RESUMO No processo de ocupação da hinterlândia da América portuguesa, os sertões do Rio Grande - localizados entre as capitanias de São Paulo e Minas Gerais e que têm como um de seus limites o curso d’água que lhes empresta o nome - foram redefinidos durante o século XVIII como espaço de disputas entre os governos civis e eclesiásticos de São Paulo, Minas Gerais e Goiás. Este trabalho pretende demonstrar o processo de constituição da rede urbana no território em disputa, onde os núcleos urbanos fundados nos interstícios das capitanias também foram instrumentos para consolidação do território e dos interesses geopolíticos lusos em contraposição aos espanhóis. A rede urbana nesse território é marcada pela presença de quilombos, pelos mecanismos do fisco do ouro e do controle dos caminhos, por meio dos registros, e pela forte presença da Igreja Católica como instrumento de ocupação dos sertões, por intermédio da ereção de capelas e da elevação de freguesias. Nesse contexto, destacamos algumas ações que visavam garantir a posse desse território, além da fundação da freguesia de N. Sra. da Conceição do Bom Sucesso do Rio Pardo (1775), evento importante nas disputas de fronteira e no povoamento desses sertões. Metodologicamente, este trabalho insere-se no campo disciplinar da história da urbanização e mobiliza uma variação de escalas geográficas. As fontes primárias incluem a cartografia histórica e cartas e ofícios dos governos civis e eclesiásticos.

ABSTRACT In the process of occupying the hinterland of Portuguese America, the hinterlands of Rio Grande - located between the Captaincies of São Paulo and Minas Gerais and bounded by the watercourse that lends its name - were being redefined, during the 18th century, as a space of disputes between the civil and ecclesiastical governments of São Paulo, Minas Gerais and Goiás. This study aims at showing the process of constituting the urban network in the disputed territory, where the urban centers founded on the interstices of the captaincies were also instruments for consolidating the territory and the Portuguese geopolitical interests as opposed to the Spanish interests. The urban network in this territory presents singular characteristics, marked by the presence of quilombos, by the mechanisms of gold taxation and the control of trails by the customs barriers, by the strong presence of the Catholic Church as an instrument of occupation of the hinterlands, by the erection of chapels and the foundation of parishes. In this context, we highlight some actions to assert the possession of this territory in São Paulo and the foundation of the parish of N. Sra. da Conceição do Bom Sucesso in Rio Pardo (1775) as an important event in the border disputes and in the settlement of these hinterlands. Methodologically, this study is classified within the disciplinary field of the History of Urbanization and works with a variation of geographic scales. Primary sources include historical cartography and letters from civil and ecclesiastical governments.

Abstract We show some estimates and approximation results of operators of convolution type defined on Riesz Bounded variation spaces in R n. We also state some embedding results that involve the collection of generalized absolutely continuous functions.

Abstract We introduce the (ϕ, 2, α)-bounded variation spaces, which are a common generalization between Riesz’s spaces, p-variation and (ϕ, 2)-bounded variation spaces. We also study its structure as Banach spaces, as well as some embedding results.

Production planning in a mine complex aims to determine the amount of material that should be mined from each site, and can be modelled as a linear programming problem. Deterministic production plans are optimized based on the estimated quantity and quality of the in-situ material. These estimations always have a level of uncertainty and impreciseness due to the insufficiency of exploration data in the planning phase. In this paper, based on the gathered data, the uncertainties of grades, recovery, and mining costs are modelled using bounded fuzzy numbers. Due to the quality variation of the material, mine planning and blending optimizations are in fact uncertainty-based optimization problems. Thus, a fuzzy linear programming model is formulated to optimize short-term production planning. The results provide a comprehensive set of solutions with a corresponding degree of membership. As an illustration, the model is applied to a limestone mine complex, and a conservative and an optimistic plan are provided.

Resumen En el presente artículo se prueba que una sucesión M: Zn → L(E) de variación acotada, es un multiplicador de Fourier sobre el espacio de Besov Bs p, q(Tn, E) para s ∈ R, 1 < p < ∞, 1 ≤ q ≤ 1 y E un espacio de Banach, si y solo si, E es un espacio UMD. Este resultado extiende el Teorema 4.2 en [3] al caso n-dimensional. Como ilustración de la aplicabilidad de este resultado, se estudia la solubilidad de dos problemas de Cauchy abstractos con condiciones de frontera periódicas.

