Caratheodory interpolation kernels

Kernels over the unit disk for which a version of Carathéodory interpolation is true are characterized in a simple computationally verifiable manner.     

Orientation-reversing involutions on handlebodies

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

     

Accurate orbital amplitudes at nuclei frog gaussian basis sets

A simple extrapolation procedure combining wavefunctions obtained from gaussian basis sets with exact solutions of the nuclear cusp equations is proposed for computing orbital amplitudes at nuclei. Comparison with exact results for atoms and diatomic molecules indicates that the procedure is capable of giving Hartree—Fock amplitudes with errors of at most 10^?2 for the low amplitude outer orbitals and errors of less than 10^?3 for the important inner orbitals. The resulting errors in the total densities are around 10^?2. These accuracies are comparable with those obtained with energy-optimized Slater basis sets.     

Nevanlinna–Pick interpolation on distinguished varieties in the bidisk

This article treats Nevanlinna–Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.     

The projective dimension of three cubics is at most 5

Let R be a polynomial ring over a field and I an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension $\mathrm{pd}(R/I)$ of $R/I$ is at most 36, although the example with largest projective dimension he constructed has $\mathrm{pd}(R/I)=5$. Based on computational evidence, it had been conjectured that $\mathrm{pd}(R/I)\le 5$. In the present paper we prove this conjectured sharp bound.     

An Improved Measurement of Isotopic Ratios by High Resolution Mass Spectrometry

The study of protein kinetics requires an accurate measurement of isotopic ratios of peptides. Although Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometers yield accurate mass measurements of analytes, the isotopologue ratios are consistently lower than predicted. Recently, we demonstrated that the magnitude of the spectral error in the FT-ICR mass spectrometer is proportional to the scan duration of ions. Here, we present a novel isotopic ratio extrapolation (IRE) method for obtaining accurate isotopic ratio measurements. Accuracy is achieved by performing scans with different duration and extrapolation of the data to the initial moment of the ion rotation; IRE minimizes the absolute isotopic ratio error to ≤1 %. We demonstrate the application of IRE in protein turnover studies using ²H₂O-metabolic labeling. Overall, this technique allows accurate measurements of the isotopic ratios of proteolytic peptides, a critical step for enabling routine studies of proteome dynamics.