On Complex Numbers in Higher Dimensions

The geometric approach to generalized complex and three-dimensional hyper-complex numbers and more general algebraic structures being based upon a general vector space structure and a geometric multiplication rule which was only recently developed is continued here in dimension four and above. To this end, the notions of geometric vector product and geometric exponential function are extended to arbitrary finite dimensions and some usual algebraic rules known from usual complex numbers are replaced with new ones. An application for the construction of directional probability distributions is presented.

Semi-supervised multi-label classification using an extended graph-based manifold regularization

Graph-based algorithms are known to be effective approaches to semi-supervised learning. However, there has been relatively little work on extending these algorithms to the multi-label classification case. We derive an extension of the Manifold Regularization algorithm to multi-label classification, which is significantly simpler than the general Vector Manifold Regularization approach. We then augment our algorithm with a weighting strategy to allow differential influence on a model between instances having ground-truth vs. induced labels. Experiments on four benchmark multi-label data sets show that the resulting algorithm performs better overall compared to the existing semi-supervised multi-label classification algorithms at various levels of label sparsity. Comparisons with state-of-the-art supervised multi-label approaches (which of course are fully labeled) also show that our algorithm outperforms all of them even with a substantial number of unlabeled examples.

PROFESSIONAL COMPETENCIES OF A HIGH SCHOOL TEACHER IN THE ERA OF DIGITALIZATION

The article reflects the results of some sociological studies, the results of which indicate the need for the formation of new, digital competencies for higher school teachers. Global economic processes and digital trends are transforming the content and technologies of pedagogical work, but many teachers are not ready for such innovations. The conclusion is made that the sustainable introduction of digital learning tools can be successful only if the general vector of digital transformation of the educational process is justified and supported by both the university administration and the teachers themselves.

“INCOMPLETE” COURT PROCEDURES IN MODERN CIVIL PROCEDURE

The development of judicial procedures is an indicator of increasing complexity of civil procedure, a clear manifestation of the general pattern – unification and differentiation of civil procedural form. And one of the main tasks of the legislator is to make sure that the objective complexity of the legal space does not lead to complication of the access to judicial protection for interested persons. This thesis, put forward by the author, acts as one of the key ideas of this study and is disclosed in the article in terms of “incomplete” judicial procedures. The “incomplete” judicial procedures, according to the author’s conception, include simplified proceedings, absentee proceeding, court-ordered proceedings and proceedings on insignificant claims. The latter should be understood as proceedings before a justice of the peace in action cases (see clauses 2–5 part 1 of Article 23 of the Civil Procedure Code of the RF). In conclusion it is concluded that the procedural nature of the Russian process, laid down in the codes of the early 20th century, now acquires conceptual importance, which requires a different methodology to solve current legislative problems. The procedures we have considered is a “litmus test” of the methods of justice, which allows us to comprehend the general vector of the further path of civilizational process reform.

Parabolic-accelerating vector waves

Complex vector light fields have become a topic of late due to their exotic features, such as their non-homogeneous transverse polarisation distributions and the non-separable coupling between their spatial and polarisation degrees of freedom (DoF). In general, vector beams propagate in free space along straight lines, being the Airy-vector vortex beams the only known exception. Here, we introduce a new family of vector beams that exhibit novel properties that have not been observed before, such as their ability to freely accelerate along parabolic trajectories. In addition, their transverse polarisation distribution only contains polarisation states oriented at exactly the same angle but with different ellipticity. We anticipate that these novel vector beams might not only find applications in fields such as optical manipulation, microscopy or laser material processing but also extend to others.

Corporate Venture Sector: The Problem of Staffing

The problem of staffing in innovation management is one of the main resources of the modern Russian economy. Based on the data of the Ministry of Education and Science of Russia, in-depth interviews with representatives of large companies, and government authorities, the authors attempted to identify the most relevant and popular approaches to solving the problem of staffing the venture capital industry in the corporate sector. The article defines the general vector of development of the corporate venture capital sector in Russia, analyzes the contribution of universities and large companies to the creation of a talent pool. It is concluded that universities do not cover the need for training highly qualified personnel for innovation management, while large companies are building up competencies in the field, using and using effective training tools for working with venture projects.

Ricci soliton biharmonic hypersurfaces in the Euclidean space

UDC 515.12 We investigate biharmonic Ricci soliton hypersurfaces whose potential field satisfies certain conditions. We obtain a result based on the average scalar curvature of the compact Ricci soliton hypersurface where is a general vector field. Then we prove that there are no proper biharmonic Ricci soliton hypersurfaces in the Euclidean space provided that the potential field is either a principal vector in grad or .

THEORY OF THE WAVE HISTORY OF ETHNOS IN THE NORTHERN HEMISPHERE

This article is devoted to the discovery of long-term cyclic psychophysical pendulum processes in the history of the ethnic groups of the northern hemisphere for the period from about 5500 BC to the 21st century. The discovery was made based on the analysis of related disciplines: DNA genealogy, linguistics, history, mythology, and climatology. And, in particular, my empirical conclusions. The "Theory of wave history " (hereinafter – TWH) is relevant for the study of deep and large-scale processes of history in large periods of time. TWH reveals the cyclical nature of history with a period of approximately 1850 years, in similar phases of which similar or similar psychophysical phenomena occur, which form the general vector of history. On the basis of the TWH, it is possible to resolve issues of white spots of history. TWH is based on the psychophysical feature of a person to create within the current and popular framework of society, because history itself puts its heroes on the lists. This shows its immanence and its worldliness. TWH does not aim to describe history as a collection of accumulated progress, it does not concern the economic and political spheres. TWH is a method of historical research.