An approximation algorithm for finding long paths in Hamiltonian graphs

In this paper we present a polynomial-time algorithm that finds paths of length Ω((logn/loglogn)²) in undirected Hamiltonian graphs, improving the previous best of Ω(logn).     

Synthesis and characterization of soluble polyimides containing trifluoromethyl groups in their backbone

A series of polyimides were synthesized from 2,2‐Bis(3,4‐dicarboxyphenyl)hexafluoropropane, 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane, and 4,4′‐oxydianiline by chemical imidization. The effects of the diamine ratios on the properties of the films were evaluated through the study of their thermal, electrical, and morphological properties. All the polymers exhibited better solubility in most of the organic solvents and hence were easily processable. Polyimides with more 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane exhibited better solubility and a low refractive index, which is highly desired for microelectronic applications. The dielectric constant and birefringence were strongly dependent on the fluorine content. With an increase in the fluorine substitution, both the dielectric constant and birefringence decreased. All the polymers exhibited high thermal stability (>400 °C). The absence of crystalline melting in differential scanning calorimetry and broad wide‐angle X‐ray diffraction patterns revealed the amorphous nature of the polymers, which was due to the presence of bulky CF₃ groups and hinged ether linkages of the diamine component. The residual stress values decreased with an increase in the 4,4′‐oxydianiline content, and the results were in agreement with the dielectric constant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4303–4312, 2004     

Balancing kinetic and thermodynamic control: the mechanism of carbocation cyclization by squalene cyclase

Molecular dynamics simulations with a combined quantum mechanical and molecular mechanical (QM/MM) potential have been carried out to investigate the squalene-to-hopene carbocation cyclization mechanism in squalene-hopene cyclase (SHC). The present study is based on free energy simulations by constructing the free energy surface for the cyclization steps along the reaction pathway. The picture that emerges for the carbocation cyclization cascade is a delicate balance of thermodynamic and kinetic control that ultimately favors the formation of the final hopanoids carbon skeleton. A key finding is that the five- to six-membered ring expansion process is not a viable reaction pathway for either C- or D-ring formation in the cyclization reaction. The only significant intermediate is the A/B-bicyclic cyclohexyl cation (III), from which two asynchronous concerted reaction pathways lead to, respectively, the 6,6,6,5-tetracyclic carbon skeleton and the 6,6,6,6,5-pentacyclic hopanoids. Experimentally, these two products are observed to have 1% and 99% yields, respectively, in the wild-type enzyme. We conclude that the product distribution in the wild-type enzyme is dictated by kinetic control of these two reaction pathways.     

The Synthesis and Bioactivity of Dimethyl (2,3- Dihydrobenzo[b][1,4]Dioxin-6-Yl)(Aryl Amino)Methylphosphonates

Abstract

A new series of α-aminophosphonates have been synthesized by a one-pot three-component reaction of 2,3-dihydrobenzo[b][1,4]dioxine-6-carbaldehyde, various amines, and dimethyl phosphite by using nano-TiO₂ as a catalyst under solvent-free conditions at 50°C. The major advantages of the present method are high yields, short reaction times, recyclable catalyst, and solvent-free reaction conditions. Among these new structurally diversified set of α-aminophosphonates, dimethyl (2,3-dihydrobenzo[b][1,4]dioxin-6-yl)(3-nitrophenylamino) methylphosphonate and dimethyl (2,3-dihydrobenzo[b][1,4]dioxin-6-yl)(4-fluoro-3-nitro-phenyl-amino) methylphosphonate have shown higher antioxidant activity in diphenyl picryl hydrazyl (DPPH) scavenging, reducing power assay, and lipid peroxidation methods.     

Synthesis and Bioassay of Ethyl-2- (2-((Diethoxyphosphoryl) (Aryl) Methylamino)Thiazol-4-Yl)-2-(Methoxyimino)Acetates

Abstract

A simple, efficient, and environmentally benign methodology has been accomplished for the synthesis of α-aminophosphonates by one-pot three-component reaction of ethyl-2-amino-α-(methoxy-imino)-4-thiazoleacetate, aldehydes, and diethylphosphite by using Amberlyst-15 as catalyst at room temperature under solvent-free conditions. Their chemical structures were characterized by infrared (IR), NMR (¹H, ¹³C & ³¹P), mass spectral, and elemental analysis. All the title compounds were screened for radical-scavenging activity by 1,1-diphenyl-2-picrylhydrazyl (DPPH), nitic oxide (NO), and hydrogen peroxide (H₂O₂) methods.

Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental files: Additional text and figures.     

BF3·OEt2-catalyzed synthesis of 1-(tetrahydropyran-3-yl)-1,3-dihydroisobenzofuran and trans-fused hexahydropyrano[3,2-c]chromene derivatives

A novel intramolecular Prins cyclization of (E)-5-(2-(hydroxymethyl)phenyl)pent-4-en-1-ol with aldehydes has been achieved using 10 mol % BF₃·Et₂O to produce 1-(tetrahydropyran-3-yl)-1,3-dihydroisobenzofuran derivatives in good to excellent yields with high selectivity. Similar type of coupling with salicylaldehydes provides the trans-fused hexahydropyrano[3,2-c]chromene derivatives in excellent yields.