A complex of incompressible surfaces for handlebodies and the mapping class group

For a genus g handlebody H _g a simplicial complex, with vertices being isotopy classes of certain incompressible surfaces in H _g , is constructed and several properties are established. In particular, this complex naturally contains, as a subcomplex, the complex of curves of the surface ${\partial H_{g}}$ . As in the classical theory, the group of automorphisms of this complex is identified with the mapping class group of the handlebody.     

Two-loop QCD amplitude for gg-->h, H in the minimal supersymmetric standard model

We present the two-loop QCD amplitude for the interaction of two gluons and a CP-even Higgs boson in the minimal supersymmetric standard model (MSSM). We apply a novel numerical method for the evaluation of Feynman diagrams with infrared, ultraviolet, and threshold singularities. We discuss subtleties in the ultraviolet renormalization of the amplitude with conventional dimensional regularization, dimensional reduction, and the four dimensional helicity scheme. Finally, we show numerical results for scenarios of supersymmetry breaking with a rather challenging phenomenology in which the Higgs signal in the MSSM is suppressed in comparison to the standard model.     

A survey on algorithmic approaches for solving tourist trip design problems

The tourist trip design problem (TTDP) refers to a route-planning problem for tourists interested in visiting multiple points of interest (POIs). TTDP solvers derive daily tourist tours, i.e., ordered visits to POIs, which respect tourist constraints and POIs attributes. The main objective of the problem discussed is to select POIs that match tourist preferences, thereby maximizing tourist satisfaction, while taking into account a multitude of parameters and constraints (e.g., distances among POIs, visiting time required for each POI, POIs visiting days/hours, entrance fees, weather conditions) and respecting the time available for sightseeing on a daily basis. The aim of this work is to survey models, algorithmic approaches and methodologies concerning tourist trip design problems. Recent approaches are examined, focusing on problem models that best capture a multitude of realistic POIs attributes and user constraints; further, several interesting TTDP variants are investigated. Open issues and promising prospects in tourist trip planning research are also discussed.     

Magnetic ionic liquid in stirring-assisted drop-breakup microextraction: Proof-of-concept extraction of phenolic endocrine disrupters and acidic pharmaceuticals

The use of magnetic ionic liquids (MILs) is in constant growth due to their switchable properties in the presence of an external magnetic field along with the outstanding properties of ionic liquids. In this study, a novel stirring-assisted drop-breakup microextraction (SADBME) approach is put forward, based on the synthesis and utilization of methyltrioctylammonium tetrachloroferrate (N_{8 8,8,1}[FeCl₄]), as a MIL. The proposed procedure complies with the principles of the green chemistry, since it uses low volumes of easily synthesized ILs-based magnetic extracting phases avoiding the use of toxic solvents. To demonstrate its applicability, the proposed microextraction procedure is studied in conjunction with HPLC for the determination of selected phenols and acidic pharmaceuticals in aqueous matrices, taking into account the main experimental variables involved. The results obtained are accurate and highly reproducible, thus making it a good alternative approach for routine analysis of phenols and acidic pharmaceuticals. The low-cost approach is straightforward, environmentally safe and exhibits high enrichment factors and absolute extraction percentages and satisfactory recoveries. To the best of our knowledge, this is the first time that a MIL is used for analytical purposes in a practical, efficient and environmentally friendly drop-breakup microextraction approach for small molecules.     

The GHP conformai Killing equations and their integrability conditions,with application to twisting type N vacuum spacetimes

The conformai Killing equations in resolved form and their first and second integrability conditions are obtained in the compact spin coefficient formalism for arbitrary spacetimes. To facilitate calculations an operatorL is introduced which agrees with the Lie derivative only when operating on quantities with GHP weights (0,0). The resulting equations are used to find the conditions for the existence of a two dimensional non-Abelian group of homothetic motions in a twisting typeN vacuum spacetime. The equivalence of two such sets of metrics is established, metrics that were recently the subject of independent investigations by Herlt on the one hand and by Ludwig and Yu on the other.     

Variable step-size implementation of sixth-order Numerov-type methods

The explicit sixth-order Numerov-type family of methods is considered. A new representative from this family is produced and equipped with a cheap step-size changing algorithm. Actually, after the completion of a step, this remains the same, halved, or doubled. The off-step points required for such technique are evaluated through local interpolant. Numerical tests over various problems illustrate the efficiency gained by this approach.     

Tailorable and Biocompatible Supramolecular-Based Hydrogels Featuring two Dynamic Covalent Chemistries

Dynamic covalent chemistry (DCC) has proven to be a valuable tool in creating fascinating molecules, structures, and emergent properties in fully synthetic systems. Here we report a system that uses two dynamic covalent bonds in tandem, namely disulfides and hydrazones, for the formation of hydrogels containing biologically relevant ligands. The reversibility of disulfide bonds allows fiber formation upon oxidation of dithiol-peptide building block, while the reaction between NH−NH₂ functionalized C-terminus and aldehyde cross-linkers results in a gel. The same bond-forming reaction was exploited for the “decoration” of the supramolecular assemblies by cell-adhesion-promoting sequences (RGD and LDV). Fast triggered gelation, cytocompatibility and ability to “on-demand” chemically customize fibrillar scaffold offer potential for applying these systems as a bioactive platform for cell culture and tissue engineering.