Fractional order models of leaves

Leaves are mainly responsible for food production in vascular plants. Studying individual leaves can reveal important characteristics of the whole plant, namely its health condition, nutrient status, the presence of viruses and rooting ability. One technique that has been used for this purpose is Electrical Impedance Spectroscopy, which consists of determining the electrical impedance spectrum of the leaf. In this paper we use EIS and apply the tools of Fractional Calculus to model and characterize six species. Two modeling approaches are proposed: firstly, Resistance, Inductance, Capacitance electrical networks are used to approximate the leaves’ impedance spectra; afterwards, fractional-order transfer functions are considered. In both cases the model parameters can be correlated with physical characteristics of the leaves.

Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.

Invisible cities: the table of contents and the labyrinths of reality

In Invisible Cities (1972), Italo Calvino contrasts a rigid outline structure with a flexible textual content. The tension comprised by the numerical structure proposed in the table of contents stands out against the set of polissemic texts which make up the subject matter of the book. The opposition between form and content point to a fruitful dichotomy in the conception of the novel linked to the theories of the open and closed work. This essay will investigate the structural construction of Invisible Cities by looking at its table of contents, seeking to discuss some models of formalistic representation proposed by the criticism and the specific contribution they may, or may not, provide. The objective is to analyse the pertinence of such theories in the light of historical and cultural approaches. Aiming to uncover possible meanings which arise from the debate, this essay will question to what extent structural complexities can be considered literary if they are not ultimately related to the culture in which a text is found.