P-matrix Approach Research Articles

Metropolis–Hastings from a stochastic population dynamics perspective

The development and application of Markov chain Monte Carlo methods based on the celebrated Metropolis-Hastings algorithm has played a major role in the recent advancement of statistical procedures. However, the approach has made relatively little impact on stochastic population modelling in spite of this field being central to many processes studied in biology, physics and chemistry. Attention is almost exclusively focussed on sampling and the construction of distributions and parameter estimates, with virtually no consideration being given to the structure of the process trajectories. This paper therefore tackles the inverse problem of determining whether there is an optimal method of selecting a proposal matrix corresponding to a given set of equilibrium probabilities, both in terms of trajectory characteristics and the coverage of the range of support. Using the discrete Cauchy distribution as a benchmark, simple and general random walk schemes are compared with the ‘small world’ scenario. It is then shown that these are all outperformed by a direct P-matrix approach based on a mass annihilation and immigration process.

Hyperon-nucleon final-state interaction in kaon photoproduction on a deuteron

Final state hyperon-nucleon interaction in strangeness photoproduction of the deuteron is investigated making use of the covariant reaction formalism and the P-matrix approach to the YN system. Remarkably simple analytical expression for the amplitude is obtained. Pronounced effects due to final state interaction are predicted including the manifestation of the 2.13 GeV resonance.

P-Matrix approach and parameters of low-energy scattering in the presence of a Coulomb potential

The scattering of two charged strongly interacting particles is described on the basis of the P-matrix approach. In the P matrix, it is proposed to isolate explicitly the background term corresponding to purely Coulomb interaction, whereby it becomes possible to improve convergence of the expansions used and to obtain a correct asymptotic behavior of observables at high energies. The expressions for the purely Coulomb background P matrix, its poles and residues, and purely Coulomb eigenfunctions in the P-matrix approach are obtained. The nuclear-Coulomb parameters of the low-energy scattering of two charged hadrons are investigated on the basis of this approach combined with the method for isolating the background P matrix. Simple explicit expressions for the nuclear-Coulomb scattering length and effective range in terms of the residual P matrix are derived. For models of short-range strong interaction, these expressions give a general form of nuclear-Coulomb parameters for low-energy scattering. Specific applications of the general expressions derived in this study are exemplified by considering, on the basis of these expressions, some exactly solvable models of strong interaction, including the hard-core model, and, for these models, the nuclear-Coulomb parameters for low-energy scattering at arbitrary values of the orbital angular momentum are found explicitly for the first time. In particular, the nuclear-Coulomb scattering length and effective range are obtained explicitly for the boundary-condition model, the model of a hard-core delta-shell potential, the Margenau model, and the model of square-well hard-core potential.

Strangeness photoproduction on a deuteron and hyperon-nucleon interaction

Pronounced effects due to final-state hyperon-nucleon interaction are predicted in a strangeness photoproduction reaction on a deuteron. Use is made of the covariant reaction formalism and of the P-matrix approach to the hyperon-nucleon interaction.

延伸プラスチックフィルム用赤外線ゲージ

This paper describes the methods and apparatus for measuring accurately the thickness of thin oriented polymer films. Three key aspects of the new method are as follows:(1) The technique eliminating optical interference effects occurred with thin films by using plane polarized light incident at Brewster's angle;(2) The implementation of multivariate regression models based on the inverse representation of Beer's law or P-matrix approach with optimal wavelengths, canceling dichroic effects with anisotropic materials such as oriented polymer films;(3) The design of optics to be quite tolerant to movement of the film in both height and angle

Analysis of Deoxyribonucleotides with Principal Component and Partial Least-Squares Regression of UV Spectra after Fourier Preprocessing

Principal component (PCR) and partial least-squares (PLS) regression with Fourier preprocessing of ultraviolet spectra have been evaluated for the analysis of mixtures of the four major nucleotides of DNA. Results have been compared with those obtained without Fourier preprocessing and with those obtained with a straightforward P-matrix approach with optimum wavelength selection. Calibrations were developed and tested with the use of sixteen standard and fourteen unknown mixtures. The standards and nine of the unknowns followed the typical base equivalences found in DNA. For these nine unknowns, the best average percent error in the Fourier domain was 0.61%, as compared to 0.65% in the spectral domain. The remaining five unknowns, in which the nucleotide concentrations were independent of each other, provided a particularly difficult test of each method's ability to distinguish the components. For these unknowns, the best errors in the Fourier and spectral domains were 1.20 and 1.85%, respectively. For assessment of the effect of protein, the analysis was repeated with varying amounts of albumin up to 36% by weight added to the mixtures. All of the full spectral methods (PCR and PLS in the spectral and Fourier domains) were able to compensate for the spectral interference of the added protein and produced results as good as those without the protein. For nucleotide mixtures, ultraviolet spectroscopy represents a rapid, economical, sensitive, and nondestructive alternative to existing techniques.

Hyperon-nucleon interaction and the 2.13 GeV strange dibaryonic system in the P-matrix approach

A description is presented of the low-energy YN (Y = Λ,∑) interactions within the Jaffe-Low P -matrix formalism. Analysing the enhancement of the Λp invariant mass near the ∑ + n threshold we conclude that it should be identified as a P -matrix partner of the deuteron and not as a six-quark dibaryon resonance.

Off-shell two-particle scattering amplitude in the P-matrix approach

A generalization of the P-matrix approach which makes it possible to describe the interaction of two particles off the energy shell is proposed. Explicit separation in the wave function of a part corresponding to free motion yields a compact expression for the off-shell scattering amplitude and gives directly a method for separable expansion of the amplitude.

The P matrix methods for the quark model

Physical foundations of the P-matrix approach, connecting P-matrix poles to multiquark states, are explored. The QCB interaction is constructed explicitly for ππ, πN, πK, KN and NN systems. Deuteron and tritium characteristics are calculated.