Ki-covers. II. Ki-perfect graphs

AK_i is a complete subgraph of size i. A K_i-cover of a graph G(V, E) is a set C of K_i?1s of G such that every K_i in G contains at least one K_i?1 in C . c_i(G) is the cardinality of a smallest K_i-cover of G. A K_i-packing of G is a set of K_is such that no two K_is have i ? 1 nodes in common. p_i(G) is the cardinality of a largest K_i-packing of G. Let F _i(G) denote the set of K_is in G and define c_i(F) and p_i(F) analogously for F ? F _i(G). G is K_i-perfect if ?F ? F _i(G), c_i(F) = p_i(F). The K₂-perfect graphs are precisely the bipartite graphs. We present a characterization of K_i-perfect graphs that is similar to the Strong Perfect Graph Conjecture, and explore the relationships between K_i-perfect graphs and normal hypergraphs. Furthermore, if iA denotes the 0 ? 1 matrix of G where the rows are the elements of F _i?1(G) that belong to at least one K_i and the columns are the elements of F _i(G), then we show that iA is perfect iff G is a K_i-perfect graph. We also characterize the K_i-perfect graphs for which iAis balanced.     

Aiding flows non-unique similarity solutions of mixed-convection boundary-layer equations

The similarity equations for mixed-convection boundary-layer flow past a wedge having one of its surfaces parallel to the horizontal are derived for the latter surface. Both cases of prescribed wall temperature and heat flux are considered. It is shown that non-unique solutions exist for aiding ( > 0) as well as opposing flows ( < 0); being the buoyancy parameter. In some situations there are four simultaneous solutions. Dual solutions for two previously studied mixed-convection boundary-layer flows are shown to exist for > 0 in addition to those already reported in the literature for < 0. Namely, these correspond to vertical flat plate and vertical cylinder problems.     

Synthesis of enantiopure (R)-(−)-massoialactone through ruthenium-SYNPHOS asymmetric hydrogenation

Total synthesis of enantiopure (R)-(−)-massoialactone was achieved. The key step includes the asymmetric hydrogenation of an achiral β-keto ester using a ruthenium-SYNPHOS^® catalyst to set the hydroxyl function in a stereocontrolled manner with excellent enantioselectivity (>99% ee). Ring closing metathesis (RCM) in the presence of Grubbs’ catalyst allows the final construction of the six-membered lactone.     

Effect of pressure on the Strecker synthesis of hindered α-aminonitriles from ketones and aromatic amines

The effect of high pressure is examined in Strecker reactions involving ketones, amines and trimethylsilyl cyanide. This effect is small when moderately hindered reactants are involved. However, in the case of aniline and N-methylaniline, the sensitivity of the reaction to pressure increases with increasing steric bulk of the alkyl groups of the ketone. The results confirm the merit of pressure activation as sterically demanding reactions are subject to higher pressure acceleration than their unhindered analogs.     

Gas phase high temperature photoelectron spectroscopy: The tin monoxide molecule

The HeI photoelectron spectrum of SnO (X¹Σ⁺) has been recorded. Two bands have been observed corresponding to ionization from the 6π and 13 ionization energies of 9.98 and 10.12 eV respectively. Vibrational structure associated with the first band has been analysed to give

and D_e = 3.23 ± 0.10 eV in the SnO⁺ (X²Π) state. An assessment has been made of the ability of Hartree-Fock-Slater calculations, multiple-scattering SCF-Xα calculations and ab ini energies for the group IV diatomic monoxide molecules.     

Catalyzed Knoevenagel reactions on inorganic solid supports: Application to the synthesis of coumarine compounds

Knoevenagel reactions involving carbonyl compounds and active methylene derivatives have been studied in the presence of alumina, KSF and K10 montmorillonites. With addition of water the ester group undergoes hydrolysis. A route is disclosed for the synthesis of coumarine compounds catalyzed by solid supports.     

