Notes on the non-autonomous Lyness equation

We prove that the solutions of the non-autonomous Lyness equation x_n+1=(x_n+b_n)/x_n−1, b_n>0, x₀>0, x₁>0, are bounded away from zero and infinity if the sequence b_n is monotonic. We also give an example to show that the solutions need not be bounded even when the sequence b_n attains only two values.     

Particle multiplicities in the fission-like reactions of 340 MeV Si on Th

Pre-scission and post-scission multiplicities of neutrons and alpha particles have been simultaneously measured for the fission-like reactions of 340 MeV ²⁸Si on ²³²Th. Dynamical model calculations using HICOL code predict that about 90% of the observed events are of quasi-fission type while the remaining 10% are from compound nucleus fission decay. Moving source fits were carried out to the observed neutron and alpha particle spectra, measured at different angles with respect to the fragment directions. The pre-scission and post-scission neutron multiplicities are deduced to be 8.7±2.0 and 9.4±2.0, respectively. The corresponding multiplicity values for alpha particles are found to be 0.22±0.08 and 0.1±0.03. From the measured post-scission neutron multiplicity, it is inferred that about 65±20 MeV of the initial excitation energy remains at scission. This may be compared to the value of 85±30 MeV estimated from PACE2 statistical model calculations, adjusted to reproduce the measured pre-scission neutron multiplicity. From a comparison of the Statistical Model predictions with the measured pre-scission neutron multiplicity, the fission delay is estimated to be of 5⁺⁷₋₃×10⁻²⁰ s which overlaps with the average duration of fission-like process from the contact to the scission point (2×10⁻²⁰ s) as determined from HICOL-based dynamical calculations. For the delay time deduced as above, the pre-scission alpha particle multiplicity calculated by the PACE2 code is about a factor two larger than the experimental one, demonstrating the difficulties in modelling the alpha particle emission from highly elongated shapes that characterize the fissioning system from the contact point to scission.     

Enantiomeric separation of amphetamine,methamphetamine and ring substituted amphetamines by means of a β-cyclodextrin-chiral stationary phase

Summary The enantioseparation of amphetamine, methamphetamine and various ring-substituted amphetamines by use of a chiral stationary phase carrying immobilized native -cyclodextrin (-CyD) selectors is reported. The system is evaluated for resolving the specified compounds directly without any derivatization and after derivatization with phenyl isothiocyanate (PITC), naphthyl isothiocyanate (NITC) and 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC). This direct enantioseparation is compared with the features of indirect separation of diasteromeric derivatives after reaction with the optically pure Marfey's reagent employing a simple non-chiral alkyl-silica (RP-8) column. A selection of those methods best suited for each single amphetamine is given.Seventeen different samples of amphetamine, confiscated by the Swedisch police, were analyzed with respect to their enantiomeric composition. Within this set of samples synthesized by the same method no significant deviation from a racemic ratio could be observed.     

Synthesis of protected derivatives of O-phosphotyrosine incorporation in a heptapeptide

The solid phase synthesis of the phosphopeptide Leu-Arg-Arg-Ala-Tyr(P)-Leu-Gly is reported via the stepwise incorporation of the protected phosphoamino acid Nα -tert-butyloxycarbonyl-O-dimethyl-phosphono-L-tyrosine.     

X-ray and mössbauer studies of tricyclohexyltin(IV) halides. The crystal structures of (cyclo-C6H11)3SnX (X = F,Br and I)

The structures of tricyclohexyltin fluoride (I), bromide (II) and iodide (III) have been determined by X-ray analysis. Compound I crystallizes in the space group P2₁/m with a = 10.422(6), b = 17.238(9), c = 5.769(3) Å, β = 104.6(1)° and Z = 2. Compounds II and III crystallize in the space group Pcmn with a = 10.427(6), b = 16.914(9), c = 11.366(6) Å, Z = 4; and a = 10.400(6), b = 16.900(10), c = 11.400(4) Å, Z = 4, respectively. All three structures consist of discrete tetrahedral (cyclo-C₆H₁₁)₃SnX units.The temperature dependence of the Mössbauer resonance areas has been examined in order to obtain information about the relationship between chemical structure and lattice dynamics.     

