Boundary Value Problems for Ordinary Differential Equations with Deviated Arguments

We discuss differential equations with nonlinear boundary conditions. We formulate sufficient conditions under which problems with deviating arguments have quasisolutions or solutions. To obtain the results, we apply the method of monotone iterations.     

Parallel and superfast algorithms for Hankel systems of equations

Summary Utilizing kernel structure properties a unified construction of Hankel matrix inversion algorithms is presented. Three types of algorithms are obtained: 1)O(n ²) complexity Levinson type, 2)O (n) parallel complexity Schur-type, and 3)O(n log² n) complexity asymptotically fast ones. All algorithms work without additional assumption (like strong nonsingularity).     

Synthesis of calixarene-cyclodextrin coupling products

The coupling of two or four mono-6-amino β-cyclodextrin (amino-CD) units, (unprotected or permethylated hydroxyls), to diisopropoxycalix[4]arene crown-6 (CAL) was realised using the N,N′-succinyldiamide linker. The resulting molecules in two series were characterised with the help of mass and NMR spectroscopies. The yields of all coupling products were improved for permethylated sugar series compared to the hydroxylated CD series or to our previous studies. The two β-cyclodextrin (β-CD) residues coupled to disubstituted CAL were orientated from the same side of the crown ether.     

Application of gas chromatography-tandem mass spectrometry to the analysis of inhibition of dimerisation of tributylphosphate under radiolysis. Identification of isomeric tributylphosphate-alkylbenzene inhibitor coupling products

Tributylphosphate (TBP), solvent used as extractant for reprocessing spent nuclear fuel, can dimerise under radiolysis. This occurs by radical radical recombination, leading to 10 isomeric dimers (TBP-TBP). These species are complexation agents and are responsible of fission product retention in the organic phase that increases the solvent degradation. In order to limit their formation two free radical inhibitors (In), isopropyl and 1,4-diisopropylbenzenes, were used. These additives reduce by about 50% the concentration of TBP-TBP dimers but this reduction is not strictly followed by TBP regeneration as mixed coupling products from TBP and inhibitor are detected. By using GC-MS-MS and selectively deuterated compounds, the identification of these different isomers (TBP-In) has been realised. From these identifications and from the analysis of the proportion of the different isomers, the major primary TBP radical generated under radiolysis was determined.