There exists no symmetric configuration with 33 points and line size 6

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Variations on the Dembowski-Wagner theorem

Let D be a symmetric design admitting a null polarity such that either all singular lines, or all nonsingular lines, have size (v − λ)/(k − λ); assume that this number is greater than λ in the case of singular lines. Then D is either a projective space or an orthogonal symmetric design. © 2003 Elsevier Ltd. All rights reserved. The Dembowski–Wagner Theorem [3] characterizes projective spaces as...

Classifying pentavalnet symmetric graphs of order $24p$

A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.

Constructing 5-Configurations with Chiral Symmetry

A 5-configuration is a collection of points and straight lines in the Euclidean plane so that each point lies on five lines and each line passes through five points. We describe how to construct the first known family of 5-configurations with chiral (that is, only rotational) symmetry, and prove that the construction works; in addition, the construction technique produces the smallest known geo...

Dosimetric evaluation of a treatment planning system using pencil beam convolution algorithm for enhanced dynamic wedges with symmetric and asymmetric fields

Background: The dosimetric performance of Eclipse 6.5 three dimensional treatment planning system (3DTPS) is evaluated by comparing the calculated and measured dose in two dimensions following the guide lines of American Association for Physicists in Medicine Task Group 53. Materials and Methods: The calculations were performed by the 3DTPS for symmetric as well as asymmetric fields for standar...