Abstract We prove in this paper that a sequence M: Zn → L(E) of bounded variation is a Fourier multiplier on the Besov space Bs p, q(Tn, E) for s ∈ R, 1 < p < ∞, 1 ≤ q ≤ 1 and E a Banach space, if and only if E is a UMD-space. This extends the Theorem 4.2 in [3] to the n-dimensional case. As illustration of the applicability of this results we study the solvability of two abstract Cauchy problems with periodic boundary conditions.

Refinements of the generalized trapezoid inequality for functions of bounded variation in terms of the cumulative variation function are given. Applications for selfadjoint operators on complex Hilbert spaces are also provided.

Damos refinamientos de la desigualdad trapezoidal generalizada para funciones de variación acotada en términos de la función de variación acumulativa. También probamos aplicaciones a operadores autoadjuntos en espacios de Hilbert complejos.

In this paper we prove existence and uniqueness of the solutions for a kind of Volterra equation, with an initial condition, in the space of the continuous functions with bounded variation which take values in an arbitrary Banach space. Then we give a parameters variation formula for the solutions of certain kind of linear integral equation. Finally, we prove exact controllability of a particular integral equation using that formula. Moreover, under certain condition, we find a formula for a control steering of a type of system which is studied in the current work, from an initial state to a final one in a prescribed time.

En este trabajo probamos existencia y unicidad de las soluciones para una ecuación de Volterra, con condición inicial, en el espacio de funciones continuas con variación acotada y valores en un espacio de Banach arbitrario. Damos una formula de variación de parámetros para las soluciones de cierta clase de ecuación lineal integral. Finalmente probamos la controlabilidad exacta de una ecuación integral particular usando esa formula. Más aún, bajo cierta condición, encontramos una formula para una dirección de control de un tipo de Sistema que se estudia en el presente trabajo, desde un estado inicial a uno final en un tiempo prescrito.

En este artículo se introduce una generalización del concepto de \hboxp-variación de Riesz y se construye un espacio de funciones que es normalizable y además es tanto espacio de Banach como un álgebra de Banach. Adicionalmente, usando el enfoque dado por Medved'ev se obtiene una caracterización integral de las funciones en dicho espacio funcional.

In this paper we introduce a generalization of the concept of Riesz p-variation and construct a function space which is normalizable and moreover is a Banach space as well as a Banach algebra. Furthermore, using Medved'ev approach we obtain an integral characterization of the functions in this function space.

En este trabajo se muestra la validez de algunos resultados de inmersión en el espacio de variación (\phi, α)-acotada, que es una generalización del espacio de Riesz de variación p-acotada.

In this paper we show the validity of some embedding results on the space of (\phi,α)-bounded variation, which is a generalization of the space of Riesz p-variation.

En este artículo demostramos que si el operador de Nemytskii lleva el espacio de variación (φ, ó)-acotada en sí mismo, y satisface cierta condición de Lipschitz, entonces existen dos funciones g y h perteneciendo al espacio de variación (φ, α)-acotada tal que <img src="img/revistas/rein/v32n1/v32n1a06e1.jpg" align="absbottom">.

In this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that <img src="img/revistas/rein/v32n1/v32n1a06e1.jpg" align="absbottom">.

In studies of floods in basins with a snow regime, the role of temperature has been found to be as important as precipitation to determine the magnitude of the floods, since it defines the contributing catchment area bounded by snow lines (H LN). Therefore, the hypsometry of the basin is also relevant since it determines the percentage of additional catchment area resulting from small variations in H LN. This study analyzes the effects of different combinations of snow line elevations and precipitation, different probabilities of exceedance, for pluvial floods with return periods of 1 000 and 10 000 years (T) in a Chilean Andean basin with a snow regime. The results obtained were compared with previous studies in which the contributing catchment area was taken as constant, finding a significant variation of up to 20% with respect to the mean peak flow of floods with T = 1 000 years. This suggests that future designs of large hydraulic works in basins with similar hydrological regimes should take into account these combinations. In addition, the possible effects of climate change, based on future scenarios A2 and B1 (2045-2065), on the magnitude of these floods were examined. In the study zone, an increase in the magnitude of daily precipitation is projected for T = 1 000 years, up to 70% on average, for scenario B1 and an average increase in temperature of +1.8 °C and +1.3 °C is projected for scenarios A2 and B1, respectively. This will lead to increases in peak flow and direct runoff volumes of up to 72 and 84%, respectively, for the period 2045 - 2065, variations that could exceed the confidence interval for extreme floods calculated for the historical period and result in the vulnerability of the dam located at the outlet of the study basin to floods under climate change scenarios.

