A convergence and stability study of the iterated Lubkin transformation and the -algorithm

In this paper we analyze the convergence and stability of the iterated Lubkin transformation and the -algorithm as these are being applied to sequences whose members behave like as , where and are complex scalars and is a nonnegative integer. We study the three different cases in which (i) , , and (logarithmic sequences), (ii) and (linear sequences), and (iii) (factorial sequences). We show that both methods accelerate the convergence of all three types of sequences. We show also that both methods are stable on linear and factorial sequences, and they are unstable on logarithmic sequences. On the basis of this analysis we propose ways of improving accuracy and stability in problematic cases. Finally, we provide a comparison of these results with analogous results corresponding to the Levin -transformation.

     

Barrenazine A and B; two new cytotoxic alkaloids from an unidentified tunicate

[structure: see text] Two novel compounds, barrenazine A (1) and B (2), were isolated from an unidentified tunicate collected at Barren Islands, Madagascar. The two new compounds are of an unprecedented heterocyclic skeleton, namely 1,3,4,6,8,9-hexahydrodipyridino[3,4-b:3',4'-e]pyrazine. The structures of the two alkaloids were elucidated by interpretation of MS, COSY, HMQC, HMBC, NOESY, and (15)N-HMBC data. Barrenazine A exhibits mild cytotoxicity against LOVO-DOX colon carcinoma (with a GI(50) value of 0.9 g/mL)     

Reactions of acetylenes with transition metals : VII steric effects in the oligomerization of diarylacetylenes

The synthesis of ortho-substituted diphenylacetylenes and their behaviour toward dichlorobis(benzonitrile)palladium(II) are described. The influence of steric factors on the oligomerization is discussed.     

The role of water molecules in a resorcinarene capsule as probed by NMR diffusion measurements

[structure: see text] NMR diffusion measurements were used to probe the role of water molecules in a resorcinarene capsule in a CDCl(3) solution. It was found that the water/resorcinarene ratio affects both the chemical shift and the diffusion coefficient of the water molecules. From the NMR diffusion measurements we could conclude that the major species in the chloroform solution is the hexamer having eight water molecules that are in fast exchange, on the NMR time scale, with the bulk water.     

Excitation wavelength dependence of the proton-transfer reaction of the green fluorescent protein

Picosecond time-correlated single-photon counting was used to measure the proton-transfer rate of green fluorescent protein (GFP) excited by several wavelengths between 266 and 405 nm. When samples of GFP in water and D2O are excited at short wavelengths, lambda(ex) < 295 nm, the fluorescence properties are largely modified with respect to excitation at a wavelength around 400 nm, the peak of the absorption band of the S0 --> S1 transition of the ROH form of the chromophore. The shorter the excitation wavelength, the longer the decay time of the ROH emission band at 450 nm and the longer the rise time of the RO- emission band at 512 nm. The proton transfer is slower by an order of magnitude and about a factor of 3 when GFP in water and D2O are excited by 266 nm, respectively.     

Ion‐exchange resins. III. Functionalization–morphology correlations in the synthesis of some macroporous,strong basic anion exchangers and uranium‐sorption properties evaluation

The synthesis and characterization of a series of macroporous, strong basic anion exchangers (SBAEs), with an average pore radius higher than 50 nm, and the evaluation of their sorption properties for uranyl chlorocomplexes from HCl solutions are reported. Finely divided macroporous styrene–divinylbenzene (S–DVB) copolymers with a narrow distribution of beads sizes, diameters within the range of 90–200 μm, were prepared for this purpose with 2‐ethyl‐1‐hexanol as a porogen, at a high dilution of monomers (D ≥ 0.55 mL/mL). Chloromethyl groups were introduced with (CH₂O)_n/Me₃SiCl as a chloromethylation agent in the presence of a Lewis acid as a catalyst (TiCl₄, SnCl₄, and FeCl₃) in CHCl₃ as a reaction medium. SnCl₄ and FeCl₃ gave comparable chloromethylation degrees in the same reaction conditions. TiCl₄ was not efficient as a catalyst in the chloromethylation with this reagent. Diethyl‐2‐hydroxyethylamine was used as a tertiary amine to prepare SBAEs. Structural and morphological characteristics were determined after every functionalization step of the macroporous network. Both the chloromethylation, in the presence of FeCl₃ as a catalyst, and the amination reactions determined a significant decrease of the pore volume, in the whole range of the nominal crosslinking degree, comparative with the starting copolymer. The specific surface area and the average pore radius varied in a different way as a function of the nominal crosslinking degree. Thus, the specific surface area increased and the average pore radius decreased after chloromethylation and amination for copolymers with a DVB content lower than 10 wt %. Small decreases of the specific surface area and the average pore radius were observed after chloromethylation and amination reactions for copolymers with a DVB content higher than 10 wt %. SBAEs were also characterized by thermogravimetric analysis and sorption capacity for uranyl chlorocomplexes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2451–2461, 2004     

Euler–Maclaurin expansions for integrals with endpoint singularities: a new perspective

Summary. In this note, we provide a new perspective on Euler–Maclaurin expansions of (offset) trapezoidal rule approximations of the finite-range integrals I[f]=^b_af(x),dx, where fC(a,b) but can have general algebraic-logarithmic singularities at one or both endpoints. These integrals may exist either as ordinary integrals or as Hadamard finite part integrals. We assume that f(x) has asymptotic expansions of the general forms where P_s(y) and Q_s(y) are some polynomials in y. Here the _s and _s are complex in general and different from –1,–2,... . The results we obtain in this work generalize, and include as special cases, those pertaining to the known special cases in which f(x)=(x–a)[log(x–a)]^pg_a(x)=(b–x)[log(b–x)]^qg_b(x), where p and q are nonnegative integers and g_aC[a,b) and g_bC(a,b]. In addition, they have the pleasant feature that they are expressed in very simple terms based only on the asymptotic expansions of f(x) as xa+ and xb–. With h=(b–a)/n, where n is a positive integer, and with one of these results reads, as h0, where (z) is the Riemann Zeta function.Mathematics Subject Classification (2000): 30E15, 40A25, 41A60, 65B15, 65D30Revised version received March 19, 2004     

Complexation in pseudorotaxanes based on alpha-cyclodextrin and different alpha,omega-diaminoalkanes by NMR diffusion measurements

The interactions of 1,4-diaminobutane (1), 1,6-diaminohexane (2), 1,8-diaminooctane (3), 1,10-diaminodecane (4), and 1,12-diaminododecane (5) with alpha-cyclodextrin (alpha-CD) were studied in aqueous solutions by NMR diffusion measurements before and after protonation. The correlation between the association constant and the length of the alkyl chain of the diamine unit was studied. The assumption that protonation on the amino groups can be used as a stopper and, as a result, to convert the pseudorotaxanes into rotaxanes was tested. In addition, other factors that can affect the pseudorotaxane stability, such as the effects of temperature, were tested. On the basis of these measurements, the following conclusions could be reached: (1) The association constant increases with the increase in the alkyl chain length. (2) For the salts (2b-5b), both in neutral and in acidic solutions, the binding constants increase as the number of CH(2) units increases. (3) The association constants of the complexes of the diaminoalkane salts and alpha-CD are lower than those of the corresponding neutral diaminoalkanes. (4) This difference between the binding constants of the diaminoalkanes and their respective salts decreases as the chain length increases. (5) By examining the effects of temperature on the (1)H NMR spectra, it was found that after addition of DCl the energy barrier for the threading-dethreading process of the salt of 5a is larger than that for the salt of 4a.