Models for selecting an effective order fulfilment

The problems of modelling cash flows are considered, which are determined by the procedures for optimising the order of execution of portfolio orders. The objective function assumes the maximisation of the average expected total income (accumulated on the deposit, taking into account the monetary amounts received from the implementation of portfolio orders) by a given point in time in the future. Considered approaches to the optimisation of such systems which allow taking into account: 1) the random nature of income from completed orders; 2) special additional costs, correlated both with the moment of the portfolio formation and with the moment of completion of order servicing.

On order determination by predictor augmentation

Summary In many dimension reduction problems in statistics and machine learning, such as in principal component analysis, canonical correlation analysis, independent component analysis and sufficient dimension reduction, it is important to determine the dimension of the reduced predictor, which often amounts to estimating the rank of a matrix. This problem is called order determination. In this article, we propose a novel and highly effective order-determination method based on the idea of predictor augmentation. We show that if the predictor is augmented by an artificially generated random vector, then the parts of the eigenvectors of the matrix induced by the augmentation display a pattern that reveals information about the order to be determined. This information, when combined with the information provided by the eigenvalues of the matrix, greatly enhances the accuracy of order determination.

Quantum phase crossover in the spherical mean-field plus quadrupole–quadrupole and pairing model with two j-orbits

The shape phase crossover in the mean-field plus the geometric quadrupole–quadrupole and pairing model within two [Formula: see text]-orbits is analyzed, for which a simple description of [Formula: see text]Sn confined in the lowest [Formula: see text] and [Formula: see text] orbits above the [Formula: see text]Sn core is demonstrated to reveal the crossover behavior of the model. It is shown that [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text] in this case may serve as effective order parameters for even–even and odd-A systems, respectively, from which the shape phase crossover from the rotation-like phase to the superconducting-like phase can be observed with variation of the number of valence neutrons.

IMPROVING THE EOQ MODEL TAKING INTO ACCOUNT THE TECHNICAL AND FINANCIAL ASPECTS OF THE ENTERPRISE

At present, the problem of calculating the necessary stock of materials, components and finished products in warehouses of industrial enterprises is becoming more and more urgent, since storage costs often make up a significant share of the total cost of products. Various models are used to calculate the optimal order size, in particular the EOQ optimal or cost-effective order size model.

What can we learn from the Interacting Boson Model in the limit of large boson numbers?

Over the years, studies of collective properties of medium and heavy mass nuclei in the framework of the Interacting Boson Approximation (IBA) model have focused on finite boson numbers, corresponding to valence nucleon pairs in specific nuclei. Attention to large boson numbers has been motivated by the study of shape/phase transitions from one limiting symmetry of IBA to another, which become sharper in the large boson number limit, revealing in parallel regularities previously unnoticed, although they survive to a large extent for finite boson numbers as well. Several of these regularities will be discussed. It will be shown that in all of the three limiting symmetries of the IBA [U(5), SU(3), and O(6)], energies of 0+ states grow linearly with their ordinal number. Furthermore, it will be proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0^+_2 ) = E(6^+_1 ), E(0^+_3 ) = E(10^+_1 ), E(0^+_4 ) = E(14^+_1 ), the energy ratio E(6^+_1 )/E(0^+_2 ) turning out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first- and second-order transitions. The energies of 0+ states near the point of the first order shape/phase transition between U(5) and SU(3) will be shown to grow as n(n+3), where n is their ordinal number, in agreement with the rule dictated by the relevant critical point symmetries studied in the framework of special solutions of the Bohr Hamiltonian. The underlying dynamical and quasi-dynamical symmetries are also discussed.

FEATURES OF THE DESIGN OF INDIVIDUAL EDUCATIONAL ROUTE AT THE LEVEL OF DISCIPLINES OF THE PROFESSIONAL MODULE

The article examines the features of designing an individual educational route at the discipline level of a professional module. After analyzing several definitions of the notion «individual educational route», the authors derive their own definition, which they rely on throughout the work. An individual educational route is an effective order for an individual-differentiated mastering of an educational program or discipline by students, which forms a personal position, a student's opinion when choosing a learning goal, the content and methods of organizing it in conditions specially created by higher education. The description of the sequence of the development of the route is shown, the factors and conditions for its implementation are formulated. The structure of individual educational routes is reflected, various options for their development are proposed. The structure selected and analyzed components from the point of view of various authors. The authors note that the professional and personal development of students and their level of readiness for the independent choice of an individual educational route depend on the literacy of building an individual educational route. The authors conducted an experiment which showed that, thanks to such an important element, as competent pedagogical conditions allow an increase in the percentage of students' readiness. The results of the work can be used to further develop the issue of building individual educational routes at the level of the disciplines of the professional module in higher education.

Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems

A family of explicit symplectic partitioned Runge-Kutta methods are derived with effective order 3 for the numerical integration of separable Hamiltonian systems. The proposed explicit methods are more efficient than existing symplectic implicit Runge-Kutta methods. A selection of numerical experiments on separable Hamiltonian system confirming the efficiency of the approach is also provided with good energy conservation.