Discreteness of spectrum and positivity criteria for Schr\"odinger operators

We provide a class of necessary and sufficient conditions for the discreteness of spectrum of Schr\"odinger operators with scalar potentials which are semibounded below. The classical discreteness of spectrum criterion by A.M.Molchanov (1953) uses a notion of negligible set in a cube as a set whose Wiener's capacity is less than a small constant times the capacity of the cube. We prove that this constant can be taken arbitrarily between 0 and 1. This solves a problem formulated by I.M.Gelfand in 1953. Moreover, we extend the notion of negligibility by allowing the constant to depend on the size of the cube. We give a complete description of all negligibility conditions of this kind. The a priori equivalence of our conditions involving different negligibility classes is a non-trivial property of the capacity. We also establish similar strict positivity criteria for the Schr\"odinger operators with non-negative potentials.Comment: 24 pages, final version, some minor misprints correcte

NOVO ALVORESCER OU ETERNO CREPÚSCULO?

The article was prepared within the project "Post-crisis world order: challenges and technologies, competition and cooperation" supported by the grant from Ministry of Science and Higher Education of the Russian Federation program for research projects in priority areas of scientific and technological development (Agreement № 075-15-2020-783).Este artigo foi preparado dentro do projeto “Ordem mundial pós-crise: desafios e tecnologias, competição e cooperação” apoiado pela bolsa do programa para projetos de pesquisa em áreas de prioridade de desenvolvimento científico e tecnológico do Ministério de Ciência e Educação Superior da Federação Russo

The socialist international and Africa: 21century

The paper will be devoted to important but insufficiently researched issue of activities of the Socialist International in Africa and its relations with political parties on the continent. Its importance is underlined by the fact that the 24th Congress of Socialist International took place last September in Cape Town. It is based on the study of documents and publications as well as on field studies, primarily in Southern African countries. In particular it examines why African political parties join Socialist International, and how influential is Socialist International in Africa in comparison with other international political formations

ÁFRICA DO SUL: CENÁRIO POLÍTICO ATUAL

South Africa is currently facing several political dilemmas that influence the entire social organization of the country. Thus, the historicity of the political processes that permeate South African society today,  the power plays of the country's elites, as well as the external influences that act internally through the political parties of South Africa, and the presence of important African nation within the scope of the BRICS, are essential elements for understanding the South African policy context. Through of experiences in loco, this article establishes a comprehensive analysis of the situation, not only pointing out the political agents which actively intervene in this game, but also constructing possible scenarios for the unfolding of the events.Atualmente, a África do Sul enfrenta diversos dilemas políticos que influenciam toda a organização social do país. Dessa forma, a historicidade dos processos políticos que permeiam a sociedade sul-africana atualmente, os jogos de poder das elites do país, bem como as influências externas que agem internamente por meio dos partidos políticos da África do Sul, e a presença dessa importante nação africana dentro do âmbito dos BRICS são elementos essenciais para a compreensão do contexto da política sul-africana. Através de experiências vivenciadas in loco, se buscou nesse artigo uma análise minuciosa e abrangente acerca de tal conjuntura, apontando os agentes políticos que interferem ativamente nesse jogo e construindo possíveis cenários para o desenrolar dos eventos

Zimbabwe’s choice

The article attempts to juxtapose myths and the realities of Zimbabwe and prove that the viewpoints wide-spread in the international media and even academic community are far removed of those realities. Against the historical background it analyses the economic and political crisis the country faced in the beginning of the 21st century and the period of the “all inclusive government”. Special attention is paid to the 2013 presidential and parliamentary election and to the reasons of Robert Mugabe’s victory

RESENHA “USA – AFRICA: THE POLICY OF PRESIDENT B. OBAMA ADMINISTRATION. 2009 – 2014”, E “USA – AFRICA: THE POLICY OF PRESIDENT B. OBAMA ADMINISTRATION. 2015 – 2016. CHRONICLE OF EVENTS” DE ANDREY URNOV

Book ReviewResenh

ÁFRICA DO SUL: UM NOVO AMANHECER?

The article analyses recent developments in South Africa after the non-voluntarily resignation Jacob Zuma and election of Cyril Ramaphosa to the post of President of the Republic. One of the key words in his “State of the Nation” report next day after his election were “New dawn”: “We should put all the negativity that has dogged our country behind us because a new dawn is upon us. We must leave behind all the negative that prevented our country, because there is a new dawn above us", he said. So the article evaluates the steps the new president took to keep his promise “to turn the country around”, and in particular to eradicate widespread corruption. A special attention is paid to the results of the May 2019 national and provincial elections in South Africa.O artigo analisa os desenvolvimentos recentes na África do Sul após a demissão não voluntária de Jacob Zuma e a eleição de Cyril Ramaphosa para o cargo de Presidente da República. Uma das palavras-chave em seu relatório “Estado da Nação” no dia seguinte à sua eleição foi “Novo amanhecer”: “Deveríamos deixar para trás toda a negatividade que perseguiu nosso país, porque um novo amanhecer está chegando. Devemos deixar para trás todos os aspectos negativos que impediram nosso país, porque há um novo amanhecer acima de nós", disse ele. Portanto, o artigo avalia os passos que o novo presidente tomou para manter sua promessa de "mudar o país" e, em particular, para erradicar a corrupção generalizada. É dada uma atenção especial aos resultados das eleições nacionais e provinciais de maio de 2019 na África do Sul