On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

Urban environmental degradation and the standard of living: the case of the Spanish mining industry (1870–1930)

This paper analyses the consequences of urban environmental degradation on the well-being of Spanish miners. It is based on analyses of differences in mortality and height. The first part of the paper examines new hypotheses regarding the urban penalty. We take into consideration existing works in economic theory that address market failures when analysing the higher urban death rate. We explain the reduction in height using the model recently created by Floud, Fogel, Harris and Hong for British cities. The second part of the paper presents information demonstrating that the urban areas in the two largest mining areas in Spain (Bilbao and the Cartagena-La Unión mountain range) experienced a higher death rate relative to rural areas as a consequence of market failures derived from what we term an ‘anarchic urbanisation’.