One‐Speed Neutron Transport in Two Adjacent Half‐Spaces

Generalizing Halfspaces Generalizing Halfspaces

Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restricted-orientation convex sets and demonstrated that this notion is a generalization of standard convexity. We now describe a restricted-orientation generalization of halfspaces and explore properties of these generaliz...

Generalizing Halfspaces

Testing halfspaces

This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(w ·x−θ).We consider halfspaces over the continuous domain R (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean cube {−1, 1} (endowed with the uniform distribution). In both cases we give an algorithm that distin...

Tropical Halfspaces

As a new concept tropical halfspaces are introduced to the (linear algebraic) geometry of the tropical semiring (R,min,+). This yields exterior descriptions of the tropical polytopes that were recently studied by Develin and Sturmfels [2004] in a variety of contexts. The key tool to the understanding is a newly defined sign of the tropical determinant, which shares remarkably many properties wi...

Neutron Transport Theory and Simulation

Devoted to describing neutron movement in media and the corresponding laws, neutron transport theory is the research basis for transmutation and activation, radiation damage to materials, radiation dose, and biological safety, among other topics. There are two methods for neutron transport calculation: the Monte Carlo method (also called the probabilistic method or the stochastic method) and th...