Trigonometric wavelets for Hermite interpolation

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.

     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

Fractional Power Series and Pairings on Drinfeld Modules

Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing

which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.

     

On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Evaluation of dead time calculation in liquid chromatography using a linearization procedure for homologous series

A mathematical method for the calculation of the dead time (t_m) in HPLC was evaluated using a computer simulation approach, in which artificial perturbations were introduced to Simulated homolog retention times. The calculation was based on a modified and extended Grobler and Bálisz (GB) method. Investigated wav how the precision of the calculated t_M is affected by: statistical fluctuations in retention times and which, and how many homolog retention times are used. Based on these simulations a two-step procedure for the t_M calculation is proposed: In the first step the linearity of log t_{R, n} vs carbon number n is checked using as many homolog retention times as possible. The slope value b^o of the first linear regression in the GB method is used for the selection of homolog retention times in the final t_M calculation. In the second step the optimal selection of homologs is made and the final t_M calculation is carried out. Guidelines for homolog selection are given.     

Hole doping and superconductivity characteristics of the s=1, 2 and 3 members of the (Cu,Mo)-12s2 homologous series of layered copper oxides

Superconductivity characteristics have been systematically evaluated for a two-CuO₂-plane copper oxide system, (Cu,Mo)-12s2, upon increasing the number of fluorite-structured layers, s, between the two CuO₂ planes. Essentially single-phase samples of (Cu_0.75Mo_0.25)Sr₂YCu₂O_7+δ (s=1), (Cu_0.75Mo_0.25)Sr₂(Ce_0.45Y_0.55)₂Cu₂O_9+δ (s=2) and (Cu_0.75Mo_0.25)Sr₂(Ce_0.67Y_0.33)₃Cu₂O_11+δ (s=3) were synthesized through a conventional solid-state route in air. To make the samples superconductive an additional high-pressure oxygenation (HPO) treatment was required. Such treatment (carried out at 5 GPa and 500 °C in the presence of 75 mol% Ag₂O₂ as an oxygen source to maximize the T_c) compressed the crystal lattice for the three members of the (Cu_0.75Mo_0.25)-12s2 series equally, i.e., by 0.01 Å for the a parameter and by 0.07 Å for the c parameter per formula unit. From both Cu L-edge and O K-edge XANES spectra the s=1 sample was found to possess the highest overall hole-doping level among the HPO samples. Accordingly it exhibited the best superconductivity characteristics. With increasing s, both the T_c (s=1: 88 K, s=2: 61 K, s=3: 53 K) and H_irr values got depressed, being well explained by the trend of decreasing CuO₂-plane hole concentration with increasing s as revealed from O K-edge XANES spectra for the same samples. Hence, the present results do not suggest any significant (negative) impact on the superconductivity characteristics from the gradually thickened fluorite-structured block itself.     

LC and LC-MS Separation of Peptides on Macrocyclic Glycopeptide Stationary Phases: Diastereomeric Series and Large Peptides

Previous work on the LC separation of peptides had shown that macrocyclic glycopeptide stationary phases to be selective for peptides of five to thirteen amino acids in length. In this work, the selectivity of the teicoplanin stationary phase is compared to that of a C18 stationary phase for seven diastereomeric enkephalin peptides. The teicoplanin stationary phase separated all seven diastereomeric enkephalin peptides in a single chromatographic run. The insertion of d-amino acids into the primary enkephalin sequence produced areas of hydrophobicity that influenced retention order on the C18 stationary phase. However, analogous trends are not observed on the teicoplanin stationary phase, which is more polar and structurally diverse. Optimization of the mobile phase and the use of a step-gradient for the enkephalin separation on the teicoplanin stationary phase is discussed. Also, the selectivity of macrocyclic glycopeptide stationary phases for peptides of 14, 28, 30, and 36 amino acids also is investigated and compared to separation on a C18 stationary phase. A method for eluting peptides with multiple basic amino acids, which tend to be strongly retained on the macrocyclic glycopeptide stationary phases, is presented.