Seiberg-Witten theory as a complex version of Abelian Higgs model

The adiabatic limit procedure associates with every solution of Abelian Higgs model in (2 + 1) dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg-Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex (2+2)-dimensional version of the (2 + 1)-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in (2+1)-dimensional case.     

Integrability of Calogero–Coulomb problems

In this short review we describe the integrability properties of the Calogero-type perturbations of one- and two-center Coulomb problems and of the Stark–Coulomb problem. We present the explicit expressions of their constants of motion and show that these systems admit partial separation of variables.     

A 9,10-anthraquinone derivative having two propenyl arms as a neutral ionophore for highly selective and sensitive membrane sensors for copper(II) ion.

New polymeric membrane (PME) and coated graphite (CGE) copper(II)-selective electrodes based on 1-hydroxy-2-(prop-2'-enyl)-4-(prop-2'-enyloxy)-9,10-anthraquinone were prepared. The electrodes reveal linear emf-pCu2+ responses over wide concentration ranges (1.0 x 10(-5)-1.0 x 10(-1) M with a slope of 27.3 mV decade-1 for PME and 8.0 x 10(-8)-5.0 x 10(-2) M with a slope of 29.1 mV decade-1 for CGE) and very low limits of detection (8.0 x 10(-6) M for PME and 5.0 x 10(-8) M for CGE). The potentiometric response is independent of the pH of the test solution in the pH range 3.0-6.0. The proposed electrodes possess very good selectivities over a wide variety of other cations, including alkali, alkaline earth, transition and heavy metal ions, the selectivity coefficients for the CGE being much improved over those for the PME. The electrodes were used as indicator electrodes in the potentiometric titration of Cu2+ and in the recovery of copper ions from wastewater.     

Synthesis of Functionalized Dihydrobenzofurans by Direct Aryl C−O Bond Formation under Mild Conditions

A method for the synthesis of dihydrobenzofurans by a direct aryl C?O bond formation is described. A mechanistic pathway for the reaction, distinct from previously described similar transformations, allows for mild reaction conditions that are expected to be compatible with functionalized substrates.     

Cyclization of dialkylpropyn‐1‐yl(allyl)(3‐isopropenylpropyn‐2‐yl)ammonium bromides and water‐base cleavage of 2,2‐dialkyl‐5‐methyl‐2,6,7,7a‐tetrahydro‐1h‐isoindolium and 2,2‐dialkyl‐5‐methylisoindolinium bromides

Dialkylpropyn‐1‐yl(or allyl)(3‐isopropenylpropyn‐2‐yl)ammonium bromides under base‐catalyzed condition instantly undergo intramolecular cyclization. The cyclization of dialkylpropyn‐1‐yl(3‐isopropenylpropyn‐2‐yl)ammonium bromides leads to the formation of 2,2‐dialkyl‐5‐methylisoindolinium salts. In case of allyl analogs, instead of the expected 2,2‐dialkyl‐6‐methyl‐3a,4‐dihydroisoindolinium salts their isomeric forms ‐ 2,2‐dialkyl‐5‐methyl‐2,6,7,7a‐tetrahydro‐1H‐isoindolium bromides are obtained. In alkaline medium they are transform into the dihydroisoindolinium salts, the cleavage of which in two directions ‐ 1,2 and 1,6 leads to the mixture of isomeric dialkyl‐1,4‐dimethyl‐ and 2,4‐dimethylbenzyl‐amines. Study of the behavior of 2,2‐dialkyl‐5‐methylisoindolinium salts under conditions of water‐base cleavage showed, that only spiro[5‐methylisoindolyn]morpholinium bromide undergoes 1,2‐elimination, forming 5‐methylisoindoline 2‐vinyl ethyl ester.     

Studies toward the synthesis of pinnatoxins: the B,C,D-dispiroketal fragment

A stereoselective synthesis of the tricyclic B,C,D-dispiroketal fragment of pinnatoxins is described. Both products of an efficient enzymatic resolution reaction are used to set the stereochemistry of C12 and C23, which have opposite configuration. The configuration of the ketal centers is established upon an optimized thermodynamically controlled spiroketalization.     

One-step Oxidative Monofluorination of Electron-Deficient Sulfoxides to Access Highly Lewis Acidic Sulfur(VI) Cations

The strongly oxidizing, powerful electrophilic fluorination reagent [FXe][OTf] is shown to effect direct oxidative monofluorination of sulfoxides. This one-step, chloride promoter-free methodology provides access to so far inaccessible, yet highly desirable strongly Lewis acidic fluorosulfoxonium cations from electron-deficient and/or sterically demanding sulfoxides that are shown to be practically unreactive towards the previously reported XeF₂/NEt₄Cl system. Experimental and density functional theory studies have been conducted to assess the Lewis acidities of the prepared sulfur(VI) cations. Preliminary results obtained with chiral sulfoxides provide early insights into the mechanism of these fluorination reactions.     

Expanding the Scope of Enantioselective FerroPHANE‐Promoted [3+2] Annulations with α,β‐Unsaturated Ketones

The planar chiral 2‐phospha[3]ferrocenophane I has been shown to be the first efficient nucleophilic organocatalyst for the enantioselective synthesis of cyclopentenylphosphonates, through [3+2] cyclizations between diethyl allenylphosphonate and α,β‐unsaturated ketones. The same catalyst has also been applied to the highly enantioselective [3+2] cyclizations of allenic esters with dibenzylideneacetone and analogous bis‐enones, leading to functionalised cyclopentenes with either monocyclic or spirocyclic structures (ee 84–95 %). It has been shown that the residual enone functions in the resulting cyclopentenes can be involved in subsequent cyclization steps to afford unprecedented C₂‐symmetric bis‐cyclopentenylketones. In order to provide insight into the behaviour of FerroPHANE I as a chiral catalyst in [3+2] cyclisations, the energetically most favoured isomers of the key phosphine‐allene adduct have been calculated by DFT methods. Factors likely to control the chiral induction process are highlighted.