We construct explicit solutions of the Hermitian Yang-Mills equations on the noncommutative space C θ . In the commutative limit they coincide with the standard instantons on CP written in local coordinates.

Minimally invasive procedures such as biopsy or thermal tumor ablations share a similar planning scenario: a linear path for a needle shaped instrument has to be found such that the needle tip can reach a defined target such as a tumor. The path should be chosen according to several criteria, which influence safety, practicability and, in the case of ablation techniques, the ablation success of...

We discuss implications of the fundamental plane parameters of clusters of galaxies derived from combined optical and X–ray data of a sample of 78 nearby clusters. In particular, we investigate the dependence of these parameters on the dynamical state of the cluster. We introduce a new concept of allocation of the fundamental plane of clusters derived from their intrinsic morphological properti...

Generalizations of barycentric coordinates in two and higher dimensions have been shown to have a number of applications in recent years, including finite element analysis, the definition of Spatches (n-sided generalizations of Bézier surfaces), free-form deformations, mesh parametrization, and interpolation. In this paper we present a new form of d dimensional generalized barycentric coordinat...

Barycentric coordinates are an established mathematical tool in computer graphics and geometry processing, providing a convenient way of interpolating scalar or vector data from the boundary of a planar domain to its interior. Many different recipes for barycentric coordinates exist, some offering the convenience of a closedform expression, some providing other desirable properties at the expen...

The proposed mathematical model in this study consists of two parts, one is the maneuvering model, called MMG (Mathematical Model Group), and other a control algorithm based on traditional PD system. used to compute ship's characteristics, ship can safely reach target coordinates with help if it encounters any obstacles along way. Because suitable hydrodynamic coefficients Esso Osaka, evaluated...

We investigate the local regularity of pointed spacetimes, that is, timeoriented Lorentzian manifolds in which a point and a future-oriented, unit timelike vector (an observer) are selected. Our main result covers the class of Einstein vacuum spacetimes. Under curvature and injectivity bounds only, we establish the existence of a local coordinate chart defined in a ball with definite size in wh...

Knowledge discovery in scientific and research datasets is an extremely challenging problem due to the high dimensionality, heterogeneity, and complex relationships within the data. When these datasets also includes temporal and geospatial components, the challenges in analyzing the data become even more difficult. A number of visualization approaches have been developed and studied to support ...

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line bundles.

Analyzing data to find trends, correlations, and stable patterns is an important problem for many industrial applications. In this paper, we propose a new technique based on parallel coordinates visualization. Previous work on parallel coordinates methods has shown that they are effective only when variables that are correlated and/or show similar patterns are displayed adjacently. Although cur...