In a recently published paper with the same title, Debreu and Koopmans have studied conditions which imply the quasiconvexity of the function $$...
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In a recently published paper with the same title, Debreu and Koopmans have studied conditions which imply the quasiconvexity of the function
$$f(x) = \mathop \sum \limits_{i = 1}^n f_i (x_i ),x_i \in X_i ,$$
wherex = (x
1,x
2,⋯,x
n
) and, fori = 1, 2,⋯, n,X
1 is a finite-dimensional open convex set andf
i a real-valued nonconstant function onX
1 These conditions involve the convexity indices of functionsf
i, a concept introduced in the Debreu and Koopmans paper. First, we give a new definition of the convexity index equivalent to that of Debreu and Koopmans. Then, by means of this definition, we can simplify the proofs given by Debreu and Koopmans and extend some of their results.
This paper presents the development of a back propagation neural network model for the prediction of weld bead geometry in pulsed gas metal arc welding process. The model is based on experimental data. The thickness o...
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This paper presents the development of a back propagation neural network model for the prediction of weld bead geometry in pulsed gas metal arc welding process. The model is based on experimental data. The thickness of the plate, pulse frequency, wire feed rate, wire feed rate/travel speed ratio, and peak current have been considered as the input parameters and the bead penetration depth and the convexity index of the bead as output parameters to develop the model. The developed model is then compared with experimental results and it is found that the results obtained from neural network model are accurate in predicting the weld bead geometry. (c) 2007 Elsevier B.V. All rights reserved.
The spatial-temporal patterns of cloud-to-ground (CG) lightning covering the period 2010-2015 over the northwest Iberian Peninsula were investigated. The analysis conducted employed three main methods: the circulation...
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The spatial-temporal patterns of cloud-to-ground (CG) lightning covering the period 2010-2015 over the northwest Iberian Peninsula were investigated. The analysis conducted employed three main methods: the circulation weather types developed by Jenkinson and Collison, the fit of a generalized additive model (GAM) for geographic variables, and the use of a concentration index for the ratio of lightning strikes and thunderstorm days. The main activity in the summer months can be attributed to situations with eastern or anticyclonic flow due to convection by insolation. In winter, lightning proves to have a frontal origin and is mainly associated with western or cyclonic flow situations which occur with advections of air masses of maritime origin. The largest number of CG discharges occurs under eastern flow and their hybrids with anticyclonic situations. Thunderstorms with greater CG lightning activity, highlighted by a higher concentration index, are located in areas with a higher density of lightning strikes, above all in mountainous areas away from the sea. The modeling of lightning density with geographic variables shows the positive influence of altitude and, particularly, distance to the sea, with nonlinear relationships due to the complex orography of the region. Likewise, areas with convex topography receive more lightning strikes than concave ones, a relation which has been demonstrated for the first time from a GAM.
Letf be a real-valued function defined on the product ofm finite-dimensional open convex setsX 1, ⋯,X m . Assume thatf is quasiconvex and is the sum of nonconstant functionsf 1, ⋯,f m defined on the respective factor ...
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Letf be a real-valued function defined on the product ofm finite-dimensional open convex setsX 1, ⋯,X m . Assume thatf is quasiconvex and is the sum of nonconstant functionsf 1, ⋯,f m defined on the respective factor sets. Then everyf i is continuous; with at most one exception every functionf i is convex; if the exception arises, all the other functions have a strict convexity property and the nonconvex function has several of the differentiability properties of a convex function. We define the convexity index of a functionf i appearing as a term in an additive decomposition of a quasiconvex function, and we study the properties of that index. In particular, in the case of two one-dimensional factor sets, we characterize the quasiconvexity of an additively decomposed functionf either in terms of the nonnegativity of the sum of the convexity indices off 1 andf 2, or, equivalently, in terms of the separation of the graphs off 1 andf 2 by means of a logarithmic function. We investigate the extension of these results to the case ofm factor sets of arbitrary finite dimensions. The introduction discusses applications to economic theory.
For strictly quasiconcave utility functions, demand is shown to be differentiable almost everywhere if (i) utility is separable or (ii) utility is concave and quasilinear or (iii) utility is differentiable and margina...
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For strictly quasiconcave utility functions, demand is shown to be differentiable almost everywhere if (i) utility is separable or (ii) utility is concave and quasilinear or (iii) utility is differentiable and marginal utilities are pointwise Lipschitzian.
Nas florestas tropicais os complexos fatores ambientais responsáveis pelos padrões de distribuição espacial da vegetação são de grande interesse de pesquisas em ecologia vegetal. O o...
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Nas florestas tropicais os complexos fatores ambientais responsáveis pelos padrões de distribuição espacial da vegetação são de grande interesse de pesquisas em ecologia vegetal. O objetivo principal desta tese foi estudar a estrutura e a composição florística da comunidade arbórea da Floresta Pluvial Atlântica (Floresta Ombrófila Densa Montana) em um gradiente de altitude, e as possíveis correlações com fatores topográficos e edáficos no Parque Estadual da Serra do Mar, Núcleos de Picinguaba, Santa Virgínia e Cunha, no sudeste do Brasil. Para tanto, esta tese foi dividida em três capítulos. No primeiro analisamos as variações na estrutura, composição e a riqueza em escala local e as relações com as variáveis topográficas e edáficas. No segundo verificamos a similaridade florística, e variações na riqueza e estrutura da comunidade arbórea entre as altitudes de 600 e 1.100 m, e verificamos as relações dos padrões florísticos e de riqueza com os fatores topográficos e edáficos. Por fim, no terceiro capítulo analisamos as variações na estrutura, composição e riqueza de espécies da comunidade arbórea relacionadas as condições edáficas, e a contribuição na diversidade beta no gradiente de altitude (600, 800, 1.000 e 1.100 m). Em cada altitude foram implantadas 4 parcelas de 50 x 50 m, subdividas em 10 x 10 m. Realizamos os levantamentos florísco-fitossociológicos aos 600 e 1.100 m de altitude, e as medições das variáveis topográficas e amostragem do solo aos 600, 1.000 e 1.100 m. Compilamos os dados dos levantamentos aos 800 e 1.000 m de altitude, e para as variáveis edáficas e topográficas da cota de 800 m. Foram amostrados os indivíduos com PAP ≥ 15 cm. Os resultados indicam que as variáveis edáficas e topográficas não influenciaram nos parâmetros estruturais da comunidade arbórea, no entanto, estiveram relacionadas com a distribuição das espécies e riqueza local. Os efeitos do solo e da topografia na distribuição das espécies e na riqueza divergem parcialmente em dife
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