In this paper the state estimator is developed for the multi area power system with SCADA and PMU measurements using WLS method. The measurement jacobian matrix has been modified for the PMU measurements. The behavior of the elements because of the current measurements in the measurement jacobian matrix is examined for any possible ill-conditioning of the state estimator gain matrix. State esti...

A new three-degrees-of-freedom (3-DOF) translational parallel manipulator (TPM) with linear actuators, i.e., 3-CRR TPM, is first proposed. The rotation singularity analysis, the inverse kinematics, the forward kinematics, and the kinematic singularity analysis of the 3CRR TPM are then performed. The analysis shows that the proposed TPM has the following kinematic merits over previous TPMs. (1) ...

A new three-degrees-of-freedom (3-DOF) translational parallel manipulator (TPM) with linear actuators, i.e., 3-CRR TPM, is first proposed. The rotation singularity analysis, the inverse kinematics, the forward kinematics, and the kinematic singularity analysis of the 3CRR TPM are then performed. The analysis shows that the proposed TPM has the following kinematic merits over previous TPMs. (1) ...

Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives sharp bounds for the indecomposability problem.

Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally invariant Jacobian...

Let f ∈ C[x, y] be a polynomial in two variables with complex coefficients. f is said to be a component of an automorphism if there exists a polynomial g ∈ C[x, y] such that F := (f, g) : C −→ C is a polynomial automorphism of C (i.e. there exists F and it is also polynomial). In turn, f is said to be a Keller’s component if there exists g ∈ C[x, y] such that the jacobian Jac(f, g) of the mappi...

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the...

This paper presents a closed-form formulation and geometrical interpretation of the derivatives of the Jacobian matrix of fully parallel robots with respect to the moving platforms’ position/orientation variables. Similar to the Jacobian matrix, these derivatives are proven to be also groups of lines that together with the lines of the instantaneous direct kinematics matrix govern the singulari...

High-throughput molecular analysis has become an integral part in organismal systems biology. In contrast, due to a missing systematic linkage of the data with functional and predictive theoretical models of the underlying metabolic network the understanding of the resulting complex data sets is lacking far behind. Here, we present a biomathematical method addressing this problem by using metab...

Conventional high-order finite element methods are rarely used for industrial problems because the Jacobian rapidly loses sparsity as the order is increased, leading to unaffordable solve times and memory requirements. This effect typically limits order to at most quadratic, despite the favorable accuracy and stability properties offered by quadratic and higher order discretizations. We present...