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Limiting case (mathematics)
About: Limiting case (mathematics) is a research topic. Over the lifetime, 358 publications have been published within this topic receiving 5973 citations.
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TL;DR: A special case of this new class of distributions, G distributions, arising from the multiplicative model, that has as many parameters as K distributions, is shown able to model extremely heterogeneous clutter, such as that of urban areas, that cannot be properly modeled with K distributions.
Abstract: A new class of distributions, G distributions, arising from the multiplicative model is presented, along with their main properties and relations. Their densities are derived for complex and multilook intensity and amplitude data. Classical distributions, such as K, are particular cases of this new class. A special case of this class called G/sup 0/, that has as many parameters as K distributions, is shown able to model extremely heterogeneous clutter, such as that of urban areas, that cannot be properly modeled with K distributions. One of the parameters of this special case is related to the degree of homogeneity, and a limiting case is that of a scaled speckle. The advantage of the G/sup 0/ distribution becomes evident through the analysis of a variety of areas (urban, primary forest and deforested) from two sensors.
522 citations
TL;DR: This article shows how to recover flexible cost functions from very limited data sets using a maximum entropy approach and argues that there exists a continuum of analysis between mathematical programming and traditional econometric techniques which is based solely upon the available information.
Abstract: Production economics problems are often ill-posed. This means that the number of parameters to be estimated is greater than the number of observations. In this article we show how to recover flexible cost functions from very limited data sets using a maximum entropy approach. We also argue that there exists a continuum of analysis between mathematical programming and traditional econometric techniques which is based solely upon the available information. The limiting case of a multi-output cost function recovered using only a single observation of a farmer's allocation decisions can be easily extended to handle more than one observation.
289 citations
TL;DR: In this paper, a logarithmic Sobolev inequality by means of the BMO-norm in the critical exponents of the Euler equation was proved, and a blow-up criterion of solutions to Euler equations was established.
Abstract: We shall prove a logarithmic Sobolev inequality by means of the BMO-norm in the critical exponents. As an application, we shall establish a blow-up criterion of solutions to the Euler equations.
224 citations
TL;DR: In this paper, it was shown that if for each t, the frozen system is stable, then the time-varying system should also be stable, provided A(t) is small enough.
Abstract: A limiting case of great importance in engineering is that of slowly varying parameters. For systems described by \dot{x} = A(t)x , one would intuitively expect that if, for each t , the frozen system is stable, then the time-varying system should also be stable. Provided A(t) is small enough, Rosenbrock has shown that this is the case [1]. Rosenbrock used a continuity argument [1, p. 75]. In this correspondence explicit bounds and slightly sharper results are obtained. Finally, it is pointed out that these results are useful in the study of the exact behavior of non-linear lumped systems with slowly varying operating points.
189 citations
TL;DR: In this paper, a nonlinear superposition of two Kerr-NUT solutions is presented, where the Tomimatsu-Sato δ = 2 solution is contained as a limiting case.
185 citations