Fractional prabhakar derivative and applications in anomalous dielectrics: A numerical approach

Fractional integrals and derivatives based on the Prabhakar function are useful to describe anomalous dielectric properties of materials whose behaviour obeys to the Havriliak–Negami model. In this work some formulas for defining these operators are described and investigated. A numerical method of product-integration type for solving differential equations with the Prabhakar derivative is derived and its convergence properties are studied. Some numerical experiments are presented to validate the theoretical results

Models of dielectric relaxation based on completely monotone functions

The relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts, Cole-Cole, Cole-Davidson, Havriliak-Negami (with its modified version) and Excess wing model are among the most famous. Their description in the time domain involves some mathematical functions whose knowledge is of fundamental importance for a full understanding of the models. In this work, we survey the main dielectric models and we illustrate the corresponding time-domain functions. In particular, we stress the attention on the completely monotone character of the relaxation and response functions. We also provide a characterization of the models in terms of differential operators of fractional order

Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays

This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gronwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result

Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays

This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gronwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result

Class 3 semaphorins in cardiovascular development

Secreted class 3 semaphorins (Sema3), which signal through holoreceptor complexes that are formed by different subunits, such as neuropilins (Nrps), proteoglycans, and plexins, were initially characterized as fundamental regulators of axon guidance during embryogenesis. Subsequently, Sema3A, Sema3C, Sema3D, and Sema3E were discovered to play crucial roles in cardiovascular development, mainly acting through Nrp1 and Plexin D1, which funnels the signal of multiple Sema3 in vascular endothelial cells. Mechanistically, Sema3 proteins control cardiovascular patterning through the enzymatic GTPase-activating-protein activity of the cytodomain of Plexin D1, which negatively regulates the function of Rap1, a small GTPase that is well-known for its ability to drive vascular morphogenesis and to elicit the conformational activation of integrin adhesion receptors

A comprehensive survey of advanced SLAM techniques

In robot navigation, precise knowledge of the robot’s position and orientation is essential for accurate trajectory tracking, obstacle avoidance, and goal attainment, especially in scenarios where human supervision is limited or absent. This paper describes the different established methods in simultaneous localization and mapping (SLAM) algorithms, such as the most advanced SLAM techniques for extreme environmental conditions, including dynamic objects, illumination and brightness variability. Namely, visual information received from cameras is less susceptible to radio interference and does not depend on any additional device, such as GPS and satellite signals. The SLAM community’s main approaches to solving these problems are introduced. Finally, we consider current research in the field of visual odometry (VO), as well as its practical implementation in robotics