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Este trabalho trata do papel das inovações matemáticas no aprimoramento do poder de cálculo das sociedades, focando nas inovações aritméticas. Aborda três grandes temas: o sistema de numeração indo-arábico, a função logarítmica e as frações decimais. Tem como objetivo principal a contextualização histórica da origem, introdução e popularização dessas inovações, e sua influência no posterior desenvolvimento científico, tecnológico e econômico. Como conclusões, salienta-se o papel fundamental de tais inovações no aumento do poder computacional à disposição da sociedade e seu impacto no desenvolvimento das finanças modernas na Itália e na Revolução Industrial na Inglaterra. Por fim, tal abordagem histórica pode ser utilizada como instrumento motivacional importante no ensino de disciplinas de matemática em cursos superiores de viés tecnológico, incentivando os estudantes a contextualizar historicamente a importância das ferramentas matemáticas para o progresso econômico, científico e tecnológico, também os ajudando a aprimorar suas capacidades críticas e reflexivas.

In this paper we introduce capital transport cost in a unidimensional spatial Solow–Swan model of economic growth with capital-induced labor migration, considered in an unbounded domain. Proceeding with a stability analysis, we show that there is a critical value for the capital transport cost where the dynamic behavior of the economy changes, provided that the intensity of capital-induced labor migration is strong enough. On the one hand, if the capital transport cost is higher than this critical value, the spatially homogeneous equilibrium of coexistence of the model is stable, and the economy converges to this spatially homogeneous state in the long run; on the other hand, if transport cost is lower than this critical value, the equilibrium is unstable, and the economy may develop different spatio-temporal dynamics, including the formation of stable economic agglomerations and spatio-temporal economic cycles, depending on the other parameters in the model. Finally, numerical simulations support the results of the stability analysis, and illustrate the spatio-temporal dynamics generated by the model, suggesting that the economy as a whole benefits from the formation of economic agglomerations and cycles, with a higher capital transport cost reducing this gain.

This paper proposes a Artificial Bee Colony (ABC) algorithm for solving a Economic Dispatch (ED). We apply the algorithm to simulate fifteen thermoelectric generator units, considering transmission losses and restrictions on the potency of the generating units. For the same problem, we compared the ABC implementation with other algorithms like the method of Particle Swarm Optimization (PSO), Fireflies Algorithm (FA) and the method of Lagrange multipliers. Our results show that the ABC solution is 0.05% better than the PSO solution, with a computational effort (number of iterations) of 69.30% lower. The FA solution, although it is 1.05% better than the ABC solution, requires a computational effort of 95.28% greater in relation to ABC. Although the ABC has not been as effective as the FA to find the best solution, it proved to be a fast convergence method and a low computational cost, of 3.45 seconds. Therefore, we conclude that the ABC proved to be the most efficient method, due to the small computational effort required in its processing.

This paper presents a new frequency estimator algorithm for electric power systems that uses the Mathematical Morphology operators of dilation and erosion to predict the Clarke Components from voltage signals of three phases of the system. The frequency is obtained as a function of phase shift between the predicted complex signal and the received complex signal given by the αβ-Transformation. The proposed method presented great accuracy and fast convergence for a wide range of different operational conditions involving transitory events of frequency deviation, amplitude variations, signal phase shifts and stable power swings. In addition, signals distorted by noises, harmonics and inter-harmonics were also tested. In order to demonstrate the quality of the new frequency estimator in each analyzed case, its estimation was compared with the responses obtained by four other methods, in terms of performance indices based on the estimation of transitory error and response convergence time. For all analyzed cases, the proposed methodology presented better results, showing great robustness and high accuracy for its task.

Neste trabalho propomos uma generalizacao do modelo de crescimento economico de Solow, com a introducao de efeitos de memoria do tipo lei de potencia [...]

O objetivo deste trabalho e resolver um problema de despacho economico de carga considerando quinze unidades geradoras termoeletricas, perdas nas linhas de transmissao e limites maximos e minimos de geracao para cada geradora. Para tanto, serao utilizadas as heuristicas otimizacao por enxame de particulas (PSO) e de vaga-lumes (FA), e os resultados comparados com a solucao obtida via metodo dos multiplicadores de Lagrange (MML). Como principal resultado, obteve-se que a melhor solucao obtida pelo FA foi muito mais precisa do que a obtida pelo PSO, quando comparados com o MML, embora a um custo computacional consideravelmente maior.

In this work we consider labor mobility in the spatial Solow model for economic growth. Besides considering that labor diffuses from regions with higher density to regions with lower density of labor, we consider that workers move from regions with lower density of capital to regions with higher density of capital, and that the labor force grows following a logistic law. Through stability analysis, we show that the introduction of capital-induced labor migration in the Solow model is a necessary condition for reaching an unstable regime that can generate a rich spatio-temporal dynamics. Numerical simulations show that, depending on the migration intensity and on the size of the economy, this modified Solow model can develop, endogenously, four kinds of behavior for the economy: (i) convergence to a homogeneous steady-state; (ii) convergence to a non-homogeneous steady-state; (iii) development of periodic spatio-temporal cycles; and (iv) development of irregular and aperiodic spatio-temporal cycles.

