron‐donating substituents or a better leaving group favor QM generation. Compounds containing an aromatic CH₃ or OMe group, or a good leaving group (Br), efficiently generate QMs under physiological conditions. Finally, a quantitative relationship between the structure and activity has been established for the arylboronic esters by using a Hammett plot. The reactivity of the arylboronic acids/esters and the inhibition or facilitation of QM formation can now be predictably adjusted. This adjustment is important as some applications may benefit and others may be limited by QM generation.