On One Method of Parameter Estimation in Chemical Kinetics Using Spectra with Unknown Spectral Components

The method of successive estimation of regression parameters, which is widely used in nonlinear regression analysis, is applied to obtain kinetic information from spectral data for the case when the spectra of individual components are unknown. Using a model example with a two-step successive reaction, the reliability of the algorithm is demonstrated. To compare the proposed method with other known methods for estimating kinetic parameters literature data are used. All simulations were done using a new software for nonlinear regression analysis: FITTER. The proposed approach is especially useful when the spectra of reaction components are unknown and when formal calibration methods do not provide desirable accuracy.     

Wave-packet continuum discretization for quantum scattering

A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets which are the normalized states constructed from exact non-normalized continuum states. Projecting the wave functions and all scattering operators like t$t$-matrix, resolvent, etc. on such a wave-packet basis results in a formulation of quantum scattering problem entirely in terms of discrete elements and linear equations with regular matrices. It is demonstrated that there is a close relation between the above stationary wave packets and pseudostates which are employed often to approximate the scattering states with a finite L₂$L_2$ basis. Such a fully discrete treatment of complicated few- and many-body scattering problems leads to significant simplification of their practical solution. Also we get finite-dimensional approximations for complicated operators like effective interactions between composite particles constructed via the Feshbach-type projection formalism. As illustrations to this general approach we consider several important particular problems including multichannel scattering and scattering in the three-nucleon system within the Faddeev framework.     

New short-range electromagnetic current in the deuteron

A new model for short-range isoscalar current in the deuteron and NN system is developed and tested on a variety of isoscalar magnetic observables such as the deuteron magnetic moment, magnetic form factor, and the circular polarization of photons at radiative capture at thermal neutron energies. The model for electromagnetic two-nucleon current proposed in the paper is based on generation of an intermediate dibaryon in the short-range NN interaction. This intermediate dibaryon, in turn, is treated within the new model for intermediate and short-range NN interaction recently proposed by the present authors. The transition current model developed here satisfies the current conservation relation by the construction. Our calculations have demonstrated that the new current model, using only one parameter (with a clear physical meaning), is able to describe, in very good agreement with the experimental data, three basic deuteron observables of magnetic type, viz., the magnetic moment, the photon circular polarization in the process, and the structure function B(Q ²) up to Q ² ≃ 60 fm⁻². The text was submitted by the authors in English.     

Angular distributions of scattered excited muonic hydrogen atoms

Coulomb deexcitation differential cross sections of excited muonic hydrogen in collisions with the hydrogen atom are studied for the first time. In the fully quantum-mechanical close-coupling approach, both the differential cross sections for the nl → n′l′ transitions and l-averaged differential cross sections have been calculated for the initial exotic atom states with n = 2–6 at kinetic energies of E _cm = 0.01–15 eV and for scattering angles of ϑ_cm = 0°–180°. The vacuum polarization shifts of the ns states are taken into account. The differential cross sections of the elastic and Stark scattering obtained in the same approach are also presented. The main features of the calculated differential cross sections are discussed, and a strong anisotropy of Coulomb deexcitation cross sections is predicted. The text was submitted by the authors in English.     

On the type II error in SIMCA method

A novel method for theoretical calculation of the type II (β) error in soft independent modeling by class analogy is proposed. It can be used to compare tentatively predicted and empirically observed results of classification. Such an approach can better characterize model quality and thus improve its validation. Method efficiency is demonstrated on the famous Fisher Iris dataset and on a real‐world example of quality control of packed raw materials in pharmaceutical industry. Copyright © 2014 John Wiley & Sons, Ltd.     

Two approaches to kinetic analysis applied to the prediction of antioxidant activity

Differential scanning calorimetry (DSC) followed by mathematical data processing can be used instead of the conventional method of long term thermal aging in predicting the activity of antioxidants in polyolefins. In this method, a regression relationship is established between the oxidation initial temperatures measured by DSC (X data) and the oxidation induction period values determined by thermal aging (Y data). Two approaches, called hard and soft, are employed in the construction of models. In the first case, nonlinear regression analysis is used in combination with successive Bayesian estimation. The second approach combines partial least squares regression and simple interval calculation. Use of a common data set makes it possible to compare these approaches and to draw inferences as to the cases in which one or the other is preferable.     

The orthogonal projection method in scattering theory

This work gives a detailed account of the orthogonal projection method in the theory of two- and three-body scattering, which is based on the employment of orthogonal projecting pseudopotentials. The method is applied to a number of physical problems, of which the following the most important: the improvement of convergence and the rearragement of Born series to make them convergent at low energies in the presence of bound states in a system, as well as the consideration of the Pauli exclusion principle in the scattering of composite particles and in the integral theory of direct nuclear reactions. The properties of eigenvalues of kernels of the equations obtained are investigated and the conditions for the convergence of their iterations are derived. For the three-body problem, the general case of three different particles is considered, as well as two particular cases, namely, two particles in the field of a heavy core and three identical particles. The proven theorems are illustrated by numerical examples. Other useful applications of the proposed approach are listed and discussed, in particular, those in solid-state physics and in the theory of electromagnetic transitions. The approach suggested is compared with those of the other authors and the prospects of using the developed formalism are discussed.