A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space

Given a set V of size N≥4 vertices in a metric space, how can one interconnect them with the possible use of a set S of size M vertices not in the set V, but in the same metric space, so that the cumulative cost of the inter-connections between all the vertices is a minimum? When one uses the Euclidean metric to compute these inter-connections, this is referred to as the Euclidean Steiner Minimal Tree Problem. This is an NP-hard problem. The Steiner Ratio ρ of a vertex set is the length of this Steiner Minimal Tree (SMT), divided by the length of the Minimum Spanning Tree (MST), and is a popular and tractable measure of solution quality.The ?-Sausage heuristic described in this paper employs a decomposition technique to explore the point set. The fixed vertices of the set are connected to a set of centroid vertices of Delaunay tetrahedrons. The path topology is preserved as far as possible, together with a cycle prevention rule, where junctions, and deviations from the ?-Sausage structure occur. Furthermore, repeated sweeps, with different root vertices are accommodated.The computational complexity of the heuristic is shown to be O(N²). Experimental results with thousands of vertices are presented. Comparisons with an exponential running time Branch and Bound algorithm are also shown.     

Microbial removal of sulfur dioxide from a gas stream with net oxidation to sulfate

A study has been conducted of the feasibility of utilizing the sulfate reducing bacteriumDesulfovibrio desulfuricans and the chemoautotrophThiobacillus denitrificans as a basis of a microbial process for the removal of sulfur dioxide from a gas with net oxidation to sulfate. In reactors-in-series, SO₂ was reduced to H₂S in the first stage by D.desulfuricans. The H₂S was then stripped with nitrogen and sent to a second stage where it was oxidized to sulfate by T.denitrificans. A sulfur balance demonstrated complete reduction of SO₂ to H₂S in the first stage and complete oxidation of H₂S to sulfate in the second stage.     

Fe3O4@S‐ABENZ@VO: Magnetically separable nanocatalyst for the efficient,selective and mild oxidation of sulfides and oxidative coupling of thiols

Oxovanadium(IV) immobilized on Fe₃O₄@S‐ABEN is reported as a highly efficient nanocatalyst for the oxidation of sulfides and oxidative coupling of thiols (using H₂O₂ as green oxidant), the products of which are obtained in high to excellent yields. The products can be separated by a simple extraction with organic solvent and the catalyst is highly efficient, especially in terms of selectivity of desired product. The catalytic system can be recycled and reused without significant loss of catalytic activity.     

Exploiting the versatility of pyridyl ligands for the preparation of diorganotin (IV) adducts: spectral,crystallographic and Hirshfeld surface analysis studies

Diorganotin (IV) complexes SnR₂X₂ (R = Me, Ph; X = Cl, NCS) form a series of versatile complexes when react with bidentate substituted pyridyl ligands. The reaction of dimethyltin dichloride with 5,5′‐dimethyl‐2,2′‐bipyridine (5,5′‐Me₂bpy) resulted in the formation of [SnMe₂Cl₂(5,5′‐Me₂bpy)] ( 1 ). Moreover, the reaction of SnMe₂(NSC)₂ with 4,4′‐di‐tert‐butyl‐2,2′‐bipyridine (bu₂bpy), 1,10‐phenanthroline (phen) and 4,7‐diphenyl‐1,10‐phenanthroline (bphen) affords the hexa‐coordinated complexes [SnMe₂(NCS)₂(bu₂bpy)] ( 2 ), [SnMe₂(NCS)₂(phen)] ( 3 ) and [SnMe₂(NCS)₂(bphen)] ( 4 ), respectively. The resulting complexes have been characterized using elemental analysis, IR, multinuclear NMR (¹H, ¹³C, ¹¹⁹Sn) and DEPT‐135^° NMR spectroscopy. On the other hand, the reaction of diphenyltin dichloride with 2,2′‐biquinoline (biq) and 4,7‐phenantroline (4,7‐phen) led to the formation of polymeric complexes of [SnPh₂Cl₂(4,7‐phen)]_n ( 5 ) and [SnPh₂Cl₂(biq)]_n ( 6 ). The NMR spectra, however, reveal the ligand lability in solution and suggest a coordination number of 5 . The X‐ray crystal structures of complexes [SnMe₂Cl₂(5,5′‐Me₂bpy)] ( 1 ), [SnMe₂(NCS)₂(bu₂bpy)] ( 2 ) and [SnMe₂(NCS)₂(bphen)] ( 4 ) have been determined which reveal that the geometry around the tin atom is distorted octahedral with trans‐[SnMe₂] configuration. Interestingly, the crystal structure of (H₂biq)₂[SnPh₂Cl₄]?2CHCl₃ ( 7 ) was characterized by X‐ray crystallography from a chloroform solution of [SnPh₂Cl₂(biq)]_n ( 6 ) indicating the formation of doubly protonated [H₂biq]⁺ and [Ph₂SnCl₄]^2? which are stabilized by a network of hydrogen bonds with a feature of trans‐[SnPh₂]. The 3D Hirshfeld surface analysis and 2D fingerprint maps were used for quantitative mapping out of the intermolecular interactions for 1 , 2 , 4 and 7 which show the presence of π‐π and hydrogen bonding interactions which are associated between donor and acceptor atoms (N, S, Cl) in the solid state.     

