background: stereotactic radiosurgery is an important clinical tool for the treatment of small lesions in the brain, including benign conditions, malignant and localized metastatic tumors. a dosimetry study was performed for elekta ‘synergy s ’ as a dedicated stereotactic radiosurgery unit, capable of generating circular radiation fields with diameters of 1-5 cm at isocentre using the beam/egs4...

In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of this Euclidean Jordan algebra is indeed the circular cone itself. The...

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

Background: Stereotactic radiosurgery is an important clinical tool for the treatment of small lesions in the brain, including benign conditions, malignant and localized metastatic tumors. A dosimetry study was performed for Elekta ‘Synergy S ’ as a dedicated Stereotactic radiosurgery unit, capable of generating circular radiation fields with diameters of 1-5 cm at isocentre using the BEAM/EGS4...

Introduction: Penumbra is an important property of the radiation beam to obtain a suitable margin surrounding the target volume. Therefore, the precise penumbra width determination in stereotactic radiotherapy is necessary for treatment planning. This study aimed to compare the obtained results of penumbra width by in-house and standard circul...

The circular cone Lθ is not self-dual under the standard inner product and includes second-order cone as a special case. In this paper, we focus on the monotonicity of fLθ and circular cone monotonicity of f . Their relationship is discussed as well. Our results show that the angle θ plays a different role in these two concepts.

Some characteristics of the inverse Compton scattering (ICS) model are reviewed. At least the following properties of radio pulsars can be reproduced in the model: core or central emission beam, one or two hollow emission cones, different emission heights of these components, diverse pulse profiles at various frequencies, linear and circular polarization features of core and cones.

Introduction Efficient fitting of quadric surfaces to unstructured point clouds or triangle meshes is an important component of many reverse engineering systems [6]. Users may prefer a given surface be fit by a specific quadric type: for example, they may want to ensure the quadric is a cone, ellipsoid, or a rotationally-symmetric subtype (spheroid, circular cone, etc). Methods for type-specifi...

Basic sphere geometric principles are used to analyze approximation schemes of developable surfaces with cone spline surfaces, i.e. G1surfaces composed of segments of right circular cones. These approximation schemes are geometrically equivalent to the approximation of spatial curves with G1-arc splines, where the arcs are circles in an isotropic metric. Methods for isotropic biarcs and isotrop...