New asymptotic estimates for spherical designs

Let N(n, t) be the minimal number of points in a spherical t-design on the unit sphere S^n in R^{n+1}. For each n >= 3, we prove a new asymptotic upper bound N(n, t) <= C(n)t^{a_n}, where C(n) is a constant depending only on n, a_3 <= 4, a_4 <= 7, a_5 <= 9, a_6 <= 11, a_7 <= 12, a_8 <= 16, a_9 <= 19, a_10 <= 22, and a_n 10.Comment: 12 page

Spherical designs via Brouwer fixed point theorem

For each N>=c_d*n^{2d*(d+1)/(d+2)} we prove the existence of a spherical n-design on S^d consisting of N points, where c_d is a constant depending only on $d$.Comment: 17 page

Mediation in the case of a juvenile committing a criminal offense or a felony

As a general rule, punishment should be necessary and sufficient to correct the person and re-educate him. At the same time, a punitive approach prevails in the criminal process in Ukraine. For criminal law, the introduction of the mediation institution determines the development of the legal institution of reconciliation. The article aims to characterize the essence of mediation in Ukraine and study foreign countries' best practices in this field. The object of the study is public relations in the field of mediation in the case of a minor committing a criminal offense or a felony for the first time. The subject of the study is mediation as an alternative to court proceedings in the case of a juvenile committing a criminal offense or a felony for the first time. The authors used some methods of scientific knowledge: analytical, phenomenological, generalization, comparative law. Particular attention in the study is paid to the analysis of the essence of punishment, the study of international experience in the use of mediation, and the practice of mediation in criminal proceedings in Ukraine, which currently takes place only as part of an experiment. The authors conclude that it is essential and urgent to use the mediation procedure more widely in criminal proceedings as an alternative to litigation. It is emphasized that the full implementation of this institution requires political will and broad support from civil society. Namely, his readiness to resolve disputes without a court, but only with the help of a mediator

Ecodesign and initiatives of sustainable development in the dimension of passion of artistic and design creativity

The fashion industry under modern circumstances is one of the most developed industries, which determines its tangible impact on people and nature. The purpose of the article is to analyze ecodesign and sustainable development initiatives through the dimension of passion for artistic and educational creativity. The theoretical and empirical methods of scientific research were used. In the results, it was established that previously the requirements of environmental friendliness were perceived to a greater extent as limitations in the creative process. They are the basis and a kind of impetus for the generation of new creative ideas. The novelty of the work consists in proving the development of clothing design as an element of the designer's personality development as a leading specialist not only in design matters, but also in creating an organic combination of all components of the product creation process. The practical significance of the work is to determine the future of the fashion industry in the use of&nbsp;environmentally friendly and technological fabrics. In the conclusions, it is noted that new creative searches are due to the vital need for a new philosophy of world perception, which will influence ecodesign in the future

Suicide among minors in Ukraine: Manifestations and ways to prevent

The article aims to find out the essentiality of such a concept as “juvenile suicide” and the search for ways to prevent it. The object of the study is social relations in the field of combating suicide among minors. During the research, the authors used a particular set of general scientific and unique scientific methods, which ensured the objectivity of the display of the research subject: the comparative legal method, the method of formal logic, the comparison method, and the hypothetical-deductive method. There is much work to improve suicide prevention methods among minors in Ukraine but using foreign experience and the help of other countries, our state can create a reliable and effective program, which the authors are sure, will reduce the risk of suicide among people under the age of 18. It should also be noted that preventing suicides among minors needs attention from both: the state and society because it is possible to overcome manifestations of suicidal behaviour&nbsp;and, in the future, to save many young lives only. The main areas of improvement of legislation aimed at combating suicide of minors have been formed. In addition, developing a criminological program to combat suicides of minors is socially determined

Review of the state anti-corruption institutions effectiveness in Ukraine

The objective of the article is a review of the state anti-corruption institutions' effectiveness in Ukraine. An important part of anti-corruption reform in Ukraine has been the complete transformation of anti-corruption institutions. That is why the authors try to use the most optimal methodology that would be able to ensure the comprehensiveness and completeness of the study: phenomenological; the descriptive; the hypothetic-deductive; the statistical; and the method of case law analysis. It is proposed to analyze the anti-corruption powers of general competence authorities in the sphere of anti-corruption. The authors analyzed the powers of specialized anti-corruption authorities' functioning: the National Agency on Corruption Prevention; the National Anti-Corruption Bureau; the National Agency for finding, tracing, and management of assets derived from corruption and other crimes; the Specialized Anti-Corruption Prosecutor’s Office and the High Anti-Corruption Court. The conclusion is drawn that, realizing the need of the anti-corruption task, the state has developed an extensive and relatively closed system of specialized anti-corruption authorities. Almost all bodies of state power and local self-government have acquired certain anti-corruption competencies. The authors made conclusion that such dispersion of powers, and in some cases their duplication, does not simplify, but rather complicates the effectiveness of combating corruption

Optimal asymptotic bounds for spherical designs

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