On submanifolds of Sasakian statistical manifolds

‎In this paper‎, ‎invariant and‎ ‎anti-invariant submanifolds of Sasakian statistical manifolds are studied‎. ‎Necessary and sufficient conditions are given for vanishing the dual connection in the normal bundle‎. ‎Moreover‎, ‎existence of a Kaehlerian structure on invariant hypersurfaces of Sasakian statistical manifolds are proved‎.

Further Results on Exponentially Robust Stability of Uncertain Connection Weights of Neutral-Type Recurrent Neural Networks

Further results on the robustness of the global exponential stability of recurrent neural network with piecewise constant arguments and neutral terms (NPRNN) subject to uncertain connection weights are presented in this paper. Estimating the upper bounds of the two categories of interference factors and establishing a measuring mechanism for uncertain dual connection weights are the core tasks and challenges. Hence, on the one hand, the new sufficient criteria for the upper bounds of neutral terms and piecewise arguments to guarantee the global exponential stability of NPRNN are provided. On the other hand, the allowed enclosed region of dual connection weights is characterized by a four-variable transcendental equation based on the preceding stable NPRNN. In this way, two interference factors and dual uncertain connection weights are mutually restricted in the model of parameter-uncertainty NPRNN, which leads to a dynamic evolution relationship. Finally, the numerical simulation comparisons with stable and unstable cases are provided to verify the effectiveness of the deduced results.

Lagrangian Submanifolds of Symplectic Structures Induced by Divergence Functions

Divergence functions play a relevant role in Information Geometry as they allow for the introduction of a Riemannian metric and a dual connection structure on a finite dimensional manifold of probability distributions. They also allow to define, in a canonical way, a symplectic structure on the square of the above manifold of probability distributions, a property that has received less attention in the literature until recent contributions. In this paper, we hint at a possible application: we study Lagrangian submanifolds of this symplectic structure and show that they are useful for describing the manifold of solutions of the Maximum Entropy principle.

Casual Nexus Between Dynamics of Population and Food Security: Economic Benchmarks for Agriculture

Food security and dynamics of population have a dual connection. Firstly, a rapid rise in the population size increases a demand for food. Secondly, a lack of food affordability and availability implies negative dynamics of population. The latter issue observed in Ukraine highlighted the goal of this research. The methodological study background was econometrics and cluster comparative analysis. The considered time series covered the period 1999 to 2018. The accessible cross-sectional data included 90 countries. The research outcome in the form of multiple regressions allowed forecasting the objective values of expenditures on food, income per capita, and daily protein intakes which could retain a stable population size. The offered EU and World Top benchmarks involved the GDP indicator, balance between crop and animal food supplies, medium age, and share of rural population by country. These findings made possible to set prospects of amplifying Ukrainian food security and improving population dynamics.

An Extended Fuzzy TODIM Approach for Multiple-Attribute Decision-Making with Dual-Connection Numbers

The TODIM is a decision-making method that can examine the psychological behavior of decision-makers (DMs). However, the traditional TODIM method has still not been having the ability to overcome fuzzy information such as interval values and linguistic variables. This paper proposes an extended TODIM decision-making model for multiple-attribute decision-making (MADM) problems in a linguistic environment using dual-connection numbers (DCNs). The extended model uses linguistic variables in which the values of alternatives and criteria for both of them are formatted in the triangular fuzzy numbers (TFNs) to express the uncertain information. First, some definitions and basic operators of the TFNs and DCNs are introduced. Then, the way how to convert fuzzy information in forms of the TFNs into DCNs and the step how to transform each criterion weight value into a crisp value using the defuzzification of Minkowski are demonstrated. Furthermore, the traditional TODIM is improved to address MADM problems with DCNs, and detailed calculation steps in determining decisions are explained. Finally, an illustrative example which is a cadre selection problem is applied to demonstrate the conformity and validity of the extended TODIM method and to compare it with some other methods.

ANALYSIS OF MODERN SOCIO-PSYCHOLOGICAL STAFF MANAGEMENT METHODS

The article focuses on the analysis of modern socio-psychological management methods. The study revealed the essence of social and psychological management methods, their structural features, the dual connection between the enterprise state development and application of social and psychological influence on labor. The conceptual and categorical basis of enterprise socio-psychological climate was formed. Based on the applied approach, the level of needed socio-psychological methods practical application on enterprise management was established. It allows to increase staff efficiency and effectiveness through environmental management and focus on staff needs. There were defined the shifting trends of the central analysis categories in enterprise management from "human capital" to "human value". The classification model of social and psychological of tools influenced on the personnel was formed. There were formed the main markers of socio-psychological leader behavior in his result focused, ability to form a working team and a favorable psychological team climate. There was proposed thr gradual step-by-step innovations integration into personnel enterprise management maked from the standpoint of psychological and social adjustment employees’ behavior. Emphasis were placed on personnel management modern challenges and socio-psychological management forms innovations. The features of ontopsychological methods, coaching, neuro-linguistic programming were revealed. Emphasis were placed on the new employers approaches to the supply on the labor market, the growing need for qualitatively new thinking and IT-skills staff. The article proposes complex ways of forming an effective team of employees, whose motivation is not limited to the range of financial and material incentives. The prospect of further research in this area is improvings in the modern combinations of enterprise management methods in order to ensure its sustainable development, security and loyalty to the business environment changes.

Golden Section and Golden Rectangles When Building Icosahedron, Dodecahedron and Archimedean Solids Based On Them

A brief history of the development of the regular polyhedrons theory is given. The work introduces the reader to modelling of the two most complex regular polyhedrons – Platonic solids: icosahedron and dodecahedron, in AutoCAD package. It is suggested to apply the method of the icosahedron and dodecahedron building using rectangles with their sides’ ratio like in the golden section, having taken the icosahedron’s golden rectangles as a basis. This method is well-known-of and is used for icosahedron, but is extremely rarely applied to dodecahedron, as in the available literature it is suggested to build the latter one as a figure dual to icosahedron. The work provides information on the first mentioning of this building method by an Italian mathematician L. Pacioli in his Divine Proportion book. In 1937, a Soviet mathematician D.I. Perepelkin published a paper On One Building Case of the Regular Icosahedron and Regular Dodecahedron, where he noted that this “method is not very well known of” and provided a building based “solely on dividing an intercept in the golden section ratio”. Taking into account the simplicity and good visualization of the building based on golden rectangles, a computer modeling of icosahedron and dodecahedron inscribed in a regular hexahedron is performed in the article. Given that, if we think in terms of the golden section concepts, the bigger side of the rectangle equals a whole intercept – side of the regular hexahedron, and the smaller sides of the icosahedron and dodecahedron rectangles are calculated as parts of the golden section ratio (of the bigger part and the smaller one, respectively). It is demonstrated how, using the scheme of a wireframe image of the dual connection of these polyhedrons as a basis, to calculate the sides of the rectangles in the golden section ratio in order to build an “infinite” cascade of these dual figures, as well as to build the icosahedron and dodecahedron circumscribed about the regular hexahedron. The method based on using the golden-section rectangles is also applied to building semiregular polyhedrons – Archimedean solids: a truncated icosahedron, truncated dodecahedron, icosidodecahedron, rhombicosidodecahedron, and rhombitruncated icosidodecahedron, which are based on icosahedron and dodecahedron.