Long-range dispersion coefficients for like centrosymmetric linear molecules and an application to H2-H2

The real spherical tensor theory of long-range intermolecular coefficients developed in previous papers is applied to derive explicit formulae for the first three dispersion coefficients for like centrosymmetric linear molecules. The expansion of angle-dependent coefficients in associated Legendre polynomials allows one to identify the isotropic and anisotropic components of the dispersion interaction in terms of London dispersion constants, the treatment of higher coefficients being simplified by the coupling of the elementary (l, l′)-polarizations to resultant angular momenta L_A and L_B onto each molecule. The contributions from all coupling schemes are given explicitly for C₆, C₈, C₁₀, and numerical results are presented for H₂-H₂ using two-term reduced spectra values from the Kaiserlautern group.     

On the supposed equilibrium Ph6Pb2Ph4Pb+Ph2Pb in solution

The reaction between pentadeuteriophenyllithium and hexaphenyldilead combined with new measurements of isotopic exchange between Ph₆Pb₂ (labelled with RaD) and Ph₄Pb, have shown that the dilead compound is undissociated in solution. These results cast doubt upon the previously reported equilibrium: Ph₆Pb₂Ph₄Pb+Ph₂Pb.     

Conformational and photophysical studies on porphyrin-containing donor-bridge-acceptor compounds. Charge separation in micellar nanoreactors

Photophysical studies with semi-rigid, 1, and flexible, 2, donor-bridge-acceptor (D-b-A2+) molecules with D a porphyrin and A2+ a methyl viologen moiety, were performed in neat polar solvents as well as included in surfactant (DTAB) aqueous and in reverse AOT/n-alkane micelles. The micelles acted as nanoreactors for the photoinduced electron transfer reaction upon laser excitation. In spite of the longer lifetime of the charge separated (CS) state in the semi-rigid tetrad 1(ca. 200 ns vs. ca. 100 ns for the flexible dyad 2), the CS formation quantum yield, for example in acetonitrile, was lower for the former (phi(CS) = 0.13) than for the latter (0.58). Comparison of the time-resolved fluorescence data in neat solvent and in the micelles yielded the phi(CS) values in the dilute micellar solutions. Application of laser-induced optoacoustic spectroscopy at various temperatures to 1 dissolved in a polar organic solvent (benzonitrile, BZN) included in aqueous DTAB nanoreactors afforded structural volume changes for the production in hundreds of ps of the CS state upon excitation of a polar molecule. The contraction during CS formation upon excitation of the collapsed conformer in BZN is attributed to the entering of solvent into the open molecular cavity. The opening upon formation of the CS state due to photoinduced electron transfer in the 1 collapsed conformation arises from the repulsion of the two positively charged ends in this state, as previously calculated. Inclusion of 1 in reverse AOT micelles in various n-alkanes also led to a contraction upon excitation, but the data had much more error due to the limited range of variability of the ratio of thermoelastic parameters. The data obtained with the more flexible "supermolecule" 2 showed the predicted large conformation flexibility of these molecules.     

Synthesis of some 2-(heteroarylamino)benzimidazoles and their cyclization with phosgene

2-(Benzimidazol-2-ylamino)pyridine (4a) , 2-(benzimidazol-2-ylamino)pyrazine (4b) , and 2-(benzimidazol-2-ylamino)thiazole (4c) underwent a ring-closure reaction on treatment with phosgene affording 6H-pyrimido-[1′,2′:5,4][1,3,5]triazino[1,2-a]benzimidazol-6-one (1a) , 6H-pyrazino[1′,2′:5,4][1,3,5]triazino[1,2-a]benzimidazol-6-one (1b) , and 5H-thiazolo[2′,3′:4,5][1,3,5]triazino[1,2-a]benzimidazol-5-one (1c) respectively. The structure of these hitherto unknown heterocyclic systems was confirmed by their ir and mass spectra.