Improving FAIMS sensitivity using a planar geometry with slit interfaces

Differential mobility spectrometry or field asymmetric waveform ion mobility spectrometry (FAIMS) is gaining broad acceptance for analyses of gas-phase ions, especially in conjunction with largely orthogonal separation methods such as mass spectrometry (MS) and/or conventional (drift tube) ion mobility spectrometry. In FAIMS, ions are filtered while passing through a gap between two electrodes that may have planar or curved (in particular, cylindrical) geometry. Despite substantial inherent advantages of the planar configuration and its near-universal adoption in current stand-alone FAIMS devices, commercial FAIMS/MS systems have employed curved FAIMS geometries that can be more effectively interfaced to MS. Here we report a new planar (p-) FAIMS design with slit-shaped entrance and exit apertures that substantially increase ion transmission in and out of the analyzer. The entrance slit interface effectively couples p-FAIMS to multi-emitter electrospray ionization (ESI) sources, improving greatly the ion current introduced to the device and allowing liquid flow rates up to ∼50 μL/min. The exit slit interface increases the transmission of ribbon-shaped ion beams output by the p-FAIMS to downstream stages such as a MS. Overall, the ion signal in ESI/FAIMS/MS analyses increases by over an order of magnitude without affecting FAIMS resolution.     

Solving VLSI design and DNA sequencing problems using bipartization of graphs

In this paper we consider the 2-layer constrained via minimization problem and the SNP haplotype assembly problem. The former problem arises in the design of integrated and printed circuit boards, and the latter comes up in the DNA sequencing process for diploid organisms. We show that, for any maximum junction degree, the problem can be reduced to the maximum bipartite induced subgraph problem. Moreover we show that the SNP haplotype assembly problem can also be reduced to the maximum bipartite induced subgraph problem for the so-called minimum error correction criterion. We give a partial characterization of the bipartite induced subgraph polytope. Using this, we devise a branch-and-cut algorithm and report some experimental results. This algorithm has been used to solve real and large instances.     

Polymerization of ionized acetylene clusters into covalent bonded ions: evidence for the formation of benzene radical cation

Since the discovery of acetylene and benzene in protoplanetary nebulae under powerful ultraviolet ionizing radiation, efforts have been made to investigate the polymerization of ionized acetylene. Here we report the efficient formation of benzene ions within gas-phase ionized acetylene clusters (C2H2)n+ with n = 3-60. The results from experiments, which use mass-selected ion mobility techniques, indicate that the (C2H2)3+ ion has unusual stability similar to that of the benzene cation; its primary fragment ions are similar to those reported from the benzene cation, and it has a collision cross section of 47.4 A2 in helium at 300 K, similar to the value of 47.9 A2 reported for the benzene cation. In other words, (C2H2)3+ structurally looks like benzene, it has stability similar to that of benzene, it fragments such as benzene, therefore, it must be benzene!     

Design of survivable IP-over-optical networks

In the past years, telecommunications networks have seen an important evolution with the advances in optical technologies and the explosive growth of the Internet. Several optical systems allow a very large transport capacity, and data traffic has dramatically increased. Telecommunications networks are now moving towards a model of high-speed routers interconnected by intelligent optical core networks. Moreover, there is a general consensus that the control plan of the optical networks should utilize IP-based protocols for dynamic provisioning and restoration of lightpaths. The interaction of the IP routers with the optical core networks permits to achieve end-to-end connections, and the lightpaths of the optical networks define the topology of the IP network. This new infrastructure has to be sufficiently survivable, so that network services can be restored in the event of a catastrophic failure. In this paper we consider a multilayer survivable network design problem that may be of practical interest for IP-over-optical neworks. We give an integer programming formulation for this problem and discuss the associated polytope. We describe some valid inequalities and study when these are facet defining. We discuss separation algorithms for these inequalities and introduce some reduction operations. We develop a Branch-and-Cut algorithm based on these results and present extensive computational results.