Lp−LqL^p-L^q-Decay Estimates for the Klein-Gordon Equation in the Anti-de~Sitter Space-Time

We derive $L^p-L^q$ - decay estimates for the solutions of the Cauchy problem for the Klein-Gordon equation in the anti-de Sitter spacetime, that is, for $\Box_g u - m^2 u = f$ in models of mathematical cosmology. The obtained $L^p$--$L^q$ estimates imply exponential decay of the solutions for large times

A Note on Wave Equation in Einstein & de Sitter Spacetime

We consider the wave propagating in the Einstein & de Sitter spacetime. The covariant d'Alembert's operator in the Einstein & de Sitter spacetime belongs to the family of the non-Fuchsian partial differential operators. We introduce the initial value problem for this equation and give the explicit representation formulas for the solutions. We also show the $L^p - L^q$ estimates for solutions

Fundamental solutions for the Dirac equation in curved spacetime and generalized Euler-Poisson-Darboux equation

We present the fundamental solutions for the spin-1/2 fields propagating in spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach

Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime

We examine the solutions of the semilinear wave equation, and, in particular, of the φq model of quantum field theory in the curved space-time. More exactly, for 1 \u3c q \u3c 4 we prove that the solution of the massless self-interacting scalar field equation in the Einstein-de Sitter universe has finite lifespan

The global existence of small self-interacting scalar field propagating in the contracting universe

We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lamaˆitre-Robertson-Walker model of the contracting universe. For the Klein- Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution

The impact of the level of financial literacy of managers, particularly the financial manager, in the economic and financial performance of SMEs, a comparison between Portugal and Russia

Mestrado APNORThe aim of this study is to explore the relationship between the level of financial literacy of managers and entrepreneurs of small and medium sized enterprises (SMEs) and its economic and financial performance. As specific objectives, it is intended to (i) to determine the financial literacy index among managers and entrepreneurs of SMEs; (ii) to analyse the relationship between companies’ performance and financial literacy level (FLL) of their owners/managers; and (iii) to compare the FLL of Portuguese and Russian SME’s managers and entrepreneurs. This research was conducted in the North of Portugal and some regions in Russian Federation for the period of March to May 2017. Secondary data for this research were gathered from SABI database (for Portuguese sample) and with the help of personal and business contacts of researchers. To achieve these objectives, it was adopted a quantitative design as research methodology. Collection of primary data (assessing the financial literacy level of SMEs’ financial managers/entrepreneurs) was obtained through the use of a structured questionnaire, that is mostly similar to International Survey of Adult Financial Literacy Competencies from OECD in 2016. To measure the financial performance, it was collected secondary data from the financial documents of companies. The results did not support the expectations that there are some influences on Financial Literacy Level (FLL) of respondents from the variables, such as Gender, Age, Company’ size, and Education level. This data' results suggest a moderate negative and statistically significant correlation between companies’ performance (as measured by Return on Equity - ROE) and its owners’ or managers’ global FLL. It also found moderate negative and statistically significant correlation with financial inclusion and management of bank accounts dimension and ROE, as well as with financial understanding dimension. There was not found statistically significant differences between other performance indicators (return on assets and sales profitability) and global FLL. Moreover, there are no statistically difference between the two countries.O objetivo deste trabalho é estudar a relação entre o nível de literacia financeira dos gestores e empresários e o desempenho económico e financeiro das pequenas e médias empresas (PME). Como objetivos específicos, pretende-se (i) determinar o nível de literacia financeira dos gestores e empresários das PME; (ii) analisar a relação existente entre o desempenho das empresas e o nível de literacia financeira dos seus gestores/empresários; e (iii) comparar o nível de literacia financeira dos gestores/empresários Russos com os Portugueses bem como o desempenho financeiro destas empresas. Esta pesquisa foi desenvolvida no norte de Portugal e em algumas regiões da Federação Russa, para o período de março a maio de 2017. Os dados secundários foram recolhidos da base de dados SABI (para a amostra Portuguesa) e com a ajuda de contactos de negócios e pessoais dos investigadores. Para alcançar os objetivos definidos, foi adotado uma metodologia quantitativa. A recolha de dados primários (para medir o nível de literacia financeira dos gestores/empresários) foi obtida através da aplicação de um questionário estruturado, baseado no relatório internacional de investigação sobre as competências de literacia financeira dos adultos da OCDE em 2016. Para medir o desempenho financeiro, foram recolhidos dados secundários dos documentos financeiros das empresas. Os resultados alcançados não validam as expectativas de relação entre o nível de literacia financeira dos inquiridos e variáveis como género, idade, dimensão da empresa e nível de educação. Os resultados indiciam correlação negativa moderada e estatisticamente significativa entre a performance das empresas (medida pela rendibilidade dos capitais próprios – RCP) e o nível global de literacia financeira dos seus gestores ou empresários. Também se observou correlação negativa moderada e estatisticamente significativa com a dimensão da “inclusão financeira e gestão das contas bancárias”, bem como com a dimensão da “compreensão financeira” e a RCP. Não foram encontradas diferenças estatisticamente significativas entre os dois países.Основная цель данной работы - исследовать отношения между уровнем финансовой грамотности менеджеров и владельцев малого и среднего бизнеса и экономической результативности компании. В качестве конкретных целей предполагается: (i) изучить взаимосвязь между финансовой грамотностью и возрастом, полом и уровнем формального образования финансовых менеджеров МСП; (ii) изучить взаимосвязь между финансовой грамотностью среди финансовых менеджеров МСП и рентабельностью в качестве показателя эффективности деятельности предприятия в общей выборке и по странам, и (iii) уровни финансовой грамотности среди менеджеров и руководителей МСП Португалии и России. Это исследование проводилось на севере Португалии и некоторых регионах Российской Федерации в период с марта по май. Данные для этого исследования были собраны из базы данных SABI и с помощью личных и деловых контактов исследователей. Сбор первичных данных (оценка уровня финансовой грамотности финансовых менеджеров МСП) был получен за счет использования структурированного вопросника, который в основном аналогичен Международному обзору компетенций в области финансовой грамотности взрослых от ОЭСР в 2016 году. Чтобы измерить финансовые показатели, были собраны вторичные данные из финансовых документов компаний. Полученные результаты не подтвердили предполагаемой взаимосвязи уровня финансовой грамотности и таких переменных, как Возраст, Размер компании, Пол, Уровень образования респондента. Результаты данных предполагают умеренную отрицательную и статистически значимую корреляцию между показателями компаний (рентабельность капитала - ROE) и уровнем финансовой грамотности менеджеров или руководителей. Также обнаруживается умеренная отрицательная и статистически значимая корреляция с финансовым ведением банковских счетов и собственного капитала. Также не были обнаружены значительные различия между двумя странами