In this work we add decreasing and increasing returns to scale in a unidimensional spatial Solow–Swan economic growth model, considering capital-induced labor migration, capital transport cost, a Cobb–Douglas production function, and a logistic organic growth for the labor force. Stability analysis results of the spatially homogeneous equilibrium of the model show that higher returns to scale ease the formation of economic agglomerations and/or cycles in the economy. Besides, through numerical simulations, we confirm the stability analysis results, and obtain the interesting result that the presence of increasing returns to scale seems to be a key factor in order to cause that economic agglomerations – which are regions with higher levels of capital and labor than their neighbors – also show a higher per capita output. This helps to explain the observed positive correlation between population and per capita GDP distributions in Brazil, suggesting the presence of increasing returns to scale in the empirical data. Finally, higher returns to scale also imply a higher aggregate per capita output for the economy as a whole.

O trabalho tem como objetivo introduzir migracao no modelo de crescimento economico de Solow [1], modelo que leva em consideracao dois fatores de producao: capital, representando maquinario, ferramentas, etc. e mao-de-obra, englobando a quantidade de trabalhadores empregados no processo produtivo. Matematicamente, o modelo e formulado como um sistema acoplado de duas equacoes diferenciais ordinarias de primeira ordem. A primeira, governa a evolucao temporal do estoque de capital, onde considera-se uma funcao de producao Cobb-Douglas e uma depreciacao do capital a taxa constante (...)

Neste trabalho introduzimos custo de transporte no modelo de crescimento economico espacial de Solow em uma dimensao espacial e, atraves de uma analise de estabilidade linear de seu ponto de equilibrio espacialmente homogeneo, mostramos que existe um valor critico para este custo onde o comportamento dinâmico da economia se altera, desde que a intensidade de migracao da mao-de-obra seja alta o suficiente. Se o custo de transporte e maior do que este valor, o equilibrio e estavel, e a economia converge para um estado homogeneo. Caso o custo de transporte seja menor do que este valor critico, o equilibrio e instavel e a economia desenvolve uma dinâmica espaco-temporal mais complexa, podendo haver a formacao de aglomerados economicos estaveis, de ciclos economicos periodicos ou de ciclos aperiodicos ou caoticos, dependendo dos valores dos parâmetros utilizados.

Neste trabalho consideramos o modelo de crescimento econˆomico de Solow, quando a força de trabalho é governada pela lei de Malthus adicionada por uma taxa de migração constante. Considerando a função de produção de Cobb-Douglas, provamos alguns resultados de estabilidade e encontramos uma solução em forma fechada, envolvendo funções hipergeométricas de Gauss, para o caso em que há emigração. Além disso, provamos que, dependendo do valor da taxa de emigração, a economia pode entrar em colapso, estabilizar em um nível constante, ou crescer mais vagarosamente do que o modelo de Solow padrão. O caso em que há imigração também pode ser analisado pelo modelo, desde que a taxa de crescimento orgânico de trabalhadores na Lei de Malthus seja negativa. In this work we dealwith the Solow economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss’ Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the standard Solow model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

This paper considers a Solow-Swan economic growth model with the labor force ruled by the logistic equation added by a constant migration rate, I. We prove the global asymptotic stability of the capital and production per capita. Considering a Cobb-Douglas production function, we show this model to have a closed-form solution, which is expressed in terms of the Beta and Appell F1 special functions. We also show, through simulations, that if I>0, it implies in a smaller capital and product per capita in the short term, but in a higher capital and product per capita in the middle and long terms. In both cases, these per capita variables converge to the same steady-state given by the model without migration. If I

In this work we deal with the Solow-Swan economic growth model, when the labor force is ruled by the Malthusian law added by a constant migration rate I. Considering a Cobb-Douglas production function, we prove some stability issues and find a closed-form solution for the emigration case, involving Gauss’ Hypergeometric functions. In addition, we prove that, depending on the value of the emigration rate, the economy could collapse, stabilize at a constant level, or grow more slowly than the Solow-Swan model. Immigration also can be analyzed by the model if the Malthusian manpower is declining.

This paper presents a Solow Growth Model with the labor force ruled by the logistic equation added by a constant migration rate, I. We prove the global asymptotic stability of the capital and production per capita. Considering a Cobb-Douglas production function, we show this model to have a closed-form solution. This transient behavior is expressed in terms of the Beta and Appell F1 functions. We also show that if I > 0, it implies in a higher (minor) output of the economy, and in a minor (greater) capital and production per capita in the short term (middle and long term); furthermore, these ratios converge to the same steady-state value of the no-migration model; if I