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A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow problems. We present a theoretical framework to analyze these variants for load (PQ)buses and generator (PV)buses. Furthermore, we compare newly developed versions in this paper with existing variants of the Newton power flow method. The convergence behavior of all methods is investigated by numerical experiments on transmission and distribution networks. We conclude that variants using the polar current-mismatch and Cartesian current-mismatch functions that are developed in this paper, performed the best result for both distribution and transmission networks.

Ray tracing (RT) and perspective projection (PP) using fiducial-based registration can be used to determine points of interest in biplanar X-ray imaging. We sought to investigate the implementation of these techniques as they pertain to X-ray imaging geometry. The mathematical solutions are presented and then implemented in a phantom and actual case with numerical tables and imaging. The X-ray imaging is treated like a Cartesian system in millimeters (mm) with a standard frame-based stereotactic system. In this space, the point source is the X-ray emitter (focal spot), the plane is the X-ray detector, and fiducials are in between the source and plane. In a phantom case, RT was able to predict locations of fiducials after moving the point source. Also, a scaled PP matrix could be used to determine imaging geometry, which could then be used in RT. Automated identification of spherical fiducials in 3D was possible using a center of mass computation with average Euclidean error relative to manual measurement of 0.23 mm. For PP, RT projection or a combinatorial approach could be used to facilitate matching 3D to 2D points. Despite being used herein for deep brain stimulation (DBS), utilization of this kind of imaging analysis has wide medical and non-medical applications.

There are many applications involving robotic hands in which teleoperation-based approaches are preferred to autonomous solutions. The main reason is that cognitive skills of human operators are desirable in some task scenarios, in order to overcome limitations of robotic hands abilities in dealing with unstructured environments and/or unpredetermined requirements. In particular, in this work we focus on the use of anthropomorphic grasping devices and, specifically, on their teleoperation based on movements of the human operator’s hand (the master hand.) Indeed, the mapping of human hand configurations to an anthropomorphic robotic hand (the slave device) is still an open problem, because of the presence of dissimilar kinematics between master and slave that produce shape and/or Cartesian errors – as addressed within our study. In this work, we propose a novel algorithm that combines joint and Cartesian mappings in order to enhance the preservation of both finger shapes and fingertip positions during the teleoperation of the robotic hand. In particular, a transition between the joint and Cartesian mappings is realized on the basis of the distance between the fingertip of the master hands’ thumb and the opposite fingers, in which the mapping of the thumb fingertip is specifically addressed. The result of the testing of the algorithm with a ROS-based simulator of a commercially available robotic hand is reported, showing the effectiveness of the proposed mapping.

The use of Cartesian and Blade techniques also affects image quality. The Cartesian technique is more commonly used in Knee MRI examinations. Cartesian technique is vulnerable to movement, giving rise to motion artifacts. This motion artifact is often caused by too long scanning time, so ETL settings are important. An alternative to reducing this risk is to use the Blade technique and by setting the appropriate ETL. The research objective was to determine the differences image quality and anatomical information and to determine the technique that produced quality images and MRI anatomical information on the sagittal knee section between the Cartesian ETL and Blade T2 Weighted TSE combination. This is experiment research. Samples of 10 volunteers, carried out scanning with Cartesian and Blade techniques with variations ETL 14, 16, 18. Focus of assessment on ACL, PCL, meniscus, fluid, and fat. Image quality includes SNR and CNR. The assessment of the anatomical information by a radiologist. Data analyzed with Anova, Friedman, and Wilcoxon test. The results study showed that overall, there are significant differences in image quality between Cartesian and Blade techniques with p-value 0.005. There are differences in anatomical information with p-value

We introduce here Cartesian splines or, for short, C-splines. C- splines are piecewise polynomials which are defined on adjacent Cartesian coordinate systems and are Cr continuous throughout. The Cr continuity is enforced by constraining the coefficients of the polynomial to lie in the null-space of some smoothness matrix H. The matrix-product of the null-space of the smoothness matrix H and the original polynomial base results in a new base, the so-called C-spline base, which automatically enforces Cr continuity throughout. In this article we give a derivation of this C-spline base as well as an algorithm to construct C-spline models.

A frequency-hopped version of the Cartesian feedback linear transmitter for use in future mobile communication systems is introduced. The essential requirements for the successful operation of such a transmitter are discussed. Using the results obtained from a hardware prototype, the problems generated by a hopping carrier are outlined and solutions introduced.

International audience; We present a finite-volume scheme for compressible Euler flows where the grid is cartesian and it does not fit to the body. The scheme, based on the definition of an ad hoc Riemann problem at solid boundaries, is simple to implement and it is formally second order accurate. Error convergence rates with respect to several exact test cases are investigated and examples of flow solutions in one, two and three dimensions are presented.