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.     

Generation of Ethyl Metathiophosphate by Thermal Fragmentation of O-Ethyl N-Substituted Phosphoramidothioates

O-Ethyl N-1-adamantylphosphoramidothioate was synthesized and found to fragment on heating in inert solvents to form the pyrophosphate AdNHP(S)(OEt)OP(S)(OEt)OH. The proposed mechanism involves an elimination of the amine portion with release of ethyl metathiophosphate (EtOP(S)O), as was confirmed in previous work for the comparable structure with oxygen. This transient compound then phosphorylates the starting phosphoramidothioate. O-Ethyl N,N-diethylphosphoramidothioate was also synthesized, and while it gave a similar pyro compound on heating, the reaction mixture was more complex. Both phosphoramidothioates, however, served effectively as thiophosphorylating agents toward alcohols, a silanol, and the silanol groups on the surface of silica gel. Exploratory experiments showed that these phosphoramidothioates also could thiophosphorylate the OH group of a monoester of phosphoric acid, as well as that of phosphinic acids, forming anhydrides with the partial structure     

An investigation of the reliability of the Galerkin-Petrov method

It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 2¹ S and 3¹ S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.     

The intermediacy of metathiophosphonate PhPSO in the reaction of N-tert-butyl-P-phenylphosphonamidothioic acid with alcohols

Kinetic studies of the reaction of N-tert-butyl-P-phenylphosphonamidothioic acid (1) with alcohols were carried out in CH2Cl2 by means of 31P NMR spectrometry. The reaction is of the first order with respect to thio acid 1. The first-order rate constant at 30 degrees C increases with increasing methanol concentration below 0.25 M, but otherwise the rate constants are either independent of alcohol concentration (MeOH above 0.25 M, BuOH) or decrease with increasing alcohol concentration (i-PrOH, t-BuOH). The effect of alcohols on the order of the reaction and parameters of activation, as well as results of competition experiments, lead us to the conclusion that reaction of 1 with alcohols occurs by an elimination-addition mechanism involving the association of the thio acid 1 and the alcohol and then formation in the rate-determining step of an encounter complex 2' ' involving metathiophosphonate 4, amine, and alcohol. Metathiophosphonate 4 reacts preferentially with the alcohol as the encounter complex (primary alcohols) or after diffusion apart as a "free" intermediate (hindered alcohols).