We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we subspace as neighborhood data points. Existing methods focus points, and information is ignored. Our able analyze shape directional gain more insights into global structure through perception structures. Local subspaces are fitted by ell...

We consider the augmented mixed finite element method introduced in [7] for the equations of plane linear elasticity with mixed boundary conditions. We develop an a posteriori error analysis based on the Ritz projection of the error and obtain an a posteriori error estimator that is reliable and efficient, but that involves a non-local term. Then, introducing an auxiliary function, we derive fu...

Adaptive composite map projections transform projections as the user changes the scale of the web map. The equal-area version of the original adaptive map projection composite uses the Lambert azimuthal equal-area projection for regional maps, and three equal-area world projections, namely the Hammer, the Eckert-Greifendorff, and the quartic authalic projections. These three projections show po...

Local projection methods which yield c'm_1) piecewise polynomials of order m + k as approximate solutions of a boundary value problem for an mth order ordinary differential equation are determined by the k linear functional at which the residual error in each partition interval is required to vanish on. We develop a condition on these k f unctionals which implies breakpoint superconvergence (of...

In this paper, we investigate a novel distributed behavioral control scheme for second-order nonlinear multi-agent systems (MAS) directed network topologies. Unlike most existing behavioral control algorithms which require global information of the underlying network, we develop a distributed adaptive behavioral control using a local adaptive strategy via distributed state estimator, null-space...

A novel objective function is presented that incorporates both local and global errors as well as model parsimony in the construction of wavelet neural networks. Two methods are presented to assist in the minimization of this objective function, especially the local error term. First, during network initialization, a locally adaptive grid is utilized to include candidate wavelet basis functions...