arXiv subjects

Anthony A. Ruffa

Publications and source records attributed to Anthony A. Ruffa.

4 recordsLinked to original sources

arXiv2007

A Novel Solution to the ATT48 Benchmark Problem

A solution to the benchmark ATT48 Traveling Salesman Problem (from the TSPLIB95 library) results from isolating the set of vertices into ten open-ended zones with nine lengthwise boundaries. In each zone, a minimum-length Hamiltonian Path (HP) is found for each combination of boundary vertices, leading to an approximation for the minimum-length Hamiltonian Cycle (HC). Determination of the optimal HPs for subsequent zones has the effect of automatically filtering out non-optimal HPs from earlier zones. Although the optimal HC for ATT48 involves only two crossing edges between all zones (with one exception), adding inter-zone edges can accommodate more complex problems.

cs.DS↗

arXiv2007

A Novel Solution to the Frenet-Serret Equations

A set of equations is developed to describe a curve in space given the curvature $κ$ and the angle of rotation $θ$ of the osculating plane. The set of equations has a solution (in terms of $κ$ and $θ$) that indirectly solves the Frenet-Serret equations, with a unique value of $θ$ for each specified value of $τ$. Explicit solutions can be generated for constant $θ$. The equations break down when the tangent vector aligns to one of the unit coordinate vectors, requiring a reorientation of the local coordinate system.

math.DG↗

arXiv2004

An Irrotational Flow Field That Approximates Flat Plate Boundary Conditions

An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow, with severe numerical difficulties in some regions.

physics.flu-dyn↗

arXiv2000

The Generalized Method of Exhaustion

The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of exhaustion) and an independent algebraic proof are provided. Applications provided as examples include use of the formula to generate new series for common functions as well as computing the group velocity distribution resulting from waves diffracted from an aperture.

math.CA↗