Application of Yttrium Iron Garnet as a Powerful and Recyclable Nanocatalyst for One-Pot Synthesis of Pyrano[2,3-c]pyrazole Derivatives under Solvent-Free Conditions

Russian Journal of Organic Chemistry - The application of yttrium iron garnet (YIG) superparamagnetic nanoparticles as a new recyclable and highly efficient heterogeneous magnetic catalyst for...     

A New Method for the Oxybromination of Aromatic Compounds with Copper(II)bromide and Potassium Dichromate

Abstract

A new and mild method for oxybromination of aromatic compounds with CuBr ₂ and K ₂ Cr ₂ O ₇ in HOAC is reported.     

Water soluble poly(ethylene oxide) functionalized norbornene polymers

The synthesis of three different poly(ethylene oxide) macromonomers with a norbornene and oxanorbornene end group is presented. The macromonomers were polymerized to comb‐polymers by ring‐opening metathesis polymerization (ROMP) using Grubbs' Catalyst G3 to produce water soluble polymers with polydispersities between 1.04 and 1.30 and molecular weights between 14,000 and 50,000 g/mol. Characterization by static and dynamic light scattering reveals that the comb‐polymers with norbornene backbone are molecularly disperse in aqueous solution, while the oxanorbornene‐backbone polymers form small water‐soluble aggregates. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2640–2648, 2008     

Hot deformation behavior and constitutive modeling of VCN200 low alloy steel

The hot working behavior of VCN200 medium carbon low alloy steel was analyzed by performing hot compression tests in temperature range of 850–1150 °C and at strain rates of 0.001–1 s⁻¹. Flow curves were typical of dynamic recrystallization during hot working over temperature range of 900–1150 °C and strain rates of 0.001–1 s⁻¹. However, at lower temperatures no indication of flow softening was observed. The constitutive analysis using the hyperbolic sine function was performed and the value of apparent activation energy for the hot deformation determined to be about 435 kJ/mol. The flow curves up to the peak were successfully modeled using a dynamic recovery model. All the factors in this model were defined in terms of the Zener–Hollomon parameter. A modified form of Avrami equation was used to estimate the fractional softening due to the dynamic recrystallization for any given strain in flow curve. Using this model, the flow curves were successfully predicted and generalized to different deformation conditions.     

Stereoselective and Convenient Synthesis of Diethyl (E)-α-Triphenylstannyl or (Z)-α-Tributylstannyl α-Alkenylphosphonates

Diethyl (E)-α-triphenylstannyl or (Z)-α-tri-n-butylstannyl α-alkenylphosphonates are conveniently and stereoselectively prepared using a “tin-Peterson-like” reaction. Protonolysis of the carbon-tin bond of α-tributylstannyl derivatives proved to be easy and stereospecific.     

A Novel,One-Pot Synthesis of 2,5-Disubstituted-1,3,4-Oxadiazoles Using 1,4-Bis(Triphenylphosphonium)-2-Butene Peroxodisulfate

An efficient and convenient synthesis of 1,3,4-oxadiazoles from aromatic aldehydes, acyl hydrazide, and 1,4- bis(triphenylphosphonium)-2-butene peroxodisulfate is reported.

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