Recent years have shown a vital synergism between numerical and perturbative approaches in the context of Cauchy evolution. In this work we try to make these benefits also accessible in the context of null-surface-based evolution. We treat the “close-limit” approximation to the post-merger phase of a binary black hole spacetime in terms of the characteristic initial value problem. We outline a ...

The paper presents a novel interactive application created in the C# programming language under the Microsoft Visual Studio environment: its introduction, theoretical grounds and application. The application allows generating two-dimensional fractals defined by iterated function systems and performing their arbitrary affine transformation. Most importantly, this transformations are easily contr...

a priori information 299 abdominal scans 184 active appearance models (AAM) 417, 436, 440, 448 active contours 3, 275, 316 formulations 318 active shape models (ASM) 417, 448 admissible functions 347 affine 348 affine intensity transformations 234 affine-invariant 221, 223 affine tangent 280 affine transformation 245, 280, 352, 369 albedo model 444 albedo recovery 445 alignment 346, 361 amplitu...

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

Gauge fields frequently used as an independent construction additional to so-called wave fields of matter. This artificial separation is of course useful in some applications (like Berry’s interactions between the “heavy” and “light” sub-systems) but it is restrictive on the fundamental level of “elementary” particles and entangled states. It is shown that the linear superposition of action sta...

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

We develop a generalized triangle geometry, using an arbitrary bilinear form in an affine plane over a general field. By introducing standardized coordinates we find canonical forms for some basic centers and lines. Strong concurrencies formed by quadruples of lines from the Incenter hierarchy are investigated, including joins of corresponding Incenters, Gergonne, Nagel, Spieker points, Mittenp...

We develop a generalized triangle geometry, using an arbitrary bilinear form in an affine plane over a general field. By introducing standardized coordinates we find canonical forms for some basic centers and lines. Strong concurrencies formed by quadruples of lines from the Incenter hierarchy are investigated, including joins of corresponding Incenters, Gergonne, Nagel, Spieker points, Mittenp...

We define a toric surface patch associated with a convex polygon, which has vertices with integer coordinates. This rational surface patch naturally generalizes classical Bézier surfaces. Several features of toric patches are considered: affine invariance, convex hull property, boundary curves, implicit degree and singular points. The method of subdivision into tensor product surfaces is introd...