The application of the fractional calculus for modeling electrochemical double layer capacitors is a novel way to get simpler and precise models. This paper provides a summarized report of several models of Electrochemical Double Layer Capacitors (EDLC). From classical models based on simple structures composed by networks of passive elements (RLC), to models which involve the fractional behavior of EDLC. The fractional models are based on one hand by a function with fractional poles and zeros and for other one by electrochemical elements (Warburg, Bounded Warburg, Havriliak-Negami). On using the impedance spectroscopy method, experimental results for different EDLCs have been obtained. Coming to the conclusion that the fractional models are fitted better than the classical models.

The application of the fractional calculus for modeling electrochemical double layer capacitors is a novel way to get simpler and precise models. On using the impedance spectroscopy method, experimental results for different values have been obtained. In this paper, several classical mathematical models are studied and a different method is introduced in order to get a model from electrochemical double layer capacitors. This method is based on distinct models with fractional elements, and some parameters of the models are fitted to the experimental data, with minimal error. Finally, a Havriliak–Negami function based model is proposed. It achieves excellent fitting to the whole frequency interval analyzed.

Many features have been proposed in on-line signature verification. Generally, these features rely on the position of the on-line signature samples and their dynamic properties, as recorded by a tablet. This paper proposes a novel feature space to describe efficiently on-line signatures. Since producing a signature requires a skeletal arm system and its associated muscles, the new feature space is based on characterizing the movement of the shoulder, the elbow and the wrist joints when signing. As this motion is not directly obtained from a digital tablet, the new features are calculated by means of a virtual skeletal arm (VSA) model, which simulates the architecture of a real arm and forearm. Specifically, the VSA motion is described by its 3D joint position and its joint angles. These anthropomorphic features are worked out from both pen position and orientation through the VSA forward and direct kinematic model. The anthropomorphic features' robustness is proved by achieving state-of-the-art performance with several verifiers and multiple benchmarks on third party signature databases, which were collected with different devices and in different languages and scripts.