Vanishing viscosity in the plane for vorticity in borderline spaces of Besov type

The existence and uniqueness of solutions to the Euler equations for initial vorticity in BΓ∩Lp₀∩Lp₁ was proved by Misha Vishik, where BΓ is a borderline Besov space parameterized by the function Γ and 1<p₀<2<p₁. Vishik established short time existence and uniqueness when Γ(n)=O(logn) and global existence and uniqueness when . For initial vorticity in BΓ∩L², we establish the vanishing viscosity limit in L²(R²) of solutions of the Navier-Stokes equations to a solution of the Euler equations in the plane, convergence being uniform over short time when Γ(n)=O(logn) and uniform over any finite time when Γ(n)=O(logκn), 0?κ<1, and we give a bound on the rate of convergence. This allows us to extend the class of initial vorticities for which both global existence and uniqueness of solutions to the Euler equations can be established to include BΓ∩L² when Γ(n)=O(logκn) for 0<κ<1.     

Results of the search for strange quark matter and Q-balls with the SLIM experiment

The SLIM experiment at the Chacaltaya high altitude laboratory was sensitive to nuclearites and Q-balls which could be present in the cosmic radiation as possible Dark Matter components. It was sensitive also to strangelets, i.e. small lumps of Strange Quark Matter predicted at such altitudes by various phenomenological models. The analysis of 427 m² of Nuclear Track Detectors exposed for 4.22 years showed no candidate event. New upper limits on the flux of downgoing nuclearites and Q-balls at the 90% C.L. were established. The null result also restricts models for strangelets propagation through the Earth atmosphere.     

Diastereoselective and enantioselective photoredox pinacol coupling promoted by titanium complexes with a red-absorbing organic dye

The pinacol coupling reaction, a reductive coupling of carbonyl compounds that proceeds through the formation of ketyl radicals in the presence of an electron donor, affords the corresponding 1,2-diols in one single step. The photoredox version of this transformation has been accomplished using different organic dyes or photoactive metal complexes in the presence of sacrificial donors such as tertiary amines or Hantzsch''s ester. Normally, the homo-coupling of such reactive ketyl radicals is neither diastereo- nor enantio-selective. Herein, we report a highly diastereoselective pinacol coupling reaction of aromatic aldehydes promoted by 5 mol% of the non-toxic, inexpensive and available Cp₂TiCl₂ complex. The key feature that allows the complete control of diastereoselectivity is the employment of a red-absorbing organic dye in the presence of a redox-active titanium complex. Taking advantage of the well-tailored photoredox potential of this organic dye, the selective reduction of Ti(iv) to Ti(iii) is achieved. These conditions enable the formation of the d,l (syn) diastereoisomer as the favored product of the pinacol coupling (d.r. > 20 : 1 in most of the cases). Moreover, employing a simply prepared chiral SalenTi complex, the new photoredox reaction gave a complete diastereoselection for the d,l diastereoisomer, and high enantiocontrol (up to 92% of enantiomeric excess).

A metallaphotoredox, diastereoselective and enantioselective pinacol coupling reaction promoted by titanium complexes with the use of a red-absorbing organic dye was developed.     

Dipeptide-catalyzed asymmetric aldol condensation of acetone with (N-alkylated) isatins

[reaction: see text] The aldol condensation of acetone with several isatins is described. The desired compound was obtained in quantitative yield and with good enantioselectivities up to 77%. The best results were obtained with 10 mol % H-D-Pro-L-beta3-hPhg-OBn as a catalyst, resulting in the preferential formation of the (R)-enantiomer. The absolute configuration of the newly formed chiral center has been assigned by an X-ray diffraction study and CD spectra analysis of the molecules.     

Sequential one-pot InBr(3)-catalyzed 1,4- then 1,2-nucleophilic addition to enones

Low sensitivity toward traces of moisture and high tolerance of different functional groups make indium tribromide suitable for carrying out multistep synthetic sequences. In particular, we have realized a 1,4-conjugated addition of indoles/thiols to alpha,beta-unsaturated ketones mediated by a catalytic amount (10 mol %) of InBr(3) obtaining the desired beta-substituted ketones in good yields. The Lewis acidity of indium salts was not affected by coordinating and acid nucleophiles; therefore, the subsequent catalytic 1,2-addition of Me(3)SiCN to carbonyl compounds can be performed in one pot. With the optimized atom-efficient protocol, several polyfunctionalized alpha-silyloxy cyanohydrins were synthesized in good to excellent yields (up to 97%) and a notable level of simple 1,3-diastereoselection (up to 84:16) was recorded in the case of 2-cyclohexen-1-one 2c.     

Imidazolyl derivatives of the thiochroman ring

The synthesis of 2-(1H-imidazol-1-yl)-4H-1-benzothiopyran- 4 -ones 3 from 3-bromo-4H-1-benzothiopyran-4-ones 1 and imidazole is described. The reaction of 1 with secondary amines gives the corresponding 3 -amino-thiochromones 11. Compounds 3 can be oxidized to the sulfones 4 from which the thiochromanols 5 and thiochromene 7 can be easily obtained. 3-Bromo-2,3-dihydro-6-methyl-4H-1-benzothiopyran-4-one 12 and imidazole led by dehydrohalogenation to thiochromone, while the ketal 13 rearranged to benzo[b]thiophene 16.