A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.     

Wiener Type Regularity of a Boundary Point for the 3D Lamé System

In this paper, we study the 3D Lamé system and establish its weighted positive definiteness for a certain range of elastic constants. By modifying the general theory developed in Maz’ya (J Duke Math 115(3): 479–512, 2002), we then show, under the assumption of weighted positive definiteness, that the divergence of the classical Wiener integral for a boundary point guarantees the continuity of solutions to the Lamé system at this point.     

Ionization state and structure of l-1,2-dipalmitoylphosphatidylglycerol monolayers at the liquid/air interface

Phosphatidylglycerols are components of biological membranes. The phase behavior of these phospholipids was extensively investigated. However, there is still no definite picture about the dependence of the ionization state and monolayer structure on subphase composition. The major problem of previous investigations is that none of the methods used allow obtaining the ionization degree directly. In the present work we apply techniques developed in the past decades for Langmuir monolayers: infrared reflection absorption spectroscopy (IRRAS) as well as X-ray diffraction and reflectivity techniques, which provide straightforward information about structure and ionization state of a L-1,2-dipalmitoylphosphatidylglycerol (DPPG) monolayer. The Gouy-Chapman model is applied to evaluate the intrinsic pKa. Therewith, the ionization degree can be determined even at low pH values. The experimental titration curves are in good agreement with theoretical curves based on the Gouy-Chapman model. The obtained instrinic pKa amounts to 1. The ionization degree of a DPPG monolayer is independent of the monovalent cation size. In contrast, the structure of a DPPG monolayer is strongly affected by the type of divalent cations.     

Development of an empirical force field for silica. Application to the quartz-water interface

Interactions of pulverized crystalline silica with biological systems, including the lungs, cause cell damage, inflammation, and apoptosis. To allow computational atomistic modeling of these pathogenic processes, including interactions between silica surfaces and biological molecules, new parameters for quartz, compatible with the CHARMM empirical force field were developed. Parameters were optimized to reproduce the experimental geometry of alpha-quartz, ab initio vibrational spectra, and interactions between model compounds and water. The newly developed force field was used to study interactions of water with two singular surfaces of alpha-quartz, (011) and (100). Properties monitored and analyzed include the variation of the density of water molecules in the plane perpendicular to the surface, disruption of the water H-bond network upon adsorption, and space-time correlations of water oxygen atoms in terms of Van Hove self-correlation functions. The vibrational density of states spectra of water in confined compartments were also computed and compared with experimental neutron-scattering results. Both the attenuation and shifting to higher frequencies of the hindered translational peaks upon confinement are clearly reproduced by the model. However, an upshift of librational peaks under the conditions of model confinement still remains underrepresented at the current empirical level.     

A tether controlled exo-selective trans-annular Diels-Alder (TADA) reaction

[reaction: see text] A fully substrate controlled stereoselective route to construct cis-hexahydronaphthalene 4 is described starting from nonracemic butenolide 6. The key step is an exo-selective transannular Diels-Alder reaction (TADA) of tetraene 5, whose intrinsic constraint allows selective formation of one stereodefined product. Compound 4 is a key intermediate in the synthesis of the novel antibiotic branimycin (1).     

Elliptic equations for measures: Regularity and global bounds of densities

We consider elliptic equations of the form L^*μ=ν for measures on . The membership of solutions in the Sobolev classes is established under appropriate conditions on the coefficients of L. Bounds of the form (x)CΦ(x)⁻¹ for the corresponding densities are obtained.     

An efficient synthesis of new C-2 aryl substituted quinolines based on three component imino Diels-Alder reaction

New effective approach to the synthesis of a wide variety of C-2 nitro or aminophenyl substituted quinolines was reported using diverse intermediate 4-(2-oxopyrrolinidyl-1)-tetrahydroquinolines that were prepared by a three component imino Diels-Alder reaction was reported. The key aromatisation process occurs cleanly with the loss of the 2-oxopyrrolinidyl-1 fragment.     

Legendrian Links, Causality, and the Low Conjecture

Let (X ^m+1, g) be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of ${\mathbb{R}^{m}}Let (X ^m+1, g) be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of \mathbbR^m{\mathbb{R}^{m}} . The Legendrian Low conjecture formulated by Natário and Tod says that two events x, y ? X{x, y \in X} are causally related if and only if the Legendrian link of spheres \mathfrakS_x, \mathfrakS_y{{\mathfrak{S}_x,\,\mathfrak{S}_y}} whose points are light geodesics passing through x and y is non-trivial in the contact manifold of all light geodesics in X. The Low conjecture says that for m = 2 the events x, y are causally related if and only if \mathfrakS_x, \mathfrakS_y{{\mathfrak{S}_x,\,\mathfrak{S}_y}} is non-trivial as a topological link. We prove the Low and the Legendrian Low conjectures. We also show that similar statements hold for any globally hyperbolic (X ^m+1, g) such that a cover of its Cauchy surface is diffeomorphic to an open domain in \mathbbR^m{\mathbb{R}^{m}} .     

Mutually disjoint designs and new 5‐designs derived from groups and codes

The article gives constructions of disjoint 5‐designs obtained from permutation groups and extremal self‐dual codes. Several new simple 5‐designs are found with parameters that were left open in the table of 5‐designs given in (G. B. Khosrovshahi and R. Laue, t‐Designs with t⩾3, in “Handbook of Combinatorial Designs”, 2nd edn, C. J. Colbourn and J. H. Dinitz (Editors), Chapman & Hall/CRC, Boca Raton, FL, 2007, pp. 79–101), namely, 5−(v, k, λ) designs with (v, k, λ)=(18, 8, 2m) (m=6, 9), (19, 9, 7m) (m=6, 9), (24, 9, 6m) (m=3, 4, 5), (25, 9, 30), (25, 10, 24m) (m=4, 5), (26, 10, 126), (30, 12, 440), (32, 6, 3m) (m=2, 3, 4), (33, 7, 84), and (36, 12, 45n) for 2⩽n⩽17. These results imply that a simple 5−(v, k, λ) design with (v, k)=(24, 9), (25, 9), (26, 10), (32, 6), or (33, 7) exists for all admissible values of λ. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 305–317, 2010     

On equivalences of derived and singular categories

Let X and Y be two smooth Deligne-Mumford stacks and consider a pair of functions f: X → $ \mathbb{A}^1 $ \mathbb{A}^1 , g:Y → $ \mathbb{A}^1 $ \mathbb{A}^1 . Assuming that there exists a complex of sheaves on X × $ \mathbb{A}^1 $ \mathbb{A}^1 Y which induces an equivalence of D ^b (X) and D ^b (Y), we show that there is also an equivalence of the singular derived categories of the fibers f ⁻¹(0) and g ⁻¹(0). We apply this statement in the setting of McKay correspondence, and generalize a theorem of Orlov on the derived category of a Calabi-Yau hypersurface in a weighted projective space, to products of Calabi-Yau hypersurfaces in simplicial toric varieties with nef anticanonical class.