I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary b...

Receiver Operating Characteristic (ROC) curves provide a powerful tool for visualizing and comparing classification results. Regression Error Characteristic (REC) curves generalize ROC curves to regression. REC curves plot the error tolerance on the xaxis versus the percentage of points predicted within the tolerance on the y-axis. The resulting curve estimates the cumulative distribution funct...

In Schramm & Kayser (1995) we introduced the complex Beltrami Equation as an appropriate framework for the analysis of arclets in cluster lensing. Corresponding real formalisms have been developed by Kaiser and Schneider & Seitz (this volume, compare also the references in Schramm & Kayser 1995). Here, we show how the solutions of the Beltrami differential equation can be used to identify multi...

Extremely dense spatial sampling is often needed to prevent aliasing when rendering objects with high frequency variations in geometry and reflectance. To accelerate the rendering process, we introduce characteristic point maps (CPMs), a hierarchy of view-independent points, which are chosen to preserve the appearance of the original model across different scales. In preprocessing, randomized m...

A Note on Handling Information Known to the Opinion Preparer A Note on Handling Excluded Opinions § 9:1 The Three-Set Opinion Pattern § 9:2 Identifying and Defining the Party Whose Status Is at Issue A Note on Entity Formation § 9:3 Opinions as to Entity Status A Note on the Significance of Status Opinions § 9:3.1 Incorporated Status, Organization, and Valid Existence [A] Incorporation [B] Orga...

(1) Frobenius splitting in commutative algebra, Karen Smith and Wenliang Zhang. (2) A survey of test ideals, Karl Schwede and Kevin Tucker. (3) Globally F-regular and log Fano varities, Karl Schwede and Karen Smith. (4) Characterizations of regular local rings of characteristic p, Ernst Kunz. (5) On Noetherian rings of characteristic p, Ernst Kunz. (6) F-purity and rational singularity, Richard...

1.1 Complex random variables 1.2 Definition and basic properties of characteristic functions 1.3 Examples 1.4 Inversion formulas 2. Applications 2.1 Characteristic function for sum of independent random variables 2.2 Characteristic functions and moments of random variables 2.3 Continuity theorem 2.4 Weak law of large numbers 2.5 Central Limit theorem 2.6 Law of small numbers 1. Definition of ch...

Let N be the set of all meromorphic functions f deened in the unit disc D that satisfy Nehari's univalence criterion (1 ? jzj 2) 2 jSf(z)j 2. In this paper we investigate certain properties of the class N. We obtain sharp estimates for the spherical distortion, and also a two-point distortion theorem that actually characterizes the set N. Finally, we study some aspects of the boundary behavior ...

The k Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, Vk(A), of the complex algebraic torus (C). In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of Vk(A). For any arrangement A, we show that the tangent cone at the identity of the...

Nowadays, estimating the ampere consumption and achieve to the optimum condition from the perspective of energy consumption is one of the most important steps to reduce the production costs. In this research it is tried to develop an accurate model for estimating the ampere consumption by using the artificial neural networks (ANN).In the first step, experimental studies were carried out on 7 ca...