A critical investigation of the effects of the radio frequency potential on the trapping of externally injected ions in ion trap mass spectrometry

The sensitivity of all ion trap mass spectrometry (ITMS) methods is dependent on the trapping efficiency of the instrument. For ITMS instruments utilizing external ion sources, such as laser desorption, trapping efficiency is known to depend on the phase and amplitude of the radio frequency (RF) potential applied to the ring electrode at the time of ion introduction. It is remarkable that, in a considerable body of literature, no consensus exists regarding the effects of these parameters on the efficacy of trapping externally generated ions. In this paper, a summary of the literature is presented in order to highlight significant discrepancies. New laser desorption ion trap mass spectrometry (LD-ITMS) data are also presented, from which conclusions are drawn in our effort to clarify some of the confusion. Copyright 1999 John Wiley & Sons, Ltd.     

Distribution of irreducible polynomials of small degrees over finite fields

D. Wan very recently proved an asymptotic version of a conjecture of Hansen and Mullen concerning the distribution of irreducible polynomials over finite fields. In this note we prove that the conjecture is true in general by using machine calculation to verify the open cases remaining after Wan's work.

     

Photoelastic determination of stresses in multiple-pin connectors

The design, fabrication, and testing of photoelastic models of double-lap, multiple-pin connectors are discussed. Interest is in the stresses in the inner laps. These stresses are determined by constructing models with photoelastic inner laps and transparent-acrylic outer laps. The connectors have two pins, in tandem, parallel to the load direction. A photoelastic-isotropic point is shown to permit the evaluation of load sharing between the two pins. A numerical scheme, utilizing the isochromatic- and isoclinic-photoelastic data and a finite-difference representation of the planestress equilibrium equations, is used to compute the stresses around the two pins. Representative stress distributions and stress-concentration factors are shown.     

Equivalence classes of matrices over finite fields

Let F=GF(q) denote the finite field of order q, and F_mn the ring of m×n matrices over F. Let Ω be a group of permutations of F. If A,B∈F_mn, then A is equivalent to B relative to Ω if there exists ?∈Ω such that ?(a_ij) = b_ij. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by various permutation groups. In particular, formulas are given if Ω is the symmetric group on q letters, a cyclic group, or a direct sum of cyclic groups.     

Iron Mössbauer spectra of lava from Jeju island and its similarities to Moon basalts

We report the result of measurements of the⁵⁷Fe Mössbauer spectrum for powder samples of lava taken from four widely separated sites on Jeju island. The spectra consist of well defined quadrupole doublets having a 2+ charge state and indicate the presence of olivine, clinopyroxene, and ilmenite. In addition we find a six line magnetically split hyperfine pattern characteristic of impure hematite, with considerable line broadening and reduced internal field. The observed spectra have a remarkable similarity to those found for moon basalts. A recently popularized “collision ejection” model for the moon formation would be consistent with our observations. The data is a particularly simple and direct illustration of the well-known fact that the iron silicates and ilmenite found on the moon are very similar in composition and relative abundance to that found on earth.     

The Number of Linearly Independent Binary Vectors with Applications to the Construction of Hypercubes and Orthogonal Arrays, Pseudo ( t, m, s)-Nets and Linear Codes

We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1kn. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.     

Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

The Stefan–Maxwell equations for multi-component diffusion result in a system of coupled continuity equations for all species in the mixture. We use a generalization of the exponential scheme to discretize this system of continuity equations with the finite volume method. The system of continuity equations in this work is obtained from a non-singular formulation of the Stefan–Maxwell equations, where the mass constraint is not applied explicitly. Instead, all mass fractions are treated as independent unknowns and the constraint is a result of the continuity equations, the boundary conditions, the diffusion algorithm and the discretization scheme. We prove that with the generalized exponential scheme, the mass constraint can be satisfied exactly, although it is not explicitly applied. A test model from the literature is used to verify the correct behavior of the scheme.     

Phosphorus-based functional groups as hydrogen bonding templates for rotaxane formation

We report on the use of the hydrogen bond acceptor properties of some phosphorus-containing functional groups for the assembly of a series of [2]rotaxanes. Phosphinamides, and the homologous thio- and selenophosphinamides, act as hydrogen bond acceptors that, in conjunction with an appropriately positioned amide group on the thread, direct the assembly of amide-based macrocycles around the axle to form rotaxanes in up to 60% yields. Employing solely phosphorus-based functional groups as the hydrogen bond accepting groups on the thread, a bis(phosphinamide) template and a phosphine oxide-phosphinamide template afforded the corresponding rotaxanes in 18 and 15% yields, respectively. X-ray crystallography of the rotaxanes shows the presence of up to four intercomponent hydrogen bonds between the amide groups of the macrocycle and various hydrogen bond accepting groups on the thread, including rare examples of amide-to-phosphinamide, -thiophosphinamide, and -selenophosphinamide groups. With a phosphine oxide-phosphinamide thread, the solid-state structure of the rotaxane is remarkable, featuring no direct intercomponent hydrogen bonds but rather a hydrogen bond network involving water molecules that bridge the H-bonding groups of the macrocycle and thread through bifurcated hydrogen bonds. The incorporation of phosphorus-based functional groups into rotaxanes may prove useful for the development of molecular shuttles in which the macrocycle can be used to hinder or expose binding ligating sites for metal-based catalysts.