En los estudios de crecida en cuencas de régimen nival, la temperatura juega un rol tan importante como la precipitación en la determinación de la magnitud de las mismas, pues define el área pluvial aportante delimitada por la línea de nieves (H LN). En este mismo sentido, la hipsometría de la cuenca es también relevante debido a que determina cuánto porcentaje de área pluvial adicional se tendrá como resultado de pequeñas variaciones de la H LN. En este estudio se analizan los efectos de considerar diferentes combinaciones de elevación de línea de nieves y precipitación, de distinta probabilidad de excedencia, en las crecidas de origen pluvial de 1 000 y 10 000 años de periodo de retorno (T), en una cuenca cordillerana chilena de régimen nival. Se comparan los resultados obtenidos con estudios previos, donde el área pluvial aportante era considerada constante, encontrando una importante dispersión que alcanza variaciones de hasta un 20% respecto a la media del caudal máximo en crecidas de T = 1 000 años, sugiriendo que se incorporen a futuro estas combinaciones para el diseño de grandes obras hidráulicas en cuencas de régimen hidrológico similar. Se examinan además los posibles efectos del cambio climático bajo los escenarios futuros A2 y B1 (2045-2065) en las magnitudes de estas crecidas. En la zona en estudio, en términos de precipitación diaria, se proyecta un incremento de las magnitudes para el evento de T = 1 000 años de hasta un 70% promedio en el escenario B1, y un aumento promedio en la temperatura de +1.8 °C y +1.3 °C en los escenarios A2 y B1, respectivamente. Esto conduciría a incrementos del caudal máximo y del volumen de escorrentía directa de hasta 72 y 84%, respectivamente, para el periodo 2045-2065, variaciones que podrían escapar de un intervalo de confianza de crecidas extremas estimadas en el periodo histórico y dejar al embalse situado a la salida de la cuenca analizada, vulnerable frente a inundaciones en los escenarios de cambio climático.

The La Pastosa beds constitute a nice example of sediments deposited in the highly meandering reach of the fluvial-tidal transition within an estuary, developed at the top of the "Rionegrense" stage, a marine-estuarine sequence of late Miocene age from Patagonia. Sedimentary facies include channel lags rich in mud intraclasts; cross-bedded sandstones with mud drapes and "set-climber" ripples; heterolithic and herringbone bedding; and inclined heterolithic stratification (IHS), and suggest a strong tidal influence. Tidal facies together with paucity of bioturbation and marine fossils indicate that sedimentation took place mainly in brackish tidal-fluvial channels, bounded by deposits formed in transgressive conditions at the base and at the top of the succession. Channel lag intraformational conglomerates are product of collapse of the cutbank due to erosion in the active margin of lateral migrating meandering channels that eroded adjacent muddy tidal flats and salt marshes. Crossbedded sandstones were accumulated above the conglomerates, forming subtidal sand dunes in the deeper parts of the channels and IHS was formed in point bars. Discontinuities at the base of the channels are the result of the entire channel-system lateral migration, whereas discontinuities capped by small mud pebbles at the base of large IHS sets are the result of seasonally increased run-off and widening of the channels. Alternation of sandy and muddy IHS suggests periodical changes in the position of the turbidity maximum due to seasonal variation of fluvial discharge, in good agreement with the seasonal climate in Patagonia during the late Miocene. IHS sets dipping alternatively to the north and south indicate lateral migration of the east-west running, high-sinuosity channels in the tightly meandering reach of the tidal-fluvial transition. The well preserved vertebrate fauna of Huayquerian mammal age is dominated by the hydrocherid Cardiatherium patagonicum together with whistling ducks and loricariid fishes. This fauna inhabited out-of-channel, freshwater, low-energy restricted environments, like marshes and ponds where the carcasses accumulated and underwent diagenetic fossilization. Repeated lateral migration of meandering channels caused erosion of these deposits and the bones were exhumed and incorporated into the channels, and finally concentrated in channel lags after short transport. Combination of fossilization in a low-energy environment and concentration after short transport in meandering channels make the fluvial-tidal transition "first class" deposits for prospecting vertebrate fossils. In spite of exhumation and transport, vertebrate fossil association closely reflects the environments adjacent to the channels. Excellent preservation is more related to rapid burial than to the energy level of the environment of final accumulation.

