Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

Organic reactions in ionic liquids: ionic liquid-accelerated facile synthesis of 3-alkyl-2,4-thiazolidinediones

The room temperature ionic liquid [bmim]PF6 is a new green solvent for the N-alkylation of 2,4-thiazolidinones. Significant rate enhancement and improved yields have been observed.

Organic reactions in ionic liquids: ionic liquid-promoted efficient synthesis of N-alkyl and N-arylphthalimides

Phthalic anhydride reacts rapidly with Aromatic and aliphatic amines in ionic liquid [Bmim][PF6] or [Bmim][BF4] at 130 °C to give N-aryl and N-alkylphthalimides in excellent yields.

Organic reactions in ionic liquids:ionic liquids ethylammonium nitrate promoted Knoevenagel condensation of aromatic aldehydes with active methylene compounds

The Knoevenagel condensation of aromatic aldehydes with active methylene compounds proceeded efficiently in a reusable ionic liquid, ethylammonium nitrate, at room temperature in the absence of any catalyst with high yields.

Organic reactions in ionic liquids: Ionic liquid-promoted three-component condensation of benzotriazole with aldehyde and alcohol

1-(alpha-Alkoxyalkyl)benzotriazoles are readily synthesized from three-component condensation of benzotriazole with aldehyde and alcohol in ionic liquid [Bmim]PF6.

Organic reactions in ionic liquids: ionic liquid-promoted efficient synthesis of disubstituted and trisubstituted thioureas derivatives

In ionic liquid [Bmim][BF4], a series of disubstituted and trisubstituted thiourea derivatives were synthesized from phenyl and butyl isothiocyanate with a variety of amine in excellent yield.

Organic reactions in ionic liquids:Ionic liquid promoted Knoevenagel condensation of aromatic aldehydes with (2-thio)barbituric acid

The Knoevenagel condensation of aromatic aldehydes with (2-thio)barbituric acid proceeded efficiently in reusable ionic liquids, EAN, BmimBF4, and BmimPF6 at room temperature in the absence of any catalyst with high yields.

Organic reactions in ionic liquids:Gewald synthesis of 2-aminothiophenes catalyzed by ethylenediammonium diacetate

Ionic liquids based on 1-butyl-3-methylimidazolium tetrafluoroborate (BmimBF4) and 1-butyl-3-methylimidazolium hexafluorophosphate (BmimPF6) were used as reusable alternatives to volatile organic solvents (VOCs) for ethylenediammonium diacetate (EDDA) catalyzed Gewald synthesis of 2-aminothiophenes. Significant rate enhancement and improvement of the yield were observed. The ionic liquids containing catalyst EDDA were recycled several times with no decreases in yields and reaction rates.

Organic reactions in ionic liquids:A new method for the synthesis of alkyl aryl sulfones by alkylation of sodium arenesulfinates with unactivated alkyl chlorides

A new method is reported for the synthesis of alkyl aryl sulfones by alkylation of sodium arenesulfinates with unactivated alkyl chlorides using ionic liquid based on 1-butyl-3-methylimidazolium tetrafluoroborate (BmimBF 4) mixed with water (2:1) as reaction media. The ionic liquid can be reused and the procedure gives the sulfones in moderate yields.

Organic reactions in ionic liquids:A simple and highly regioselective N-substitution of pyrrole

In ionic liquids [Bmim][PF6] or [Bmim][BF4], pyrrole replaced the halogen atom of an alkyl halide to give the corresponding N-substituted pyrrole in excellent yield. Benzenesulfonyl chloride, p-methylbenzenesulfonyl chloride and benzoyl chloride reacted similarly with pyrroles to afford the N-substituted pyrroles in quantitative yield. Michael addition reaction of pyrrole with electrophilic olefins was completed in a highly regioselective manner to afford the N-alkylpyrroles.

Organic reactions in ionic liquids: ionic liquid-promoted efficient synthesis of N-alkyl and N-arylimides

In the ionic liquids [Bmim][PF6] or [Bmim][BF4], a series of succinimide, maleimide and phthalimide derivatives were synthesized from corresponding anhydrides with a variety of primary amines in excellent yield.

Organic reactions in ionic liquids: an efficient method for the N-alkylation of benzotriazole

The N-alkylation of benzotriazole with alkyl halides proceeds efficiently in the presence of potassium hydroxide in ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim][BF4]).

Organic reactions in ionic liquids:An efficient method for selective S-alkylation of 2-mercaptobenzothia(xa)zole with alkyl halides

Ionic liquids based on 1-butyl-3-methylimidazolium hexafluorophosphate (BmimPF6) and 1-butyl-3-methylimidazolium tetrafluoroborate (BmimBF4) are used as reusable reaction medium in the selective S-alkylation of 2-mercaptobenzothia(xa)zole with alkyl halides in the presence of potassium carbonate. This procedure is convenient, efficient, and generally gives rise to the S-alkylated product exclusively.

Organic reactions in ionic liquids: N-alkylation of cyclic imides with alkyl halides promoted by potassium fluoride

An ionic liquid based on 1-butyl-3-methylimidazolium hexafluorophosphate is used as an efficient reusable reaction medium in the N-alkylation of cyclic imides with alkyl halides promoted by fluoride ion.