The Wünsch’s calculus for conformal Riemannian invariants is reformulated and essentially generalized to all parabolic geometries. Our approach is based on the canonical Cartan connections and the Weyl connections underlying all such geometries. The differential invariants for various geometric structures are the core ingredients for numerous applications both in geometry and geometric analysis...

Early in the development of Computer Graphics it was realized that projective geometry was well suited for the representation of transformations. Now, it seems that another change of paradigm is lying ahead of us based on Geometric Computing using Conformal Geometric Algebra. Due to its geometric intuitiveness, elegance and simplicity, the underlying Conformal Geometric Algebra appears to be a ...

We present a coordinate-invariant approach, based on a Pauli-Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in...

radiotherapy plays an essential role in the management of breast cancer. three-dimensional conformal radiation therapy (3d-crt) is applied based on 3d image information of anatomy of patients. in three-dimensional conformal radiation therapy (3d-crt) for breast cancer one of the common techniques is tangential technique. in this project, various parameters of tangential and supraclavicular fiel...

The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixed, the rotation of sides, polarization, symmetrization, and averaging transformation of the quadrilaterals. Some open problems are formulated. 2000 Mathematics Subject Classification. Primary 30C85. Secondary 30C75.

In this article, using an idea of the physics superselection principal, we study a modularity on vertex operator algebras arising from semisimple primary vectors. We generalizes the theta functions on vertex operator algebras and prove that the internal automorphisms do not change the genus one twisted conformal blocks.

In this paper, we study the existence of a skew Killing spinor (see the definition below) on 2 and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.

ionization radiation caused to incidence of complications in the exposed organs. in prostate radiotherapy, rectum and bladder have been radiated unwantedly and indicated some complications during and after treatment. the purpose of present study is to consider and to compare clinical complications of rectum and bladder in custom block and mlc for 3- d conformal radiotherapy, in order to determi...

Berwald and Wagner manifolds are two important classes of spaces in Finsler geometry. They are closely related to each other via the conformal change of the metric. After discussing the basic definitions and the elements of the theory we present general methods to construct examples of them.