Los estratos de La Pastosa constituyen un buen ejemplo de sedimentos depositados en la porción meandriforme de alta sinuosidad de un sistema de transición fluvial/mareal en un estuario. Estos representan el tope del "Rionegrense", una sucesión marino marginal del Mioceno tardío de Patagonia. Facies sedimentarias tales como residuos de canal con abundantes intraclastos pelíticos; areniscas con estratificación entrecruzada, cortinas de fango y ondulitas ascendentes en caras de avalancha; estratificación heterolítica horizontal; estratificación tipo "hueso de arenque" (herringbone); y estratificación heterolítica inclinada (IHS) indican una importante influencia mareal. Todo ello, sumado a la escasez de bioturbación y fósiles marinos, indican que la sedimentación ocurrió principalmente en canales de mareafluviales, limitados por depósitos transgresivos tanto en la base como en el tope de la sucesión. Los conglomerados residuales intraformacionales son producto del colapso de la pared erosiva (cutbank) por la migración lateral de canales meandrosos que erodaron las planicies de mareas fangosas y marismas adyacentes. Las areniscas con estratificación entrecruzada se acumularon por encima de los conglomerados, en forma de dunas arenosas submareales dentro del canal y las IHS se formaron por migración de barras en espolón. Las discontinuidades de la base de los canales son el resultado de la migración del sistema canalizado en su totalidad mientras que las discontinuidades en la base de los grandes sets de IHS se deben al incremento estacional de la descarga fluvial con el consecuente ensanchamiento del canal. La alternancia de porciones fangosas y arenosas en las IHS sugiere cambios periódicos en la posición del máximo de turbidez causados por variaciones estacionales en la descarga fluvial, en concordancia con el clima marcadamente estacional que se registra en la Patagonia durante el Mioceno tardío. Los sets de IHS que inclinan al N y al S indican la recurrencia de la migración lateral de canales meandrosos de alta sinuosidad orientados en sentido E-O. La fauna de vertebrados muy bien preservados de edad mamífero Huayqueriense, está dominada por el hidroquérido Cardiatherium patagonicum junto con patos silbadores y peces loricárdidos. Estos organismos vivían fuera de los canales, en ambientes restringidos de agua dulce y baja energía como marismas y lagunas, en donde los esqueletos se acumularon y fosilizaron durante la diagénesis temprana. La repetida migración lateral de los canales produjo erosión de estos depósitos y los huesos fueron exhumados e incorporados a los canales, para finalmente ser concentrados en los depósitos residuales luego de un corto transporte. La combinación de la fosilización en ambientes de baja energía y la posterior concentración luego de un breve transporte en canales meandrosos hacen a los depósitos de la transición fluvial/mareal un objetivo de primera clase en la búsqueda de vertebrados fósiles. Pese a la exhumación y al transporte sufrido, la asociación de vertebrados fósiles refleja fielmente el ambiente adyacente al canal. La excelente preservación depende en mayor medida del rápido sepultamiento antes que de la energía del ambiente de acumulación final.

We show that if f is lying on the intersection of the space of Henstock-Kurzweil integrable functions and the space of the bounded variation functions in the neighborhood of ±8, then its Fourier Transform exists in all R. This result is more general than the classical result which enunciates that if f is Lebesgue integrable, then the Fourier Transform of f exists in all R, because we also have proved that there are functions which belong to the intersection of the space of the Henstock-Kurzweil integrable functions and the space of the bounded variation functions which are not Lebesgue integrable.

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft and aerospace structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. This article shows some steps that should be followed in the design of a smart structure. It is discussed: the optimal placement of actuators, the model reduction and the controller design through techniques involving linear matrix inequalities (LMI). It is considered as constraints in LMI: the decay rate, voltage input limitation in the actuators and bounded output peak (output energy). Two controllers robust to parametric variation are designed: the first one considers the actuator in non-optimal location and the second one the actuator is put in an optimal placement. The performance are compared and discussed. The simulations to illustrate the methodology are made with a cantilever beam with bonded piezoelectric actuators.

We propose a discrete approximation scheme to a class of Linear Quadratic Continuous Time Problems. It is shown, under positiveness of the matrix in the integral cost, that optimal solutions of the discrete problems provide a sequence of bounded variation functions which converges almost everywhere to the unique optimal solution. Furthermore, the method of discretization allows us to derive a number of interesting results based on finite dimensional optimization theory, namely, Karush-Kuhn-Tucker conditions of optimality and weak and strong duality. A number of examples are provided to illustrate the theory.