An optimal control problem for the variable-order fractional-integer mathematical model of vaccination Covid 19 is presented in this research, where order derivatives varies during course time interval, becoming fractional or classical when it more favourable. The are defined here using both integral Riemann–Liouville and Caputo derivative. existence, uniqueness, boundedness positivity solution...

This paper delves into the extension and characterization of radial positive definite functions non-integer dimensions. We provide a thorough investigation by employing Riemann–Liouville fractional integral Caputo derivatives, enabling comprehensive understanding these functions. Additionally, we introduce secondary based on Bernstein completely monotone The practical significance our study is ...

In the presence of an alkene, three different modes of photocycloaddition with benzene derivatives can occur; the [2 + 2] or ortho, the [3 + 2] or meta, and the [4 + 2] or para photocycloaddition. This short review aims to demonstrate the synthetic power of these photocycloadditions.

In this paper it is shown how to perform hand-eye calibration using only the normal flow field and knowledge about the motion of the hand. The proposed method comprise a simple way to calculate the handeye calibration when a camera is mounted on a robot. Firstly, it is shown how the orientation of the optical axis can be estimated from at least two different translational motions of the robot. ...

This paper presents a new technique to the instantaneous 3D motion estimation. The main contributions are as follows. First, we show that the 3D camera or scene velocity can be retrieved from image derivatives only assuming that the scene contains a dominant plane. Second, we propose a new robust algorithm that simultaneously provides the Least Trimmed Square solution and the percentage of inli...

We continue the development of a linear algebraic framework for the shape-from-shading problem, exploiting the manner in which tensors arise when scalar (e.g. image) and vector (e.g. surface normal) fields are differentiated multiple times. In this paper we apply that framework to develop Taylor expansions of the normal field and build a boot-strapping algorithm to find these polynomial surface...

We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized...

Traditionally, hand-eye calibration has been done using point correspondences, reducing the problem to a matrix equation. This approach requires reliably detected and tracked points between images taken from fairly widespread locations. In this paper we present a completely new approach to performing hand-eye calibration. The novelty of the proposed method lies in the fact that instead of point...