Maximal Type Elements for Families

In this paper, we present a variety of existence theorems for maximal type elements in a general setting. We consider multivalued maps with continuous selections and multivalued maps which are admissible with respect to Gorniewicz and our existence theory is based on the author’s old and new coincidence theory. Particularly, for the second section we present presents a collectively coincidence coercive type result for different classes of maps. In the third section we consider considers majorized maps and presents a variety of new maximal element type results. Coincidence theory is motivated from real-world physical models where symmetry and asymmetry play a major role.

Coincidence Theory in the Coercive Case and Minimax Inequalities

We established coincidence results between maps with continuous selections and admissible maps. Both the compact and coercive cases were considered, and our argument relied on new coincidence ideas established recently by the author. Using our coincidence theory, we established new analytic alternatives, which then generate new minimax inequalities of the Neumann–Sion type.

Topological Transversality Coincidence Theory for Multivalued Maps with Selections in a Given Class

This paper presents the topological transversality coincidence theorem for general multivalued maps who have selections in a given class of maps.

NEW PRAGMATIC APPROACH TO FISCALIZATION OF PUBLIC FINANCE

Introduction. Turbulence in the field of public finance on both national and global scale testifies to the existence of unresolved problems in reconciling the scientific postulates behind transformation and development of the institution of state. Crisis of the early twentieth century and the pandemic of 2019-2020 have revealed the ineffectiveness of liberal models of statehood, thus heightening the urgency of reinforcing scientific efforts directed at studying and fixing the aforementioned issue. The purpose of the article is to systemize the scientific grounds of the latest theoretical dimensions of the public finance institute and to determine a new pragmatic approach to its fiscalization. Methods. The methods of dialectic analysis, synthesis and logical generalization, as well as comparison and formalization are used. Results. The essential parameters of the relationship between global crises and changes in the technological framework have been revealed. Financial policy is viewed as the art of managing finance with the purpose of creating conditions for sustainable socio-economic develop ment. The contradictions accumulated in the field of public finance and fiscal space have been analyzed and the evolution of the institution of state has been traced. It has been proven that in view of the new directions of societal development precipitated by the globalization crisis and the pandemic it is advisable to determine a new pragmatic approach to fiscalization of public finance, which would be defined by values, formal and informal institutions, and policy based on the main features of the coincidence theory.

A LOCALISED BOUNDARY OBJECT: SEVENTEENTH-CENTURY WESTERN MUSIC THEORY IN CHINA

In 1685, the Portuguese Jesuit Thomas Pereira was ordered by the Qing Kangxi emperor to write books on Western music theory in Chinese. Presented in the books were seventeenth-century practical and speculative music theories, including the coincidence theory of consonance. Invoking the concept of ‘boundary object’, this article shows that the cultural exchange, which gave rise to new knowledge by means of selection, synthesis and reinterpretation, was characterised by a lack of consensus between the transmitter and the receivers over the functions of the imported theories. Although the coincidence theory of consonance could potentially effect the transition from a pure numerical to a physical understanding of pitch, as in the European scientific revolution, it failed to flourish in China not only because of different theoretical concerns between European and Chinese musical traditions, but also because of its limited dissemination caused by Chinese print culture.

A Topological Coincidence Theory for Multifunctions via Homotopy

A new simple result is presented which immediately yields the topological transversality theorem for coincidences.

Issuses in Developmental and Pedagogical Psychology: L.S. Vygotsky and D.N Uznadze

The article analyzes the interrelation between L.S. Vygotsky’s and Uznadze’s views on some important issues of developmental and pedagogical psychology. This, in particular, refers to the problem of concept formation, periodisation of child development, relation between development and teaching, motive forces of development. Special attention is paid to “coincidence theory” and the principle of solving “empirical postulate” which is a methodological basis for the whole system of D.N. Uznadze’s psychological conception including issues of development and education. It is pointed out that in spite of not being very well acquainted with each other’s works, the difference between viewpoints of L.S. Vygotsky and D.N. Uznadze is considerably less than the things they have in common. As for the principal questions, their approaches are often consistent and, in some cases, identical. Also, a lot of interesting outcomes can be expected from a deeper analysis of the general psychological views of the author of the cultural-historical concept and the author of the theory of set.