Synthesis and new rearrangements of 4-isoxazolin-4,5-dicarboxylic acid derivatives

Acyclic nitrones react with dimethyl acetylenedicarboxylate (DMAD) to give stable isoxazolines, from which the ones that contain electron-donating aromatic rings at the C3 position (R¹) were shown to undergo unprecedented fragmentation at room temperature, giving the R¹-aldehyde and inseparable product mixtures, probably due to the formation of highly reactive species such as iminocarbenes. Attempts to convert the isoxazolines to the corresponding stable azomethine ylides, by refluxing in toluene, again led to the same product mixtures as above (e.g., the room temperature decomposition). Isoxazolines when reacted with methoxide at room temperature afforded highly functionalised diastereomeric mixtures. Also, isoxazolines, when reacted with propylamine, gave the corresponding amides regioselectively, all of which were more stable than the parent isoxazolines.     

Synthesis of stable azomethine ylides by the rearrangement of 1,3-dipolar cycloadducts of 3,4-dihydroisoquinoline-2-oxides with DMAD

1-Aryl-6,7-dimethoxy-1,2,3,4-tetrahydroisoquinolines were prepared according to a one-pot procedure involving the reaction of 2-(3,4-dimethoxyphenyl)-ethylamine with aromatic aldehydes in TFA at reflux. The tetrahydroisoquinolines were treated with H₂O₂-WO₄²⁻ in methanol at room temperature to give the corresponding 3,4-dihydroisoquinoline-2-oxides. Treatment of these cyclic nitrones with DMAD in toluene at room temperature gave the corresponding isoxazolo[3,2-a]isoquinolines. These compounds were heated in toluene at reflux to give the corresponding ylides in high yields (Method A). The effect of the substituents on the rate of the rearrangement of such compounds prompted us to discuss a new mechanism involving consecutive C-C bond heterolysis and 1,3-sigmatropic shift. A one-pot reaction involving the treatment of the nitrones with equimolar amounts of DMAD in refluxing toluene also gave the ylides (Method B). The structures of the prepared compounds were elucidated by spectral means and elemental analyses.     

Substituent control in the diastereoselectivity of dipolar cycloadditions of nitrones and their Zn(II) complexes with N-arylmaleimides

The π-π stacking interactions between maleimide's and nitrone's aromatic rings during the 1,3-dipolar cycloaddition were assumed to control the exo-endo selectivity of the reaction. The exo-endo ratios change during the reactions until they reach a constant value, which depends on the substituent. Electron-withdrawing groups favour the exo adduct while electron-donating groups favour the endo adduct. The nitrone ZnBr₂ complexes react much more slowly than the free nitrone and the cycloaddition is exo selective in all cases independent of the substituents on the maleimide's aromatic ring. Thermal retrocycloaddition of the cycloadducts produce the corresponding nitrones. The ring opening in the presence of secondary amines did not induce imine formation. endo Adducts were shown for the first time to be the stable paramagnetic compounds.     

Beckmann Fragmentation of Diphenylcarbamoylated N-Aryldiphenacylamine Dioximes. New Method for the Synthesis of Imidazooxadiazolones

N-Aryl-N,N-diphenacylamine dioximes were prepared by the reaction of corresponding arylamines with α-bromoacetophenone oxime in ethanol-water at room temperature. These compounds reacted with aryl isocyanates in acetonitrile to give imidazooxadiazolones 9. The probable mechanism of the reaction is discussed.     

Thermal rearrangements of tetrahydroimidazo[1,5-b]isoxazole-2,3-dicarboxylates. Synthesis of 3H-imidazol-1-ium ylides and their silver derivatives

Isoxazolines 2 from the cycloaddition of imidazoline 3-oxides 1 with DMAD undergo rearrangement to 3,4-dihydro-2H-imidazol-1-ium-1-(1,2-bis-methoxycarbonyl-2-oxo-ethanides) 3, which spontaneously undergo elimination to give 3H-imidazol-1-ium-1-(1,2-bis-methoxycarbonyl-2-oxo-ethanides) 5 or 1H-imidazoles 6 when heated in toluene at reflux. The presence of the aromatic ring at C-6 decelerated the conversion and enhanced the yield of 5. Solvents more polar than toluene (e.g., DMSO) provided quantitative conversion of 2 into 6 in mild conditions, while in less polar solvents such as CCl₄, the reaction rate was lowered and the yield of 5 enhanced. C-2 unsubstituted ylides 5 were treated with Ag₂O or AgNO₃ in the presence of Et₃N at room temperature to give C-2 metallated derivatives 9 in excellent yields.     

Efficient algorithms for robust and stable principal component pursuit problems

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data ranking. It has been shown that under certain conditions, the solution to the NP-hard RPCA problem can be obtained by solving a convex optimization problem, namely the robust principal component pursuit (RPCP). Moreover, if the observed data matrix has also been corrupted by a dense noise matrix in addition to gross sparse error, then the stable principal component pursuit (SPCP) problem is solved to recover the low-rank matrix. In this paper, we develop efficient algorithms with provable iteration complexity bounds for solving RPCP and SPCP. Numerical results on problems with millions of variables and constraints such as foreground extraction from surveillance video, shadow and specularity removal from face images and video denoising from heavily corrupted data show that our algorithms are competitive to current state-of-the-art solvers for RPCP and SPCP in terms of accuracy and speed.     

An efficient catalytic method for fulvene synthesis

The effects of the nature and amount of base, substrate structure, amount of added water and solvent on the condensation of carbonyl compounds with cyclopentadiene in the presence of secondary amines were investigated. Based on these studies, a new efficient and green synthesis of fulvenes was developed.     

Optimal iterative perturbation technique for solving Jeffery--Hamel flow with high magnetic field and nanoparticle

In this research paper, a different semi-analytical analysis of modified magnetohydrodynamic Jeffery--Hamel flow is conducted via the newly developed technique. We use the optimal iterative perturbation method with multiple parameters to see the effects of the magnetic field and nanoparticle on the Jeffery--Hamel flow. Comparing our new approximate solutions with some earlier works proved the excellent accuracy of the newly proposed technique. Convergence analysis of the proposed method is also discussed and error estimation is given to anticipate the accuracy of higher-order approximate solutions.     

Inequalities for the gamma function

Some inequalities for the gamma function are given. These results refine the classical Stirling approximation and its many recent improvements. Received: 2 May 2008, Revised: 2 September 2008     

Inequalities for the double gamma function

We establish various new upper and lower bounds in terms of the classical gamma and digamma functions for the double gamma function (or Barnes G-function).